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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 3\n",
+ "\n",
+ "## 1. Poisson statistics\n",
+ "This exercise is about two variants of a counting experiment: in the first, simpler case, we will see that the observations are well described by a Poisson distribution. In the second case we will have events which are not independent from each other and we will see that the results deviate from a Poisson distribution.\n",
+ "\n",
+ "Consider a beam of particles impinging on a thin target. Most particles will go through the target without interacting, while a few will be absorbed. The target is connected to a detector, which fires a signal when a particle is absorbed by the target. In the first part of the exercise we assume to have a perfect detector: it is able to detect each and every particle hitting the target.\n",
+ "\n",
+ "The experiment consists in counting how many particles are absorbed by the target in a fixed time interval, e.g. 1s. We will repeat the counting *n* times and see how the results are distributed.\n",
+ "\n",
+ "To simulate the setup, assume the following numbers:<br>\n",
+ "- Number of particles arriving at the target per second\n",
+ "- Probability that a particle is absorbed by the target"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "ename": "ImportError",
+ "evalue": "No module named tqdm",
+ "output_type": "error",
+ "traceback": [
+ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+ "\u001b[0;31mImportError\u001b[0m Traceback (most recent call last)",
+ "\u001b[0;32m<ipython-input-1-2665767b3ae4>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstats\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mpoisson\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mtqdm\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mtqdm_notebook\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mtqdm\u001b[0m \u001b[0;31m# provides a nice progress bar during long computations\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m '''\n",
+ "\u001b[0;31mImportError\u001b[0m: No module named tqdm"
+ ]
+ }
+ ],
+ "source": [
+ "'''\n",
+ "Let's start by importing some useful modules and functions...\n",
+ "'''\n",
+ "from numpy.random import rand\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy.stats import poisson\n",
+ "from tqdm import tqdm_notebook as tqdm # provides a nice progress bar during long computations\n",
+ "\n",
+ "'''\n",
+ "... and by defining the relevant parameters of the experiment\n",
+ "(feel free to change the values and see how the result changes)\n",
+ "'''\n",
+ "particle_rate = 1e6 # Number of particles arriving at the target per second\n",
+ "delta_t = 1 # duration of one experiment in seconds\n",
+ "absorption_probability = 2e-6 # Probability that a particle is absorbed by the target\n",
+ "n_trials = 200 # How many times you repeat the experiment"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Write a function which decides if a single particle is absorbed by the target (return True) or not (return False).\n",
+ "\n",
+ "Hint: generate a uniformly distributed random number between 0 and 1 with the *rand()* function. Use it do decide if the particle is detected or not, based on the known *absorption_probability*."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def particle_is_detected(absorption_probability=absorption_probability):\n",
+ " if rand()<absorption_probability:\n",
+ " return True\n",
+ " else:\n",
+ " return False"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now write a function to simulate the experiment running for a time *delta_t*. It should do the following:\n",
+ "- compute how many particles reach the target during *delta_t* with the known *particle_rate*,\n",
+ "- for each of those check if they get absorbed or not (cf. *particle_is_detected()*),\n",
+ "- return the number of particles which are absorbed by the target during *delta_t*."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def run_experiment(particle_rate=particle_rate,delta_t=delta_t,absorption_probability=absorption_probability):\n",
+ " n_particles = int(particle_rate * delta_t)\n",
+ " counted_particles = 0\n",
+ " for i in range(n_particles):\n",
+ " if particle_is_detected(absorption_probability): counted_particles += 1\n",
+ " return counted_particles"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You are now ready to run the experiment, i.e. run the function. Do this a few times to get a feeling for the results: is the number of counted particles the same every time or does it change? What kind of result do you expect from the chosen *particle_rate, delta_t* and *absorption_probability*?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "for i in range(10):\n",
+ " print run_experiment()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's now analyse the results more systematically: run the experiment *n_trials* times and save the results in a list or array. Depending on your computer, this might take some time."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def repeat_experiment(single_experiment=run_experiment,n_trials=n_trials):\n",
+ " progress_bar = tqdm(total=n_trials, unit=' trials')\n",
+ " counted_all = []\n",
+ "\n",
+ " for i in range(n_trials):\n",
+ " counted_all.append(single_experiment())\n",
+ " progress_bar.update()\n",
+ " return counted_all\n",
+ "\n",
+ "counted_all = repeat_experiment()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Before plotting the results in a histogram, let's define the expected Poisson distribution in order to make a comparison. If you are not sure how to do this, have a look at last week's exercise. What is the expected *mu* paramter for the given *particle_rate, delta_t* and *absorption_probability*?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "from numpy import sqrt\n",
+ "mu = particle_rate * delta_t * absorption_probability\n",
+ "n_bins = int(mu+5*sqrt(mu)) if mu>=1 else 5\n",
+ "bins = range(n_bins)\n",
+ "pois_distr = poisson.pmf(bins,mu)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now plot the results of the experiment together with the parent distribution. Again, have a look at last week's exercise if you need help. When plotting the histogram remember to set *density=True* in order to have it normalized to unity for a meaningful comparison with the Poisson distribution (if this option does not work, which might be the case for older versions, try replacing it with *normed=True*)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "plt.hist(counted_all,bins,density=True,rwidth=0.9,align='left',label='Data')\n",
+ "plt.plot(bins,pois_distr,'k+',label='Poisson distribution',ms=8)\n",
+ "plt.xlabel('Counted particles')\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "What do you observe? Is the data from the experiment well described by the Poisson distribution?\n",
+ "\n",
+ "Let's now make a different assumption about the detector: it has no longer perfect efficiency, but whenever it detects a particle it needs some time to process the signal. Durign this time the detector is blind to any particle which might be absorbed by the target. In this way the recorded particles are not independent from each other anymore, and as you will see this will cause the result of the experiment to deviate from a Poisson distribution.\n",
+ "\n",
+ "Modify your implementation of the function *run_experiment()* in order to account for the dead time of the detector. Assume that whenever the detector records a particle it is blind to the next 500000 particles reaching the target."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def run_experiment_dead_time(particle_rate=particle_rate,delta_t=delta_t,absorption_probability=absorption_probability,dead_time=500000):\n",
+ " n_particles = int(particle_rate * delta_t)\n",
+ " counted_particles = 0\n",
+ " particle_iterator = 0\n",
+ " while particle_iterator<n_particles:\n",
+ " if particle_is_detected(absorption_probability):\n",
+ " counted_particles += 1\n",
+ " particle_iterator += dead_time\n",
+ " else:\n",
+ " particle_iterator += 1\n",
+ " return counted_particles\n",
+ "\n",
+ "counted_all_dead_time = repeat_experiment(run_experiment_dead_time)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Plot the new results with detector dead time together with the same Poisson distribution from before. What do you observe?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "plt.hist(counted_all_dead_time,bins,density=True,rwidth=0.9,align='left',label='Data')\n",
+ "plt.plot(bins,pois_distr,'k+',label='Poisson distribution',ms=8)\n",
+ "plt.xlabel('Counted particles')\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 2. Correlated variables and error matrix\n",
+ "\n",
+ "In this exercise you will work on a pair of correlated variables, compute the error matrix and visualize the error ellipse. Let's start from the case of two uncorrelated variables, saved in the file *data_uncorrelated.txt*. Have a look at the file: each line represents one measurement, the first number being the value of the *x* variable and the second number the value of the *y* variable."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "from matplotlib import pyplot as plt\n",
+ "\n",
+ "data = np.genfromtxt('data_uncorrelated.txt')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Plot the data. How can you recognise that *x* and *y* are not correlated? Compare the 2D distribution in the *xy* plane and the histograms of the *x* and *y* values. What do you notice about e.g. the range of the axes and the position of the means?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "f, ax = plt.subplots(1,3, figsize=(20, 6))\n",
+ "ax = ax.flatten()\n",
+ "\n",
+ "ax[0].set_xlabel(r'$x$')\n",
+ "ax[0].set_ylabel(r'$y$')\n",
+ "ax[0].axis('equal')\n",
+ "ax[0].plot(data[:,0],data[:,1],'.')\n",
+ "\n",
+ "ax[1].set_xlabel(r'$x$')\n",
+ "ax[1].hist(data[:,0],bins=range(-7,7),rwidth=.9)\n",
+ "\n",
+ "ax[2].set_xlabel(r'$y$')\n",
+ "ax[2].hist(data[:,1],bins=range(-7,7),rwidth=.9)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute the covariance matrix. You can either write a function to do this yourself, or use the numpy implementation. Have a look at last week's exercise if you feel lost."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "covmat = np.cov(data[:,0],data[:,1], bias=True)\n",
+ "print covmat"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compare your result with the error matrix you expect for two uncorrelated variables, cf. slides from Lecture 3: $\\text{diag}(\\sigma_x^2,\\sigma_y^2)$. Is your result compatible with this expression?\n",
+ "<br> We will now compute the eigenvectors and eigenvalues of the covariance matrix and interpret them in terms of the properties of the distributions we just saw. As before, you can compute the values yourself or use the numpy implementation *np.linalg.eig(matrix)*"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "#Use this block to compute eigenvalues and eigenvectors of the covariance matrix and print the result\n",
+ "eigval,eigvec = np.linalg.eig(covmat)\n",
+ "#eigvec0 = eigvec[:,0]\n",
+ "print eigval\n",
+ "print eigvec"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For this easy case of uncorrelated variables you should recognize the following: the eigenvectors are aligned with the $x$ and $y$ axes and the eigenvalues are the variances of the data along the same axes; this means that the standard deviation in the $x$ and $y$ directions are the square root of the respective eigenvalue. Keep this in mind, as we will later see what changes if the variables are correlated.\n",
+ "\n",
+ "For a visual interpretation do the following: plot again the 2D distribution of the data together with the eigenvectors multiplied by the square root of the corresponding eigenvalue (in this way the length of the vector will be the corresponding standard deviation)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "sigma = np.sqrt(eigval)\n",
+ "print sigma\n",
+ "\n",
+ "plt.plot(data[:,0],data[:,1],'.',zorder=0)\n",
+ "plt.axis('equal')\n",
+ "\n",
+ "#Use the following function to draw the vectors. The options are needed to draw them in the correct size\n",
+ "for i in range(2):\n",
+ " plt.quiver(sigma[i]*eigvec[0,i],sigma[i]*eigvec[1,i],angles='xy', scale_units='xy', scale=1,zorder=1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's now draw an ellipse with half-axes $\\sigma_x$ and $\\sigma_y$: this is the equivalent of the $1 \\sigma$ interval for a 1D Gaussian distribution. Fill in the values for $\\sigma_x,\\sigma_y$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "phi = np.linspace(0,2*np.pi)\n",
+ "ellipse_x = sigma[0]*np.cos(phi) # x-coordinates of the points on the ellipse\n",
+ "ellipse_y = sigma[1]*np.sin(phi) # y-coordinates of the points on the ellipse\n",
+ "\n",
+ "plt.plot(ellipse_x,ellipse_y,'r')\n",
+ "plt.axis('equal')\n",
+ "\n",
+ "plt.plot(data[:,0],data[:,1],'.',zorder=0)\n",
+ "center = [np.mean(data[:,0]), np.mean(data[:,1])]\n",
+ "for i in range(2):\n",
+ " plt.quiver(center[0],center[1],np.sqrt(eigval[i])*eigvec[0,i],np.sqrt(eigval[i])*eigvec[1,i],angles='xy', scale_units='xy', scale=1,zorder=1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let us now look at the case of two correlated measurements. Load the data from *data_uncorrelated.txt* and repeat the steps from above up to the drawing of the vectors; do not draw the ellipse yet, we will do that in the next step. You should be able to copy-paste most of the code from the uncorrelated case."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "data = np.genfromtxt('data_correlated.txt')\n",
+ "\n",
+ "covmat = np.cov(data[:,0],data[:,1], bias=True)\n",
+ "eigval,eigvec = np.linalg.eig(covmat)\n",
+ "sigma = np.sqrt(eigval)\n",
+ "\n",
+ "f, ax = plt.subplots(1,3, figsize=(20, 6))\n",
+ "ax = ax.flatten()\n",
+ "\n",
+ "ax[0].set_xlabel(r'$x$')\n",
+ "ax[0].set_ylabel(r'$y$')\n",
+ "ax[0].axis('equal')\n",
+ "ax[0].plot(data[:,0],data[:,1],'.',zorder=0)\n",
+ "for i in range(2):\n",
+ " ax[0].quiver(sigma[i]*eigvec[0,i],sigma[i]*eigvec[1,i],angles='xy', scale_units='xy', scale=1,zorder=1)\n",
+ "\n",
+ "ax[1].set_xlabel(r'$x$')\n",
+ "ax[1].hist(data[:,0],bins=range(-7,7),rwidth=.9)\n",
+ "\n",
+ "ax[2].set_xlabel(r'$y$')\n",
+ "ax[2].hist(data[:,1],bins=range(-7,7),rwidth=.9)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You should now see that the eigenvectors are not aligned with the coordinate axes anymore. However, as before, the eigenvectors represent the direction of the largest spread of the data, and the eigenvalues, i.e. the variances, define how large this spread is.\n",
+ "\n",
+ "Let's now draw the ellipse. There are different ways in which this can be done. Let's start by determining the angle of rotation *theta*. *Hint*: take the *x* and *y* components of one of the eigenvectors and use the *math.atan2()* function."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "theta = np.arctan2(eigvec[0,1],eigvec[0,0])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To draw the rotated ellipse, define the $x$ and $y$ coordinates as before, and than rotate them by multiplying them with a rotation matrix by the angle *theta*."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "phi = np.linspace(0,2*np.pi)\n",
+ "ellipse_x = sigma[0]*np.cos(phi) # x-coordinates of the points on the ellipse\n",
+ "ellipse_y = sigma[1]*np.sin(phi) # y-coordinates of the points on the ellipse\n",
+ "\n",
+ "rotation = np.array([[np.cos(theta),np.sin(theta)],[-np.sin(theta),np.cos(theta)]])\n",
+ "ellipse = np.dot(rotation,[ellipse_x,ellipse_y]) # dot product"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we are ready to plot everything together."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true,
+ "scrolled": true
+ },
+ "outputs": [],
+ "source": [
+ "plt.plot(data[:,0],data[:,1],'.',zorder=0)\n",
+ "for i in range(2):\n",
+ " plt.quiver(sigma[i]*eigvec[0,i],sigma[i]*eigvec[1,i],angles='xy', scale_units='xy', scale=1,zorder=1)\n",
+ "plt.plot(ellipse[0,:],ellipse[1,:],'r')\n",
+ "plt.axis('equal')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Bonus\n",
+ "\n",
+ "The data for this exercise has been generated with the following code. Feel free to change the parameters and rerun the exercise."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "n_samples = 1000\n",
+ "mu = np.array([0.,0.])\n",
+ "var_x = 4.\n",
+ "var_y = 1.\n",
+ "cov_xy = 1.\n",
+ "r = np.array([\n",
+ " [ var_x, cov_xy,],\n",
+ " [ cov_xy, var_y,]\n",
+ " ])\n",
+ "\n",
+ "y = np.random.multivariate_normal(mu, r, size=n_samples)\n",
+ "\n",
+ "with open('output.txt', 'w') as outfile:\n",
+ " np.savetxt(outfile, y, fmt='%3.2f')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 3. Computing uncertainties on inefficiencies\n",
+ "\n",
+ "Consider an imperfect particle detector: out of all the particles hitting the detector, a fraction passes through unnoticed. The efficiency of the detector, i.e. the fraction of particles which are detected, is a very important parameter for any experimental setup. Suppose you want to measure the efficiency of a new detector. A possible approach is the following: you shoot $n$ particles on the detector, and count the number of signals $k$ which are recorded. The efficiency is then given by $\\varepsilon = k\\,/\\,n$. What is the uncertainty on this quantity? As a first approach, let's assume that $k$ and $n$ are Poisson distributed (and thus $\\delta k = \\sqrt{k}$ and $\\delta n = \\sqrt{n}$) and that we can apply the standard error propagation formula you saw in lecture 1:\n",
+ "$$ \\delta f = \\sqrt{ \\sum_{i=1}^N \\left(\\left. \\frac{\\partial f}{\\partial x_i}\\right\\vert_{x_i=x_i^0} \\delta x_i \\right)^2}. $$\n",
+ "- Show that this formula yelds the following result:\n",
+ "$$ \\delta \\varepsilon = \\sqrt{\\frac{k}{n^2} + \\frac{k^2}{n^3}}. $$\n",
+ "\n",
+ "What happens to the uncertainty for *extreme* values of $k$, i.e. $k=0$ and $k=n$? Do these results make sense? Remember that the efficiency is by definition a number between 0 and 1.\n",
+ "\n",
+ "The source of the problem is that $k$ and $n$ are not independent (the particles which are recorded are a subset of all particles which hit the detector). A way to handle this is noting that the efficiency measurement is in fact a binomial process with total events $n$ and success probability $\\varepsilon$ (see slides of Lecture 3).\n",
+ "- Using the known variance of the binomial distribution show that in this case the uncertainty is given by \n",
+ "$$ \\delta \\varepsilon = \\sqrt{\\frac{\\varepsilon (1-\\varepsilon)}{n}}.$$\n",
+ "\n",
+ "An equivalent approach is to consider, instead of the total number of particles $n$, the number $n_f$ of particles which fail to be detected. In this approach, $n = k + n_f$ is not fixed anymore and $k$ and $n_f$ are uncorrelated; thus, the standard error formula is valid.\n",
+ "- Show that applying the standard error formula to $\\varepsilon = k\\,/\\,(k+n_f)$ yelds again $$ \\delta \\varepsilon = \\sqrt{\\frac{\\varepsilon (1-\\varepsilon)}{n}}.$$\n",
+ "\n",
+ "Note that when evaluating this formula one has to use the measured (estimated) value of $\\varepsilon$, since the true value is unknown. This is a good approximation for *intermediate* values of $k$, i.e. $\\varepsilon$ not too close to 0 or 1. The exact meaning of *too close* is a matter of judgement - the extreme values $\\varepsilon = 0$ and $\\varepsilon = 1$ are clearly too close, as they yeld 0 uncertainty which is nonsense.\n",
+ "\n",
+ "For a discussion of these and more cases, as well as a more involved approach using Bayes' theorem you can have a look at<br>\n",
+ "https://www-cdf.fnal.gov/physics/statistics/notes/cdf7168_eff_uncertainties.ps and<br>\n",
+ "http://home.fnal.gov/~paterno/images/effic.pdf"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.12"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/.ipynb_checkpoints/Exercise_6_DRAFT-checkpoint.ipynb b/exercises/.ipynb_checkpoints/Exercise_6_DRAFT-checkpoint.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..ac9e49899fb9d56435b99299a3cde80fb45d9461
--- /dev/null
+++ b/exercises/.ipynb_checkpoints/Exercise_6_DRAFT-checkpoint.ipynb
@@ -0,0 +1,1801 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 6: Arbitrary distributions, moving averages, and Monte-Carlo\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 262,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# General imports\n",
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import datetime\n",
+ "import scipy.stats as stats\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1. Sampling from an arbitrary distribution\n",
+ "As seen in exercise 4, you can use uniformly distributed random variables, which are in principle themselves simple to generate, to draw samples from the normal distribution via the Box-Muller transform. A more general approach is to sample according to the inverse of the cumulative distribution function (CDF).\n",
+ "\n",
+ "A simple example is to generate numbers from the exponential distribution.\n",
+ "\n",
+ "$$ f(t;\\lambda) = \\lambda e^{-\\lambda t} $$\n",
+ "\n",
+ "* Write the CDF $F(T,\\lambda)$ and find its inverse ($T=...$)\n",
+ "* Write a function to compute this, and compare your result to that from scipy (hint: sometimes called percent-point function or quantile function)\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 221,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/Users/matt/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:5: RuntimeWarning: divide by zero encountered in log\n",
+ " \"\"\"\n"
+ ]
+ },
+ {
+ "data": {
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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1a21f10d68>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Quantile function\n",
+ "def exp_quantile(p, l):\n",
+ " p[p<0] = 0\n",
+ " p[p>=1] = 1\n",
+ " return -np.log(1-p)/l # scipy equivalent: stats.expon.ppf(p,0,1/l)\n",
+ "\n",
+ "p = np.linspace(0, 1, 100)\n",
+ "l = 0.2\n",
+ "plt.figure()\n",
+ "plt.plot(p, exp_quantile(p, l))\n",
+ "plt.plot(p, stats.expon.ppf(p,0,1/l))\n",
+ "plt.xlabel('x')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Now draw N samples from the uniform distribution $[0,1]$. For each sample, calculate $F^{-1}(u,\\lambda)$\n",
+ "* Plot a histogram and compare the distribution of points to the exponential pdf\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 242,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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8LjGeg2OrmVF0M/zqYHj8YljxAiR1pVXJb5bJZnsz+xZwExAH7nD3683sGqDM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\nSUWcvAAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1a23364358>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "N = 500\n",
+ "l = 0.2\n",
+ "x = np.random.rand(N)\n",
+ "y = exp_quantile(x, l)\n",
+ "q = np.linspace(0, 25, 200)\n",
+ "\n",
+ "plt.hist(y, bins=np.arange(25), normed=True)\n",
+ "plt.plot(q, stats.expon.pdf(q, scale=1/l))\n",
+ "plt.show()\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 2. Smoothing data\n",
+ "## 2.1 Moving average\n",
+ "The moving average, or rolling mean, is a simple technique which can be used to remove short term or periodic (e.g. seasonal) variations in time series data, for example. It can be viewed as a \"smoothing\", and can ease trend spotting, for instance. One has to be careful when interpreting and using the result; for instance, it is generally improper to fit on such data.\n",
+ "\n",
+ "The simplest moving average can be computed using a \"sliding window\" of length $N$, with all weights equal. For example, for a 3 point moving average, the window would be $\\frac{1}{3}[1,1,1]$.\n",
+ "\n",
+ "* Write a function to compute the $N$ point moving average of a data series"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 270,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def moving_average(y, length):\n",
+ " return np.convolve(np.ones(length)/length, y, 'same')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The following line of code loads a dataset (into a ```pandas DataFrame```) containing monthly measurements of variation in the global surface temperature, stretching back as far as 1750. (More data like this can be found on http://berkeleyearth.org)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 258,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<div>\n",
+ "<style>\n",
+ " .dataframe thead tr:only-child th {\n",
+ " text-align: right;\n",
+ " }\n",
+ "\n",
+ " .dataframe thead th {\n",
+ " text-align: left;\n",
+ " }\n",
+ "\n",
+ " .dataframe tbody tr th {\n",
+ " vertical-align: top;\n",
+ " }\n",
+ "</style>\n",
+ "<table border=\"1\" class=\"dataframe\">\n",
+ " <thead>\n",
+ " <tr style=\"text-align: right;\">\n",
+ " <th></th>\n",
+ " <th>Year</th>\n",
+ " <th>Month</th>\n",
+ " <th>MDiff</th>\n",
+ " <th>MUnc</th>\n",
+ " <th>YDiff</th>\n",
+ " <th>YUnc</th>\n",
+ " <th>5YDiff</th>\n",
+ " <th>5YUnc</th>\n",
+ " <th>10YDiff</th>\n",
+ " <th>10YUnc</th>\n",
+ " <th>20YDiff</th>\n",
+ " <th>20YUnc</th>\n",
+ " <th>Date</th>\n",
+ " </tr>\n",
+ " </thead>\n",
+ " <tbody>\n",
+ " <tr>\n",
+ " <th>0</th>\n",
+ " <td>1750</td>\n",
+ " <td>1</td>\n",
+ " <td>-0.121</td>\n",
+ " <td>4.187</td>\n",
+ " <td>-0.687</td>\n",
+ " <td>2.557</td>\n",
+ " <td>-0.364</td>\n",
+ " <td>0.897</td>\n",
+ " <td>-0.160</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-01-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1</th>\n",
+ " <td>1750</td>\n",
+ " <td>2</td>\n",
+ " <td>-1.278</td>\n",
+ " <td>3.177</td>\n",
+ " <td>-0.691</td>\n",
+ " <td>1.733</td>\n",
+ " <td>-0.381</td>\n",
+ " <td>0.904</td>\n",
+ " <td>-0.169</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-02-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2</th>\n",
+ " <td>1750</td>\n",
+ " <td>3</td>\n",
+ " <td>0.112</td>\n",
+ " <td>3.550</td>\n",
+ " <td>-0.721</td>\n",
+ " <td>1.568</td>\n",
+ " <td>-0.401</td>\n",
+ " <td>0.918</td>\n",
+ " <td>-0.164</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-03-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3</th>\n",
+ " <td>1750</td>\n",
+ " <td>4</td>\n",
+ " <td>0.026</td>\n",
+ " <td>2.862</td>\n",
+ " <td>-0.734</td>\n",
+ " <td>1.609</td>\n",
+ " <td>-0.452</td>\n",
+ " <td>0.951</td>\n",
+ " <td>-0.168</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>4</th>\n",
+ " <td>1750</td>\n",
+ " <td>5</td>\n",
+ " <td>-1.420</td>\n",
+ " <td>2.611</td>\n",
+ " <td>-1.043</td>\n",
+ " <td>1.553</td>\n",
+ " <td>-0.439</td>\n",
+ " <td>1.022</td>\n",
+ " <td>-0.167</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>5</th>\n",
+ " <td>1750</td>\n",
+ " <td>6</td>\n",
+ " <td>-1.029</td>\n",
+ " <td>3.379</td>\n",
+ " <td>-1.004</td>\n",
+ " <td>1.271</td>\n",
+ " <td>-0.414</td>\n",
+ " <td>1.060</td>\n",
+ " <td>-0.176</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>6</th>\n",
+ " <td>1750</td>\n",
+ " <td>7</td>\n",
+ " <td>-0.262</td>\n",
+ " <td>2.722</td>\n",
+ " <td>-1.049</td>\n",
+ " <td>1.026</td>\n",
+ " <td>-0.411</td>\n",
+ " <td>1.023</td>\n",
+ " <td>-0.183</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-07-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>7</th>\n",
+ " <td>1750</td>\n",
+ " <td>8</td>\n",
+ " <td>0.290</td>\n",
+ " <td>3.219</td>\n",
+ " <td>-1.137</td>\n",
+ " <td>0.792</td>\n",
+ " <td>-0.466</td>\n",
+ " <td>0.933</td>\n",
+ " <td>-0.210</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-08-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>8</th>\n",
+ " <td>1750</td>\n",
+ " <td>9</td>\n",
+ " <td>-0.851</td>\n",
+ " <td>2.121</td>\n",
+ " <td>-1.107</td>\n",
+ " <td>0.775</td>\n",
+ " <td>-0.375</td>\n",
+ " <td>0.945</td>\n",
+ " <td>-0.230</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-09-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>9</th>\n",
+ " <td>1750</td>\n",
+ " <td>10</td>\n",
+ " <td>-1.448</td>\n",
+ " <td>3.078</td>\n",
+ " <td>-1.167</td>\n",
+ " <td>0.826</td>\n",
+ " <td>-0.394</td>\n",
+ " <td>1.023</td>\n",
+ " <td>-0.211</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-10-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>10</th>\n",
+ " <td>1750</td>\n",
+ " <td>11</td>\n",
+ " <td>-3.518</td>\n",
+ " <td>1.996</td>\n",
+ " <td>-1.160</td>\n",
+ " <td>1.283</td>\n",
+ " <td>-0.423</td>\n",
+ " <td>1.094</td>\n",
+ " <td>-0.226</td>\n",
+ " <td>0.879</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-11-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>11</th>\n",
+ " <td>1750</td>\n",
+ " <td>12</td>\n",
+ " <td>-2.538</td>\n",
+ " <td>4.091</td>\n",
+ " <td>-1.210</td>\n",
+ " <td>1.458</td>\n",
+ " <td>-0.451</td>\n",
+ " <td>1.143</td>\n",
+ " <td>-0.250</td>\n",
+ " <td>0.894</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-12-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>12</th>\n",
+ " <td>1751</td>\n",
+ " <td>1</td>\n",
+ " <td>-0.659</td>\n",
+ " <td>3.318</td>\n",
+ " <td>-1.094</td>\n",
+ " <td>1.533</td>\n",
+ " <td>-0.464</td>\n",
+ " <td>1.148</td>\n",
+ " <td>-0.258</td>\n",
+ " <td>0.844</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-01-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>13</th>\n",
+ " <td>1751</td>\n",
+ " <td>2</td>\n",
+ " <td>-2.341</td>\n",
+ " <td>4.503</td>\n",
+ " <td>-1.047</td>\n",
+ " <td>1.776</td>\n",
+ " <td>-0.482</td>\n",
+ " <td>1.131</td>\n",
+ " <td>-0.231</td>\n",
+ " <td>0.914</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-02-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>14</th>\n",
+ " <td>1751</td>\n",
+ " <td>3</td>\n",
+ " <td>0.477</td>\n",
+ " <td>2.778</td>\n",
+ " <td>-1.068</td>\n",
+ " <td>1.673</td>\n",
+ " <td>-0.488</td>\n",
+ " <td>1.200</td>\n",
+ " <td>-0.201</td>\n",
+ " <td>0.952</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-03-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>15</th>\n",
+ " <td>1751</td>\n",
+ " <td>4</td>\n",
+ " <td>-0.690</td>\n",
+ " <td>2.489</td>\n",
+ " <td>-0.933</td>\n",
+ " <td>1.504</td>\n",
+ " <td>-0.492</td>\n",
+ " <td>1.245</td>\n",
+ " <td>-0.184</td>\n",
+ " <td>1.004</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>16</th>\n",
+ " <td>1751</td>\n",
+ " <td>5</td>\n",
+ " <td>-1.338</td>\n",
+ " <td>3.435</td>\n",
+ " <td>-0.771</td>\n",
+ " <td>1.606</td>\n",
+ " <td>-0.486</td>\n",
+ " <td>1.336</td>\n",
+ " <td>-0.184</td>\n",
+ " <td>1.019</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>17</th>\n",
+ " <td>1751</td>\n",
+ " <td>6</td>\n",
+ " <td>-1.637</td>\n",
+ " <td>3.336</td>\n",
+ " <td>-0.721</td>\n",
+ " <td>1.085</td>\n",
+ " <td>-0.539</td>\n",
+ " <td>1.393</td>\n",
+ " <td>-0.188</td>\n",
+ " <td>1.075</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>18</th>\n",
+ " <td>1751</td>\n",
+ " <td>7</td>\n",
+ " <td>1.130</td>\n",
+ " <td>3.753</td>\n",
+ " <td>-0.876</td>\n",
+ " <td>1.400</td>\n",
+ " <td>-0.527</td>\n",
+ " <td>1.212</td>\n",
+ " <td>-0.208</td>\n",
+ " <td>1.084</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-07-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>19</th>\n",
+ " <td>1751</td>\n",
+ " <td>8</td>\n",
+ " <td>0.858</td>\n",
+ " <td>2.757</td>\n",
+ " <td>-0.409</td>\n",
+ " <td>1.841</td>\n",
+ " <td>-0.538</td>\n",
+ " <td>1.097</td>\n",
+ " <td>-0.221</td>\n",
+ " <td>1.106</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-08-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>20</th>\n",
+ " <td>1751</td>\n",
+ " <td>9</td>\n",
+ " <td>-1.098</td>\n",
+ " <td>2.928</td>\n",
+ " <td>-0.382</td>\n",
+ " <td>1.840</td>\n",
+ " <td>-0.531</td>\n",
+ " <td>1.123</td>\n",
+ " <td>-0.225</td>\n",
+ " <td>1.119</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-09-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>21</th>\n",
+ " <td>1751</td>\n",
+ " <td>10</td>\n",
+ " <td>0.169</td>\n",
+ " <td>4.986</td>\n",
+ " <td>-0.429</td>\n",
+ " <td>1.791</td>\n",
+ " <td>-0.446</td>\n",
+ " <td>1.151</td>\n",
+ " <td>-0.219</td>\n",
+ " <td>1.148</td>\n",
+ " <td>-0.276</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-10-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>22</th>\n",
+ " <td>1751</td>\n",
+ " <td>11</td>\n",
+ " <td>-1.577</td>\n",
+ " <td>2.326</td>\n",
+ " <td>-0.302</td>\n",
+ " <td>1.688</td>\n",
+ " <td>-0.437</td>\n",
+ " <td>1.160</td>\n",
+ " <td>-0.222</td>\n",
+ " <td>1.178</td>\n",
+ " <td>-0.286</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-11-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>23</th>\n",
+ " <td>1751</td>\n",
+ " <td>12</td>\n",
+ " <td>-1.935</td>\n",
+ " <td>3.412</td>\n",
+ " <td>-0.129</td>\n",
+ " <td>1.784</td>\n",
+ " <td>-0.426</td>\n",
+ " <td>1.293</td>\n",
+ " <td>-0.258</td>\n",
+ " <td>1.173</td>\n",
+ " <td>-0.316</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-12-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>24</th>\n",
+ " <td>1752</td>\n",
+ " <td>1</td>\n",
+ " <td>-2.523</td>\n",
+ " <td>4.962</td>\n",
+ " <td>-0.154</td>\n",
+ " <td>1.757</td>\n",
+ " <td>-0.431</td>\n",
+ " <td>1.296</td>\n",
+ " <td>-0.262</td>\n",
+ " <td>1.160</td>\n",
+ " <td>-0.299</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-01-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>25</th>\n",
+ " <td>1752</td>\n",
+ " <td>2</td>\n",
+ " <td>3.263</td>\n",
+ " <td>4.891</td>\n",
+ " <td>-0.311</td>\n",
+ " <td>1.743</td>\n",
+ " <td>-0.461</td>\n",
+ " <td>1.061</td>\n",
+ " <td>-0.216</td>\n",
+ " <td>1.213</td>\n",
+ " <td>-0.299</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-02-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>26</th>\n",
+ " <td>1752</td>\n",
+ " <td>3</td>\n",
+ " <td>0.804</td>\n",
+ " <td>3.040</td>\n",
+ " <td>-0.166</td>\n",
+ " <td>1.570</td>\n",
+ " <td>-0.480</td>\n",
+ " <td>1.053</td>\n",
+ " <td>-0.192</td>\n",
+ " <td>1.258</td>\n",
+ " <td>-0.303</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-03-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>27</th>\n",
+ " <td>1752</td>\n",
+ " <td>4</td>\n",
+ " <td>-1.259</td>\n",
+ " <td>2.243</td>\n",
+ " <td>-0.263</td>\n",
+ " <td>1.645</td>\n",
+ " <td>-0.447</td>\n",
+ " <td>1.072</td>\n",
+ " <td>-0.185</td>\n",
+ " <td>1.364</td>\n",
+ " <td>-0.295</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>28</th>\n",
+ " <td>1752</td>\n",
+ " <td>5</td>\n",
+ " <td>0.196</td>\n",
+ " <td>1.576</td>\n",
+ " <td>-0.090</td>\n",
+ " <td>1.758</td>\n",
+ " <td>-0.449</td>\n",
+ " <td>1.030</td>\n",
+ " <td>-0.178</td>\n",
+ " <td>1.431</td>\n",
+ " <td>-0.293</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>29</th>\n",
+ " <td>1752</td>\n",
+ " <td>6</td>\n",
+ " <td>0.434</td>\n",
+ " <td>3.225</td>\n",
+ " <td>0.040</td>\n",
+ " <td>1.815</td>\n",
+ " <td>-0.390</td>\n",
+ " <td>1.072</td>\n",
+ " <td>-0.179</td>\n",
+ " <td>1.504</td>\n",
+ " <td>-0.293</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>...</th>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3195</th>\n",
+ " <td>2016</td>\n",
+ " <td>4</td>\n",
+ " <td>1.796</td>\n",
+ " <td>0.111</td>\n",
+ " <td>1.454</td>\n",
+ " <td>0.042</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3196</th>\n",
+ " <td>2016</td>\n",
+ " <td>5</td>\n",
+ " <td>1.260</td>\n",
+ " <td>0.112</td>\n",
+ " <td>1.433</td>\n",
+ " <td>0.040</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3197</th>\n",
+ " <td>2016</td>\n",
+ " <td>6</td>\n",
+ " <td>0.882</td>\n",
+ " <td>0.078</td>\n",
+ " <td>1.387</td>\n",
+ " <td>0.034</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3198</th>\n",
+ " <td>2016</td>\n",
+ " <td>7</td>\n",
+ " <td>0.935</td>\n",
+ " <td>0.046</td>\n",
+ " <td>1.385</td>\n",
+ " <td>0.029</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-07-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3199</th>\n",
+ " <td>2016</td>\n",
+ " <td>8</td>\n",
+ " <td>1.433</td>\n",
+ " <td>0.102</td>\n",
+ " <td>1.348</td>\n",
+ " <td>0.028</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-08-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3200</th>\n",
+ " <td>2016</td>\n",
+ " <td>9</td>\n",
+ " <td>1.058</td>\n",
+ " <td>0.082</td>\n",
+ " <td>1.321</td>\n",
+ " <td>0.027</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-09-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3201</th>\n",
+ " <td>2016</td>\n",
+ " <td>10</td>\n",
+ " <td>1.019</td>\n",
+ " <td>0.062</td>\n",
+ " <td>1.280</td>\n",
+ " <td>0.031</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-10-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3202</th>\n",
+ " <td>2016</td>\n",
+ " <td>11</td>\n",
+ " <td>1.079</td>\n",
+ " <td>0.095</td>\n",
+ " <td>1.278</td>\n",
+ " <td>0.031</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-11-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3203</th>\n",
+ " <td>2016</td>\n",
+ " <td>12</td>\n",
+ " <td>1.259</td>\n",
+ " <td>0.077</td>\n",
+ " <td>1.271</td>\n",
+ " <td>0.035</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-12-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3204</th>\n",
+ " <td>2017</td>\n",
+ " <td>1</td>\n",
+ " <td>1.569</td>\n",
+ " <td>0.082</td>\n",
+ " <td>1.275</td>\n",
+ " <td>0.038</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-01-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3205</th>\n",
+ " <td>2017</td>\n",
+ " <td>2</td>\n",
+ " <td>1.746</td>\n",
+ " <td>0.062</td>\n",
+ " <td>1.244</td>\n",
+ " <td>0.039</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-02-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3206</th>\n",
+ " <td>2017</td>\n",
+ " <td>3</td>\n",
+ " <td>1.831</td>\n",
+ " <td>0.052</td>\n",
+ " <td>1.231</td>\n",
+ " <td>0.037</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-03-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3207</th>\n",
+ " <td>2017</td>\n",
+ " <td>4</td>\n",
+ " <td>1.301</td>\n",
+ " <td>0.144</td>\n",
+ " <td>1.253</td>\n",
+ " <td>0.038</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3208</th>\n",
+ " <td>2017</td>\n",
+ " <td>5</td>\n",
+ " <td>1.235</td>\n",
+ " <td>0.132</td>\n",
+ " <td>1.249</td>\n",
+ " <td>0.036</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3209</th>\n",
+ " <td>2017</td>\n",
+ " <td>6</td>\n",
+ " <td>0.803</td>\n",
+ " <td>0.089</td>\n",
+ " <td>1.268</td>\n",
+ " <td>0.040</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3210</th>\n",
+ " <td>2017</td>\n",
+ " <td>7</td>\n",
+ " <td>0.973</td>\n",
+ " <td>0.079</td>\n",
+ " <td>1.235</td>\n",
+ " <td>0.038</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-07-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3211</th>\n",
+ " <td>2017</td>\n",
+ " <td>8</td>\n",
+ " <td>1.066</td>\n",
+ " <td>0.086</td>\n",
+ " <td>1.180</td>\n",
+ " <td>0.039</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-08-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3212</th>\n",
+ " <td>2017</td>\n",
+ " <td>9</td>\n",
+ " <td>0.906</td>\n",
+ " <td>0.093</td>\n",
+ " <td>1.142</td>\n",
+ " <td>0.042</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-09-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3213</th>\n",
+ " <td>2017</td>\n",
+ " <td>10</td>\n",
+ " <td>1.275</td>\n",
+ " <td>0.048</td>\n",
+ " <td>1.145</td>\n",
+ " <td>0.041</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-10-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3214</th>\n",
+ " <td>2017</td>\n",
+ " <td>11</td>\n",
+ " <td>1.035</td>\n",
+ " <td>0.080</td>\n",
+ " <td>1.138</td>\n",
+ " <td>0.040</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-11-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3215</th>\n",
+ " <td>2017</td>\n",
+ " <td>12</td>\n",
+ " <td>1.487</td>\n",
+ " <td>0.073</td>\n",
+ " <td>1.161</td>\n",
+ " <td>0.040</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-12-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3216</th>\n",
+ " <td>2018</td>\n",
+ " <td>1</td>\n",
+ " <td>1.171</td>\n",
+ " <td>0.093</td>\n",
+ " <td>1.172</td>\n",
+ " <td>0.038</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-01-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3217</th>\n",
+ " <td>2018</td>\n",
+ " <td>2</td>\n",
+ " <td>1.093</td>\n",
+ " <td>0.102</td>\n",
+ " <td>1.166</td>\n",
+ " <td>0.035</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-02-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3218</th>\n",
+ " <td>2018</td>\n",
+ " <td>3</td>\n",
+ " <td>1.366</td>\n",
+ " <td>0.091</td>\n",
+ " <td>1.158</td>\n",
+ " <td>0.042</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-03-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3219</th>\n",
+ " <td>2018</td>\n",
+ " <td>4</td>\n",
+ " <td>1.342</td>\n",
+ " <td>0.112</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3220</th>\n",
+ " <td>2018</td>\n",
+ " <td>5</td>\n",
+ " <td>1.147</td>\n",
+ " <td>0.170</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3221</th>\n",
+ " <td>2018</td>\n",
+ " <td>6</td>\n",
+ " <td>1.078</td>\n",
+ " <td>0.122</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3222</th>\n",
+ " <td>2018</td>\n",
+ " <td>7</td>\n",
+ " <td>1.112</td>\n",
+ " <td>0.039</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-07-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3223</th>\n",
+ " <td>2018</td>\n",
+ " <td>8</td>\n",
+ " <td>0.991</td>\n",
+ " <td>0.107</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-08-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3224</th>\n",
+ " <td>2018</td>\n",
+ " <td>9</td>\n",
+ " <td>0.804</td>\n",
+ " <td>0.161</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-09-15</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "<p>3225 rows × 13 columns</p>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ " Year Month MDiff MUnc YDiff YUnc 5YDiff 5YUnc 10YDiff 10YUnc \\\n",
+ "0 1750 1 -0.121 4.187 -0.687 2.557 -0.364 0.897 -0.160 NaN \n",
+ "1 1750 2 -1.278 3.177 -0.691 1.733 -0.381 0.904 -0.169 NaN \n",
+ "2 1750 3 0.112 3.550 -0.721 1.568 -0.401 0.918 -0.164 NaN \n",
+ "3 1750 4 0.026 2.862 -0.734 1.609 -0.452 0.951 -0.168 NaN \n",
+ "4 1750 5 -1.420 2.611 -1.043 1.553 -0.439 1.022 -0.167 NaN \n",
+ "5 1750 6 -1.029 3.379 -1.004 1.271 -0.414 1.060 -0.176 NaN \n",
+ "6 1750 7 -0.262 2.722 -1.049 1.026 -0.411 1.023 -0.183 NaN \n",
+ "7 1750 8 0.290 3.219 -1.137 0.792 -0.466 0.933 -0.210 NaN \n",
+ "8 1750 9 -0.851 2.121 -1.107 0.775 -0.375 0.945 -0.230 NaN \n",
+ "9 1750 10 -1.448 3.078 -1.167 0.826 -0.394 1.023 -0.211 NaN \n",
+ "10 1750 11 -3.518 1.996 -1.160 1.283 -0.423 1.094 -0.226 0.879 \n",
+ "11 1750 12 -2.538 4.091 -1.210 1.458 -0.451 1.143 -0.250 0.894 \n",
+ "12 1751 1 -0.659 3.318 -1.094 1.533 -0.464 1.148 -0.258 0.844 \n",
+ "13 1751 2 -2.341 4.503 -1.047 1.776 -0.482 1.131 -0.231 0.914 \n",
+ "14 1751 3 0.477 2.778 -1.068 1.673 -0.488 1.200 -0.201 0.952 \n",
+ "15 1751 4 -0.690 2.489 -0.933 1.504 -0.492 1.245 -0.184 1.004 \n",
+ "16 1751 5 -1.338 3.435 -0.771 1.606 -0.486 1.336 -0.184 1.019 \n",
+ "17 1751 6 -1.637 3.336 -0.721 1.085 -0.539 1.393 -0.188 1.075 \n",
+ "18 1751 7 1.130 3.753 -0.876 1.400 -0.527 1.212 -0.208 1.084 \n",
+ "19 1751 8 0.858 2.757 -0.409 1.841 -0.538 1.097 -0.221 1.106 \n",
+ "20 1751 9 -1.098 2.928 -0.382 1.840 -0.531 1.123 -0.225 1.119 \n",
+ "21 1751 10 0.169 4.986 -0.429 1.791 -0.446 1.151 -0.219 1.148 \n",
+ "22 1751 11 -1.577 2.326 -0.302 1.688 -0.437 1.160 -0.222 1.178 \n",
+ "23 1751 12 -1.935 3.412 -0.129 1.784 -0.426 1.293 -0.258 1.173 \n",
+ "24 1752 1 -2.523 4.962 -0.154 1.757 -0.431 1.296 -0.262 1.160 \n",
+ "25 1752 2 3.263 4.891 -0.311 1.743 -0.461 1.061 -0.216 1.213 \n",
+ "26 1752 3 0.804 3.040 -0.166 1.570 -0.480 1.053 -0.192 1.258 \n",
+ "27 1752 4 -1.259 2.243 -0.263 1.645 -0.447 1.072 -0.185 1.364 \n",
+ "28 1752 5 0.196 1.576 -0.090 1.758 -0.449 1.030 -0.178 1.431 \n",
+ "29 1752 6 0.434 3.225 0.040 1.815 -0.390 1.072 -0.179 1.504 \n",
+ "... ... ... ... ... ... ... ... ... ... ... \n",
+ "3195 2016 4 1.796 0.111 1.454 0.042 NaN NaN NaN NaN \n",
+ "3196 2016 5 1.260 0.112 1.433 0.040 NaN NaN NaN NaN \n",
+ "3197 2016 6 0.882 0.078 1.387 0.034 NaN NaN NaN NaN \n",
+ "3198 2016 7 0.935 0.046 1.385 0.029 NaN NaN NaN NaN \n",
+ "3199 2016 8 1.433 0.102 1.348 0.028 NaN NaN NaN NaN \n",
+ "3200 2016 9 1.058 0.082 1.321 0.027 NaN NaN NaN NaN \n",
+ "3201 2016 10 1.019 0.062 1.280 0.031 NaN NaN NaN NaN \n",
+ "3202 2016 11 1.079 0.095 1.278 0.031 NaN NaN NaN NaN \n",
+ "3203 2016 12 1.259 0.077 1.271 0.035 NaN NaN NaN NaN \n",
+ "3204 2017 1 1.569 0.082 1.275 0.038 NaN NaN NaN NaN \n",
+ "3205 2017 2 1.746 0.062 1.244 0.039 NaN NaN NaN NaN \n",
+ "3206 2017 3 1.831 0.052 1.231 0.037 NaN NaN NaN NaN \n",
+ "3207 2017 4 1.301 0.144 1.253 0.038 NaN NaN NaN NaN \n",
+ "3208 2017 5 1.235 0.132 1.249 0.036 NaN NaN NaN NaN \n",
+ "3209 2017 6 0.803 0.089 1.268 0.040 NaN NaN NaN NaN \n",
+ "3210 2017 7 0.973 0.079 1.235 0.038 NaN NaN NaN NaN \n",
+ "3211 2017 8 1.066 0.086 1.180 0.039 NaN NaN NaN NaN \n",
+ "3212 2017 9 0.906 0.093 1.142 0.042 NaN NaN NaN NaN \n",
+ "3213 2017 10 1.275 0.048 1.145 0.041 NaN NaN NaN NaN \n",
+ "3214 2017 11 1.035 0.080 1.138 0.040 NaN NaN NaN NaN \n",
+ "3215 2017 12 1.487 0.073 1.161 0.040 NaN NaN NaN NaN \n",
+ "3216 2018 1 1.171 0.093 1.172 0.038 NaN NaN NaN NaN \n",
+ "3217 2018 2 1.093 0.102 1.166 0.035 NaN NaN NaN NaN \n",
+ "3218 2018 3 1.366 0.091 1.158 0.042 NaN NaN NaN NaN \n",
+ "3219 2018 4 1.342 0.112 NaN NaN NaN NaN NaN NaN \n",
+ "3220 2018 5 1.147 0.170 NaN NaN NaN NaN NaN NaN \n",
+ "3221 2018 6 1.078 0.122 NaN NaN NaN NaN NaN NaN \n",
+ "3222 2018 7 1.112 0.039 NaN NaN NaN NaN NaN NaN \n",
+ "3223 2018 8 0.991 0.107 NaN NaN NaN NaN NaN NaN \n",
+ "3224 2018 9 0.804 0.161 NaN NaN NaN NaN NaN NaN \n",
+ "\n",
+ " 20YDiff 20YUnc Date \n",
+ "0 NaN NaN 1750-01-15 \n",
+ "1 NaN NaN 1750-02-15 \n",
+ "2 NaN NaN 1750-03-15 \n",
+ "3 NaN NaN 1750-04-15 \n",
+ "4 NaN NaN 1750-05-15 \n",
+ "5 NaN NaN 1750-06-15 \n",
+ "6 NaN NaN 1750-07-15 \n",
+ "7 NaN NaN 1750-08-15 \n",
+ "8 NaN NaN 1750-09-15 \n",
+ "9 NaN NaN 1750-10-15 \n",
+ "10 NaN NaN 1750-11-15 \n",
+ "11 NaN NaN 1750-12-15 \n",
+ "12 NaN NaN 1751-01-15 \n",
+ "13 NaN NaN 1751-02-15 \n",
+ "14 NaN NaN 1751-03-15 \n",
+ "15 NaN NaN 1751-04-15 \n",
+ "16 NaN NaN 1751-05-15 \n",
+ "17 NaN NaN 1751-06-15 \n",
+ "18 NaN NaN 1751-07-15 \n",
+ "19 NaN NaN 1751-08-15 \n",
+ "20 NaN NaN 1751-09-15 \n",
+ "21 -0.276 NaN 1751-10-15 \n",
+ "22 -0.286 NaN 1751-11-15 \n",
+ "23 -0.316 NaN 1751-12-15 \n",
+ "24 -0.299 NaN 1752-01-15 \n",
+ "25 -0.299 NaN 1752-02-15 \n",
+ "26 -0.303 NaN 1752-03-15 \n",
+ "27 -0.295 NaN 1752-04-15 \n",
+ "28 -0.293 NaN 1752-05-15 \n",
+ "29 -0.293 NaN 1752-06-15 \n",
+ "... ... ... ... \n",
+ "3195 NaN NaN 2016-04-15 \n",
+ "3196 NaN NaN 2016-05-15 \n",
+ "3197 NaN NaN 2016-06-15 \n",
+ "3198 NaN NaN 2016-07-15 \n",
+ "3199 NaN NaN 2016-08-15 \n",
+ "3200 NaN NaN 2016-09-15 \n",
+ "3201 NaN NaN 2016-10-15 \n",
+ "3202 NaN NaN 2016-11-15 \n",
+ "3203 NaN NaN 2016-12-15 \n",
+ "3204 NaN NaN 2017-01-15 \n",
+ "3205 NaN NaN 2017-02-15 \n",
+ "3206 NaN NaN 2017-03-15 \n",
+ "3207 NaN NaN 2017-04-15 \n",
+ "3208 NaN NaN 2017-05-15 \n",
+ "3209 NaN NaN 2017-06-15 \n",
+ "3210 NaN NaN 2017-07-15 \n",
+ "3211 NaN NaN 2017-08-15 \n",
+ "3212 NaN NaN 2017-09-15 \n",
+ "3213 NaN NaN 2017-10-15 \n",
+ "3214 NaN NaN 2017-11-15 \n",
+ "3215 NaN NaN 2017-12-15 \n",
+ "3216 NaN NaN 2018-01-15 \n",
+ "3217 NaN NaN 2018-02-15 \n",
+ "3218 NaN NaN 2018-03-15 \n",
+ "3219 NaN NaN 2018-04-15 \n",
+ "3220 NaN NaN 2018-05-15 \n",
+ "3221 NaN NaN 2018-06-15 \n",
+ "3222 NaN NaN 2018-07-15 \n",
+ "3223 NaN NaN 2018-08-15 \n",
+ "3224 NaN NaN 2018-09-15 \n",
+ "\n",
+ "[3225 rows x 13 columns]"
+ ]
+ },
+ "execution_count": 258,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "df = pd.read_csv('Material/Complete_TAVG_complete.txt', skipinitialspace=True, delimiter=' ', comment='%')\n",
+ "df['Date'] = df.apply(lambda row: datetime.datetime(\n",
+ " int(row['Year']), int(row['Month']), 15), axis=1)\n",
+ "df"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Plot the data. To plot the monthly differences, for example, you can directly write ```df2['MDiff'].plot()```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 261,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.axes._subplots.AxesSubplot at 0x11fa1d6d8>"
+ ]
+ },
+ "execution_count": 261,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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4+ZMn8G+/OSi2uhW7u8x/bX8KaV3BYd/pRdWa2QadPWeKJhQWEBUqzKL/L0rX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\niiOsnqrChAMoyurSNCrSdkIs95x1Qe+ZRsE/n9ZwZJY7g56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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1a22bcefd0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "df.query('Year>1980 & Year<2000').plot(x='Date', y='MDiff')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Apply your moving average filter to the monthly data ```MDiff```. Try (for example) 6 months, 5 years, 10 years. Plot these on top of cuts of the original data to compare."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 274,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.axes._subplots.AxesSubplot at 0x1a221296d8>"
+ ]
+ },
+ "execution_count": 274,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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EQt/3i2XRD8eeEOuniRwn+2iRms/iotcXMem1he1y7D8LIQT/+X7DHqd9bSo9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\nbFBHPvjx+fU+etNoakKtLHal1AvACzU93kkJB+pde3TMw92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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1a227b9588>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "df['6MA'] = moving_average(df['MDiff'], 6)\n",
+ "df['5Y'] = moving_average(df['MDiff'], 60)\n",
+ "df['20Y'] = moving_average(df['MDiff'], 240)\n",
+ "\n",
+ "df.plot(x='Date', y=['6MA', '5Y', '20Y'])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 2.2 Electronic response of RC circuit\n",
+ "\n",
+ "In general, the response of a linearly time invariant system is found to be the convolution of the its impulse response $h(t)$ and the input voltage. Consider a resistor and capacitor connected in series, driven by a time-varying voltage $u(t)$. The impulse response for such a circuit is:\n",
+ "\n",
+ "$$h_c(t) = \\frac{1}{RC} e^{-t/RC} u(t)$$\n",
+ "\n",
+ "* Write a function to calculate the impulse response as a function of time, the resistance, and the capacitance, and input. Take care to normalise the integral.\n",
+ "\n",
+ "* Now consider a noisy sinusoidal input voltage $u_N(t) = u(t) + \\epsilon(t)$, where $\\epsilon$ is a vector comprising samples draw from $N~(0,1)$. Plot the noisy signal and superimpose the clean signal.\n",
+ "\n",
+ "* Calculate the circuit response for your signal and compare the result to the noisy signal and the clean, original signal\n",
+ "\n",
+ "Play with the RC time constant and see the effect on the signal.\n",
+ "\n",
+ "\n",
+ "Note: this first order low pass filter is exactly equivalent to an exponential moving average. The \"memory\" of the output is effectively determined by the time constant.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 287,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Cutoff: 0.0005\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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yHK+lCHbF6KBy7m+JtTzCRa3X54VJnf3tR1m5qzyOslI42GPgC3H57aMXW1Pi\n7bjJmQigWkoqzBrW+aaU44pkCytGF9JspFX00i8zBLvZgtD7GRKCL+ohWYLKCIo2lIq4ysS1GgHY\nqsdZKMKbQCjGfoSQ/KfrOTZVHHBjCKu6JMc+AMKkat7N/Kq+jv9rbuQj6sMTzozO5f/uXcvu3pGS\nUvafKUNt/EdC6uFMxBhRahbusL9wFTJzKrF2pGvwIderlFqVaGJtzOCH+s8QIRmoqXFGN7McGwPo\nzXq/PCVxm65RMYo5Z7I5pAR74Niab5sZW2wP6U+8XZrGnc4F4eNjHahSIszG9IduJdKpoE2LU8fo\nL7pe/xzS1Tg+meQvNdV8T/9V1vH2/gQ3PDp1IYanf+vhks09Y6V85XM9ThObeJUotdiTRI214yZn\npD7pTS5gqe45uq2CW12JYnTTbCnUiBEuUNMLSKA9b9PD2xAEoY7zLJuPm5/POub674xidHGasjkr\noS093lMcGk0vMmK1XOCPbWanrnGl/vui3xhAq13BoAqnJxI8WllBnyp4IHbFqOPGw1TFxJc7qGCs\n0Zj9CSurZEKA4r9fb1BWAWAnZ7JX02hSOzlNFJ7Dit7FbD/c9H/tj6Y+d5PNAKzTq7DlgRWth5xg\nl1Lhg+4KjleyO5u4ZhMAm7VKqgi3K+vGPuZaNl2yIWdsIx06fEx7cNRnUKs3UjfSzIf6B9mraWw0\n9FG96JNN+ySVZf17GQV7PQP8Nfa//Cl2VUnnC60foSZY6Gtdf7TPw03ORBq9dBNjZkglPfDqtAjF\n5DL5JJBdOyjYnT2tzSQh8zXowHY617LZLmdkHZNWPVIq7PQXhQtCTEFKrAMpBSfbnhN+k/TMPbbV\nxG4tWIiKCzmteiOtts0Xu3pxheDJynjR88dDEFUSyNtChcwmk/GaYh7f0MGKnWMLcvi3W18MKZkg\nUWLtOImZrHfnskc2UpX07ONbDL1oIIUwuqm0KnnGOZ5h0r+PtBqQrspD6nxMdHJ/a6F3UTH317Qn\nxt4nYqwcUoIdJ446NJewTW2wVd6sVVInwu19Wmwf8y2LTrJrJ7tWI7s1b8JWFFgUAITWixrr5Kxh\nk7MS3nkrYjHm5jnFJD96ZCN/eal87c8OBKNpWmOJhHg49sXMK496vmJ4f9MFfqzwK/Io3ISXKPS8\n3sT5BWzswg91nOsnGF1hfSJ1zLWakFIwaAwRF1Ze9FSgsc+xbXbL5pwrq0irntWq9+5UiBAN0OjE\nsKqI50ZOqlTnAAAgAElEQVTUWI10ahoJIZhNsSJnEq1qM2eMOJCYSbXr8oqfPFfMNDBR1rcXCDYo\nE+VU2D92ywvjKmSXi1AHUbRh3OQMXquuwZQ6GxJnALBZ13mf+mT4QCWJog2yyBphD405B1Vcq4l2\nQ1IpkrxKZAtwJdaJVr0JRBQVk4XZfR5zdl0EwHPusdkH3RiuXUW/nuT9oT+Kg2v0sNCy6JR1WUek\n1cBuXcMFPqndU/D+QWGps5JDzLYdGhyHVTGD+SE21x89son//uPBU8ZzPIw2IX8Q0qEqrEjVMWIH\nLSItPC4ZtVBbOhY92Ik97R6P45tlRmJ9fses/HsFWvcc2xPsd2bGnEsNaTWyW/f0xVaRHWusGF1U\n2RrC1RkhX1N2zUae0TzHfdguTYl1UGHWho4D2KOpRWsZCa0PoY5wZnKI7XImJyRNVvvJc+coawqO\nmygTqRx5qBIoAMfYnvl1vrIP02pGujqbDZ2L1BeySgMEBO/XcfYAe2VT3nE32UKv4S36ubtTRfcW\n9VptZvm+SAEOKcF+7MwaaoUXanad9YG849JsYre/Va4ie3spjG4QLgstm/05gt01G7GEoENVs5pi\n56L6WYXvtDcjAGdkDqtjBgsKONOmio4SMvHGw2hJHreEREyEdXb6ePWvuWjOEXyzqQEJvM63aRZD\n6N1IV+VN0ls8hmUcaTUiXY3Vuuewagypj64YXanM5Fvst5C76XfNZp7yhfNblOyMQmF0cYw9WNDx\n5VpNSN1zjNfnOdpdFKOTKtOLpMkNxQXP/6OKIk45//1aaFl0y1oaE9VsNAxMQCmjPTxPjB/icl1o\n/VQuuJ6KeTelyk5c+9CGov0DFN0T7DeQ6ffwEtm2+A76sGCKQOE40jYZlvn5FK7ZwrA+HJpJoxjd\nSCdGhVIXcrS8HFKCXQjBh1WvSXIyxCDjWo3s8k0q71azC2upwdbestgo5+aNA9itabxDLVzWUzH2\n4Vq1VPsCrzOxmG26zjyRXda23IlEo/HJ3y2flOuOJ0MuLEnrz40mu3WNP9fWsDwe483q6M+rGD1I\nq4H3qV4Z1AQ6oOCaLSzTPcGc6RhNjdO7EXYNBoSYUzyNatgYwgWu1G/LGxuYcMJwzUaENsw2arMa\nZwAIvReh2LRa3vv3G/vNqWPS8nw6uzUtVUUw9DvHvOiRRabFH5w3sHLkbGwh2KHrNIQsYoWRfEBd\nQmURs2JAwnKKmtwOdLu6nzy2ib7h4o1wjMYnUON70ao2e12zgI37iuekBAL6CL/s8kfNLwFeZMtq\nzQvMCAt7FP6CMMe26aAh77hrtiCFZJevYGbWnVGMLlyrCWUKisUcUoJdEXC8Hze6O2wbZDaxW9Mw\ngQGZ3f29IebZ5RaYlu/YyBgXTDxdo1YUdiQpsU6kn5reKetwzVZsIZgdy65OuKlj9Emo4GbZ8yfL\nAToRxqMj3v5cdmje0do61lVKPtHbh+qqPFA1etkH8IRs8LsA9GcklO3TvckSVjFRGN1oljcxu3Mi\np8CbeK7i0K7lRNUIE0XvZ55l83fnNaHPJC3vnVuj1YeYcbyImCNNB0uqdJHWyqRdg3Q1dmgGjaLw\nu6EYHRi2ToPr0iEb2Jg8DfByLI4U4S30doQ0bfiguoRr9Bv5hf7DgvcKOPbKB/i3WwvXiF+3t59L\nfv1caN35UpnIXuMHD23kyrtXk7Ac5l9xb+jVtbpXeNPQMAuSLnptaeZP7/2qYdD13pEl7imA934N\n6DaDQnCKsiV/nNFNreNQ60oed07NOx6UrviO8Bb2zKRHRe9KmRYnm0NMsAuedo+nR1bTGbpaNoOA\nXbqWZwOtju2kxbapCSvnaTUgpWCLVkG3X2ogHxcl1kGj6W2/WkRf6kdUY9kZoqPZLF+rrKIt/i+s\ni/8bX9G8reBkdVkaC1JKbnxiC11+aNgT48h8bc9pSXZWjVfr5o1DIyQGj+WRitrQiJRchN6NamXa\nq72/qWu24OgDjAjB20N2V4reTaVvDukmxN7tR8b8Vj3d/8R7HwINbq5t83yu/yYYa3o7gPV6VV5R\nr8CMcow1wj4acLOmlsC1GtmrK1xWxIej+u+XKwVd1KaedZ1exUwRblZ4/TWP5312ufo375i6KrQj\n0Fi08F09IyzbtJ/Vu8fvYJ2o83TYtOkfCdfaFaMDRRvkdcMjvHW4H7ViOyijR/kIvRvFqqNZ9JOU\nGqn3KxkkLOp8Vvtb/v30bmqsOLtlU9biHRCE1AYy4QtakC/hIoyeSLCHIQRUiwRDIY4tSDvadmg6\nNTma94gxwELL5sNmSElNqSHtWl5UWwrWIRFaH0IxmW2mZ0U6q1Dj/Urp1fZuM76T+velWpgWMnHe\nfsMyzrq6tK44QfjbKzt7+fZ96/nin1eO+7652/qtFSY1jsuxpokzMp8uXdKtkidwLr4xQ0grCRRt\nmGq/JtBv7TelDrnJVoSQrNWq8t8DYaLoA9RansOxS4Y5Mr3fbIPm7ehivjU0cIrNs+zQcd5Yz2S3\nTdM5RWmjNiPvQTE6ce0qFrl9tMvcaAnfQe+bCcPLBEiU2D5mmQpd1OKggjRwrXo26vFQe+/9BTpb\nzVPSC/L3tBuzjiUsZ5SSx6VTajenMG1/rKWBC91J9ctOvMpvUYcAtWL0hC7F6Em9JzGR/j2CTPQ2\n386eG42k6N202OT56VK4cVy7hg6/vMlRilcfSOi9COEgI8GejxCCKhIM5phZAlx/q7xd1/hwVi0Q\niYx1Md+yQjUY8CZtl+4yW3SxWOSHKQYa2f+4Xj2Yi82vgltBs+2wVde51vhFKmW82DurxPbwo4a6\nVO1ngFiOLa+3SFGuQmzpzLYprtnTX7JTNRDGlhPUox9/c28358+7zzA51jS5w74QZ/hI79niWp6N\n+pm2dIZj4Ni6SnoaU4dMh6cGCUvrjQpenRNhouieVttke691mClGOtVIJ06f4Qm3IOdBpEIdrYKC\n3RO0tUjDu8/K+L+n7+0X/5opukMFu2s2sl0zkBAagy+0AYSa4Cyri0wx5iZb2K6roY20P/X7l/I+\nM7QufthQx3pfMH1Ay1Y4Lr/9pVS28lg06bB3+tant5U0tm0S+w3EY9upcxxm2w4n+2Un/qvmR0V9\nGWAjtD7qfMG+zDkxdUSajUipcqvqhT7OIvO3chF6D6fZXUWLfLnJZjbo3q7xccczpwWKQ+DPm2wO\nKcGuCqhmmEHCBTtOFdKpYKeucZyyM/Wx0AYYVgQLTYuX3aNCh0qrkUHdm+TX6j/POx44thb66eab\n/Foj7ebClMP2au1m734Fv4FNxdzf8Ov6Or7a0sR219MOzlVWZ51VSvPhXL6UoWVPNNNvIsOzI2lc\numMjzDaFXyL5CIQUrIsZPB//TMFrBGaRdMhiOpPYNZv8RKH8V1f4Avdc29OSukJMMUExsJjhRTJ9\nSvu7f8/91DiSOlfSQ/6CkHn/zXraT1DjFwRTjE7cZAuLlL20yxAzodXIiAr9isLskIbaQdz+q+zu\nrNBQ12xin04qGmw0Tpr9I26ur+PyGS2hFU8eWVe881Ahwt7psGzOMCaa4VpsYTDiezjatBBApZQs\ntCzWx4xQx3qApz1LLnI939iP7fdmHFVxk8106d53uzTDdCa0foTipN7LQrhmKxj7MaVKtW85COpU\nvd7aRUVy4mUaRuOQEuyKELSIvsLbILyJsD3HIx1MmjmWGxqfDN7E69MkCSFQQ7R6JdaBa1dT76uk\ng/51vLho736vUdcChbeZWs06FL2PM0YSPFcR52I+BcDNRnZ98anuSBY8bym74zoGi0ZbZD660Huw\nFMmMpG9TlxqK2cCmUeqmZEUeyHr2Z9kyNaTZmKqhn2UO8bWiD7reIpcoYFZzky2s94Xzv2v38T3t\nRvTYXo42vckcpumnxprN7MpYVD6n3YVQh1C0IWotT+EIa70nzXTI4xvUsKxVPyLGsljinJK+n9XI\niCpRldG1XqHvZ2OlxRkjCfZpGk9Ves/TQi/fuX8dlpP9Xk9E4Eop+fmSfOdi+Lnjvg0AbfuHClzD\nxYp1s9hM7zCPMi026zq2LFxdMVAcdiSPAWClXJh9VbOVoZi3A/6o9lBajmS8l086JxS8vms2I7QR\ndirVqfdTiXWgOAY3q7+kabDUshrj55AS7K9d3MwM0ZO1Nc/FNZvZoXmCI/1H9SbNcVZhgZSZRLLW\nPTLvuGp0UJ1MO1YDoeGaDexVtVTcqoFF11C4JqNWbaLCga93eS9IT1V4pMN4yIzZHetEenFbtmmg\n2PAV8Ut5wPifgsczdwtqzNOKG830DiuRmMMao5LHQiIKAhS9B5wYta7kh/b78447ZivdfhLIvIxo\nEUXvRroGllNbxAnu2dltfZghfyX7oLYELbaPRf5uLMwplvp+VhNCG2LQH3u+8krq/Zqd9D570jkp\n/56+mXCnrvEp7R/53znWgXBiNDlu1sIQhEqqRk+eyS4XrdqL+f/G/m6kE2eJL9j/V/8tv1zaxg+K\ndJ0ajVxlJddJXozJUlSE3oNUbBb7Leputi9isWmxW9eIKYXDHQMBfY69B1cKEmR3PXKTLZj6AP7P\nmdqVBUlNcyybu5zXA7CwuYpcAgfsSr025WRXjH1UmjUIIKlFcexZfPKc2dSLIfaFbHUDXLOJPZpG\nUqQTDJTYPmodr/FssXEAT6qzQ0LSJEqsg1mW9+e6xEwXZXKtRhDQ7ptjGhgoGMceq1rPOYlhFlo2\nWLXIimxb/rJNnf7dppY7/PZ5oynscV9Tz3TOZdKfsLK2+oFfInNBdJMz6NThbK1wWJpidFPv10QP\n2z25yVaGjSEs4J6M/pLC6MY1G1CRPBjS1Pzq93q21NxiYPtVBUc1WWSO7lsI3pO3Si/uuZfqlGD/\nnuv5BLbK/MxC1/Te2cBsl4tidHCiNYAgO1vWzYiBP0IU38LXVa1inmUx37ZxhuenyhHMFl7E1S+f\nyLYLX/fw2DtyjYfcRLek7dAXGuUifcdyaTMgCDFdZFp8wfokV9kf4bmR8wC4uOrOIuO60aXkPaxk\ngAryk9haQcB2X0Fc6OepKHoPQsIs2+ZoxZu7zdVhSUp+9JRWlfKnGLF23mJ7odrHL5pX0vebCIeU\nYK9Iei9oB8U1dgTs1HTuM74CQDy2m6Msi2UhmlRAUB1yry54bU5mZODYeqvtTYxtGQWiAo3qf/h/\nQGFbqFCHkEY/p/oF/a2Reag5gv2SXz/vXXOiNvIxnv9sW7bGHtZRyWhcSuUxV3FXtaehzCZbuDuu\nZNnG7JBNoXdTb0uSbmaZZE/oBZ2MwhB6Ny2Wr/26J+Ydd5OtIGSqIFegySp6N9VWnBbRF/qOnDKn\n3h/vCfbLxCXes/imoUWWxQeSXy/4XJBeFPYaknbZwBb3CBRjH5qjcbTrKQS5tYgAkDFcuzqVuBLP\naeagxDo42tc8M01BboYJZ7SEo4aKzZycNLnVfjNOYi5tus6AEAU7ii3ZUN52fYXIFexhpYDV6rVU\nH/0NLj3iP9gW/2deU0IJhVSSkeXwF79F3eMjXgTV01p+clqAVzPfRgHqQuZroHFfo3i+ndOUzf79\nuqiyDXTgCffkgtf3ioFpbDF0ZokuhDqIq42wwFccFs+bW3BsuTikBDsD3ta+o5jG7guODYZOpUhS\nT58n2E2LDbLwH1Q6VUjXYEQfISbsrDAnxfA0ss6E1xx5Z4ZgDzSqHj9pplAXpsDOH2z33cQcFKOb\nH7hvx5bKpBZ5KoU9vSNs95Ndcp1VQh3EaHkYS3G5trGBESF4Kv65rHOufzQ7SQu8iTfHtuglrbEH\n9V626HoB04KLovdwruM5QLeFar/Z/Us9IeCiGF180PUW5SFZuCpiUAxsn+5yi/0W1via7TGmxQvS\ns7sWSg50k81IqaLE9tIlazlG2Ul9fCvzLSdD7wsfLM1GXlI9jf9m/Zr02eogijbEQn/ir5XzM25Y\ngeEo7NY07o19teB3QvG6gy0yLVa4i3BG5oKAdTGDE5TtWRmQ42EiuZLOqJqGS3zGPQg1ye/qatmi\na9yoXzfqdRW9G80VCKc6lTfgWo3EXNhlFH5iRe9mdhEHqGu2IKXgZd1boIMuSYqxn0rTU2w2uL4s\nCb2Ngms2sVeHFtHPm6vuBuB403/f44eIKUYIcZEQYoMQYrMQYnKKRwMM+gK2mPM02Yp0Vdb73cIv\ni9/BsOpt137nvKngOC9aopGXVG+lzwxzCkwK73HW+8kMaaRVh5QKvZo3KS/RwgtcZdYBecVdiJPw\n0uK3GwqacIu2Wxsr49H4z/nuY3z+T+HmEa1mLUKxeV3nLAZUhacr8oXmmt19ec5XRe9mrm1l9IX0\ndkaKq9Cm66EtDIU2iFDsjMiD/JkTaNwrdC/q5Wr9ZoTeg1DslHCMF+l7i9SQZhNKvJ2PaQ+yMmYw\n37TYbB+Vup+uFpoaGm5yBmp8Dy6Ck5U29NgeTrE8bf29yW8WvG1mFdFzfEc7pN+NRZZFv6zMS27S\nrJqUg74QSkbJjH+4r0mFhQaL34wiNZBKodSw84ViD48an8/eXYzyPirxPShGN3M7TkZIyUNVlXl5\nKK//fn4iljC6abKUnPBUhdkmdBqFf3/d2J8S7KG/l9SRVgMjhvd+fkr9OwIHxUgnKBbKpQlwzVY6\nY96u7KTKJ1Gk5ISkL9jV4r9lOZiwYBdCqMBPgbcCxwMXCyGOn+h1Q/EFezGN3QtXmsk6vyrejrj3\nxzwyqbIjp8Z2Lq7VSNLwNO67Yt9Ifa7EOsCJc4LblZXMENxPWvUM+OFR7/Jrm+SixDrQXEG1ZfAe\n8//SW3rd09Sb/BC3pO3w0QIt8YQ6RGzmX9Fqxp9ANB7Uys24Vi3n9RnUOC6PVNSy2p2fdc6j6zv4\ndFZctYOi9zLHtrM0dlCot2JsMXQ+o92dd6/AsSXNeh4IsZN7B2O4Vj2/8bNHZ4uurIUT4AbnveFj\nfeyR+WiVbVxmXs6KeIyTk0nOVNI250+9YVHBsU7iCJT4Hk5UtrFD0+hTVU5Mer9/boRFJq7ZiKkP\n5S05qd2caVErhjlmRnZUTp81mz25JRByr+F//00jp2Kj+c27Y/xd83aZR2eE/xbGxmh5AL3xCXIN\neu/72dPhQ3J4LPYFFil7eb+ajp8fLY9Jq/J2e7cOP8DJSZNlFZ7TtzZj92uG+McUvZuZtszLO6gw\na/2m0iE3VhK4apLZts1ydzEvy8Whz+QmW5Exz2S0UGnnbOM5hGpytOUtOGG1qjJxhuczoifYpam8\nEo+x2LSonMJwt3Jo7GcBm6WUbVJKE7gTePcoY8bHYAdSKHQXiTMGb+I9Z9QzInWG4l0YrqQpMXqN\nEmk2skdTkZAlVJTYPk6zegtuR12rAdfoZ4s7K7+ccHANo4NWU6fPj9aQVj3S1ek2vIUnSKg45msP\nFHy+WOu9GA3PUT379zxVfUme7fTJTZ6Ne7yxyoVQq7biDC/kQ+oyTk4mWR6r5ERlG68W6wqOEXof\nCMkcy+bonIQvJ9lKm66H2n6Fn2T0arc9S9PPxU224sTSWqjhx6UvsCx+Yb+D0YwHzuBihJrgsXqL\nblXlnJFs+3WloXLBsa3h904cgaIN8YQyj5VxT4E4OeH9jk5GZ6cbLzkje1yOoz1AiXVguIIZjsPx\niZs5P+e+0vSyViWF+wUoRge6lAgrsO8Lr6CV7s2VzN6chdAbnyHWvIT4jPtQq7Idq3aOdP7u/cVD\n9nqLRCXlolZuxUnMpFXanJ5IsiYWIylgZfzSIqMkit7DCXYfFtl/z3mmS4em8Xotv0l4oDgcYTt8\n3fpYwau7ZiuKsT9lwLL8HIn3OMHfpfj7ZQ8dDcC91VUsj8c4d8RbEOYnbi86rlyUQ7DPBjLVgV3+\nZ+VncB+isjlnq5qPM7wQ1ARbYoL2yn5OMJNYBWKaM3GtRlBsulSFj2kP+pmkEsXo8CJZgAWJ/ObC\nrtWA0HvYIo/Iy4YMUGL7ONXqzXgJFVyzmQHDM8E0iVFqcSgJtLoVxAfm4wjBvVVVPBvLTvL52K2e\n8/Wy28KqJzrEZ/+eyvk/QWil1/0Q6gCKNoCb8OLGT0kmaTccBoXg34vVrs+I+V0vs6MAOpKL2a1r\ndIh8wZ2uumfzerXwzsRNtnpJQf7/x2J7aLC9BKN17uhRB/bQsUgnTmzG/aiuwuuHS+8i5Ax52vxX\njfN5Ph6nxnFZZFnc55yV/V2E4Kf/dHrq/4NY9j8pJ9Hmpn0HSmwfM02FFe5Cholz9sLs7ETXamRE\nUehSFJoKFBHTYu3Mtyz6Mx2vyRZco4tOWVc0YSdAr38eZ2Qurl2NXl+4MBjA3a/kd9cyWu7nnbNn\nscYwskogjFbCQInvzXq/XAHrDKPoGKEOI9Qkc2yb89VsE2J30vt9ZsRC/D6+4jDHslO5KGE4yRaE\nYqdMZ7PinkBfUELkFIA0m3ESR/CThnpsIXjL0HDeLncyKYdgD1u68vYcQohLhRAvCiFe7Owcpzf+\nou/Apfm2tlycoaORUvC7uhrWxmKcNzzCScq2UccFEQg7/R/zTGVDqtPKYt/xIUP+ZNJsQtEGea3m\nmSLm5VbiUxIoej+LLdNvEOHfL9lK0rfjFZqwAWplG0I4zO45ipMTSZZWVtAoBrM0OKuIl0qrewW9\ndhVqxS6MpscKnpeLEvc04blJTxN1RuYgBWw0jLzyx1njfAE927b5g/OGrGOB/ff8ikdCa3HE7Rgx\nCffnCMqsa5itCMXi0/JfARDx3Rxven+Le9zw6ozZF4iR7Hgbrl3F0L53ckXysxyfuDn01AU5scqu\n2Ypr1dFVs4u/VMzgtSMjqMDnrcuyzhMiOwkoiGVvNbayUGmnzjc1KLF9nG71cWqBNPVUWemQ4nYB\nWmwfi0yLPrKbKyv6AC/JuQWd+qln1btRY51YfadgDxyPVrURxuBwVeK7iTUvZZuh872mej6sPs4c\n4c3z3AzVzJh4b34NIJKtWFLlxaE3ALAmNopgz1Acfmq/K+vY037IY4+Rn08iMt7LomHT/jt6sfB2\nDVUVbbTaNs2uy+fNywqOy7gTyX3vwLVq+Oe+AY43LS4Oq1M1SZRDsO8CMmf4HCBvOZdS3iilPFNK\neWZLS8v47mRUQd2cvI8XtmRPPOlU4Qwew33VVWhS8rbB0hyTwcRb69dj/jf1AU6reArwMtpyX6D0\nOO8FuVl4AuU9ylNZxwMb6kLL4m/OOelxZhOu3o8Fo9S2AK1qM9LVOTbpcmYiwdqYQVLA/1OfKDou\nQK99BTfZjNV3ClrtKhglCueCa5d4zx7zFqIZpmdTfHj4rQCs1KupprCWK/RuNCmZYTtZ5gkgy7H3\nCfW+LJOM0Lup8DM4b7LfVvD6QUjaTkMyLAR2rJuTkiYb3Dl59yuE1XsWQ5uuxOp9Dfe6Z2f1rxSI\nlBP6a28/LvfbYfWegVa9CUUboq3nIr5sfTwvq1nKbL9hUL53n2+e/Zp2my/YBjkqQxPMTQYKNP3d\nmsZV2i35X0SYSL2XhZaVZQIJYu5XaI20iF6KBcKqlV4WqTO0GGd4IUJN0hLbmDWmoz/Bql3h5S60\nmpUgFT7e28fL8TjN+k6ejH0u9J6Zzn0l7r1fc5MKunDYax0JTjzl9C1EsCOcbdl5kVPD1gzirssx\nFfm1dBS9B8MV9NtNBTOTIR151WN4O481hsGJvvPzUfe0os8W4AwvZGjzV/l0l7fADBQqhTIJlEOw\nvwAsFkIsEEIYwIeBv5fhuiUTtmVItL+bIwZa+VZnF7Mch5MTvxr1OkEBoG8pXvu9Y5WdzIp7ppWj\nTKugzTfQ9F/yY2f/W/9z1vFU1INpZZlqXKsRISTtmsZb1eeLPpsSa8dNzOJ4dnNUAmwhWG8YhQtW\nZSIs1Mqt2EPHYA8cj6INocSL92MNQh7VWDuuVcP3Fc8E1WnNRToxthoKpyrFOrn30GzDPRkLWYBr\nNiGkoM3Q+ap+O/+jpZNJFKOHBssTzPuLZIA6idlIV6OrsptVMQMEnJRMcoxSnj6zFx7XSl2FJ1xi\nIY5Ls+s8zJ6zSHa+iRcH38YdzoUlXNVrFPKi4dnBP6A9geJn5y4ussUPFIddmsbr1NXkCkvF6ATh\nvV+Zjupg3E7doFaMZJVfyEWNtSNdHWk2cW7SE5pfrP0h/6ndlTrn/B8s4Z0/Ce8FqlWvp2J4Ju8a\n9O6xzG/CHUQ+FeqPG3z/P0ivCuU+mrCTM1mmB8I6fDHKrCc0k+6coyoLLJstus7xYlv2OL2HI+0k\nRxZIskvhxnESs5BV2+hWFLYZOif5gr13FB9fLmckf8GJiZuYylZVExbsUkobuBx4EFgH/FFKOXkN\nGkP44Jn5JgFpN7Bh13/xjqFhHnZOTzVqKI7qlYWNp00pzfHNNDoOTa5bsElCkNy0TPULg+Vs8dRY\nB5rrbf/COuvs0lROUIo7t5RYB5pZz0e0hzkj6U2e1TEjLyws9FvFdyMUm/cmdvEp07NHfrP2at6l\njB7poBj7kWYLc0SQHNaIm5zJDkNwslK4qbBidDPbshkKrcSpopl1Ka3sKLHb/9xBaH28yfFMErkN\nUbKQOs7wAoardrG0sgJdSs5IJPm2dXHWaUe1pgVdqUEJz3/lQha2VHPVe07kynccz7lHhZRalTGS\n7e/D3H8hY5mwbmIWq/T0uzgr7jmgF1smrvRr9uTdy0Da1amQx39Xs0s9BwWmFlkWPSHJTXMMzz78\nkSK9ZpVYJ67Zwtb4R7hV3ES947AmZmT1px0yC5hmlCRKrIOakWYWWDYNjsMKPzfgZN+8dOI3Hkyd\nvmxTOpFNMfaDHafBr8HU5s7CTc6gzxhCAucp4X4WoXfT6DhUSsn2kGg3MzmTLYbO8TnzqtHYwewi\nXbIysQePRq3cznmxjwPwmpH8uVbKL2+hMUhpDWbKRVni2KWU90kpj5ZSLpJSXl2Oa5bK/Z97HZe+\nvlCImeDsxI/5nHV56pPjZxXXcN3EzJQWAV6i01GmxYPOmfzA/mDoGC+5SU85ZnKbIihGBzMtgQb8\nwgRbZQAAACAASURBVHln+l7+xNuujeLYVYZRtEHm+GGws1wb6cRp0/WUnbbocH/H8FnnaT4vHmCm\nbbMyZnCD8ZNRxwqjiwV22lZpo+EkZ7DZ0JHk16tOjdO7mW8nC5ZJVpLNqZrXFSLpj/Gq7hVLHsnE\n6j8ZGevmd3W1nDs8QpWU3Jjx9wX4/SdeXdK1Mgnkf21c5+OvXTDm2uFh1wpwkjMR+gC9ijf1Tq94\nilrHpdlxud5+HxAeM+6a6Rj43J6xSmwfmpTMs2w2yyMyBlUinTj3qV6Exr6Q5jSpaxgdkPR2nAJv\nB7FF10Pbw+WixncjhOS8ZAcCOClpssoX7LcY1yBwU4vq+vZ+7lmZttQqejdNdnpHtI9G3OQMRlTo\nVNV8f1XqeXuY4wvov7v5u8JNiVNp1zS+YdzIf6h/8T+VWPoAs22HH9vvyTr/iLp8R6o9cBJCuDDz\nQRSzlt8M/SsLQ4InDkYOrczTEGbVxRFC8L7TwgNx2mnKsp2eMreeez772oLXc5KzUPR+jrZ+RkII\nNhgGJyaTfNL6b2wKJRZ4yU3C6GZfSIEyJdbBidZg6twAaXvJTY+oC4sWrQo0svNsz8zwgPMq3OQM\n2nSdr+h3ZJ3rhgQNK8Z+NBdm+g0PTkyarB3FOeUNTKJoQ1T4HYk+lLzSu0eylV5VpVtRwht5C2/c\nHNtGK+CAM5Mz2enX9DlL2eA/p/c951ulRR7Y/afhDM+jxnH5TG+47XdGbYbdvET5XM5w49xksSAz\neqO/qO2Mm5yUTCKA6x2v4Fmlkf+eZfbzXSGzY+zjxm7mWTY6kMwtaGU10O3nStQU8okIE8Xo5XQr\nrZAstCzadD20Vk8ugVnvM7YXSbN86DzaDJ1h/w9+mkib7C760TL29acVBcXoQjGz50zgg9mgx0Jr\n14NXyXN2kSS2ZNKTB1t1PWUaFVo/I4rCAsviaTe7OuNfP3Nu3jXcxBys3tORrspQxzv5o3PBqBF5\nBwuHxlMWYMu330Z9pf8ilzhp//edx3Pi7CKZqwnvhXAq9nKR+A9sIbhtoHC8a4C0GlH0Hv7unMOI\nzJhcwkToPSy0LF5wj84ZpSCtBrp013dEFrInegLvYser2/4D+4NeLHhIl5ewUEdhdFJlVaZcikeZ\nFjs1jcQoki4og3uJ603Y1X6qu5vRZSaIfMh+Xj+kzLZTKfq5DJtzcYVIFVqC9AK2wLK53b4gb8z5\nx+Q43aXG8PZPcdTmD3FsCWFopQrsidYPL0bwfn1UvZh+RbDZMDg1mR29UV8Z1qi9gb2aV0U0t2Wb\nGutIJWbljTMbcfU+bKnQUMCUGLxflzhpZ+Njw29kQFUY0Jy83/iN1y3Nvn98D65VR5NvThlJeqbR\n9X6XqveoXjBBfl9fB6H3UmNl71gDx/gqvYYZOS0Ig3FB8lshgtIV6ZpEMis795kcwR74U3JJ7P0g\ngxu+iT2QX2dqVl2cOQ1pE8umq9/KGUcWS56cOg5pwa6Oo9t3XM93hM1tTNuBnZF5SFdDq9zMnsoB\npBR0j4yeSOtaDSh6N12yhgphpoo8KbFOhJAsMrPtn6lxZgM9mo0hnFSbtlwUoxNchSP8F7lXVuOa\nrXT7WvOrRLoc60Nr87euirGfo/ySxZ2ylkWWhRQiVd2wEIrfVWix7UUVBWnUwcRr03VmhXUDyohY\nWOaEF0sKrvFX7ZjUbqUx1kaj41Dvunzd/mjemFs+Fhb+KHjCPYP5idvLlvwxUY19pr9LqAsR0NKp\n8p1yO3gh7p13eiLJ3oyuS4taqjl9Xo4WazbiCkKacNvYRh8LTYvPmpeTi7QaEXoPXVSHlnCA9IKa\nmauxPekJsjZd5z4ju0rI5o5s859i7E/9np2yjv7kfADu0LxrfMQvs/HKzmwhLfQehHBptrz3MAgj\nDLpcbdTjNIU1LPeT32ZbNr+w35l33PveDRiupM3342yL/zOnxL2EpQUhi2BxHSd8ntz0r2eiZcgg\nXVWm0D1anENasGcyWgPpXDK1oqyJ7DvltJq1aLUrPUHvjJ5F55qNCNWkUfNME+mKcOk6IHvDWqZZ\njalyBIXCB9VYB9VWZer16qMqNZG26XpBTczDQTG6ONX2tOjLzP+iLeFVTNyi6xxB4SbaQUjZXCt7\nyyvtOqRj0KbrIREJGaFots1ewns8umYzUgrW63Eqg0qHxv6UGaaw2Wvyya1GOFaWfPEN3HjJGbxq\nfngbNGdoMWrFVq6vmUOt43BaIslFye9mnZO7iAUO+sDOHvguFGM/CMkiywotZ+BajQjFpk2pLaKx\ndyCl4Ej/by9R0rsyXadWjHBcwcxViWJ0Uu+3mXvBPSYVXXa/tgCAp/ymFD9+LDthKIhs+bS7DIC7\n3Nf5RwRuspXthprXNBzSSUazbZuV7oICz6Xims0s1WelPjmj4hmqXZdl5tn51xyHHyVM5kx1ye1C\nTB/BXsLvUhPPFxbvOuUIbv5odk0Sq/fVKEYPaqwDq7dAvZIcgiSS+1TP9BD00lRiHSi+Y+s6+wN5\n46TVgKlZDAvBmUp4IwTF6GSW6f1UxyZuwUZL3W+XrnG1Hp5YA2mtaL4vnJfLY/j+0OVoUrLF0HmD\nuoJCr6MwunDtSkbcOm63z888gmu2skGPMyNEY1eMHipcNxXpEIr0Qus6DIe4sIiTIGn0scC0eV/y\nGwWHhTm5ys1ENfa4rvLmE2YWvJbZ+yqE4rC1Msm7BofQgT6ylYdc00CqfK+/y2r0e6BmKg6dIf6d\nYNwWvbJgVJcS66TaimMAS/0dlhdzr6fud4ESnrkq1EGEmuRyXzgvcU8haC/nxHp4zj0WxX+/1uzJ\n3jEEO8K5IbZyx2ylQ7c5QdlOVY7CIzIUh2Ld1EaSc9iip82ibbrOAtNieUjZj/Fo2hKJqmaP1MZh\nRZgMpo9gH+c533zXCRydU3TJHjiBxL63kex4M3bf6SGj8gk0qp2qNyFPUbyEDyW2j3rLCJ28kF1v\nuyIsAkHYCKOL822vakOQVCHNBqQU7NQ0mouUI1Binkae7ZDUMMwatug639Z/zQfUpeFjjW6k1Uir\n6M1LvnGTrewwFP5Jy88E9sqiOvwkJ/IgF68TkrcAthrbcTST402TgSKhYU9/uZR48YMbabYwsuuf\nsLrO5fKevoL1hbLG+I72W4SnbdaJdNaqIiVHWnaq89K33p22HwcKwFY1Tgth9mpvcTjT9oTl71Px\n+F5AwJ8Uz5wSttv0xgYOb084P+Z488U1Z6DE9pGQBvOVEAc7vg/H1WhxHJ53s30xbrKVfg16FYVv\naL/JuWcPSC8YoFiug1fvpYeLrS/gAmtjBseZXhJb3rOMM/LpS2/Jfu7PvTG8qNhUM20Eeyk014xe\nL8ZDYHW/HrPrAkr9EwUdcgb8ol6BbVCN7WOmqbHDDc+2zdS8w+rFKHoXQsgQ55iGtOqynI9hZE68\nT5npGuqmOYNtvv3xGv3G8LF6Vyqk7H3qsuznNlvp1FQGhcgLedT1/cyxrKIp2+BFPwwZXou6r1Z/\nH+D/t3fmcW6T197/HVmyPftk9kySycxkMtn3IRtkDwkQlgKBQljCUkKhkJaWQgPcvtDSNqUtLaUr\n3Xt7aSkF2r4vl1K4tFC4hZYtrAFCEkICWSckmcWWbD3vH5I8si3ZsiV7PJ7n+/nkkxlbkp9nLB0d\nneec38GUcNgysyifuA3FmLFbiI0cm47Q/tNwTugruES+wcGRtIV2I2xXZWr7OFJR8VxkGqxcF6ZU\ngzHCLknS03ATx6NC8B+MyR0/Y2psoio16Je09ZVym3qJRMfBMLRquB4kHYZf6Is9vSZC/kPoiPSB\noIVw4kZlCgWdI8ZXVwtSN0ojAUhA6v7H+gLqc1IdvkInoUcQMDUsJ9W0jCiVHGdMJRJL3jB+L3GQ\nbZYHisawO/lisslpdgwLQI1UaDFPQPNkSQZJ3WgJI07Dw0zMsIsirraSsQ0MrOQnasGrSk2s2tWu\nkYLgP4jSKKFaVeN6O8rhkdglaY3Ifmi5AKVlLFTqGQuPJEjoGpro2/0SpsZV9zG9wUYkpW4+oIlp\nMWJ4PhjAy8EA/CpDp6zgqMWTTaY8feMyPP7ZJXGvOc12aajIfbjH4A3WattgPRFVrkGvXuK+UXwI\npQhBCOzDJCVsr3jKJLBIJfaKhFIKJ+n+k9QNEqKxBcVeU9k7k2vA/EfAAFxjcW4C2vlFqoCmSBS7\n2UDXIlWuBxHDU74xtr1aBak75jgkykcMnF/J4VND1REYaIJhRbRfE4MTy7bj2YD295kalnGMeVMs\nZBVjnzQys6rUXDFkDfvSxNS3NJw1axRGVuVWq0ENNcYVNwmB/SBiWBXZBb+NeBOipWDRAHaLoqUQ\nmBFDbVUiSVrwqlwb8+Dulu62PLzgP4BqvTmAOXc3LDchQoQ9orWwlBabZ7hQ1VLgNkfWxQ/b5FH9\nX3PfUV8vokIUoyJRpJXO7R8LqCL+UVqCJ0tLMDcUSqNy7ZzRI0rjqk6d8sTnlqDE70xrxgle5sSr\n4UbI/o8QBbDUtwUvllwOn/8gOmQFJwsmSYoEL0eVa2IdvhLzwgdSTJMzRVSlFiTIOCQIlouYgJZK\n26AI8AH4D5MMrtFvYJckIEARC+OuOQCSUomdaiMOI75w0Ggvt91CM4biOiDZn2MsUoloaCR85Vux\nvawHDZEIOhQlp5otborZvGRIGvadm9fgl5apb85JvOAeujq5ei1T1HAjhMB+vKhq2QlmHRB7DRPS\nik/0RarEhSIhcAB+pRSljGG9fGP8HJQa9IlR9BFZFwpB86hmR7RFKnPxipFVs0OSMMYyF31AiwNI\n9oyYXAPSOyEBwHXi/dpsTBkLf1Nn2szZOIgE5dhU3FdZgfclCat6+3C+PND+LSlvPQ+017t7Wti5\neU3c7xObHGj5OCQabgSEaKxQabskAsQwXpax0VRdnWhamFKDXkk7r5IMuym3e5Nyedx7iQu2Vovs\ngv8gpka0EKL5+1b1KtaKgLY2dFxCYgD5ekCCgq7I/vhq2YEjQ5XrY+eXaDgfpECQjjmuTo4cnQGx\ndCfEytdRfqwV3awiqftRtsY4l/UObhmShj0b7L4C4zstC7hPr4uGm0CCgi2irtERfA2Sal71t0aV\na7FDlxVITCsze9xb1Pak/QBNZvgfqkWjbgpDkI5aFq8YndTfkkpQR8m5wkbK4tFws/65iSe/DxG5\nHjv0i/7T4kMYT7tj+9XKAmRIeOGWlfjpxV22cw8fXAFVqUKgrwl1R8fgRXVg8alwLxvnTG6uTMpJ\nzxajavUdvejmHV2zvENR8EJS8ZtpP2UEIlIfwpTck1cIHIAvUoIqlWFvwgKpoXZqyFgnV66qEKRu\nVMpBbFObEXeOsABUpQrP66FCJSGMSCbHYaWNVrwabsA2STv3jRz8WKqjEsH1ypW2czaQD89HtH80\nVLkGrxy8CHPCP7aU3iYifNxCc8oJrbX51YFxwrAx7HZ4+6isXXilgV0AgDGlW9ARVuEDsCL8Ddv9\nmFKDPaIEFYkNN1QIgf2o1yVzExd9zAuvG8R4YSjALiPG2LkUaqQc/xQb0EjJ/TAFfzeY6kN7tAc7\nLBpKA9A79Ax4uI8FbtAKshjD6/IMAEBteSBlIRmT69G77Qs4+N5ncJH8xaSS+GKg0qaqMR3tiTrw\n4UYwRnjZr8VxXwn4Ua6qGKtEcChldohmoPeIIqop3rD7/PsxS5cSCCX87ZmiZV79XNAycRLVIUk8\nChKiaI/0J2W1aJ9bj490TfSyhMVXcyOWzcp5NuNuwD5JQB9RbPHWSAZoUyLosRSYSzxIEH07r0Hv\nu58Hi6Re88nUAzdi7H+65gQ88bklabbOL0Vj2E+bYfU4l1/UcBOY6sPv/J2QoTULmBfWLqR3mX1T\nKVWuAROi2O/zYRQdir2uXTgKzopqUr+JOhXmVEkgWZDLWMgdq0RwjXytxefWYbckoBmHkmKgJHUj\noJShVTgQy0NOnm8DDkoMB0xhmgr/LjRHotgbHWm5T22ZleEujLhkrsjWeXji+qXxukbMDzXciF9L\nk7Aw9F28HAhgeiicpD6fGFkwL9DHOwAMQuBA7IlO87rNb2u9U49I2rlRSfELr8b5NTHSY5lyq4br\nIeuLr4nFd0YO+6hIBI+r1inFA0V4Iur1p0pjTaBVURwJlA2Q/hwzvqfEnrPpqCqRXIfwvKZoDPuM\nMakfdxPFmAw8XetgEqL9LdhWIuOlYAAKEWaFk7u4tNeV4eGNAxesceG9KwYx0mTYLynVlOSsFra0\nHUvBIqXYJRmPyokX3gGAAS2RSJKUMKBdON3+MARieiMG877d6NClBFpt4veq3AAQwzz25YG5BV9D\nm6LY5hcXQ3gll2z54qq43xN1jaJ97VBLd+NDUcI7fgmzwmE8FbUIw5lgJgfAkF8GjOKi/phhP2Ch\n/qjKA/H55PNL87pbIpGkGLq2bx2YT8Yhn5B8U5AOxzpl2fY5MElXbBI1uYjmwFY0RCIoZywW01+/\nYCz8PvemzDg3Lzm+FSMs5CCGEkVj2DPFztC7Jdo7Hiy4Dz+vqkRQVTG/P4TTwrfHbTNqRAmmNA9c\nsMaj8utiFZpNF15HUNOiTtVnUVVq8bhPK6tenCjn6j+IQKQUQcYs9aBVuQ6KqOAjQUBDQvGK0QEe\nAHYx7QKb2BTvyRgpaYJ/P+aFvgcVmnfVpijxqY5Z3jztvqLEBUq3xyskrPRlzER6x4MEBcGRD4AR\nYVlvPy5WNsVtk5iGx6LlYKqEx3zxazRm0TU7VKUWIT3FMtE4k3Qo1iVrfjhZAtrIRd8hSTGPe2Df\nblTK2tObXa8EVa4F0xuyGPn1zYG30KZEcH9kcazgb+LISvzgAmeFhFYkrR4JhHOyjLcXCkVj2N1e\ntKUepbgpR+YAEPC/pSU4ubcPX5PX41ULDQ8zRhHJNrEUzXrWQi2O4F1JQkVUjanmWaHKtejRParv\n+eNTHgX/QZTrkru9Fm3AjAtvZ2KMXugD+UKQ9ZS1W5TLbD67HowRhMB+7EMNPhB9COmyqKkKR/LN\nlOb4zBS/OHDaJ/YzdcOi8XXpN3JJtKcTqlIFsfxtVIcq8J3e5P6byU+hWhWppIdO1vseRZzaod5v\nwAom10EVtSKyxBi74D+EBgXwIVkuGBi48e+QJHxafDBh326MiPjQz/wp1lVEMLkWOyQJV4t/xmW+\nh7HdL6FNURCkgTAMAVg5uRH/usldVfJQuPE7pWgMe6YkpjiZ5TedYuU5skgV+ndfCHTPxb0ffA3/\nGV2VvI1+Av3yUqPoxwemVON90R/z2GcJ2/CuX8J4RQYBWB7+puUYVLkWstRnEW3UxJmq9Iwaq05G\nRkraDknCSb5/x143HrHXqtoTgNEKbEmSbK4EpoyIeX4PiZpO+KSwfSimaxBkTf98zQnY9pWTY79P\naKxAS432fddYxvyzY5ZNONBbe+FD/+6LIR+ej917NuARJ427oS3QG9lat0m/wiLhVQiBfShRgaZo\nNCkF0CCWeSWJFjH2Q6hVfHhWTewJq39mpBJMlWKZUzEoAhKPYkbkMEoodZw8KjfEUh4vLrkPvYKA\nyWEZ37LQXWqodFdY9sCLWkryGx8czdkTfb4oHsOe4feQzRc3v91aLyORaM8kHNt3FiKq9SKMsfo+\nwRTaUJVa7PMz1OMIJERwge8xbJMkjJMV3KmsxXbLXF89bZGYKddYwxBnqtFV96wuXK0IxIcd+oUz\ngbRsHnPGgpkbVidrmkTDjfAFtI44rwQDkBjDBFmOkxMw30LvOs9ZI+BETnexOO4TCKJNDPbzq631\n4hPZuXkNnvlCskb8YKCGRiG892NgsvM8f1WuQZ/UF6tPbqZDEAL7UB4uBwH4um1mimbYd4liQtUq\n0yUnonENtOMRoMp1+LdYF1c1bRS/zYwestnP9PnhJuyQJPQQab1tAdSHSrCTWS/OO+UnF3fhrvOs\n6yx2H+6zfD2RsoB3hWxeUzSGnfSZWCk4ptwvgwDwd8/PzijZYa6E1RYyQwAxNNEhTPW/hqM+H/7R\nvxzfjZ5lewxzLjtgknPVvej1Ua1JRtiyptMHVamNeVT3+7+k7at77HK4Dg9HBwrBrNIWo73jIAQO\ngsTDeCtImBSW8Ybabvt4XeL3ISA6O+3O6RoQa3L6tw9KAhorU2sCmR/WmjLw8kZVZ1exWAgLcWq4\nCRAisQyqOhxGVXAHFkf2QmY+27Z5McMuSVjoG2hlTL5ekE9GWySMwym6f6nhenwoAQQGw/uKyTor\nUfy/aGqZD012Ang+GMSWYAAlqooLe74dt43ZRXNabVxb7sfxHdahM1FIfX7Oa6vBLy89DmNrvQvj\neU3RGPbKoISvnjkNj3x6keX7if55VgVJDGivd/9lWj0sqOEmRIUo9ogiHvFvwn0+rfx/e2hG6mMp\nAxceMFCAYqSijY8YAkzWNzA1XB8TAzMetQX/fqhKBabRh9jLrPXUDaK9WkGRVP0iuoNHEOqdiLXy\nrSn3ccqp0zP30l+7dTWeudHaszakcCc1VcYZ97lt2pPYlUtSr4VkyxWLcnNcO6zKBqJ6jcUdPk1+\n+dLAg+j1MXTICg6jArYr3LoG0i5JxHzhzdjLpKcrdiq9lqqlBqpcj2OSDCZEMV5vWm7WPwpZrP3E\njbt/LHyqgKdKg3iytAT1fbVAUoLnAP/ntPRNceww6gY6mypSxttba8uwdEJD1p+TD4rGsAPAunkt\njmPlv71iPjadPDFtFkIiv7ncvZCY1UkTDWmPlm/7JZRTCBXBnQAGip5sjxXVGhbfK2iPlUYzBcG/\nH1DFWJ9TO1S5Hu9JUqx3Uyt9CCFwAKP0F6YIO9Ps34BoqAmB+sdAxPDSkTOgJDTJGD0i3tPNZfRS\n9Am2YZfWujI8cNUC3GaStTWPZZnbi9Umd1b05TdP3+op1ChuekzSsj3eNqpWZRndLE2Dd7kWu0Qx\nTnXTcBzaomk8drkejIBdooQ1vmf1fQ8gGPFhhKrGt5G0gokIHZuO+ysrsFcUMbEntUeeifxu4nW4\nbKL2/Vemeeq3al1YaBSVYc+E1royXLlkXPoNTTAAzVk+jscfJ9m0GRee0eR4SzCAUUrEsnvTZce3\nYc10I8ZIUOU6HNEr/GIee2A/gnJFCt9G/1z9wjNi9KNpPwT/fkxXtBvEPZF0qYWE8L5ToUbKIB86\nwfJG1NEQv9awekrqm1UumTO2BkHJl9eSqPENFVg4LvWTj5dYVlAyv9aXN/AhAOCVoB/EGKaEZVv1\nxdiuci22SSX4wKTeqNVICBijRPBRKo89lhkj4gLf49q+gf0olbVz4u7ImWnnEz6wEj65Cif09eOv\nhy9Ku32mZFzLMgTq6YaNYXdyJ3/79pPx3E0r8LWzrAs+crpQzvxQww14Mag9mr4S8GO6RXETAHzx\ntMmYOXrAe1LlWvRLWipaNQ0Y9mWKtspv1Qsztq9+4X2BtAusxHcI5AvHysyfULXY9pmz7Ctno30d\n6H3nPxDef2r6eQL41jmpw0uDhdvv104TxicQ7jw3jSBaHoj2t8BX+h4YgC2BAMYpCioYw26WehFW\nletwRGQgGjgfhcA+VMmaJvqhFB6/ofK4U5LweHQOAE3GYFlEOzePoQSrpzSm/Hym1OGjdzfhkffu\nwjF4J6pmmIRAYh9ZpH6qLLOQErYi0/U+Lxk2ht1JnNMvCmisDOL8uS2W79eWe5MaZ2dAon0deD5Q\niq1+CftEEft67Y2B2StT5VpEpB6EiLTMBQpDkD5CR0xj236B0Ljw3hS1+KIU1Dy6DsXw4rx3T/wO\nF09Tcc9Fc7B+wdi419I9QqfDbRVyocRd7RICIr3tEMQevOGX8GIwgDH92nmR2OQiEUMwTjJJUvsC\n+zFP0cIxKWsWmB+qUoUdfgnni38D+Y6BxL5YtWs/AviGxY1eykP4qrbMj8+d2Inf6H0ajE9kbOAa\nDUrJ56rTtZhXb12Nv12/1IORZs6wMexeFCBJHpQtA/beQKSnExGB4fP12oX01NG1tsdQTQdRwyMB\nYtgmSZgubDd1nTeaE6e4SNQSqJFyyAGtMlANahfvJDlBOybVhAaBVVOasCAhvGEXW09Fpmmvf/ik\ns7zxRPLZCtNOdC3aOx6MES6om4w+QcDDR9bjtPDt+Fn0FMvtY/vp6z9v+f04Q3gaIAUkdWOcXrGa\nvlNWPXbqoT6hRPPUp4a182vV5CZUBgcnZk1EuHbF+FiRmnFjNztNbXXJYSYrD98OLwvgMmHYGPZC\nws6YRHvHQw3XYadfwuLeUEo1OnP7tmhIyx55MyDhUvFRVAW0fqsduhSBucGG5bHCDTHteKnkPbTK\nCipVho3yp5xPKkf8+KI5+MUlzhqKZ5JW6HVDhMeuW5zy/fqKgOOceTdsWNyOE21CGyxSjcixyYgG\nDmvNpns78CprR5/pic7KU2ZKDcpUFW8G/LjL/wMIgX0gYhin3/w/ROr1A1VuwFYpCAVAU8lrIAZM\nlGV8Wzk7+4lyUlLUht2oLswHnY3O1d0qbD0UAX3vX4ayfYvw7O4vpDyG+d7AlBqwaBBb9UyHOWV/\nR0VURUskgo+Fv5SUU35WQrw82tcOIfgBDgkCXg4GYrH9l1mH4zmlY928liStGSesntIUy1ZIR7r8\nYyu8WDa59xPzMD6NIiAR4VPLvPt72nHTKZMgpng8CH14NkL71qDv/UuRmDb4rXNmxArI4kX1BPSF\nWmLnV1WJJvg1TZbxu8jSpM/446eOj/s92jsOEYHh5WAAnWXPYIIso5Qx3B9dYhv+yuRBygsBsKTP\n18+MQntSdYqrvwgRfYOIthLRK0T0EBENbhfiBMbUuM9g2XSydQf5xIWRTB4nv5li8ZApNdjbvQaH\n1NSZI6o5FgNCNNSMv/u1ePmeYBjTwmEIsDbOExIMbKSnE0QMd9VU4yOfD4v7NO2ZD8w57C7P8K+e\nOQ1/+Uxqr9ZMor6LNUP1ssstQdGHsXbNH9RSKN2LYvUPZtrqy2J/0ZEJhVvh0Fhs9UuQAUwv4CRk\n2gAAF51JREFU/QcqIgJGRqJ4IJr8nc5MkFaI9I0DMeCP5WV4KRjAon7t/DoA9+biupWdOGOmt5Ld\nQ1xNAIB7j/0xAFMZY9MBvA1gU5rt84oXX5BVSuT3183Gf2+ML4Ry+lErJzXG6ZM4rcJMZPXUeMMf\n7RuH/cEQ3pIk7PFHMSscRg9z2CQ5NBrRcAMeqihHZTSKRf0h/DM6GRFTPvrnVuU+jGCmRHISx4z/\nq+ej3aRg5Q0X2P1FEAhPfn5ZVvuumNSI844bE5frDwCR3nEICQJeCAbwdqmCUf0lOMCq8W9m7fjE\noQahHJuGP1eUI0qE6UdL0Rq6FwrEpIXe02c045Y1kxx/l59eOT7t2oqVg2d1+LpyLSPNnKeeeF2/\ncMtKZwMbZFwZdsbYXxljhqDIswBGp9o+34wwGdBML/q/Xb8UT99ofXGsmT4SYzIM8yzurMfpM5px\n6+nxlXHZ3nvGN5Tjk6abTqRHu8BuaKjT5Fz7+vGdiHUMM/lvISD0wVpU99bhywe78URkHs5Xbonb\nIttyejvcVAgmYninmdzIz5+rFeoYF7NTZo2pxsYV4011BMVDqd8Hvyhg89nT0ZjgsUd7O8BUEZtr\na9AjRnFx6D1Ljf/fXjHf8tihfWvQ1lOOGw4dxtLoh7Zj+O75s/CJRe2eec3Hd1jH/60Of/kJbbhj\n7XScM2eM7efXZni+mNn65ZPw2m2rs94/E7wMTl0G4BEPj+ea0SNKYkYsk4o0QFvNzkTxMd3R/T4B\n3z1/VtIxM82WMISoiAhXLxsw7GqoGdG+Fmz3S5gZCqNTVrAtRdemRNRQC0bvPhnL+/rxjup8v2xJ\nl/Lo7OvK3lW+YlE7dnztFE1mIAMjQkT47ImdcUVWmegNZcMnMyyky5aUjbeZH8qR2djul1ATjWJF\nbz/6LeQA7HK3WaQah96/EhcdPYar5Y1eDTklv7psLn5xyVzHNwnRJ+DcrjHWT2UZYBdGDEo+lHvQ\nW9kJaT+FiB4HYBXwvZkx9id9m5sBRAD8V4rjbACwAQBaWqzzxHPB0zcux59f/iCprD0TrlnWgQ8+\nSmzk6w13rJ2Bjb+1buabyMiqYJznHB/GIfTvuRAzqh7Ct0KPgwD8Xc2sKOaf6hRcKG/CP1X33vS9\nn5iHAz3WBVZOOGVaeo/YyODIJpzldVaMG2aOqcbL739k+77bod5w0gT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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1a23522550>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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f42TXABY4Hbh5iX8brdr6BHG3TcS3/g9ILXbuqYs638glF5IFe7pS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\nAAAASUVORK5CYII=\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1a22d56240>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "def rc_impulse(t, R, C):\n",
+ " RC = R*C\n",
+ " return 1/RC * np.exp(-t/RC)\n",
+ "\n",
+ "def rc_response(t, u, R, C):\n",
+ " return np.convolve(rc_impulse(t, R, C), u)[:len(t)]*dt\n",
+ "\n",
+ "t = np.linspace(0, 0.1, 5000)\n",
+ "dt = t[1]-t[0]\n",
+ "R = 5e3\n",
+ "C = 100e-9\n",
+ "tc = R*C\n",
+ "\n",
+ "fw = 200\n",
+ "u = np.sin(2*np.pi*fw*t) + np.cos(2*np.pi*0.1*fw*t)\n",
+ "un = u + np.random.randn(len(u))\n",
+ "\n",
+ "print('Cutoff: ', tc)\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.plot(t, un)\n",
+ "plt.plot(t, rc_response(t, un, R, C))\n",
+ "plt.plot(t, u)\n",
+ "plt.xlabel('Time (s)')\n",
+ "\n",
+ "# Try different cutoffs (remove noise, fast ripple, then whole thing)\n",
+ "plt.figure()\n",
+ "plt.plot(t, un)\n",
+ "plt.plot(t, rc_response(t, un, R, C))\n",
+ "plt.plot(t, rc_response(t, un, 20*R, C))\n",
+ "plt.plot(t, rc_response(t, un, 200*R, C))\n",
+ "plt.xlabel('Time (s)')\n",
+ "plt.show()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 3. Monte Carlo methods\n",
+ "### 3.1. Particle propagation\n",
+ "The elementary process of particle absorption and scattering are random in their nature. Propagatiomn of particles through a slab of material (photons, neutrons, charged particles or any other) with multiple scattering events may be impossible to calculate analytically, but can easily be simulated wiht Monte Carlo methods. The following exercise is a simple example of using random numbers with custom distributions.\n",
+ "\n",
+ "(a) Simulate exponential decay of particle beam intensity in a uniformly absorbing, non-scattering medium (Beer-Lambert-Bouger law). Consider 1-D case. Use uniformly distributed random numbers to simulate absorption event in a slice of material. Plot a histogram of distances travelled before absorption (free paths).\n",
+ "\n",
+ "$I(x) = I_{0}e^{-\\alpha x }$ , where $\\alpha$ is absorption coefficient"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 142,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Generated absorption probability (mean) = 0.18107\n",
+ "Fraction of escaped particles = 0.0\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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/AkuBz4FPwxpVFGre7jQA9m3fEOFIjDEmskK5qupHbvJxEXkLSFbVFeENK/qk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\nd/PJQKybPgf4b8B6J8XhXsftQKZbr5X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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1a21e75ef0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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mZoUvNJuZWeFQMDOzwqFgZmaFQ8HMzAqHgpmZFf8f0VEXxRTLLHQAAAAASUVO\nRK5CYII=\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x11fe02be0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "4.391\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "N_slices = 100 # Slices of material\n",
+ "N_particles = 1000 # Number of particles to simulate\n",
+ "alpha = 0.2 # absorption coefficient\n",
+ "P_abs = 1- np.exp(-alpha) # Absorption probability in a slice\n",
+ "\n",
+ "# Generate N_slices x N_particles matrix of unofrmly distributed random numbers. \n",
+ "# Transform it into a matrix of absorption events, where True = absorption, False = no absorption, \n",
+ "# mean(ABs_events) = P_abs\n",
+ "Abs_events = np.random.uniform(0,1,(N_slices,N_particles)) < P_abs \n",
+ "\n",
+ "\n",
+ "\n",
+ "free_path = np.empty((N_particles,)) # array to store the number of slices propagated before absorption\n",
+ "N_absorbed = np.empty((N_slices,)) # array to store the number of absorbed particles in a slice N\n",
+ "\n",
+ "for i in range(0,N_particles-1):\n",
+ " idx = np.nonzero(Abs_events[:,i]) # returns an array of indexes of non-zero (non-False) elements\n",
+ " if np.size(idx)!=0:\n",
+ " free_path[i] = idx[0][0] # the first index of idx array is the slice number, in which absorption happened \n",
+ " else:\n",
+ " free_path[i] = np.inf # some particles may not get absorbed at all in a finite medium\n",
+ " \n",
+ "for i in range(0,N_slices-1):\n",
+ " N_absorbed[i] = (np.sum(free_path == i))\n",
+ " \n",
+ "N_transmitted = np.append([N_particles],[N_particles - np.cumsum(N_absorbed)])\n",
+ "N_escaped_final = np.sum(free_path == np.inf)\n",
+ "\n",
+ "print('Generated absorption probability (mean) = ', np.mean(Abs_events))\n",
+ "print('Fraction of escaped particles = ',N_escaped_final/N_particles)\n",
+ "\n",
+ "x = np.linspace(0,N_slices);\n",
+ "plt.plot(x,N_particles*np.exp(-x*alpha), label = 'Beer-Lambert-Bouguer law') \n",
+ "plt.plot(N_transmitted, label = 'Simulation')\n",
+ "plt.legend()\n",
+ "plt.xlabel('Propagation distance (slice #)')\n",
+ "plt.ylabel('# of transmitted particles')\n",
+ "plt.title('Transmission of %i particles' %N_particles)\n",
+ "plt.show()\n",
+ "#plt.hist(free_path[free_path!=np.inf],30,normed='True')\n",
+ "ax = plt.figure()\n",
+ "plt.hist(free_path,int(N_particles/5),normed='True')\n",
+ "plt.xlabel('Free propagation distance')\n",
+ "plt.ylabel('#')\n",
+ "plt.title('Histogram distribution of free paths')\n",
+ "plt.show()\n",
+ "print(np.mean(free_path))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 3.2. Monte-Carlo integration\n",
+ "\n",
+ "In a so-called ’hit-and-miss’ approach, or ’simple sampling’, one can estimate the integral\n",
+ "of some arbitrary well-behaved function over some interval by scattering many points over\n",
+ "some rectangular area A. The probability of a point landing below the curve is proportional\n",
+ "to the function’s integral.\n",
+ "A classic problem is to determine the value of π.\n",
+ "(a) Uniformly distribute N points over a unit area. Calculate the proportion that are\n",
+ "within the bounds of a quarter circle.\n",
+ "(b) Plot the convergence by subtracting the computed value of pi from the cumulative\n",
+ "average (log-log). Compare this to the expected rate of convergence (1/\n",
+ "√\n",
+ "N).\n",
+ "(c) Add error bars to the plot"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 138,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# Helper functions...\n",
+ "def mc_integrate_1d(f, dist_x, dist_y, n_iter):\n",
+ " # Hit and miss version\n",
+ " #\n",
+ " # f: function to be evaluated\n",
+ " # dist_x, dist_y: distributions from which to draw (x,y)\n",
+ " # Does not handle -ve y\n",
+ " x = dist_x(n_iter)\n",
+ " y = dist_y(n_iter)\n",
+ " h = f(x)\n",
+ " return np.cumsum(y < f(x)) / np.arange(1,n_iter+1)\n",
+ "\n",
+ "def mc_integrate_1d_2(f, dist_x, n_iter):\n",
+ " # Sampling\n",
+ " x = dist_x(n_iter)\n",
+ " return np.cumsum(f(x))/np.arange(1,n_iter+1)\n",
+ "\n",
+ "def plot_convergence(est, sol):\n",
+ " x = np.arange(1,len(est)+1)\n",
+ " plt.figure()\n",
+ " plt.loglog(x, np.abs(est-sol)/sol, 'b', x, 1/np.sqrt(x), 'r')\n",
+ " plt.legend(('Result', '1/sqrt(N)'))\n",
+ " plt.xlabel('N iterations')\n",
+ " plt.ylabel('Fractional error')\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 140,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Pi estimate: 3.14\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/Users/matt/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:12: MatplotlibDeprecationWarning: axes.hold is deprecated.\n",
+ " See the API Changes document (http://matplotlib.org/api/api_changes.html)\n",
+ " for more details.\n",
+ " if sys.path[0] == '':\n"
+ ]
+ },
+ {
+ "data": {
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T3/3d39H69eungH+//fajP/qjP1Jj+XnRsQ3YKYBTR7+ICRSNZD1dUJw0iEdH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\nwFnmH5GdLyXLS6Sf/OQnBIAWL15M7fau5sN3/ktLyKMG9lrUjOwg+e4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MVxJRdtKonZgs\nc+QL6Czoo6qqJei4eO7pay37QxZe/ATAyQBQVdVz0QH8n/W1ljsHfRHA73SjdU4A8BgRPRB7qFGX\nDjWXlmHgyMiLPwGwN4DPdtetf0JEr5y1SjdERl7sEmTkxY0Afq2qqjsBtAC8hYj+a/Zq3QwZefH7\nAK6pqur30HFhvG4uKohVVf0NOi68Jd31igkAuwEAEf05OusXp6FzyuBTAM4xlTsHeTWkIQ1pSENS\naLjTdkhDGtKQdhEaAv6QhjSkIe0iNAT8IQ1pSEPaRWgI+EMa0pCGtIvQEPCHNKQhDWkXoSHgD2lI\nQxrSLkJDwB/SkIY0pF2E/j/kkUfElWwMjQAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x120874cc0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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YcX//nf+yrlplX0wGDrRAuXu3Z9/RozkD1DPPBD5fZqbqxRf7Jrlw33bvylLd\ntEn1449V77/fEiOWLu054IwzVC+5RPXee1UnTrQZz0k+sZgBisila1fVSpX8NzGF4uhRW9qjXr3k\natrzVrasao8elvqoc2ffbBlXXmmVh6uusk+WSy9VffllPZ0+CbB9mZmqzz2nOfqsBg60bflpkn3v\nPcs9e/HF9p57ByZvPXrY+zhkiCeO5HVewCpFDz/sG6Duv9+WJfGRmWmBaOJEC0yXXGIZMNxPKl3a\nAtn991tg27QpsqlHHI4Bisjl66/tL/399/N3nmeesfPMmROZchVE7uU3ChfO2cR5yy2WOs/9Gewe\n/NChg+rll3u2r1plAe7qq32f/8MPtr9Hj/DKtnWrb+B4++3cj83M9OQWrFjRljTp08ezdNXs2da3\n1qiRva6KFVVbtbLnrV2r2ratJxC7g3GeTp60F//uu9bZ1qKFNQm6T1Khgv2yHnvMOvwi2S7tMEkZ\noNgHRf5kZVmm8+bNw/+SeuiQ1R6yf6gmG/doPX+DGdwBvGpVy4Tu/txdtszS6bkft2ljAe7XX3Oe\no3VrC2bhuOsuzzXq1Qu+68ddc3Pfsgc6923evJzP9d4flmPHbHDF2LFWkCZNbPCF+6RnnWVNAMOG\n2WCNHTvCvJCzJGWAct9Yg6Ls3EPOV6zI3/OjMWS9IHngAetS8bd68Ycf2u9o3Dj7PHUPP1e11q7b\nbvN87t54o//z9+plXyZC9fffnmZEQHXSpOCfe8stvoFmwAD/Acof9/iI1NQIttAdPqz67beqo0db\nluCGDa0j1V2Qs8+2X9TIkTYsfu/eCF04doINUAk1UdeNmSQou61bLQ3bSy8BQ4eG9tysLJv0W7Ik\n8MMPyZ3K7dAhyz1Yu3bOfYcPA598AvTvb5k1eve2+a9Nm9p+93sAWDaiRo1ynuOee4APPgD27Quu\nPOnpNvn20CFg5Ejg++8tb2HfvsGnhZo5E+jc2ZLvZmba+3vmmcB11wF16wILFgBPPml/A9lt3gy8\n8ALw+uvA/v1A6dLBXTNkBw4AK7wmFqenW/Jct3r1fLNhNGtmf7AOlZSZJNwYoMifc88FGjSwD89Q\nzJ5tKY0+/NA+fClvWVnA7t1ApUqebZmZQIkSlhJq+nT/zxs5Enj4YQs4JUrkfv5Fi4CaNYFatexx\nmTJA+/bAlCnhlVfVAu+ZZ9rjCROAG28M7rkTJwLXX28ZMerXD+/6YdmzB1i+3JMJIz3d8k0BFp0b\nNvRNlNv9KR54AAAdC0lEQVSkSXQTU4Yg2ABVOBaFiRWvVEfxLgo5UNu29g0/MzO0pSr+8x+gShXg\n2mujVrSEU6iQb3AC7Hc+Z459bubGnSZp2zarvXg7dAho1Qp47DGgTx/fGtL+/bYMSbhEgIoVgcKF\ngbJlQ1tW5KyzPGWOaYAqXx644gq7uW3f7huwvvrKElIC9uIaN/ataZ1/vmUCdqiEClCqOgPAjLS0\ntEHxLgs5T9u2ljdv1SprAQnGr7/a//iwYUCRIlEtXlJo0ybwfneA2rrVE6C2b7dln5YssabBPn1s\ne1aW53nnnGPvb34UKgR062bnCaWi4V3muDvzTGuv7NzZHqtamnnvoDVliv0jALaOStOmvkGrQYPY\nLTaWh4QKUESBuJfCmD8/+AA1dqwFpttui1qxyIu7NrJli/XrdO9uTXkA0KlTzuMrVbKmuYEDI7MU\nydSpoT+nShX7+fff+b9+xIlYtvYaNYAePWybKrBpk6cva9kyq2WNGWP7S5Sw5LjezYN16sRlrZeA\nAUpECgFoparfxqg8RFFTrZr1Jc+fbwsaBmPWLODyyz19ExRd7mbBzz+3FXw//tizz52J3Nsrr9iA\nimD7i6KhTBmrcOzeHb8yHD1qfaXdu9tAkZYtAwzmEbGAU6eOpy0zK8uaC7xrWm++CRw7ZvvLlPFd\n/PEf//BE5igKGKBUNUtEXgLQOuolIYqB//s/a+EIph9q2zbr+L755tiUjTzLMH32mf1ctMizLzPT\nc79vX2t6vfrqwIMpYqFQIesO8l6tI5a+/9765ryNHGmrLwfNPaiiYUMb8QHYIo9r1vgGrZdfBk6e\ntJ/BfsvLhzxH8YnIMACrAHyqBWTIH0fxUW4++shG4v34Y97NfJMm2Qeho5Y5TwKlS9siiNmVLWu1\n2W++sSbAffs8TYLx5q6tRHWoeR7X9latmnU9Rdzx49aJW7WqZ85AGIIdxRdMo+JQAJ8AOCEiB0Tk\noIgcCLtkUSQiXUVk3P79++NdFHIo736ovMybZx+K7nk8FBvly/s+dtd0W7WyUZg7dwLFizsnOHkb\nOTK21/MeKOLtkkuidMGiRa1PKh/BKRR5BihVLaWqhVQ1VVVLux7H+DtCcFR1hqreWqZMmXgXhRyq\nenXP5Mu8fPONjTpzyICmpOEOUO6aSNeu9rNbN6stOPH9uPtu+zliRGyv+9NP9vPDDz2jGwHfvjtv\ny5f7r506VVDDMkSkm4i86Lp1iXahiKKpbVtg4cLcv30CNt/xt9+Ayy6LWbHIpWJFqx21bWsjKN97\nz2pOTh5J+dRTnvvNm9sXoewNOSdO5J4h48SJ0K+paoPtAKBdO6Bnz5z7ve3aZeMbbr019GvFS54B\nSkRGArgXwFrX7V7XNqICqW1bYO9ea0rPzbx59pMBKvaefRb473+BAQOAp5+2ZtZrronLKOegeTdL\n/vij9ZHNnu17TKdOnkEgx44BM2bYyL/77rOWMxHg66+Dv+a6dZ77Vava7ygrCxg1yrYdOeJ7/Leu\nsdiTJwd/jXgLZh7UVQCaqmoWAIjI+wBWAHgomgUjihbvfqjc+pfmzQMqVLCJ9xRbF10U7xKE54or\nfANM8eK++7/5xn6q2uhufym3rrzSvjgF83e3dKn99M7YIeJpGn3/fRtwd++99njJEs9xx49bUHS6\nYL+TlPW6zw4eKtCqV7cpILkNlFC1D5O2bZ39rZ2cxZ0Gz23FCs997+a+W24JnA/ygguCu557oPLm\nzb7b3QHqrruAIUMsaH34oacGBQArVwZ3jXgLpgY1AsAKEZkHQAC0AfBwVEtFFGVt2wKffmrBKPsw\n3d9/t3/6Bx6IS9GogHrrLU/tHLAM6MWLWxqma67xbB8/Pu9z5TVPb+JEm0d70UU50zLt2pXz+Btu\n8J0v1qpVzj4qJwr4/VBEBMBiAK0AfOq6tVZVR7Zicpg5BatOHeuHOn485z72P1E43AHg/PM92x54\nwDc45WbuXN/Hf/6Z+3ElS3rm0vob6JN9sITb4cPAHXfkXRYnCRigXBNzP1PVbar6uapOV1UnZpwC\nwGHmFDz3UjmHDuXct2ABULly4KzbRNk1aWLrWX35ZXDHv/GG5367djYEvGNHe/z22/5rOP/+twUa\ntw4dch5TvXru1yxoWVGCaWFfKiItol4Sohhyf9v1/md327bNaljJvDAhha5wYVuaxZ3c1p8uXpN0\nevWyxRLdgx0uvNDTRDhypK1JlV32mtXjjwcuk/fwd8AWXXQv2LlokWUwcrJgAtRlAL4Tkd9EZJWI\n/CwiAQboEjlfoBrU4cPxz+9GBZu/TGt//QX88YfnceXKNvS8ZUvPNu/Jttu25TyH9zyqLVtyH4n3\n+ut2rief9E3pVbw4cMYZdr9NG+ePmAxmkISfJPdEBVteAapy5diWhxJL9nRNgDW9uQcw5LZ2lHfv\nRPZk4d7JcoHAqZ7uustugOWf7NvXghUQ36zroQpmuY0vVfX8QMcRFTSBAlRey40T5aWsa2LOjTd6\nFrQFbOTopEm5r1RR1mtCz6+/+u77/XfP/WLFgm+CbtjQd8j7qVPBPc8J8hokkQXgJxEJ0KpKVPDk\nVYNy7ycKR7lytoDh2LH2+M037Wfr1sDo0cEFl+eft2wTbr/9Zj8XLbL1n8I1fLjvYycPNw+mie8s\nAGtE5AcAp7uUVbVb1EpFFGWBBkmwD4oiwb3IZagBYPFiWw8Q8F1jyj1A4uyz81cu78wTALB6tXMz\npgQToIZFvRREMZZbDUqVAYri6+KLPfeHDrWBEcOGWYBKSYnMMiP33msjDgFnj1YNZrmNBQD+AJDq\nur8MwI9RLhdRVOUWoI4etSDFAEXxkj1gPP20/dy82QZaFA6mWpGHV18Fpk2z+ydP5v980RJMNvNB\nAKYAeMu1qRqAz6JZKKJocweg7AHK3eTHPihymj//zH/znjd3iqRjxyJ3zkgLZh7UXQAuAXAAAFR1\nA4CYDsIVkatF5G0RmS4iV8by2pSYChe2OSTZ+6Dcj1mDIiepVMkGRwSaBBwq9xwqf+m+nCKYAHVc\nVU8vpyUihQEE3e0nIuNFZIeIrM62vaOI/CoiG0Uk4NIdqvqZqg4CMABA72CvTRRIyZK516AYoCie\nsq+I654/VaNG5K7hbkp0cs7JYALUAhF5BEBxEbkCwCcAZuTxHG8TAHT03iAiKQDGwCYBNwLQR0Qa\niUhjEfki2827tvaY63lE+eYvQLkfM0BRPP3zn74LErq5RwZGwpYtkTtXtATT3fYQgIEAfgZwG4CZ\nAN4J9gKqulBEamXbfBGAjaq6CQBEZDKA7qo6AkCOJeVdWdVHAvhKVf0O0BCRWwHcCgA1I1kPpoQV\nqAbFPiiKtwYNcm6LZIaTKwtAZ0meAco1Wfdt1y1SqgHwXt4rA0DLXI4FgLsBtAdQRkTqqupYP+Uc\nB2AcAKSlpTl46hk5BZv4qKDJPofJKeeKlnitF+pv5H2uQUVVR6tqc1W93V9wOn1SrgdFIShRgoMk\nyNmyr+0U6aDSuXNkRwZGWrwCVAYA7+6+6gBySZ8YPK4HRaEI1AfFJj5ygqpVfR9HOolxpUqeRQ9X\nrwZefDGy58+veAWoZQDqiUhtESkC4DoAn+f3pKxBUSjYxEdON2qU7+OKFSN7/qJFbZj5f/9r6Y7u\nv983vVK85doHJSIzELjZLahcfCIyCUBbABVFJAPAk6r6rogMBjAbQAqA8aq6JpSC51KmGQBmpKWl\nDcrvuSjxMUCR07nXbnJLTY3s+YsUAU6cAPr182yrV8+yqezZA+zdC8ybB3TvHp8+q0CDJCJS2VPV\nPrlsnwkbEUgUF7k18aWk2D8ukRMsWmRB4qGAs0XDU7QocPCg/30VKnjuT50KfPVV5K+fl1wDlCvv\nXoEiIl0BdK1bt268i0IFQIkSwJEj1gZfyNXY7V5qw8kJNCm5/OMfnuzmkVa0aM6FEP3Zsyc6189L\nMLn46onIFBFZKyKb3LdYFC5UHCRBoShZ0poyvNfWYSZzSiaffBLcce68fbEWzCCJ9wC8CeAUgMsA\nfADgw2gWiigW/GU0Z4CiZLJ+vf/tf/3l+9jJAaq4qs4FIKr6p6o+BaBddIsVHo7io1D4C1Bc7p0o\n5xIc7sSysRZMgDomIoUAbBCRwSLSAzHOZh4sNvFRKPytqsvl3imZTJnif3v20YJOrkENAXAGgHsA\nNAdwPYAbo1koolhgEx8lu+wTgd3ck3fd4lWDCiYX3zLX3UMAbopucfKHo/goFLkFqOrV41MeoljL\nbV7V9Om+j1NSol8Wf4IZxXeua7HAOSLyjfsWi8KFik18FAr2QRF5TJzouf/117773n8fWLs2tuUB\ngltu4xMAY2HZzIMYMU9UMORWg2IfFCUL78EQvXoB/fvb/e3bcx77009Ao0axKZdbMAHqlKq+GfWS\nEMVYboMkWIOiZOE9Sde7n2nHjpzHxqMfKphBEjNE5E4ROUtEyrtvUS8ZUZRlr0FlZtqkXQYoShat\nWnnuiwDDh9t9d+aI9u09++OR/iuYAHUjgPsBfAtgueuWHs1ChYvzoCgU7kSc7gB15Ij9ZICiZFE4\nWxta/fr2092Nn5bm2efIGpSq1vZzOycWhQsVB0lQKAoVsmDkDlBc7p2SnXu03qWX2s9HHvHsi0eA\nyrMPSkRSAdwBoI1r03wAb6nqyVyfRFRAeK+qy6U2KBn9+9+epj530mR3a0Lx4p7jss+NioVgmvje\nhE3QfcN1a+7aRlTgeS+5wQBFyejFF4FrrrH76loBcP16C1aFC3uGn2cfeh4LwQSoFqp6o6p+47rd\nBKBFtAtGFAveAcr9kwGKktXChfZz3TpPjalWLfv53HOxL08wASpTROq4H4jIOXDofCgOkqBQ+atB\nsQ+KklX2JLGAp9kvHoK59P0A5onIfBFZAOAbAP+ObrHCw0ESFCo28RF5+OtnileaIyC4XHxzRaQe\ngPoABMAvqno86iUjioESJYCtW+0+AxQlu7wC1JEjwPHjQLlysSlPrjUoEWnn+tkTQGcAdQHUAdDZ\ntY2owGMfFJFH27Y5t3k38V1wAVA+hmkaAtWg/g/WnNfVzz4F8GlUSkQUQ+yDIvK45JKc27xrUL/9\nFruyAAEClKo+6br7tKr+7r1PRGpHtVREMcI+KCKPTD/D30RiXw63YAZJTPWzLZd1GIkKlhIlgGPH\n7B/z8GHLN5Y9/QtRsjh1Kuc2f0Fry5bolwUIUIMSkQYAzgNQJlufU2kAcVoAmCiy3M15hw9bTYrN\ne5TM/AUjf0FrxQqgWrXolyfQd8X6ALoAKAvffqiDAAZFs1Dh4oq6FCrvjOZcaoOS3Tl+sqz6G9nn\nL2hFQ6A+qOkApotIa1X9LjbFyR9VnQFgRlpamiMDKDkPAxSRh785T+70R95iFaCC6YO6XUTKuh+I\nSDkRGR/FMhHFDAMUUWClSuXc5i9oRUMwAeoCVd3nfqCqewE0i16RiGLHe1Vd9kEReZR1VUv8LfMe\nq8zmwQSoQiJyet6wazVdjnOihMAaFJF/7jWh/PE3mCIaggk0LwH4VkTcQ8v/CWB49IpEFDsMUET+\nBZpuEfdBEm6q+oGILAdwGSwXX09VXRv1khHFAAMUkX+Bspj7y3oelTIEc5CqrgHwMYDpAA6JSM2o\nloooRtwB6dAh9kERAcCkSfYzUBbzEydiU5Y8A5SIdBORDQB+B7AAwB8AvopyuYhiwnuiLmtQRJ4B\nEAUiQAF4BkArAOtVtTaAywEsiWqpiGKkWDFryti3z/7pGKAo2bkDlHcTX/b/CycFqJOquhs2mq+Q\nqs4D0DTK5TpNRBqKyFgRmSIid8TqupQcRKwWtX27PWaAomTnL0BlF6tRfMEEqH0iUhLAQgAfich/\nAAQ1hkNExovIDhFZnW17RxH5VUQ2ishDgc6hqutU9XYA1wJIC+a6RKEoWRL4+2/PfaJk1qULcN55\nwCOPeLZln5jrb25UNAQToLoDOALgXwBmAfgN/teI8mcCgI7eG0QkBcAYAJ0ANALQR0QaiUhjEfki\n262y6zndACwGMDfI6xIFrUQJYMcOz32iZFa+PLB6NdCggWdb9om5jpgH5Qom01W1PYAsAO+HcnJV\nXSgitbJtvgjARlXd5LrGZADdVXUELDmtv/N8DuBzEfkSwH9DKQNRXtjERxRY9hqUIwKUqmaKyBER\nKaOq+yN0zWoA/vJ6nAGgZW4Hi0hbAD0BFAUwM8BxtwK4FQBq1uQoeApeyZL2jRFggCLyx5EByuUY\ngJ9F5GsAh90bVfWeMK/pb33GXFMPqup8APPzOqmqjgMwDgDS0tJilMqQEkHJkp6Jh+yDIsrJyQHq\nS9ctUjIA1PB6XB3A1kicmOtBUTi8a02sQRHllD1AxSpZbKAVdWuq6mZVDanfKQjLANQTkdoAtgC4\nDkDfSJyY60FROLxrTQxQRDnFqwYVaBTfZ+47IjI1nJOLyCQA3wGoLyIZIjJQVU8BGAxgNoB1AD52\npVLKNxHpKiLj9u+PVHcZJQMGKKLAnNjE591X5Gch4Lypap9cts9EgAEP4WINisLhHaDYB0WUU/YA\n5YQFCzWX+0QJxTsonXFG/MpB5FSO64MC0EREDsBqUsVd9+F6rKpaOuqlCxEHSVA43M16xYsHTu9C\nRCbuNShVTVHV0qpaSlULu+67HzsuOAHWxKeqt5YpUybeRaECxF2DYvMeUXCctOQ7UUJzByYOkCAK\nTtxrUAURR/FROBigiELDGlQY2MRH4XAHJgYoouCwBkUUI+yDIgoNa1BhYBMfhYNNfEShqVcvNtdJ\nqADFJj4KBwMUUWg6dYrNdRIqQBGFgwGKyJkYoCjpuQMT+6CInIUBipJekSJA9erAOWFlnCSiaAlm\nPagCg6mOKFzr11ugIiLnSKgaFAdJULiKFwdSUuJdCiLyllABioiIEgcDFBERORIDFBEROVJCBShm\nkiAiShwJFaA4SIKIKHEkVIAiIqLEwQBFRESOxABFRESOxABFRESOxABFRESOxABFRESOlFABivOg\niIgSR0IFKM6DIiJKHAkVoIiIKHEwQBERkSMxQBERkSMxQBERUUAi8bkuAxQRETkSAxQRETkSAxQR\nEQXEJj4iIiIvBSJAiUgJEVkuIl3iXRYiomTTpEl8rhvVACUi40Vkh4iszra9o4j8KiIbReShIE71\nIICPo1NKIiIKZNq0+Fy3cJTPPwHA6wA+cG8QkRQAYwBcASADwDIR+RxACoAR2Z5/M4ALAKwFUCzK\nZSUiIj/ilT0uqgFKVReKSK1smy8CsFFVNwGAiEwG0F1VRwDI0YQnIpcBKAGgEYCjIjJTVbP8HHcr\ngFsBoGbNmpF8GURESS1egySiXYPypxqAv7weZwBomdvBqvooAIjIAAC7/AUn13HjAIwDgLS0NI1U\nYYmIKD7iEaD8xeI8A4qqToh8UYiIKC/JNMw8A0ANr8fVAWyNxIm5HhQRUeKIR4BaBqCeiNQWkSIA\nrgPweSROzPWgiIgSR7SHmU8C8B2A+iKSISIDVfUUgMEAZgNYB+BjVV0ToeuxBkVEFGHxauIT1cQb\nT5CWlqbp6enxLgYRUUI4eBAoXdrzOL9hQ0SWq2paXscViEwSwWINiogo8pJpkETUsA+KiChxJFSA\nIiKiyGMNKgLYxEdElDgSKkCxiY+IKPK8a1DvvRe76yZUgCIiouhKSYndtRigiIjIkRIqQLEPiogo\n8ryb+GI5YCKhAhT7oIiIEkdCBSgiIoo8DjMnIiLyklABin1QRESRxxpUBLAPiogocSRUgCIiosTB\nAEVERI7EAEVERAFxHhQREZGXhApQHMVHRBRdNWvG7loJFaA4io+IKLouvTR210qoAEVERNFTuHBs\nr8cARUREAXGiLhEROVIhV6Ro1Sq2141xhY2IiAqalBRg2TKgXr3YXpcBioiI8pSWFvtrsomPiIgc\nKaECFOdBEREljoQKUJwHRUSUOBIqQBERUeJggCIiIkdigCIiIkdigCIiIkdigCIiIkcSVY13GSJO\nRHYC+NPPrjIAso9B97etIoBdUShaKPyVK9bnC+U5eR0b7v5Qtifa+xbuuYJ9XjDHBTom1H18zyLz\nvET4XztbVSvleZSqJs0NwLggt6U7sayxPl8oz8nr2HD3h7I90d63cM8V7POCOS7QMaHu43sWmecl\n0/9asjXxzQhymxNEulzhnC+U5+R1bLj7Q90eb5EsV7jnCvZ5wRwX6JhQ9/E9i8zzkuZ/LSGb+PJL\nRNJVNQ6Zpyg/+L4VPHzPCqZYvW/JVoMK1rh4F4DCwvet4OF7VjDF5H1jDYqIiByJNSgiInIkBigi\nInIkBigiInIkBigiInIkBqggiEgJEXlfRN4WkX7xLg/lTUTOEZF3RWRKvMtCwRORq13/Z9NF5Mp4\nl4fyJiINRWSsiEwRkTsiee6kDVAiMl5EdojI6mzbO4rIryKyUUQecm3uCWCKqg4C0C3mhSUAob1n\nqrpJVQfGp6TkLcT37TPX/9kAAL3jUFx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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1a21dac6d8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "N_trials = int(1e3)\n",
+ "p = np.random.uniform(0,1,size=(N_trials, 2))\n",
+ "r = np.sqrt(np.sum(p**2, 1))\n",
+ "\n",
+ "print('Pi estimate:', 4 * np.sum(r<=1) / N_trials)\n",
+ "\n",
+ "sel = (r<=1, r>1)\n",
+ "\n",
+ "def plot_pi(p, r, sel):\n",
+ " x = np.linspace(0,1,200)\n",
+ " fh, ax = plt.subplots()\n",
+ " ax.hold(True)\n",
+ " ax.scatter(p[sel[0],0], p[sel[0],1], c='r', marker='x')\n",
+ " ax.scatter(p[sel[1],0], p[sel[1],1], c='b', marker='x')\n",
+ " ax.plot(x, np.sqrt(1-x**2), 'k', linewidth=2)\n",
+ " ax.set_xlim([0, 1])\n",
+ " ax.set_ylim([0, 1])\n",
+ "\n",
+ "if N_trials <= 1e4:\n",
+ " plot_pi(p,r,sel)\n",
+ "\n",
+ "x = np.arange(1,N_trials+1)\n",
+ "c_est = 4*np.cumsum(sel[0])/x\n",
+ "c_err = np.abs(c_est-np.pi)/np.pi\n",
+ "\n",
+ "# Std: sqrt(1/N(N-1) sum{(x_i-pi)^2})\n",
+ "# If we wanted to use error bars, we would have to downsample.\n",
+ "# Error band of course an option, and should be implemented in plot_convergence.\n",
+ "plot_convergence(c_est, np.pi)\n",
+ "plt.tight_layout()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "## To be removed."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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ym3rbHGjXDe74XBSyfmIvTRlELY2BJArYsLw97TZ2eLKqci8Ftv5wHVtih2St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\nIt0CAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x11f29f4a8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "df = pd.read_csv('http://swiss-glaciers.glaciology.ethz.ch//download/aletsch.csv', skiprows=11, skipinitialspace=True)\n",
+ "df.plot('reference year', 'Length Change (m)')\n",
+ "plt.show()\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.plot(df['reference year'], df['Length Change (m)'])\n",
+ "plt.plot(df['reference year'], moving_average(df['Length Change (m)'], 5)[2:-2])\n",
+ "plt.plot(df['reference year'], moving_average(df['Length Change (m)'], 11)[5:-5])\n",
+ "plt.plot(df['reference year'], moving_average(df['Length Change (m)'], 101)[50:-50])\n",
+ "plt.show()"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.12"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/.ipynb_checkpoints/Solutions_5-checkpoint.ipynb b/exercises/.ipynb_checkpoints/Solutions_5-checkpoint.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..42e6aa1f0dc75e689535f0720e1a02f195d17eb7
--- /dev/null
+++ b/exercises/.ipynb_checkpoints/Solutions_5-checkpoint.ipynb
@@ -0,0 +1,649 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Solution Exercise 5\n",
+ "This week, we are working on least squares fits and parameter estimation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy.optimize import curve_fit\n",
+ "from scipy.stats import norm, chi2, lognorm"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Fit a polynomial\n",
+ "We start by fitting a polynomial to a given data set, in particular, a parabola. Compare a linear fit and a cubic fit to our parabolic fit and check the goodness of fits with chi squared distributions. Explore how the different uncertainties affect the outcome and uncertainties of the fit."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "# Create some data distribuited as parabola with normally distributed errors.\n",
+ "def parabola(x, a, b, c):\n",
+ " return a*x**2 + b*x + c\n",
+ "def error(x, sigma):\n",
+ " return norm.rvs(0.0, sigma, x.size) \n",
+ "a = -0.1\n",
+ "b = 0\n",
+ "c = 1\n",
+ "x = np.linspace(-5, 5, 21)\n",
+ "sigma_y = 0.0015\n",
+ "delta_y = error(x, sigma_y)\n",
+ "y_true = parabola(x, a, b, c)\n",
+ "y = y_true + delta_y\n",
+ "y_error = sigma_y * np.ones(x.size)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def fit_polynomial(x, y, degree, weight):\n",
+ " \"\"\"Fit polynomial of degree to data x, y with y weight = 1/sigma_y\n",
+ " \n",
+ " Return fit, covariance matrix, residuals and chi-squared and degrees of freedom.\n",
+ " \"\"\"\n",
+ " \n",
+ " dof = x.shape[0] - degree\n",
+ " fit, cov = np.polyfit(x, y, degree, w=weight, cov=True)\n",
+ " residuals = np.sum((y - np.polyval(fit, x))**2 / y_error**2)\n",
+ " chisq = residuals / (dof)\n",
+ " return fit, cov, residuals, chisq, dof\n",
+ " \n",
+ "fit, cov, res, chisq, dof = fit_polynomial(x, y, 2, 1/y_error) # Fit parabola\n",
+ "fit_1, cov_1, res_1, chisq_1, dof_1 = fit_polynomial(x, y, 1, 1/y_error) # Fit line\n",
+ "fit_3, cov_3, res_3, chisq_3, dof_3 = fit_polynomial(x, y, 3, 1/y_error) # Fit cubic\n",
+ "\n",
+ "def evaluate_chisq(chisq, dof):\n",
+ " return chi2.sf(chisq, dof)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Reduced chi^2:\n",
+ "parabola 0.992095154842\n",
+ "line 311170.605008\n",
+ "cubic 1.00698239496\n"
+ ]
+ }
+ ],
+ "source": [
+ "print('Reduced chi^2:')\n",
+ "print('parabola', chisq)\n",
+ "print('line', chisq_1)\n",
+ "print('cubic', chisq_3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Chi^2 distributions:\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "(0.99999999927784466, 0.0, 0.99999999635390924)"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "print('Chi^2 distributions:')\n",
+ "evaluate_chisq(chisq, dof), evaluate_chisq(chisq_1, dof_1), evaluate_chisq(chisq_3, dof_3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Error estimates:\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "(array([ 4.34814754e-05, 1.17346291e-04, 5.33940597e-04]),\n",
+ " array([ 0.06541325, 0.19804844]),\n",
+ " array([ 1.67125703e-05, 4.40364561e-05, 2.99509423e-04,\n",
+ " 5.40755607e-04]))"
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "print('Error estimates:')\n",
+ "np.sqrt(np.diag(cov)), np.sqrt(np.diag(cov_1)), np.sqrt(np.diag(cov_3))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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UlETv3r39+AyJhI/iDkwX6fScHLvCwsJSOZ2I8ePHM3z4cDZu3Midd97JnDlzuOaaa1i3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\nur3Fy0PRLnN/NbOjfIdJFcZEkvGQcJM4J7Fpkp6L5XObEF2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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1a0bac0b90>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
+ "ax[0].set_title('fits')\n",
+ "ax[0].errorbar(x, y, yerr=y_error, fmt='k.')\n",
+ "ax[0].plot(x, y_true, 'k-')\n",
+ "ax[0].plot(x, np.polyval(fit, x), label='parabola', color='blue')\n",
+ "ax[0].plot(x, np.polyval(fit_1, x), label='line', color='green')\n",
+ "ax[0].plot(x, np.polyval(fit_3, x), label='cubic', color='red')\n",
+ "\n",
+ "ax[0].legend()\n",
+ "ax[1].plot(y_true - np.polyval(fit, x), '.', color='blue')\n",
+ "ax[1].plot(y_true - np.polyval(fit_1, x), '.', color='green')\n",
+ "ax[1].plot(y_true - np.polyval(fit_3, x), '.', color='red')\n",
+ "ax[1].set_title('residuals')\n",
+ "ax[1].fill_between(ax[1].get_xlim(), -sigma_y, sigma_y, color='grey', alpha=0.4, label=r'$1\\sigma$')\n",
+ "ax[1].legend()\n",
+ "f.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 114,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x182c02487f0>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure(figsize=(5, 5))\n",
+ "chisq_arr = np.linspace(0, 100, 1001)\n",
+ "plt.title('p-values')\n",
+ "plt.xlabel(r'$\\chi^2$')\n",
+ "for n in [1, 2, 3, 4, 6, 8, 10, 15, 20, 25, 30, 40, 50]:\n",
+ " plt.loglog(chisq_arr, chi2.sf(chisq_arr, n))\n",
+ "plt.loglog(chisq_arr, chi2.sf(chisq_arr, dof), 'k-', lw=2, label='dof={0}'.format(dof))\n",
+ "plt.ylim(1e-3, 1.1)\n",
+ "plt.plot(chisq, chi2.sf(chisq, dof), 'o', color='blue', label='parabola')\n",
+ "plt.plot(chisq_1, chi2.sf(chisq_1, dof_1), '^', color='green', label='line')\n",
+ "plt.plot(chisq_3, chi2.sf(chisq_3, dof_3), 'x', color='red', label='cubic', ms=5)\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We observe that the residuals are not uniformly distributed around zero with the expected variance $\\sigma_y$ in the case of the line fit. This reflected in the $\\chi^2$-distribution. Only in 7% of the cases we would expect to draw data that give a worse fit. Note that overfitting with a cubic is not easily spotted in the residuals."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Fit a nonlinear function\n",
+ "Next, we consider a Gaussian as an example of a nonlinear function. We are measuring some feature which has a Gaussian distribution in $x$. This could be an inhomogeneous spectral line for $x=E$ the energy of emitted photons. We are interested in the resonance frequency and the linewidth, i. e. we want to estimate them form our observations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 115,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def gaussian_parent(x, mu, sigma):\n",
+ " return norm.pdf(x, mu, sigma) \n",
+ "\n",
+ "def gaussian_sample(mu, sigma, sample_size):\n",
+ " return norm.rvs(mu, sigma, sample_size)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 116,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x182c044e438>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Create sample\n",
+ "## SAMPLE SIZE\n",
+ "sample_size = 200\n",
+ "##################\n",
+ "\n",
+ "# Prepare fake data\n",
+ "mu = 1540 # True values that we will try to estimate\n",
+ "sigma = 11 # using a least-squares fit\n",
+ "\n",
+ "x_arr = np.linspace(1500, 1600, 101)\n",
+ "bins = 12\n",
+ "sample = gaussian_sample(mu, sigma, sample_size)\n",
+ "hist = np.histogram(sample, bins=bins, range=(1500, 1580))\n",
+ "bin_width = np.diff(hist[1])[0]\n",
+ "normalization = bin_width * sample_size\n",
+ "x = hist[1][:-1]+bin_width/2\n",
+ "y_error_const = 0\n",
+ "y = hist[0]/normalization + gaussian_sample(0, y_error_const, bins)\n",
+ "y_errors = np.sqrt((np.sqrt(hist[0]) / normalization)**2 + y_error_const**2)\n",
+ "\n",
+ "# Plot our fake measurement results\n",
+ "plt.figure(figsize=(5, 4))\n",
+ "plt.xlabel(r'$E$ (meV)')\n",
+ "plt.ylabel('count rate')\n",
+ "plt.plot(x_arr, gaussian_parent(x_arr, mu, sigma), '-', color='black', label='parent')\n",
+ "plt.errorbar(x, y, yerr=y_errors, fmt='.', ms=7, capsize=3, label='sample')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "# Save data\n",
+ "data = np.vstack((x, y, y_errors))\n",
+ "np.savetxt('data', data)\n",
+ "np.savetxt('sample', sample)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 117,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# Load data from disk. Format (3,12): (x, y, y_error) x N \n",
+ "data = np.loadtxt('data')\n",
+ "x = data[0, :]\n",
+ "y = data[1, :]\n",
+ "y_error = data[2, :]\n",
+ "# The sample used to generate\n",
+ "sample = np.loadtxt('sample')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 118,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# Function we want to fit to our data set\n",
+ "def model_function(x, *args):\n",
+ " mu, sigma = args[0:2]\n",
+ " return norm.pdf(x, mu, sigma)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 123,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Fit Results:\n",
+ "mu = 1539.5 +- 0.6\n",
+ "sigma = 10.8 +- 0.5\n",
+ "mu estimator 1538.9 +- 0.8\n",
+ "sigma estimator 11.6\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Perform the fit minimizing least squares\n",
+ "initial_guess = [1545, 9]\n",
+ "p_opt, p_cov = curve_fit(model_function, x, y, p0=initial_guess, sigma=None, absolute_sigma=False, check_finite=True)\n",
+ "p_err = np.sqrt(np.diag(p_cov))\n",
+ "# pcov(absolute_sigma=False) = pcov(absolute_sigma=True) * chisq(popt)/(M-N)\n",
+ "print('Fit Results:')\n",
+ "print('mu = {:1.1f} +- {:1.1f}'.format(p_opt[0], p_err[0]))\n",
+ "print('sigma = {:1.1f} +- {:1.1f}'.format(p_opt[1], p_err[1]))\n",
+ "\n",
+ "print('mu estimator {:1.1f} +- {:1.1f}'.format(np.mean(sample), np.std(sample, ddof=1)/np.sqrt(sample.size)))\n",
+ "print('sigma estimator {:1.1f}'.format(np.std(sample, ddof=1)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Plot the result"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 124,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x182be9feb00>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x_arr = np.linspace(1500, 1600, 101)\n",
+ "\n",
+ "plt.figure(figsize=(5, 4))\n",
+ "plt.xlabel(r'$E$ (meV)')\n",
+ "plt.ylabel('count rate')\n",
+ "plt.errorbar(x, y, yerr=y_errors, fmt='.', ms=7, capsize=3, label='sample')\n",
+ "plt.plot(x_arr, model_function(x_arr, *initial_guess), '-', color='grey', label='guess')\n",
+ "plt.plot(x_arr, model_function(x_arr, *p_opt), '-', color='black', label='fit')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Biased estimator example?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 133,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Expectation value: 3.648721270700128\n",
+ "Sample mean: 3.1303941671784665\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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SVRdX1Q7mX7L4b1X1x81jtUlywfAENcOv3G8HHumd6uyrqqeAJ5P82rDoKjbYxxl0vBPuSuA9wMPDuU+Aj1TVVxtm6bYN2Dd8eNHPMP9yvU3/EiyxFfjS/LEK5wKfq6qv9Y7U5oPA7cMrIH4I/GnzPCvqrL8MTZI0z7+IIUlNDLAkNTHAktTEAEtSEwMsSU0MsCQ1McCS1MQAS1KT/wfkwKx0On2IJwAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x182bea6e0f0>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "log_sample = lognorm.rvs(s=0.5, loc=2, scale=1, size=1000)\n",
+ "plt.figure(figsize=(5, 4))\n",
+ "plt.hist(log_sample, bins=16, rwidth=0.85)\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "print('Expectation value:', lognorm.mean(s=1, loc=2, scale=1))\n",
+ "print('Sample mean:', np.mean(log_sample))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Bonus: Errors in x and y\n",
+ "So far, we considered uncertainties only on y. Consider the following data set with errors in both x and y. Try to fit a line to the data below, taking into account both errors. Compare with fits neglecting the x errors or both. \n",
+ " \n",
+ "Hint: A detailed solution is already on the moodle. You may chose if you want to try to write your own solution, implement a known solution (see references in solution notebook) or just try it with the scipy package ODR (orthogonal distance regression). \n",
+ "https://docs.scipy.org/doc/scipy/reference/odr.html\n",
+ " \n",
+ "The solution contains a python implementation of York's equation, comparison with ODR and MC tests. \n",
+ "Week 3: \"Linear Regression errors x and y\""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 122,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x182bec20da0>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Test data\n",
+ "X = np.array([0.0, 0.9, 1.8, 2.6, 3.3, 4.4, 5.2, 6.1, 6.5, 7.4])\n",
+ "Y = np.array([5.9, 5.4, 4.4, 4.6, 3.5, 3.7, 2.8, 2.8, 2.4, 1.5])\n",
+ "wX = np.array([1000, 1000, 500, 800, 200, 80, 60, 20, 1.8, 1])\n",
+ "wY = np.array([1, 1.8, 4, 8, 20, 20, 70, 70, 100, 500])\n",
+ "sigma_x = 1.0/np.sqrt(wX)\n",
+ "sigma_y = 1.0/np.sqrt(wY)\n",
+ "\n",
+ "plt.figure(figsize=(4, 3))\n",
+ "plt.errorbar(X, Y, xerr=sigma_x, yerr=sigma_y, fmt='o', label='oberservations')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "hide_input": false,
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.12"
+ },
+ "toc": {
+ "base_numbering": 1,
+ "nav_menu": {},
+ "number_sections": true,
+ "sideBar": true,
+ "skip_h1_title": false,
+ "title_cell": "Table of Contents",
+ "title_sidebar": "Contents",
+ "toc_cell": false,
+ "toc_position": {},
+ "toc_section_display": true,
+ "toc_window_display": true
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/.ipynb_checkpoints/straight_line_fit-checkpoint.ipynb b/exercises/.ipynb_checkpoints/straight_line_fit-checkpoint.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..39ba50b9c7b09a1d450e3cd53ea7ae04b68f7a52
--- /dev/null
+++ b/exercises/.ipynb_checkpoints/straight_line_fit-checkpoint.ipynb
@@ -0,0 +1,714 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Finding the best line for data with errors in x and y"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We want to find a straight line $y = a + bx$ fitting $N$ data points $X, Y = (X_i, Y_i)$ with errors $(\\sigma(X_i), \\sigma(Y_i))$, $i=1,...,N$. \n",
+ "We follow Yorks equations for the case of uncorrelated but non-constant errors (see references below for the inclusion of correlations between errors) which are derived by minimizing $$S = \\sum_i \\omega(X_i)(x_i-X_i)^2 + \\omega(Y_i)(y_i-Y_i)^2,$$\n",
+ "where $(x_i, y_i)$ are the adjusted values that lie on the line and $(\\omega(X_i), \\omega(Y_i)) = (1/\\sigma(X_i)^2, 1/\\sigma(Y_i)^2)$ the weights. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 139,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np\n",
+ "import scipy.odr as so"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## TL;DR: Quick How To"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You can conveniently use the scipy package for orthogonal distance regression (ODR) to achieve this task. \n",
+ "Check out https://docs.scipy.org/doc/scipy/reference/odr.html for documentation. Here I provide a short example."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 144,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Beta: [-0.4805337 5.4799117]\n",
+ "Beta Std Error: [ 0.07062028 0.35924657]\n",
+ "Beta Covariance: [[ 0.00336226 -0.01647255]\n",
+ " [-0.01647255 0.08700776]]\n",
+ "Residual Variance: 1.483294149297378\n",
+ "Inverse Condition #: 0.09285611904588402\n",
+ "Reason(s) for Halting:\n",
+ " Sum of squares convergence\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1eeb4aaa9b0>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# 0. Test data\n",
+ "X = np.array([0.0, 0.9, 1.8, 2.6, 3.3, 4.4, 5.2, 6.1, 6.5, 7.4])\n",
+ "Y = np.array([5.9, 5.4, 4.4, 4.6, 3.5, 3.7, 2.8, 2.8, 2.4, 1.5])\n",
+ "wX = np.array([1000, 1000, 500, 800, 200, 80, 60, 20, 1.8, 1])\n",
+ "wY = np.array([1, 1.8, 4, 8, 20, 20, 70, 70, 100, 500])\n",
+ "sigma_x = 1.0/np.sqrt(wX)\n",
+ "sigma_y = 1.0/np.sqrt(wY)\n",
+ "\n",
+ "# 1. Define the function you want to fit against.\n",
+ "def f(B, x):\n",
+ " '''Linear function y = m*x + b'''\n",
+ " return B[0]*x + B[1]\n",
+ "\n",
+ "# 2. Create a Model.\n",
+ "linear = so.Model(f)\n",
+ "\n",
+ "# 3. Create a Data or RealData instance.\n",
+ "mydata = so.RealData(X, Y, sx=sigma_x, sy=sigma_y) # should provide std errors not var\n",
+ "\n",
+ "# 4. Instantiate ODR with your data, model and initial parameter estimate.\n",
+ "myodr = so.ODR(mydata, linear, beta0=[-0.5, 5.5])\n",
+ "\n",
+ "# 5. Run the fit.\n",
+ "myoutput = myodr.run()\n",
+ "\n",
+ "# 6. Examine output.\n",
+ "myoutput.pprint()\n",
+ "odr_b, odr_a = myoutput.beta\n",
+ "odr_sb, odr_sa = myoutput.sd_beta\n",
+ "\n",
+ "# 7. Plot results\n",
+ "plt.figure(figsize=(6, 4))\n",
+ "plt.errorbar(X, Y, xerr=sigma_x, yerr=sigma_y, fmt='o', label='oberservations')\n",
+ "plt.plot(X, odr_a + odr_b * X, 'g-', label='odr fit')\n",
+ "# rough visualization of error estimates\n",
+ "plt.fill_between(X, odr_a-odr_sa + (odr_b-odr_sb)*X, odr_a+odr_sa + (odr_b+odr_sb)*X, color='g', alpha=0.35)\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This is all you need. If your interested in more details, go on. You can check our small python implementation for this task and some benchmarks to check its validity below."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Further details\n",
+ "## Our python implementation\n",
+ "Inspired by the references below, we try a naive python implementation to learn how it works."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 145,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "class York_eq_fit():\n",
+ " debug = False\n",
+ " \n",
+ " def __init__(self, X, Y, SX, SY):\n",
+ " \"\"\"Observed points X,Y (1d arrays) and standard error SX, SY.\"\"\"\n",
+ " \n",
+ " self.X = np.array(X)\n",
+ " self.Y = np.array(Y)\n",
+ " self.N = np.size(self.X) # number of obervations\n",
+ " assert np.size(self.X) == np.size(self.Y), 'X and Y must have the same length'\n",
+ " if np.size(SX) == 1:\n",
+ " self.SX = np.ones(self.N) * SX\n",
+ " else:\n",
+ " assert np.size(SX) == self.N, 'SX and X must have the same length or SX must be a constant'\n",
+ " self.SX = SX\n",
+ " if np.size(SY) == 1:\n",
+ " self.SY = np.ones(self.N) * SY\n",
+ " else:\n",
+ " assert np.size(SY) == self.N, 'SY and Y must have the same length or SX must be a constant'\n",
+ " self.SY = SY \n",
+ " self.wX = 1.0 / self.SX**2 # weights of X observations\n",
+ " self.wY = 1.0 / self.SY**2 # weights of Y observations\n",
+ " \n",
+ " # For later: include correlations (not implemented yet)\n",
+ " self.alpha = np.sqrt(self.wX * self.wY)\n",
+ " self.r = 0.0 # correlations between SX and SY\n",
+ " \n",
+ " def run(self, rtol=1e-15, atol=1e-10, maxiter=1000):\n",
+ " \"\"\"Perform fit and return result a,b and error estimates sa, sb\"\"\"\n",
+ " \n",
+ " self.guess_b()\n",
+ " self.update_W()\n",
+ " self.update_b()\n",
+ " self.iterate(rtol, atol, maxiter)\n",
+ " self.evaluate()\n",
+ " return self.a, self.b, self.sa, self.sb\n",
+ "\n",
+ " def guess_b(self):\n",
+ " \"\"\"Find an initial guess for the slope b\"\"\"\n",
+ " \n",
+ " self.b, self.a = np.polyfit(self.X, self.Y, 1, w=1/self.SY)\n",
+ " return self.b\n",
+ " \n",
+ " def update_W(self):\n",
+ " \"\"\"Update W given an estimate for b and knowing weights wX, wY\"\"\"\n",
+ " \n",
+ " self.W = self.wX * self.wY / (self.wX + self.b**2 * self.wY - 2 * self.b * self.r * self.alpha)\n",
+ " # also update quantities that directly depend on W\n",
+ " self.MX = np.sum(self.W * self.X) / np.sum(self.W) \n",
+ " self.MY = np.sum(self.W * self.Y) / np.sum(self.W)\n",
+ " self.U = self.X - self.MX\n",
+ " self.V = self.Y - self.MY\n",
+ " beta_correction = (self.b * self.U + self.V) * self.r / self.alpha\n",
+ " self.beta = self.W * (self.U/self.wY + self.b*self.V/self.wX - beta_correction)\n",
+ " \n",
+ " def update_b(self):\n",
+ " \"\"\"Update the estimate of slope b\"\"\"\n",
+ " \n",
+ " self.old_b = self.b\n",
+ " self.b = np.sum(self.W * self.beta * self.V) / np.sum(self.W * self.beta *self.U)\n",
+ " \n",
+ " def iterate(self, rtol=1e-15, atol=1e-10, maxiter=1000):\n",
+ " self.iterations = 0\n",
+ " while abs(self.old_b - self.b) / self.b > rtol or abs(self.old_b-self.b) > atol:\n",
+ " if York_eq_fit.debug:\n",
+ " print(self.iterations, abs(self.old_b-self.b)/self.b)\n",
+ " # repeat iteration until estimate for b converges\n",
+ " self.update_W()\n",
+ " self.update_b()\n",
+ " self.iterations += 1\n",
+ " if self.iterations > maxiter:\n",
+ " print('Maximum number of iterations reached.')\n",
+ " break\n",
+ " if York_eq_fit.debug:\n",
+ " print('Iteration converged after {0} steps.'.format(self.iterations))\n",
+ " \n",
+ " def evaluate(self, prefactor=True):\n",
+ " \"\"\"Evaluate results for a, b, Sa, Sb\"\"\"\n",
+ " \n",
+ " self.update_W()\n",
+ " self.a = self.MY - self.b * self.MX\n",
+ " self.x = self.MX + self.beta # adjusted values x_i\n",
+ " self.mx = np.sum(self.W * self.x) / np.sum(self.W)\n",
+ " self.u = self.x - self.mx \n",
+ " self.sb = np.sqrt(1.0 / (np.sum(self.W * self.u**2)))\n",
+ " self.sa = np.sqrt(1.0 / np.sum(self.W) + self.mx**2 * self.sb**2)\n",
+ " self.S = np.sum(self.W * (self.Y - self.X * self.b -self.a)**2)\n",
+ " if prefactor:\n",
+ " self.sb = self.sb * np.sqrt(self.S/(self.N-2))\n",
+ " self.sa = self.sa * np.sqrt(self.S/(self.N-2))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Test if our implementation works"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 146,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# TEST CASE: Pearsons' data (copied from Reed Am. J. Phys. 60, 1 (1992))\n",
+ "X = np.array([0.0, 0.9, 1.8, 2.6, 3.3, 4.4, 5.2, 6.1, 6.5, 7.4])\n",
+ "Y = np.array([5.9, 5.4, 4.4, 4.6, 3.5, 3.7, 2.8, 2.8, 2.4, 1.5])\n",
+ "wX = np.array([1000, 1000, 500, 800, 200, 80, 60, 20, 1.8, 1])\n",
+ "wY = np.array([1, 1.8, 4, 8, 20, 20, 70, 70, 100, 500])\n",
+ "# weight = 1/errors**2 <-> error = 1/weight**0.5\n",
+ "sigma_x = 1.0/np.sqrt(wX)\n",
+ "sigma_y = 1.0/np.sqrt(wY)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 147,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Offset a, slope b, std a, std b\n",
+ "Result: 5.47991022403 -0.480533407446 0.359246522551 0.0706202695288\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Do the fit with our code\n",
+ "fit = York_eq_fit(X, Y, sigma_x, sigma_y)\n",
+ "a, b, sa, sb = fit.run(rtol=1e-15, atol=1e-15, maxiter=1000)\n",
+ "print('Offset a, slope b, std a, std b')\n",
+ "print('Result:', a, b, sa, sb)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 148,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# compare this with numpy results for regression of y on x (only errors in y considered!)\n",
+ "np_fit = np.polyfit(X, Y, 1, w=1/np.ones(np.size(X))*sigma_y)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 149,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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dDlAn87aK70ng9UsVfMeARzpuSHCmiX+o1/u4UiqwLZo7nGff2X3FD6aRocEsmtv2BqS2mY3/mtqo0FrL6NGjL+8PdTVPyIFsBb9582Y++OADxo8fz44dO7DW8t///d/MnTv3itetXr36itcC3H///SxZsoRz585d3mPp9ddfJz8/n9zcXEJDQxk4cGCL+0k19/1B0xskxsXFsXPnTnJycnj55Zd56623Ls8Qncqr56CstTsu3V8aa62db6292JGD6hsb2aqPK6UC2/wJKfxkQRphwXJJSomN5CcL0tq1YjJt2jSWLl1KZWUlFRUVvPvuu9x6661NblQ4fPhw8vPzL3/c5XKxd+/eJs979OhRpkyZwg9/+EMSExM5deoUc+fO5Ve/+tXl3WUPHTpERUVFk69/8MEHefPNN1myZMnlirySkhJ69+5NaGgoq1at4sSJE8D1N0acNm0ar7/++uWvd/Lkyet2FC8oKMDtdvOFL3yBH/3oR9dsUuhEjuxm3uRPU9SyaEgR1NVASPh1Xq2UCkTzJ6TwxpaTAG1e1mts4sSJPPzww0yePBmAxx57jLi4uCY3KgwLC2PJkiX8wz/8AyUlJdTV1fHUU08xevToa867aNEiDh8+jLWWWbNmMW7cOMaOHcvx48eZOHEi1lqSkpJYunRpk+MaPXo0ZWVlpKSkXF5G/PKXv8w999xDRkYG48ePZ8SIEcC1GyN+61vfunyeb37zm3zjG98gLS2NkJAQXnvttStmTlc7ffo0jzzyCG633Nf7yU9+0rY3thOZ600T2yojI8Nu3bq1XedYuv00zyzZSW29m5Sgahb1yGa+6y8Q0x9mPgdjF0JQ6/dZ8QVPVZEv/idSqqvav38/I0eO9PcwlJ819e/AGJNrrc1o6bWO7cU3f0IKE/pGMyWkkg0jq5gfOQrCHoQKNyz9O/jlZNj3V+iAgFVKKeV/jlziu0ZICNxwA3ADVE6G/I1wcRW89RWIGwG3Pw8js+Cqm59KKaUCV2AEVGNRUTBgNrhnwPk1ULwc3noQokfCtOdg4l3Qhi2WlVK+Z629pmpOdR/tvYXk2CW+FgWFwA2zYMi/QtLfQPlJ+OAr8MLN8OEf4cIFXf5Tyo8iIiIoLCxs90VKBSZrLYWFhURERLT5HIE3g7paUCjEz4LYqbLsV5QDW56E3NHQ+164KQtuvBGio/09UqW6lX79+pGXl4f25uy+IiIi6NevX5tfH/gB5REUDglZEHsrFK2Aiyvh7Avw3kcQMhWGjIfx4yE1FcLC/D1apbq80NDQyx0UlGqLrhNQHsE9IGk+xM2Ewo+geB3U74GjU+BIBoTFwNixMGqUFF7o+rhSSjlS1wsoj5AYSH4Q4mZD4ftQugGCtkLkbbCrFrZtk2W/9HQYNgxiY/09YqWUUo103YDyCEuEGx6G+DlQ8B5c/BCC10J8FoRNhjVrYNUq6NcPJk6EQYOgHTf1lFJK+UbXDyiP8L6Q8gRUHYeCZZC/BEI+gYQ7odfNUFYG770HQUEwYoQsA6akaMm6Ukr5SfcJKI/IgdD/21B5EPKXwvnXpagi8R7olw5uC8eOwd69EBkJEyZIYPlgE0allFLec3RAzVvxZ45E94ZRw31fzBA1HFKfgYrdkL8Mzv5WStQT74XEMfL1ampg82bYuFECKiNDStaVUkp1OMc2i6W8nOK+qcSWXYQBA2DuXLjllo4pEbduKNsq96hc+RA5GBLnQ9TQK8bDxYssrenFM5X9qLWGlJgIFmWN0E0UlVKqFbxtFuvcgAIe+q+PmfrJEr6x60M4dUqq7m67DW6/HeLjfTDSq9h6KNkAhR9AXQlEjYKkeyFiAABLi0J4Ni+SKtswm4sMgp/cPoD5M0ZrybpSSnmhSwTUwpfXwdmzLB5VB/v2QU4O5OZKIcOkSZCVBUOH+j4Y3LVQvBoKc8BdAT0nQuI8Mo8O4bTr2u5QKUG1bOh/TkvWlVLKC94GlKPvQV1mDIweLb8uXIAVK6Q0/NNP5Z5QVhbcdJN0PfeFoDApS4+5FS5+DEUfQ/l2zrj+1OThZ9yhsvToKVnv319K1gcO1JJ1pZRqo8AIqMZ694Yvfxm+8AVYtw6ys+GVV+DPf4bZs2HWLIiJ8c3XCo6U6r7YGVCUTd9zhZy2idcc1jfUSpf1qChpUFtaCsuWSYn6yJGQlqYl60op1UqBF1AeERFyL2rWLNi9W4JqyRJYuhRuvlmKKnxVcRcSDb3/hkWmhmfPuKgi9PKnIo2bRX2qG441RgIyJgbq6+HoUdizR0rWPUuAWrKulFItCtyA8ggKgnHj5NfZs3Kfau1amV0NGybLf5Mm+WT2Mj8pHIJdPJtnqLLBpFDAopClzLcx4J4pDWsbCw5uCKOaGti0Cdavv7JkvWfPdo9LKaW6osAPqMZuuAEefhgeeEDuB+XkwEsvScXfnDkwc2a7t92YH1/HG0VhQD2L+12AggIoWCXd0xPulG0/TBNva3i4LPOBlKxnZ8vvhwyRcE1NhdDQa1+nlFLdVNcKKI+oKLjjDlnm275dwuDNN+Htt2HqVPl4amr7v05Ef+j3Lag8AgVL4cKbcHEFJNwDvSaDaWY/yJ495ZfbDWfOwOHDUmTh6bLep4+WrCulur2uGVAeQUFy3yc9XZ6jysmRJbZVq6QicO5cqbYLaufGwlFDoP93oXKftE8699qlrhTzoOf45sMmKAgSEuSXywU7d8LWrXL/Kj1dSui1ZF0p1U117YBqrH9/eOwxWLhQAmrFCvjZz6QqcM4cmD4devRo+/mNgR6jIWoklG+Hgr/CmVflId/E+RA14vqzotBQWaIEqKyUMa5cqSXrSqluq/sElEd0NMybB3fdJbOVnBz405/gL3+BadNkVtW3b9vPb4IgOl1mTqWboeB9yPuF9P5LvBcivagsbKpkPShIZn1jxmjJulKqW+h+AeURHAxTpsivzz+XoPLMrMaNk+q/tLS2L/+ZYIi5BaInQck62d335H9Az7ESVOFe9O+7umT98GEpqY+KklnV8OGQeO1zWUop1RUERquj0fU+GJUXSkrgk0/g44+huFiW3ObOlZlVo+W1hUeiAFg8pNL7c7urpdKvaIX8PnqSPAQc1oZnompqoLAQ6upkiTI9HQYPbt8SpVJKdZKu0eooyMgM5vRJSE72XSuj5sTEwIIFsgS4ebNU/732GixeDDNmyL2q5OS2nTso4lIZ+nQoWi5hVbYVYjLl46Fx3p8rPLxhGbKsDD76SGZbQ4fK7K9/fy1ZV0oFPK+u+MaY40AZUA/UeZN8PhEULCXXo5Ngyxa5CHdGUIWEQGam/Dp8WJb/li+XwJo4kdFp97J3UFrbzh3cA5Lug7jboPBDKF4HpZ9KO6WEuRDcygd3o6Pll9sNp0/DoUNSsj5unLRZ0pJ1pVSA8mqJ71JAZVhrC7w5qc+W+F7dBMDiJy5tyb5tG3z2mXyyM4KqsaIiWfr75BMoK+Nk71RS582REAsPb/n1zanNl+09SjdLJ4q42yF+lsy42srlkgeIXS4pU/eUrPuqR6FSSrWDT7fbcERAeZSXS1Bt2SJVbsnJnbucVVvLr5bmcsen7zHw3HF54NazR1VCQtvPW3NGStPLd8gsKj5LlgOD2vm9VVZKuNbXy8PJWrKulPIzXwfU58BFwAKvWmt/fb3jOzSgPMrLpUvE5s2dHlQLj0gJ+OK6bbLst3WrLKN59qgaNqzty2pVn0PBMqg8ACFxkHAXxNwsVYHtYa0UgZSWSgVj45L19j6orJRSreDrIolMa+0ZY0xvYIUx5oC1du1VX/Bx4HGAVF+0EWpJz55w660yI9ixQ/aGcrs7L6iMkXs8I0dCfr6Up69cKYE5cKAE1c03t34skYOg/1NQcUCC6vyfpKgicR5ET2y+fZI3442NlV91dXKvatcuLVlXSjlWq8vMjTHPA+XW2hebO6ZTZlBXq6yUoNq0SYKqd28pFugAzZaZV1fDhg0yqzp9Gnr1kj2qZs9uW8sia6FiF+Qvg9ozEN5fgqrHGN8VPlRXS8l6fb2Ee3q6dFlvR8l6q/7elFLdjs9mUMaYHkCQtbbs0u/nAD/0wRh9KyoKbrkFxo+XnnabNslFtwOD6hoREbI/1W23yR5Q2dnw7rvSCeKmm2RWNXiw9+czBnqOgx5pUPYZFLwHp1+GyCHysG/UUN+M2dNl3VOyDlqyrpTyO2+W+JKBd438xB4C/Nlam92ho7qkTT+BR0XJ0ponqDZulCWt5OTOCypjpAtFWhqcOycl6mvWyOxq6FB5+HfyZO+rEE0Q9JoiLZRKNkLBB3DqP6X3X+K9ECFLqm16gLix5krWx4+XpczkZC1ZV0p1mhavkNbaY8C4ThiLb0VGyqxl3Di517Jxo5Rdd2ZQgTyH9NWvwv33y0aKOTnwy1/KHlWzZ8tsq1cv785lQiB2GvS6CYpXQ2EOnPgx9JwoS3/4aAfhq7us79ghVZNasq6U6kTO7iThC5GR0m/PE1QbNshFt3fv9j2/1FpRUbLEN2eOzOyys+Gtt2QJMDNTZlUDBnh3rqAwiJ8DMbfK/lNFn0D5dr5hprLE3AdE+W7coaESstDQZf3jj6UQZMIE+W9nvo9KqW6j6weUR0SELKuNHdswo6qpkRlVZ15gg4Lkwj5hAuTlNexRtXq1LKNlZcksxZvS7+BImTnFzoCiHDIvrmWq3QTnb4WEOyDEy5mZtxp3Wb94EZYu1ZJ1pVSHcXSz2A5VXS2dwTdsgNpaSEry+uHVdt/ruVp5uQTU8uXSASIxUWZaM2ZIOb2Xvnm4ii/Ypcyy68CESjul+Nsh2IczqqvV1UkVYHW1jHXiRBZuq4PQUK3iU0o1yacP6rZWQASUR02NVNytWye/7927xaDyeUB51NdDbq7Mqvbvl5nd1Kkyq0ppeXuOy+NKPSb7UJVthaAoiJ8LcTNlabAjXSpZX1icKgG1YIhULUZ1YEAqpQJO1+hm3hnCw2VJbcwY2LtXltvy81s1o/KZ4GBZhpw8GY4flxnV2rXS/y8tTYJq3LiWl9HC+kDfx6B6jrRPKngXLn5yqZv6VCm26AiekvWqcAlbT8n6sGGytKol60qpVtAZ1NVqa2HfPgmGqqomZ1QdNoNqSmmpdKhYsULu+/Tp07BHVWSkd+OqPAIFS6HqCIQmQsLd0Gty27tStOCKcbjdMu6KCi1ZV0oBusTXfp6gWrdOqteSki4HQqcGlEddnZR6Z2fDkSMylunT5V7VpSq7647LWqjcB/lLoeYUhPWVAoue43weFM2Oo7ZW7lfV1kqZvadk3dsye6VUl6AB5Su1tXI/aN06KWZISmLhGelZ16kB1diRI3KfytN/cPx4yMpiYcRkMOb647JuKN8uS3+15yFiACTOhx4jfTK0pUUhPJMXSa2FlFDLoj7VzI+vu/ZAT5d1t1vK6ydOlP9qybpSXZ4GlK+5XHDggHSEqKiQSjt/3/y/eLFhi/rSUk4l9Sf7prv52wWTW77Q23rZKLHgfai7CFHDpStFZNsf9l1aFMKzeZFU2YYZWaSx/KRfVdMhBTKzKy6WNkshIXIvcPRo2TFYS9aV6pI0oDqKywUHD0pZuFOCyuWCTZs4tmw5N549Jo1eZ86UPaqSkq7/WrcLStZCYTbUl8mSX+I8CG+5avBqmft6ctp1baikhLrZMKq85RN4StZrauR7SE+XAov27LOllHIcDaiO5gmqtWulkCEpye9BtfBwJMNP7ueHe5bJzsPWQkaGVP+NGHH9e03uari4Urb2cNdIEUXC3RDWQsA1MmhnNJZrv4bB8vm4stZ9M427rPfp09Bl3d8/DCil2k0DqrPU1TUEVUmJzKjasVVFe1xRnFBQIJV/q1bJvbMBAxr2qLpeL8L6CgmpiytlGTBmKiTeCSEtbxfS7hlUc0pL5b0FmVF5uqx722xXKeUoGlCdzbMJ4Jo1cjFNSGhVFwhfaLJ6rqamYY+qvDypmPNsUR8X1/zJ6oqh8CMoXie7+cbNlP5/wc1/T226B9UabrcUVlRVyfNUEyfKzLB3by1ZVyqAaED5S309HD4s96iKizs1qFosM9+3T4Jq2zYpQJgyRWZVQ4Y0f9LafCh8H0q3QFC4hFTcbRDU9EPMXlfxtZenZN0K1XHGAAAgAElEQVTlkqDNyJDvQ0vWlXI8DSh/8wTVmjVSbdfBQdWqYDh/XrpUrF4ts5HBgyWopkxpftms5rSUppfvhOBoiM+SrT+Cru0M0enPiVVUyHtsbUOX9dRULVlXyqE0oJyivl6eW1qzRpanOiCo2ry0VlUl986WL4ezZ2W/p9mzZVfg5vZ7qvocCpZB5QEIiZNCipibZBnwEr88yAxasq5UgNCAcpr6ejh6VIKqoECCKjraJ6dud3GC2y1bkGRny39DQ6WYIitLZiRNqTgg7ZOqj0NoMiTeA9ETwQT5L6Aaa1yy3rNnQ8l6fLz/xqSUAjSgnMvtlqBavVqCKj6+3fdNfFreffp0Q5PamhopQvDsURUcfOWx1sqSX8FfofYMhPeHxHtZeHZSyx0tOlPjkvUbbpDvZdAgLVlXyk80oJzOE1Rr18KFC+0Kqg4p766oaNijKj9fyudvv10eAL56idK6ofQzKHwPXAXsZxhvBP0NPxzav21fuyOVlsoyYFAQDB8uXdb79dOSdaU6kQZUoHC74fPPZenv/HmpSGvu/k8zOrS82+2Wqr/sbKkCDAtr2KOqX78rj7V1ULyBogsfEU8x9Bgt7ZMiUts3ho7gKVmvrJRu9ePHa8m6Up1EAyrQuN2yB9SaNXDuXKuDqlPKu0+ebNii3uWSIoS5c6VqrlERwlcOB5NlP+bL5j1wV0J0utyjCuvj2/H4SuMu6wkJUrI+eLCWrCvVQTSgApW1DUF19myrgqrTihNKS6VDxYoVMgtJTpZtP6ZPh6iohnEMKoSLK6DoE7AuiLkZEu6CUAcXKnhK1t1uuU81YYJ04bhe9w2lVKtoQAU6a+HECQmqM2ekBDz2+u2GOr16rq4Otm6V5b9Dh2SpbPp0vj3iXs4l9G0YR10pFGVD8Vr5c+w0eY4qxMEzlKtL1tPSpGT9hhu0ZF2pdtKA6io8QbV2rVTYXSeo/FrefeyYBNWmTVItd2mPKtLSGu7puIqg8AMo2QgmDOJnQdztEBx5/XP7m5asK+VTGlBdjbVyD2jtWumpFxNzTS89Rzx/VFws+1N98on0JExJkeW/W2+VGRZA7TkoeA/KciEoCuLnSq+/oABYRquulscD3G6ZTWVkyFJgpMNDVikH0YDqqqyFU6dkh9+TJ68IKkcElIfLBZs3y6zq2DF55mjmTAkrzx5V1SelK0XFXgiOgYQ7ITYTTICUfHu6rBujJetKtYIGVFdnrcyk1q6VoOrVi4VFUvbtiIDysFZ6EmZnw5YtDXtUzZ0LI0fKxb3ysARV1REITYSEe6DXJDABcq/H7ZYlwKoqmUmNGyffW1KSlqwr1QQNqO7CE1Tr1rFwbzAEB7N4pMvfo2paYaFU/q1c2bBH1dy5cMst0l6pYq8EVc0pCOsrO/v2HBdYF/naWlkCrKuTkvX0dOmy7qO2Vkp1BRpQ3Y21LPxv2Ytqccg+uSDGxzvz4l5b27BH1alTMtbLe1TFQtk2uUflOg8RAyFxPvQY4e9Rt155uZSsQ0PJemqqlqyrbk8Dqhta+OomABbfnSoP0x475uygshb275egys2V8u1Jky7tUXUjlG6WvajqLkLUCOlKETnI36NuPS1ZV+oK3gaU13dzjTHBwFbgtLX27vYMTnWwlBRYuFCen1q3ToKqZ09ZcnJSUBkDo0bJrwsXGrao//RTuPFGCarJP4CKjVCYDSf/XZb8EudBeIq/R+89Y6SQJS5Olv727oXt2+WHh4wMGDr0+rsbK9VNeT2DMsb8I5AB9GopoHQG5R+XZ1BP3HzlJ86elRnV0aNSTZeY6Kygaqy6WkI1J6fhAeVZs+C2W8G9FYqWg7sGek2WvajCkvw94rarqpJOHPX1smeVp8u6lqyrLs6nS3zGmH7AH4B/A/5RA8qZmg0oj7Nn5d7P4cPQo4ezg8rtht27Jah27JClsZtvhjnToNdBuLgKbD3ETpXy9JDrd9lwNGulZL20VP4+RoxoKFm/eosTpboAXy/x/Rx4Bmi2FMkY8zjwOEBqqgO7Vyu553H//dKMduNGaU/k1BlVUJCUa48bJ8GakyMl9evWSReHO+6D1LNQvB5KNsmDvvFzINi3uxV3CmPkebaYmIbu9vv2yUzK02VdS9ZVN9TiDMoYczdwp7X2m8aYGcDTOoNyphZnUFc7f15mVIcOycXQ6RfBykrpTZiT07CH1l2ZMLoMqrZDULi0ToqfBUER/h5t+3lK1l0u+SHC02VdS9ZVgPPlDCoTmGeMuROIAHoZY/5krX2ovYNUfpacDAsWSFBt2gQHDkg7oqQkZ1aXRUXBHXfIs1Pbt0v13/+9J89QzUmHyXWyaWLxakjIgphpEBTq71G3XViY3JsCKVlfvlx+ryXrqptoVZm5zqCcrdUzqKtduCAVdPv3Q3i4c4OqsVOnGvaoqq2FqYNheiiEnIGQOCmkiLkJjHPv5bSqRZXbLSXr5eVyX27sWKmC1JJ1FUA65DkoDahuIj9fZlT79jl7RtVYebl0qFixQjpWjE+AuT0gohhCk2XDxOiJjmyf1OYeinV1sgRYWyubK6ana8m6Cgj6oK5qv/x8mVHt2xc4M6r6etmjKidHlizHRMIdvSCqCsL7y8O+PUY76l6bT5r8Xl2ynpEBAwdqybpyJA0o5TsFBRJUe/fKPY/evZ0fVCDVcDk5sGkjjDQwJxp61EHEYEi6D6KG+HuEgI+70HtK1ktKpER9xAjpXKEl68pBNKCU7xUWyhYau3cHVlCVlMj+VCtXwI2VMDMKoixEjITk+yDCv49FdNg2KVd3WZ8wQbYFcXq1puryNKBUxykqkq0zduyQpb9ACaq6OgnYFR9BYh5MDYdIA6Gjod8DEJbc6UNaWhTCM3mR1FpICbUs6lPN/Pg633+hxl3Wk5Jg4kQtWVd+owGlOp4nqHbulFLv5OTACCqQbhqffAghO2FKKIQYYBQM/jKEJXTKEJYWhfBsXiRVtmE2E2ksP+lX1TEh5aFd1pWfaUCpznPxYkNQBQdDnz5+Cao2LZUVFcHqD6FmHYxFlr6qhsLIr0FUYscMFBnr9spgau21S21hxjIhqr7jN55sXLIeGnpll3VdAlQdyOfdzJVqVlycPDw7ZUrD0l9IiCz9Of3GfHw8LHgIah+AT1dASQ4MOQRHvw+FA2H0VyGpYzqn1zbzs2FzH/e5oCD5/uPjZelvzx7Ytk1L1pVj6AxK+V5xsZR6b9smAZWc3ClB5ZNiA2vhwEY4vxRuKINKCyeTYcQDMMy35emZ+3py2nXtTDMl1M2GUeU++zqtVlUlxRVut1T/TZyoJevKp3SJT/lfSYkEVW6uBFTv3jKz6iA+r4Y7uxNOvQkxF6HMDXt7wqB74OapsiTWTn67B+UtLVlXHUQDSjlHSYmE1NatsqyUnNwhQdVh5drFe+HknyG8EIrcsDkI+s2C2bfLflXt0GlVfO3VVMm6p8u6Uq2kAaWcp7RUlv0++0yWynwcVB0WUCCzifI9kPcmBBXC+XpY44L4DMi6Q0q226hDx90Rri5ZT0+X779nAG51ovxCA0o5V1lZQ1CBT4Kq02Yi1g1l2+D8O+AugjNuWFEFoTdKocjkya3+XgIuoBprXLI+eLDsX9W/v5asq+vSgFLOV1Ym22Zs2SJ/bmNQ+eVejq2XjRIL3of6YsgLgo9KoToWZs+G226TajgvBHRAeVxdst64y7qWrKuraECpwFFeLjOqLVtkKS05uVVFCMN2RTf5PFGnVMO5XVC8Foo+gvpyOBMJS/OhOBgyM2VWNWDAdU/RJQKqsbo6aTRcVyedKtLTZRfkdt6vU12HBpQKPOXl8gzVp5+2KqgG7owGrg0og+XzcWUdMNAmuKuh6BO4uEJ+fyEB3j4DF2pg5EjIypILdRMPMHe5gGqsslIehm5csj5okGzjorotDSgVuCoqGoLK7W4xqBz1PFF9ORTmyK6+1g3F/eDdM3CyULZtnzMHZszofgUFnpL10lIJ6ZEjpWQ9JUVL1rshDSgV+CorG4Kqvl6eo2ri5rsjnydyXYTCj6BkvezmWzUCsgtg50FpsDt1qsyqUjqmS4Wj1dfLrMpTsj5xYkOXddUtaECprqOyUvr8bdrUbFA59nmi2gtSSFH2GQRFgJkEq4th3WZwuWQWkZUF48YFTqNdX6qpkZL1+noJqIwMuPHG7jfD7GY0oFTXU1UlQbVxo9yAT06+IqgcfS+n5jQULIPyXRAcDT1mwpZqWP6JlGn36SPLf9Ond9+WQk2VrKem+qRrh3IWDSjVdVVVwa5dElQu1+WgcnRAeVQdk6CqPAgh8RB3BxwwkL0cjhyRcJo+XcKqTx9/j9Y/3G4JqooK+QHEU7Lep4+WrHcRGlCq66uubgiq2loWVg2FoCBnBxRIwUDlAShYCtUnZKPExHlwrhcsX95QHDJ+vCz/jRnTfS/MLpcsAdbWQkyMlqx3ERpQqvu4FFQL3zsB1kpAhYf7e1QtsxbKd0DBX6H2LISnQtK9UHMDrFwJH38sVW8pKRJUU6cGxvfVUSorpR+gtdKtwtNlXUvWA44GlOp+qqtlT6P16+Un7qSkwLh4WTeUboHC98BVCJFDIfFeCB0ghSHZ2XD8OPToATNnwu23d++Kt8Zd1oOCZPlPS9YDigaU6r5qahqCqrpaqv4CIqjqoHg9FH4I9aXQY4wEVXg/OHhQgmrrVrlAZ2TIrGrEiO67/AdS/VdYKH/PUVENJeuJHbcbsmo/DSilampg796GoAqUGZW7Bi6uhqIccFdCdAYk3iP3qgoKYMUKWQKsqJA2SllZcPPN2qC1pkbCytNlXUvWHUsDSimP2lrYtw/WrpUKwECZUdVXQtEKuPiJzK5iboaEuyA0Xi7GGzbIrCovTxrT3nabLP/pNu1Ssl5UJLPLIUMauqxrybojaEApdTVPUK1bJzfck5IC45mjutJLXSnWyZ9jp0N8FoREy3Lfvn0SVNu2yT2ZKVNkVjVkiH/H7QRXl6yPGydtlrRk3a80oJRqTm0t7N8vQVVeLkEVFeXvUbXMVQgFH0DpJjBhED8b4mZD8KWQPX9eytRXr5aZ4uDBElRTpnTIDsYBp3HJemxsQ8l6TIy/R9btaEAp1RKXCw4cgDVr5CfsxMTACKqac1KaXr4NgnpAwlyInQFBl+5BVVXJcuby5XD2rFyMZ8+GWbP0YuzhKVl3u6VbhZasdyoNKKW8FahBVX0C8pdB5T4IiZH7UzGZ0pwW5OK7a5cs/+3aJbOoW26RWdXAgX4dumNYK+XqJSXy/oweLQ9G9+2rJesdyGcBZYyJANYC4UAIsMRa+/+u9xoNKBWQXC4p5167Vnb7DZSgqjwE+Uuh+hiEJknFX3QGmEbNZ0+flhnV2rVSYDFihGymmJGhF2IPLVnvNL4MKAP0sNaWG2NCgfXAt621nzb3Gg0oFdDq6hqCqrQUEhLkIVknsxYq9kifv5o8CEuBpHnQY+yVxQAVFXKPavly2fU2MVEq/2bO1HLsxjxd1j1NiT0l607/dxAgOmSJzxgThQTU31lrNzd3nAaU6hLq6uDwYbmgl5RIUDn9Im7dUJYr96hc+RAxCJLmQ9TwK49zu6XqLztbqgDDwqSV0ty5Uo6tGpSVSSWgMTB0qFQCasl6u/g0oIwxwUAuMAR42Vr7vSaOeRx4HCA1NTX9xIkTrR60Uo5UX39lUMXHB0BQ1UPJRij8AOqKIWqkdKWIHHjtsSdPSlBt2CDLnKNHy32qCRO65x5VzWmqZH3UKJlhacl6q3TUDCoWeBd40lq7p7njdAaluiRPUK1ZIxeqQJhRuV1QvAaKsmU7+p4T5B5VeN9rjy0thVWrpFNFUZE80Dx3rmz/EQj34jqTp2Td5WooWR86VKskvdRhVXzGmP8HVFhrX2zuGA0o1aXV18veTWvWyIU8Ph6io/09quurr4KLK+HiCmml1GsKJN4NoU0UANTVSc+/7Gw4dEhKr6dNk7C64YbOH7vTVVbKv4P6eilZT0+XKsnu3Hm+Bb4skkgCXNbaYmNMJLAc+Hdr7fvNvUYDSnUL9fVw9KgEVUGBBFWvXv4e1fXVlUuPv+LVcr8qdiok3AkhMU1v+HjsmATVpk3y/Y4bJ8t/Y8d26rJWQGxG6SlZLy2VykhPyXpKii6VXsWXATUW+AMQDAQBb1lrf3i912hAqW7F7W4Iqvz8wAgq10Xpml6yQZ6biruNR4vnU2F6NB0CxcXwySeyR1VJiTwnNHcu3HprpzzcGhAB1VhdXUPJes+eUrI+bJiWrF+iD+oq1dncbplxeIIqLs75QVV7AQreY+nFMP69biFnSSAl1M2iPjXMj6+79niXS3b8zc6Gzz+Xe1OePap69+6QIS4tCuGZvEhqLaSEWhb1qW56bE5VXS1hVV8vBRXp6d2+ZF0DSil/cbvl4r1mjfTHi4tz9M3zpUUhPJsXQZVtWIaKNHX8JKWK+QnNXB+slYKR7GzYskX+nJ4uy38jR/ps+U/GFkmVbThfpLH8pF9VYIWUh2ejRejWJesaUEr5m9stO+GuWQPnzjkuqDzLZtsrg6m11wZKH4r4auRO1plbeGNoTfMnKixs2KOqvFwKBebOhcxMr/ao8oyjKc2NLcxYJkTVX/PxgFkCvLpkfeZM2RKkm/A2oPTOnVIdJShIlnIefhgefFC29jh+vOEnaIeobeZn1PPE8U37v7zofg7KtsksqSkJCfL9/fKX8Ld/K8f97//C3/89vPmmBJiPx9bcxwNGUJC8b6mp8u9i/35/j8iRdAalVGexFk6ckBnVmTPy/ExsrL9HRea+npx2Xfuzakqomw3910n7pNpzEJ56qStFC0t41soFNzsbcnPl2MmTZflv6NBWLf9dd2yjyr0+j6OVlsq9yi9+0d8j6TTezqB0kxilOosx8nzMgAESVGvXyowqJsavu+Au6lPd5H2eRX2qIXoC9BwHpZuh4D3Iewkih0pQRQ5u+oTGSIeFUaPgwgVZ/lu1SoorbrxRlv9uusmr+y7XHZvq8nQGpZS/WCtthtaulW3b/RhUXlXKuV1Qsl52960vhR5p0j4pol/LX6C6WjaIzMmR2WNMTMMeVS3MIgO+iq8lOoNq/jgNKKX8zFo4dUou4CdPysUqPt7fo2qeuwYuroKi5eCuhOhJ0pUiLNmL17ph924Jqh075IHWm2+W5b8bb+z4sTuRBlTzx2lAKeUQ1spMat06WQJ0elDVV0DRCmmhZOsg5hbZNDHUy1ng2bMSVGvXygxr2DAJqoyM7rVFvQZU88dpQCnlMFcHVXS0VHw5VV2pLPsVr5X7T7EzID4LQrxspFtZKYUjOTlyzyo+vmGPKqc/6OwLGlDNH6cBpZRDWSs74a5fLw/+RkfLxdupWzu4CqDgAyj9FEwYxM+GuNkQHOnd691u2L5dqv/27pUiisxMmVWlpnbs2P1JA6r54zSglAoAnqA6dsz5QVVzVjZMLN8OwT1kNhU7HYJafmj3slOnZEa1fj3U1kpF4Ny50q2iqzVe1YBq/jgNKKUCyJkzsvR37Jg0IU1IcG5QVZ+A/GVQuQ9CYuX+VMwt0pzWW+XlUqK+fLk88JuUBHPmwIwZXaeXnQZU88dpQCkVgM6eldnFkSNyoU5MdG5QVR6C/KVQfQxCkyBxHkSng2nFTKi+XvaoysmBAwdkr6Vp0ySsUlI6buydQQOq+eM0oJQKYGfPwsaN0rg1Ksq5QWUtVOyWrhQ1pyE8RZ6h6pHW+vF+/rkE1caNsq3F2LENe1RdZ/nPsVt2aEA1f5wGlFJdwLlzcsE+dMjhQeWGsly5R+XKh4gbIeleiBre+nOVlDTsUVVcLLv9zpkjM6vIKwszHP2wrwZU88dpQCnVhZw/L0F18KBcpJOSHBpU9VCyEQo/gLpiiBolQRUxoPXnqquDzZul+u/oUfm+Z8yQsEpOdv6WHRpQzR+nAaVUF3ThggTVgQOy421SkiOq367eWiPU1jLHfsJ8+x69KGczGSwO+gKnTdvuKw09dZCsT9/npr0bCbJucodP4uG7vkdFSPg1xza3ZUdHaXZpUQOqWd3ocW2lupHevWH+fAmqTz+V7uLh4Y4JKg+XCeMDcwcr7QzustncZT9ikjuXtSaTJeY+8k1Sq853uP9wDvcfzp/mPsycLdnM3ppDZXDTTWkDfsuObkBnUEp1B/n5ElT79skGeb17OyqoLqsrh6JsKF4thRWxt0LCHRDSxo0ea2vJ3BPF6eBrN0V0zJYdOoNqlgP/hSqlfC4pCe65B77+dRgyRB6EPX9eujc4SUhP6H0/DPqRPDNVvBaO/bOUqddXtP58YWEsGij3nBqLdFWzaMe7sgTaAT+kK9/QJT6lupPERAmqm2+WGdXevc6cUYXGQZ8vQ/ztsg9VUY6EVfwciJsJQdfeU2qOFEJUNVTxBdex6NR65q9cDO9Xyh5dWVnynnixR5XqPLrEp1R3VlgoFXC7dzszqDyq8+QZqordENxLlv1ipkJQOwKluloeds7JkVZSvXo17FHVmfty6RJf88dpQCmlKCqCLVtkj6awMEhOdmZQVR2V5b6qwxASL/tQ9bqpdV0prmYt7NkjZeo7dsj3fdNN0vtvyBDfjb05GlDNH6cBpZS67OLFhqAKDXVmUFkLlfslqGpOQlgfaZ/Uc0L7n/k6d65hj6qqKgmorCyYPLnj9qjSgGr+OA0opdQ1GgdVSIgEVXArmrx2BmulY3rBX6H2HISnQtJ8iBrZ/qCqrJSQysmRYpK4ONmj6rbbfL9HlQZU88dpQCmlmlVcfGVQ9e7twKByQ+lmKaaoK4LIoRJUkYPbf263G3bulOW/3btlVnnLLTKrGtCGrhdN0YBq/jgNKKVUi0pK4LPPYNs2CSgnzqjcLihZL7v71pdKI9rEeyGin2/On5fXsEdVTQ2MHNmwR1V73gsNqOaP04BSSnmtpARyc2Xri6AgCaqOujfTVu4auLgKipaDuwqiM6SYIizZN+cvL4fVq2WPqoICKd33bFHf08tt7hvTgGr+OA0opVSrlZZKSDk5qOoroGgFXFwJtg5iMiHhTnnGyifnr5ewzslpaCU1darMqvq1YtamAdX8cS0FlDGmP/BHoA/gBn5trf3F9V6jAaVUN1FaKst+n30mhQlODKq6EijMlgd9jYHYGbINfUgbZjvNOX68YY8qlwvS0uQ+1bhxLVdBakA1f5wXAXUDcIO1dpsxJhrIBeZba/c19xoNKKW6mbKyhqACZwaVqwAK3peCiqBwiJsFcbMhOLLl13qrtBRWroQVK6QSMjlZZlTTpsk+Xc29RgOq6eNau8RnjFkG/NJau6K5YzSglOqmyspg+3ap/ANnBlXNGan4K98OwT1kNhU7HYLCfPc16urkPcjOhiNHZI+qadMkrPr0ufJYDajmj2tNQBljBgJrgTHW2tKrPvc48DhAampq+okTJ1ozXqVUV1JeLkG1ebM8r5Sc7Lw+d9UnIH8ZVO6DkFhIuEsa1BofVyceOSLLf59+KmXr48fL8t+YMbLkqAHV/HHeBpQxpiewBvg3a+071ztWZ1BKKQAqKiSoPv3UuUFVeVCCqvoYhCZJV4ro9Pa1T2rKxYsNW9SXlkJKisyoxo2TbvMaUNce501AGWNCgfeBHGvtz1o6XgNKKXWFigp52Nczi3BaUFkrjWjzl0HtaQhPkWeoeqS1vyvF1Vwu2LRJlv+OH5d7Uw88AL//vW+/joP5bEddY4wBfgvs9yaclFLqGj16QGYmTJjQEFT19dKZIsyH937ayhjoORZ6jIGyXGmfdPoViLjxUvukYb77WqGhcj/q1lvh0CF4773mCyi6OW+q+KYC64DdSJk5wHPW2g+be43OoJRS11VZCbt2SVm2k4LKw9ZDyUYofF/K1KNGQdK9EOGj9kaN6T2oZrU4g7LWrgd8PMdVSnVrUVGypcW4cdLrbuNGqXxLTnZGUJlg2W6+1xQoXiPb0J/4iXRMT5wH4Tf4e4TdgsPqP5VS3UpkZENQeWZULpdzgiooTHb1jZkKFz+Goo+hfIfsQZV4F4Qm+nuEXZoGlFLK/yIjYcqUK4OqpkaCKtz77d07THAkJN4jXSiKcqB4NZRugdhpsrtviI+34FCABpRSykkiImRzwLFjZXuLDRugtlbuUTkhqEKioff90oWi8ANZ/ivZAHG3yUwruIe/R9ilaEAppZwnIgImTZKg2rMH1q2ToEpKks/5W2gc9HlIQqngfblHVbwW4udA3ExppaTaTQNKKeVc4eGy39KYMRJU69fDhQsyo3JCUIUlQ9+vQ/VcKFgGBUule3rCnRA7FYxeYttD3z2llPM1Dqp9+2RG5aSgiugH/b4FlUckqC68CRdXQMLdUgno664U3YQGlFIqcISHy8O+o0dfGVRJSVJo4W9RQ6D/P0p/v/xlcO4PUlSReC/0HO/7rhRdnAaUUirwhIVJ09VRoxqCKj/fGUFlDPQYLQ/3lm+TzulnXpWHfBPvhaiRGlRe0oBSSgWuxkG1f/+VMyp/tw8yRprO9hwve1AVvA95L0HkMGmfFHmjf8cXADSglFKBLyxMnqEaNQoOHIA1a6CgABITHRBUwbKNR/QkKFkPhR/Cyf+Q3n+J9wLR/h2fg+mdO6VU1xEaKtutP/EE3HUXVFfDiRPS+8/fgkKlBP3GH0kwVR5m6ZGVZB6PZtDOaDJfWMnS7af9PUpH0RmUUqrrCQ2Vir/hw+HgQVi7VmZUCQnSWd2fgiIg4Q6WModnT0dTZeUyfLq4imff2Q3A/Akp/hyhY2hAKaW6pIWvbmr4Q9B4CKuEUyXSPT0kBIJ9vHNuK22vDKbWXlksUeWq55klu3hjy0k/jer6Fj9xc6d+PQ0opVTXZwxE9YDIKKiqguJiWf4LDfVbUNU2s9NRbb276U90QxpQSqku6bo/7dfXw+HDUkxRXAzx8dCzZ+cNDsjc15PTrmvLzVNiIzt9puJUWiShlOp+gvjr/YYAAAWDSURBVINhxAh47DGYP1+2fD9xAsrLO20Ii/pUE2munEZFhgazaO7wThuD0+kMSinVfQUHSyHFkCFw5IjMqE6ckBlVdMeWf8+PrwOq+OmZMM7UB9M3NopFc4drgUQjGlBKKeUJqqFDrwyquDjZjr2DzI+vY35I0aUt3+/usK8TqDSglFLKIygIhg2TGdXRoxJUx4/LjKoDg0o1TQNKKaWuFhQks6nBg+Hzz2H1ag0qP9CAUkqp5gQFSUgNGiRB5ZlRxcVBTIy/R9flaUAppVRLGgfV8eMaVJ1EA0oppbwVFAQ33tgQVGvXalB1IA0opZRqLWMkpAYOlGo/z4wqNlZ+KZ/QgFJKqbYyRkJqwAA4ebJhRhUTI7Mq1S7aSUIppdrLGAmphx6CL31JKv2OH4eLF/09soCmMyillPIVT1ClpsKpU7LD7/HjEljx8f4eXcDRgFJKKV8zRkLqS1+CvDwNqjbSgFJKqY5iDPTvD1/8Ipw+DevXy/NU0dGyeaK6rhbvQRljfmeMuWCM2dMZA1JKqS7HGOjXDx58EL7yFUhMlBlVYaG/R+Zo3hRJvAZkdfA4lFKqe/AE1Ve/CklJcP68v0fkWC0u8Vlr1xpjBnb8UJRSqhtJSYGFC+HMGais9PdoHMln96CMMY8DjwOkpqb66rRKKdW19e3r7xE4ls+eg7LW/tpam2GtzUhKSvLVaZVSSnVT+qCuUkopR9KAUkop5UjelJm/AWwChhtj8owxX+/4YSmllOruvKni+2JnDEQppZRqTJf4lFJKOZIGlFJKKUfSgFJKKeVIGlBKKaUcyVhrfX9SY/KBEz46XSJQ4KNzKaHvqe/pe+pb+n76npPe0wHW2hY7OnRIQPmSMWartTbD3+PoSvQ99T19T31L30/fC8T3VJf4lFJKOZIGlFJKKUcKhID6tb8H0AXpe+p7+p76lr6fvhdw76nj70EppZTqngJhBqWUUqob0oBSSinlSI4NKGNMljHmoDHmiDHmn/w9nkBnjOlvjFlljNlvjNlrjPm2v8fUVRhjgo0x240x7/t7LF2BMSbWGLPEGHPg0r/Xm/09pkBnjPnOpf/v9xhj3jDGRPh7TN5wZEAZY4KBl4E7gFHAF40xo/w7qoBXB3zXWjsSuAn4lr6nPvNtYL+/B9GF/ALIttaOAMah7227GGNSgH8AMqy1Y4Bg4EH/jso7jgwoYDJwxFp7zFpbC7wJ3OvnMQU0a+1Za+22S78vQ/6nT/HvqAKfMaYfcBfwG3+PpSswxvQCpgG/BbDW1lpri/07qi4hBIg0xoQAUcAZP4/HK04NqBTgVKM/56EXU58xxgwEJgCb/TuSLuHnwDOA298D6SJuBPKB319aNv2NMaaHvwcVyKy1p4EXgZPAWaDEWrvcv6PyjlMDyjTxMa2H9wFjTE/gbeApa22pv8cTyIwxdwMXrLW5/h5LFxICTAR+Za2dAFQAeg+6HYwxccgK1CCgL9DDGPOQf0flHacGVB7Qv9Gf+xEgU1InM8aEIuH0urX2HX+PpwvIBOYZY44jy9C3GWP+5N8hBbw8IM9a65ndL0ECS7XdbOBza22+tdYFvAPc4ucxecWpAfUZMNQYM8gYE4bc0Purn8cU0IwxBlnX32+t/Zm/x9MVWGuftdb2s9YORP6NrrTWBsRPpk5lrT0HnDLGDL/0oVnAPj8OqSs4CdxkjIm6dB2YRYAUnoT4ewBNsdbWGWP+HshBKk5+Z63d6+dhBbpM4CvAbmPMjksfe85a+6Efx6RUU54EXr/0w+kx4BE/jyegWWs3G2OWANuQat7tBEjbI211pJRSypGcusSnlFKqm9OAUkop5UgaUEoppRxJA0oppZQjaUAppZRyJA0opZRSjqQBpZRSypH+PwwPi/1NOXioAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1eeb5b1bcc0>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# plot data with results\n",
+ "plt.figure(figsize=(6, 4))\n",
+ "plt.errorbar(X, Y, xerr=sigma_x, yerr=sigma_y, fmt='o', label='oberservations')\n",
+ "plt.plot(X, fit.a+fit.b*X,'r-', label='our fit')\n",
+ "# rough visualization of error estimates\n",
+ "plt.fill_between(X, a-sa + (b-sb)*X, a+sa + (b+sb)*X, color='red', alpha=0.35)\n",
+ "plt.plot(X, np.polyval(np_fit, X), label=r'np fit (neglects $\\sigma_x$)')\n",
+ "\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We see that it makes quite a difference to neglect the errors in x. Of course it depends on your data set if the errors are marginal or not."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Compare against scipy ODR"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 150,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Beta: [-0.4805337 5.4799117]\n",
+ "Beta Std Error: [ 0.07062028 0.35924657]\n",
+ "Beta Covariance: [[ 0.00336226 -0.01647255]\n",
+ " [-0.01647255 0.08700776]]\n",
+ "Residual Variance: 1.483294149297378\n",
+ "Inverse Condition #: 0.09285611904588402\n",
+ "Reason(s) for Halting:\n",
+ " Sum of squares convergence\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Lets compare our code against scipy orthogonal distance regression, which should be correct.\n",
+ "import scipy.odr as so\n",
+ "\n",
+ "#1. Define the function you want to fit against.\n",
+ "def f(B, x):\n",
+ " '''Linear function y = m*x + b'''\n",
+ " return B[0]*x + B[1]\n",
+ "\n",
+ "#2. Create a Model.\n",
+ "linear = so.Model(f)\n",
+ "\n",
+ "#3. Create a Data or RealData instance.\n",
+ "mydata = so.RealData(X, Y, sx=sigma_x, sy=sigma_y) # should provide std errors not var\n",
+ "\n",
+ "# 4. Instantiate ODR with your data, model and initial parameter estimate.\n",
+ "myodr = so.ODR(mydata, linear, beta0=[-0.5, 5.5])\n",
+ "\n",
+ "# 5. Run the fit.\n",
+ "myoutput = myodr.run()\n",
+ "\n",
+ "# 6. Examine output.\n",
+ "myoutput.pprint()\n",
+ "\n",
+ "odr_b, odr_a = myoutput.beta\n",
+ "odr_sb, odr_sa = myoutput.sd_beta"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 151,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1eeb4a9c0b8>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot ODR fit against our python fit\n",
+ "plt.figure(figsize=(6, 4))\n",
+ "plt.errorbar(X, Y, xerr=sigma_x, yerr=sigma_y, fmt='o', label='oberservations')\n",
+ "plt.plot(X, fit.a+fit.b*X,'r-', label='our fit')\n",
+ "plt.plot(X, odr_a + odr_b * X, 'g--', label='odr fit')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Very nice, the parameter estimates fall together perfectly! But what about the quality of error estimates?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Comparison with a literature result"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 162,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# literature results (copied from Reed 1992)\n",
+ "m, c = (-0.4805, 5.4799)\n",
+ "S = 11.866\n",
+ "sm_obs, sc_obs = (0.0702, 0.3555)\n",
+ "sm_adj, sc_adj = (0.0706, 0.3592) # these are the relevant ones if I understood correctly"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 163,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(5.4799116973248427,\n",
+ " -0.48053369607371221,\n",
+ " 0.35924657332337567,\n",
+ " 0.070620283604428083)"
+ ]
+ },
+ "execution_count": 163,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# ODR agrees very well!\n",
+ "odr_a, odr_b, odr_sa, odr_sb"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 164,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(1.105, 0.577, 0.35924652255111161, 0.070620269528770943)"
+ ]
+ },
+ "execution_count": 164,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Our naive implementation agrees also! :)\n",
+ "prefactor = (S / np.size(X))\n",
+ "a, b, sa, sb"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Monte Carlo testing\n",
+ "To check the methods, we sample our line many times and fit. By averaging we check if our estimates converge the same values and its sample variances match with the estimated variances."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 165,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "results = []\n",
+ "results_odr = []; S_odr = []\n",
+ "repetitions = 2000\n",
+ "for i in range(repetitions):\n",
+ " N = 101\n",
+ " a = 1.105\n",
+ " b = 0.577\n",
+ " x = np.linspace(-1, 1, N)\n",
+ " y = a + b * x\n",
+ " sigma_x = 0.1\n",
+ " sigma_y = 0.15\n",
+ " error_x = np.random.randn(N) * sigma_x\n",
+ " error_y = np.random.randn(N) * sigma_y\n",
+ " X = x + error_x\n",
+ " Y = y + error_x\n",
+ " fit = York_eq_fit(X, Y, sigma_x, sigma_y)\n",
+ " result = fit.run()\n",
+ " results.append(result)\n",
+ "\n",
+ " mydata = so.RealData(X, Y, sx=sigma_x, sy=sigma_y)\n",
+ " myodr = so.ODR(mydata, linear, beta0=[0.5, 1.])\n",
+ " myoutput = myodr.run()\n",
+ " result_odr = *myoutput.beta, *myoutput.sd_beta\n",
+ " results_odr.append(result_odr)\n",
+ " S_odr.append(myoutput.sum_square)\n",
+ "\n",
+ "\n",
+ "results = np.array(results)\n",
+ "results_odr = np.array(results_odr)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 166,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "True values a, b: 1.105 0.577\n",
+ "Average of estimates: 1.10497185974 0.589964877481\n",
+ "Std of estimates: 0.00407683840214 0.00672996955892\n",
+ "Average of estimated std: 0.00413703767094 0.00699568925361\n"
+ ]
+ }
+ ],
+ "source": [
+ "print('True values a, b:', a, b)\n",
+ "print('Average of estimates:', *np.mean(results, axis=0)[0:2]) \n",
+ "print('Std of estimates:', *np.std(results, axis=0)[0:2])\n",
+ "print('Average of estimated std:', *np.mean(results, axis=0)[2:4])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 167,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "True values b, a: 1.105 0.577\n",
+ "Average of estimates: 1.10497186026 0.589964657057\n",
+ "Std of estimates: 0.00407683973494 0.00672996788168\n",
+ "Average of estimated std: 0.00413703813533 0.00699568854485\n"
+ ]
+ }
+ ],
+ "source": [
+ "print('True values b, a:', a, b)\n",
+ "print('Average of estimates:', *np.mean(results_odr, axis=0)[0:2][::-1]) \n",
+ "print('Std of estimates:', *np.std(results_odr, axis=0)[0:2][::-1])\n",
+ "print('Average of estimated std:', *np.mean(results_odr, axis=0)[2:4][::-1])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## References\n",
+ "Derek York: Least-Squares Fitting of a Straight Line, Canadian Journal of Physics, 44 1079 (1966). \n",
+ "http://www.nrcresearchpress.com/doi/10.1139/p66-090#.W7pY7Wgzb4Y \n",
+ "\n",
+ "B. Cameron Reed: Linear least-squares fits.. \n",
+ "https://aapt.scitation.org/doi/10.1119/1.15963 \n",
+ "\n",
+ "Reed: Comments on parameter variances... \n",
+ "https://aapt.scitation.org/doi/10.1119/1.17044 \n",
+ "\n",
+ "Derek York, Norman M. Evensen, Margarita Lopez Martinez and Jonas Basabe Delgado: Unified equations for the slope, intercept, and standard errors of the best straight line, Am. J. Phys. 72 3 (2004). \n",
+ "https://aapt.scitation.org/doi/10.1119/1.1632486"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "hide_input": false,
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.12"
+ },
+ "toc": {
+ "nav_menu": {},
+ "number_sections": true,
+ "sideBar": true,
+ "skip_h1_title": false,
+ "toc_cell": false,
+ "toc_position": {
+ "height": "658px",
+ "left": "0px",
+ "right": "1388px",
+ "top": "110px",
+ "width": "212px"
+ },
+ "toc_section_display": "block",
+ "toc_window_display": true
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Exercise1/.ipynb_checkpoints/Exercise_1-checkpoint.ipynb b/exercises/Exercise1/.ipynb_checkpoints/Exercise_1-checkpoint.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..d8992d719658d6778e674df747001c97878ab6d8
--- /dev/null
+++ b/exercises/Exercise1/.ipynb_checkpoints/Exercise_1-checkpoint.ipynb
@@ -0,0 +1,572 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You **can** use this notebook as template to solve your exercises. The **TODO:** indicates where you should put the missing code. You are also free to start a new notebook from scratch."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 1. Basic plotting with matplotlib"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In our first example, we plot a simple curve with matplotlib."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## a) Generating set of data"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First we need to create an array of our x values for the curve to plot."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Import basic libraries:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "%matplotlib inline\n",
+ "# the commands above is needed to have the plots displayed inside this \n",
+ "# notebook instead of in an external window"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "None\n"
+ ]
+ },
+ {
+ "ename": "TypeError",
+ "evalue": "'bool' object is not iterable",
+ "output_type": "error",
+ "traceback": [
+ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+ "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
+ "\u001b[0;32m<ipython-input-2-5c30e497ab77>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;31m# test your function, it should print 'True' twice\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m print(all(equallySpacedNumbers(2.0,10.0,9) \n\u001b[0;32m---> 10\u001b[0;31m == [2.,3.,4.,5.,6.,7.,8.,9.,10.]))\n\u001b[0m\u001b[1;32m 11\u001b[0m print(all(abs(equallySpacedNumbers(-1.2,0.2,6) \n\u001b[1;32m 12\u001b[0m - [-1.2,-0.92,-0.64,-0.36,-0.08,0.2]) < 1e-6))\n",
+ "\u001b[0;31mTypeError\u001b[0m: 'bool' object is not iterable"
+ ]
+ }
+ ],
+ "source": [
+ "def equallySpacedNumbers(start, end, number):\n",
+ " return # TODO: use numpy to return a 1-d array of equidistant\n",
+ " # floating point numbers between start and end\n",
+ "\n",
+ "# look at the function output by printing:\n",
+ "print(equallySpacedNumbers(2.0,3.0,4))\n",
+ "\n",
+ "# test your function, it should print 'True' twice\n",
+ "print(all(equallySpacedNumbers(2.0,10.0,9) \n",
+ " == [2.,3.,4.,5.,6.,7.,8.,9.,10.]))\n",
+ "print(all(abs(equallySpacedNumbers(-1.2,0.2,6) \n",
+ " - [-1.2,-0.92,-0.64,-0.36,-0.08,0.2]) < 1e-6))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Note that in the second case, we can not make an exact comparison due to rounding errors. Having such test functions is useful in case we want to replace our generator of equally spaces numbers with a different (e.g. faster) version later."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### b) Simple plots"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As example, we now want to make a plot of the fall time vs. the height of which an apple is dropped. For both x and y we need one-dimensional numpy arrays of the same length.\n",
+ " \n",
+ "\n",
+ "You find some help on basic plot functionalities here: \n",
+ "https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html\n",
+ " \n",
+ "For more special plots, first have a look in the gallery: \n",
+ "https://matplotlib.org/gallery/index.html \n",
+ "which already includes many common types of plots."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def Falltime(x, g):\n",
+ " return np.sqrt(2*x/g)\n",
+ "\n",
+ "# create a dataset\n",
+ "true_g = 9.8\n",
+ "data_x = # TODO: create array of 50 equally spaced points \n",
+ " # between 0 and 2.0 (height in m)\n",
+ "data_y = # TODO: compute fall time for all height values\n",
+ "\n",
+ "# the simplest way to plot\n",
+ "# TODO: create plot out of x/y data\n",
+ "\n",
+ "# always label the axes (the '$...$' for latex style)\n",
+ "# hint: use raw strings, e.g. r'height [m]'\n",
+ "# TODO: set labels for x and y-axis\n",
+ "\n",
+ "# make the plot appear\n",
+ "# TODO: draw plot"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### c) Load measurements from text file"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Above plot now shows the prediction of the fall time. To make a comparison with our measurements, we first have to load them from the text file **measurement.txt**.\n",
+ "\n",
+ "Numpy provides a very convenient function for this purpose! look at the Numpy reference: \n",
+ "https://docs.scipy.org/doc/numpy/reference/generated/numpy.loadtxt.html"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# load data from textfile\n",
+ "# format: height[m] time[s] height_error[m] time_error[s]\n",
+ "measurements = # TODO: load measurements from measurement.txt\n",
+ "\n",
+ "# look at it\n",
+ "print(\"shape:\", measurements.shape, \"\\n\")\n",
+ "print(\"data:\\n\", measurements, \"\\n\")\n",
+ "print(\"first column:\", measurements[:, 0], \"\\n\")\n",
+ "print(\"last row, first two columns:\", measurements[-1,0:2])\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### d) Plot with error bars"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we want to plot the measurement data (from the text file) with error bars together with the prediction from theory. In many cases there is a non-negligible uncertainty also on the theoretical prediction. One way of visualizing this is to plot an error band, which in practice can be done by shading the area between two curves. \n",
+ "In this example, use $\\sigma_g = 0.4 \\frac{\\text{m}}{\\text{s}^2}$ as the uncertainty of $g$. \n",
+ " \n",
+ "There are examples of plots with error bars in the gallery linked above. For more detailed options look at the reference here: \n",
+ "https://matplotlib.org/api/_as_gen/matplotlib.pyplot.errorbar.html"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# create additional dataset for the uncertainty band\n",
+ "# use 0.4 m/s^2 as symmetric uncertainty on g\n",
+ "data_y_m = # TODO: g varied down by the uncertainty\n",
+ "data_y_p = # TODO: g varied up by the uncertainty\n",
+ "\n",
+ "# plot uncertainty band of theory prediction\n",
+ "# TODO: plot filled area between the two curves created \n",
+ "# above, hint: use plt.fill_between\n",
+ "\n",
+ "# plot mean value on top\n",
+ "# TODO: add curve for nominal value of g in a different \n",
+ "# color than the uncertainty band\n",
+ "\n",
+ "# TODO: label the axes\n",
+ "\n",
+ "# plot measurement with errors\n",
+ "# TODO: plot measurements loaded from text file on top of \n",
+ "# the theory curve with circular markers, no line between \n",
+ "# them and also include errorbars! hint: plt.errorbar\n",
+ "\n",
+ "\n",
+ "# legend\n",
+ "# TODO: create a legend, hint(1): you can give a label to the \n",
+ "# individual plots with e.g. label='theory' in the creation \n",
+ "# of the plots above\n",
+ "# hint(2): use numpoints=1 as argument for plt.legend to \n",
+ "# have only 1 point of your measurements in the legend\n",
+ "\n",
+ "\n",
+ "# optional: set axis limits\n",
+ "# TODO: set axes limits to [0, 2.0] for x and [0, 0.8] for y-axis\n",
+ "\n",
+ "# optional: grid lines\n",
+ "# TODO: display grid lines\n",
+ "\n",
+ "# save the figure to a pdf file\n",
+ "# TODO: save the plot as \"exercise-1-plot.pdf\"\n",
+ "\n",
+ "# make the plot appear\n",
+ "# TODO: show the plot in the notebook"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### e) Histograms"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "A qualitative way to check compatibility of the measurement points with theory is to make a histogram of the pulls (pulls are defined below in the code). Create the histogram of pulls and overlay the expected pull distribution, which is Gaussian. \n",
+ " \n",
+ "Instead of putting the formula for the Gaussian yourself, you can use `scipy.stats.norm.pdf`, see here:\n",
+ "https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [],
+ "source": [
+ "import scipy.stats\n",
+ "\n",
+ "# as approximation we ignore the errors on the measured \n",
+ "# height since they are relatively small!\n",
+ "\n",
+ "heights = measurements[:, 0]\n",
+ "times = measurements[:, 1]\n",
+ "time_errors = measurements[:, 3]\n",
+ "predictions = Falltime(heights, true_g)\n",
+ "\n",
+ "# compute pulls\n",
+ "pulls = (times - predictions)/time_errors\n",
+ "\n",
+ "# histogram of pulls\n",
+ "# TODO: create normalized histogram (meaning sum of all bin \n",
+ "# contents equals 1) with 10 bins\n",
+ "# hint: use histtype='stepfilled'\n",
+ "\n",
+ "# unit gaussian\n",
+ "x = # TODO: 50 points between -3.0 and 3.0\n",
+ "y = # TODO: unit gaussian, hint: scipy.stats.norm.pdf\n",
+ "plt.plot(x, y, '--', color='r', linewidth=3.0)\n",
+ "\n",
+ "# always label the axes, also for histograms\n",
+ "# TODO: labels\n",
+ "\n",
+ "# annotation\n",
+ "# TODO: create a annotation with text 'unit gaussian' pointing \n",
+ "# to the curve plotted above. hint: plt.annotate\n",
+ "\n",
+ " \n",
+ "# save the figure to a pdf file\n",
+ "# TODO: save as 'exercise-1-histogram.pdf'\n",
+ "\n",
+ "# TODO: show in notebook"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### f) (optional) Creating a text file of toy measurements"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# create toy experiments instead of real measurements here\n",
+ "\n",
+ "# TODO: create a text file in the same format as the \n",
+ "# 'measurement.txt' with 1000 random toy experiments, \n",
+ "# assuming the same uncertainties as above\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 2. Error propagation with Python"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We consider a LC circuit with resonance frequency $\\omega_0 = \\frac{1}{\\sqrt{LC}}$. \n",
+ "$C = 150 \\pm 8 \\,\\text{pF}$ \n",
+ "$L = 1 \\pm 0.1 \\,\\text{mH}$ \n",
+ " \n",
+ "What is the resonance frequency and its uncertainty? "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## a) Calculation by hand"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The mean value is computed to: \n",
+ " \n",
+ "$\\omega_0 =$ \n",
+ " \n",
+ "Since the uncertainties for both quantities come from independent electronic components, they can safely be assumed as uncorrelated and one can compute the uncertainty of $\\omega_0$ to \n",
+ " \n",
+ "$\\sigma_{\\omega_0} =$ "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## b) Installation of 'uncertainties' package"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "There are packages, which make handling of uncertainties very easy, e.g. the package simply called \"uncertainties\". It is not included in standard packages of Anaconda and therefore has to be installed with: \n",
+ "`conda install -c conda-forge uncertainties` \n",
+ "This can take several minutes, since anaconda has to resolve a lot of dependencies. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## c) Use of 'uncertainites' package"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Look at the example on the official website on how to use the library: \n",
+ "https://pythonhosted.org/uncertainties/ \n",
+ " \n",
+ "Define $L$ and $C$ as `ufloat`s and compute the resonance frequency and print the result. \n",
+ "How can one obtain the central value and the uncertainty separately from the `ufloat` object?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from uncertainties import ufloat\n",
+ "from uncertainties.umath import *\n",
+ "\n",
+ "# TODO: ..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## d) (optional) write your own uncertainty package"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can also try to write our own class for propagating uncertainties. Look at the myufloat class below and add the missing pieces marked with **TODO:**. Then test your **myufloat** class with the LC circuit example from above. It should lead to the same result (up to floating point rounding errors). \n",
+ " \n",
+ "Addition and the square root already have been implemented, complete the minimal example by adding subtraction, multiplication and division."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class myufloat:\n",
+ " def __init__(self, n, s=0.0):\n",
+ " self.n = float(n)\n",
+ " self.s = float(s)\n",
+ " \n",
+ " def __add__(self, operand):\n",
+ " n = self.n + operand.n\n",
+ " s = np.sqrt(self.s * self.s + operand.s * operand.s)\n",
+ " return myufloat(n, s)\n",
+ "\n",
+ " def __sub__(self, operand):\n",
+ " return # TODO: implement subtraction\n",
+ " \n",
+ " def __mul__(self, operand):\n",
+ " return # TODO: implement multiplication\n",
+ " \n",
+ " def __div__(self, operand):\n",
+ " return # TODO: implement division\n",
+ " \n",
+ " # for Python3\n",
+ " def __truediv__(self, operand):\n",
+ " return self.__div__(operand)\n",
+ " \n",
+ " # used in np.sqrt\n",
+ " def sqrt(self):\n",
+ " return myufloat(np.sqrt(self.n), np.abs(0.5/np.sqrt(self.n)*self.s))\n",
+ " \n",
+ " def __str__(self):\n",
+ " return \"%1.2e ± %1.2e\"%(self.n, self.s)\n",
+ " \n",
+ " # used for print function\n",
+ " def __repr__(self):\n",
+ " return \"%1.2e ± %1.2e\"%(self.n, self.s)\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "C = myufloat(150e-12, 8e-12)\n",
+ "L = myufloat(1e-3, 0.1e-3)\n",
+ "\n",
+ "print(myufloat(1.0)/np.sqrt(C*L))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "So the results agree for this case! (If not check your implementation) \n",
+ "Lets check some other cases: \n",
+ "create two values with uncertainties: \n",
+ " \n",
+ "$a = 1.0 \\pm 0.1$ \n",
+ "$b = 2.0 \\pm 0.05$ \n",
+ " \n",
+ "and compute the result including uncertainty both with the uncertainties package (ufloat) and your own implementation (using myufloat) of: \n",
+ " \n",
+ "$c = \\frac{a+b}{a-b}$ \n",
+ " \n",
+ "are they the same? If not, why?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "a1 = ufloat(1.0, 0.1)\n",
+ "b1 = ufloat(2.0, 0.05)\n",
+ "\n",
+ "a2 = myufloat(1.0, 0.1)\n",
+ "b2 = myufloat(2.0, 0.05)\n",
+ "\n",
+ "c1 = (a1+b1)/(a1-b1)\n",
+ "c2 = (a2+b2)/(a2-b2)\n",
+ "\n",
+ "print(c1)\n",
+ "print(c2)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "What is happening here?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Exercise1/Exercise_1.ipynb b/exercises/Exercise1/Exercise_1.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..d8992d719658d6778e674df747001c97878ab6d8
--- /dev/null
+++ b/exercises/Exercise1/Exercise_1.ipynb
@@ -0,0 +1,572 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You **can** use this notebook as template to solve your exercises. The **TODO:** indicates where you should put the missing code. You are also free to start a new notebook from scratch."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 1. Basic plotting with matplotlib"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In our first example, we plot a simple curve with matplotlib."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## a) Generating set of data"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First we need to create an array of our x values for the curve to plot."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Import basic libraries:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "%matplotlib inline\n",
+ "# the commands above is needed to have the plots displayed inside this \n",
+ "# notebook instead of in an external window"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "None\n"
+ ]
+ },
+ {
+ "ename": "TypeError",
+ "evalue": "'bool' object is not iterable",
+ "output_type": "error",
+ "traceback": [
+ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+ "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
+ "\u001b[0;32m<ipython-input-2-5c30e497ab77>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;31m# test your function, it should print 'True' twice\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m print(all(equallySpacedNumbers(2.0,10.0,9) \n\u001b[0;32m---> 10\u001b[0;31m == [2.,3.,4.,5.,6.,7.,8.,9.,10.]))\n\u001b[0m\u001b[1;32m 11\u001b[0m print(all(abs(equallySpacedNumbers(-1.2,0.2,6) \n\u001b[1;32m 12\u001b[0m - [-1.2,-0.92,-0.64,-0.36,-0.08,0.2]) < 1e-6))\n",
+ "\u001b[0;31mTypeError\u001b[0m: 'bool' object is not iterable"
+ ]
+ }
+ ],
+ "source": [
+ "def equallySpacedNumbers(start, end, number):\n",
+ " return # TODO: use numpy to return a 1-d array of equidistant\n",
+ " # floating point numbers between start and end\n",
+ "\n",
+ "# look at the function output by printing:\n",
+ "print(equallySpacedNumbers(2.0,3.0,4))\n",
+ "\n",
+ "# test your function, it should print 'True' twice\n",
+ "print(all(equallySpacedNumbers(2.0,10.0,9) \n",
+ " == [2.,3.,4.,5.,6.,7.,8.,9.,10.]))\n",
+ "print(all(abs(equallySpacedNumbers(-1.2,0.2,6) \n",
+ " - [-1.2,-0.92,-0.64,-0.36,-0.08,0.2]) < 1e-6))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Note that in the second case, we can not make an exact comparison due to rounding errors. Having such test functions is useful in case we want to replace our generator of equally spaces numbers with a different (e.g. faster) version later."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### b) Simple plots"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As example, we now want to make a plot of the fall time vs. the height of which an apple is dropped. For both x and y we need one-dimensional numpy arrays of the same length.\n",
+ " \n",
+ "\n",
+ "You find some help on basic plot functionalities here: \n",
+ "https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html\n",
+ " \n",
+ "For more special plots, first have a look in the gallery: \n",
+ "https://matplotlib.org/gallery/index.html \n",
+ "which already includes many common types of plots."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def Falltime(x, g):\n",
+ " return np.sqrt(2*x/g)\n",
+ "\n",
+ "# create a dataset\n",
+ "true_g = 9.8\n",
+ "data_x = # TODO: create array of 50 equally spaced points \n",
+ " # between 0 and 2.0 (height in m)\n",
+ "data_y = # TODO: compute fall time for all height values\n",
+ "\n",
+ "# the simplest way to plot\n",
+ "# TODO: create plot out of x/y data\n",
+ "\n",
+ "# always label the axes (the '$...$' for latex style)\n",
+ "# hint: use raw strings, e.g. r'height [m]'\n",
+ "# TODO: set labels for x and y-axis\n",
+ "\n",
+ "# make the plot appear\n",
+ "# TODO: draw plot"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### c) Load measurements from text file"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Above plot now shows the prediction of the fall time. To make a comparison with our measurements, we first have to load them from the text file **measurement.txt**.\n",
+ "\n",
+ "Numpy provides a very convenient function for this purpose! look at the Numpy reference: \n",
+ "https://docs.scipy.org/doc/numpy/reference/generated/numpy.loadtxt.html"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# load data from textfile\n",
+ "# format: height[m] time[s] height_error[m] time_error[s]\n",
+ "measurements = # TODO: load measurements from measurement.txt\n",
+ "\n",
+ "# look at it\n",
+ "print(\"shape:\", measurements.shape, \"\\n\")\n",
+ "print(\"data:\\n\", measurements, \"\\n\")\n",
+ "print(\"first column:\", measurements[:, 0], \"\\n\")\n",
+ "print(\"last row, first two columns:\", measurements[-1,0:2])\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### d) Plot with error bars"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we want to plot the measurement data (from the text file) with error bars together with the prediction from theory. In many cases there is a non-negligible uncertainty also on the theoretical prediction. One way of visualizing this is to plot an error band, which in practice can be done by shading the area between two curves. \n",
+ "In this example, use $\\sigma_g = 0.4 \\frac{\\text{m}}{\\text{s}^2}$ as the uncertainty of $g$. \n",
+ " \n",
+ "There are examples of plots with error bars in the gallery linked above. For more detailed options look at the reference here: \n",
+ "https://matplotlib.org/api/_as_gen/matplotlib.pyplot.errorbar.html"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# create additional dataset for the uncertainty band\n",
+ "# use 0.4 m/s^2 as symmetric uncertainty on g\n",
+ "data_y_m = # TODO: g varied down by the uncertainty\n",
+ "data_y_p = # TODO: g varied up by the uncertainty\n",
+ "\n",
+ "# plot uncertainty band of theory prediction\n",
+ "# TODO: plot filled area between the two curves created \n",
+ "# above, hint: use plt.fill_between\n",
+ "\n",
+ "# plot mean value on top\n",
+ "# TODO: add curve for nominal value of g in a different \n",
+ "# color than the uncertainty band\n",
+ "\n",
+ "# TODO: label the axes\n",
+ "\n",
+ "# plot measurement with errors\n",
+ "# TODO: plot measurements loaded from text file on top of \n",
+ "# the theory curve with circular markers, no line between \n",
+ "# them and also include errorbars! hint: plt.errorbar\n",
+ "\n",
+ "\n",
+ "# legend\n",
+ "# TODO: create a legend, hint(1): you can give a label to the \n",
+ "# individual plots with e.g. label='theory' in the creation \n",
+ "# of the plots above\n",
+ "# hint(2): use numpoints=1 as argument for plt.legend to \n",
+ "# have only 1 point of your measurements in the legend\n",
+ "\n",
+ "\n",
+ "# optional: set axis limits\n",
+ "# TODO: set axes limits to [0, 2.0] for x and [0, 0.8] for y-axis\n",
+ "\n",
+ "# optional: grid lines\n",
+ "# TODO: display grid lines\n",
+ "\n",
+ "# save the figure to a pdf file\n",
+ "# TODO: save the plot as \"exercise-1-plot.pdf\"\n",
+ "\n",
+ "# make the plot appear\n",
+ "# TODO: show the plot in the notebook"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### e) Histograms"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "A qualitative way to check compatibility of the measurement points with theory is to make a histogram of the pulls (pulls are defined below in the code). Create the histogram of pulls and overlay the expected pull distribution, which is Gaussian. \n",
+ " \n",
+ "Instead of putting the formula for the Gaussian yourself, you can use `scipy.stats.norm.pdf`, see here:\n",
+ "https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [],
+ "source": [
+ "import scipy.stats\n",
+ "\n",
+ "# as approximation we ignore the errors on the measured \n",
+ "# height since they are relatively small!\n",
+ "\n",
+ "heights = measurements[:, 0]\n",
+ "times = measurements[:, 1]\n",
+ "time_errors = measurements[:, 3]\n",
+ "predictions = Falltime(heights, true_g)\n",
+ "\n",
+ "# compute pulls\n",
+ "pulls = (times - predictions)/time_errors\n",
+ "\n",
+ "# histogram of pulls\n",
+ "# TODO: create normalized histogram (meaning sum of all bin \n",
+ "# contents equals 1) with 10 bins\n",
+ "# hint: use histtype='stepfilled'\n",
+ "\n",
+ "# unit gaussian\n",
+ "x = # TODO: 50 points between -3.0 and 3.0\n",
+ "y = # TODO: unit gaussian, hint: scipy.stats.norm.pdf\n",
+ "plt.plot(x, y, '--', color='r', linewidth=3.0)\n",
+ "\n",
+ "# always label the axes, also for histograms\n",
+ "# TODO: labels\n",
+ "\n",
+ "# annotation\n",
+ "# TODO: create a annotation with text 'unit gaussian' pointing \n",
+ "# to the curve plotted above. hint: plt.annotate\n",
+ "\n",
+ " \n",
+ "# save the figure to a pdf file\n",
+ "# TODO: save as 'exercise-1-histogram.pdf'\n",
+ "\n",
+ "# TODO: show in notebook"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### f) (optional) Creating a text file of toy measurements"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# create toy experiments instead of real measurements here\n",
+ "\n",
+ "# TODO: create a text file in the same format as the \n",
+ "# 'measurement.txt' with 1000 random toy experiments, \n",
+ "# assuming the same uncertainties as above\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 2. Error propagation with Python"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We consider a LC circuit with resonance frequency $\\omega_0 = \\frac{1}{\\sqrt{LC}}$. \n",
+ "$C = 150 \\pm 8 \\,\\text{pF}$ \n",
+ "$L = 1 \\pm 0.1 \\,\\text{mH}$ \n",
+ " \n",
+ "What is the resonance frequency and its uncertainty? "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## a) Calculation by hand"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The mean value is computed to: \n",
+ " \n",
+ "$\\omega_0 =$ \n",
+ " \n",
+ "Since the uncertainties for both quantities come from independent electronic components, they can safely be assumed as uncorrelated and one can compute the uncertainty of $\\omega_0$ to \n",
+ " \n",
+ "$\\sigma_{\\omega_0} =$ "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## b) Installation of 'uncertainties' package"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "There are packages, which make handling of uncertainties very easy, e.g. the package simply called \"uncertainties\". It is not included in standard packages of Anaconda and therefore has to be installed with: \n",
+ "`conda install -c conda-forge uncertainties` \n",
+ "This can take several minutes, since anaconda has to resolve a lot of dependencies. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## c) Use of 'uncertainites' package"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Look at the example on the official website on how to use the library: \n",
+ "https://pythonhosted.org/uncertainties/ \n",
+ " \n",
+ "Define $L$ and $C$ as `ufloat`s and compute the resonance frequency and print the result. \n",
+ "How can one obtain the central value and the uncertainty separately from the `ufloat` object?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from uncertainties import ufloat\n",
+ "from uncertainties.umath import *\n",
+ "\n",
+ "# TODO: ..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## d) (optional) write your own uncertainty package"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can also try to write our own class for propagating uncertainties. Look at the myufloat class below and add the missing pieces marked with **TODO:**. Then test your **myufloat** class with the LC circuit example from above. It should lead to the same result (up to floating point rounding errors). \n",
+ " \n",
+ "Addition and the square root already have been implemented, complete the minimal example by adding subtraction, multiplication and division."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 35,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class myufloat:\n",
+ " def __init__(self, n, s=0.0):\n",
+ " self.n = float(n)\n",
+ " self.s = float(s)\n",
+ " \n",
+ " def __add__(self, operand):\n",
+ " n = self.n + operand.n\n",
+ " s = np.sqrt(self.s * self.s + operand.s * operand.s)\n",
+ " return myufloat(n, s)\n",
+ "\n",
+ " def __sub__(self, operand):\n",
+ " return # TODO: implement subtraction\n",
+ " \n",
+ " def __mul__(self, operand):\n",
+ " return # TODO: implement multiplication\n",
+ " \n",
+ " def __div__(self, operand):\n",
+ " return # TODO: implement division\n",
+ " \n",
+ " # for Python3\n",
+ " def __truediv__(self, operand):\n",
+ " return self.__div__(operand)\n",
+ " \n",
+ " # used in np.sqrt\n",
+ " def sqrt(self):\n",
+ " return myufloat(np.sqrt(self.n), np.abs(0.5/np.sqrt(self.n)*self.s))\n",
+ " \n",
+ " def __str__(self):\n",
+ " return \"%1.2e ± %1.2e\"%(self.n, self.s)\n",
+ " \n",
+ " # used for print function\n",
+ " def __repr__(self):\n",
+ " return \"%1.2e ± %1.2e\"%(self.n, self.s)\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "C = myufloat(150e-12, 8e-12)\n",
+ "L = myufloat(1e-3, 0.1e-3)\n",
+ "\n",
+ "print(myufloat(1.0)/np.sqrt(C*L))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "So the results agree for this case! (If not check your implementation) \n",
+ "Lets check some other cases: \n",
+ "create two values with uncertainties: \n",
+ " \n",
+ "$a = 1.0 \\pm 0.1$ \n",
+ "$b = 2.0 \\pm 0.05$ \n",
+ " \n",
+ "and compute the result including uncertainty both with the uncertainties package (ufloat) and your own implementation (using myufloat) of: \n",
+ " \n",
+ "$c = \\frac{a+b}{a-b}$ \n",
+ " \n",
+ "are they the same? If not, why?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "a1 = ufloat(1.0, 0.1)\n",
+ "b1 = ufloat(2.0, 0.05)\n",
+ "\n",
+ "a2 = myufloat(1.0, 0.1)\n",
+ "b2 = myufloat(2.0, 0.05)\n",
+ "\n",
+ "c1 = (a1+b1)/(a1-b1)\n",
+ "c2 = (a2+b2)/(a2-b2)\n",
+ "\n",
+ "print(c1)\n",
+ "print(c2)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "What is happening here?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Exercise1/Exercise_1.pdf b/exercises/Exercise1/Exercise_1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..69ec1a03254b29b73f1f5a860dd10c65c6c0b5b6
Binary files /dev/null and b/exercises/Exercise1/Exercise_1.pdf differ
diff --git a/exercises/Exercise1/measurement.txt b/exercises/Exercise1/measurement.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1038d5dc83ec37619c7822f99031bdcc5282172b
--- /dev/null
+++ b/exercises/Exercise1/measurement.txt
@@ -0,0 +1,10 @@
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+8.052292433523977611e-01 4.407017550224799907e-01 1.000000000000000021e-02 5.000000000000000278e-02
+9.704434451011637597e-01 4.982765800216331642e-01 1.000000000000000021e-02 5.000000000000000278e-02
+1.129455114674715155e+00 4.537414756680630545e-01 1.000000000000000021e-02 5.000000000000000278e-02
+1.285083611438478268e+00 5.281917212757096802e-01 1.000000000000000021e-02 5.000000000000000278e-02
+1.435421444857490014e+00 6.421928523153139778e-01 1.000000000000000021e-02 5.000000000000000278e-02
+1.591387685845770950e+00 6.063640103412939464e-01 1.000000000000000021e-02 5.000000000000000278e-02
+1.727425218084549075e+00 5.999229259846586837e-01 1.000000000000000021e-02 5.000000000000000278e-02
+1.897833779891006545e+00 5.580646104775206506e-01 1.000000000000000021e-02 5.000000000000000278e-02
diff --git a/exercises/Exercise2/Exercise_2.ipynb b/exercises/Exercise2/Exercise_2.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..d1f2227184687ea3d3ab3cc61b34920835b77074
--- /dev/null
+++ b/exercises/Exercise2/Exercise_2.ipynb
@@ -0,0 +1,502 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 2\n",
+ "General hint: You can always ask for help from within python if you forgot how a certain function works or what the correct ordering of input parameters is. Executing \"some_function?\" spawns the docstring of the function and \"some_function??\" the source code."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import scipy.stats\n",
+ "scipy.stats.kurtosis?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Probability density function (pdf)\n",
+ "We will look at a few common distributions and investigate their basic properties."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For your convenience, we define a few pdfs and functions to draw samples from them. Have a look at https://docs.scipy.org/doc/scipy/reference/stats.html for more details. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def gaussian_pdf(x, mu, sigma):\n",
+ " \"\"\"Gaussian distribution with mean mu and standard deviation sigma\"\"\"\n",
+ " return scipy.stats.norm.pdf(x, loc=mu, scale=sigma)\n",
+ "\n",
+ "def gaussian_sample(number, mu, sigma):\n",
+ " \"\"\"Draw samples from a Gaussian distribution\n",
+ " \n",
+ " mu: mean\n",
+ " sigma: standard deviation:\n",
+ " number: number of samples to be drawn\n",
+ " \"\"\"\n",
+ " return scipy.stats.norm.rvs(loc=mu, scale=sigma, size=number)\n",
+ "\n",
+ "def lognormal_pdf(x, mu, sigma):\n",
+ " return scipy.stats.lognorm.pdf(x, loc=0, scale=1, s=sigma)\n",
+ "\n",
+ "def lognormal_sample(number, mu, sigma):\n",
+ " return scipy.stats.lognorm.rvs(size=number, loc=0, s=sigma, scale=1)\n",
+ " \n",
+ "def binomial_pmf(x, n, p):\n",
+ " return scipy.stats.binom.pmf(x, n, p)\n",
+ "\n",
+ "def binomial_sample(number, n, p):\n",
+ " return scipy.stats.binom.rvs(n, p, size=number)\n",
+ "\n",
+ "def poisson_pmf(k, mu):\n",
+ " return scipy.stats.poisson.pmf(k, mu)\n",
+ "\n",
+ "def poisson_sample(number, mu):\n",
+ " return scipy.stats.poisson.rvs(mu, size=number)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**1a) Generate arrays from the lognormal and poisson pdfs and draw an array of samples from each distribution.**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Generate arrays for parent pdf and samples\n",
+ "sample_size = 1000\n",
+ "x_float = np.linspace(0, 10, 1000)\n",
+ "x_int = np.arange(0, 30)\n",
+ "mu = 4.0\n",
+ "p = 0.5\n",
+ "sigma = 1\n",
+ "\n",
+ "# Gaussian\n",
+ "g_parent = gaussian_pdf(x_float, mu, sigma)\n",
+ "g_sample = gaussian_sample(sample_size, mu, sigma)\n",
+ "\n",
+ "# Lognormal\n",
+ "# logn_parent = ...\n",
+ "# logn_sample = ...\n",
+ "\n",
+ "# Binomial\n",
+ "bin_pdf = binomial_pmf(x_int, n=int(mu/p), p=p)\n",
+ "bin_sample = binomial_sample(sample_size, n=int(mu/p), p=p)\n",
+ "\n",
+ "# Poisson\n",
+ "#pois_parent = ...\n",
+ "#pois_sample = ..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**1b) Display your results in axes 1 and 3 in the figure below.**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 720x432 with 4 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot the generated arrays, comparing the parent distribution and a sample\n",
+ "f, ax = plt.subplots(2, 2, figsize=(10, 6))\n",
+ "ax = ax.flatten()\n",
+ "n_bins = 16\n",
+ "\n",
+ "ax[0].set_title(r'Gauss')\n",
+ "ax[0].plot(x_float, g_parent, 'k', label='pdf')\n",
+ "ax[0].hist(g_sample, n_bins, density=True, rwidth=0.9, label='sample', range=(0, 8))\n",
+ "ax[0].set_xlim(0, 8)\n",
+ "ax[0].set_xlabel(r'$x$')\n",
+ "ax[0].legend()\n",
+ "\n",
+ "ax[1].set_title(r'Lognormal')\n",
+ "# ...\n",
+ "\n",
+ "ax[2].set_title('Binomial')\n",
+ "ax[2].plot(x_int, bin_pdf, 'k+', label='pmf', ms=8)\n",
+ "ax[2].hist(bin_sample, n_bins, density=True, rwidth=0.9, label='sample', range=(0, 15), align='mid')\n",
+ "ax[2].set_xlim(0, 15)\n",
+ "ax[2].set_xlabel(r'$k$')\n",
+ "ax[2].legend()\n",
+ "\n",
+ "ax[3].set_title('Poisson')\n",
+ "# ...\n",
+ "\n",
+ "f.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Mean, variance and their estimators\n",
+ "**2a) To familiarize yourself with the properties of the distributions, write a function that calculates the first five moments of a sample as well as the mode and median values. Compare your results with the expected values.** \n",
+ "Hints: If you like, you can try your own implementations and test them against scipy.stats. You can find functions in numpy and scipy implementing all tasks. The 0th moment is just the total probability, following the convention in the lecture notes. Sometimes the value 3 is subtracted from kurtosis to shift a normal distribution to zero kurtosis."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def moments(sample):\n",
+ " pass\n",
+ "\n",
+ "\n",
+ "def mode(sample):\n",
+ " pass\n",
+ "\n",
+ "\n",
+ "def median(sample):\n",
+ " pass"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Calculate moments\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "None None\n"
+ ]
+ },
+ {
+ "ename": "NameError",
+ "evalue": "name 'logn_sample' is not defined",
+ "output_type": "error",
+ "traceback": [
+ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
+ "\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)",
+ "\u001b[1;32m<ipython-input-9-e9b6f1fa7aea>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmode\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mg_sample\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmedian\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mg_sample\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmode\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlogn_sample\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmedian\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlogn_sample\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 3\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmode\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbin_sample\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmedian\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbin_sample\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmode\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpois_sample\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmedian\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpois_sample\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+ "\u001b[1;31mNameError\u001b[0m: name 'logn_sample' is not defined"
+ ]
+ }
+ ],
+ "source": [
+ "print(mode(g_sample), median(g_sample))\n",
+ "print(mode(logn_sample), median(logn_sample))\n",
+ "print(mode(bin_sample), median(bin_sample))\n",
+ "print(mode(pois_sample), median(pois_sample))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "What did you expect, knowing the parent distributions? Hint: scipy can also help you here, see for example \"scipy.stats.norm.stats\". You can check wikipedia to quickly recap some analytical results if neccessary. \n",
+ "https://en.wikipedia.org/wiki/Normal_distribution \n",
+ "https://en.wikipedia.org/wiki/Log-normal_distribution \n",
+ "https://en.wikipedia.org/wiki/Binomial_distribution \n",
+ "https://en.wikipedia.org/wiki/Poisson_distribution \n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# ..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Estimation\n",
+ "Obviously, there is some discrepancy between the expected or \"true\" values from the parent distribution and the calculated sample moments. We would like to work on the inverse problem of guessing the first two moments given only a sample and knowing that the sample was drawn from a normal distribution (but not knowing its \"true\" parameters). \n",
+ "**2b) Remember how to estimate the mean and variance from a sample.** \n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**2c) How to quantify the uncertainty of the estimation of the mean?** \n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**2d) Given that it can be very cheap to repeatedly sample a distribution with a computer, try to come up with an alternative approach to estimate the uncertainty of the mean. We will come back to this idea at the end of the course.**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Multidimensional pdf: covariance and correlation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Imagine your're an astronomer and are measuring a specific parameter called the \"Clumping factor\". You're interested whether the clumping factor varies with temperature and how. You have 8 measurements with the following values:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "clumping = [0.5, 0.4, 0.3, 0.2, 0.4, 0.3, 0.3, 0.2] \n",
+ "temperature = [2700, 4600, 5120, 5550, 3600, 3990, 4190, 3900] # [K]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**3a) Write a function in python that computes the Covariance and compare the result to a python numpy or scipy function.** "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**3b) Calculate the correlation coefficient.** "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**3c) Interpret your results of covariance and correlation coefficient.** "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**3d) If the two variables are uncorrelated, does this also mean they are independent of each other?** "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Counter example?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Bonus\n",
+ "### 3D Plots"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Try playing with three dimensional graphs to visualize properties of pdfs with two variables. For example, try visualizing marginal and conditional distributions as was done in lecture 2.\n",
+ "<img src=\"MultivariateNormal.png\" style=\"height:250px\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### nbextensions\n",
+ "There are some useful extensions to jupyter notebooks, check https://github.com/ipython-contrib/jupyter_contrib_nbextensions if you are interested. There are features like a table of contents to navigate around in notebooks, line numbering for all code cells and options to collapse certain cells to to keep a better overview.\n",
+ "\n",
+ "conda install -c conda-forge jupyter_contrib_nbextensions\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "hide_input": false,
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.15"
+ },
+ "toc": {
+ "nav_menu": {},
+ "number_sections": true,
+ "sideBar": true,
+ "skip_h1_title": false,
+ "toc_cell": false,
+ "toc_position": {
+ "height": "658px",
+ "left": "0px",
+ "right": "1388px",
+ "top": "110px",
+ "width": "212px"
+ },
+ "toc_section_display": "block",
+ "toc_window_display": true
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Exercise2/Exercise_2.pdf b/exercises/Exercise2/Exercise_2.pdf
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diff --git a/exercises/Exercise3/.ipynb_checkpoints/Exercise_3-checkpoint.ipynb b/exercises/Exercise3/.ipynb_checkpoints/Exercise_3-checkpoint.ipynb
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+++ b/exercises/Exercise3/.ipynb_checkpoints/Exercise_3-checkpoint.ipynb
@@ -0,0 +1,501 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 3\n",
+ "\n",
+ "In these week's exercises you will practice Poissonian statistics, delve deeper into the meaning of the error matrix and see an example of a case in which the standard error propagation formula is not directly applicable.\n",
+ "\n",
+ "For the first exercise you should install the package *tqdm* from the Anaconda navigator. It provides a progress bar, which is nice to have when a long computation is running.\n",
+ "\n",
+ "## 1. Poisson statistics\n",
+ "This exercise is about two variants of a counting experiment: in the first, simpler case, we will see that the observations are well described by a Poisson distribution. In the second case we will have events which are not independent from each other and we will see that the results deviate from a Poisson distribution.\n",
+ "\n",
+ "Consider a beam of particles impinging on a thin target. Most particles will go through the target without interacting, while a few will be absorbed. The target is connected to a detector, which fires a signal when a particle is absorbed by the target. In the first part of the exercise we assume to have a perfect detector: it is able to detect each and every particle hitting the target.\n",
+ "\n",
+ "The experiment consists in counting how many particles are absorbed by the target in a fixed time interval, e.g. 1s. We will repeat the counting *n* times and see how the results are distributed.\n",
+ "\n",
+ "To simulate the setup, assume the following numbers:<br>\n",
+ "- Number of particles arriving at the target per second\n",
+ "- Probability that a particle is absorbed by the target\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "'''\n",
+ "Let's start by importing some useful modules and functions...\n",
+ "'''\n",
+ "from numpy.random import rand\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy.stats import poisson\n",
+ "from tqdm import tqdm_notebook as tqdm # Nice progress bar for long computations. Install the tqdm package from the navigator\n",
+ "%matplotlib inline \n",
+ "\n",
+ "'''\n",
+ "... and by defining the relevant parameters of the experiment\n",
+ "(feel free to change the values and see how the result changes)\n",
+ "'''\n",
+ "particle_rate = 1e6 # Number of particles arriving at the target per second\n",
+ "delta_t = 1 # duration of one experiment in seconds\n",
+ "absorption_probability = 2e-6 # Probability that a particle is absorbed by the target\n",
+ "n_trials = 200 # How many times you repeat the experiment"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Write a function which decides if a single particle is absorbed by the target (return True) or not (return False).\n",
+ "\n",
+ "Hint: generate a uniformly distributed random number between 0 and 1 with the *rand()* function. Use it do decide if the particle is detected or not, based on the known *absorption_probability*."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def particle_is_detected(...):\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now write a function to simulate the experiment running for a time *delta_t*. It should do the following:\n",
+ "- compute how many particles reach the target during *delta_t* with the known *particle_rate*,\n",
+ "- for each of those check if they get absorbed or not (cf. *particle_is_detected()*),\n",
+ "- return the number of particles which are absorbed by the target during *delta_t*."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def run_experiment(...):\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You are now ready to run the experiment, i.e. run the function. Do this a few times to get a feeling for the results: is the number of counted particles the same every time or does it change? What kind of result do you expect from the chosen *particle_rate, delta_t* and *absorption_probability*?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "for i in range(10):\n",
+ " print run_experiment()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's now analyse the results more systematically: run the experiment *n_trials* times and save the results in a list or array. Depending on your computer, this might take some time."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "progress_bar = tqdm(total=n_trials, unit=' trials')\n",
+ "results = []\n",
+ "for i in range(n_trials):\n",
+ " results.append(run_experiment(...))\n",
+ " progress_bar.update()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Before plotting the results in a histogram, let's define the expected Poisson distribution in order to make a comparison. If you are not sure how to do this, have a look at last week's exercise. What is the expected *mu* paramter for the given *particle_rate, delta_t* and *absorption_probability*?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "mu = ..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now plot the results of the experiment together with the parent distribution. Again, have a look at last week's exercise if you need help. When plotting the histogram remember to set *density=True* in order to have it normalized to unity for a meaningful comparison with the Poisson distribution (if this option does not work, which might be the case for older versions, try replacing it with *normed=True*)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "plt.hist(...) # histogram for the measurements\n",
+ "plt.plot(...) # plot of the Poisson distribution\n",
+ "plt.xlabel('Counted particles')\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "What do you observe? Is the data from the experiment well described by the Poisson distribution?\n",
+ "\n",
+ "Let's now make a different assumption about the detector: it has no longer perfect efficiency, but whenever it detects a particle it needs some time to process the signal. Durign this time the detector is blind to any particle which might be absorbed by the target. In this way the recorded particles are not independent from each other anymore, and as you will see this will cause the result of the experiment to deviate from a Poisson distribution.\n",
+ "\n",
+ "Modify your implementation of the function *run_experiment()* in order to account for the dead time of the detector. Assume that whenever the detector records a particle it is blind to the next 500000 particles reaching the target."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def run_experiment_dead_time(...):\n",
+ " \n",
+ "# Run the function n_trials times and save the results as before\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Plot the new results with detector dead time together with the same Poisson distribution from before. What do you observe?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "plt.hist(...) # histogram for the measurements\n",
+ "plt.plot(...) # plot of the Poisson distribution\n",
+ "plt.xlabel('Counted particles')\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 2. Correlated variables and error matrix\n",
+ "\n",
+ "In this exercise you will work on a pair of correlated variables, compute the error matrix and visualize the error ellipse. Let's start from the case of two uncorrelated variables, saved in the file *data_uncorrelated.txt*. Have a look at the file: each line represents one measurement, the first number being the value of the *x* variable and the second number the value of the *y* variable."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "from matplotlib import pyplot as plt\n",
+ "\n",
+ "data = np.genfromtxt('data_uncorrelated.txt')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Plot the data. How can you recognise that *x* and *y* are not correlated? Compare the 2D distribution in the *xy* plane and the histograms of the *x* and *y* values. What do you notice about e.g. the range of the axes and the position of the means?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "f, ax = plt.subplots(1,3, figsize=(20, 6))\n",
+ "ax = ax.flatten()\n",
+ "\n",
+ "ax[0].set_xlabel(r'$x$')\n",
+ "ax[0].set_ylabel(r'$y$')\n",
+ "ax[0].axis('equal')\n",
+ "ax[0].plot(data[:,0],data[:,1],'.')\n",
+ "\n",
+ "ax[1].set_xlabel(r'$x$')\n",
+ "ax[1].hist(data[:,0],bins=range(-7,7),rwidth=.9)\n",
+ "\n",
+ "ax[2].set_xlabel(r'$y$')\n",
+ "ax[2].hist(data[:,1],bins=range(-7,7),rwidth=.9)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute the covariance matrix. You can either write a function to do this yourself, or use the numpy implementation. Have a look at last week's exercise if you feel lost."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compare your result with the error matrix you expect for two uncorrelated variables, cf. slides from Lecture 3: $\\text{diag}(\\sigma_x^2,\\sigma_y^2)$. Is your result compatible with this expression?\n",
+ "<br> We will now compute the eigenvectors and eigenvalues of the covariance matrix and interpret them in terms of the properties of the distributions we just saw. As before, you can compute the values yourself or use the numpy implementation *np.linalg.eig(matrix)*"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#Use this block to compute eigenvalues and eigenvectors of the covariance matrix and print the result\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For this easy case of uncorrelated variables you should recognize the following: the eigenvectors are aligned with the $x$ and $y$ axes and the eigenvalues are the variances of the data along the same axes; this means that the standard deviation in the $x$ and $y$ directions are the square root of the respective eigenvalue. Keep this in mind, as we will later see what changes if the variables are correlated.\n",
+ "\n",
+ "For a visual interpretation do the following: plot again the 2D distribution of the data together with the eigenvectors multiplied by the square root of the corresponding eigenvalue (in this way the length of the vector will be the corresponding standard deviation)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "plt.plot(data[:,0],data[:,1],'.',zorder=0)\n",
+ "plt.axis('equal')\n",
+ "\n",
+ "#Compute the x and y components of the two vectors:\n",
+ "vector1_x = ...\n",
+ "vector1_y = ...\n",
+ "vector2_x = ...\n",
+ "vector2_y = ...\n",
+ "\n",
+ "#Use the following function to draw the vectors. The options are needed to draw them in the correct size\n",
+ "plt.quiver(vector1_x, vector1_y ,angles='xy', scale_units='xy', scale=1,zorder=5)\n",
+ "plt.quiver(vector2_x, vector2_y ,angles='xy', scale_units='xy', scale=1,zorder=5)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's now draw an ellipse with half-axes $\\sigma_x$ and $\\sigma_y$: this is the equivalent of the $1 \\sigma$ interval for a 1D Gaussian distribution. Fill in the values for $\\sigma_x,\\sigma_y$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sigma_x = ...\n",
+ "sigma_y = ...\n",
+ "\n",
+ "phi = np.linspace(0,2*np.pi)\n",
+ "ellipse_x = sigma_x*np.cos(phi) # x-coordinates of the points on the ellipse\n",
+ "ellipse_y = sigma_y*np.sin(phi) # y-coordinates of the points on the ellipse\n",
+ "\n",
+ "plt.plot(ellipse_x,ellipse_y,'r')\n",
+ "plt.axis('equal')\n",
+ "\n",
+ "plt.plot(data[:,0],data[:,1],'.',zorder=0)\n",
+ "\n",
+ "#Redraw also the vectors (copy-paste from previous block)\n",
+ "plt.quiver(vector1_x, vector1_y ,angles='xy', scale_units='xy', scale=1,zorder=5)\n",
+ "plt.quiver(vector2_x, vector2_y ,angles='xy', scale_units='xy', scale=1,zorder=5)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let us now look at the case of two correlated measurements. Load the data from *data_uncorrelated.txt* and repeat the steps from above up to the drawing of the vectors; do not draw the ellipse yet, we will do that in the next step. You should be able to copy-paste most of the code from the uncorrelated case."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "data_correlated = np.genfromtxt('data_correlated.txt')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You should now see that the eigenvectors are not aligned with the coordinate axes anymore. However, as before, the eigenvectors represent the direction of the largest spread of the data, and the eigenvalues, i.e. the variances, define how large this spread is.\n",
+ "\n",
+ "Let's now draw the ellipse. There are different ways in which this can be done. Let's start by determining the angle of rotation *theta*. *Hint*: take the *x* and *y* components of one of the eigenvectors and use the *np.arctan2()* function."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "theta = ..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To draw the rotated ellipse, define the $x$ and $y$ coordinates as before, and than rotate them by multiplying them with a rotation matrix by the angle *theta*."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "phi = np.linspace(0,2*np.pi)\n",
+ "ellipse_x = sigma[0]*np.cos(phi) # x-coordinates of the points on the ellipse\n",
+ "ellipse_y = sigma[1]*np.sin(phi) # y-coordinates of the points on the ellipse\n",
+ "\n",
+ "rotation = np.array([[np.cos(theta),np.sin(theta)],[-np.sin(theta),np.cos(theta)]])\n",
+ "ellipse = np.dot(rotation,[ellipse_x,ellipse_y]) # dot product"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we are ready to plot everything together."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "plt.plot(data_correlated[:,0],data_correlated[:,1],'.',zorder=0)\n",
+ "for i in range(2):\n",
+ " plt.quiver(sigma[i]*eigvec[0,i],sigma[i]*eigvec[1,i],angles='xy', scale_units='xy', scale=1,zorder=5)\n",
+ "plt.plot(ellipse[0,:],ellipse[1,:],'r')\n",
+ "plt.axis('equal')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Bonus\n",
+ "\n",
+ "The data for this exercise has been generated with the following code. Feel free to change the parameters and rerun the exercise."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "n_samples = 1000\n",
+ "mu = np.array([0.,0.])\n",
+ "var_x = 4.\n",
+ "var_y = 1.\n",
+ "cov_xy = 1.\n",
+ "r = np.array([\n",
+ " [ var_x, cov_xy,],\n",
+ " [ cov_xy, var_y,]\n",
+ " ])\n",
+ "\n",
+ "y = np.random.multivariate_normal(mu, r, size=n_samples)\n",
+ "\n",
+ "with open('output.txt', 'w') as outfile:\n",
+ " np.savetxt(outfile, y, fmt='%3.2f')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 3. Computing uncertainties on inefficiencies\n",
+ "\n",
+ "Consider an imperfect particle detector: out of all the particles hitting the detector, a fraction passes through unnoticed. The efficiency of the detector, i.e. the fraction of particles which are detected, is a very important parameter for any experimental setup. Suppose you want to measure the efficiency of a new detector. A possible approach is the following: you shoot $n$ particles on the detector, and count the number of signals $k$ which are recorded. The efficiency is then given by $\\varepsilon = k\\,/\\,n$. What is the uncertainty on this quantity? As a first approach, let's assume that $k$ and $n$ are Poisson distributed (and thus $\\delta k = \\sqrt{k}$ and $\\delta n = \\sqrt{n}$) and that we can apply the standard error propagation formula you saw in lecture 1:\n",
+ "$$ \\delta f = \\sqrt{ \\sum_{i=1}^N \\left(\\left. \\frac{\\partial f}{\\partial x_i}\\right\\vert_{x_i=x_i^0} \\delta x_i \\right)^2}. $$\n",
+ "- Show that this formula yields the following result:\n",
+ "$$ \\delta \\varepsilon = \\sqrt{\\frac{k}{n^2} + \\frac{k^2}{n^3}}. $$\n",
+ "\n",
+ "What happens to the uncertainty for *extreme* values of $k$, i.e. $k=0$ and $k=n$? Do these results make sense? Remember that the efficiency is by definition a number between 0 and 1.\n",
+ "\n",
+ "The source of the problem is that $k$ and $n$ are not independent (the particles which are recorded are a subset of all particles which hit the detector). A way to handle this is noting that the efficiency measurement is in fact a binomial process with total events $n$ and success probability $\\varepsilon$ (see slides of Lecture 3).\n",
+ "- Using the known variance of the binomial distribution show that in this case the uncertainty is given by \n",
+ "$$ \\delta \\varepsilon = \\sqrt{\\frac{\\varepsilon (1-\\varepsilon)}{n}}.$$\n",
+ "\n",
+ "An equivalent approach is to consider, instead of the total number of particles $n$, the number $n_f$ of particles which fail to be detected. In this approach, $n = k + n_f$ is not fixed anymore and $k$ and $n_f$ are uncorrelated; thus, the standard error formula is valid.\n",
+ "- Show that applying the standard error formula to $\\varepsilon = k\\,/\\,(k+n_f)$ yields again $$ \\delta \\varepsilon = \\sqrt{\\frac{\\varepsilon (1-\\varepsilon)}{n}}.$$\n",
+ "\n",
+ "Note that when evaluating this formula one has to use the measured (estimated) value of $\\varepsilon$, since the true value is unknown. This is a good approximation for *intermediate* values of $k$, i.e. $\\varepsilon$ not too close to 0 or 1. The exact meaning of *too close* is a matter of judgement - the extreme values $\\varepsilon = 0$ and $\\varepsilon = 1$ are clearly too close, as they yeld 0 uncertainty which is nonsense."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.7"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Exercise3/Exercise_3.ipynb b/exercises/Exercise3/Exercise_3.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..94586fc1c6280dca18ae3aa0a07cdfe8ccdaa86f
--- /dev/null
+++ b/exercises/Exercise3/Exercise_3.ipynb
@@ -0,0 +1,501 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 3\n",
+ "\n",
+ "In these week's exercises you will practice Poissonian statistics, delve deeper into the meaning of the error matrix and see an example of a case in which the standard error propagation formula is not directly applicable.\n",
+ "\n",
+ "For the first exercise you should install the package *tqdm* from the Anaconda navigator. It provides a progress bar, which is nice to have when a long computation is running.\n",
+ "\n",
+ "## 1. Poisson statistics\n",
+ "This exercise is about two variants of a counting experiment: in the first, simpler case, we will see that the observations are well described by a Poisson distribution. In the second case we will have events which are not independent from each other and we will see that the results deviate from a Poisson distribution.\n",
+ "\n",
+ "Consider a beam of particles impinging on a thin target. Most particles will go through the target without interacting, while a few will be absorbed. The target is connected to a detector, which fires a signal when a particle is absorbed by the target. In the first part of the exercise we assume to have a perfect detector: it is able to detect each and every particle hitting the target.\n",
+ "\n",
+ "The experiment consists in counting how many particles are absorbed by the target in a fixed time interval, e.g. 1s. We will repeat the counting *n* times and see how the results are distributed.\n",
+ "\n",
+ "To simulate the setup, assume the following numbers:<br>\n",
+ "- Number of particles arriving at the target per second\n",
+ "- Probability that a particle is absorbed by the target\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "'''\n",
+ "Let's start by importing some useful modules and functions...\n",
+ "'''\n",
+ "from numpy.random import rand\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy.stats import poisson\n",
+ "from tqdm import tqdm_notebook as tqdm # Nice progress bar for long computations. Install the tqdm package from the navigator\n",
+ "%matplotlib inline \n",
+ "\n",
+ "'''\n",
+ "... and by defining the relevant parameters of the experiment\n",
+ "(feel free to change the values and see how the result changes)\n",
+ "'''\n",
+ "particle_rate = 1e6 # Number of particles arriving at the target per second\n",
+ "delta_t = 1 # duration of one experiment in seconds\n",
+ "absorption_probability = 2e-6 # Probability that a particle is absorbed by the target\n",
+ "n_trials = 200 # How many times you repeat the experiment"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Write a function which decides if a single particle is absorbed by the target (return True) or not (return False).\n",
+ "\n",
+ "Hint: generate a uniformly distributed random number between 0 and 1 with the *rand()* function. Use it do decide if the particle is detected or not, based on the known *absorption_probability*."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def particle_is_detected(...):\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now write a function to simulate the experiment running for a time *delta_t*. It should do the following:\n",
+ "- compute how many particles reach the target during *delta_t* with the known *particle_rate*,\n",
+ "- for each of those check if they get absorbed or not (cf. *particle_is_detected()*),\n",
+ "- return the number of particles which are absorbed by the target during *delta_t*."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def run_experiment(...):\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You are now ready to run the experiment, i.e. run the function. Do this a few times to get a feeling for the results: is the number of counted particles the same every time or does it change? What kind of result do you expect from the chosen *particle_rate, delta_t* and *absorption_probability*?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "for i in range(10):\n",
+ " print run_experiment()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's now analyse the results more systematically: run the experiment *n_trials* times and save the results in a list or array. Depending on your computer, this might take some time."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "progress_bar = tqdm(total=n_trials, unit=' trials')\n",
+ "results = []\n",
+ "for i in range(n_trials):\n",
+ " results.append(run_experiment(...))\n",
+ " progress_bar.update()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Before plotting the results in a histogram, let's define the expected Poisson distribution in order to make a comparison. If you are not sure how to do this, have a look at last week's exercise. What is the expected *mu* paramter for the given *particle_rate, delta_t* and *absorption_probability*?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "mu = ..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now plot the results of the experiment together with the parent distribution. Again, have a look at last week's exercise if you need help. When plotting the histogram remember to set *density=True* in order to have it normalized to unity for a meaningful comparison with the Poisson distribution (if this option does not work, which might be the case for older versions, try replacing it with *normed=True*)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "plt.hist(...) # histogram for the measurements\n",
+ "plt.plot(...) # plot of the Poisson distribution\n",
+ "plt.xlabel('Counted particles')\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "What do you observe? Is the data from the experiment well described by the Poisson distribution?\n",
+ "\n",
+ "Let's now make a different assumption about the detector: it has no longer perfect efficiency, but whenever it detects a particle it needs some time to process the signal. Durign this time the detector is blind to any particle which might be absorbed by the target. In this way the recorded particles are not independent from each other anymore, and as you will see this will cause the result of the experiment to deviate from a Poisson distribution.\n",
+ "\n",
+ "Modify your implementation of the function *run_experiment()* in order to account for the dead time of the detector. Assume that whenever the detector records a particle it is blind to the next 500000 particles reaching the target."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def run_experiment_dead_time(...):\n",
+ " \n",
+ "# Run the function n_trials times and save the results as before\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Plot the new results with detector dead time together with the same Poisson distribution from before. What do you observe?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "plt.hist(...) # histogram for the measurements\n",
+ "plt.plot(...) # plot of the Poisson distribution\n",
+ "plt.xlabel('Counted particles')\n",
+ "plt.legend()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 2. Correlated variables and error matrix\n",
+ "\n",
+ "In this exercise you will work on a pair of correlated variables, compute the error matrix and visualize the error ellipse. Let's start from the case of two uncorrelated variables, saved in the file *data_uncorrelated.txt*. Have a look at the file: each line represents one measurement, the first number being the value of the *x* variable and the second number the value of the *y* variable."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "from matplotlib import pyplot as plt\n",
+ "\n",
+ "data = np.genfromtxt('data_uncorrelated.txt')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Plot the data. How can you recognise that *x* and *y* are not correlated? Compare the 2D distribution in the *xy* plane and the histograms of the *x* and *y* values. What do you notice about e.g. the range of the axes and the position of the means?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "f, ax = plt.subplots(1,3, figsize=(20, 6))\n",
+ "ax = ax.flatten()\n",
+ "\n",
+ "ax[0].set_xlabel(r'$x$')\n",
+ "ax[0].set_ylabel(r'$y$')\n",
+ "ax[0].axis('equal')\n",
+ "ax[0].plot(data[:,0],data[:,1],'.')\n",
+ "\n",
+ "ax[1].set_xlabel(r'$x$')\n",
+ "ax[1].hist(data[:,0],bins=range(-7,7),rwidth=.9)\n",
+ "\n",
+ "ax[2].set_xlabel(r'$y$')\n",
+ "ax[2].hist(data[:,1],bins=range(-7,7),rwidth=.9)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute the covariance matrix. You can either write a function to do this yourself, or use the numpy implementation. Have a look at last week's exercise if you feel lost."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compare your result with the error matrix you expect for two uncorrelated variables, cf. slides from Lecture 3: $\\text{diag}(\\sigma_x^2,\\sigma_y^2)$. Is your result compatible with this expression?\n",
+ "<br> We will now compute the eigenvectors and eigenvalues of the covariance matrix and interpret them in terms of the properties of the distributions we just saw. As before, you can compute the values yourself or use the numpy implementation *np.linalg.eig(matrix)*"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#Use this block to compute eigenvalues and eigenvectors of the covariance matrix and print the result\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For this easy case of uncorrelated variables you should recognize the following: the eigenvectors are aligned with the $x$ and $y$ axes and the eigenvalues are the variances of the data along the same axes; this means that the standard deviation in the $x$ and $y$ directions are the square root of the respective eigenvalue. Keep this in mind, as we will later see what changes if the variables are correlated.\n",
+ "\n",
+ "For a visual interpretation do the following: plot again the 2D distribution of the data together with the eigenvectors multiplied by the square root of the corresponding eigenvalue (in this way the length of the vector will be the corresponding standard deviation)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "plt.plot(data[:,0],data[:,1],'.',zorder=0)\n",
+ "plt.axis('equal')\n",
+ "\n",
+ "#Compute the x and y components of the two vectors:\n",
+ "vector1_x = ...\n",
+ "vector1_y = ...\n",
+ "vector2_x = ...\n",
+ "vector2_y = ...\n",
+ "\n",
+ "#Use the following function to draw the vectors. The options are needed to draw them in the correct size\n",
+ "plt.quiver(vector1_x, vector1_y ,angles='xy', scale_units='xy', scale=1,zorder=5)\n",
+ "plt.quiver(vector2_x, vector2_y ,angles='xy', scale_units='xy', scale=1,zorder=5)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's now draw an ellipse with half-axes $\\sigma_x$ and $\\sigma_y$: this is the equivalent of the $1 \\sigma$ interval for a 1D Gaussian distribution. Fill in the values for $\\sigma_x,\\sigma_y$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sigma_x = ...\n",
+ "sigma_y = ...\n",
+ "\n",
+ "phi = np.linspace(0,2*np.pi)\n",
+ "ellipse_x = sigma_x*np.cos(phi) # x-coordinates of the points on the ellipse\n",
+ "ellipse_y = sigma_y*np.sin(phi) # y-coordinates of the points on the ellipse\n",
+ "\n",
+ "plt.plot(ellipse_x,ellipse_y,'r')\n",
+ "plt.axis('equal')\n",
+ "\n",
+ "plt.plot(data[:,0],data[:,1],'.',zorder=0)\n",
+ "\n",
+ "#Redraw also the vectors (copy-paste from previous block)\n",
+ "plt.quiver(vector1_x, vector1_y ,angles='xy', scale_units='xy', scale=1,zorder=5)\n",
+ "plt.quiver(vector2_x, vector2_y ,angles='xy', scale_units='xy', scale=1,zorder=5)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let us now look at the case of two correlated measurements. Load the data from *data_uncorrelated.txt* and repeat the steps from above up to the drawing of the vectors; do not draw the ellipse yet, we will do that in the next step. You should be able to copy-paste most of the code from the uncorrelated case."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "data_correlated = np.genfromtxt('data_correlated.txt')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "You should now see that the eigenvectors are not aligned with the coordinate axes anymore. However, as before, the eigenvectors represent the direction of the largest spread of the data, and the eigenvalues, i.e. the variances, define how large this spread is.\n",
+ "\n",
+ "Let's now draw the ellipse. There are different ways in which this can be done. Let's start by determining the angle of rotation *theta*. *Hint*: take the *x* and *y* components of one of the eigenvectors and use the *np.arctan2()* function."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "theta = ..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To draw the rotated ellipse, define the $x$ and $y$ coordinates as before, and than rotate them by multiplying them with a rotation matrix by the angle *theta*."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "phi = np.linspace(0,2*np.pi)\n",
+ "ellipse_x = sigma[0]*np.cos(phi) # x-coordinates of the points on the ellipse\n",
+ "ellipse_y = sigma[1]*np.sin(phi) # y-coordinates of the points on the ellipse\n",
+ "\n",
+ "rotation = np.array([[np.cos(theta),np.sin(theta)],[-np.sin(theta),np.cos(theta)]])\n",
+ "ellipse = np.dot(rotation,[ellipse_x,ellipse_y]) # dot product"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we are ready to plot everything together."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "plt.plot(data_correlated[:,0],data_correlated[:,1],'.',zorder=0)\n",
+ "for i in range(2):\n",
+ " plt.quiver(sigma[i]*eigvec[0,i],sigma[i]*eigvec[1,i],angles='xy', scale_units='xy', scale=1,zorder=5)\n",
+ "plt.plot(ellipse[0,:],ellipse[1,:],'r')\n",
+ "plt.axis('equal')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Bonus\n",
+ "\n",
+ "The data for this exercise has been generated with the following code. Feel free to change the parameters and rerun the exercise."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "n_samples = 1000\n",
+ "mu = np.array([0.,0.])\n",
+ "var_x = 4.\n",
+ "var_y = 1.\n",
+ "cov_xy = 1.\n",
+ "r = np.array([\n",
+ " [ var_x, cov_xy,],\n",
+ " [ cov_xy, var_y,]\n",
+ " ])\n",
+ "\n",
+ "y = np.random.multivariate_normal(mu, r, size=n_samples)\n",
+ "\n",
+ "with open('output.txt', 'w') as outfile:\n",
+ " np.savetxt(outfile, y, fmt='%3.2f')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 3. Computing uncertainties on inefficiencies\n",
+ "\n",
+ "Consider an imperfect particle detector: out of all the particles hitting the detector, a fraction passes through unnoticed. The efficiency of the detector, i.e. the fraction of particles which are detected, is a very important parameter for any experimental setup. Suppose you want to measure the efficiency of a new detector. A possible approach is the following: you shoot $n$ particles on the detector, and count the number of signals $k$ which are recorded. The efficiency is then given by $\\varepsilon = k\\,/\\,n$. What is the uncertainty on this quantity? As a first approach, let's assume that $k$ and $n$ are Poisson distributed (and thus $\\delta k = \\sqrt{k}$ and $\\delta n = \\sqrt{n}$) and that we can apply the standard error propagation formula you saw in lecture 1:\n",
+ "$$ \\delta f = \\sqrt{ \\sum_{i=1}^N \\left(\\left. \\frac{\\partial f}{\\partial x_i}\\right\\vert_{x_i=x_i^0} \\delta x_i \\right)^2}. $$\n",
+ "- Show that this formula yields the following result:\n",
+ "$$ \\delta \\varepsilon = \\sqrt{\\frac{k}{n^2} + \\frac{k^2}{n^3}}. $$\n",
+ "\n",
+ "What happens to the uncertainty for *extreme* values of $k$, i.e. $k=0$ and $k=n$? Do these results make sense? Remember that the efficiency is by definition a number between 0 and 1.\n",
+ "\n",
+ "The source of the problem is that $k$ and $n$ are not independent (the particles which are recorded are a subset of all particles which hit the detector). A way to handle this is noting that the efficiency measurement is in fact a binomial process with total events $n$ and success probability $\\varepsilon$ (see slides of Lecture 3).\n",
+ "- Using the known variance of the binomial distribution show that in this case the uncertainty is given by \n",
+ "$$ \\delta \\varepsilon = \\sqrt{\\frac{\\varepsilon (1-\\varepsilon)}{n}}.$$\n",
+ "\n",
+ "An equivalent approach is to consider, instead of the total number of particles $n$, the number $n_f$ of particles which fail to be detected. In this approach, $n = k + n_f$ is not fixed anymore and $k$ and $n_f$ are uncorrelated; thus, the standard error formula is valid.\n",
+ "- Show that applying the standard error formula to $\\varepsilon = k\\,/\\,(k+n_f)$ yields again $$ \\delta \\varepsilon = \\sqrt{\\frac{\\varepsilon (1-\\varepsilon)}{n}}.$$\n",
+ "\n",
+ "Note that when evaluating this formula one has to use the measured (estimated) value of $\\varepsilon$, since the true value is unknown. This is a good approximation for *intermediate* values of $k$, i.e. $\\varepsilon$ not too close to 0 or 1. The exact meaning of *too close* is a matter of judgement - the extreme values $\\varepsilon = 0$ and $\\varepsilon = 1$ are clearly too close, as they yeld 0 uncertainty which is nonsense."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
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diff --git a/exercises/Exercise3/data_uncorrelated.txt b/exercises/Exercise3/data_uncorrelated.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9b1ca744d46c5380e3663407b72d5bc1a3b686d5
--- /dev/null
+++ b/exercises/Exercise3/data_uncorrelated.txt
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diff --git a/exercises/Exercise4/Exercise_4.ipynb b/exercises/Exercise4/Exercise_4.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..704d95b89424bb9d8d241d83e6a62c96d14ed685
--- /dev/null
+++ b/exercises/Exercise4/Exercise_4.ipynb
@@ -0,0 +1,436 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 4\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function # For Python < 3\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "import scipy.stats as stats\n",
+ "\n",
+ "%matplotlib inline \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1. Approximations to the binomial\n",
+ "\n",
+ "For np < 10, large n, the Poisson distribution is a good approximation for the binomial.\n",
+ "\n",
+ "* Show analytically that the binomial distribution converges to the Poisson distribution in the limit of large n. (Hint: $e = \\lim_{n\\to\\infty}(1+\\frac{1}{x})^x$)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Keeping $n p$ fixed, plot the binomial probability mass function for an increasing number of observations $n$, comparing in each case to the equivalent Poisson distribution ($\\lambda=n p$). For convenience, you should use the relevant functions in ```scipy.stat```."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n_trials = [5, 10, 100]\n",
+ "p0 = 0.8\n",
+ "...\n",
+ "\n",
+ "# Plot the PMFs\n",
+ "fh, ax = plt.subplots(1,len(n_trials), sharey=True, figsize=(10,4))\n",
+ "for idx, nt in enumerate(n_trials):\n",
+ " ...\n",
+ " ax[idx].bar(...)\n",
+ " ax[idx].bar(...)\n",
+ "\n",
+ "..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For np > 10, n(1-p) > 10, the discrete binomial distribution can be reasonably approximated by the continuous normal distribution.\n",
+ "\n",
+ "* Choose a large n (> 30, with p close to 0.5). To start with, choose n=100 and p=0.45. Plot the binomial pmf, and, with equivalent parameters, the normal pdf \n",
+ "* Calculate the probability that X >= 55 for each. Don't forget to apply the continuity correction\n",
+ "* What happens to the relative difference as n increases?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n_trials = 100\n",
+ "p0 = 0.45\n",
+ "mu = ... # Expectation\n",
+ "std = ... # Standard deviation\n",
+ "\n",
+ "#...\n",
+ "\n",
+ "print('Binomial (exact):', ...)\n",
+ "print('Gaussian (approximate):', ...)\n",
+ "\n",
+ "\n",
+ "# Plots\n",
+ "..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 2. Random walk\n",
+ "\n",
+ "Consider a simple 1D random walk. A person starts at the position $x=0$. With equal probability $p=0.5$, they may take one step forwards or one step backwards, corresponding to a displacement of +1 and -1 respectively.\n",
+ "\n",
+ "* Show that for an N step walk, the expected absolute distance from the starting position is given by $\\sqrt{N}$.\n",
+ "\n",
+ "* Write a function to simulate such a random walk, parameterised by the number of steps. The output should be an array, with the displacement at each step index.\n",
+ "\n",
+ "* Plot a single walk."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def random_walk(n_steps):\n",
+ " return ...\n",
+ "\n",
+ "n_steps = 100\n",
+ "w = random_walk(n_steps)\n",
+ "\n",
+ "..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Simulate ~1000 random walks of 500 steps.\n",
+ "\n",
+ "* Plot the average distance (rms) of these over the whole set with respect to step index (time). Does the average converge to the expected distance?\n",
+ "\n",
+ "* (Optional) sample and plot the running average to show how the convergence improves with number of walks."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n_steps = 500\n",
+ "n_walks = 1000\n",
+ "n = np.arange(n_steps) +1\n",
+ "\n",
+ "print('Expected distance for {} steps: {}'.format(...))\n",
+ "\n",
+ "W = [] # Final distance\n",
+ "A = [] # Running average over whole set\n",
+ "T = 0\n",
+ "for idx in range(n_walks):\n",
+ " ...\n",
+ "\n",
+ "# ...\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Now consider the case $p \\ne 0.5$, where the \"person\" is more likely to step in one direction than another. Find again analytically the expectation and the variance for the (rms) distance travelled in terms of $N$ and $p$.\n",
+ "\n",
+ "* Modify the random_walk function to account for the unequal probability between the directions."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Run a series of random walks as before, and plot again the histogram of distances travelled. On top of this, plot the Gaussian PDF with the $\\mu$ and $\\sigma$ parameters as determined above."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Plot histogram\n",
+ "n_steps = 2000\n",
+ "n_trials = 5000\n",
+ "p = 0.4\n",
+ "\n",
+ "V = []\n",
+ "for n in range(n_trials):\n",
+ " ...\n",
+ " \n",
+ "..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 3. Small sample sizes: t-distribution\n",
+ "### 3.1 Compare to normal distribution\n",
+ "\n",
+ "Student's t-distributions are interesting for cases where you have few samples and the population variance is unknown, but the underlying distribution of the means can be assumed normal. They are parameterised by the degrees of freedom (\"df\"), which is usually equal the number of samples minus one. As the number of degrees of freedom increases, the t-distribution converges to the normal distribution.\n",
+ "\n",
+ "* Plot the standard t-distribution for several increasing degrees of freedom and compare this to the normal PDF.\n",
+ "* Plot and compare the cumulative distribution functions\n",
+ "* Plot the variance of the t-distribution as a function of degrees of freedom. Compare to the standard normal variance (=1)\n",
+ "* (optional) make a Q-Q plot (see Wiki) and compare the distributions\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "x = np.linspace(-5, 5, 200)\n",
+ "df_all = [1,2,5,10,30]\n",
+ "\n",
+ "fh, ax = plt.subplots(2,2, figsize=(10,8))\n",
+ "\n",
+ "# PDF\n",
+ "for df in df_all:\n",
+ " ...\n",
+ " ax[0,0].plot(...)\n",
+ "\n",
+ "# CDF\n",
+ "for df in df_all:\n",
+ " ...\n",
+ " ax[1,0].plot(...)\n",
+ "ax[1,0].plot(...)\n",
+ "\n",
+ "# Variance vs degrees of freedom\n",
+ "...\n",
+ "ax[0,1].set_xlabel('DOF')\n",
+ "ax[0,1].set_ylabel('Var(T)')\n",
+ "\n",
+ "# Q-Q plot (optional)\n",
+ "for df in df_all:\n",
+ " ...\n",
+ " ax[1,1].plot(...)\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 3.2 Eggs\n",
+ "An egg producer claims to supply eggs with an average egg weight of 63 g. In a box of 12, the following weights were measured (all in g):\n",
+ "\n",
+ " 62.75, 56.98, 53.30, 62.65, 57.63, 57.23, 56.65, 64.89, 57.87, 60.42, 57.01, 63.65\n",
+ " \n",
+ "* Calculate the sample mean and (adjusted -- see ```ddof``` option) sample standard deviation.\n",
+ "\n",
+ "* What is the probability of obtaining this average weight or lighter, given the supplier's claim?\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "s = [62.75, 56.98, 53.30, 62.65, 57.63, 57.23, 56.65, 64.89, 57.87, 60.42, 57.01, 63.65]\n",
+ "n_samples = ...\n",
+ "dof = ... # degrees of freedom\n",
+ "mu_samp = ... # Sampling mean\n",
+ "sig_samp = np.std(s, ddof=1)\n",
+ "mu_claim = ... # Claimed population mean\n",
+ "\n",
+ "...\n",
+ "print('Probability of this sample mean ({:.2f}) against claimed mean ({:.2f}): {:.2f} %'.format(\n",
+ " ...))\n",
+ "\n",
+ "plt.figure()\n",
+ "...\n",
+ "plt.xlabel('Egg weight (g) (W)')\n",
+ "plt.ylabel('P(W)')\n",
+ "\n",
+ "plt.show()\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Within what range would 95% of samples follow? And how would this compare with an equivalent normal distribution?\n",
+ "* Plot again the two distributions, marking the 95% intervals"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "...\n",
+ "print('Normal: 95% of samples between {} and {}'.format(...))\n",
+ "print('T-distribution: 95% of samples between {} and {}'.format(...))\n",
+ "\n",
+ "plt.figure()\n",
+ "...\n",
+ "plt.xlabel('Egg weight (g) (W)')\n",
+ "plt.ylabel('P(W)')\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Bonus\n",
+ "A pair of independent, standard normal random variables can be generated by sampling a uniform distribution. One approach to this is the Box-Muller transform (see https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform).\n",
+ "\n",
+ "* Generate a long sequence of numbers drawn from U(0,1)\n",
+ "* Use the Box-Muller transform to convert these to normal random variables\n",
+ "* Plot the normal samples on a scatter plot - verify they are not correlated\n",
+ "* Plot the histograms, and superimpose the normal PDF\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "u1 = ...\n",
+ "u2 = ...\n",
+ "n1 = ...\n",
+ "n2 = ...\n",
+ "\n",
+ "...\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Improbable events\n",
+ "In this example, we tabulate the amplitude deviation against the probability, odds (inverse probability), and equivalent timescale (once in 10 thousand years). Modify the code and try with different distributions - especially those which look similar to the normal distribution, but carry a fatter tail."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from IPython.display import display\n",
+ "import pandas as pd\n",
+ "\n",
+ "def format_days(d):\n",
+ " if d < 365:\n",
+ " if d > 90:\n",
+ " return '{:1.0f} months'.format(d/30)\n",
+ " elif d > 7:\n",
+ " return '{:1.0f} weeks'.format(d/7)\n",
+ " else:\n",
+ " return '{:1.0f} days'.format(d)\n",
+ " d /= 365\n",
+ " \n",
+ " if d > 1e9:\n",
+ " return '{:1.1f} billion years'.format(d*1e-9)\n",
+ " elif d > 1e6:\n",
+ " return '{:1.1f} million years'.format(d*1e-6)\n",
+ " elif d > 1e3:\n",
+ " return '{:1.1f} millenia'.format(d*1e-3)\n",
+ " else:\n",
+ " return '{:1.1f} years'.format(d)\n",
+ "\n",
+ "\n",
+ "z = np.linspace(0, 10, 500)\n",
+ "\n",
+ "data = []\n",
+ "for n in range(1,8):\n",
+ " p = 2*(1-stats.norm.cdf(n))\n",
+ " data.append([n, p, 1/p, format_days(1/p)])\n",
+ " \n",
+ "display(pd.DataFrame(data, columns=[r'|X| ($\\sigma)$', 'p', '1 in', 'time equivalent']))\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Code to generate \"egg\" distribution"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [],
+ "source": [
+ "# Generate small dataset for T-dist question\n",
+ "# True parameters:\n",
+ "sig = 3\n",
+ "mu = 58\n",
+ "n_samples = 12\n",
+ "\n",
+ "s = stats.norm.rvs(size=n_samples, loc=mu, scale=sig)\n",
+ "print(('{:.2f}, '*n_samples).format(*s)[:-2])\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Exercise4/Exercise_4.pdf b/exercises/Exercise4/Exercise_4.pdf
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index 0000000000000000000000000000000000000000..c25bc6b9ae8dcc015e7756b5e5530b762eea6ca6
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diff --git a/exercises/Exercise5/Exercise_5.ipynb b/exercises/Exercise5/Exercise_5.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..f0901bfb63fd378c30526ea5a5e2dce9ee3a7635
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+++ b/exercises/Exercise5/Exercise_5.ipynb
@@ -0,0 +1,406 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Solution Exercise 5\n",
+ "This week, we are working on least squares fits and parameter estimation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy.optimize import curve_fit\n",
+ "from scipy.stats import norm, chi2, lognorm"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Fit a polynomial\n",
+ "We start by fitting a polynomial to a given data set, in particular, a parabola. Compare a linear fit and a cubic fit to our parabolic fit and check the goodness of fits with chi squared distributions. Explore how the different uncertainties affect the outcome and uncertainties of the fit. \n",
+ "\n",
+ "Hint: You can consider a plot similar to the lecture notes week 5 page 29. and/or plot the residuals for the different cases.\n",
+ "\n",
+ "Extra: Do you see any way to decide wether the data is better described by the parabola or the cubic?\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Create some data distribuited as parabola with normally distributed errors.\n",
+ "def parabola(x, a, b, c):\n",
+ " return a*x**2 + b*x + c\n",
+ "def error(x, sigma):\n",
+ " return norm.rvs(0.0, sigma, x.size) \n",
+ "a = -0.1\n",
+ "b = 0\n",
+ "c = 1\n",
+ "sigma_y = 0.0015\n",
+ "\n",
+ "x = np.linspace(0, 1, 21)\n",
+ "y_true = parabola(x, a, b, c)\n",
+ "delta_y = error(x, sigma_y)\n",
+ "y = y_true + delta_y\n",
+ "y_error = sigma_y * np.ones(x.size)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def fit_polynomial(x, y, degree, weight):\n",
+ " pass"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x2bbf82dc240>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot the fit results and their residuals\n",
+ "f, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
+ "ax[0].set_title('fits')\n",
+ "ax[0].errorbar(x, y, yerr=y_error, fmt='k.', label='data')\n",
+ "ax[0].plot(x, y_true, 'k-', label='true')\n",
+ "ax[0].legend()\n",
+ "\n",
+ "\n",
+ "ax[1].set_title('residuals')\n",
+ "ax[1].plot(y_true - y, 'k.', label='data')\n",
+ "f.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Draw the plot form lecture notes week 5, page 29 and plot your chi-squares for the different fits.\n",
+ "pass"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# ..."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Fit a nonlinear function\n",
+ "Next, we consider a Gaussian as an example of a nonlinear function. We are measuring some feature which has a Gaussian distribution in $x$. This could be an inhomogeneous spectral line for $x=E$ the energy of emitted photons. We are interested in the resonance frequency and the linewidth, i. e. we want to estimate them form our observations. \n",
+ "\n",
+ "Finally, create your own data set and vary the sample size!"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 45,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def gaussian_parent(x, mu, sigma):\n",
+ " return norm.pdf(x, mu, sigma) \n",
+ "\n",
+ "def gaussian_sample(mu, sigma, sample_size):\n",
+ " return norm.rvs(mu, sigma, sample_size)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 46,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Load data from disk. Format (3,12): (x, y, y_error) x N \n",
+ "data = np.loadtxt('data')\n",
+ "x = data[0, :]\n",
+ "y = data[1, :]\n",
+ "y_error = data[2, :]\n",
+ "# The sample used to generate\n",
+ "sample = np.loadtxt('sample')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 47,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Function we want to fit to our data set\n",
+ "def model_function(x, *args):\n",
+ " pass"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Plot the result"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 48,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x2bbf99d2860>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x_arr = np.linspace(1500, 1600, 101)\n",
+ "\n",
+ "plt.figure(figsize=(5, 4))\n",
+ "plt.xlabel(r'$E$ (meV)')\n",
+ "plt.ylabel('count rate')\n",
+ "plt.errorbar(x, y, yerr=y_errors, fmt='.', ms=7, capsize=3, label='sample')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Biased estimator example\n",
+ "Take a lognormal sample and try to estimate its mean. Try it by fitting a Gaussian - what do you observe?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 44,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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4cP4oU/La8uE/ci8BfrN7lnFU1SeTvAf4FHAC+DQwLR8x9t4kTwG+Cbx2Cp+o7XkZmiRpC+wBS9LZygBLUhMDLElNDLAkNTHAktTEAEtSEwMsSU3+HyHlvRYlbpdpAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x2bbf97e9320>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "log_sample = lognorm.rvs(s=0.5, loc=3, scale=1, size=1000)\n",
+ "\n",
+ "plt.figure(figsize=(5, 4))\n",
+ "h = plt.hist(log_sample, bins=32, rwidth=0.85, normed=True)\n",
+ "x_arr = np.linspace(2, 5, 51)\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Bonus: Errors in x and y\n",
+ "So far, we considered uncertainties only on y. Consider the following data set with errors in both x and y. Try to fit a line to the data below, taking into account both errors. Compare with fits neglecting the x errors or both. \n",
+ " \n",
+ "Hint: A detailed solution is already on the moodle. You may chose if you want to try to write your own solution, implement a known solution (see references in solution notebook) or just try it with the scipy package ODR (orthogonal distance regression). \n",
+ "https://docs.scipy.org/doc/scipy/reference/odr.html\n",
+ " \n",
+ "The solution contains a python implementation of York's equation, comparison with ODR and MC tests. \n",
+ "Week 3: \"Linear Regression errors x and y\""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x2fb04639160>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Test data\n",
+ "X = np.array([0.0, 0.9, 1.8, 2.6, 3.3, 4.4, 5.2, 6.1, 6.5, 7.4])\n",
+ "Y = np.array([5.9, 5.4, 4.4, 4.6, 3.5, 3.7, 2.8, 2.8, 2.4, 1.5])\n",
+ "wX = np.array([1000, 1000, 500, 800, 200, 80, 60, 20, 1.8, 1])\n",
+ "wY = np.array([1, 1.8, 4, 8, 20, 20, 70, 70, 100, 500])\n",
+ "sigma_x = 1.0/np.sqrt(wX)\n",
+ "sigma_y = 1.0/np.sqrt(wY)\n",
+ "\n",
+ "plt.figure(figsize=(4, 3))\n",
+ "plt.errorbar(X, Y, xerr=sigma_x, yerr=sigma_y, fmt='o', label='oberservations')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "hide_input": false,
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.6"
+ },
+ "toc": {
+ "base_numbering": 1,
+ "nav_menu": {},
+ "number_sections": true,
+ "sideBar": true,
+ "skip_h1_title": false,
+ "title_cell": "Table of Contents",
+ "title_sidebar": "Contents",
+ "toc_cell": false,
+ "toc_position": {
+ "height": "calc(100% - 180px)",
+ "left": "10px",
+ "top": "150px",
+ "width": "225.438px"
+ },
+ "toc_section_display": true,
+ "toc_window_display": true
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Exercise5/Exercise_5.pdf b/exercises/Exercise5/Exercise_5.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..b463ebddb4ba075650069371899855d24fc8ef19
Binary files /dev/null and b/exercises/Exercise5/Exercise_5.pdf differ
diff --git a/exercises/Exercise5/data b/exercises/Exercise5/data
new file mode 100644
index 0000000000000000000000000000000000000000..2f9e9460dfeb54bd334d083e778ea829ee602f51
--- /dev/null
+++ b/exercises/Exercise5/data
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diff --git a/exercises/Exercise5/sample b/exercises/Exercise5/sample
new file mode 100644
index 0000000000000000000000000000000000000000..391dbdd251d00864cca913e3e720bf71c7d87468
--- /dev/null
+++ b/exercises/Exercise5/sample
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diff --git a/exercises/Exercise6/Complete_TAVG_complete.txt b/exercises/Exercise6/Complete_TAVG_complete.txt
new file mode 100644
index 0000000000000000000000000000000000000000..754acdd512bf2bf6a6a03c1e461057a614fa5c3f
--- /dev/null
+++ b/exercises/Exercise6/Complete_TAVG_complete.txt
@@ -0,0 +1,3259 @@
+% This file contains a detailed summary of the land-surface average
+% results produced by the Berkeley Averaging method. Temperatures are
+% in Celsius and reported as anomalies relative to the Jan 1951-Dec 1980
+% average. Uncertainties represent the 95% confidence interval for
+% statistical and spatial undersampling effects.
+%
+% The current dataset presented here is described as:
+%
+% Estimated Global Land-Surface TAVG based on the Complete Berkeley Dataset
+%
+%
+% This analysis was run on 21-Oct-2018 08:22:38
+%
+% Results are based on 38983 time series
+% with 16951483 data points
+%
+% Estimated Jan 1951-Dec 1980 absolute temperature (C): 8.63 +/- 0.11
+%
+% As Earth's land is not distributed symmetrically about the equator, there
+% exists a mean seasonality to the global land-average.
+%
+% Estimated Jan 1951-Dec 1980 monthly absolute temperature:
+% Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
+% 2.59 3.21 5.31 8.32 11.33 13.47 14.34 13.87 12.09 9.25 6.09 3.62
+% +/- 0.13 0.12 0.11 0.11 0.12 0.12 0.11 0.11 0.11 0.11 0.12 0.12
+%
+% For each month, we report the estimated land-surface average for that
+% month and its uncertainty. We also report the corresponding values for
+% year, five-year, ten-year, and twenty-year moving averages CENTERED about
+% that month (rounding down if the center is in between months). For example,
+% the annual average from January to December 1950 is reported at June 1950.
+%
+% Year, Month, Monthly Anomaly, Monthly Unc., Annual Anomaly, Annual Unc., Five-year Anomaly, Five-year Unc., Ten-year Anomaly, Unc., Ten-year Anomaly, Unc.
+ Year Month MDiff MUnc YDiff YUnc 5YDiff 5YUnc 10YDiff 10YUnc 20YDiff 20YUnc
+ 1750 1 -0.121 4.187 -0.687 2.557 -0.364 0.897 -0.160 NaN NaN NaN
+ 1750 2 -1.278 3.177 -0.691 1.733 -0.381 0.904 -0.169 NaN NaN NaN
+ 1750 3 0.112 3.550 -0.721 1.568 -0.401 0.918 -0.164 NaN NaN NaN
+ 1750 4 0.026 2.862 -0.734 1.609 -0.452 0.951 -0.168 NaN NaN NaN
+ 1750 5 -1.420 2.611 -1.043 1.553 -0.439 1.022 -0.167 NaN NaN NaN
+ 1750 6 -1.029 3.379 -1.004 1.271 -0.414 1.060 -0.176 NaN NaN NaN
+ 1750 7 -0.262 2.722 -1.049 1.026 -0.411 1.023 -0.183 NaN NaN NaN
+ 1750 8 0.290 3.219 -1.137 0.792 -0.466 0.933 -0.210 NaN NaN NaN
+ 1750 9 -0.851 2.121 -1.107 0.775 -0.375 0.945 -0.230 NaN NaN NaN
+ 1750 10 -1.448 3.078 -1.167 0.826 -0.394 1.023 -0.211 NaN NaN NaN
+ 1750 11 -3.518 1.996 -1.160 1.283 -0.423 1.094 -0.226 0.879 NaN NaN
+ 1750 12 -2.538 4.091 -1.210 1.458 -0.451 1.143 -0.250 0.894 NaN NaN
+ 1751 1 -0.659 3.318 -1.094 1.533 -0.464 1.148 -0.258 0.844 NaN NaN
+ 1751 2 -2.341 4.503 -1.047 1.776 -0.482 1.131 -0.231 0.914 NaN NaN
+ 1751 3 0.477 2.778 -1.068 1.673 -0.488 1.200 -0.201 0.952 NaN NaN
+ 1751 4 -0.690 2.489 -0.933 1.504 -0.492 1.245 -0.184 1.004 NaN NaN
+ 1751 5 -1.338 3.435 -0.771 1.606 -0.486 1.336 -0.184 1.019 NaN NaN
+ 1751 6 -1.637 3.336 -0.721 1.085 -0.539 1.393 -0.188 1.075 NaN NaN
+ 1751 7 1.130 3.753 -0.876 1.400 -0.527 1.212 -0.208 1.084 NaN NaN
+ 1751 8 0.858 2.757 -0.409 1.841 -0.538 1.097 -0.221 1.106 NaN NaN
+ 1751 9 -1.098 2.928 -0.382 1.840 -0.531 1.123 -0.225 1.119 NaN NaN
+ 1751 10 0.169 4.986 -0.429 1.791 -0.446 1.151 -0.219 1.148 -0.276 NaN
+ 1751 11 -1.577 2.326 -0.302 1.688 -0.437 1.160 -0.222 1.178 -0.286 NaN
+ 1751 12 -1.935 3.412 -0.129 1.784 -0.426 1.293 -0.258 1.173 -0.316 NaN
+ 1752 1 -2.523 4.962 -0.154 1.757 -0.431 1.296 -0.262 1.160 -0.299 NaN
+ 1752 2 3.263 4.891 -0.311 1.743 -0.461 1.061 -0.216 1.213 -0.299 NaN
+ 1752 3 0.804 3.040 -0.166 1.570 -0.480 1.053 -0.192 1.258 -0.303 NaN
+ 1752 4 -1.259 2.243 -0.263 1.645 -0.447 1.072 -0.185 1.364 -0.295 NaN
+ 1752 5 0.196 1.576 -0.090 1.758 -0.449 1.030 -0.178 1.431 -0.293 NaN
+ 1752 6 0.434 3.225 0.040 1.815 -0.390 1.072 -0.179 1.504 -0.293 NaN
+ 1752 7 0.831 1.966 0.222 1.538 -0.386 1.030 -0.171 1.657 -0.298 NaN
+ 1752 8 -1.027 1.386 -0.140 1.327 -0.390 0.956 -0.146 1.677 -0.293 NaN
+ 1752 9 0.642 2.557 -0.087 1.373 -0.408 0.990 -0.145 1.681 -0.294 NaN
+ 1752 10 -0.994 2.816 -0.050 1.361 -0.398 1.019 -0.188 1.640 -0.306 NaN
+ 1752 11 0.505 1.992 -0.036 1.516 -0.366 1.108 -0.201 1.701 -0.307 NaN
+ 1752 12 -0.383 3.917 -0.084 1.361 -0.334 1.151 -0.204 1.647 -0.321 NaN
+ 1753 1 -0.333 3.751 -0.148 1.244 -0.318 1.128 -0.232 1.563 -0.337 NaN
+ 1753 2 -1.083 4.958 -0.086 1.230 -0.333 1.064 -0.268 1.563 -0.351 NaN
+ 1753 3 1.435 3.525 -0.117 1.036 -0.336 1.142 -0.242 1.567 -0.363 NaN
+ 1753 4 -0.809 3.659 -0.057 1.005 -0.266 1.130 -0.255 1.601 -0.365 NaN
+ 1753 5 0.359 2.669 -0.158 1.148 -0.216 1.199 -0.292 1.622 -0.368 NaN
+ 1753 6 -0.142 2.707 -0.386 0.997 -0.203 1.291 -0.310 1.638 -0.385 NaN
+ 1753 7 0.060 1.606 -0.366 0.982 -0.174 1.293 -0.323 1.651 -0.382 NaN
+ 1753 8 -0.277 1.721 -0.488 0.994 -0.084 1.443 -0.351 1.655 -0.386 NaN
+ 1753 9 0.263 2.096 -0.659 0.937 -0.095 1.425 -0.373 1.701 -0.395 NaN
+ 1753 10 -0.272 2.003 -0.223 1.130 -0.054 1.392 -0.415 1.715 -0.393 NaN
+ 1753 11 -0.708 3.137 -0.140 1.242 -0.004 1.384 -0.408 1.738 -0.398 NaN
+ 1753 12 -3.115 2.735 -0.113 1.281 0.028 1.473 -0.418 1.800 -0.399 NaN
+ 1754 1 -0.097 4.243 -0.070 1.369 0.001 1.474 -0.395 1.759 -0.403 NaN
+ 1754 2 -2.538 5.537 -0.171 1.410 -0.032 1.497 -0.368 1.771 -0.387 NaN
+ 1754 3 -0.625 3.212 -0.325 1.395 -0.021 1.471 -0.361 1.802 -0.384 NaN
+ 1754 4 4.427 2.526 -0.248 1.480 -0.039 1.507 -0.371 1.829 -0.393 NaN
+ 1754 5 1.356 3.564 -0.183 1.432 -0.037 1.589 -0.392 1.839 -0.398 NaN
+ 1754 6 0.179 3.515 0.119 1.456 -0.046 1.613 -0.389 1.868 -0.416 NaN
+ 1754 7 0.577 1.705 0.139 1.791 -0.037 1.574 -0.414 1.884 -0.429 NaN
+ 1754 8 -1.486 1.583 0.225 1.963 -0.063 1.622 -0.414 1.525 -0.430 NaN
+ 1754 9 -1.591 1.746 0.197 2.094 -0.079 1.647 -0.411 1.527 -0.437 NaN
+ 1754 10 0.655 2.919 -0.124 1.896 -0.051 1.719 -0.412 1.529 -0.430 NaN
+ 1754 11 0.077 2.709 -0.192 1.834 -0.036 1.796 -0.433 1.510 -0.435 NaN
+ 1754 12 0.502 3.293 -0.135 1.967 -0.000 1.833 -0.438 1.523 -0.425 NaN
+ 1755 1 0.140 5.142 -0.125 1.955 0.022 1.927 -0.467 1.502 -0.416 NaN
+ 1755 2 -1.506 4.365 -0.051 2.012 0.088 1.944 -0.455 1.494 -0.414 NaN
+ 1755 3 -0.954 4.793 -0.004 2.164 0.111 1.742 -0.479 1.456 -0.402 NaN
+ 1755 4 0.578 3.205 0.173 2.225 0.075 1.674 -0.490 1.430 -0.402 NaN
+ 1755 5 0.534 2.783 0.122 2.345 0.038 1.707 -0.490 1.459 -0.405 NaN
+ 1755 6 0.858 5.570 -0.065 2.160 0.006 1.490 -0.498 1.446 -0.426 NaN
+ 1755 7 0.702 3.033 0.010 1.938 -0.053 1.429 -0.522 1.439 -0.434 NaN
+ 1755 8 -0.593 1.923 0.391 2.250 -0.071 1.470 -0.537 1.412 -0.446 NaN
+ 1755 9 -1.034 2.347 0.456 2.041 -0.109 1.467 -0.547 1.428 -0.454 NaN
+ 1755 10 2.787 4.106 0.558 1.946 -0.115 1.469 -0.554 1.415 -0.459 NaN
+ 1755 11 -0.542 3.503 0.647 1.848 -0.161 1.442 -0.529 1.458 -0.464 1.277
+ 1755 12 -1.743 3.887 0.600 1.741 -0.168 1.447 -0.528 1.490 -0.471 1.281
+ 1756 1 1.043 2.940 0.505 1.779 -0.181 1.468 -0.540 1.525 -0.492 1.259
+ 1756 2 3.068 4.190 0.458 1.761 -0.220 1.484 -0.525 1.577 -0.487 1.275
+ 1756 3 -0.177 4.549 0.510 1.712 -0.258 1.508 -0.522 1.576 -0.468 1.288
+ 1756 4 1.804 2.923 0.198 1.747 -0.338 1.499 -0.523 1.558 -0.468 1.315
+ 1756 5 1.606 3.980 0.121 1.812 -0.331 1.463 -0.500 1.539 -0.474 1.323
+ 1756 6 0.285 4.037 0.063 1.785 -0.297 1.481 -0.463 1.519 -0.478 1.332
+ 1756 7 -0.433 1.903 -0.190 1.832 -0.264 1.514 -0.440 1.509 -0.491 1.340
+ 1756 8 -1.163 2.242 -0.303 1.931 -0.199 1.560 -0.441 1.506 -0.491 1.344
+ 1756 9 -0.408 2.234 -0.301 2.104 -0.191 1.572 -0.434 1.525 -0.489 1.344
+ 1756 10 -0.954 3.386 -0.418 2.337 -0.297 1.570 -0.459 1.519 -0.483 1.348
+ 1756 11 -1.461 3.777 -0.457 2.640 -0.347 1.563 -0.453 1.535 -0.471 1.343
+ 1756 12 -2.440 4.869 -0.268 2.713 -0.352 1.533 -0.483 1.490 -0.481 1.341
+ 1757 1 -1.991 3.612 -0.050 3.119 -0.397 1.546 -0.435 1.458 -0.487 1.337
+ 1757 2 1.704 5.413 0.291 3.070 -0.366 1.554 -0.452 1.498 -0.470 1.338
+ 1757 3 -0.151 4.729 0.494 2.980 -0.342 1.561 -0.469 1.506 -0.450 1.338
+ 1757 4 0.406 5.121 0.309 2.602 -0.377 1.546 -0.458 1.501 -0.455 1.360
+ 1757 5 1.131 4.566 0.287 2.506 -0.416 1.546 -0.468 1.492 -0.459 1.369
+ 1757 6 2.553 5.010 0.299 2.334 -0.486 1.542 -0.481 1.473 -0.468 1.375
+ 1757 7 2.181 2.865 0.144 1.935 -0.548 1.532 -0.498 1.465 -0.477 1.413
+ 1757 8 2.928 3.741 -0.179 1.632 -0.520 1.559 -0.489 1.468 -0.470 1.418
+ 1757 9 2.027 2.197 -0.238 1.492 -0.550 1.506 -0.512 1.310 -0.477 1.423
+ 1757 10 -3.170 2.786 -0.368 1.281 -0.581 1.460 -0.526 1.295 -0.485 1.424
+ 1757 11 -1.721 3.095 -0.665 1.205 -0.613 1.445 -0.527 1.313 -0.474 1.446
+ 1757 12 -2.305 4.124 -0.924 1.136 -0.662 1.424 -0.535 1.136 -0.474 1.442
+ 1758 1 -3.844 7.286 -1.167 1.137 -0.725 1.437 -0.548 1.165 -0.491 1.436
+ 1758 2 -2.179 3.918 -1.628 1.021 -0.740 1.432 -0.557 1.181 -0.514 1.430
+ 1758 3 -0.848 4.045 -1.961 0.960 -0.758 1.410 -0.599 1.166 -0.510 1.429
+ 1758 4 -1.158 4.034 -2.123 1.226 -0.842 1.408 -0.602 1.162 -0.515 1.441
+ 1758 5 -2.434 2.151 -2.001 1.236 -0.843 1.432 -0.617 1.156 -0.530 1.454
+ 1758 6 -0.556 2.631 -1.901 1.290 -0.852 1.382 -0.632 1.153 -0.540 1.462
+ 1758 7 -0.735 2.202 -1.422 1.383 -0.906 1.436 -0.618 1.159 -0.543 1.473
+ 1758 8 -2.602 1.502 -1.127 1.599 -0.967 1.393 -0.618 1.161 -0.549 1.478
+ 1758 9 -1.975 1.825 -1.071 1.736 -0.949 1.377 -0.629 1.174 -0.553 1.499
+ 1758 10 -5.106 3.186 -1.134 1.739 -0.993 1.386 -0.650 1.173 -0.557 1.507
+ 1758 11 -0.266 2.936 -1.070 1.683 -0.995 1.377 -0.657 1.155 -0.555 1.513
+ 1758 12 -1.104 3.054 -1.031 1.786 -0.954 1.322 -0.639 1.163 -0.556 1.534
+ 1759 1 1.905 3.048 -1.145 1.935 -0.882 1.294 -0.651 1.176 -0.551 1.510
+ 1759 2 1.365 4.971 -0.902 1.772 -0.849 1.278 -0.609 1.182 -0.547 1.510
+ 1759 3 -0.174 2.807 -0.749 1.714 -0.847 1.322 -0.606 1.177 -0.545 1.517
+ 1759 4 -1.912 4.162 -0.444 1.487 -0.878 1.298 -0.649 1.181 -0.537 1.529
+ 1759 5 -1.675 1.517 -0.610 1.567 -0.868 1.281 -0.672 1.189 -0.532 1.533
+ 1759 6 -0.088 1.439 -0.825 1.707 -0.919 1.263 -0.692 1.173 -0.523 1.545
+ 1759 7 -2.103 1.996 -1.283 1.756 -0.834 1.214 -0.711 1.187 -0.526 1.552
+ 1759 8 0.318 2.531 -1.379 1.517 -0.840 1.205 -0.708 1.185 -0.526 1.227
+ 1759 9 -0.135 2.151 -1.594 1.423 -0.860 1.193 -0.703 1.173 -0.524 1.227
+ 1759 10 -1.452 2.161 -1.546 1.255 -0.865 1.155 -0.698 1.170 -0.534 1.226
+ 1759 11 -2.251 3.076 -1.521 1.297 -0.901 1.123 -0.699 1.165 -0.548 1.210
+ 1759 12 -3.694 5.478 -1.684 1.371 -0.962 1.107 -0.685 1.146 -0.554 1.206
+ 1760 1 -3.586 3.405 -1.768 1.744 -1.019 1.074 -0.673 1.112 -0.555 1.189
+ 1760 2 0.211 3.130 -1.919 1.837 -1.066 1.028 -0.659 1.131 -0.547 1.183
+ 1760 3 -2.755 2.492 -2.085 1.970 -1.135 1.033 -0.640 1.110 -0.562 1.172
+ 1760 4 -1.331 2.319 -2.152 1.952 -1.126 1.045 -0.636 1.091 -0.554 1.161
+ 1760 5 -1.369 2.044 -2.012 1.834 -1.092 1.046 -0.643 1.078 -0.552 1.175
+ 1760 6 -2.054 2.720 -1.897 1.424 -1.076 1.062 -0.675 1.058 -0.555 1.156
+ 1760 7 -3.110 2.134 -1.779 1.568 -1.043 1.108 -0.684 1.043 -0.566 1.158
+ 1760 8 -1.495 1.504 -1.844 1.432 -1.043 1.142 -0.682 1.039 -0.574 1.144
+ 1760 9 -2.119 1.520 -1.543 1.528 -1.089 1.164 -0.678 1.029 -0.573 1.156
+ 1760 10 -2.261 2.222 -1.499 1.617 -1.090 1.127 -0.707 1.024 -0.566 1.153
+ 1760 11 -0.566 3.687 -1.261 1.492 -1.074 1.119 -0.703 1.019 -0.551 1.154
+ 1760 12 -2.322 2.815 -0.861 1.222 -1.096 1.139 -0.692 1.000 -0.536 1.173
+ 1761 1 -2.165 4.523 -0.277 0.968 -1.055 1.139 -0.727 1.017 -0.521 1.171
+ 1761 2 -0.574 4.049 -0.086 0.961 -1.015 1.133 -0.742 1.001 -0.528 1.195
+ 1761 3 0.856 2.658 0.065 1.179 -1.001 1.138 -0.736 0.982 -0.542 1.187
+ 1761 4 -0.795 2.574 0.019 1.174 -0.962 1.121 -0.752 0.983 -0.548 1.178
+ 1761 5 1.482 1.394 -0.003 1.019 -0.984 1.101 -0.764 0.986 -0.548 1.180
+ 1761 6 2.748 2.215 -0.272 1.160 -0.981 1.082 -0.767 0.992 -0.538 1.186
+ 1761 7 3.892 1.844 0.171 0.850 -1.038 1.085 -0.773 1.001 -0.544 1.188
+ 1761 8 0.798 1.778 0.328 1.113 -1.019 1.022 -0.761 0.995 -0.543 1.184
+ 1761 9 -0.300 3.709 0.148 1.220 -1.021 0.995 -0.753 1.000 -0.539 1.173
+ 1761 10 -2.817 1.919 0.223 1.222 -1.002 0.974 -0.748 0.980 -0.533 1.173
+ 1761 11 -0.831 2.535 0.011 1.143 -0.996 1.000 -0.720 0.962 -0.531 1.179
+ 1761 12 -5.545 2.430 -0.307 1.227 -1.033 1.000 -0.704 0.935 -0.526 1.119
+ 1762 1 3.147 3.876 -0.735 1.260 -1.026 1.019 -0.712 0.934 -0.518 1.106
+ 1762 2 1.308 6.277 -0.793 1.262 -1.050 1.033 -0.724 0.894 -0.541 1.111
+ 1762 3 -1.306 4.391 -0.944 1.051 -1.064 1.018 -0.708 0.861 -0.556 1.100
+ 1762 4 0.115 1.958 -0.932 1.025 -1.019 0.999 -0.725 0.844 -0.548 1.089
+ 1762 5 -1.063 3.375 -0.834 1.122 -0.982 0.963 -0.739 0.821 -0.555 1.094
+ 1762 6 -1.072 2.285 -0.485 1.142 -0.883 0.895 -0.758 0.806 -0.562 1.093
+ 1762 7 -1.244 1.532 -0.901 1.371 -0.798 0.823 -0.783 0.796 -0.565 1.093
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diff --git a/exercises/Exercise6/Exercise_6_Problems.ipynb b/exercises/Exercise6/Exercise_6_Problems.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..d7404e0a154d9048c7d8be6fe98f2d3b967e8d9e
--- /dev/null
+++ b/exercises/Exercise6/Exercise_6_Problems.ipynb
@@ -0,0 +1,308 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 6: Arbitrary distributions, moving averages, and Monte-Carlo"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import datetime\n",
+ "import scipy.stats as stats\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1. Sampling from an arbitrary distribution\n",
+ "As seen in exercise 4, you can use uniformly distributed random variables, which are in principle themselves simple to generate, to draw samples from the normal distribution via the Box-Muller transform. A more general approach is to sample according to the inverse of the cumulative distribution function (CDF).\n",
+ "\n",
+ "A simple example is to generate numbers from the exponential distribution.\n",
+ "\n",
+ "$$ f(t;\\lambda) = \\lambda e^{-\\lambda t} $$\n",
+ "\n",
+ "* Write the CDF $F(T,\\lambda)$ and find its inverse ($T=...$)\n",
+ "* Write a function to compute this, and compare your result to that from scipy (hint: sometimes called percent-point function or quantile function)\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Quantile function\n",
+ "def exp_quantile(p, l):\n",
+ " ...\n",
+ "\n",
+ "p = np.linspace(0, 1, 100)\n",
+ "l = 0.2\n",
+ "..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Now draw N samples from the uniform distribution $[0,1]$. For each sample, calculate $F^{-1}(u,\\lambda)$\n",
+ "* Plot a histogram and compare the distribution of points to the exponential pdf\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "N = 1000\n",
+ "l = 0.2\n",
+ "x = ...\n",
+ "y = ...\n",
+ "\n",
+ "...\n",
+ "\n",
+ "print('Actual lambda:', l)\n",
+ "print('Estimated lambda: ', ...)\n",
+ "\n",
+ "...\n",
+ "\n",
+ "# Check the fit\n",
+ "...\n",
+ "\n",
+ "# Plot histogram, fit, and calculated pdf\n",
+ "...\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 2. Smoothing data\n",
+ "## 2.1 Moving average\n",
+ "The moving average, or rolling mean, is a simple technique which can be used to remove short term or periodic (e.g. seasonal) variations in time series data, for example. It can be viewed as a \"smoothing\", and can ease trend spotting, for instance. One has to be careful when interpreting and using the result; for instance, it is generally improper to fit on such data.\n",
+ "\n",
+ "The simplest moving average can be computed using a \"sliding window\" of length $N$, with all weights equal. For example, for a 3 point moving average, the window would be $\\frac{1}{3}[1,1,1]$.\n",
+ "\n",
+ "* Write a function to compute the $N$ point moving average of a data series"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def moving_average(y, length):\n",
+ " ..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The following line of code loads a dataset (into a ```pandas DataFrame```) containing monthly measurements of variation in the global surface temperature, stretching back as far as 1750. (More data like this can be found on http://berkeleyearth.org)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "df = pd.read_csv('Material/Complete_TAVG_complete.txt', skipinitialspace=True, delimiter=' ', comment='%')\n",
+ "df['Date'] = df.apply(lambda row: datetime.datetime(\n",
+ " int(row['Year']), int(row['Month']), 15), axis=1)\n",
+ "df"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Plot the data. To plot the monthly differences, for example, you can directly write ```df2['MDiff'].plot()```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# For example...\n",
+ "df.query('Year>1980 & Year<2000').plot(x='Date', y='MDiff')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Apply your moving average filter to the monthly data ```MDiff```. Try (for example) 6 months, 5 years, 10 years. Plot these on top of cuts of the original data to compare."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 2.2 Electronic response of RC circuit\n",
+ "\n",
+ "In general, the response of a linearly time invariant system is found to be the convolution of the its impulse response $h(t)$ and the input voltage. Consider a resistor and capacitor connected in series, driven by a time-varying voltage $u(t)$. The impulse response for such a circuit is:\n",
+ "\n",
+ "$$h_c(t) = \\frac{1}{RC} e^{-t/RC} u(t)$$\n",
+ "\n",
+ "* Write a function to calculate the impulse response as a function of time, the resistance, and the capacitance, and input. Take care to normalise the integral.\n",
+ "\n",
+ "* Now consider a noisy sinusoidal input voltage $u_N(t) = u(t) + \\epsilon(t)$, where $u(t)=sin(2\\pi f_1 t) + cos(2\\pi f_2 t)$, and $\\epsilon$ is a vector comprising samples draw from $N~(0,1)$. $f_1$ should be a lower frequency (~factor 10) than ($f_2$), where the cosine represents a faster ripple riding the fundamental tone. Plot the noisy signal and superimpose the clean signal.\n",
+ "\n",
+ "* Calculate the circuit response for your signal and compare the result to the noisy signal and the clean, original signal\n",
+ "\n",
+ "* Play with the RC time constant and see the effect on the signal. \n",
+ "\n",
+ "Note: this first order low pass filter is exactly equivalent to an exponential moving average. The \"memory\" of the output is effectively determined by the time constant.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def rc_impulse(t, R, C):\n",
+ " # Impulse response\n",
+ " ...\n",
+ "\n",
+ "def rc_response(t, u, R, C):\n",
+ " # Cumulative response\n",
+ " ...\n",
+ "\n",
+ "t = np.linspace(0, 0.1, 5000)\n",
+ "dt = t[1]-t[0]\n",
+ "R = 5e3\n",
+ "C = 100e-9\n",
+ "tc = R*C\n",
+ "\n",
+ "f1 = 200\n",
+ "f2 = 0.1 * f1\n",
+ "u = ...\n",
+ "un = ...\n",
+ "\n",
+ "print('Cutoff: ', tc)\n",
+ "\n",
+ "...\n",
+ "\n",
+ "# Try different cutoffs (remove noise, fast ripple, then whole thing)\n",
+ "...\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 3. Monte Carlo methods\n",
+ "### 3.1. Particle propagation\n",
+ "The elementary processes of particle absorption and scattering are random in their nature. Propagation of particles through a slab of material with multiple scattering events may be impossible to calculate analytically, but can easily be simulated with Monte Carlo methods.\n",
+ "\n",
+ "* Consider a beam of photons propagating through an absorbing medium with absorption coefficient $\\alpha=0.2$ per unit length. What is the probability of a photon being absorbed in a unit length slab of material?\n",
+ "\n",
+ "* Now take a piece of 1D material made up of 100 slices, each unit length. Starting at x=0, propagate a beam of 1000 photons through the material, slice-by-slice. At each interface, you should \"measure\" each photon to determine whether it has been transmitted or absorbed (hint: uniform distribution, $P(abs)$)\n",
+ "\n",
+ "* Plot the number of photons which are transmitted at the end of each slice, and compare that to the Beer-Lambert-Bouger law\n",
+ "\n",
+ "* Plot a histogram of the distance travelled before absorption for each photon (free paths).\n",
+ "\n",
+ "$I(x) = I_{0}e^{-\\alpha x }$ , where $\\alpha$ is absorption coefficient"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "N_slices = 100 # Slices of material\n",
+ "N_particles = 1000 # Number of particles to simulate\n",
+ "alpha = 0.2 # absorption coefficient\n",
+ "P_abs = ...\n",
+ "\n",
+ "# Generate N_slices x N_particles matrix of uniformly distributed random numbers. \n",
+ "# Transform it into a matrix of absorption events, where True = absorption, False = no absorption, \n",
+ "# mean(Abs_events) = P_abs\n",
+ "Abs_events = ...\n",
+ "\n",
+ "...\n",
+ "\n",
+ "print('Generated absorption probability (mean) = ', np.mean(Abs_events))\n",
+ "print('Fraction of escaped particles = ',N_escaped_final/N_particles)\n",
+ "\n",
+ "# Plots\n",
+ "..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 3.2. Monte-Carlo integration: estimate $\\pi$\n",
+ "\n",
+ "In a so-called ’hit-and-miss’ approach, or ’simple sampling’, one can estimate the integral\n",
+ "of an arbitrary, well-behaved function over some interval by scattering many points over\n",
+ "some rectangular area A. The probability of a point landing below the curve is proportional\n",
+ "to the function’s integral.\n",
+ "A classic problem is to determine the value of π.\n",
+ "\n",
+ "* Uniformly distribute N points over a unit area. Plot these on top of a unit circle (or quarter circle)\n",
+ "* Calculate the proportion that are within the bounds of your shape for some number of samples N (for large N, it would be unwise to plot)\n",
+ "* Repeat the exercise for increasing N. For each run, you should compute and store the error $\\epsilon = \\bar{\\pi} - \\pi$\n",
+ "* Plot log-log the convergence of your estimate to the actual value (to machine precision) of $\\pi$, i.e. $\\epsilon$ vs the number of points $N$. Compare this to the expected rate of convergence $(1/\\sqrt N)$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Python [Anaconda3]",
+ "language": "python",
+ "name": "Python [Anaconda3]"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.5.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Exercise6/Exercise_6_Problems.pdf b/exercises/Exercise6/Exercise_6_Problems.pdf
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diff --git a/exercises/Exercise7/Exercises_7.ipynb b/exercises/Exercise7/Exercises_7.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..5640fc5ef6ec65d288d2e055d7884ebea3ecb2a2
--- /dev/null
+++ b/exercises/Exercise7/Exercises_7.ipynb
@@ -0,0 +1,362 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 7\n",
+ "Maximum Likelihood method"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy.optimize import curve_fit, minimize, fsolve\n",
+ "from scipy.stats import norm, chi2, lognorm"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 151,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "measurements = np.array([97.8621, 114.105, 87.7593, 93.2134, 86.6624, 87.4629, 79.7712, \\\n",
+ "91.5024, 87.7737, 89.6926, 133.506, 91.4124, 94.4401, 97.3968, \\\n",
+ "108.424, 103.197, 88.2166, 142.217, 89.0393, 102.438, 95.7987, \\\n",
+ "94.5177, 96.8171, 90.903, 132.463, 92.3394, 84.1451, 87.3447, \\\n",
+ "92.2861, 84.4213, 124.017, 90.4941, 95.7992, 92.3484, 95.9813, \\\n",
+ "88.0641, 101.002, 97.7268, 137.379, 96.213, 140.795, 99.9332, \\\n",
+ "130.087, 108.839, 90.0145, 100.313, 87.5952, 92.995, 114.457, \\\n",
+ "90.7526, 112.181, 117.857, 95.2804, 115.922, 117.043, 104.317, \\\n",
+ "126.728, 87.8592, 89.9614, 100.377, 107.38, 88.8426, 93.3224, \\\n",
+ "138.947, 102.288, 123.431, 114.334, 88.5134, 124.7, 87.7316, 84.7141, \\\n",
+ "91.1646, 87.891, 121.257, 92.9314])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1-D Maximum likelihood fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We have a set of measurements which are distributed according to the sum of two Gaussians (e.g. this can be signal and background).\n",
+ "\n",
+ "$\\rho = \\frac{1}{3}\\frac{1}{\\sqrt{2\\pi \\sigma^2}} e^{-\\frac{1}{2}\\left(\\frac{x-p}{\\sigma}\\right)^2} + \\frac{2}{3}\\frac{1}{\\sqrt{2\\pi \\sigma_b^2}} e^{-\\frac{1}{2}\\left(\\frac{x-p_b}{\\sigma_b}\\right)^2}$ \n",
+ "\n",
+ "where for one of the two peaks the parameters are known already\n",
+ "\n",
+ "$p_b = 91.0$ \n",
+ "$\\sigma_b = 5.0$ \n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 228,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood_point(x, position, width):\n",
+ " return ..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First, we assume the width of the peak we want to fit is already known: $\\sigma = 15.0$.\n",
+ "Perform a 1-D Maximum Likelihood fit for the position of the peak $p$.\n",
+ "\n",
+ "Complete the functions below which return the likelihood and negative log likelihood (NLL)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 347,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood_1d(params):\n",
+ " # hint: for products use np.prod\n",
+ " return ...\n",
+ "\n",
+ "def nll_1d(params):\n",
+ " return -np.log(likelihood_1d(params))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the NLL and give the best-fit result, including asymetric errors and plot the NLL."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# find numeric minimum of NLL\n",
+ "# hint: use e.g. minimize from scipy.optimize\n",
+ "...\n",
+ "\n",
+ "# hint: to compute the errors (solve roots of equation) use fsolve from scipy.optimize\n",
+ "print(\"position:\", ...)\n",
+ "print(\"negative error:\", ...)\n",
+ "print(\"positive error:\", ...)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "What happens if you try to maximize the likelihood directly?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 2-D Likelihood fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we perform the 2-D Maximum Likelihood fit, fitting for both $\\sigma$ and $p$ at the same time."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 350,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood(params):\n",
+ " return ...\n",
+ "\n",
+ "def nll(params):\n",
+ " return -np.log(likelihood(params))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the NLL and find the best-fit result."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "solution = ...\n",
+ "print(\"position:\", ..., \"width:\", ...)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Create a 2D contour plot of the 1, 2 and 3 $\\sigma$ contours of the NLL and plot the best-fit solution."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#\n",
+ "p1 = plt.contour(...)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute numerically the error matrix of the NLL for the 2-D fit."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from scipy.misc import derivative\n",
+ "\n",
+ "# compute the error matrix\n",
+ "# hint: * you can use \"derivative\" from scipy.misc to compute numeric derivatives\n",
+ "# * for the mixed partial terms, the use of lambda functions might be practical to convert the \n",
+ "# function depending on more than one variable to a function depending on one variable only\n",
+ "\n",
+ "A = np.linalg.inv([\n",
+ " [\n",
+ " derivative(...),\n",
+ " derivative(...)\n",
+ " ],\n",
+ " [\n",
+ " derivative(...),\n",
+ " derivative(...)\n",
+ " ]\n",
+ "])\n",
+ "print(A, \"\\nsigma(position):\", np.sqrt(A[0,0]), \"sigma(width):\", np.sqrt(A[1,1]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Binned ML fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "With the same data as above, we now perform a binned ML fit and compare with the unbinned fit.\n",
+ "First, create a histogram of the data using np.histogram."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "nBins = 10\n",
+ "histoMax = 170\n",
+ "histoMin = 70\n",
+ "binWidth = (histoMax - histoMin)/nBins\n",
+ "h0 = np.histogram(...)\n",
+ "print(h0[0])\n",
+ "print(h0[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute the binned NLL:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 375,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def nll_binned(params):\n",
+ " # params is a list of [position, sigma]\n",
+ " #...\n",
+ " return #..."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the binned NLL:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 376,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " fun: -138.93433719876123\n",
+ " jac: array([-1.90734863e-06, 1.90734863e-06])\n",
+ " message: 'Optimization terminated successfully.'\n",
+ " nfev: 60\n",
+ " nit: 6\n",
+ " njev: 15\n",
+ " status: 0\n",
+ " success: True\n",
+ " x: array([116.43876363, 15.33581135])\n"
+ ]
+ }
+ ],
+ "source": [
+ "solution_binned=...\n",
+ "print(solution_binned)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Make a contour plot of the 1,2, and 3 $\\sigma$ contours for the binned NLL and overlay it with the unbinned contours."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# show the two contour plots superimposed\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Repeat the same for 50 bins:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# show the two contour plots superimposed for 50 bins"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.15"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Exercise7/Exercises_7.pdf b/exercises/Exercise7/Exercises_7.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..26a8974b7a59f3a825f0a9da0d14d6148a8301af
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diff --git a/exercises/Solution2/.ipynb_checkpoints/Solution_2_v2-checkpoint.ipynb b/exercises/Solution2/.ipynb_checkpoints/Solution_2_v2-checkpoint.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..7cd0952fd9c8e88a129c7cdb4f2472f5b679dc1e
--- /dev/null
+++ b/exercises/Solution2/.ipynb_checkpoints/Solution_2_v2-checkpoint.ipynb
@@ -0,0 +1,616 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 2: Solutions\n",
+ "General hint: You can always ask for help from within python if you forgot how a certain function works or what the correct ordering of input parameters is. Executing \"some_function?\" spawns the docstring of the function and \"some_function??\" the source code."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# scipy.stats.kurtosis?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Probability density function (pdf)\n",
+ "We will look at a few common distributions and investigate their basic properties."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "import scipy.stats\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For your convenience, we define a few pdfs and functions to draw samples from them. Have a look at https://docs.scipy.org/doc/scipy/reference/stats.html for more details. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def gaussian_pdf(x, mu, sigma):\n",
+ " \"\"\"Gaussian distribution with mean mu and standard deviation sigma\"\"\"\n",
+ " return scipy.stats.norm.pdf(x, loc=mu, scale=sigma)\n",
+ "\n",
+ "def gaussian_sample(number, mu, sigma):\n",
+ " \"\"\"Draw samples from a Gaussian distribution\n",
+ " \n",
+ " mu: mean\n",
+ " sigma: standard deviation:\n",
+ " number: number of samples to be drawn\n",
+ " \"\"\"\n",
+ " return scipy.stats.norm.rvs(loc=mu, scale=sigma, size=number)\n",
+ "\n",
+ "def lognormal_pdf(x, mu, sigma):\n",
+ " return scipy.stats.lognorm.pdf(x, loc=0, scale=1, s=sigma)\n",
+ "\n",
+ "def lognormal_sample(number, mu, sigma):\n",
+ " return scipy.stats.lognorm.rvs(size=number, loc=0, s=sigma, scale=1)\n",
+ " \n",
+ "def binomial_pmf(x, n, p):\n",
+ " return scipy.stats.binom.pmf(x, n, p)\n",
+ "\n",
+ "def binomial_sample(number, n, p):\n",
+ " return scipy.stats.binom.rvs(n, p, size=number)\n",
+ "\n",
+ "def poisson_pmf(k, mu):\n",
+ " return scipy.stats.poisson.pmf(k, mu)\n",
+ "\n",
+ "def poisson_sample(number, mu):\n",
+ " return scipy.stats.poisson.rvs(mu, size=number)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**1a) Generate arrays from the lognormal and poisson pdfs and draw an array of samples from each distribution.**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Generate arrays for parent pdf and samples\n",
+ "sample_size = 1000\n",
+ "x_float = np.linspace(0, 10, 1000)\n",
+ "x_int = np.arange(0, 30)\n",
+ "mu = 4.0\n",
+ "p = 0.5\n",
+ "sigma = 1\n",
+ "\n",
+ "# Gaussian\n",
+ "g_parent = gaussian_pdf(x_float, mu, sigma)\n",
+ "g_sample = gaussian_sample(sample_size, mu, sigma)\n",
+ "\n",
+ "# Lognormal\n",
+ "logn_parent = lognormal_pdf(x_float, mu, sigma)\n",
+ "logn_sample = lognormal_sample(sample_size, mu, sigma)\n",
+ "\n",
+ "# Binomial\n",
+ "bin_pdf = binomial_pmf(x_int, n=int(mu/p), p=p)\n",
+ "bin_sample = binomial_sample(sample_size, n=int(mu/p), p=p)\n",
+ "\n",
+ "# Poisson\n",
+ "pois_parent = poisson_pmf(x_int, mu=mu)\n",
+ "pois_sample = poisson_sample(sample_size, mu=mu)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**1b) Display your results in axes 1 and 3 in the figure below.**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x154d1f655f8>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot the generated arrays, comparing the parent distribution and a sample\n",
+ "f, ax = plt.subplots(2, 2, figsize=(10, 6))\n",
+ "ax = ax.flatten()\n",
+ "n_bins = 16\n",
+ "\n",
+ "ax[0].set_title(r'Gauss')\n",
+ "ax[0].plot(x_float, g_parent, 'k', label='pdf')\n",
+ "ax[0].hist(g_sample, n_bins, normed=True, rwidth=0.9, label='sample', range=(0, 8))\n",
+ "ax[0].set_xlim(0, 8)\n",
+ "ax[0].set_xlabel(r'$x$')\n",
+ "ax[0].legend()\n",
+ "\n",
+ "ax[1].set_title(r'Lognormal')\n",
+ "ax[1].plot(x_float, logn_parent, 'k', label='pdf')\n",
+ "ax[1].hist(logn_sample, n_bins, normed=True, rwidth=0.9, label='sample', range=(0, 8))\n",
+ "ax[1].legend()\n",
+ "ax[1].set_xlabel(r'$x$')\n",
+ "ax[1].set_xlim(0, 8)\n",
+ "\n",
+ "ax[2].set_title('Binomial')\n",
+ "ax[2].plot(x_int, bin_pdf, 'k+', label='pmf', ms=8)\n",
+ "ax[2].hist(bin_sample, n_bins, normed=True, rwidth=0.9, label='sample', range=(0, 15), align='mid')\n",
+ "ax[2].set_xlim(0, 15)\n",
+ "ax[2].set_xlabel(r'$k$')\n",
+ "ax[2].legend()\n",
+ "\n",
+ "ax[3].set_title('Poisson')\n",
+ "ax[3].plot(x_int, pois_parent, 'k+', label='pmf', ms=8)\n",
+ "ax[3].hist(pois_sample, n_bins, normed=True, rwidth=0.9, label='sample', range=(0, 15), align='mid')\n",
+ "ax[3].set_xlim(0, 15)\n",
+ "ax[3].set_xlabel(r'$k$')\n",
+ "ax[3].legend()\n",
+ "\n",
+ "f.tight_layout()\n",
+ "\n",
+ "# Note: Depending on you matplotlib version, the keyword for normalization is \"density\" or \"normed\"!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Mean, variance and their estimators\n",
+ "**2a) To familiarize yourself with the properties of the distributions, write a function that calculates the first five moments of a sample as well as the mode and median values. Compare your results with the expected values.** \n",
+ "Hints: If you like, you can try your own implementations and test them against scipy.stats. You can find functions in numpy and scipy implementing all tasks. The 0th moment is just the total probability, following the convention in the lecture notes. Sometimes the value 3 is subtracted from kurtosis to shift a normal distribution to zero kurtosis."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def moments(sample):\n",
+ " \"\"\"Calculate the first 4 moments of a sample\"\"\"\n",
+ " m0 = scipy.stats.moment(sample, 0)\n",
+ " m1 = np.mean(sample)\n",
+ " m2 = scipy.stats.moment(sample, 2)\n",
+ " m3 = scipy.stats.skew(sample)\n",
+ " m4 = scipy.stats.kurtosis(sample)\n",
+ " return np.array([m0, m1, m2, m3, m4])\n",
+ "\n",
+ "def mode(sample):\n",
+ " return scipy.stats.mode(sample)[0][0]\n",
+ "\n",
+ "def mode_sample(sample):\n",
+ " h = np.histogram(sample, bins=15)\n",
+ " return (h[1][np.argmax(h[0])]+h[1][np.argmax(h[0])+1])/2.0 if np.argmax(h[0]) < len(h[0])-1 else h[1][np.argmax(h[0])]\n",
+ "\n",
+ "def median(sample):\n",
+ " return np.median(sample)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Sample: \t mass, mean, variance, skewness, kurtosis\n",
+ "Gaussian: \t [ 1. 4.03 1.04 -0.1 -0.05]\n",
+ "Lognormal: \t [ 1. 1.68 4.46 4.05 24.39]\n",
+ "Binomial: \t [ 1. 4. 1.89 -0.06 -0. ]\n",
+ "Poisson: \t [1. 3.98 4.2 0.55 0.42]\n"
+ ]
+ }
+ ],
+ "source": [
+ "print('Sample: \\t mass, mean, variance, skewness, kurtosis')\n",
+ "print('Gaussian: \\t', moments(g_sample).round(2))\n",
+ "print('Lognormal: \\t', moments(logn_sample).round(2))\n",
+ "print('Binomial: \\t', moments(bin_sample).round(2))\n",
+ "print('Poisson: \\t', moments(pois_sample).round(2))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "3.8596744792409305 4.05525317035419\n",
+ "0.7756969873870149 1.0424239898265104\n",
+ "4 4.0\n",
+ "4 4.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(mode_sample(g_sample), median(g_sample))\n",
+ "print(mode_sample(logn_sample), median(logn_sample))\n",
+ "print(mode(bin_sample), median(bin_sample))\n",
+ "print(mode(pois_sample), median(pois_sample))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "What did you expect, knowing the parent distributions? Hint: scipy can also help you here, see for example \"scipy.stats.norm.stats\". You can check wikipedia to quickly recap some analytical results if neccessary. \n",
+ "https://en.wikipedia.org/wiki/Normal_distribution \n",
+ "https://en.wikipedia.org/wiki/Log-normal_distribution \n",
+ "https://en.wikipedia.org/wiki/Binomial_distribution \n",
+ "https://en.wikipedia.org/wiki/Poisson_distribution \n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "4.0 1.0 0.0 0.0\n",
+ "1.6487212707001282 4.670774270471604 6.184877138632554 110.9363921763115\n",
+ "4.0 2.0 0.0 -0.25\n",
+ "4.0 4.0 0.5 0.25\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(*scipy.stats.norm.stats(mu, sigma, moments='mvsk'))\n",
+ "print(*scipy.stats.lognorm.stats(loc=0, s=sigma, scale=1, moments='mvsk'))\n",
+ "print(*scipy.stats.binom.stats(n=mu/p, p=p, moments='mvsk'))\n",
+ "print(*scipy.stats.poisson.stats(mu=mu, moments='mvsk'))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Estimation\n",
+ "Obviously, there is some discrepancy between the expected or \"true\" values from the parent distribution and the calculated sample moments. We would like to work on the inverse problem of guessing the first two moments given only a sample and knowing that the sample was drawn from a normal distribution (but not knowing its \"true\" parameters). \n",
+ "**2b) Remember how to estimate the mean and variance from a sample.** \n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The estimation of the mean coincides with the sample mean. The estimation for the variance is $n/(n-1)$ the sample variance."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**2c) How to quantify the uncertainty of the estimation of the mean?** \n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Given $$\\bar{x}=\\frac{1}{N} \\sum_{i=1}^{N}x_i$$ one can recover its uncertainty with the Gaussian error propagation formula: \n",
+ "$$\\sigma_{\\bar{x}} = \\frac{\\sigma}{\\sqrt{N}}$$ with the sample variance estimation $$\\sigma=\\frac{1}{N-1}\\sum (x_i - \\bar{x})^2$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "mean estimator: 3.952626606381409\n",
+ "uncertainty estimator: 0.030539967040206582\n"
+ ]
+ }
+ ],
+ "source": [
+ "N = np.size(g_sample)\n",
+ "mean = np.mean(g_sample)\n",
+ "uncertainty_mean = np.sqrt(1/(N-1) * np.sum((g_sample-mean)**2)) * 1/np.sqrt(N)\n",
+ "print('mean estimator:', mean)\n",
+ "print('uncertainty estimator:', uncertainty_mean)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**2d) Given that it can be very cheap to repeatedly sample a distribution with a computer, try to come up with an alternative approach to estimate the uncertainty of the mean. We will come back to this at the end of the course.**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "4.001435884220608\n",
+ "0.033109197212323395\n"
+ ]
+ }
+ ],
+ "source": [
+ "# We just repeat sampling the distribution and calculate the standard deviations of the averages:\n",
+ "reps = 1000\n",
+ "averages = np.zeros(reps)\n",
+ "for i in range(reps):\n",
+ " g_sample = gaussian_sample(sample_size, mu, sigma)\n",
+ " averages[i] = np.mean(g_sample)\n",
+ " \n",
+ "print(np.mean(averages))\n",
+ "print(np.std(averages, ddof=1))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Multidimensional pdf: covariance and correlation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Imagine your're an astronomer and are measuring a specific parameter called the \"Clumping factor\". You're interested whether the clumping factor varies with temperature and how. You have 8 measurements with the following values:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "clumping = [0.5, 0.4, 0.3, 0.2, 0.4, 0.3, 0.3, 0.2]\n",
+ "temperature = [2700, 4600, 5120, 5550, 3600, 3990, 4190, 3900] # [K]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**3a) Write a function in python that computes the Covariance and compare the result to a python numpy or scipy function.** "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "naive implementation: -53.28124999999977\n",
+ "[[ 9.37500000e-03 -5.32812500e+01]\n",
+ " [-5.32812500e+01 6.96598438e+05]]\n",
+ "numpy implementation: -53.28125\n"
+ ]
+ }
+ ],
+ "source": [
+ "def cov(x,y):\n",
+ " x_mean = np.mean(x)\n",
+ " y_mean = np.mean(y)\n",
+ " xy = np.multiply(x,y)\n",
+ " xy_mean = np.mean(xy)\n",
+ " return xy_mean - x_mean*y_mean\n",
+ "\n",
+ "print('naive implementation:', cov(clumping, temperature))\n",
+ "# Covariance matrix\n",
+ "print(np.cov(clumping, temperature, bias=True))\n",
+ "# Off-diagonal entry\n",
+ "print('numpy implementation:', np.cov(clumping, temperature, bias=True)[0, 1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**3b) Calculate the correlation coefficient.** "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "-0.6593219263134944\n",
+ "[[ 1. -0.65932193]\n",
+ " [-0.65932193 1. ]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "def corr(x, y):\n",
+ " return cov(x, y) / (np.var(x)*np.var(y))**(1/2)\n",
+ "\n",
+ "print(corr(clumping, temperature))\n",
+ "print(np.corrcoef(clumping, temperature))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**3c) Interpret your results of covariance and correlation coefficient.** "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The covariance tells us that the clumping factor increases with lower temperatures. This picture is confirmed by the correlation coefficient. It is negative, meaning there is an anti-correlation between the clumping factor and the temperature."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**3d) If the two variables are uncorrelated, does this also mean they are independent of each other?** "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "No, the covariance only tells us about linear correlations. Consider for example $y=x^2$ on $[-1, 1]$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[1.0000000e+00 1.8069255e-17]\n",
+ " [1.8069255e-17 1.0000000e+00]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.linspace(-1, 1, 11)\n",
+ "y = x**2\n",
+ "print(np.corrcoef(x, y))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Bonus\n",
+ "### 3D Plots"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Try playing with three dimensional graphs to visualize properties of pdfs with two variables. For example, try visualizing marginal and conditional distributions as was done in lecture 2.\n",
+ "<img src=\"MultivariateNormal.png\" style=\"height:250px\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### nbextensions\n",
+ "There are some useful extensions to jupyter notebooks, check https://github.com/ipython-contrib/jupyter_contrib_nbextensions if you are interested. There are features like a table of contents to navigate around in notebooks, line numbering for all code cells and options to collapse certain cells to to keep a better overview.\n",
+ "\n",
+ "conda install -c conda-forge jupyter_contrib_nbextensions\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "hide_input": false,
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.3"
+ },
+ "toc": {
+ "base_numbering": 1,
+ "nav_menu": {},
+ "number_sections": true,
+ "sideBar": true,
+ "skip_h1_title": false,
+ "title_cell": "Table of Contents",
+ "title_sidebar": "Contents",
+ "toc_cell": false,
+ "toc_position": {
+ "height": "690px",
+ "left": "0px",
+ "right": "1388px",
+ "top": "110px",
+ "width": "212px"
+ },
+ "toc_section_display": "block",
+ "toc_window_display": true
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Solution2/MultivariateNormal.png b/exercises/Solution2/MultivariateNormal.png
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diff --git a/exercises/Solution2/Solution_2_v2.ipynb b/exercises/Solution2/Solution_2_v2.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..7139455c7707407c1ef4465b6d6809156e876c23
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+++ b/exercises/Solution2/Solution_2_v2.ipynb
@@ -0,0 +1,616 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 2: Solutions\n",
+ "General hint: You can always ask for help from within python if you forgot how a certain function works or what the correct ordering of input parameters is. Executing \"some_function?\" spawns the docstring of the function and \"some_function??\" the source code."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# scipy.stats.kurtosis?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Probability density function (pdf)\n",
+ "We will look at a few common distributions and investigate their basic properties."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "import scipy.stats\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For your convenience, we define a few pdfs and functions to draw samples from them. Have a look at https://docs.scipy.org/doc/scipy/reference/stats.html for more details. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def gaussian_pdf(x, mu, sigma):\n",
+ " \"\"\"Gaussian distribution with mean mu and standard deviation sigma\"\"\"\n",
+ " return scipy.stats.norm.pdf(x, loc=mu, scale=sigma)\n",
+ "\n",
+ "def gaussian_sample(number, mu, sigma):\n",
+ " \"\"\"Draw samples from a Gaussian distribution\n",
+ " \n",
+ " mu: mean\n",
+ " sigma: standard deviation:\n",
+ " number: number of samples to be drawn\n",
+ " \"\"\"\n",
+ " return scipy.stats.norm.rvs(loc=mu, scale=sigma, size=number)\n",
+ "\n",
+ "def lognormal_pdf(x, mu, sigma):\n",
+ " return scipy.stats.lognorm.pdf(x, loc=0, scale=1, s=sigma)\n",
+ "\n",
+ "def lognormal_sample(number, mu, sigma):\n",
+ " return scipy.stats.lognorm.rvs(size=number, loc=0, s=sigma, scale=1)\n",
+ " \n",
+ "def binomial_pmf(x, n, p):\n",
+ " return scipy.stats.binom.pmf(x, n, p)\n",
+ "\n",
+ "def binomial_sample(number, n, p):\n",
+ " return scipy.stats.binom.rvs(n, p, size=number)\n",
+ "\n",
+ "def poisson_pmf(k, mu):\n",
+ " return scipy.stats.poisson.pmf(k, mu)\n",
+ "\n",
+ "def poisson_sample(number, mu):\n",
+ " return scipy.stats.poisson.rvs(mu, size=number)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**1a) Generate arrays from the lognormal and poisson pdfs and draw an array of samples from each distribution.**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Generate arrays for parent pdf and samples\n",
+ "sample_size = 1000\n",
+ "x_float = np.linspace(0, 10, 1000)\n",
+ "x_int = np.arange(0, 30)\n",
+ "mu = 4.0\n",
+ "p = 0.5\n",
+ "sigma = 1\n",
+ "\n",
+ "# Gaussian\n",
+ "g_parent = gaussian_pdf(x_float, mu, sigma)\n",
+ "g_sample = gaussian_sample(sample_size, mu, sigma)\n",
+ "\n",
+ "# Lognormal\n",
+ "logn_parent = lognormal_pdf(x_float, mu, sigma)\n",
+ "logn_sample = lognormal_sample(sample_size, mu, sigma)\n",
+ "\n",
+ "# Binomial\n",
+ "bin_pdf = binomial_pmf(x_int, n=int(mu/p), p=p)\n",
+ "bin_sample = binomial_sample(sample_size, n=int(mu/p), p=p)\n",
+ "\n",
+ "# Poisson\n",
+ "pois_parent = poisson_pmf(x_int, mu=mu)\n",
+ "pois_sample = poisson_sample(sample_size, mu=mu)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**1b) Display your results in axes 1 and 3 in the figure below.**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x154d1f655f8>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot the generated arrays, comparing the parent distribution and a sample\n",
+ "f, ax = plt.subplots(2, 2, figsize=(10, 6))\n",
+ "ax = ax.flatten()\n",
+ "n_bins = 16\n",
+ "\n",
+ "ax[0].set_title(r'Gauss')\n",
+ "ax[0].plot(x_float, g_parent, 'k', label='pdf')\n",
+ "ax[0].hist(g_sample, n_bins, normed=True, rwidth=0.9, label='sample', range=(0, 8))\n",
+ "ax[0].set_xlim(0, 8)\n",
+ "ax[0].set_xlabel(r'$x$')\n",
+ "ax[0].legend()\n",
+ "\n",
+ "ax[1].set_title(r'Lognormal')\n",
+ "ax[1].plot(x_float, logn_parent, 'k', label='pdf')\n",
+ "ax[1].hist(logn_sample, n_bins, normed=True, rwidth=0.9, label='sample', range=(0, 8))\n",
+ "ax[1].legend()\n",
+ "ax[1].set_xlabel(r'$x$')\n",
+ "ax[1].set_xlim(0, 8)\n",
+ "\n",
+ "ax[2].set_title('Binomial')\n",
+ "ax[2].plot(x_int, bin_pdf, 'k+', label='pmf', ms=8)\n",
+ "ax[2].hist(bin_sample, n_bins, normed=True, rwidth=0.9, label='sample', range=(0, 15), align='mid')\n",
+ "ax[2].set_xlim(0, 15)\n",
+ "ax[2].set_xlabel(r'$k$')\n",
+ "ax[2].legend()\n",
+ "\n",
+ "ax[3].set_title('Poisson')\n",
+ "ax[3].plot(x_int, pois_parent, 'k+', label='pmf', ms=8)\n",
+ "ax[3].hist(pois_sample, n_bins, normed=True, rwidth=0.9, label='sample', range=(0, 15), align='mid')\n",
+ "ax[3].set_xlim(0, 15)\n",
+ "ax[3].set_xlabel(r'$k$')\n",
+ "ax[3].legend()\n",
+ "\n",
+ "f.tight_layout()\n",
+ "\n",
+ "# Note: Depending on you matplotlib version, the keyword for normalization is \"density\" or \"normed\"!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Mean, variance and their estimators\n",
+ "**2a) To familiarize yourself with the properties of the distributions, write a function that calculates the first five moments of a sample as well as the mode and median values. Compare your results with the expected values.** \n",
+ "Hints: If you like, you can try your own implementations and test them against scipy.stats. You can find functions in numpy and scipy implementing all tasks. The 0th moment is just the total probability, following the convention in the lecture notes. Sometimes the value 3 is subtracted from kurtosis to shift a normal distribution to zero kurtosis."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def moments(sample):\n",
+ " \"\"\"Calculate the first 4 moments of a sample\"\"\"\n",
+ " m0 = scipy.stats.moment(sample, 0)\n",
+ " m1 = np.mean(sample)\n",
+ " m2 = scipy.stats.moment(sample, 2)\n",
+ " m3 = scipy.stats.skew(sample)\n",
+ " m4 = scipy.stats.kurtosis(sample)\n",
+ " return np.array([m0, m1, m2, m3, m4])\n",
+ "\n",
+ "def mode(sample):\n",
+ " return scipy.stats.mode(sample)[0][0]\n",
+ "\n",
+ "def mode_sample(sample):\n",
+ " h = np.histogram(sample, bins=15)\n",
+ " return (h[1][np.argmax(h[0])]+h[1][np.argmax(h[0])+1])/2.0 if np.argmax(h[0]) < len(h[0])-1 else h[1][np.argmax(h[0])]\n",
+ "\n",
+ "def median(sample):\n",
+ " return np.median(sample)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Sample: \t mass, mean, variance, skewness, kurtosis\n",
+ "Gaussian: \t [ 1. 4.03 1.04 -0.1 -0.05]\n",
+ "Lognormal: \t [ 1. 1.68 4.46 4.05 24.39]\n",
+ "Binomial: \t [ 1. 4. 1.89 -0.06 -0. ]\n",
+ "Poisson: \t [1. 3.98 4.2 0.55 0.42]\n"
+ ]
+ }
+ ],
+ "source": [
+ "print('Sample: \\t mass, mean, variance, skewness, kurtosis')\n",
+ "print('Gaussian: \\t', moments(g_sample).round(2))\n",
+ "print('Lognormal: \\t', moments(logn_sample).round(2))\n",
+ "print('Binomial: \\t', moments(bin_sample).round(2))\n",
+ "print('Poisson: \\t', moments(pois_sample).round(2))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "3.8596744792409305 4.05525317035419\n",
+ "0.7756969873870149 1.0424239898265104\n",
+ "4 4.0\n",
+ "4 4.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(mode_sample(g_sample), median(g_sample))\n",
+ "print(mode_sample(logn_sample), median(logn_sample))\n",
+ "print(mode(bin_sample), median(bin_sample))\n",
+ "print(mode(pois_sample), median(pois_sample))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "What did you expect, knowing the parent distributions? Hint: scipy can also help you here, see for example \"scipy.stats.norm.stats\". You can check wikipedia to quickly recap some analytical results if neccessary. \n",
+ "https://en.wikipedia.org/wiki/Normal_distribution \n",
+ "https://en.wikipedia.org/wiki/Log-normal_distribution \n",
+ "https://en.wikipedia.org/wiki/Binomial_distribution \n",
+ "https://en.wikipedia.org/wiki/Poisson_distribution \n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "4.0 1.0 0.0 0.0\n",
+ "1.6487212707001282 4.670774270471604 6.184877138632554 110.9363921763115\n",
+ "4.0 2.0 0.0 -0.25\n",
+ "4.0 4.0 0.5 0.25\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(*scipy.stats.norm.stats(mu, sigma, moments='mvsk'))\n",
+ "print(*scipy.stats.lognorm.stats(loc=0, s=sigma, scale=1, moments='mvsk'))\n",
+ "print(*scipy.stats.binom.stats(n=mu/p, p=p, moments='mvsk'))\n",
+ "print(*scipy.stats.poisson.stats(mu=mu, moments='mvsk'))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Estimation\n",
+ "Obviously, there is some discrepancy between the expected or \"true\" values from the parent distribution and the calculated sample moments. We would like to work on the inverse problem of guessing the first two moments given only a sample and knowing that the sample was drawn from a normal distribution (but not knowing its \"true\" parameters). \n",
+ "**2b) Remember how to estimate the mean and variance from a sample.** \n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The estimation of the mean coincides with the sample mean. The estimation for the variance is $n/(n-1)$ the sample variance."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**2c) How to quantify the uncertainty of the estimation of the mean?** \n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Given $$\\bar{x}=\\frac{1}{N} \\sum_{i=1}^{N}x_i$$ one can recover its uncertainty with the Gaussian error propagation formula: \n",
+ "$$\\sigma_{\\bar{x}} = \\frac{\\sigma}{\\sqrt{N}}$$ with the sample variance estimation $$\\sigma=\\frac{1}{N-1}\\sum (x_i - \\bar{x})^2$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "mean estimator: 3.952626606381409\n",
+ "uncertainty estimator: 0.030539967040206582\n"
+ ]
+ }
+ ],
+ "source": [
+ "N = np.size(g_sample)\n",
+ "mean = np.mean(g_sample)\n",
+ "uncertainty_mean = np.sqrt(1/(N-1) * np.sum((g_sample-mean)**2)) * 1/np.sqrt(N)\n",
+ "print('mean estimator:', mean)\n",
+ "print('uncertainty estimator:', uncertainty_mean)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**2d) Given that it can be very cheap to repeatedly sample a distribution with a computer, try to come up with an alternative approach to estimate the uncertainty of the mean. We will come back to this at the end of the course.**"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "4.001435884220608\n",
+ "0.033109197212323395\n"
+ ]
+ }
+ ],
+ "source": [
+ "# We just repeat sampling the distribution and calculate the standard deviations of the averages:\n",
+ "reps = 1000\n",
+ "averages = np.zeros(reps)\n",
+ "for i in range(reps):\n",
+ " g_sample = gaussian_sample(sample_size, mu, sigma)\n",
+ " averages[i] = np.mean(g_sample)\n",
+ " \n",
+ "print(np.mean(averages))\n",
+ "print(np.std(averages, ddof=1))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Multidimensional pdf: covariance and correlation"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Imagine your're an astronomer and are measuring a specific parameter called the \"Clumping factor\". You're interested whether the clumping factor varies with temperature and how. You have 8 measurements with the following values:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "clumping = [0.5, 0.4, 0.3, 0.2, 0.4, 0.3, 0.3, 0.2]\n",
+ "temperature = [2700, 4600, 5120, 5550, 3600, 3990, 4190, 3900] # [K]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**3a) Write a function in python that computes the Covariance and compare the result to a python numpy or scipy function.** "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "naive implementation: -53.28124999999977\n",
+ "[[ 9.37500000e-03 -5.32812500e+01]\n",
+ " [-5.32812500e+01 6.96598438e+05]]\n",
+ "numpy implementation: -53.28125\n"
+ ]
+ }
+ ],
+ "source": [
+ "def cov(x,y):\n",
+ " x_mean = np.mean(x)\n",
+ " y_mean = np.mean(y)\n",
+ " xy = np.multiply(x,y)\n",
+ " xy_mean = np.mean(xy)\n",
+ " return xy_mean - x_mean*y_mean\n",
+ "\n",
+ "print('naive implementation:', cov(clumping, temperature))\n",
+ "# Covariance matrix\n",
+ "print(np.cov(clumping, temperature, bias=True))\n",
+ "# Off-diagonal entry\n",
+ "print('numpy implementation:', np.cov(clumping, temperature, bias=True)[0, 1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**3b) Calculate the correlation coefficient.** "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "-0.6593219263134944\n",
+ "[[ 1. -0.65932193]\n",
+ " [-0.65932193 1. ]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "def corr(x, y):\n",
+ " return cov(x, y) / (np.var(x)*np.var(y))**(1/2)\n",
+ "\n",
+ "print(corr(clumping, temperature))\n",
+ "print(np.corrcoef(clumping, temperature))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**3c) Interpret your results of covariance and correlation coefficient.** "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The covariance tells us that the clumping factor increases with lower temperatures. This picture is confirmed by the correlation coefficient. It is negative, meaning there is an anti-correlation between the clumping factor and the temperature."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**3d) If the two variables are uncorrelated, does this also mean they are independent of each other?** "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "No, the covariance only tells us about linear correlations. Consider for example $y=x^2$ on $[-1, 1]$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[1.0000000e+00 1.8069255e-17]\n",
+ " [1.8069255e-17 1.0000000e+00]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "x = np.linspace(-1, 1, 11)\n",
+ "y = x**2\n",
+ "print(np.corrcoef(x, y))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Bonus\n",
+ "### 3D Plots"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Try playing with three dimensional graphs to visualize properties of pdfs with two variables. For example, try visualizing marginal and conditional distributions as was done in lecture 2.\n",
+ "<img src=\"MultivariateNormal.png\" style=\"height:250px\">"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### nbextensions\n",
+ "There are some useful extensions to jupyter notebooks, check https://github.com/ipython-contrib/jupyter_contrib_nbextensions if you are interested. There are features like a table of contents to navigate around in notebooks, line numbering for all code cells and options to collapse certain cells to to keep a better overview.\n",
+ "\n",
+ "conda install -c conda-forge jupyter_contrib_nbextensions\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "hide_input": false,
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.7"
+ },
+ "toc": {
+ "base_numbering": 1,
+ "nav_menu": {},
+ "number_sections": true,
+ "sideBar": true,
+ "skip_h1_title": false,
+ "title_cell": "Table of Contents",
+ "title_sidebar": "Contents",
+ "toc_cell": false,
+ "toc_position": {
+ "height": "690px",
+ "left": "0px",
+ "right": "1388px",
+ "top": "110px",
+ "width": "212px"
+ },
+ "toc_section_display": "block",
+ "toc_window_display": true
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Solution2/Solution_2_v2.pdf b/exercises/Solution2/Solution_2_v2.pdf
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index 0000000000000000000000000000000000000000..6687c306d0e769278d12015ee42b8ff5a4fb2e62
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diff --git a/exercises/Solution5/.ipynb_checkpoints/LeastSquaresFits-checkpoint.ipynb b/exercises/Solution5/.ipynb_checkpoints/LeastSquaresFits-checkpoint.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..a15bd2fa0ca639b43eb58efb279370179ee68650
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+++ b/exercises/Solution5/.ipynb_checkpoints/LeastSquaresFits-checkpoint.ipynb
@@ -0,0 +1,693 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Solution Exercise 5\n",
+ "This week, we are working on least squares fits and parameter estimation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy.optimize import curve_fit\n",
+ "from scipy.stats import norm, chi2, lognorm"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Fit a polynomial\n",
+ "We start by fitting a polynomial to a given data set, in particular, a parabola. Compare a linear fit and a cubic fit to our parabolic fit and check the goodness of fits with chi squared distributions. Explore how the different uncertainties affect the outcome and uncertainties of the fit. \n",
+ "\n",
+ "Hint: You can consider a plot similar to the lecture notes week 5 page 29.\n",
+ "\n",
+ "Extra: Do you see any way to decide wether the data is better described by the parabola or the cubic?\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Create some data distribuited as parabola with normally distributed errors.\n",
+ "def parabola(x, a, b, c):\n",
+ " return a*x**2 + b*x + c\n",
+ "def error(x, sigma):\n",
+ " return norm.rvs(0.0, sigma, x.size) \n",
+ "a = -0.1\n",
+ "b = 0\n",
+ "c = 1\n",
+ "sigma_y = 0.0015\n",
+ "\n",
+ "x = np.linspace(0, 1, 21)\n",
+ "y_true = parabola(x, a, b, c)\n",
+ "delta_y = error(x, sigma_y)\n",
+ "y = y_true + delta_y\n",
+ "y_error = sigma_y * np.ones(x.size)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def fit_polynomial(x, y, degree, weight):\n",
+ " \"\"\"Fit polynomial of degree to data x, y with y weight = 1/sigma_y\n",
+ " \n",
+ " Return fit, covariance matrix, residuals and chi-squared and degrees of freedom.\n",
+ " \"\"\"\n",
+ " \n",
+ " dof = x.shape[0] - degree\n",
+ " fit, cov = np.polyfit(x, y, degree, w=weight, cov=True)\n",
+ " residuals = np.sum((y - np.polyval(fit, x))**2 / y_error**2)\n",
+ " chisq = residuals / (dof)\n",
+ " return fit, cov, residuals, chisq, dof\n",
+ " \n",
+ "fit, cov, res, chisq, dof = fit_polynomial(x, y, 2, 1/y_error) # Fit parabola\n",
+ "fit_1, cov_1, res_1, chisq_1, dof_1 = fit_polynomial(x, y, 1, 1/y_error) # Fit line\n",
+ "fit_3, cov_3, res_3, chisq_3, dof_3 = fit_polynomial(x, y, 3, 1/y_error) # Fit cubic\n",
+ "\n",
+ "def evaluate_chisq(chisq, dof):\n",
+ " return chi2.sf(chisq, dof)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Reduced chi^2:\n",
+ "parabola 0.9459782161747974\n",
+ "line 32.15822425109619\n",
+ "cubic 0.9557527151822285\n"
+ ]
+ }
+ ],
+ "source": [
+ "print('Reduced chi^2:')\n",
+ "print('parabola', chisq)\n",
+ "print('line', chisq_1)\n",
+ "print('cubic', chisq_3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Chi^2 distributions:\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "(0.9999999995308976, 0.04164125577461551, 0.9999999976681199)"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "print('Chi^2 distributions:')\n",
+ "evaluate_chisq(chisq, dof), evaluate_chisq(chisq_1, dof_1), evaluate_chisq(chisq_3, dof_3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Error estimates:\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "(array([0.00424588, 0.00439779, 0.00094897]),\n",
+ " array([0.00664986, 0.00388699]),\n",
+ " array([0.0162819 , 0.0247968 , 0.01051785, 0.00118487]))"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "print('Error estimates:')\n",
+ "np.sqrt(np.diag(cov)), np.sqrt(np.diag(cov_1)), np.sqrt(np.diag(cov_3))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c0577f908>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
+ "ax[0].set_title('fits')\n",
+ "ax[0].errorbar(x, y, yerr=y_error, fmt='k.')\n",
+ "ax[0].plot(x, y_true, 'k-')\n",
+ "ax[0].plot(x, np.polyval(fit, x), label='parabola', color='blue')\n",
+ "ax[0].plot(x, np.polyval(fit_1, x), label='line', color='green')\n",
+ "ax[0].plot(x, np.polyval(fit_3, x), label='cubic', color='red')\n",
+ "\n",
+ "ax[0].legend()\n",
+ "ax[1].plot(y_true - np.polyval(fit, x), '.', color='blue')\n",
+ "ax[1].plot(y_true - np.polyval(fit_1, x), '.', color='green')\n",
+ "ax[1].plot(y_true - np.polyval(fit_3, x), '.', color='red')\n",
+ "ax[1].plot(y_true - y, 'k.', label='data')\n",
+ "ax[1].set_title('residuals')\n",
+ "ax[1].fill_between(ax[1].get_xlim(), -sigma_y, sigma_y, color='grey', alpha=0.4, label=r'$1\\sigma$')\n",
+ "ax[1].legend()\n",
+ "f.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c059cd588>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Draw the plot form lecture notes week 5, page 29\n",
+ "plt.figure(figsize=(5, 5))\n",
+ "chisq_arr = np.linspace(0, 100, 1001)\n",
+ "plt.title('p-values')\n",
+ "plt.xlabel(r'$\\chi^2$')\n",
+ "for n in [1, 2, 3, 4, 6, 8, 10, 15, 20, 25, 30, 40, 50]:\n",
+ " plt.loglog(chisq_arr, chi2.sf(chisq_arr, n))\n",
+ "plt.loglog(chisq_arr, chi2.sf(chisq_arr, dof), 'k-', lw=2, label='dof={0}'.format(dof))\n",
+ "plt.ylim(1e-3, 1.1)\n",
+ "plt.plot(chisq, chi2.sf(chisq, dof), 'o', color='blue', label='parabola')\n",
+ "plt.plot(chisq_1, chi2.sf(chisq_1, dof_1), '^', color='green', label='line')\n",
+ "plt.plot(chisq_3, chi2.sf(chisq_3, dof_3), 'x', color='red', label='cubic', ms=5)\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We observe that the residuals are not uniformly distributed around zero with the expected variance $\\sigma_y$ in the case of the line fit. This reflected in the $\\chi^2$-distribution. Only in 7% of the cases we would expect to draw data that give a worse fit. Note that overfitting with a cubic is not easily spotted in the residuals. However we do observe higher errors on the parameter estimates in the cubic case and we could try a different approach: let's fit only a subset of our data and then compare the fit results on the complement."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c057b7f60>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fit, cov, res, chisq, dof = fit_polynomial(x, y, 2, 1/y_error) # Fit parabola\n",
+ "fit_1, cov_1, res_1, chisq_1, dof_1 = fit_polynomial(x, y, 1, 1/y_error) # Fit line\n",
+ "fit_3, cov_3, res_3, chisq_3, dof_3 = fit_polynomial(x, y, 3, 1/y_error) # Fit cubic\n",
+ "\n",
+ "x_new = np.linspace(1, 2, 21)\n",
+ "y_new = parabola(x_new, a, b, c) + error(x_new, sigma_y)\n",
+ "\n",
+ "f, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
+ "ax[0].set_title('extrapolated fits')\n",
+ "ax[0].plot(x, y, 'k.')\n",
+ "ax[0].errorbar(x_new, y_new, yerr=y_error, fmt='r.')\n",
+ "\n",
+ "ax[0].plot(x_new, np.polyval(fit, x_new), label='parabola', color='blue')\n",
+ "ax[0].plot(x_new, np.polyval(fit_1, x_new), label='line', color='green')\n",
+ "ax[0].plot(x_new, np.polyval(fit_3, x_new), label='cubic', color='red')\n",
+ "\n",
+ "ax[0].legend()\n",
+ "ax[0].set_xlim(0, 2)\n",
+ "ax[1].plot(y_new - np.polyval(fit, x_new), '.', color='blue')\n",
+ "ax[1].plot(y_new - np.polyval(fit_1, x_new), '.', color='green')\n",
+ "ax[1].plot(y_new - np.polyval(fit_3, x_new), '.', color='red')\n",
+ "ax[1].set_title('residuals')\n",
+ "ax[1].fill_between(ax[1].get_xlim(), -sigma_y, sigma_y, color='grey', alpha=0.4, label=r'$1\\sigma$')\n",
+ "ax[1].legend()\n",
+ "f.tight_layout()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here it becomes very obvious that the hypothesis of a parabola holds against a cubic. We cheated a bit by adding data points instead of working with the initial set, but this illustrates the point of this method. An overfitted model usually does not generalize well when presented with addtional data."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Fit a nonlinear function\n",
+ "Next, we consider a Gaussian as an example of a nonlinear function. We are measuring some feature which has a Gaussian distribution in $x$. This could be an inhomogeneous spectral line for $x=E$ the energy of emitted photons. We are interested in the resonance frequency and the linewidth, i. e. we want to estimate them form our observations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def gaussian_parent(x, mu, sigma):\n",
+ " return norm.pdf(x, mu, sigma) \n",
+ "\n",
+ "def gaussian_sample(mu, sigma, sample_size):\n",
+ " return norm.rvs(mu, sigma, sample_size)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c06c9afd0>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Create sample\n",
+ "## SAMPLE SIZE\n",
+ "sample_size = 200\n",
+ "##################\n",
+ "\n",
+ "# Prepare fake data\n",
+ "mu = 1540 # True values that we will try to estimate\n",
+ "sigma = 11 # using a least-squares fit\n",
+ "\n",
+ "x_arr = np.linspace(1500, 1600, 101)\n",
+ "bins = 12\n",
+ "sample = gaussian_sample(mu, sigma, sample_size)\n",
+ "hist = np.histogram(sample, bins=bins, range=(1500, 1580))\n",
+ "bin_width = np.diff(hist[1])[0]\n",
+ "normalization = bin_width * sample_size\n",
+ "x = hist[1][:-1]+bin_width/2\n",
+ "y_error_const = 0\n",
+ "y = hist[0]/normalization + gaussian_sample(0, y_error_const, bins)\n",
+ "y_errors = np.sqrt((np.sqrt(hist[0]) / normalization)**2 + y_error_const**2)\n",
+ "\n",
+ "# Plot our fake measurement results\n",
+ "plt.figure(figsize=(5, 4))\n",
+ "plt.xlabel(r'$E$ (meV)')\n",
+ "plt.ylabel('count rate')\n",
+ "plt.plot(x_arr, gaussian_parent(x_arr, mu, sigma), '-', color='black', label='parent')\n",
+ "plt.errorbar(x, y, yerr=y_errors, fmt='.', ms=7, capsize=3, label='sample')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "# Save data\n",
+ "data = np.vstack((x, y, y_errors))\n",
+ "np.savetxt('data', data)\n",
+ "np.savetxt('sample', sample)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Load data from disk. Format (3,12): (x, y, y_error) x N \n",
+ "data = np.loadtxt('data')\n",
+ "x = data[0, :]\n",
+ "y = data[1, :]\n",
+ "y_error = data[2, :]\n",
+ "# The sample used to generate\n",
+ "sample = np.loadtxt('sample')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Function we want to fit to our data set\n",
+ "def model_function(x, *args):\n",
+ " mu, sigma = args[0:2]\n",
+ " return norm.pdf(x, mu, sigma)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Fit Results:\n",
+ "mu = 1539.0 +- 0.4\n",
+ "sigma = 10.3 +- 0.3\n",
+ "mu estimator 1538.4 +- 0.7\n",
+ "sigma estimator 10.4\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Perform the fit minimizing least squares\n",
+ "initial_guess = [1545, 9]\n",
+ "p_opt, p_cov = curve_fit(model_function, x, y, p0=initial_guess, sigma=None, absolute_sigma=False, check_finite=True)\n",
+ "p_err = np.sqrt(np.diag(p_cov))\n",
+ "# pcov(absolute_sigma=False) = pcov(absolute_sigma=True) * chisq(popt)/(M-N)\n",
+ "print('Fit Results:')\n",
+ "print('mu = {:1.1f} +- {:1.1f}'.format(p_opt[0], p_err[0]))\n",
+ "print('sigma = {:1.1f} +- {:1.1f}'.format(p_opt[1], p_err[1]))\n",
+ "\n",
+ "print('mu estimator {:1.1f} +- {:1.1f}'.format(np.mean(sample), np.std(sample, ddof=1)/np.sqrt(sample.size)))\n",
+ "print('sigma estimator {:1.1f}'.format(np.std(sample, ddof=1)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Plot the result"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c06ec26a0>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x_arr = np.linspace(1500, 1600, 101)\n",
+ "\n",
+ "plt.figure(figsize=(5, 4))\n",
+ "plt.xlabel(r'$E$ (meV)')\n",
+ "plt.ylabel('count rate')\n",
+ "plt.errorbar(x, y, yerr=y_errors, fmt='.', ms=7, capsize=3, label='sample')\n",
+ "plt.plot(x_arr, model_function(x_arr, *initial_guess), '-', color='grey', label='guess')\n",
+ "plt.plot(x_arr, model_function(x_arr, *p_opt), '-', color='black', label='fit')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Biased estimator example"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Expectation value: 4.133148453066826\n",
+ "Sample mean: 4.144495254000121\n",
+ "Gauss fit: 3.946186931764501\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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YNA8sEjIVcFTU17N7ZDEf5A/zneR0WgsskhIq4Kior4/GfeB6U1oK55yjEbBIyFTAUdHQQFNxBKcf4OQdklXAIqFSAUfBkSOwbRtNUZz/jVMBi4Qu13cAIVhdYEZjFJegARX3PMs9zXD7pnpmfvMPmAt+bjfed63nZCKZTSPgKIhd8DxypyF3s7XoPIZ2Hmdsuy5LKRIWFXAUxH61j9R1gHuIHyCc1LbDcxKR7KECjoL6eigoYG8U7oTch/j0SPyaxSKSPBVwFNTXB7eAj8KdkPuwo7CU40NyNAIWCZEKOArq6k6ebRZRnUNyaB41hkmx2yaJSPJUwL51dkJjY+QLGGBLURmT9m33HUMka6iAfdu6FY4fD6YgIm5L8XnBCFh3SBYJhQrYt/jJDRkyAi48eojiDw74jiKSFVTAvsXWAGdEAcdOldY8sEg4VMC+1ddDfj6MH+87yVmdWAuseWCRUKiAfauvDy73mBOhOyH3YWvReXThNAIWCYkK2Lf6+oyYfgA4mpvPzoLRGgGLhEQF7JNZRqwB7q6p6DyNgEVCogL2afduOHQoI5agxTUWl+lsOJGQqIB9yqAlaHFNRedReqiNkUcP+44ikvFUwD5lYAHHV0JM3K9pCJFkqYB9qquDIUOgosJ3koTpqmgi4UmogJ1z1zjnNjjn6pxz95xhu/nOuQ7n3E3hRcximzbBxIkwdKjvJAlrKtZ1gUXCctYCds7lAA8Ci4DZwC3Oudl9bPd94KWwQ2atTZtg2jTfKfqlfehIWocXagQsEoJERsALgDozazCzY8DjwA29bHcX8ASwO8R82cssIwsYgpUQk7UWWCRpiRTweGBrt6+bY8+d4JwbD3wK+El40bJcayvs35+ZBXxuGRV7VcAiyQrrINz9wDfNrOtMG7W0tFBVVXXio6amJqTdZ6BNm4LHDFoDHLe5uIxxB1vhsJaiifSlpqbmRNcBJb1tk8ht6bcBE7p9XR57rrsq4HEX3FKnBPhr51yHmT3dfaPS0lKWL1+eYPwsFy/gTBwBF5cFn9TVwYc/7DeMSERVV1dTXV0NgHNuT2/bJDICXgZMc85Nds7lAzcDi7tvYGaTzazCzCqA3wN/37N8pYdNm4IlaJMn+07Sb5vjBRz/ISIiA3LWEbCZdTjn7gReBHKAR82s1jl3R+z1h1OcMTvV1QXrf/PzfSfptxMj4I0b/QYRyXCJTEFgZs8Bz/V4rtfiNbPbko81CGzalJHzvwCHho6gZWQRpRoBiyRFZ8L5kMFL0OI2F5dpCkIkSSpgH1pa4MCBjC7gRhWwSNJUwD5k8AqIuMbiMti1K/hBIiIDogL2IX4jzgydA4ZuKyHifxYR6TcVsA+bNgX3gMvAJWhxjedqKZpIslTAPmzaFCxBy8vznWTAGotUwCLJUgH7kOErIAA+yB8G48ergEWSoAJON7PgBIbp030nSd60aSpgkSSogNNt27bgRpwzZvhOkjwVsEhSVMDptmFD8Dhzpt8cYZgxA/bsgb17fScRyUgq4HSLF3A2jIDjf4b4n0lE+kUFnG7r18M550BZme8kyYuP4tev95tDJEOpgNNtw4Zg5BhcOzmzxa/mpgIWGRAVcLqtX58d0w8AubnBgTgVsMiAqIDT6fBhaGrKjgNwcTNnqoBFBkgFnE7xJVvZMgKG4M/S0ADHj/tOIpJxVMDpFB8pZtsIuKMD6ut9JxHJOCrgdNqwITj4luGnIZ9CKyFEBkwFnE7r18PEiTB8uO8k4YlPp6iARfpNBZxOGzZk1/QDQGFhsKZZBSzSbyrgdDE7uQY428yYobPhRAZABZwu8YvwZNsIGE4uRTPznUQko6iA0yX+K3o2joBnzoS2Nti923cSkYyiAk6X2trg8fzz/eZIBa2EEBkQFXC61NbC6NEwZozvJOGLF/DatX5ziGQYFXC61NYGo99suAhPTxMmQEHByVG+iCREBZwOZrBmDVxwge8kqeFc8GdTAYv0iwo4HbZtgwMHsnP+N+7882H1aq2EEOkHFXA6ZPMBuLgLLoDWVq2EEOkHFXA6DJYCBk1DiPRDru8Ag0JtbbD6oaTEd5LQVdzzLAAlh/axHPjn//UbfvbSBzTed63fYCIZQCPgdMjmA3Axe0YUsXd4IdP3bPEdRSRjqIBTzSxYH5vN0w8AzrGxZCIzWlTAIolSAadaUxMcPJj9BQxsKJ3EtD1NWgkhkiAVcKoNhgNwMRtLJlF47DDj2vf4jiKSEVTAqbZmTfA4CAp4Q+kkAE1DiCRIBZxqtbUwbhwUF/tOknIbS4IC1oE4kcSogFNt1SqYO9d3irQ4MOwcdp5zLtP3NPmOIpIRVMCpdPRosAJikBQwwIbSCma2NPqOIZIRVMCpVFsb3LL9wgt9J0mbtWOmML1lCxw75juKSOSpgFNp5crgcRCNgGvHTiG/q0PXBhZJgAo4lVatgnPOgcpK30nSZs3Y2J91xQq/QUQygAo4lVauhDlzYMjg+WveUjyO9vzhJ0f/ItKnwdMM6dbVBe+9N6jmfwHMDWHdmMkqYJEEqIBTpb4+OAV5EM3/xtWOrQymXzo7fUcRiTQVcKqsWhU8DtYCPnQI6up8RxGJNBVwqqxcCbm5g+IU5J5qx04JPtE0hMgZJXRBdufcNcCPgBzgETO7r8fr/w34JuCAduDvzOy9kLNmllWrYNYsGDbMd5K02zR6IuTnw8qVVKwq6HUbXbBdJIERsHMuB3gQWATMBm5xzs3usdlm4KNm9iHgX4GasINmnJUrB90BuLiOnNzgAvRaiiZyRomMgBcAdWbWAOCcexy4ATix0t7M3u62/VKgPMyQGWf7dti587QCjt++pzdZNyK86CJ46im4yILb1ovIaRKZAx4PbO32dXPsub58CXi+txdaWlqoqqo68VFTk6UD5XfeCR4vvthvDp8uvBBaWylrb/GdRMSLmpqaE10H9HpDyFBvyumcu5KggD/S2+ulpaUsX748zF1G09KlkJc3aKcgAJg/H4C52zeyvXCM5zAi6VddXU11dTUAzrle71KQyAh4GzCh29flsedO4Zz7MPAIcIOZtfY7bTZ5552gfAfhAbgT5syBYcO4aNs630lEIiuRAl4GTHPOTXbO5QM3A4u7b+Ccmwg8CXzBzDaGHzODdHTAsmWDe/oBglUQ8+Zx4fYNvpOIRNZZC9jMOoA7gReBdcBvzazWOXeHc+6O2Gb/BIwGHnLOrXLODYJ5hj7U1sLhw3DJJb6T+HfppVywq478juO+k4hEUkInYpjZc2Y23cwqzex/xp572Mwejn3+ZTMrNrO5sY+qVIaOtKVLg8fBPgIGuPRShnZ2cP6uet9JRCJJZ8KFbelSKCmBKVN8J/Ev9luApiFEeqcCDts77wTFo7WvUFZGc2EpF21f7zuJSCSpgMPU1gbr1mn6oZtVZTOZqwIW6ZUKOEzLlgWPOgB3woqymZQfaGFM++BemSjSGxVwmN56K7j7RewkBIGVZTMANA0h0gsVcJiWLAlOwBg1yneSyKgdW8nRnDzm6YQMkdOogMPywQfBCogrr/SdJFKO5eaxYvxMLm1a7TuKSOSogMPy9ttw7JgKuBdvT/wws3c1UPTBAd9RRCJFBRyWJUsgJwcuv9x3ksh5a9JchmBcolGwyClUwGF57TWoqoKC3u8AMZi9P24aB/OHs3DL4L5JikhPKuAwHDwYLEHT9EOvOnJy+XP5+Vy25X3fUUQiRQUchjffDK6CpgLu09uTPkzl3mbGtvd6WVSRQUkFHIYlS4ILsC9c6DtJZL09aS6ARsEi3aiAw/Daa7BgAYwc6TtJZK0bU8He4YUqYJFuVMDJ2rkTli+HRYt8J4k0c0P408QPsXDLKjDzHUckElTAyXrmmeDx+uv95sgA/zVlHmXte5i9e7PvKCKRoAJO1uLFMGkSXHCB7ySR91rlArpwXL1pqe8oIpEQ6l2RB53Dh+Hll+ErX9H1fxPQOrKI5eWz+HiCBVxxz7O9Pt9437VhxhLxRiPgZLzyChw5oumHfnh56iWcv7sBGht9RxHxTgWcjMWLobAQrrjCd5KM8fK02MXqFy8+84Yig4AKeKC6uoIDcNdcE9yCXRLSeO54No6eCE8/7TuKiHcq4IFauhR27YJPfMJ3kozz0vRL4I03YO9e31FEvFIBD9Rjj8Hw4Zr/HYCXpl0CnZ0aBcugp1UQA3HkCPzmN/CpTwVzwNIv7583DaZP553v/Tuf3Ti212200kEGAxXwQPzhD8EdkP/2b30nyUzOwe23c/G3vkXF3m00nju+32/R1xI1UHlL5tAUxEA89hiMHw9XXeU7Sea69VY63RBuWvOq7yQi3qiA+2vXLnj+efj854M7YMjAlJXx+uSL+PTqVxnS1ek7jYgXKuD++tWvggNIt97qO0nG+92HPsa4g618pHGV7ygiXqiA+6OzEx58EC65BGbP9p0m47069WL2DSvgb1a/4juKiBc6CNcfTz0F9fXw/e/7TpIVjuXm8dAln+FYbp7vKCJeqIATZQY/+AFMnQqf/KTvNFnjPy6+0XcEEW9UwIl6/fXgxpsPP6yDbyISCs0BJ+oHP4AxY3TwTURCoxFwIv74x2Dp2b33BqcfS+TpWsKSCTQCPpvOTvj616G8HO6+23caEckiGgGfzU9/CqtWwa9/rbsei0ioNAI+k3374Dvfgcsvh89+1ncaEckyKuC+mMFddwXXrH3gAd3zTURCpymIvjz6KPzyl/Av/wJz5/pOIyJZSCPg3qxeDXfeCR/7GHz7277TiEiW0gi4p+bm4Ey3oiL4xS900kUW0rWEJSpUwN1t3w5XXgl79sDLL8PY3u/WICISBk1BxNXXB+W7cye88AIsWOA7kYhkORUwwJNPwkUXQUtLUL6XXuo7kYgMAoO7gHfsgC99CT79aZgxA1asgIULfacSkUFicBbwjh3wve/BtGnw85/DP/wDvPkmVFT4TiYig0hCB+Gcc9cAPwJygEfM7L4er7vY638NHAZuM7MVYYWsqamhuro6uTfZuxdeegl+9ztYvBg6OuDGG4OLq0+d6j9fCrWveoGCudf4jtGnqOXruUoini+RFRLJXAToTN97ppUb356yLdL//0X934fPfGcdATvncoAHgUXAbOAW51zP+/EsAqbFPqqBn4QZsqamJvGNjx+HLVvg1VeDa/d+9atQVQWlpXDLLcGVze6+GzZsgCeeSLp8+53Pg4PvveA7whkpX3Ki/v+f8vUtkRHwAqDOzBoAnHOPAzcAa7ttcwPwmJkZsNQ5V+ScG2dmO5JO+Pzz/N22bXDPPUG5Hj8OR4/CkSNw6BAcPAj79wcfu3dDa+up319UBPPmwXe/C4sWwfz5WtsrA5bMGuJsXH+cyst++rqkaDr364LOPMMGzt0EXGNmX459/QXgYjO7s9s2zwD3mdmbsa9fBb5pZst7vFc7p466W4A9CeQsSXA7X5QvOcqXHOVLTqrylQClsc+7zKyg5wZpPRGjtwAiIoNVIqsgtgETun1dHnuuv9uIiEg3iRTwMmCac26ycy4fuBlY3GObxcCtLnAJsD+U+V8RkSx21ikIM+twzt0JvEiwDO1RM6t1zt0Re/1h4DmCJWh1BMvQbk9dZBGR7HDWg3A+OecmAI8BYwEDaszsR35TneScGwa8AQwl+GH2ezP7nt9Up4otI1wObDOz63zn6ck51wi0A51Ah5lV+U10knOuCHgEuIDg/78vmtmf/KYKOOdmAL/p9tQU4J/M7H5PkU7jnPvvwJcJ/u5WA7eb2RG/qU5yzn0D+ArggP/w8XcX9QIeB4wzsxXOuQLgXeCTZrb2LN+aFrETUEaa2UHnXB7wJvANM1vqOdoJzrn/AVQBhREu4Cozi9xRcufcfwJ/NLNHYtNvI8yszXeunmI/ZLcRrE7a4jsPgHNuPMG/h9lm9oFz7rfAc2b2M7/JAs65C4DHCZbZHgNeAO4ws7p05oj0qchmtiN+Rp2ZtQPrgPF+U51kgYOxL/NiH5H5ieacKweuJRjFST8450YBVwA/BTCzY1Es35jxgMHOAAACcUlEQVSrgPqolG83ucBw51wuMALY7jlPd7OAd8zssJl1AK8DN6Y7RKQLuDvnXAVwIfCO3ySncs7lOOdWAbuBl80sSvnuB/4R6PId5AwMeMU5965zLkrnq04mWKf+f51zK51zjzjnonpb7JuBX/sO0Z2ZbQP+N9AE7CA4MP+S31SnWANc7pwb7ZwbQXAMa8JZvid0GVHAzrlzgCeAu83sgO883ZlZp5nNJVh6tyD2q413zrnrgN1m9q7vLGfxkdjf3yLga865K3wHiskFLgJ+YmYXAoeAe/xGOl1sauR64He+s3TnnCsmOEN2MlAGjHTOfd5vqpPMbB3wfeAlgumHVQTHIdIq8gUcm1t9AvilmT3pO09fYr+eLgGiclWZhcD1sTnWx4G/dM79wm+k08VGSpjZbuApgjm5KGgGmrv9RvN7gkKOmkXACjPb5TtIDx8DNptZi5kdB54ELvOc6RRm9lMzm2dmVwD7gI3pzhDpAo4d5PopsM7M/t13np6cc6WxI+U454YDVwPr/aYKmNm3zKzczCoIfkV9zcwiMwIBcM6NjB1cJfbr/ccJfjX0zsx2Altjqw0gmGeNxMHfHm4hYtMPMU3AJc65EbF/x1cRHMOJDOfcmNjjRIL531+lO0PU7wm3EPgCsDo2zwrwbTN7zmOm7sYB/xk7Cj0E+K2ZPeM5UyYZCzwV/PskF/iVmUXp0mN3Ab+M/ZrfQMTWt8d+aF0NfNV3lp7M7B3n3O+BFUAHsBKI2mXRnnDOjQaOA1/zcZA10svQRESyWaSnIEREspkKWETEExWwiIgnKmAREU9UwCIinqiARUQ8UQGLiHjy/wFgxpd0YzQJMwAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c06fc1b00>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "log_sample = lognorm.rvs(s=0.5, loc=3, scale=1, size=1000)\n",
+ "plt.figure(figsize=(5, 4))\n",
+ "h = plt.hist(log_sample, bins=32, rwidth=0.85, normed=True)\n",
+ "\n",
+ "\n",
+ "def model_function(x, *args):\n",
+ " A, mu, sigma = args[0:3]\n",
+ " return A * norm.pdf(x, mu, sigma)\n",
+ "\n",
+ "\n",
+ "x = h[1][:-1]+np.diff(h[1])[0]/2\n",
+ "y = h[0]\n",
+ "initial_guess = [0.95, 3.3, 0.3]\n",
+ "gauss_fit_large = curve_fit(model_function, x, y, p0=initial_guess)\n",
+ "#local = np.where(np.abs(x-np.mean(log_sample))<0.5)\n",
+ "#gauss_fit_local = curve_fit(model_function, x[local], y[local], p0=initial_guess)\n",
+ "\n",
+ "x_arr = np.linspace(2, 5, 51)\n",
+ "plt.plot(x_arr, model_function(x_arr, *gauss_fit_large[0]), '-', color='red', label='fit')\n",
+ "#plt.plot(x[local], model_function(x[local], *gauss_fit_large[0]), '-', color='orange', label='fit small')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "print('Expectation value:', lognorm.mean(s=0.5, loc=3, scale=1))\n",
+ "print('Sample mean:', np.mean(log_sample))\n",
+ "print('Gauss fit:', gauss_fit_large[0][1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Fitting a Gaussian and gives a biased estimate of mu"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Bonus: Errors in x and y\n",
+ "So far, we considered uncertainties only on y. Consider the following data set with errors in both x and y. Try to fit a line to the data below, taking into account both errors. Compare with fits neglecting the x errors or both. \n",
+ " \n",
+ "Hint: A detailed solution is already on the moodle. You may chose if you want to try to write your own solution, implement a known solution (see references in solution notebook) or just try it with the scipy package ODR (orthogonal distance regression). \n",
+ "https://docs.scipy.org/doc/scipy/reference/odr.html\n",
+ " \n",
+ "The solution contains a python implementation of York's equation, comparison with ODR and MC tests. \n",
+ "Week 3: \"Linear Regression errors x and y\""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c06f95da0>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Test data\n",
+ "X = np.array([0.0, 0.9, 1.8, 2.6, 3.3, 4.4, 5.2, 6.1, 6.5, 7.4])\n",
+ "Y = np.array([5.9, 5.4, 4.4, 4.6, 3.5, 3.7, 2.8, 2.8, 2.4, 1.5])\n",
+ "wX = np.array([1000, 1000, 500, 800, 200, 80, 60, 20, 1.8, 1])\n",
+ "wY = np.array([1, 1.8, 4, 8, 20, 20, 70, 70, 100, 500])\n",
+ "sigma_x = 1.0/np.sqrt(wX)\n",
+ "sigma_y = 1.0/np.sqrt(wY)\n",
+ "\n",
+ "plt.figure(figsize=(4, 3))\n",
+ "plt.errorbar(X, Y, xerr=sigma_x, yerr=sigma_y, fmt='o', label='oberservations')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "hide_input": false,
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.7"
+ },
+ "toc": {
+ "base_numbering": 1,
+ "nav_menu": {},
+ "number_sections": true,
+ "sideBar": true,
+ "skip_h1_title": false,
+ "title_cell": "Table of Contents",
+ "title_sidebar": "Contents",
+ "toc_cell": false,
+ "toc_position": {
+ "height": "calc(100% - 180px)",
+ "left": "10px",
+ "top": "150px",
+ "width": "225.438px"
+ },
+ "toc_section_display": true,
+ "toc_window_display": true
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Solution5/.ipynb_checkpoints/Solutions_5-checkpoint.ipynb b/exercises/Solution5/.ipynb_checkpoints/Solutions_5-checkpoint.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..4e1698eeccbe33d45fa126be2a7d469b4a97f5e1
--- /dev/null
+++ b/exercises/Solution5/.ipynb_checkpoints/Solutions_5-checkpoint.ipynb
@@ -0,0 +1,693 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Solution Exercise 5\n",
+ "This week, we are working on least squares fits and parameter estimation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy.optimize import curve_fit\n",
+ "from scipy.stats import norm, chi2, lognorm"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Fit a polynomial\n",
+ "We start by fitting a polynomial to a given data set, in particular, a parabola. Compare a linear fit and a cubic fit to our parabolic fit and check the goodness of fits with chi squared distributions. Explore how the different uncertainties affect the outcome and uncertainties of the fit. \n",
+ "\n",
+ "Hint: You can consider a plot similar to the lecture notes week 5 page 29.\n",
+ "\n",
+ "Extra: Do you see any way to decide wether the data is better described by the parabola or the cubic?\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Create some data distribuited as parabola with normally distributed errors.\n",
+ "def parabola(x, a, b, c):\n",
+ " return a*x**2 + b*x + c\n",
+ "def error(x, sigma):\n",
+ " return norm.rvs(0.0, sigma, x.size) \n",
+ "a = -0.1\n",
+ "b = 0\n",
+ "c = 1\n",
+ "sigma_y = 0.0015\n",
+ "\n",
+ "x = np.linspace(0, 1, 21)\n",
+ "y_true = parabola(x, a, b, c)\n",
+ "delta_y = error(x, sigma_y)\n",
+ "y = y_true + delta_y\n",
+ "y_error = sigma_y * np.ones(x.size)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def fit_polynomial(x, y, degree, weight):\n",
+ " \"\"\"Fit polynomial of degree to data x, y with y weight = 1/sigma_y\n",
+ " \n",
+ " Return fit, covariance matrix, residuals and chi-squared and degrees of freedom.\n",
+ " \"\"\"\n",
+ " \n",
+ " dof = x.shape[0] - degree\n",
+ " fit, cov = np.polyfit(x, y, degree, w=weight, cov=True)\n",
+ " residuals = np.sum((y - np.polyval(fit, x))**2 / y_error**2)\n",
+ " chisq = residuals / (dof)\n",
+ " return fit, cov, residuals, chisq, dof\n",
+ " \n",
+ "fit, cov, res, chisq, dof = fit_polynomial(x, y, 2, 1/y_error) # Fit parabola\n",
+ "fit_1, cov_1, res_1, chisq_1, dof_1 = fit_polynomial(x, y, 1, 1/y_error) # Fit line\n",
+ "fit_3, cov_3, res_3, chisq_3, dof_3 = fit_polynomial(x, y, 3, 1/y_error) # Fit cubic\n",
+ "\n",
+ "def evaluate_chisq(chisq, dof):\n",
+ " return chi2.sf(chisq, dof)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Reduced chi^2:\n",
+ "parabola 0.9459782161747974\n",
+ "line 32.15822425109619\n",
+ "cubic 0.9557527151822285\n"
+ ]
+ }
+ ],
+ "source": [
+ "print('Reduced chi^2:')\n",
+ "print('parabola', chisq)\n",
+ "print('line', chisq_1)\n",
+ "print('cubic', chisq_3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Chi^2 distributions:\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "(0.9999999995308976, 0.04164125577461551, 0.9999999976681199)"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "print('Chi^2 distributions:')\n",
+ "evaluate_chisq(chisq, dof), evaluate_chisq(chisq_1, dof_1), evaluate_chisq(chisq_3, dof_3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Error estimates:\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "(array([0.00424588, 0.00439779, 0.00094897]),\n",
+ " array([0.00664986, 0.00388699]),\n",
+ " array([0.0162819 , 0.0247968 , 0.01051785, 0.00118487]))"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "print('Error estimates:')\n",
+ "np.sqrt(np.diag(cov)), np.sqrt(np.diag(cov_1)), np.sqrt(np.diag(cov_3))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c0577f908>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
+ "ax[0].set_title('fits')\n",
+ "ax[0].errorbar(x, y, yerr=y_error, fmt='k.')\n",
+ "ax[0].plot(x, y_true, 'k-')\n",
+ "ax[0].plot(x, np.polyval(fit, x), label='parabola', color='blue')\n",
+ "ax[0].plot(x, np.polyval(fit_1, x), label='line', color='green')\n",
+ "ax[0].plot(x, np.polyval(fit_3, x), label='cubic', color='red')\n",
+ "\n",
+ "ax[0].legend()\n",
+ "ax[1].plot(y_true - np.polyval(fit, x), '.', color='blue')\n",
+ "ax[1].plot(y_true - np.polyval(fit_1, x), '.', color='green')\n",
+ "ax[1].plot(y_true - np.polyval(fit_3, x), '.', color='red')\n",
+ "ax[1].plot(y_true - y, 'k.', label='data')\n",
+ "ax[1].set_title('residuals')\n",
+ "ax[1].fill_between(ax[1].get_xlim(), -sigma_y, sigma_y, color='grey', alpha=0.4, label=r'$1\\sigma$')\n",
+ "ax[1].legend()\n",
+ "f.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c059cd588>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Draw the plot form lecture notes week 5, page 29\n",
+ "plt.figure(figsize=(5, 5))\n",
+ "chisq_arr = np.linspace(0, 100, 1001)\n",
+ "plt.title('p-values')\n",
+ "plt.xlabel(r'$\\chi^2$')\n",
+ "for n in [1, 2, 3, 4, 6, 8, 10, 15, 20, 25, 30, 40, 50]:\n",
+ " plt.loglog(chisq_arr, chi2.sf(chisq_arr, n))\n",
+ "plt.loglog(chisq_arr, chi2.sf(chisq_arr, dof), 'k-', lw=2, label='dof={0}'.format(dof))\n",
+ "plt.ylim(1e-3, 1.1)\n",
+ "plt.plot(chisq, chi2.sf(chisq, dof), 'o', color='blue', label='parabola')\n",
+ "plt.plot(chisq_1, chi2.sf(chisq_1, dof_1), '^', color='green', label='line')\n",
+ "plt.plot(chisq_3, chi2.sf(chisq_3, dof_3), 'x', color='red', label='cubic', ms=5)\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We observe that the residuals are not uniformly distributed around zero with the expected variance $\\sigma_y$ in the case of the line fit. This reflected in the $\\chi^2$-distribution. Only in 7% of the cases we would expect to draw data that give a worse fit. Note that overfitting with a cubic is not easily spotted in the residuals. However we do observe higher errors on the parameter estimates in the cubic case and we could try a different approach: let's fit only a subset of our data and then compare the fit results on the complement."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c057b7f60>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fit, cov, res, chisq, dof = fit_polynomial(x, y, 2, 1/y_error) # Fit parabola\n",
+ "fit_1, cov_1, res_1, chisq_1, dof_1 = fit_polynomial(x, y, 1, 1/y_error) # Fit line\n",
+ "fit_3, cov_3, res_3, chisq_3, dof_3 = fit_polynomial(x, y, 3, 1/y_error) # Fit cubic\n",
+ "\n",
+ "x_new = np.linspace(1, 2, 21)\n",
+ "y_new = parabola(x_new, a, b, c) + error(x_new, sigma_y)\n",
+ "\n",
+ "f, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
+ "ax[0].set_title('extrapolated fits')\n",
+ "ax[0].plot(x, y, 'k.')\n",
+ "ax[0].errorbar(x_new, y_new, yerr=y_error, fmt='r.')\n",
+ "\n",
+ "ax[0].plot(x_new, np.polyval(fit, x_new), label='parabola', color='blue')\n",
+ "ax[0].plot(x_new, np.polyval(fit_1, x_new), label='line', color='green')\n",
+ "ax[0].plot(x_new, np.polyval(fit_3, x_new), label='cubic', color='red')\n",
+ "\n",
+ "ax[0].legend()\n",
+ "ax[0].set_xlim(0, 2)\n",
+ "ax[1].plot(y_new - np.polyval(fit, x_new), '.', color='blue')\n",
+ "ax[1].plot(y_new - np.polyval(fit_1, x_new), '.', color='green')\n",
+ "ax[1].plot(y_new - np.polyval(fit_3, x_new), '.', color='red')\n",
+ "ax[1].set_title('residuals')\n",
+ "ax[1].fill_between(ax[1].get_xlim(), -sigma_y, sigma_y, color='grey', alpha=0.4, label=r'$1\\sigma$')\n",
+ "ax[1].legend()\n",
+ "f.tight_layout()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here it becomes very obvious that the hypothesis of a parabola holds against a cubic. We cheated a bit by adding data points instead of working with the initial set, but this illustrates the point of this method. An overfitted model usually does not generalize well when presented with addtional data."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Fit a nonlinear function\n",
+ "Next, we consider a Gaussian as an example of a nonlinear function. We are measuring some feature which has a Gaussian distribution in $x$. This could be an inhomogeneous spectral line for $x=E$ the energy of emitted photons. We are interested in the resonance frequency and the linewidth, i. e. we want to estimate them form our observations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def gaussian_parent(x, mu, sigma):\n",
+ " return norm.pdf(x, mu, sigma) \n",
+ "\n",
+ "def gaussian_sample(mu, sigma, sample_size):\n",
+ " return norm.rvs(mu, sigma, sample_size)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c06c9afd0>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Create sample\n",
+ "## SAMPLE SIZE\n",
+ "sample_size = 200\n",
+ "##################\n",
+ "\n",
+ "# Prepare fake data\n",
+ "mu = 1540 # True values that we will try to estimate\n",
+ "sigma = 11 # using a least-squares fit\n",
+ "\n",
+ "x_arr = np.linspace(1500, 1600, 101)\n",
+ "bins = 12\n",
+ "sample = gaussian_sample(mu, sigma, sample_size)\n",
+ "hist = np.histogram(sample, bins=bins, range=(1500, 1580))\n",
+ "bin_width = np.diff(hist[1])[0]\n",
+ "normalization = bin_width * sample_size\n",
+ "x = hist[1][:-1]+bin_width/2\n",
+ "y_error_const = 0\n",
+ "y = hist[0]/normalization + gaussian_sample(0, y_error_const, bins)\n",
+ "y_errors = np.sqrt((np.sqrt(hist[0]) / normalization)**2 + y_error_const**2)\n",
+ "\n",
+ "# Plot our fake measurement results\n",
+ "plt.figure(figsize=(5, 4))\n",
+ "plt.xlabel(r'$E$ (meV)')\n",
+ "plt.ylabel('count rate')\n",
+ "plt.plot(x_arr, gaussian_parent(x_arr, mu, sigma), '-', color='black', label='parent')\n",
+ "plt.errorbar(x, y, yerr=y_errors, fmt='.', ms=7, capsize=3, label='sample')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "# Save data\n",
+ "data = np.vstack((x, y, y_errors))\n",
+ "np.savetxt('data', data)\n",
+ "np.savetxt('sample', sample)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Load data from disk. Format (3,12): (x, y, y_error) x N \n",
+ "data = np.loadtxt('data')\n",
+ "x = data[0, :]\n",
+ "y = data[1, :]\n",
+ "y_error = data[2, :]\n",
+ "# The sample used to generate\n",
+ "sample = np.loadtxt('sample')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Function we want to fit to our data set\n",
+ "def model_function(x, *args):\n",
+ " mu, sigma = args[0:2]\n",
+ " return norm.pdf(x, mu, sigma)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Fit Results:\n",
+ "mu = 1539.0 +- 0.4\n",
+ "sigma = 10.3 +- 0.3\n",
+ "mu estimator 1538.4 +- 0.7\n",
+ "sigma estimator 10.4\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Perform the fit minimizing least squares\n",
+ "initial_guess = [1545, 9]\n",
+ "p_opt, p_cov = curve_fit(model_function, x, y, p0=initial_guess, sigma=None, absolute_sigma=False, check_finite=True)\n",
+ "p_err = np.sqrt(np.diag(p_cov))\n",
+ "# pcov(absolute_sigma=False) = pcov(absolute_sigma=True) * chisq(popt)/(M-N)\n",
+ "print('Fit Results:')\n",
+ "print('mu = {:1.1f} +- {:1.1f}'.format(p_opt[0], p_err[0]))\n",
+ "print('sigma = {:1.1f} +- {:1.1f}'.format(p_opt[1], p_err[1]))\n",
+ "\n",
+ "print('mu estimator {:1.1f} +- {:1.1f}'.format(np.mean(sample), np.std(sample, ddof=1)/np.sqrt(sample.size)))\n",
+ "print('sigma estimator {:1.1f}'.format(np.std(sample, ddof=1)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Plot the result"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c06ec26a0>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x_arr = np.linspace(1500, 1600, 101)\n",
+ "\n",
+ "plt.figure(figsize=(5, 4))\n",
+ "plt.xlabel(r'$E$ (meV)')\n",
+ "plt.ylabel('count rate')\n",
+ "plt.errorbar(x, y, yerr=y_errors, fmt='.', ms=7, capsize=3, label='sample')\n",
+ "plt.plot(x_arr, model_function(x_arr, *initial_guess), '-', color='grey', label='guess')\n",
+ "plt.plot(x_arr, model_function(x_arr, *p_opt), '-', color='black', label='fit')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Biased estimator example"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Expectation value: 4.133148453066826\n",
+ "Sample mean: 4.144495254000121\n",
+ "Gauss fit: 3.946186931764501\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c06fc1b00>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "log_sample = lognorm.rvs(s=0.5, loc=3, scale=1, size=1000)\n",
+ "plt.figure(figsize=(5, 4))\n",
+ "h = plt.hist(log_sample, bins=32, rwidth=0.85, normed=True)\n",
+ "\n",
+ "\n",
+ "def model_function(x, *args):\n",
+ " A, mu, sigma = args[0:3]\n",
+ " return A * norm.pdf(x, mu, sigma)\n",
+ "\n",
+ "\n",
+ "x = h[1][:-1]+np.diff(h[1])[0]/2\n",
+ "y = h[0]\n",
+ "initial_guess = [0.95, 3.3, 0.3]\n",
+ "gauss_fit_large = curve_fit(model_function, x, y, p0=initial_guess)\n",
+ "#local = np.where(np.abs(x-np.mean(log_sample))<0.5)\n",
+ "#gauss_fit_local = curve_fit(model_function, x[local], y[local], p0=initial_guess)\n",
+ "\n",
+ "x_arr = np.linspace(2, 5, 51)\n",
+ "plt.plot(x_arr, model_function(x_arr, *gauss_fit_large[0]), '-', color='red', label='fit')\n",
+ "#plt.plot(x[local], model_function(x[local], *gauss_fit_large[0]), '-', color='orange', label='fit small')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "print('Expectation value:', lognorm.mean(s=0.5, loc=3, scale=1))\n",
+ "print('Sample mean:', np.mean(log_sample))\n",
+ "print('Gauss fit:', gauss_fit_large[0][1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Fitting a Gaussian and gives a biased estimate of mu"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Bonus: Errors in x and y\n",
+ "So far, we considered uncertainties only on y. Consider the following data set with errors in both x and y. Try to fit a line to the data below, taking into account both errors. Compare with fits neglecting the x errors or both. \n",
+ " \n",
+ "Hint: A detailed solution is already on the moodle. You may chose if you want to try to write your own solution, implement a known solution (see references in solution notebook) or just try it with the scipy package ODR (orthogonal distance regression). \n",
+ "https://docs.scipy.org/doc/scipy/reference/odr.html\n",
+ " \n",
+ "The solution contains a python implementation of York's equation, comparison with ODR and MC tests. \n",
+ "Week 3: \"Linear Regression errors x and y\""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c06f95da0>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Test data\n",
+ "X = np.array([0.0, 0.9, 1.8, 2.6, 3.3, 4.4, 5.2, 6.1, 6.5, 7.4])\n",
+ "Y = np.array([5.9, 5.4, 4.4, 4.6, 3.5, 3.7, 2.8, 2.8, 2.4, 1.5])\n",
+ "wX = np.array([1000, 1000, 500, 800, 200, 80, 60, 20, 1.8, 1])\n",
+ "wY = np.array([1, 1.8, 4, 8, 20, 20, 70, 70, 100, 500])\n",
+ "sigma_x = 1.0/np.sqrt(wX)\n",
+ "sigma_y = 1.0/np.sqrt(wY)\n",
+ "\n",
+ "plt.figure(figsize=(4, 3))\n",
+ "plt.errorbar(X, Y, xerr=sigma_x, yerr=sigma_y, fmt='o', label='oberservations')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "hide_input": false,
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.3"
+ },
+ "toc": {
+ "base_numbering": 1,
+ "nav_menu": {},
+ "number_sections": true,
+ "sideBar": true,
+ "skip_h1_title": false,
+ "title_cell": "Table of Contents",
+ "title_sidebar": "Contents",
+ "toc_cell": false,
+ "toc_position": {
+ "height": "calc(100% - 180px)",
+ "left": "10px",
+ "top": "150px",
+ "width": "225.438px"
+ },
+ "toc_section_display": true,
+ "toc_window_display": true
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Solution5/Solutions_5.ipynb b/exercises/Solution5/Solutions_5.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..a15bd2fa0ca639b43eb58efb279370179ee68650
--- /dev/null
+++ b/exercises/Solution5/Solutions_5.ipynb
@@ -0,0 +1,693 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Solution Exercise 5\n",
+ "This week, we are working on least squares fits and parameter estimation"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy.optimize import curve_fit\n",
+ "from scipy.stats import norm, chi2, lognorm"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Fit a polynomial\n",
+ "We start by fitting a polynomial to a given data set, in particular, a parabola. Compare a linear fit and a cubic fit to our parabolic fit and check the goodness of fits with chi squared distributions. Explore how the different uncertainties affect the outcome and uncertainties of the fit. \n",
+ "\n",
+ "Hint: You can consider a plot similar to the lecture notes week 5 page 29.\n",
+ "\n",
+ "Extra: Do you see any way to decide wether the data is better described by the parabola or the cubic?\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Create some data distribuited as parabola with normally distributed errors.\n",
+ "def parabola(x, a, b, c):\n",
+ " return a*x**2 + b*x + c\n",
+ "def error(x, sigma):\n",
+ " return norm.rvs(0.0, sigma, x.size) \n",
+ "a = -0.1\n",
+ "b = 0\n",
+ "c = 1\n",
+ "sigma_y = 0.0015\n",
+ "\n",
+ "x = np.linspace(0, 1, 21)\n",
+ "y_true = parabola(x, a, b, c)\n",
+ "delta_y = error(x, sigma_y)\n",
+ "y = y_true + delta_y\n",
+ "y_error = sigma_y * np.ones(x.size)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def fit_polynomial(x, y, degree, weight):\n",
+ " \"\"\"Fit polynomial of degree to data x, y with y weight = 1/sigma_y\n",
+ " \n",
+ " Return fit, covariance matrix, residuals and chi-squared and degrees of freedom.\n",
+ " \"\"\"\n",
+ " \n",
+ " dof = x.shape[0] - degree\n",
+ " fit, cov = np.polyfit(x, y, degree, w=weight, cov=True)\n",
+ " residuals = np.sum((y - np.polyval(fit, x))**2 / y_error**2)\n",
+ " chisq = residuals / (dof)\n",
+ " return fit, cov, residuals, chisq, dof\n",
+ " \n",
+ "fit, cov, res, chisq, dof = fit_polynomial(x, y, 2, 1/y_error) # Fit parabola\n",
+ "fit_1, cov_1, res_1, chisq_1, dof_1 = fit_polynomial(x, y, 1, 1/y_error) # Fit line\n",
+ "fit_3, cov_3, res_3, chisq_3, dof_3 = fit_polynomial(x, y, 3, 1/y_error) # Fit cubic\n",
+ "\n",
+ "def evaluate_chisq(chisq, dof):\n",
+ " return chi2.sf(chisq, dof)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Reduced chi^2:\n",
+ "parabola 0.9459782161747974\n",
+ "line 32.15822425109619\n",
+ "cubic 0.9557527151822285\n"
+ ]
+ }
+ ],
+ "source": [
+ "print('Reduced chi^2:')\n",
+ "print('parabola', chisq)\n",
+ "print('line', chisq_1)\n",
+ "print('cubic', chisq_3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Chi^2 distributions:\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "(0.9999999995308976, 0.04164125577461551, 0.9999999976681199)"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "print('Chi^2 distributions:')\n",
+ "evaluate_chisq(chisq, dof), evaluate_chisq(chisq_1, dof_1), evaluate_chisq(chisq_3, dof_3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Error estimates:\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "(array([0.00424588, 0.00439779, 0.00094897]),\n",
+ " array([0.00664986, 0.00388699]),\n",
+ " array([0.0162819 , 0.0247968 , 0.01051785, 0.00118487]))"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "print('Error estimates:')\n",
+ "np.sqrt(np.diag(cov)), np.sqrt(np.diag(cov_1)), np.sqrt(np.diag(cov_3))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c0577f908>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
+ "ax[0].set_title('fits')\n",
+ "ax[0].errorbar(x, y, yerr=y_error, fmt='k.')\n",
+ "ax[0].plot(x, y_true, 'k-')\n",
+ "ax[0].plot(x, np.polyval(fit, x), label='parabola', color='blue')\n",
+ "ax[0].plot(x, np.polyval(fit_1, x), label='line', color='green')\n",
+ "ax[0].plot(x, np.polyval(fit_3, x), label='cubic', color='red')\n",
+ "\n",
+ "ax[0].legend()\n",
+ "ax[1].plot(y_true - np.polyval(fit, x), '.', color='blue')\n",
+ "ax[1].plot(y_true - np.polyval(fit_1, x), '.', color='green')\n",
+ "ax[1].plot(y_true - np.polyval(fit_3, x), '.', color='red')\n",
+ "ax[1].plot(y_true - y, 'k.', label='data')\n",
+ "ax[1].set_title('residuals')\n",
+ "ax[1].fill_between(ax[1].get_xlim(), -sigma_y, sigma_y, color='grey', alpha=0.4, label=r'$1\\sigma$')\n",
+ "ax[1].legend()\n",
+ "f.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c059cd588>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Draw the plot form lecture notes week 5, page 29\n",
+ "plt.figure(figsize=(5, 5))\n",
+ "chisq_arr = np.linspace(0, 100, 1001)\n",
+ "plt.title('p-values')\n",
+ "plt.xlabel(r'$\\chi^2$')\n",
+ "for n in [1, 2, 3, 4, 6, 8, 10, 15, 20, 25, 30, 40, 50]:\n",
+ " plt.loglog(chisq_arr, chi2.sf(chisq_arr, n))\n",
+ "plt.loglog(chisq_arr, chi2.sf(chisq_arr, dof), 'k-', lw=2, label='dof={0}'.format(dof))\n",
+ "plt.ylim(1e-3, 1.1)\n",
+ "plt.plot(chisq, chi2.sf(chisq, dof), 'o', color='blue', label='parabola')\n",
+ "plt.plot(chisq_1, chi2.sf(chisq_1, dof_1), '^', color='green', label='line')\n",
+ "plt.plot(chisq_3, chi2.sf(chisq_3, dof_3), 'x', color='red', label='cubic', ms=5)\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We observe that the residuals are not uniformly distributed around zero with the expected variance $\\sigma_y$ in the case of the line fit. This reflected in the $\\chi^2$-distribution. Only in 7% of the cases we would expect to draw data that give a worse fit. Note that overfitting with a cubic is not easily spotted in the residuals. However we do observe higher errors on the parameter estimates in the cubic case and we could try a different approach: let's fit only a subset of our data and then compare the fit results on the complement."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c057b7f60>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fit, cov, res, chisq, dof = fit_polynomial(x, y, 2, 1/y_error) # Fit parabola\n",
+ "fit_1, cov_1, res_1, chisq_1, dof_1 = fit_polynomial(x, y, 1, 1/y_error) # Fit line\n",
+ "fit_3, cov_3, res_3, chisq_3, dof_3 = fit_polynomial(x, y, 3, 1/y_error) # Fit cubic\n",
+ "\n",
+ "x_new = np.linspace(1, 2, 21)\n",
+ "y_new = parabola(x_new, a, b, c) + error(x_new, sigma_y)\n",
+ "\n",
+ "f, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
+ "ax[0].set_title('extrapolated fits')\n",
+ "ax[0].plot(x, y, 'k.')\n",
+ "ax[0].errorbar(x_new, y_new, yerr=y_error, fmt='r.')\n",
+ "\n",
+ "ax[0].plot(x_new, np.polyval(fit, x_new), label='parabola', color='blue')\n",
+ "ax[0].plot(x_new, np.polyval(fit_1, x_new), label='line', color='green')\n",
+ "ax[0].plot(x_new, np.polyval(fit_3, x_new), label='cubic', color='red')\n",
+ "\n",
+ "ax[0].legend()\n",
+ "ax[0].set_xlim(0, 2)\n",
+ "ax[1].plot(y_new - np.polyval(fit, x_new), '.', color='blue')\n",
+ "ax[1].plot(y_new - np.polyval(fit_1, x_new), '.', color='green')\n",
+ "ax[1].plot(y_new - np.polyval(fit_3, x_new), '.', color='red')\n",
+ "ax[1].set_title('residuals')\n",
+ "ax[1].fill_between(ax[1].get_xlim(), -sigma_y, sigma_y, color='grey', alpha=0.4, label=r'$1\\sigma$')\n",
+ "ax[1].legend()\n",
+ "f.tight_layout()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here it becomes very obvious that the hypothesis of a parabola holds against a cubic. We cheated a bit by adding data points instead of working with the initial set, but this illustrates the point of this method. An overfitted model usually does not generalize well when presented with addtional data."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Fit a nonlinear function\n",
+ "Next, we consider a Gaussian as an example of a nonlinear function. We are measuring some feature which has a Gaussian distribution in $x$. This could be an inhomogeneous spectral line for $x=E$ the energy of emitted photons. We are interested in the resonance frequency and the linewidth, i. e. we want to estimate them form our observations."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def gaussian_parent(x, mu, sigma):\n",
+ " return norm.pdf(x, mu, sigma) \n",
+ "\n",
+ "def gaussian_sample(mu, sigma, sample_size):\n",
+ " return norm.rvs(mu, sigma, sample_size)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c06c9afd0>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Create sample\n",
+ "## SAMPLE SIZE\n",
+ "sample_size = 200\n",
+ "##################\n",
+ "\n",
+ "# Prepare fake data\n",
+ "mu = 1540 # True values that we will try to estimate\n",
+ "sigma = 11 # using a least-squares fit\n",
+ "\n",
+ "x_arr = np.linspace(1500, 1600, 101)\n",
+ "bins = 12\n",
+ "sample = gaussian_sample(mu, sigma, sample_size)\n",
+ "hist = np.histogram(sample, bins=bins, range=(1500, 1580))\n",
+ "bin_width = np.diff(hist[1])[0]\n",
+ "normalization = bin_width * sample_size\n",
+ "x = hist[1][:-1]+bin_width/2\n",
+ "y_error_const = 0\n",
+ "y = hist[0]/normalization + gaussian_sample(0, y_error_const, bins)\n",
+ "y_errors = np.sqrt((np.sqrt(hist[0]) / normalization)**2 + y_error_const**2)\n",
+ "\n",
+ "# Plot our fake measurement results\n",
+ "plt.figure(figsize=(5, 4))\n",
+ "plt.xlabel(r'$E$ (meV)')\n",
+ "plt.ylabel('count rate')\n",
+ "plt.plot(x_arr, gaussian_parent(x_arr, mu, sigma), '-', color='black', label='parent')\n",
+ "plt.errorbar(x, y, yerr=y_errors, fmt='.', ms=7, capsize=3, label='sample')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "# Save data\n",
+ "data = np.vstack((x, y, y_errors))\n",
+ "np.savetxt('data', data)\n",
+ "np.savetxt('sample', sample)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Load data from disk. Format (3,12): (x, y, y_error) x N \n",
+ "data = np.loadtxt('data')\n",
+ "x = data[0, :]\n",
+ "y = data[1, :]\n",
+ "y_error = data[2, :]\n",
+ "# The sample used to generate\n",
+ "sample = np.loadtxt('sample')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Function we want to fit to our data set\n",
+ "def model_function(x, *args):\n",
+ " mu, sigma = args[0:2]\n",
+ " return norm.pdf(x, mu, sigma)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Fit Results:\n",
+ "mu = 1539.0 +- 0.4\n",
+ "sigma = 10.3 +- 0.3\n",
+ "mu estimator 1538.4 +- 0.7\n",
+ "sigma estimator 10.4\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Perform the fit minimizing least squares\n",
+ "initial_guess = [1545, 9]\n",
+ "p_opt, p_cov = curve_fit(model_function, x, y, p0=initial_guess, sigma=None, absolute_sigma=False, check_finite=True)\n",
+ "p_err = np.sqrt(np.diag(p_cov))\n",
+ "# pcov(absolute_sigma=False) = pcov(absolute_sigma=True) * chisq(popt)/(M-N)\n",
+ "print('Fit Results:')\n",
+ "print('mu = {:1.1f} +- {:1.1f}'.format(p_opt[0], p_err[0]))\n",
+ "print('sigma = {:1.1f} +- {:1.1f}'.format(p_opt[1], p_err[1]))\n",
+ "\n",
+ "print('mu estimator {:1.1f} +- {:1.1f}'.format(np.mean(sample), np.std(sample, ddof=1)/np.sqrt(sample.size)))\n",
+ "print('sigma estimator {:1.1f}'.format(np.std(sample, ddof=1)))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Plot the result"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c06ec26a0>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x_arr = np.linspace(1500, 1600, 101)\n",
+ "\n",
+ "plt.figure(figsize=(5, 4))\n",
+ "plt.xlabel(r'$E$ (meV)')\n",
+ "plt.ylabel('count rate')\n",
+ "plt.errorbar(x, y, yerr=y_errors, fmt='.', ms=7, capsize=3, label='sample')\n",
+ "plt.plot(x_arr, model_function(x_arr, *initial_guess), '-', color='grey', label='guess')\n",
+ "plt.plot(x_arr, model_function(x_arr, *p_opt), '-', color='black', label='fit')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Biased estimator example"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Expectation value: 4.133148453066826\n",
+ "Sample mean: 4.144495254000121\n",
+ "Gauss fit: 3.946186931764501\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c06fc1b00>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "log_sample = lognorm.rvs(s=0.5, loc=3, scale=1, size=1000)\n",
+ "plt.figure(figsize=(5, 4))\n",
+ "h = plt.hist(log_sample, bins=32, rwidth=0.85, normed=True)\n",
+ "\n",
+ "\n",
+ "def model_function(x, *args):\n",
+ " A, mu, sigma = args[0:3]\n",
+ " return A * norm.pdf(x, mu, sigma)\n",
+ "\n",
+ "\n",
+ "x = h[1][:-1]+np.diff(h[1])[0]/2\n",
+ "y = h[0]\n",
+ "initial_guess = [0.95, 3.3, 0.3]\n",
+ "gauss_fit_large = curve_fit(model_function, x, y, p0=initial_guess)\n",
+ "#local = np.where(np.abs(x-np.mean(log_sample))<0.5)\n",
+ "#gauss_fit_local = curve_fit(model_function, x[local], y[local], p0=initial_guess)\n",
+ "\n",
+ "x_arr = np.linspace(2, 5, 51)\n",
+ "plt.plot(x_arr, model_function(x_arr, *gauss_fit_large[0]), '-', color='red', label='fit')\n",
+ "#plt.plot(x[local], model_function(x[local], *gauss_fit_large[0]), '-', color='orange', label='fit small')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()\n",
+ "\n",
+ "print('Expectation value:', lognorm.mean(s=0.5, loc=3, scale=1))\n",
+ "print('Sample mean:', np.mean(log_sample))\n",
+ "print('Gauss fit:', gauss_fit_large[0][1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Fitting a Gaussian and gives a biased estimate of mu"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Bonus: Errors in x and y\n",
+ "So far, we considered uncertainties only on y. Consider the following data set with errors in both x and y. Try to fit a line to the data below, taking into account both errors. Compare with fits neglecting the x errors or both. \n",
+ " \n",
+ "Hint: A detailed solution is already on the moodle. You may chose if you want to try to write your own solution, implement a known solution (see references in solution notebook) or just try it with the scipy package ODR (orthogonal distance regression). \n",
+ "https://docs.scipy.org/doc/scipy/reference/odr.html\n",
+ " \n",
+ "The solution contains a python implementation of York's equation, comparison with ODR and MC tests. \n",
+ "Week 3: \"Linear Regression errors x and y\""
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x15c06f95da0>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Test data\n",
+ "X = np.array([0.0, 0.9, 1.8, 2.6, 3.3, 4.4, 5.2, 6.1, 6.5, 7.4])\n",
+ "Y = np.array([5.9, 5.4, 4.4, 4.6, 3.5, 3.7, 2.8, 2.8, 2.4, 1.5])\n",
+ "wX = np.array([1000, 1000, 500, 800, 200, 80, 60, 20, 1.8, 1])\n",
+ "wY = np.array([1, 1.8, 4, 8, 20, 20, 70, 70, 100, 500])\n",
+ "sigma_x = 1.0/np.sqrt(wX)\n",
+ "sigma_y = 1.0/np.sqrt(wY)\n",
+ "\n",
+ "plt.figure(figsize=(4, 3))\n",
+ "plt.errorbar(X, Y, xerr=sigma_x, yerr=sigma_y, fmt='o', label='oberservations')\n",
+ "plt.legend()\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "hide_input": false,
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.7"
+ },
+ "toc": {
+ "base_numbering": 1,
+ "nav_menu": {},
+ "number_sections": true,
+ "sideBar": true,
+ "skip_h1_title": false,
+ "title_cell": "Table of Contents",
+ "title_sidebar": "Contents",
+ "toc_cell": false,
+ "toc_position": {
+ "height": "calc(100% - 180px)",
+ "left": "10px",
+ "top": "150px",
+ "width": "225.438px"
+ },
+ "toc_section_display": true,
+ "toc_window_display": true
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Solution5/Solutions_5.pdf b/exercises/Solution5/Solutions_5.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..51de0b724b050c48bbcd6cbfa5332c49a9b0663c
Binary files /dev/null and b/exercises/Solution5/Solutions_5.pdf differ
diff --git a/exercises/Solution5/data b/exercises/Solution5/data
new file mode 100644
index 0000000000000000000000000000000000000000..2f9e9460dfeb54bd334d083e778ea829ee602f51
--- /dev/null
+++ b/exercises/Solution5/data
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diff --git a/exercises/Solution5/sample b/exercises/Solution5/sample
new file mode 100644
index 0000000000000000000000000000000000000000..391dbdd251d00864cca913e3e720bf71c7d87468
--- /dev/null
+++ b/exercises/Solution5/sample
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diff --git a/exercises/Solutions1/.ipynb_checkpoints/Solutions_1-checkpoint.ipynb b/exercises/Solutions1/.ipynb_checkpoints/Solutions_1-checkpoint.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..2e4a4a32354ee52a1dbc317f1a20a13666955862
--- /dev/null
+++ b/exercises/Solutions1/.ipynb_checkpoints/Solutions_1-checkpoint.ipynb
@@ -0,0 +1,756 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Solutions 1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 1. Basic plotting with matplotlib"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In our first example, we plot a simple curve with matplotlib."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## a) Generating set of data"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First we need to create an array of our x values for the curve to plot."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Import basic libraries:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[2. 2.33333333 2.66666667 3. ]\n",
+ "True\n",
+ "True\n"
+ ]
+ }
+ ],
+ "source": [
+ "def equallySpacedNumbers(start, end, number):\n",
+ " return np.linspace(start, end, number)\n",
+ " \n",
+ "# look at the function output by printing:\n",
+ "print(equallySpacedNumbers(2.0, 3.0, 4))\n",
+ "\n",
+ "print(all(equallySpacedNumbers(2.0,10.0,9) \n",
+ " == [2.,3.,4.,5.,6.,7.,8.,9.,10.]))\n",
+ "print(all(abs(equallySpacedNumbers(-1.2,0.2,6) \n",
+ " - [-1.2,-0.92,-0.64,-0.36,-0.08,0.2]) < 1e-6))\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "There is also **np.arange**, which has step size parameter instead of number of entries, be aware of rounding errors having unwanted influencing on array length, see examples below\n",
+ "(therefore: in most cases better use np.linspace)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1. 1.1]\n",
+ "[1. 1.1]\n",
+ "[1. 1.1 1.2 1.3]\n",
+ "[1. 1.1 1.2 1.3]\n",
+ "[1. 1.1 1.2 1.3 1.4]\n",
+ "[1. 1.1 1.2 1.3 1.4 1.5 1.6]\n",
+ "[1. 1.1 1.2 1.3 1.4 1.5 1.6]\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(np.arange(1, 1.1, 0.1))\n",
+ "print(np.arange(1, 1.2, 0.1))\n",
+ "print(np.arange(1, 1.3, 0.1))\n",
+ "print(np.arange(1, 1.4, 0.1))\n",
+ "print(np.arange(1, 1.5, 0.1))\n",
+ "print(np.arange(1, 1.6, 0.1))\n",
+ "print(np.arange(1, 1.7, 0.1))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### b) Simple plots"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As example, we now want to make a plot of the fall time vs. the height of which an apple is dropped. For both x and y we need one-dimensional numpy arrays of the same length.\n",
+ " \n",
+ "\n",
+ "You find some help on basic plot functionalities here: \n",
+ "https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html\n",
+ " \n",
+ "For more special plots, first have a look in the gallery: \n",
+ "https://matplotlib.org/gallery/index.html \n",
+ "which already includes many common types of plots."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "def Falltime(x, g):\n",
+ " return np.sqrt(2*x/g)\n",
+ "\n",
+ "# create a dataset\n",
+ "true_g = 9.8\n",
+ "data_x = equallySpacedNumbers(0.0,2.0,50)\n",
+ "data_y = Falltime(data_x, true_g)\n",
+ "\n",
+ "# the simplest way to plot\n",
+ "plt.plot(data_x, data_y,color='blue',label='theory')\n",
+ "\n",
+ "# always label the axes (use r'$...$' for latex style)\n",
+ "plt.xlabel(r'height $h$ [m]')\n",
+ "plt.ylabel(r'time $t$ [s]')\n",
+ "\n",
+ "# make the plot appear\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### c) Import measurements from text file"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "shape: (10, 4) \n",
+ "\n",
+ "data:\n",
+ " [[0.49805377 0.3304071 0.01 0.05 ]\n",
+ " [0.67623611 0.28373072 0.01 0.05 ]\n",
+ " [0.80522924 0.44070176 0.01 0.05 ]\n",
+ " [0.97044345 0.49827658 0.01 0.05 ]\n",
+ " [1.12945511 0.45374148 0.01 0.05 ]\n",
+ " [1.28508361 0.52819172 0.01 0.05 ]\n",
+ " [1.43542144 0.64219285 0.01 0.05 ]\n",
+ " [1.59138769 0.60636401 0.01 0.05 ]\n",
+ " [1.72742522 0.59992293 0.01 0.05 ]\n",
+ " [1.89783378 0.55806461 0.01 0.05 ]] \n",
+ "\n",
+ "first column: [0.49805377 0.67623611 0.80522924 0.97044345 1.12945511 1.28508361\n",
+ " 1.43542144 1.59138769 1.72742522 1.89783378] \n",
+ "\n",
+ "last row, first two columns: [1.89783378 0.55806461]\n"
+ ]
+ }
+ ],
+ "source": [
+ "# load data from textfile\n",
+ "# format: height time height_error time_error\n",
+ "measurements = np.loadtxt('measurement.txt')\n",
+ "\n",
+ "# look at it\n",
+ "print(\"shape:\", measurements.shape, \"\\n\")\n",
+ "print(\"data:\\n\", measurements, \"\\n\")\n",
+ "print(\"first column:\", measurements[:, 0], \"\\n\")\n",
+ "print(\"last row, first two columns:\", measurements[-1,0:2])\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We have seen that **np.loadtxt** conveniently loads text files into numpy arrays. There is also a **np.savetxt** function to do the opposite, see solution for part **f)**."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### d) Plot with error bars"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we want to plot the measurement data (from the text file) with error bars together with the prediction from theory. In many cases there is a non-negligible uncertainty also on the theoretical prediction. One way of visualizing this is to plot an error band, which in practice can be done by shading the area between two curves. \n",
+ "In this example, use $\\sigma_g = 0.4 \\frac{\\text{m}}{\\text{s}^2}$ as the uncertainty of $g$. \n",
+ " \n",
+ "There are examples of plots with error bars in the gallery linked above. For more detailed options look at the reference here: \n",
+ "https://matplotlib.org/api/_as_gen/matplotlib.pyplot.errorbar.html"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# create an additional dataset for the uncertainty band\n",
+ "data_y_m = Falltime(data_x, true_g - 0.4)\n",
+ "data_y_p = Falltime(data_x, true_g + 0.4)\n",
+ "\n",
+ "# plot uncertainty band of theory prediction\n",
+ "plt.fill_between(data_x, data_y_m, data_y_p, facecolor='#ddddff', color='#ddddff')\n",
+ "\n",
+ "# plot mean value on top\n",
+ "plt.plot(data_x, data_y, color='blue', label='theory')\n",
+ "\n",
+ "# always label the axes (the r'$...$' make the axes have a latex style)\n",
+ "plt.xlabel(r'height $h$ [m]')\n",
+ "plt.ylabel(r'time $t$ [s]')\n",
+ "\n",
+ "# plot measurement with errors\n",
+ "plt.errorbar(\n",
+ " measurements[:,0], measurements[:,1], \n",
+ " xerr=measurements[:,2], yerr=measurements[:,3], \n",
+ " marker='o', color='black', label='measurement', linestyle='none'\n",
+ ")\n",
+ "\n",
+ "# legend\n",
+ "plt.legend(loc='upper left',fontsize='15', numpoints=1)\n",
+ "\n",
+ "# optional: set axis limits\n",
+ "plt.xlim([0,2.0])\n",
+ "plt.ylim([0,0.8])\n",
+ "\n",
+ "# optional: grid lines\n",
+ "plt.grid(True)\n",
+ "\n",
+ "# save the figure to a pdf file\n",
+ "plt.savefig('exercise-1-plot.pdf')\n",
+ "\n",
+ "# make the plot appear\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### e) Histograms"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "A qualitative way to check compatibility of the measurement points with theory is to make a histogram of the pulls (pulls are defined below in the code). Create the histogram of pulls and overlay the expected pull distribution, which is Gaussian. \n",
+ " \n",
+ "Instead of putting the formula for the Gaussian yourself, you can use `scipy.stats.norm.pdf`, see here:\n",
+ "https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import scipy.stats\n",
+ "\n",
+ "heights = measurements[:, 0]\n",
+ "times = measurements[:, 1]\n",
+ "time_errors = measurements[:, 3]\n",
+ "predictions = Falltime(heights, true_g)\n",
+ "\n",
+ "# compute pulls\n",
+ "pulls = (times - predictions)/time_errors\n",
+ "\n",
+ "# histogram of pulls\n",
+ "plt.hist(pulls, 10, density=1, \n",
+ " histtype='stepfilled', facecolor='#99bbff', alpha=0.75)\n",
+ "\n",
+ "# unit gaussian\n",
+ "x = np.linspace(-3.0, 3.0, 50)\n",
+ "plt.plot(x, scipy.stats.norm.pdf(x, 0.0, 1.0), '--', color='r', linewidth=3.0)\n",
+ "\n",
+ "# always label the axes, also for histograms\n",
+ "plt.xlabel(r'pull')\n",
+ "plt.ylabel(r'count (normalized)')\n",
+ "\n",
+ "# annotation\n",
+ "plt.annotate('unit gaussian', xy=(-0.8, 0.3), \n",
+ " arrowprops=dict(arrowstyle='->'), xytext=(-2, 0.5))\n",
+ " \n",
+ "# save the figure to a pdf file\n",
+ "plt.savefig('exercise-1-histogram.pdf')\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### f) (optional) Creating a text file of toy measurements"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# create toy experiments instead of real measurements here\n",
+ "n_toys = 1000\n",
+ "toy_true_height = equallySpacedNumbers(0.5, 1.9, n_toys)\n",
+ "toy_true_time = Falltime(toy_true_height, true_g)\n",
+ "\n",
+ "# uncertainty on measurements\n",
+ "height_uncertainty = 0.01\n",
+ "time_uncertainty = 0.05\n",
+ "\n",
+ "# toy with uncertainties, sample from normal distribution\n",
+ "toy_height = toy_true_height + np.random.normal(0, height_uncertainty, n_toys)\n",
+ "toy_time = toy_true_time + np.random.normal(0, time_uncertainty, n_toys)\n",
+ "\n",
+ "# error bars for plotting\n",
+ "toy_height_errors = np.full(n_toys, height_uncertainty)\n",
+ "toy_time_errors = np.full(n_toys, time_uncertainty)\n",
+ "\n",
+ "# save to text file\n",
+ "np.savetxt('measurement_%dtoys.txt'%n_toys, \n",
+ " np.transpose([toy_height, toy_time, \n",
+ " toy_height_errors, toy_time_errors]))\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 2. Error propagation with Python"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We consider a LC circuit with resonance frequency $\\omega_0 = \\frac{1}{\\sqrt{LC}}$. \n",
+ "$C = 150 \\pm 8 \\,\\text{pF}$ \n",
+ "$L = 1 \\pm 0.1 \\,\\text{mH}$ \n",
+ " \n",
+ "What is the resonance frequency and its uncertainty? \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## a) Calculation by hand"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The mean value is computed to: \n",
+ " \n",
+ "$\\omega_0 = \\frac{1}{\\sqrt{LC}} = 2.58 \\cdot 10^6 \\,\\frac{1}{\\text{s}}$ \n",
+ " \n",
+ "Since the uncertainties for both quantities come from independent electronic components, they can safely be assumed as uncorrelated and one can compute the uncertainty of $\\omega_0$ to \n",
+ "$\\sigma_{\\omega_0} = \\sqrt{\\left(\\frac{\\partial \\omega_0}{\\partial C} \\sigma_C\\right)^2 + \\left(\\frac{\\partial \\omega_0}{\\partial L} \\sigma_L\\right)^2 } = 1.46 \\cdot 10^5\\,\\frac{1}{\\text{s}}$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## b) Installation of 'uncertainties' package"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "There are packages, which make handling of uncertainties very easy, e.g. the package simply called \"uncertainties\". It is not included in standard packages of Anaconda and therefore has to be installed with: \n",
+ "`conda install -c conda-forge uncertainties` \n",
+ "This can take several minutes, since anaconda has to resolve a lot of dependencies. \n",
+ "(If you are annoyed by the slowness of anaconda, look at \"pip\" which is a conceptually different way of installing Python modules)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## c) Use of 'uncertainites' package"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Look at the example on the official website on how to use the library: \n",
+ "https://pythonhosted.org/uncertainties/ \n",
+ " \n",
+ "Define $L$ and $C$ as `ufloat`s and compute the resonance frequency and print the result. \n",
+ "How can one obtain the central value and the uncertainty separately from the `ufloat` object?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(2.58+/-0.15)e+06\n",
+ "nominal: 2581988.8974716114\n",
+ "standard deviation: 146312.704190058\n"
+ ]
+ }
+ ],
+ "source": [
+ "from uncertainties import ufloat\n",
+ "from uncertainties.umath import *\n",
+ "\n",
+ "C = ufloat(150e-12, 8e-12)\n",
+ "L = ufloat(1e-3, 0.1e-3)\n",
+ "\n",
+ "omega0 = 1/sqrt(L*C)\n",
+ "print(omega0)\n",
+ "print(\"nominal:\",omega0.n)\n",
+ "print(\"standard deviation:\", omega0.s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Note that the uncertainties package treats correlations correctly (if you tell it about them)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "correlated: 0.0\n",
+ "uncorrelated: 1.131370849898476e-11\n"
+ ]
+ }
+ ],
+ "source": [
+ "C2 = ufloat(150e-12, 8e-12)\n",
+ "C3 = C2\n",
+ "print(\"correlated:\", (C3-C2).s)\n",
+ "print(\"uncorrelated:\",(C3-C).s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "There's lots of things you can do to plots. Have a look here for more inspiration: https://matplotlib.org/gallery.html"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## d) (optional) write your own uncertainty package"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can also try to write our own class for propagating uncertainties. Look at the myufloat class below and add the missing pieces marked with **TODO:**. Then test your **myufloat** class with the LC circuit example from above. It should lead to the same result (up to floating point rounding errors)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class myufloat:\n",
+ " def __init__(self, n, s=0.0):\n",
+ " self.n = float(n)\n",
+ " self.s = float(s)\n",
+ " \n",
+ " def __add__(self, operand):\n",
+ " n = self.n + operand.n\n",
+ " s = np.sqrt(self.s * self.s + operand.s * operand.s)\n",
+ " return myufloat(n, s)\n",
+ "\n",
+ " def __sub__(self, operand):\n",
+ " n = self.n - operand.n\n",
+ " s = np.sqrt(self.s * self.s + operand.s * operand.s)\n",
+ " return myufloat(n, s)\n",
+ " \n",
+ " def __mul__(self, operand):\n",
+ " n = self.n * operand.n\n",
+ " r1 = self.s / self.n\n",
+ " r2 = operand.s / operand.n\n",
+ " s = np.abs(n) * np.sqrt(r1*r1 + r2*r2)\n",
+ " return myufloat(n, s)\n",
+ " \n",
+ " def __div__(self, operand):\n",
+ " n = self.n / operand.n\n",
+ " r1 = self.s / self.n\n",
+ " r2 = operand.s / operand.n\n",
+ " s = np.abs(n) * np.sqrt(r1*r1 + r2*r2)\n",
+ " return myufloat(n, s)\n",
+ " \n",
+ " # for Python3\n",
+ " def __truediv__(self, operand):\n",
+ " return self.__div__(operand)\n",
+ "\n",
+ " def sqrt(self):\n",
+ " return myufloat(np.sqrt(self.n), np.abs(0.5/np.sqrt(self.n)*self.s))\n",
+ " \n",
+ " def __str__(self):\n",
+ " return \"%1.2e ± %1.2e\"%(self.n, self.s)\n",
+ " \n",
+ " def __repr__(self):\n",
+ " return \"%1.2e ± %1.2e\"%(self.n, self.s)\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "2.58e+06 ± 1.46e+05\n"
+ ]
+ }
+ ],
+ "source": [
+ "C = myufloat(150e-12, 8e-12)\n",
+ "L = myufloat(1e-3, 0.1e-3)\n",
+ "\n",
+ "print(myufloat(1.0)/np.sqrt(C*L))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "So the results agree for this case!\n",
+ "Lets check some other cases: \n",
+ "create two values with uncertainties: \n",
+ " \n",
+ "$a = 1.0 \\pm 0.1$ \n",
+ "$b = 2.0 \\pm 0.05$ \n",
+ " \n",
+ "and compute the result including uncertainty both with the uncertainties package (ufloat) and your own implementation (using myufloat) of: \n",
+ " \n",
+ "$c = \\frac{a+b}{a-b}$ \n",
+ " \n",
+ "are they the same? If not, why?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "-3.0+/-0.4\n",
+ "-3.00e+00 ± 3.54e-01\n"
+ ]
+ }
+ ],
+ "source": [
+ "a1 = ufloat(1.0, 0.1)\n",
+ "b1 = ufloat(2.0, 0.05)\n",
+ "\n",
+ "a2 = myufloat(1.0, 0.1)\n",
+ "b2 = myufloat(2.0, 0.05)\n",
+ "\n",
+ "c1 = (a1+b1)/(a1-b1)\n",
+ "c2 = (a2+b2)/(a2-b2)\n",
+ "\n",
+ "print(c1)\n",
+ "print(c2)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We neglected correlations in our **myufloat** class that e.g. the **a** in the numerator and the **a** in the denominator are the same and therefore 100% correlated! The uncertainties package takes this into account."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Solutions1/Solutions_1.ipynb b/exercises/Solutions1/Solutions_1.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..54eb5dd6ffbf8a1c0759865070ff9d2a556e1b8e
--- /dev/null
+++ b/exercises/Solutions1/Solutions_1.ipynb
@@ -0,0 +1,756 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Solutions 1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 1. Basic plotting with matplotlib"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In our first example, we plot a simple curve with matplotlib."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## a) Generating set of data"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First we need to create an array of our x values for the curve to plot."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Import basic libraries:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[2. 2.33333333 2.66666667 3. ]\n",
+ "True\n",
+ "True\n"
+ ]
+ }
+ ],
+ "source": [
+ "def equallySpacedNumbers(start, end, number):\n",
+ " return np.linspace(start, end, number)\n",
+ " \n",
+ "# look at the function output by printing:\n",
+ "print(equallySpacedNumbers(2.0, 3.0, 4))\n",
+ "\n",
+ "print(all(equallySpacedNumbers(2.0,10.0,9) \n",
+ " == [2.,3.,4.,5.,6.,7.,8.,9.,10.]))\n",
+ "print(all(abs(equallySpacedNumbers(-1.2,0.2,6) \n",
+ " - [-1.2,-0.92,-0.64,-0.36,-0.08,0.2]) < 1e-6))\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "There is also **np.arange**, which has step size parameter instead of number of entries, be aware of rounding errors having unwanted influencing on array length, see examples below\n",
+ "(therefore: in most cases better use np.linspace)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[1. 1.1]\n",
+ "[1. 1.1]\n",
+ "[1. 1.1 1.2 1.3]\n",
+ "[1. 1.1 1.2 1.3]\n",
+ "[1. 1.1 1.2 1.3 1.4]\n",
+ "[1. 1.1 1.2 1.3 1.4 1.5 1.6]\n",
+ "[1. 1.1 1.2 1.3 1.4 1.5 1.6]\n"
+ ]
+ }
+ ],
+ "source": [
+ "print(np.arange(1, 1.1, 0.1))\n",
+ "print(np.arange(1, 1.2, 0.1))\n",
+ "print(np.arange(1, 1.3, 0.1))\n",
+ "print(np.arange(1, 1.4, 0.1))\n",
+ "print(np.arange(1, 1.5, 0.1))\n",
+ "print(np.arange(1, 1.6, 0.1))\n",
+ "print(np.arange(1, 1.7, 0.1))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### b) Simple plots"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As example, we now want to make a plot of the fall time vs. the height of which an apple is dropped. For both x and y we need one-dimensional numpy arrays of the same length.\n",
+ " \n",
+ "\n",
+ "You find some help on basic plot functionalities here: \n",
+ "https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html\n",
+ " \n",
+ "For more special plots, first have a look in the gallery: \n",
+ "https://matplotlib.org/gallery/index.html \n",
+ "which already includes many common types of plots."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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R/MolJL4yszuA44HxZrZBjseL/Mz770OPHtC3L2y6Kbz6algIaIcdkq5MRKrl8kP+eMJAuF7RmIiWwB/zUpU0avPmwZlnhoV/Pv44jJiePDlcRYhIYcl6xLW7/wg8kbL9NfB1PoqSxmnFitCMNGwY/PgjXHBBGCm96aZJVyYimdR6JWFm79fHPlLcXnop3LE0ZAjssw98+GGYpVUBIVLYsrmS2NHMpq7hdQNa1FM90sjMnh1mY338cdhuu7CE6OGHJ12ViGQrm5DolMU+lbXvIsVk+XK46Sa45pqwffXVcOGFup1VpKGpNSTc/cs4CpHG4/nn4fe/D+Mcjj4a/vY32HrrpKsSkbrQLaxSb+bOhRNOgEMPDaOjn38+NDMpIEQarqxDwsz0X13SqqwMdy116hTGOQwbBlOnwiGHJF2ZiKytXK4knqz5hJl1r8dapAGaPBn22APOOw+6dw93LV1+udaUFmkssrkF9ngzuw5obmY7mlmTlJdH5q80KWSLF8P550O3blBRAQ89FKbx1gJAIo1LNnc3TQSaAmcAfwN2MLPvCQsRLc1jbVKgnnsOzjoL5swJE/Fdc43GO4g0Vtnc3fQVcJ+ZfebuE+G/S5puA3yc5/qkgMyfH0ZJjxkDO+4IEybAXnslXZWI5FMu03JMTHm8AFiQl4qk4LjDgw/CH/4AixbBn/8cZmxVv4NI45d1SEhxqqiAgQNDE9Mee8CoUdClS9JViUhcNE5C0nKHu++GnXaCN96AW24JK8UpIESKSy7jJMzM+pvZFdF2ezPrlss3M7NeZvaJmZWb2dA0r59lZtPMbIqZTTCzzrm8v9SPr76CI46A006DXXcNYx7OPx+aNKn9WBFpXHK5kvgHsCfQL9peDAzP9uDo1tnhwKFAZ6BfmhB40N13dvddgRsId1NJTNzh/vvD1cJrr8Gtt4Y/t9su6cpEJCm5hMQe7n4usAzA3ReS2/Kl3YByd5/l7iuAsUDv1B3c/YeUzWaA5/D+sha++Qb69IGTTw5NTFOnhgFy66hBUqSo5dJxvTK6GnAAM2sNVOVwfBtgTsp2BbBHzZ3M7FxgMCGADsjh/aWOnn4azjgDliwJk/Gdd56alkQkyOX3xNsIU3NsYWbXABOA/5fD8ZbmudWuFNx9uLtvB/wJuCztG5kNNLMyMyubP39+DiVIqiVLwjKiffpAu3ZhzekLLlBAiMhPchknMcbMJgMHEn7g93H3GTl8rwqgXcp2W8Ko7UzGAiMy1DKSaEqQkpISNUnVQWkp9O8Ps2bB0KHwl7/A+rk0HopIUchpnIS7f0zdR1lPAjqa2TbAV0Bf4MTUHcyso7vPjDYPB2Yi9WrlyjCNxtVXQ5s28Prr0KNH0lWJSKHKOiTMrAS4FNg6Os4Ad/ddsjne3VeZ2SDgBaAJMNrdp5vZMKDM3ccBg8ysJ7ASWAicktPfRtboyy+hXz945x347W/D9N4ttPCsiKxBLlcSY4A/AtPIrcP6v9x9PDC+xnNXpDw+vy7vK7V78skw7qGyMkyx0a9f7ceIiOQSEvOj3/alAVm2DIYMgeHDYbfdYOxYTectItnLJST+bGajgFeA5dVPuvsT9V6V1ItPPw3LiU6ZEu5auu46dU6LSG5yCYlTgU7AevzU3OSAQqIAjRkDv/sdNG0KzzwTptkQEclVLiHR1d13zlslUi9WrIDBg0Pz0j77hP6Htm2TrkpEGqpcBtOVasK9wlZRAfvuGwJiyBB49VUFhIisnVyuJPYGTjGzzwl9EjndAiv59dpr0Lcv/PgjPPooHHts0hWJSGOQS0j0ylsVUmfucNNNYdT0L34RBsftuGPSVYlIY5HLtBxf5rMQyd2SJTBgADz+eLhyGD0amjdPuioRaUxqDQkzm+Due5vZYn4+IV91c9MmeatOMpo9G446CqZNC1cSgweDpZtCUURkLdQaEu6+d/RwhLtflPqamd2Ql6pkjd5+G37zmzBQ7l//gl5qCBSRPMnl7qaeaZ7Tj6eY3Xcf7L9/aFYqLVVAiEh+1RoSZna2mU0DOpnZ1JSvzwnzOEkMKivhT3+CU06BvfeGd99VB7WI5F82HdcPAs8B1wJDU55f7O4L8lKV/MySJXDiiWHk9FlnwW23wXrrJV2ViBSDbPokFgGLAM0bmoB58+Dww8OqcX//O5x7btIViUgxyWnRIYlXeXnoc5g7F556Co48MumKRKTYKCQK1HvvhUn5qqrC9BrduyddkYgUo1zubpKYjB8f7mBq1gwmTlRAiEhyFBIF5u67wyC5HXYIy4zusEPSFYlIMVNIFJAbbwxLjB5wALzxBmy5ZdIViUixU0gUiKuugosuCivJPfus5mASkcKgkEiYO1x2GVxxBZx8clhRTkuMikih0N1NCXIPVw833QRnnAF33AHrKLZFpIDE+iPJzHqZ2SdmVm5mQ9O8PtjMPoqm/XjFzLaOs744VVXBeeeFgBg0SAEhIoUpth9LZtYEGA4cCnQG+qVZDvXfQEm02t1jQKOcZbaqKkyv8fe/w4UXhmk2FBAiUoji/NHUDSh391nuvgIYC/RO3cHdX3P3H6PNUqDRrdDsDr/7Hdx5J1xySbijSetAiEihijMk2gBzUrYroucyOZ0wsWCjUd0HMWoUXHopXHONAkJEClucHdfpfhx6mucws/5ACbBvhtcHAgMB2rdvX1/15d111/3UB3HVVUlXIyJSuzivJCqAdinbbYG5NXcys57ApcBR7r483Ru5+0h3L3H3ktatW+el2Po2YkRoXjrpJLj1Vl1BiEjDEGdITAI6mtk2ZrY+0BcYl7qDmf0SuIMQEPNirC2vHnooTPF95JFh2g11UotIQxHbjyt3XwUMAl4AZgCPuPt0MxtmZkdFu90IbAw8amZTzGxchrdrMP71rzBIrkcPePhhLRYkIg1LrIPp3H08ML7Gc1ekPE63jnaD9dZbcOyx0LUrjBsHG26YdEUiIrlRw0eezJwJvXtDhw7w3HOwySZJVyQikjuFRB4sWhQCYp11wtoQDaRvXURkNZq7qZ5VVoY7mGbOhJdegm22SboiEZG6U0jUs0suCZ3VI0bAfvslXY2IyNpRc1M9euABuOEGOPvsMDeTiEhDp5CoJ++9F6b73m+/MFhORKQxUEjUg7lzoU8f2GorePRRjYUQkcZDfRJracUK+M1v4Icf4J13oFWrpCsSEak/Com1NGxYaGp67DHYeeekqxERqV9qbloLb78N114Lp54KxxyTdDUiIvVPIVFHS5aEOZnat4dbbkm6GhGR/FBzUx0NGQKzZsHrr2vKDRFpvHQlUQfjx8Mdd4T1qXv0SLoaEZH8UUjk6Ntv4bTToEsXrS4nIo2fmpty4B5GUi9YAC+8AE2bJl2RiEh+KSRy8MAD8PjjYa3qrl2TrkZEJP/U3JSluXNh0CDYe+/QaS0iUgwUEln6y19g6dKwRnWTJklXIyISD4VEFj79FO66K/RHbL990tWIiMRHIZGFyy8PndSXXpp0JSIi8VJI1GLyZHjkERg8GP7nf5KuRkQkXgqJWlxyCWy+eRg4JyJSbGINCTPrZWafmFm5mQ1N83oPM3vfzFaZ2bFx1pbOq6/Ciy+GoGjRIulqRETiF1tImFkTYDhwKNAZ6GdmnWvsNhsYADwYV12ZuMPFF0PbtnDOOUlXIyKSjDgH03UDyt19FoCZjQV6Ax9V7+DuX0SvVcVYV1pPPRXWibjrLo2sFpHiFWdzUxtgTsp2RfRcwVm1KtzJ1KlTmA5cRKRYxXklYWme8zq9kdlAYCBA+/bt16amtO6/H2bMCFNwrKuJS0SkiMV5JVEBtEvZbgvMrcsbuftIdy9x95LWrVvXS3HVli2DK6+E3XcPa1eLiBSzOH9PngR0NLNtgK+AvsCJMX7/rIwZA7Nnw+jRYOmufUREikhsVxLuvgoYBLwAzAAecffpZjbMzI4CMLPdzawCOA64w8ymx1VftTfegC23hAMOiPs7i4gUnlhb3N19PDC+xnNXpDyeRGiGSkxpKXTvrqsIERHQiOuf+fZbmDkT9twz6UpERAqDQiLFu++GP7t3T7YOEZFCoZBIUVoa1orYbbekKxERKQwKiRTvvBOWJW3WLOlKREQKg0IiUlkZpuFQU5OIyE8UEpEZM2DxYoWEiEgqhUTknXfCn7qzSUTkJwqJSGlpWFxou+2SrkREpHAoJCIaRCcisjqFBPD99/DRR2pqEhGpSSFBuKsJ1GktIlKTQoLQ1GQWpgcXEZGfKCQIdzbttBNssknSlYiIFJaiD4mqqjBnk/ojRERWV/QhMXMmLFyo/ggRkXSKPiSqB9EpJEREVlf0IVFaCi1aQKdOSVciIlJ4FBKlsMcesE7RnwkRkdUV9Y/GxYth2jQ1NYmIZFLUIVFWFu5u0p1NIiLpFXVIlJaGP7t1S7YOEZFCVdQh8c47sMMO0LJl0pWIiBSmWEPCzHqZ2SdmVm5mQ9O8voGZPRy9/q6ZdchXLe7hSkJNTSIimcUWEmbWBBgOHAp0BvqZWecau50OLHT37YGbgevzVc/nn8P8+eq0FhFZkzivJLoB5e4+y91XAGOB3jX26Q3cGz1+DDjQLD8rPGgQnYhI7eIMiTbAnJTtiui5tPu4+ypgEbB5PoopLYVmzaBLl3y8u4hI4xBnSKS7IvA67IOZDTSzMjMrmz9/fp2K6dgRTjsNmjSp0+EiIkVh3Ri/VwXQLmW7LTA3wz4VZrYu0AJYUPON3H0kMBKgpKRktRDJxnnn1eUoEZHiEueVxCSgo5ltY2brA32BcTX2GQecEj0+FnjV3esUAiIisvZiu5Jw91VmNgh4AWgCjHb36WY2DChz93HAXcD9ZlZOuILoG1d9IiKyujibm3D38cD4Gs9dkfJ4GXBcnDWJiEhmRT3iWkRE1kwhISIiGSkkREQkI4WEiIhkpJAQEZGMrKEPQzCz+cCXdTy8FfBtPZZTX1RXblRXblRXbhprXVu7e+vadmrwIbE2zKzM3UuSrqMm1ZUb1ZUb1ZWbYq9LzU0iIpKRQkJERDIq9pAYmXQBGaiu3Kiu3Kiu3BR1XUXdJyEiImtW7FcSIiKyBo02JMysl5l9YmblZjY0zesbmNnD0evvmlmHlNcujp7/xMwOibmuwWb2kZlNNbNXzGzrlNcqzWxK9FVzmvV81zXAzOanfP8zUl47xcxmRl+n1Dw2z3XdnFLTp2b2fcpreTlfZjbazOaZ2YcZXjczuy2qeaqZ/SrltXyeq9rqOimqZ6qZvW1mXVNe+8LMpkXnqizmuvYzs0Up/1ZXpLy2xn//PNf1x5SaPow+Ty2j1/J5vtqZ2WtmNsPMppvZ+Wn2ie8z5u6N7oswFflnwLbA+sAHQOca+5wD/DN63Bd4OHrcOdp/A2Cb6H2axFjX/sBG0eOzq+uKtpckeL4GAH9Pc2xLYFb052bR483iqqvG/r8nTEGf7/PVA/gV8GGG1w8DniOstNgdeDff5yrLuvaq/n7AodV1RdtfAK0SOl/7Ac+u7b9/fddVY98jCevbxHG+tgJ+FT1uDnya5v9jbJ+xxnol0Q0od/dZ7r4CGAv0rrFPb+De6PFjwIFmZtHzY919ubt/DpRH7xdLXe7+mrv/GG2WElbwy7dszlcmhwAvufsCd18IvAT0SqiufsBD9fS9M3L3N0mzYmKK3sB9HpQCm5rZVuT3XNVal7u/HX1fiO+zlc35ymRtPpf1XVcsny0Ad//a3d+PHi8GZgBtauwW22essYZEG2BOynYFq5/k/+7j7quARcDmWR6bz7pSnU74baFaUwtre5eaWZ96qimXuo6JLm0fM7PqpWgL4nxFzXLbAK+mPJ2v81WbTHXn81zlquZny4EXzWyymQ1MoJ49zewDM3vOzHaKniuI82VmGxF+0D6e8nQs58tCM/gvgXdrvBTbZyzWRYdiZGmeq3kbV6Z9sjm2rrJ+bzPrD5QA+6Y83d7d55rZtsCrZjbN3T+Lqa5ngIfcfbmZnUW4Cjsgy2PzWVe1vsBj7l6Z8ly+zldtkvhsZc3M9ieExN4pT/86OldbAC+Z2cfRb9pxeJ8wRcQSMzsMeAroSIGcL0JT00R3T73qyPv5MrONCcH0B3f/oebLaQ7Jy2essV5JVADtUrbbAnNQK4tWAAAEgklEQVQz7WNm6wItCJee2Rybz7ows57ApcBR7r68+nl3nxv9OQt4nfAbRix1uft3KbXcCeyW7bH5rCtFX2o0B+TxfNUmU935PFdZMbNdgFFAb3f/rvr5lHM1D3iS+mtirZW7/+DuS6LH44H1zKwVBXC+Imv6bOXlfJnZeoSAGOPuT6TZJb7PWD46XpL+IlwhzSI0P1R3eO1UY59z+XnH9SPR4534ecf1LOqv4zqbun5J6KzrWOP5zYANosetgJnUUydelnVtlfL4N0Cp/9RR9nlU32bR45Zx1RXttwOhI9HiOF/Re3Ygc0fs4fy8U/G9fJ+rLOtqT+hj26vG882A5imP3wZ6xVjXltX/doQftrOjc5fVv3++6oper/7lsVlc5yv6u98H3LKGfWL7jNXbyS60L0Lv/6eEH7iXRs8NI/x2DtAUeDT6T/MesG3KsZdGx30CHBpzXS8D/wGmRF/jouf3AqZF/1GmAafHXNe1wPTo+78GdEo59rToPJYDp8ZZV7R9JXBdjePydr4Iv1V+Dawk/OZ2OnAWcFb0ugHDo5qnASUxnava6hoFLEz5bJVFz28bnacPon/jS2Oua1DKZ6uUlBBL9+8fV13RPgMIN7KkHpfv87U3oYloasq/1WFJfcY04lpERDJqrH0SIiJSDxQSIiKSkUJCREQyUkiIiEhGCgkREclIISEiIhkpJEREJCOFhDR6ZtYh05oBazjm7bq8p5ltambn1HJsTzO7v5b3XmpmU7KvGMxsw2h9gxXRtBYia00hIZKGu+9Vx0M3JaxVsiZdgX/Xss9n7r5rLt/Y3ZdGxyQxv5E0UgoJKRZNzOzOaKWvF81sQwiz7ZrZe9Fv4HeYWZPo+SXVB5rZ5Wb2sZm9ZGYPmdmQNbzndcB20fvdmKGWrsCWZvaWmX0TTeiYUXRl8bGZjYpWSBsTXY1MjFYfi20yPik+CgkpFh2B4e6+E/A9YW2MHYETCNM+7wpUAielHmRmJcAxhIkXjyZM357xPYGhRFcB7v7HDLV0Bb51930IVx0nZdgv1fbArcAuQCfgRMIcP0OAS7I4XqROGut6EiI1fe7u1W38kwmzf25KmPJ8UliUkA2BeTWO2xt42t2XApjZM7W854Q1FRFNAd0SuCl6al1CwGRT/7ToPaYDr7i7m9m06PuK5IVCQorF8pTHlYRAMOBed794DcelW8RlTe9Zm87AB+5eFW3vAmTTqZ76vapStqvQ/2PJIzU3STF7BTg2Wl0MM2sZLYOaagJwpJk1jVYKO7yW91xMWLw+k66EKaar7UKYElqkICkkpGi5+0fAZYS1iqcSFo3fqsY+k4BxhB/sTwBlhPXQM73nd8DEqIM5Xcd1V34eCl3I7kpCJBFaT0KkFma2sYf1lzcC3gQGuvv7efx+HYBn3b1LHY//grAIzbf1WJYUKV1JiNRuZDSw7X3g8XwGRKQSaFHXwXTAeoS+CpG1pisJERHJSFcSIiKSkUJCREQyUkiIiEhGCgkREclIISEiIhkpJEREJCOFhIiIZKSQEBGRjP4/ZyEyUVr2LDwAAAAASUVORK5CYII=\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "def Falltime(x, g):\n",
+ " return np.sqrt(2*x/g)\n",
+ "\n",
+ "# create a dataset\n",
+ "true_g = 9.8\n",
+ "data_x = equallySpacedNumbers(0.0,2.0,50)\n",
+ "data_y = Falltime(data_x, true_g)\n",
+ "\n",
+ "# the simplest way to plot\n",
+ "plt.plot(data_x, data_y,color='blue',label='theory')\n",
+ "\n",
+ "# always label the axes (use r'$...$' for latex style)\n",
+ "plt.xlabel(r'height $h$ [m]')\n",
+ "plt.ylabel(r'time $t$ [s]')\n",
+ "\n",
+ "# make the plot appear\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### c) Import measurements from text file"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "shape: (10, 4) \n",
+ "\n",
+ "data:\n",
+ " [[0.49805377 0.3304071 0.01 0.05 ]\n",
+ " [0.67623611 0.28373072 0.01 0.05 ]\n",
+ " [0.80522924 0.44070176 0.01 0.05 ]\n",
+ " [0.97044345 0.49827658 0.01 0.05 ]\n",
+ " [1.12945511 0.45374148 0.01 0.05 ]\n",
+ " [1.28508361 0.52819172 0.01 0.05 ]\n",
+ " [1.43542144 0.64219285 0.01 0.05 ]\n",
+ " [1.59138769 0.60636401 0.01 0.05 ]\n",
+ " [1.72742522 0.59992293 0.01 0.05 ]\n",
+ " [1.89783378 0.55806461 0.01 0.05 ]] \n",
+ "\n",
+ "first column: [0.49805377 0.67623611 0.80522924 0.97044345 1.12945511 1.28508361\n",
+ " 1.43542144 1.59138769 1.72742522 1.89783378] \n",
+ "\n",
+ "last row, first two columns: [1.89783378 0.55806461]\n"
+ ]
+ }
+ ],
+ "source": [
+ "# load data from textfile\n",
+ "# format: height time height_error time_error\n",
+ "measurements = np.loadtxt('measurement.txt')\n",
+ "\n",
+ "# look at it\n",
+ "print(\"shape:\", measurements.shape, \"\\n\")\n",
+ "print(\"data:\\n\", measurements, \"\\n\")\n",
+ "print(\"first column:\", measurements[:, 0], \"\\n\")\n",
+ "print(\"last row, first two columns:\", measurements[-1,0:2])\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We have seen that **np.loadtxt** conveniently loads text files into numpy arrays. There is also a **np.savetxt** function to do the opposite, see solution for part **f)**."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### d) Plot with error bars"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we want to plot the measurement data (from the text file) with error bars together with the prediction from theory. In many cases there is a non-negligible uncertainty also on the theoretical prediction. One way of visualizing this is to plot an error band, which in practice can be done by shading the area between two curves. \n",
+ "In this example, use $\\sigma_g = 0.4 \\frac{\\text{m}}{\\text{s}^2}$ as the uncertainty of $g$. \n",
+ " \n",
+ "There are examples of plots with error bars in the gallery linked above. For more detailed options look at the reference here: \n",
+ "https://matplotlib.org/api/_as_gen/matplotlib.pyplot.errorbar.html"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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tLQLRxKaiIsjLg337IDcXiovddi03Be3+/fDFF/DJJ+6xcqU7JjERglwZ+5AsgQRhxowZpKens3///pJtSUlJzJgxI4JRHVrLli2Jj49n8eLFFS4x27p1azIzM/nqq6945513GD58OADZ2dkH9Y5q164dM2fOpLi4mKVLlzJt2jRGjhzJhg0bOOyww0hISOCA/08dn507d1YYV/mG55YtWwLw1ltvHZRcAHr06BH8D12BYO6D8VYs/j5Fmirk57uEsG+fK3GIHJwwCgpgxYrShPHVV25bw4bQpw9ccw2ceir07g3nnVfzuCyBBGHcuHEATJw4kfz8fDp27MiMGTNKtkejwYMHU1RUxJ49exg6dGiFx/gTRePGjUu2bdiwgcWLF3PccccddHxcXBz9+/dn6tSpnHrqqaxfv57DDjuM9u3b89FHH5U59r333gsqzlNOOYXExEQ2bdp0UPVWOARzH4JlJZLwiMXfp0goKChNGP7a8sCE4dqwYc2a0oSxdKnrYSUCPXvC+PEuYfTrB0lJ4Y/REkiQxo0bx2OPPQYcXMUVjXr06MHvf/97xowZw6RJk+jbty95eXmsXLmSNWvW8Pjjj3PUUUfRvn17brjhBu68806ys7O5/fbbadeuXcl19uzZw9lnn82vf/1runfvTn5+Pvfddx9t27bl6KOPBuDCCy/kiSee4LrrrmPEiBEsXLiQefPmBRVnSkoK06ZN49prr2X9+vWceeaZFBcXs2bNGhYuXBjUWvA1vQ/BSktLIzExkaeffprmzZvTsGFD+vbtW6P46qtY+33yQnGxq46qqlpq82ZYvNgljMWLwVcLTMeOcP75cNpp0L8/BDTn1RpLIHXYww8/TPfu3XnssceYMmUKycnJ9OzZk4kTJwKu5PHqq6/yxz/+kdGjR5ckkyVLlpSM30hISODYY4/lwQcfZOPGjSQlJdG/f3/mz59PYmIi4BrG//rXv/LII4/w+OOPM2rUKB544AFGjRoVVJyTJk3iiCOO4P777+e+++4jISGB7t27c+mll3pyH4KVkJDAY489xvTp0xkwYAAFBQWuK6Mx1aDqGrn9pYwDByqulsrOhiVLSpPGjz+67S1bumRx6qnu34C/+yrlv37DhrBr147tNf0ZJNZ/AXr06KGrV6+ucN+qVatK/koOB/9o1ur8xZSdnU2zZjUft1PbYiHOWIgR4KuvvuL444+PdBhVysjIiMhI7VB/n6obZ01+b6tz7UPFWVhYtpQBFbdjfP01LFrkHitWuEbzxEQ46SSXLE47Dbp3hwqa9crwJ4z4eFeFlZjoHnFxICJfqGqNitBWAjHG1Fn+Ee/5+fl06tTJ87YWVddbyl/KKCw8uJShCmvXumSxeDF89plrx4iLg2OPhf/3/+D00+H448HXDFcp/7UbNHAJIykJEhLc69pgCSQEVldrTOyYNWsW6enpJeO11q9fT3p6OkCtJhFVN97iUI3fO3eWtmF8/LFr1wBIS3PtGKefDqecApX0Pi/h79Qo4koWTZq4hBHv0Te7pwlERIYDDwINgMdV9W8VHHMJMA03OvVrVb3MyxiNMXXD5MmTy3QVBti/fz+TJ08OSwIJLN2kpXXi1ltncM454ygocAkiMGkcOOC61H78sStpfPut25+c7NowrrrKJY2qhsIE9oJPTCytlmrYsMY/TrV4lkBEpAHwMDAUyAKWicgcVf0u4JhuwC3Aaaq6S0Ssk74xplpqc8T7//43i9//vrR0s3Hjeq6/Pp3cXOjVqx3FxW5E+Mcfu8eSJa4aKz7ejce49lo44ww45piqSwv+pNG4sUsYo0YNRCQ6akS8LIGcBGSq6loAEXkBGAV8F3DM74CHVXUXgKpuO+gqIVJVmzXVeC7WO6fUBeEc8e5vy9i3zz1uuWUyubllSze5ufu5667J9O//CStWgH8WnrQ0+NWvXAmjf3+oqv+Hvx2jUSNXJZWY6JJHYHVVtPAygbQDNga8zgJOLndMdwARWYyr5pqmqu+Wv5CIpAPpAKmpqZVm4uTkZHbs2FFmoFykFBUVkZ2dHekwqhQLccZCjPn5+RQWFkbFX4lVycnJiUicu3fvBoL/SzrUOC+//HL+8Y9/lJmzrnHjxlx++eVBX6eoyI3HOHgsRsWlmJ07N7BwYSp9+mznggt2cuKJOzniiNKBp1u3ukdl4uJKH5UJ9b7VJi8TSEV5s/yfafFAN2Ag0B74WESOUdXdZU5SfRR4FFw33sq6zO3du5etW7fSrl07EhMTI1oSiZWup7EQZzTHqKrk5uaya9cu8vLyYmIho0h14/XPPRbse4ca58CBAzn66KODHvHuny7EX8rwz7MZmDy2b3dVUgkJaeTmHly6adUqjaef/oSjjhoAtKrwfQJLEv6eUomJwfeUCvW+1SYvE0gW0CHgdXtgUwXHLFHVAuAnEVmNSyjLqvOGycnJAGzatImCgoLqXCJs8vLySEhIiGgMwYiFOKM9xoYNG9KmTRubxbcKXvwFXdWI96Ki0i62FY3LKCiA5cvhww/ho4/cZIQATZrMoEGDdIqKSquxEhOTuPXWGcTHH1x96U8aCQmlSSNSDd/h5GUCWQZ0E5HOwM/AGKB8D6vXgbHATBFphavSWluTN01OTi5JJJGUkZERM4PKoj3OWIjRRKfA0d85ORVPSrhlS2nCWLTIHdegAZxwAtxwA5x5JvTsOY4334Sbb57IgQP5HHFER268cQajRo0jMzOjynaMusKzBKKqhSJyNTAP177xpKquFJE7gM9VdY5v3zAR+Q4oAm5S1R1exWiMqZuKimDbNpc4/JMQ+h04AF9+CRkZLnH4J7Zo2xbOPRcGDnRdbcvXmo4aNY4XX3Slm+efzwBK2y/atHGljapGisc6T8eBqOpcYG65bVMCnitwve9hjDHVUlhY2pbhnzw5J6d0/9atroSRkVFayoiPh7594S9/gQED3FQhhyox+PfFxUGrVq6UER8PP/1UOzPfRiMbiW6MOUhtzh9VG/xVUzk5FTeAq8bxxRelpQx/W0bbtjBihEsYFZUyApWvlvJPEwJVd82tqyyBGGNiUuD05xVVTe3c6XpMZWbexp49/bjkEteWceKJMGmSq5o6VCkjsIQR2FuqrldLhcISiDEmZhQWljaA5+WVbQBXhVWrYOFC9/j6a5dk4uNPICXlU6ZOHc7pp7vpQyoTOOrbX8qIpt5SkZ4csjxLIMaYqKXqekr5l3HdsKFs0ti3z01K+MEHrnrKP0jv2GPh6qth0CC4++6LEFHOPXf4QdcPnO48sFoqGntLRWpyyEOxBGKMiSrlpw3xjwT3J42sLFfC+OAD+PRT1/bRtKmbKmTQINeekZpaej2RsuMy/MnBP3utv/E72tX25JDVEQO3zRhT1/nbM3JyXBUVlCaMoiJXHfXyy51Zvry0m21aGowb55JGv35Vr5XRsKErYTRpEptjMmpzcsjqsgRijImIoiJXwqioPWPfPte9dsECV9rYuRPi4tLo1w9uuQUGD4bOnatuAE9MhPfeyyApqfYWVfJKOCeHDBdLIMYYz/jbM3JyDl4DfNMmVy31/vtu+vMDB1z32AEDYMgQ6NBhMccff3qF1y3fluFVKcPLbs4zZswgPT29TDVWUlISM2bM8CyG8iyBGFNDsTZmwkv+RvCcHPcIHJ+h6hZW8icN/9iMtDS4/HJXyujbt7QXVGZmYZlrB84v1bRp7LRlVJe/nSPYySG9UIdvtzEmEvyz2voH9QVOh37ggFvz+/333WPLFpcITjjBjc0YMgS6dDl01VRcXGkpI1p7TNWWqiaH9JolEGNMGdUZa+DvOeVPGoG9prKzXTvG+++7UeA5Oa60cPrpcN11bkBfq4pnPi+pmmrc2LVhtG8fXeMy6jtLIMaYEqGMNVB1Paeysw/uObV5s2sAf+89155RWAiHHeYmJxw61E0bUtmM/CKla2X4u9nGxcEPP1jyiDaWQIwxJaoaa+DvbpudXXb9DFX48UeYP98ljRUr3L7OneE3v4GzznJrgVfUE8pfymjYsLRqqlGj+lU1FassgRhjShxqrMHmzaUz26q6to2vvy5NGj/95Pb17g033gjDhrn2jIoEThnStKkrbdTlBvC6yv7LjDElKhtrcPjhaeTmuh5VS5eWJo2tW90X/ymnwJVXukbwtm0rvnZg1VTTpvVjvYy6zhKIMQZwJYrbb5/BNdekk5tbWo2VkJDE2WfP4KabXLvGnj3uy3/AAFfKGDy44gkK/aWMBg1cwrCqqbrHEogx9VhxsXts2uSqpwYPHseMGXDzzb/lwIE8EhI6UlQ0g6eeGkdysksWZ58NZ5zhGrfLC+w15U8aVjVVd9l/rTH1THGx6zW1d69LGoWF7t89e1wJY968cRQUXAw0okkTV8o4+2zo37/iXlCB04b42zOsaqp+8DSBiMhw4EHcmuiPq+rfyu2fAPwd+Nm36V+q+riXMRoTimhbn6Ey/qTh7z3lLyns3AnvvtuWL75w06IXFsLhh0ObNnNo0eIj3njjn5X2nBJxJQx/e4ZVTdU/niUQEWkAPAwMBbKAZSIyR1W/K3foi6p6tVdxGVNd0bg+QyDVsknDv237dtcI/u67boxGUdFRpKW5RvBzzoHjjoNx4/4FlHa7DWzP8CcNa8+IjGgYge7nZQnkJCBTVdcCiMgLwCigfAIxJiZEYn2Gqubdqmxw3/btMG8ezJ3relEVF0OnTpCeDscc8zlnn9230mTQqFFpe4YN5DOBvEwg7YCNAa+zgJMrOO4iETkTWANcp6obyx8gIulAOkBqampUZeTK5OTkWJxhEi0xHmrMREZGRq3EuXv3buDgBKLqJiosLg48tiGLFqXy0UepfPNNCsXFQocO+xgz5hfOOOMXOnfehwjk5eXw449lr5ebu9v3s4Q3/pqIlv/3qsRKnOHgZQKp6O8bLff6TeB5Vc0Xkd8DTwODDzpJ9VHgUYAePXqo/6+yaJaRkYHFGR7REuOh1mcYOHBgrcSZkpICwIABAzlwwJU0cnJKR4Pv2FFa0vjsM5dQjjwSrrrKTSPSvXsTRJoAnUqumZmZQbduA0lIcNOnJyVBixbufaLhPvtFy/97VWIlznDwMoFkAR0CXrcHNgUeoKo7Al4+BtzjQVymDvJiivVIrM/gL2ls2FA6y+3u3a5N4+233RKvRUVuCpE//AFGjIDu3Q9uqwjsORUfDx07Ws8pEzovE8gyoJuIdMb1shoDXBZ4gIgcrqqbfS9HAqs8jM+YkHi1PkNRkStpZGe7adLBJY3333dJY9EiN0K8QwfXpjFiBBx1VOVJw98Inpjotn3/vSUPUz2eJRBVLRSRq4F5uG68T6rqShG5A/hcVecAfxKRkUAhsBOY4FV8xlRHba3PUFzspkXfu9clDRHXOL5jxwB27BjMSSe5tTUOPxx+/Ws47zw49thDJ41mzay7rQkvT8eBqOpcYG65bVMCnt8C3OJlTMZEC38Pqr17S7vdHjjgShhvveXmntq3bzoNG+5k7FhX0jjhhINLDzZGw3ilygQiIi2DuE6xqu4OQzzG1CuqlDSGZ2e7bUVF8MUX8MYbbqzGrl1urqkRI2DFihtITl7O1KkLylwnMGk0a1bz9cDrSy8iUzPBlEA2+R6H+jg2ANLCEpEx9UBhYWnS8He/Xb3aJY0333QLMiUmutltzz/fzT3VuDFcdtkXJdcId9IwJlTBJJBVqnr8oQ4Qka/CFI8xdVZF7RpZWTBnjkscP/zgRnqfcUbp+uBNmlR8rWbNLGmYyAsmgZwSpmOMqXf8a4Xv3Vs6Mnz3bjdO4403YNkyt61vX7jjDhg+3C39GsifIN59dxbLl7t5t/r1i955t0z9UWUCUdU8ABG5GHhXVbNF5HbgeOAuVf3Sf4wxxikocFVT69eXJpGMDJc0Fi507R5dusANN8DIkdC+fdnz/UkjKcmVNF57bRY33hi9826Z+imUXli3q+pLInI6MAz4B/BvKp6OxJh6p7jYjQrfu9clkMJCV8J47TU3XmPvXmjVCsaNgwsugF69ylY/BQ7u848I92+LxLxbxlQllARS5Pt3BPBvVX1DRKaFPyRjYod/bfDCQlfaAPfvG2/Aiy+ezObNrhvtsGFw4YVw6qlAGABOAAAetUlEQVRlF1jyT6uekOB6WlW2lsah5t0yJlJCSSA/i8h/gbOAe0SkMWDjV03U8WKNDn8vqr17XXVUYWETXnjBlTaWLXOJoXfvPK67LpGzz3bjMfz8SaNRI5c0mjShwjU3Ah1q3i1jIiWUBHIJMBz4h6ruFpHDgZtqJyxjqqc21+jwr6+xZ49r0ygudoswtWmTwfz5buzGkUfCjTfCqFGwf//XdO06sOR8EZcokpNdQgllqddIzLtlTFWC/gir6n7g1YDXm4HNlZ9hjPdqo62goMCVNLKzXRJZuxZeecWVNrZscQnhoovc47jjStstMjNLx2r4u902alS9n8urebeMCUUwI9G/VNUTanqMMV4IV1uBf8zGnj0ugWRnu663L70EX37p2inOPBMmT3bjNRo3Lj3Xn0Di4txcVeEaq1Fb824ZU13BlECOFpEVh9gvQPMwxWNMjdS0reDAAZc0/GtsLFvmksbcuW5+qi5d3CC/Cy+E1q1Lz/MniMDG8PXr3Wtj6qpgEshRQRxTVPUhxtS+6rQVlO9+u2ULvPqqSxzr17v2ipEj4eKLoU+fg7veNmzoqqeaNq26MdyYuiSYgYQH/zlnTJQKpa0gsLRRWOgG+M2e7f4tLoaTT4arr3ajw5OSSs/zt2skJ7vEYeuEm/rK0+ncjfHCodoKVF3C8LdtrF/vksYrr8C2bZCa6hZluvhi6NSp9LzAkeHJyTZFujEQQgIRkY5WGjGxyt+Tyj9uY/58eOEF1w03Lg4GDoRLLnH/BpYoRMqO17CV+4wpFUoJ5DWgTE8rEemvqkvCG5Ix4bN/v5u8MD8ffvoJXnwRXn4Zdu6Edu3guutc99vDDy89x6qojAlOMN14L8EljmYicjSwRlX9jeaPAsfVYnzGhKyoyLVpFBbCxo1lSxsNGrhut2PHwumnl5YoAuehat7cqqiMCUYwJZDFQALwW+D/gB4ishu3yFRuKG8mIsOBB3ELUD2uqn+r5LjRwEtAP1X9PJT3MPVXfr4rbezfD/v2tWXbtvM47TTYscOVNq6/HkaPhjZtSs8RcSPC/aUNq6IyJnjB9ML6GfifiPyoqouhZJnbzsD3wb6RiDQAHgaGAlnAMhGZo6rflTuuGfAn4LOgfwpTb/kbxf3VVB9+CLNmwfLlzwHKWWfBZZe50oa/i62/ZNGsmUsc1R0dbkx9F8pUJosDnu8Edob4XicBmaq6FkBEXgBGAd+VO+5O4F7gxhCvb+qRoiLXk2rvXvjlF9eT6vnn4eefXU+qdu2eITX1Lf7735dKzvE3iDdv7hrEY7GKykagm2jiZTfedsDGgNdZlFtLRESOBzqo6lsiUmkCEZF0IB0gNTU1Jn6pcnJyLM4wcCWOHN5/P4PVq5vxxhvt+eijVAoL4+jdexcTJmzi1FO3c8st91NcDJmZGYArfcTFeZs0ov1e+lmc4RUrcYaDlwmkol9dLdkpEgfcD0yo6kKq+iiuAZ8ePXrowIEDwxNhLcrIyMDirB5VNy/V7t2uuuqJJ1Yxb97RfPONG/09dixcfjl07doCaAFAYmIKInDaaQPLLMzkpWi8lxWxOMMrVuIMh1DGgQgwDjhSVe8QkTSgraouDfISWUCHgNftcQ3xfs2AY4AM91a0BeaIyEhrSK+fiotdFdXu3ZCV5do2XnwRdu06mq5dYfp0t7Kff60Nf5JITi6dwLBJk8jFb0xdF0oJ5BGgGBgM3AFkA68A/YI8fxnQTUQ6Az8DY4DL/DtVdQ/Qyv9aRDKAGy151D8FBaXtG8uWwcyZrisuwFlnwZAhy7nooj4lCaOito0PP8yIVPjG1BuhJJCTVfUEEfkKQFV3iUjQ/VdUtVBErgbm4brxPqmqK0XkDuBzVZ0TUuSmzsnLg127XPJ48014+mlYudIlht/+Fq64Ao44AjIzd5d0t23a1O23nlTGeC+UBFLg64qrACKSiiuRBE1V5wJzy22bUsmxA0O5tqkZf53ttGnTPH1f/yp/u3bBpk2ummrWLDd2o1s3uPNOV03ln8zQX+o47DCXPGzchjGRE0oC+SduOpPWIjIDGA3cVitRmTpP1S3StGsXfPcdPPkkzJnj5qkaNAgmTIDTTiudVgRcEmne3E2AmJwc0fCNMYQ2DmSWiHwBDMH1qLpAVVfVWmSmTioudlVUu3fDRx/BE0/Axx+7qUMuucQljs6d3bH+5NG8uUsYttaGMdElpG68qvo9IYw+N8avsNAlje3b4Y03XOL44Qc36O+GG1xX3BauB27JIk0pKbE74M+Y+iCUbrx9gclAR995Aqiq2mSKplIFBa6aavNm17Yxc6YbOX7UUXDvvXDeeaXriYu4aqqUlLJrjBtjolMoJZBZwE3AN4TYeG7qn/x8lzjWroWnnnKz4ebkuDmp/vGPsu0b/qnTmze3aipjYkkoCeQX62prqpKf79ba+OYbePRR1zBeXAznngu/+x306uWOE3HJokUL15vKqqmMiT2hJJCpIvI4sADI929U1VfDHpWJOXl5ruvt0qXwyCPw/vtubY2xY+E3v4EOvjkIRFyDeUqKrblhTKwLJYFcCRwFNKS0CksBSyD1lKpLHNu3ux5VjzziFm1KSYFrr3UD/1q0KE0STZq417bCnzF1QygJpLeqHltrkZiY4U8cv/wC8+a5xLF8ObRuDbfeCmPGlO091by5tW8YUxeFkkCWiEjP8gtAmfolNxe2bXNtG//6F6xZA2lpcNdd8KtflU5iGBfnSiK2yp8xdVcoCeR0YLyI/IRrA7FuvHXErFmzWLJkCfn5+YwZM4b77ruPcePGlTnGnzheew0efhgyM91UI//3fzBihFsW1r88bMuWRGwKdWOMd0JJIMNrLQoTMbNmzSI9PZ38fNcvYuvWraSnpwMwbtw48vJg61Z4+WWXOH76Cbp3h4ceguHDSxdpatTIJQ5rGDem/ghlKpP1tRmIiYzJkyezf//+Mtv279/PrbdO5owzxvHii66qasMGOPpo194xdGhp4khIcImjugP//JM41pcV3IypS6pMICKySFVPF5FsAlYQpLQKy6a1i2EbNmyodPuAAbBunRu78Z//wJAhpYkjKcn1qLJp1I2pv6pMIKp6uu/pv1V1UuA+Ebm3VqIynklLS2P9+ooKl2k0buwSx1lnlY4Yt664xhi/UPrHnFXBNmsXiXF33jmDxMSkMttEkrjiihm89VZpdVWzZm4wYOvWljyMMU4wVVh/AK4CuojIioBdzYBPaiswU7tU3bTq8fHjaN0a1q+fDGwgObktU6b8nQsvHIeISxwpKa53lTHGBArma+E54B3gbuDmgO3ZqrqzVqIytUbVTWr48cduNtwPP4S2bcfRufMmWrV6l7vuup1u3QbStKmrqrLEYYypTJVVWKq6R1XXqepYVV0f8Ag5eYjIcBFZLSKZInJzBft/LyLfiMhyEVkkIj1DfQ9TudxcWLwYLr/cjd1YvhxuvhkWLIDWrd8mLq6IuDhXVZWaasnDGHNonn1F+NZTfxgYCmQBy0RkTrmR7c+p6n98x48E/g9rZ6mxggJYtcoN+nvuOTelyB/+AOnpbhp1/8y48fGlD2OMqYqXXxUnAZmquhZARF4ARgElCURV9wYc34Sy3YZNiIqL4eef4Z//dL2pcnPh4ovhT3+CNm1Ku+O2bGkN48aY0HmZQNoBGwNeZwEnlz9IRP4IXA80AgZXdCERSQfSAVJTU2NiEFpOTo6ncRYUwIIFrXnqqSPZti2B/v2389vf/kiHDrlkZ7t2EP/0IwC7d++OSJz+9w3lPb2OsboszvCyOKOPlwmkogkuDiphqOrDwMMichlwGzC+gmMeBR4F6NGjh/pHM0ezjIwMvIgzNxfmzoU774Svv3aDAO+/H/r3b4VIKxo1glatDh45npKSAkDTpk09ibP8+4bynl7dy5qyOMPL4ow+Xs6TmgV0CHjdHth0iONfAC6o1YjqkMJC+OwzuOgiGD3azV/197/D66/DKae4Kqq2baFdu+hZb9w/ieOHH35Ip06dmDVrVqRDMsaEwMsSyDKgm4h0Bn4GxgCXBR4gIt1U9QffyxHAD5hDUoXNm+Huu90SsvHx8Oc/w29/Wzoj7mGHRd+yseUncVy/fn2ZSRyNMdHPsxKIqhYCVwPzgFXAbFVdKSJ3+HpcAVwtIitFZDmuHeSg6itTav9+1zjet6+b8HD4cHjvPbjmmtK5qjp2dIMBoyl5QOWTOE6ePDlCERljQuVph01VnQvMLbdtSsDza72MJ1YVFsKiRW71v08/dbPk3n8/9OtHyejxFi2iewXAQ03iaIyJDdbjP4aowsaNMHUqPPOMq5aaPh3GjnVVVwkJroG8Ol1y/b1GvOo9UtkkjmlpaZ68vzGm5myx0RiRn19aXfX003DJJfD++3DFFa5RvE0bOPzw2BnPMWPGDJKSyk7imJSUxIwZMyIUkTEmVFYCiXKq8NVXcP31bt6qXr1cY/lxx7nqqpYtS0eTxxJ/Q/nEiRPJz8+nY8eOzJgxwxrQjYkhlkCiWHY23HWXG0neoAHcdpsrcTRs6KqvWraM7naOqowbN47HHnsMsBUJjYlFlkCiUHExvPOOK3WsWQPDhsGUKXDEEa6to3Xr6BnLYYypvyyBRJkdO+DGG2HmTJcwHn3ULSUby9VVxpi6yRJIlCguhjlz3ESHWVkwfjzccIOrqkpKcr2rYrm6yhhT91gCiQLbt7vqqmeecQP/nn8eTjrJJYzWrV33XGOMiTaWQCJI1c1V9ac/uWnXf/Mbl0iSkqB5czcY0KqrjDHRyhJIhOze7aYcefZZ6NwZXnzRjfFo2NCVOho1inSExhhzaJZAIuCjj2DCBFi3DiZOdKWOxERX4mje3EodxpjYYAnEQwUFbuqRe+5xjeLPPuumWm/UyJU6YmUUuTHGgCUQz2zb1pgzz4QlS+Ccc9wAwRYt3FTr0ThbrldsAKExscsSSC1Thf/9D66+ui/Fxa70MXq0K3W0aWOlDmNM7LIEUov27YPf/c51y+3RI5dHHmlI587Ww8oYUzdYAqklq1a55WVXrYI//AHOO+8runQZQNu2Ng2JMaZusARSC2bPdkvKxsXB44/D4MHw449Khw5umzHG1AX2dRZGhYWuS+6ll0JaGrzxhkserVu7SRAteRhj6hJPv9JEZLiIrBaRTBG5uYL914vIdyKyQkQWiEhHL+OriS1bYNAgt7TsJZfAyy/DkUdChw7QpEmkozPGmPDzLIGISAPgYeAcoCcwVkR6ljvsK6Cvqh4HvAzc61V8NbFoEZxwAixbBn/7m3scdhi0b+9KHsYYUxd5WQI5CchU1bWqegB4ARgVeICqLlTV/b6XS4D2HsZXLc8+66Zbj4+Hl15ypY/UVPewXlbGmLpMVNWbNxIZDQxX1d/6Xl8BnKyqV1dy/L+ALap6VwX70oF0gNTU1BNnz55de4FXQhWefTaNJ588kl69djN16kpSUgqIj684ceTk5NC0aVPP4wxVLMQZCzGCxRluFmd4DRo06AtV7Vuji6iqJw/gYuDxgNdXAA9VcuzluBJI46qu2717d/VaXp7qZZepgurIkaqrVqlu2aJaVFT5OQsXLvQsvpqIhThjIUZVizPcLM7wAj7XGn6ve1lDnwV0CHjdHthU/iAROQuYDAxQ1XyPYgvazp0wciQsXuymYb/2WjcoMCXFqqyMMfWLlwlkGdBNRDoDPwNjgMsCDxCR44H/4qq6tnkYW1AyM908VuvXw9//7gYKpqa6VQONMaa+8SyBqGqhiFwNzAMaAE+q6koRuQNXlJoD/B1oCrwk7s/5Dao60qsYD+WTT1zJo7AQnn7azaJ7+OE2qtwYU3952slUVecCc8ttmxLw/Cwv4wlWRgacd57rmvvkk9C9u0se1kXXGFOf2VdgFd57D0aNgiOOcF12O3VyI8ttVLkxpr6zr8FDmDsXzj/fjSZ/7jno0sVNwW7JwxhjLIFU6vXX4cILXdLwJ49WraynlTHG+FkCqcDLL8PFF0OPHq7aqnNn1/5hycMYY0pZAinnuedgzBg49lh45hmXPFq2jHRUxhgTfSyBBJg9G664Ak480XXV7dzZDRA0xhhzMOuF5bN4Mfz619Cnj+uqm5YGzZpFOipjjIlelkBwI8xHjYK2beG//4WOHW10uTHGVKXeV2Ht2AHDh0NxMTzxhBskaMnDGGOqVq9LIHl5bnqSjRtdg3mfPpCcHOmojDEmNtTbBFJcDOPHuzmuHnwQBgyw3lbGGBOKeluFNXmy63U1aZKbVbd1axvnYYwxoaiXCeSxx9y65WPGwB//6CZGtORhjDGhqXcJ5LPP4A9/gDPOgDvvdJMk2txWxhgTunr11ZmX59o9WreGhx5yYz1sSnZjjKmeevX1OWUKrF7tRpl36waNGkU6ImOMiV31pgTy2Wdw331w6aVu3EdSUqQjMsaY2FYvEkheHkyY4NbyuPVWNy27McaYmvE0gYjIcBFZLSKZInJzBfvPFJEvRaRQREaH632nToXvv4e//tWNNLdGc2OMqTnPvkpFpAHwMHAO0BMYKyI9yx22AZgAPBeu9126FP7xD7jkEreueUJCuK5sjDH1m5eN6CcBmaq6FkBEXgBGAd/5D1DVdb59xeF4Q3/VVevWrurKRpobY0z4eJlA2gEbA15nASfX5htOmwarVrnp2Xv0sKorY4wJJy8TSEVjvbVaFxJJB9IBUlNTycjIOOiY779vxt//fgJnn72FtLTVLFlSnXcKn5ycnArjjDaxEGcsxAgWZ7hZnFFIVT15AKcA8wJe3wLcUsmxM4HRwVy3e/fuWl5RkWqvXqpt26ouX65aXHzQIZ5buHBhpEMISizEGQsxqlqc4WZxhhfwudbwe93LSp1lQDcR6SwijYAxwJzaeKMvv4SVK+G66+Coo2yeK2OMqQ2eJRBVLQSuBuYBq4DZqrpSRO4QkZEAItJPRLKAi4H/isjK6rzX/Pnu38GDoXHjcERvjDGmPE+nMlHVucDcctumBDxfBrSv6fvMmwe9erkxH8YYY2pHneuXlJ3tFok6/XRbmtYYY2pTnUsgCxdCYaGbrt267RpjTO2pc1+x8+dDYiKcdlqkIzHGmLqtziWQefOgf39o2zbSkRhjTN1WpxLI2rWQmenaP6z3lTHG1K46lUD83XfPPNPGfhhjTG2rcwnkiCPg+OMjHYkxxtR9dSaBFBTAggWu91VKSqSjMcaYuq/OJJClS2HvXpdAGjSIdDTGGFP31ZkEMm+eG/dx5pmRjsQYY+qHOpNA5s+H3r3hyCMjHYkxxtQPdSKB7NwJy5a56qukpEhHY4wx9UOdSCALFkBxsRv/Yd13jTHGG3UigcybB82awamnRjoSY4ypP+pEApk/3yWP1q0jHYkxxtQfMZ9ADhyIY+NG1/7RsGGkozHGmPoj5hPIvn1uTawzzohwIMYYU8/EfALZv78BnTvDccdFOhJjjKlf6kACief00yE5OdKRGGNM/eJpAhGR4SKyWkQyReTmCvY3FpEXffs/E5FOVV1T1Y0+t9UHjTHGW5597YpIA+Bh4BygJzBWRHqWO2wisEtVuwL3A/cEc21r/zDGGO95+Xf7SUCmqq5V1QPAC8CocseMAp72PX8ZGCJy6KGBiYlFpKWFPVZjjDFViPfwvdoBGwNeZwEnV3aMqhaKyB7gMGB74EEikg6kAzRs2IikJPmitoIOo1aU+zmiVCzEGQsxgsUZbhZnePWo6QW8TCAVlSS0Gsegqo8CjwKIyOeq2rfm4dUuizN8YiFGsDjDzeIMLxH5vKbX8LIKKwvoEPC6PbCpsmNEJB5oDuz0JDpjjDEh8TKBLAO6iUhnEWkEjAHmlDtmDjDe93w08IGqHlQCMcYYE3meVWH52jSuBuYBDYAnVXWliNwBfK6qc4AngGdEJBNX8hgTxKUfrbWgw8viDJ9YiBEsznCzOMOrxnGK/YFvjDGmOmz4nTHGmGqxBGKMMaZaojqB1GTqExG5xbd9tYicHcEYrxeR70RkhYgsEJGOAfuKRGS571G+Q4HXcU4QkV8C4vltwL7xIvKD7zG+/Lkex3l/QIxrRGR3wD5P7qeIPCki20Tk20r2i4j80/czrBCREwL2eXkvq4pznC++FSLyiYj0Dti3TkS+8d3LGnf3rGGcA0VkT8D/7ZSAfYf8vHgc500BMX7r+zy29O3z5H6KSAcRWSgiq0RkpYhcW8Ex4ft8qmpUPnAN7T8CRwKNgK+BnuWOuQr4j+/5GOBF3/OevuMbA51912kQoRgHAUm+53/wx+h7nRNF93IC8K8Kzm0JrPX928L3vEWk4ix3/DW4zhhe388zgROAbyvZfy7wDm5cU3/gM6/vZZBxnup/f9wUQ58F7FsHtIqS+zkQeKumn5fajrPcsefjepF6ej+Bw4ETfM+bAWsq+F0P2+czmksgNZn6ZBTwgqrmq+pPQKbvep7HqKoLVXW/7+US3PgXrwVzLytzNvCequ5U1V3Ae8DwKIlzLPB8LcVSKVX9iEOPTxoF/E+dJUCKiByOt/eyyjhV9RNfHBC5z2Yw97MyNflchyzEOCP12dysql/6nmcDq3AzfAQK2+czmhNIRVOflL8RZaY+AfxTnwRzrlcxBpqIy/x+CSLyuYgsEZELaiE+v2DjvMhXpH1ZRPyDPr26lyG9l68qsDPwQcBmr+5nVSr7Oby8l6Eq/9lUYL6IfCFu6qBIO0VEvhaRd0Skl29bVN5PEUnCffG+ErDZ8/sprkr/eOCzcrvC9vn0ciqTUNVk6pOgpkQJg6DfR0QuB/oCAwI2p6nqJhE5EvhARL5R1R8jFOebwPOqmi8iv8eV7AYHeW64hPJeY4CXVbUoYJtX97Mqkf5chkREBuESyOkBm0/z3cvWwHsi8r3vL/BI+BLoqKo5InIu8DrQjSi9n7jqq8WqGlha8fR+ikhTXAL7s6ruLb+7glOq9fmM5hJITaY+CeZcr2JERM4CJgMjVTXfv11VN/n+XQtk4P5aqA1VxqmqOwJieww4MdhzvYwzwBjKVRF4eD+rUtnP4eW9DIqIHAc8DoxS1R3+7QH3chvwGrVTBRwUVd2rqjm+53OBhiLSiii8nz6H+mzW+v0UkYa45DFLVV+t4JDwfT5ru1GnBo1B8bhGnM6UNpD1KnfMHynbiD7b97wXZRvR11I7jejBxHg8rqGvW7ntLYDGvuetgB+opQbAIOM8POD5hcASLW1Y+8kXbwvf85aRitN3XA9co6RE4n763qMTlTf6jqBsI+VSr+9lkHGm4doHTy23vQnQLOD5J8DwCMbZ1v9/jfvi3eC7t0F9XryK07ff/0dsk0jcT999+R/wwCGOCdvns9ZudJhuxrm4XgQ/ApN92+7A/SUPkAC85PslWAocGXDuZN95q4FzIhjj+8BWYLnvMce3/VTgG9+H/htgYoTv5d3ASl88C4GjAs79je8eZwJXRjJO3+tpwN/KnefZ/cT9dbkZKMD91TYR+D3we99+wS2e9qMvlr4RupdVxfk4sCvgs/m5b/uRvvv4te8zMTnCcV4d8NlcQkDCq+jzEqk4fcdMwHXgCTzPs/uJq4ZUYEXA/+u5tfX5tKlMjDHGVEs0t4EYY4yJYpZAjDHGVIslEGOMMdViCcQYY0y1WAIxxhhTLZZAjDHGVIslEGOMMdViCcTUeSLSqbI1HA5xzifVuaaIpIjIVVWce5aIPFPFtXNFZHnwEYOIJPrWmzjgm+rDmFplCcSYCqjqqdU8NQW3Ts2h9Aa+quKYH1W1TyhvrKq5vnOiYT4oUw9YAjH1RQMRecy3Stt8EUkEN0uyiCz1/eX+XxFp4Nue4z9RRG4Xke9F5D0ReV5EbjzENf8GdPFd7++VxNIbaCsiH4vIFt9km5XylUi+F5HHfSvdzfKVYhb7Vo6L2ESHpn6zBGLqi27Aw6raC9iNW/vkaOBS3FTbfYAiYFzgSSLSF7gINynmr3BT8ld6TeBmfKUHVb2pklh6A9tV9QxcaWVcJccF6go8CBwHHAVchpv36Ebg1iDONybsonk9EGPC6SdV9bcpfIGbVTUFN239MreQJYnAtnLnnQ68oaq5ACLyZhXXXHSoIHxTbbcE/uHbFI9LPsHE/43vGiuBBaqqIvKN732N8ZwlEFNf5Ac8L8IlCwGeVtVbDnFeRYvsHOqaVekJfK2qxb7XxwHBNPAHvldxwOti7PfYRIhVYZn6bAEw2rdKHCLS0rdUbqBFwPkikuBb5W1EFdfMBpodYn9v3LTefsfhpt42JuZYAjH1lqp+B9yGW6t6BfAecHi5Y5YBc3Bf+q8CnwN7DnHNHcBiX2N3RY3ovSmbMI4huBKIMVHH1gMxpgoi0lTdetxJwEdAuqp+WYvv1wl4S1WPqeb563CLBG0PY1jGHMRKIMZU7VHfoL4vgVdqM3n4FAHNqzuQEGiIaxsxplZZCcQYY0y1WAnEGGNMtVgCMcYYUy2WQIwxxlSLJRBjjDHVYgnEGGNMtVgCMcYYUy2WQIwxxlTL/weNniU2HvIpBgAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# create an additional dataset for the uncertainty band\n",
+ "data_y_m = Falltime(data_x, true_g - 0.4)\n",
+ "data_y_p = Falltime(data_x, true_g + 0.4)\n",
+ "\n",
+ "# plot uncertainty band of theory prediction\n",
+ "plt.fill_between(data_x, data_y_m, data_y_p, facecolor='#ddddff', color='#ddddff')\n",
+ "\n",
+ "# plot mean value on top\n",
+ "plt.plot(data_x, data_y, color='blue', label='theory')\n",
+ "\n",
+ "# always label the axes (the r'$...$' make the axes have a latex style)\n",
+ "plt.xlabel(r'height $h$ [m]')\n",
+ "plt.ylabel(r'time $t$ [s]')\n",
+ "\n",
+ "# plot measurement with errors\n",
+ "plt.errorbar(\n",
+ " measurements[:,0], measurements[:,1], \n",
+ " xerr=measurements[:,2], yerr=measurements[:,3], \n",
+ " marker='o', color='black', label='measurement', linestyle='none'\n",
+ ")\n",
+ "\n",
+ "# legend\n",
+ "plt.legend(loc='upper left',fontsize='15', numpoints=1)\n",
+ "\n",
+ "# optional: set axis limits\n",
+ "plt.xlim([0,2.0])\n",
+ "plt.ylim([0,0.8])\n",
+ "\n",
+ "# optional: grid lines\n",
+ "plt.grid(True)\n",
+ "\n",
+ "# save the figure to a pdf file\n",
+ "plt.savefig('exercise-1-plot.pdf')\n",
+ "\n",
+ "# make the plot appear\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### e) Histograms"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "A qualitative way to check compatibility of the measurement points with theory is to make a histogram of the pulls (pulls are defined below in the code). Create the histogram of pulls and overlay the expected pull distribution, which is Gaussian. \n",
+ " \n",
+ "Instead of putting the formula for the Gaussian yourself, you can use `scipy.stats.norm.pdf`, see here:\n",
+ "https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "import scipy.stats\n",
+ "\n",
+ "heights = measurements[:, 0]\n",
+ "times = measurements[:, 1]\n",
+ "time_errors = measurements[:, 3]\n",
+ "predictions = Falltime(heights, true_g)\n",
+ "\n",
+ "# compute pulls\n",
+ "pulls = (times - predictions)/time_errors\n",
+ "\n",
+ "# histogram of pulls\n",
+ "plt.hist(pulls, 10, density=1, \n",
+ " histtype='stepfilled', facecolor='#99bbff', alpha=0.75)\n",
+ "\n",
+ "# unit gaussian\n",
+ "x = np.linspace(-3.0, 3.0, 50)\n",
+ "plt.plot(x, scipy.stats.norm.pdf(x, 0.0, 1.0), '--', color='r', linewidth=3.0)\n",
+ "\n",
+ "# always label the axes, also for histograms\n",
+ "plt.xlabel(r'pull')\n",
+ "plt.ylabel(r'count (normalized)')\n",
+ "\n",
+ "# annotation\n",
+ "plt.annotate('unit gaussian', xy=(-0.8, 0.3), \n",
+ " arrowprops=dict(arrowstyle='->'), xytext=(-2, 0.5))\n",
+ " \n",
+ "# save the figure to a pdf file\n",
+ "plt.savefig('exercise-1-histogram.pdf')\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### f) (optional) Creating a text file of toy measurements"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# create toy experiments instead of real measurements here\n",
+ "n_toys = 1000\n",
+ "toy_true_height = equallySpacedNumbers(0.5, 1.9, n_toys)\n",
+ "toy_true_time = Falltime(toy_true_height, true_g)\n",
+ "\n",
+ "# uncertainty on measurements\n",
+ "height_uncertainty = 0.01\n",
+ "time_uncertainty = 0.05\n",
+ "\n",
+ "# toy with uncertainties, sample from normal distribution\n",
+ "toy_height = toy_true_height + np.random.normal(0, height_uncertainty, n_toys)\n",
+ "toy_time = toy_true_time + np.random.normal(0, time_uncertainty, n_toys)\n",
+ "\n",
+ "# error bars for plotting\n",
+ "toy_height_errors = np.full(n_toys, height_uncertainty)\n",
+ "toy_time_errors = np.full(n_toys, time_uncertainty)\n",
+ "\n",
+ "# save to text file\n",
+ "np.savetxt('measurement_%dtoys.txt'%n_toys, \n",
+ " np.transpose([toy_height, toy_time, \n",
+ " toy_height_errors, toy_time_errors]))\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 2. Error propagation with Python"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We consider a LC circuit with resonance frequency $\\omega_0 = \\frac{1}{\\sqrt{LC}}$. \n",
+ "$C = 150 \\pm 8 \\,\\text{pF}$ \n",
+ "$L = 1 \\pm 0.1 \\,\\text{mH}$ \n",
+ " \n",
+ "What is the resonance frequency and its uncertainty? \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## a) Calculation by hand"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The mean value is computed to: \n",
+ " \n",
+ "$\\omega_0 = \\frac{1}{\\sqrt{LC}} = 2.58 \\cdot 10^6 \\,\\frac{1}{\\text{s}}$ \n",
+ " \n",
+ "Since the uncertainties for both quantities come from independent electronic components, they can safely be assumed as uncorrelated and one can compute the uncertainty of $\\omega_0$ to \n",
+ "$\\sigma_{\\omega_0} = \\sqrt{\\left(\\frac{\\partial \\omega_0}{\\partial C} \\sigma_C\\right)^2 + \\left(\\frac{\\partial \\omega_0}{\\partial L} \\sigma_L\\right)^2 } = 1.46 \\cdot 10^5\\,\\frac{1}{\\text{s}}$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## b) Installation of 'uncertainties' package"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "There are packages, which make handling of uncertainties very easy, e.g. the package simply called \"uncertainties\". It is not included in standard packages of Anaconda and therefore has to be installed with: \n",
+ "`conda install -c conda-forge uncertainties` \n",
+ "This can take several minutes, since anaconda has to resolve a lot of dependencies. \n",
+ "(If you are annoyed by the slowness of anaconda, look at \"pip\" which is a conceptually different way of installing Python modules)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## c) Use of 'uncertainites' package"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Look at the example on the official website on how to use the library: \n",
+ "https://pythonhosted.org/uncertainties/ \n",
+ " \n",
+ "Define $L$ and $C$ as `ufloat`s and compute the resonance frequency and print the result. \n",
+ "How can one obtain the central value and the uncertainty separately from the `ufloat` object?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(2.58+/-0.15)e+06\n",
+ "nominal: 2581988.8974716114\n",
+ "standard deviation: 146312.704190058\n"
+ ]
+ }
+ ],
+ "source": [
+ "from uncertainties import ufloat\n",
+ "from uncertainties.umath import *\n",
+ "\n",
+ "C = ufloat(150e-12, 8e-12)\n",
+ "L = ufloat(1e-3, 0.1e-3)\n",
+ "\n",
+ "omega0 = 1/sqrt(L*C)\n",
+ "print(omega0)\n",
+ "print(\"nominal:\",omega0.n)\n",
+ "print(\"standard deviation:\", omega0.s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Note that the uncertainties package treats correlations correctly (if you tell it about them)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "correlated: 0.0\n",
+ "uncorrelated: 1.131370849898476e-11\n"
+ ]
+ }
+ ],
+ "source": [
+ "C2 = ufloat(150e-12, 8e-12)\n",
+ "C3 = C2\n",
+ "print(\"correlated:\", (C3-C2).s)\n",
+ "print(\"uncorrelated:\",(C3-C).s)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "There's lots of things you can do to plots. Have a look here for more inspiration: https://matplotlib.org/gallery.html"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## d) (optional) write your own uncertainty package"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can also try to write our own class for propagating uncertainties. Look at the myufloat class below and add the missing pieces marked with **TODO:**. Then test your **myufloat** class with the LC circuit example from above. It should lead to the same result (up to floating point rounding errors)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "class myufloat:\n",
+ " def __init__(self, n, s=0.0):\n",
+ " self.n = float(n)\n",
+ " self.s = float(s)\n",
+ " \n",
+ " def __add__(self, operand):\n",
+ " n = self.n + operand.n\n",
+ " s = np.sqrt(self.s * self.s + operand.s * operand.s)\n",
+ " return myufloat(n, s)\n",
+ "\n",
+ " def __sub__(self, operand):\n",
+ " n = self.n - operand.n\n",
+ " s = np.sqrt(self.s * self.s + operand.s * operand.s)\n",
+ " return myufloat(n, s)\n",
+ " \n",
+ " def __mul__(self, operand):\n",
+ " n = self.n * operand.n\n",
+ " r1 = self.s / self.n\n",
+ " r2 = operand.s / operand.n\n",
+ " s = np.abs(n) * np.sqrt(r1*r1 + r2*r2)\n",
+ " return myufloat(n, s)\n",
+ " \n",
+ " def __div__(self, operand):\n",
+ " n = self.n / operand.n\n",
+ " r1 = self.s / self.n\n",
+ " r2 = operand.s / operand.n\n",
+ " s = np.abs(n) * np.sqrt(r1*r1 + r2*r2)\n",
+ " return myufloat(n, s)\n",
+ " \n",
+ " # for Python3\n",
+ " def __truediv__(self, operand):\n",
+ " return self.__div__(operand)\n",
+ "\n",
+ " def sqrt(self):\n",
+ " return myufloat(np.sqrt(self.n), np.abs(0.5/np.sqrt(self.n)*self.s))\n",
+ " \n",
+ " def __str__(self):\n",
+ " return \"%1.2e ± %1.2e\"%(self.n, self.s)\n",
+ " \n",
+ " def __repr__(self):\n",
+ " return \"%1.2e ± %1.2e\"%(self.n, self.s)\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "2.58e+06 ± 1.46e+05\n"
+ ]
+ }
+ ],
+ "source": [
+ "C = myufloat(150e-12, 8e-12)\n",
+ "L = myufloat(1e-3, 0.1e-3)\n",
+ "\n",
+ "print(myufloat(1.0)/np.sqrt(C*L))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "So the results agree for this case!\n",
+ "Lets check some other cases: \n",
+ "create two values with uncertainties: \n",
+ " \n",
+ "$a = 1.0 \\pm 0.1$ \n",
+ "$b = 2.0 \\pm 0.05$ \n",
+ " \n",
+ "and compute the result including uncertainty both with the uncertainties package (ufloat) and your own implementation (using myufloat) of: \n",
+ " \n",
+ "$c = \\frac{a+b}{a-b}$ \n",
+ " \n",
+ "are they the same? If not, why?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "-3.0+/-0.4\n",
+ "-3.00e+00 ± 3.54e-01\n"
+ ]
+ }
+ ],
+ "source": [
+ "a1 = ufloat(1.0, 0.1)\n",
+ "b1 = ufloat(2.0, 0.05)\n",
+ "\n",
+ "a2 = myufloat(1.0, 0.1)\n",
+ "b2 = myufloat(2.0, 0.05)\n",
+ "\n",
+ "c1 = (a1+b1)/(a1-b1)\n",
+ "c2 = (a2+b2)/(a2-b2)\n",
+ "\n",
+ "print(c1)\n",
+ "print(c2)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We neglected correlations in our **myufloat** class that e.g. the **a** in the numerator and the **a** in the denominator are the same and therefore 100% correlated! The uncertainties package takes this into account."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.7"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
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diff --git a/exercises/Solutions4/.ipynb_checkpoints/Solutions_4-checkpoint.ipynb b/exercises/Solutions4/.ipynb_checkpoints/Solutions_4-checkpoint.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..8cdd87113ee8f7f7b672e69715fb5426c4697c10
--- /dev/null
+++ b/exercises/Solutions4/.ipynb_checkpoints/Solutions_4-checkpoint.ipynb
@@ -0,0 +1,788 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 4 Solutions\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function # For Python < 3\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "import scipy.stats as stats\n",
+ "\n",
+ "%matplotlib inline \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1. Approximations to the binomial\n",
+ "\n",
+ "For np < 10, large n, the Poisson distribution is a good approximation for the binomial.\n",
+ "\n",
+ "* Show analytically that the binomial distribution converges to the Poisson distribution in the limit of large n. (Hint: $e = \\lim_{n\\to\\infty}(1+\\frac{1}{x})^x$)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$P(x=k) = \\binom{n}{k}p^k (1-p)^{n-k}$\n",
+ "\n",
+ "$\\lambda = np$\n",
+ "\n",
+ "$\\lim_{n\\to\\infty} \\frac{n!}{(n-k)!k!} \\frac{\\lambda}{n}^k (1-\\frac{\\lambda}{n})^{n-k}$\n",
+ "\n",
+ "$\\lim_{n\\to\\infty} \\frac{n}{n} \\frac{n-1}{n} \\bigl ( ... \\bigr ) \\frac{n-k+1}{n} (1-\\frac{\\lambda}{n})^{n} (1-\\frac{\\lambda}{n})^{-k}$\n",
+ "\n",
+ "Remembering $e = \\lim_{n\\to\\infty}(1+\\frac{1}{x})^x$\n",
+ "\n",
+ "$\\frac{\\lambda}{k!}e^{-\\lambda}$\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Keeping $n p$ fixed, plot the binomial probability mass function for an increasing number of observations $n$, comparing in each case to the equivalent Poisson distribution ($\\lambda=n p$). For convenience, you should use the relevant functions in ```scipy.stat```."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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ntfec1/7JdF4raeasVLd0KJEPRcQuSccC90n6c/JJbj1zXquT81qmKmmkX7a3\ndIiIXcnf54GfkftqWw7+Q9K7AJK/z5c4ns44r73nvPZD1vNaSUU/ze0gBp2kIyQd2fEcOAvY0n2v\nQZN/e4x5wM9LGEtXnNfec177yHklNzFDpTyAjwP/DjwFfLXU8SQxTQAeTR5bSxUXcCfwHPAmuVHW\nfGAUuasAnkz+vrPU/17Oq/PqvJY2r74Ng5lZhlTS4R0zM+snF30zswxx0TczyxAXfTOzDHHRNzPL\nEBd9M7MMcdE3M8uQ/w/eiXuGcmEQ6wAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x107ecaf60>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "n_trials = [5, 10, 100]\n",
+ "p0 = 0.8\n",
+ "n_p = n_trials[0] * p0\n",
+ "x = range(12)\n",
+ "\n",
+ "fh, ax = plt.subplots(1,3, sharey=True)\n",
+ "for idx, nt in enumerate(n_trials):\n",
+ " p = n_p / nt\n",
+ " ax[idx].bar(x, stats.binom.pmf(x, nt, p), width=1, alpha=1, label='Binomial')\n",
+ " ax[idx].bar(x, stats.poisson.pmf(x, n_p), fill=False, width=1, alpha=1, label='Poisson')\n",
+ " \n",
+ " ax[idx].set_title('n={}'.format(nt))\n",
+ "\n",
+ " if idx==2:\n",
+ " plt.legend()\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For np > 10, n(1-p) > 10, the discrete binomial distribution can be reasonably approximated by the continuous normal distribution.\n",
+ "\n",
+ "* Choose a large n (> 30, with p close to 0.5). To start with, choose n=100 and p=0.45. Plot the binomial pmf, and, with equivalent parameters, the normal pdf \n",
+ "* Calculate the probability that X >= 55 for each. Don't forget to apply the continuity correction\n",
+ "* What happens to the relative difference as n increases?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Binomial (exact): 0.4911796759527426\n",
+ "Gaussian (approximate): 0.48595290935296537\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x10d046d30>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "n_trials = 100\n",
+ "p0 = 0.45\n",
+ "mu = n_trials * p0\n",
+ "std = np.sqrt(stats.binom.stats(n_trials, p0, moments='v'))\n",
+ "\n",
+ "xd = np.arange(int(mu), int(1.5*mu))\n",
+ "x = np.linspace(xd[0], xd[-1], 200)\n",
+ "\n",
+ "x_ch = 55\n",
+ "sel_d = xd >= 55\n",
+ "sel_cont = x >= 55\n",
+ "p_bin = stats.binom.cdf(x_ch, n_trials, p0)/2\n",
+ "p_gauss = stats.norm.cdf(x_ch-0.5, mu, std)/2\n",
+ "\n",
+ "print('Binomial (exact):', p_bin)\n",
+ "print('Gaussian (approximate):', p_gauss)\n",
+ "\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.bar(xd, stats.binom.pmf(xd, n_trials, p0), width=1)\n",
+ "plt.bar(xd[sel_d], stats.binom.pmf(xd[sel_d], n_trials, p0), width=1, color='g')\n",
+ "plt.plot(x, stats.norm.pdf(x, mu, std), 'r')\n",
+ "plt.show()\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 2. Random walk\n",
+ "\n",
+ "Consider a simple 1D random walk. A person starts at the position $x=0$. With equal probability $p=0.5$, they may take one step forwards or one step backwards, corresponding to a displacement of +1 and -1 respectively.\n",
+ "\n",
+ "* Show that for an N step walk, the expected absolute distance from the starting position is given by $\\sqrt{N}$.\n",
+ "\n",
+ "* Write a function to simulate such a random walk, parameterised by the number of steps. The output should be an array, with the displacement at each step index.\n",
+ "\n",
+ "* Plot a single walk."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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6exvy3gH5zzuA3rfzq7e3S8Q5HAqgwIHPvizjwrgXQ261tZx+DT/9TQkuhw2X\nJ9uXIdoo+ufk965LCAYGMKplLnczRkWCbiFursWNlRv10MWsnwKjjfpOnXYbZmf82EqkMeSy4/zY\nYYGycEjAlpZcVCzckaJxWuHSfvT3eCuRLqlmqF+T8vHzY0MYctmxlUhjdtoPp7370qXHAvSeozp6\nLKAb2djdf1cI09BLejZyOzojeDAy5OrZMqDl7CQzkHYPGnaH6NtdDQolBcrCRW6WyaLWcsVJKlep\nKFfbKX6Piz+vk34Pxn3uinGbjeFqWSyk2+ixAKD086PHAshCJ1oiKikYHXJhRqjfZ6RTgdGVvQMk\nqrTr2k6ksZPMVIzHU1msKpXlb4/bbkz/0kfKvvxGD9IalRrPjw3B76GAaLvR+3YClQIdqSHcxngP\nucSMz1mV2vxL63EcZDoboyJBtxDFKzcaIRISsLyRaFtglHOO9/7GV/Ef/29liZ9/8vwr+LFPvVIx\n/gtfuIkf+I2/qqgpLRathmiEa2dHYGPAG86NlIzPTgvwuh0V46NeNy5OePGGs6XjRPt48twILowP\nGb7n4vEhlx2zM/6KcRsDXn9muJPTPJI3nhuBx2mrLOWsxQIWVztrpTs6ejSibRxk8ljeSODts5MN\n7xMOCsgXOBZXY3jdafO/JNLuAdZjaVx/bbdkPJsv4NWHe7AxhnyBG02sAeDl+ztYUVJYVVKYCRwu\nvRRl5VjW87mxIbz4M09X3K0MuOz4i5/6zqp1Wn7vH70ZHifZOJ3iX3/fLFLZyrr8/+CvncN7nwhi\n0FUqT8/MTuLFn3kawUDtJbmd5v1PnsYzs1MIDJZ+nozAqKTg9Wc6ZyTQp9ciLK6qxYuOU7AoXPSh\naweH5WkTJbeey+tqv9ODbL6kcUEyncPtjUTJvjqipBy7GFMwMFD1bmXC76kaVBsZclWICNE+Bl2O\nqiUcnHab0fy7GMZYT4k5ADjsNkxVcXHqsQCzetw2Cgm6RdBdEsdpyjDlV5tEtMuPrq8b1+8CdIoz\nVIuPvbh6WEa1eJvNeBorSoqWExJ9RXGpiU5Bgm4RorKirdxovAcmYwyRkNC2EgCipCaNqP8vqq6n\n9TsdctlLxnVxn/J7SoR+vsEMUYLoJcIhAbc3E0hWWRTQLkjQLcK8rCByjICoTjgo4PZGoqRjjxno\nNTf+xpUJjHndJY2BRUntd3p1pnRp17ysYNLvxndeHsd8UZMKUVbUrEESdKKPMGoEdTBjlATdAui+\n52YK/odKWOWaAAAZMElEQVSDQkXHHjO4v72PeCqHSEgouQtQ+53GEQkFEA4JWFiJIac1rI5KewgH\n1fHd/Syk3QNtXA2Iet3k3yb6h8MaQZ1zu5CgWwDd99yMj1kPjJr9oStu46bfBSTTObXfaV7tdxoJ\nCUjnCljeSJRUrKsooyrvUcNmou+Y8Hkw5fd0NHmPTB4LoItxMz7mSb8Hk3636VltorRn1NxYU1La\nmtyYsYpFryWjbqtAOciCc/UH5pEpH5x2hqik4NqZYazH0uQ/J/qScFHzlE5Agm4B5vWKdVWWejWC\n3ljZTERZwaPTfrgctpLlkcsbCaPfKeeA1602rI6lstpcBLgddlyZ8htlbgFqOEH0J5GggD+/sY54\nKgtfBzKQyeViAaLSXksNc8NBwejYYwZqY4kYwlq9juK7gHn5sN+pTWtcENXK1s4I6jJKQPU/RqU9\nfFtSYGOoyBokiH5gTguMLpgco6oFCXqfU+x7bhY9Gr9gkpV+bzuJRDpX0sQ3HBTw8v3din6n4aCA\nGysxvPJgt6RGRyQkIJbK4Y+jK7g44aWEH6Iv0V2FnVqP3pKgM8YCjLHPMMZuMsZuMMbebNbEiMZY\n0Fp4tVKwSLfuzXK76B/ekjrXWjOA8n6n4VAAmXwB0u5BSeBT/yLc2UxSOVuibxnzuhEMDHTMj96q\n2fMRAH/COf9BxpgLwKAJcyKOgRlJN+M+N2a0jj1mIMoK3A4bLk0cdmUvEfHi+tfB6uOXJ31wOWzI\n5ArkPyf6mrDWVq8TNG2hM8b8AL4DwMcAgHOe4Zz3R3FtC1Hue26WORPTlEVJweyMH46iein6XUB5\nv9Mzo4PwefSuNIfC7XLY8OiUr2RfguhHwiEB97aSUA6ybT9WKy6X8wA2AfwPxti3GGMfZYwN1duJ\nAF6+v4ur//pPIO3ut/xaesncVomEBNzdShqrTZolX+CYX6nsLDTuU289I6FASTYrYwyPhQI4NTJQ\nUQHxsVMBOO0Ms9MUECX6F/27YFaM6ihacbk4ALwOwI9xzl9ijH0EwM8C+FfFGzHGngXwLACcPn26\nhcNZhxeWNpHM5PGNezsIDTfvpYqlsri3lcQPvj7U8pz0lnTzsoKnLow1/Tp3NxPYz+SrJgL91o+8\nvmq258+/Z65qvYsfe/oS3hmexoDL3vR8CKLbPBYK4J+/8wpOjbTfI92KhS4BkDjnL2mPPwNV4Evg\nnD/HOb/GOb82Pj7ewuGsw7yRAdnaL7aZRav012jV13fUuvG5oICzY5U3cefGhqreZYz73HjT+dGW\n5kMQ3UYYdOLZ77jQ24LOOV8D8JAx9og29FYAi6bMysJwzo2Id6s+a7GFDNFyRoZcajS+xTlFJQUD\nTjsujHvrb0wQhKm0usrlxwA8r61wuQvg77c+JWuzHktjM56G1+0wClM5muxgHpUVhIYrfc/NohbR\nat1CvzrjL+lCRBBEZ2hpHTrn/FXNnRLhnL+Hc75bf6+TTVQr1PPeJ4Jax55k068lSoqpS/rCIQH3\nt/eh7DcXGM3lC1hYUXqqiS9BnCQoU7TDzMsK7DaGv/OGUwCa96Mr+1k82Nk3NelGz+ycX2luTnc2\nk0hlad04QXQLEvQOE5UVXJrwYnbaX9Gx5zi0o2iV7otv1o+u331QZidBdAcS9A7COYcoqWu0bTaG\nq8HmS2vq/TrnZswTdGHQidMjg023pBNlBUMuO85XWclCEET7IUHvICtKCtvJjGFVR4ICFos69hwH\nUVJwZnQQwqC5JTnDIaEFC13BVe3HiiCIzkOC3kEOi1YFtL+HHXuO/VpyZTamGUSCAqTdA+wmM8fa\nL5sv4MZqrKQ2C0EQnYUEvYOI8h4cNoYrWo0SPZvyuOvRd5IZrTqh+eIZDjVXeXF5PYF0rkArXAii\ni5Cgd5CopODypA8ep5rKfmZkED63w/CHN4outu0oWtVsKV3d706t4giie5CgdwjOOUS5dN242rHn\n+FUO9ZUx7RB0v8eJc2NDxoqVRolKCnxuB86OUkCUILoFCXqHkHYPsLefrXBJREICbqzGkck1HhiN\nSgrOjw3B36YeheFmfmS0qo8UECWI7kGC3iGMdeNla7TDIQGZfAFL6/GS8VQ2jw98/Bt49WGlpaz3\n5WwXkZCAFSWFrUS6oe0zuQJursYpoYggugwJeoeISgqcdobLU6VFq8I1fNairOCFpU18QVwtGd+M\np7GipNrqqz6uH31pPY5MvkCNKAiiy5CgdwhR3sOVKT/cjtLa3qdHBuH3OCrWfuuPy33ZZpbMrcXV\nGT8Ya3z1jT5XstAJoruQoHcAzjmiUnU3CWMMkVCgIjtTD3zOyzEUCtwYj0oKGAOutlHQfR4nzo8N\nNZxgJMp78HscON2Bes8EQdSGBL0D3N/eRzyVq5l0Ew4JuLUWRzqXN8ZEWYHDxpBI5/DadrJk/MK4\nt2rnHzOp9iNTC3X1TmlrOYIgOg8Jegeot248HBSQzXPcWlMDo/FUFne3knj71cmS/dX/73Vkrfdc\nUMB6LI2NWOrI7VLZPG6txcl/ThA9AAl6BxBlBS6HDZcnfVWfL69yuLASA+fA33wiBLfDZoyvx1JY\nj6U7IuiRBjNGb63Fkc1z8p8TRA9Agt4BotIeHp32w+Wo/naHhgcwPOg0gpD638dPB3B1xl8x3gnx\nnJ32w8bql9KNdiBISxBEY5Cgt5lCgWNePrpoFWMM4VDAsIZFWUEwMIAxrxuRUAALKwryBTXT1MaA\n2Rl/2+c95Hbg4oS3roU+LykYHnQiNDzQ9jkRBHE0JOht5t52Eol0rq4FGw76sbQeRyqb17IuVdGe\nCwpIZvK4t5WAKCu4OOHFoKu9AVGduaBaSpdzXnObqJYhSgFRgug+JOhtxlg3XsdNEg4GkCtwvHRv\nB/e2kkYlRt298u2Hirr0sYPdgCJBAVuJNNZj1TNGU9k8ltYpQ5QgegUS9DYTlRS4HTZcmvAeuZ0u\nip966QGAQ5/0hXEvBpx2fHFxHVuJdEfFU6/bXqtQ1+JqDPkCp5ZzBNEjtCzojDE7Y+xbjLHPmzEh\nqyFKCq7O+OGwH/1WTwsejHld+OKNdQCHgm63McwF/YfjHRT02Wk/7DZW048+34a+pgRBNI8ZFvqH\nAdww4XUsR77AMb/SWGchxtRSuvkCV1e9DLmM5/Rxu41hdrr9AVGdAZcdlya8NVe6RCUFo0MuTAue\njs2JIIjatCTojLEQgO8F8FFzpmMt7m4msJ/JG66LeugrYcotXv3xpQmv0RyjU4SDAkS5emBU1MoZ\nUECUIHqDVi30XwHw0wCO3+X4BHDcolVGr9HyErvB0gBpJ4mEBOwkM5D3DkrGDzJ5LG/EqYcoQfQQ\nTQs6Y+xdADY45y/X2e5Zxth1xtj1zc3NZg/Xl4iyggGnHRfGjw6I6rzx/Aj++qUxfLeW8q9zfmwI\n3xuexnseD7Zjmkei/8jMl/nRF1cVFHh7uiYRBNEcrVjobwHw/Yyx1wD8LoCnGWP/q3wjzvlznPNr\nnPNr4+PjLRyu/xBlNSBqb7CLj9/jxG9/6I04X/YDYLMx/PoPvQ5PXRxrxzSP5MqUDw4bq1neN9Kg\nO4kgiPbTtKBzzn+Ocx7inJ8F8D4Af8E5/2HTZtbn5PIFLKy0t7NQJ/A47bg86atswCEpGPe5Mel3\nd2lmBEGUQ+vQ28TtzQRS2YIllvRFQpWB0aisIEIZogTRU5gi6Jzzr3DO32XGa1kFvZCWFZJuwiEB\ne/tZSLtqYDSZzuHOZqLv7z4IwmqQhd4mRFnBkMuO82ND3Z5Ky9Qq70sVFgmityBBbxNRScHVoABb\ngwHRXuaRKR+c9sOMUb0UAAk6QfQWJOhtIJsvYHH16JK5/YTbYceVKb/Rkk6UFUz5PZjwU4YoQfQS\nJOhtYHk9gUyuYCkfczgkQNRK6Ypy/6/eIQgrQoLeBnRL1kouiXBQQCyVw8JKDHc3k5Y6N4KwCiTo\nbSAqKfC5HTg72v8BUR1dwD/1Da28L1noBNFzkKC3AVHr4mOFgKjO5UkfXA4b/vBbMgBr3X0QhFUg\nQTeZTK6Am6vW6+Ljctjw6LQfyUze6HdKEERvQYJuMkvrcWTyBUsWrQobfU47V5OdIIjGIUE3meOW\nzO0nIkYZ3/7PfiUIK0KCbjKivAe/x4HTI4PdnorpvPnCKPweB/76pc5XfSQIoj6Obk/Aaoiygkgo\nYMmiVadGBhH9t9/d7WkQBFEDstBNJJXN49ZanJb0EQTRFUjQTeTWWhzZPKclfQRBdAUSdBOJynrJ\nXBJ0giA6Dwm6icxLCoYHnQgND3R7KgRBnEBI0E0kKisIWzQgShBE70OCbhKpbB5L63Ej+YYgCKLT\nkKCbxOJqDPkCt0TLOYIg+hMSdJMQLZwhShBEf0CCbhKirGDM68K0QF18CILoDiToJiFKaslcCogS\nBNEtmhZ0xtgpxtiXGWM3GGMLjLEPmzmxfmI/k8PyRtwyPUQJguhPWqnlkgPwU5zzVxhjPgAvM8a+\nyDlfNGlufcPiSgwFDoSpCiFBEF2kaQudc77KOX9F+38cwA0AQbMmVot0Lo9V5aDafPBge7/qPve3\nk8c6xkYshYNMvuHtRZkCogRBdB9TfOiMsbMAngDwkhmvdxS/9f/u4plffgGpbKngfj66iu/6pS9X\niPq8rOA7//NX8OLyZkOvzznH9//aV/Gf/uRmw3MSJQXjPjcm/RQQJQiie7Qs6IwxL4DPAvgJznms\nyvPPMsauM8aub242JqpH8c3XdpBI53BrLV4xXuDAKw92K8bVv6XjtXi4c4C1WMrYrxGiskL+c4Ig\nuk5Lgs4Yc0IV8+c5579fbRvO+XOc82uc82vj4+OtHA6cc6MjkF4IS8cYl0rH9fXhorTX0DGisrrd\nrbV4xV1ANRLpHO5sJqhkLkEQXaeVVS4MwMcA3OCc/7J5U6qNtHsA5SALQC2EpZPNF3BjVb05mC8T\net2/LcoxcM7rHkPfPlfgFXcB1VhciYFz8p8TBNF9WrHQ3wLgRwA8zRh7Vfv3TpPmVRXd+h73uUss\n9OX1BNK5AsZ9bsyvKMgXVOFOpnO4vZnAuM+NrUQaa7FU3WPo/nCg8i6g+pxUi96KTaEJgugvWlnl\n8pecc8Y5j3DOH9f+fcHMyZUTlffgstvw3ieCWFo/dImImpvkfW84hf1MHnc3EwCABc16ft8bTqn7\nS0cLdKHAIcoKnpmdxPCgsyE3jSgrmPJ7MOGjgChBEN2lrzJFRUnBlWkfXn9mGPkCx6LmZolKCnwe\nB94VmTEeq39VQf7b107BbmOGP70W93f2EU/l8FhIQDgUqPsDoM+J/OcEQfQCfSPonKvWczgoGP5q\n3V8+r41fnPBi0GU3/ODzsoJpwYNTI4O4POkzxmuhPz8XFBAJCljeSBwZGI2nsri7laQVLgRB9AR9\nI+j3t1XrORwUMOX3YMzrQlRSkMkVcGM1jnBQgN3GcHXGbwhzVFYM33Y4qI4fFRgVpT24HDZcnvRh\nLiiU3AVUY15WnyMLnSCIXqBvBN3o1xlSC2CFgwJEScHSehyZfMEQ1XAwgIUVBXv7GdzdPLSew6EA\ndpIZyHuVWabGMSQFs9N+OO024y7gKDeN7runHqIEQfQCfSPoxdYzoAr08kYcX7+7DQCIaI0lIiEB\nqWwBf/gtWdtO0J4/WqALBY6FlZghztPC4V1ALaKSgmBgAKNetwlnSBAE0Rr9I+jyofUMqAJd4MCn\nv/kQwoATp0bUxsy6gD//0gP1sSbQV6Z9cNpZTT/6ve0kEumcsb9+F1C+rr0Y3XdPEATRC/SFoBcK\nHPNyrEQ8deFd3kggXFSH/NzoELxuB5Y3EiXWs9thPzIwWq3jUDgoYHkjjv1MrmJ7ZT+L17b3yX9O\nEETP0BeCXm49A8Ck34MJLQGoeNymBUaBSt92JCQgKlUPjEYlBR6nDRfHvcZYOBRAgavZoOXMryhV\nj0EQBNEt+kLQa/XrjJT5x8vHy63ncDAA5SCLhzuVgVFR3sPstB8O++Fbor9ONT+6PkaCThBEr9Af\ngi5XWs8AENEaSpQLtz7+WFnDCUOg5dIM0HxZQFRHvwuo5qaZlxWEhgcwPORq4owIgiDMp5WORR3j\nrY9O4NTwQIn1DAAffPNZPDrtR2h4sGT8HXNT+Mj7HsdTF0ZLxi9P+uCy2yDKipFVCgB3NxPYz+SN\nH4JiIiGhqqBH5b2KHwyCIIhu0hcW+lMXxvD33nKuYlwYdOKZ2cmKcafdhnc/HoTNVtqw2eWw4cq0\nr2LpouE+qRLgnAsKuLOZQCJ9GBjdTWbwcOeACnIRBNFT9IWgm0k4KFRkjIqyggGnHRfKXDqAaqFz\nDiwUWel6QJRK5hIE0UucOEGPhATEUzncL2pVJ8oK5oJ+2MsseuCwLG6x20W36OdmSNAJgugdTpyg\nh7WMUr2UQC5fwMKKYoyXM+HzYFrwlAi6KCk4OzoIYdDZ/gkTBEE0yIkT9EuTXrgcNqPW+e3NBFLZ\nAsIhf8195rS6MTpiUdEvgiCIXuHECbrTbsPstL+iB2ktCx1Q17nf3UoilspiO5GGvHdA/nOCIHqO\nEyfogOpHX1iJqR2KJAVDLjvOjw3V3D5cVH9dd70c9QNAEATRDU6koIeDAhLpHO5tJw33SfkSx/Lt\nAU3Q9YBosLaLhiAIohucTEHXLO5X7u9icbUyQ7ScUa8bwcAAopJqoZ8fG4LPQwFRgiB6i77IFDWb\ni+NeeJw2fPYVCZlcoaGKifr69UyugCfPjXRglgRBEMejJQudMfYOxtgtxthtxtjPmjWpduOw23B1\nRsDX7+4AQNWU/3LCIQH3t/exqqSoIBdBED1J04LOGLMD+HUA3wNgFsD7GWOzZk2s3eii7PM4cGZk\nsM7WpVmhjfwAEARBdJpWLPQnAdzmnN/lnGcA/C6Ad5szrfajC/rczNEBUR09K5QxGPXWCYIgeolW\nfOhBAA+LHksA3tjadDqHUUu9wfXkw0MunBoZgNthx5D7RIYeCILocVpRpmpmbUUrIMbYswCeBYDT\np0+3cDhzuTDuxY8/fRHveSLY8D4//d1X4GjAmicIgugGrQi6BOBU0eMQgJXyjTjnzwF4DgCuXbtW\n2futS9hsDP/s7Y8ca5/ve2ym/kYEQRBdohUf+jcBXGKMnWOMuQC8D8DnzJkWQRAEcVyattA55znG\n2I8C+FMAdgAf55wvmDYzgiAI4li0FN3jnH8BwBdMmgtBEATRAicy9Z8gCMKKkKATBEFYBBJ0giAI\ni0CCThAEYRFI0AmCICwC47xzuT6MsU0A95vcfQzAlonT6RdO4nmfxHMGTuZ5n8RzBo5/3mc45+P1\nNuqooLcCY+w65/xat+fRaU7ieZ/EcwZO5nmfxHMG2nfe5HIhCIKwCCToBEEQFqGfBP25bk+gS5zE\n8z6J5wyczPM+iecMtOm8+8aHThAEQRxNP1noBEEQxBH0haD3azPq48AYO8UY+zJj7AZjbIEx9mFt\nfIQx9kXG2LL2d7jbczUbxpidMfYtxtjntcfnGGMvaef8aa08s6VgjAUYY59hjN3UrvmbrX6tGWM/\nqX225xljn2KMeax4rRljH2eMbTDG5ovGql5bpvKrmrZFGWOva+XYPS/o/d6M+hjkAPwU5/xRAG8C\n8E+18/xZAF/inF8C8CXtsdX4MIAbRY//E4D/op3zLoAPdWVW7eUjAP6Ec34FwGNQz9+y15oxFgTw\n4wCucc7noJbcfh+sea0/AeAdZWO1ru33ALik/XsWwG+2cuCeF3T0eTPqRuGcr3LOX9H+H4f6BQ9C\nPddPapt9EsB7ujPD9sAYCwH4XgAf1R4zAE8D+Iy2iRXP2Q/gOwB8DAA45xnO+R4sfq2hluseYIw5\nAAwCWIUFrzXn/AUAO2XDta7tuwH8T67ydQABxth0s8fuB0Gv1oy68UagfQhj7CyAJwC8BGCSc74K\nqKIPYKJ7M2sLvwLgpwEUtMejAPY45zntsRWv93kAmwD+h+Zq+ihjbAgWvtaccxnALwF4AFXIFQAv\nw/rXWqfWtTVV3/pB0BtqRm0VGGNeAJ8F8BOc81i359NOGGPvArDBOX+5eLjKpla73g4ArwPwm5zz\nJwAkYSH3SjU0n/G7AZwDMANgCKq7oRyrXet6mPp57wdBb6gZtRVgjDmhivnznPPf14bX9Vsw7e9G\nt+bXBt4C4PsZY69BdaU9DdViD2i35YA1r7cEQOKcv6Q9/gxUgbfytX4bgHuc803OeRbA7wN4Cta/\n1jq1rq2p+tYPgn4imlFrvuOPAbjBOf/loqc+B+CD2v8/COCPOj23dsE5/znOeYhzfhbqdf0LzvkP\nAfgygB/UNrPUOQMA53wNwEPG2CPa0FsBLMLC1xqqq+VNjLFB7bOun7Olr3URta7t5wB8QFvt8iYA\niu6aaQrOec//A/BOAEsA7gD4F92eT5vO8a9BvdWKAnhV+/dOqD7lLwFY1v6OdHuubTr/7wLwee3/\n5wF8A8BtAP8bgLvb82vD+T4O4Lp2vf8QwLDVrzWAfwfgJoB5AL8NwG3Faw3gU1DjBFmoFviHal1b\nqC6XX9e0TYS6CqjpY1OmKEEQhEXoB5cLQRAE0QAk6ARBEBaBBJ0gCMIikKATBEFYBBJ0giAIi0CC\nThAEYRFI0AmCICwCCTpBEIRF+P86OddqGMrfTgAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x107eca2e8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "def random_walk(n_steps, p=0.5):\n",
+ " return np.cumsum(2*(np.random.binomial(size=n_steps, n=1, p=0.5)-0.5)) # Bernoulli\n",
+ "\n",
+ "n_steps = 100\n",
+ "w = random_walk(n_steps)\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.plot(range(n_steps), w)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Simulate ~1000 random walks of 500 steps.\n",
+ "\n",
+ "* Plot the average distance (rms) of these over the whole set with respect to step index (time). Does the average converge to the expected distance?\n",
+ "\n",
+ "* (Optional) sample and plot the running average to show how the convergence improves with number of walks."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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2kC+MH0rLMU8WJH2pNBxfokQAIDcLNn2kQj4UJwan16gw0kHN4Nbx0G60Ch2h\nqbSUKARCiMnA3cB6YAcQD7gDTYFpFpF4UUp50P5majSOJ92Uzoz9M1i4azb/OujFHbuycE834962\nOYGvP4RPnz4I50rayD5aqOvSrx7s/Fb9jfkLGt5RtO6mj9VnbqaaM6BFoNJT2lW7S0o5uYRtHwsh\ngoF6ZW+SRlOxkFLy49EfWbj2K3ptTeXrwwJDXirevXoR+MjDeLRvX7lni0sJEZuh1TD1hl+zGWz5\nVLUKIrdcKQSZSepz2Hflb6vGLpQoBFLKpZeXCSGcAG8ppVFKGY9qJTgMKWXlvgGvAR3VtPzJMGWw\n5MxiDq6dT9MVx5lySiJdXagxfBgBY8fi1tCO4ZzLk7MbVXawRr0grJMq6/0GnFgOMXuL1s3JgIvH\nofvLUO/W8rdVYxeu2o4VQvwCPAHkAXsAPyHEx1LK6fY2rjTc3d1JTEwkMDCwyouBlJLExETc3d0d\nbUq14VxSBLO+fJz2a88xOhZyvN0JHP8wAaNH41wowmylJ3+Q2KcOtB5RdFtoJ9g7Bw79D06tgh4T\nIT1RTSILaecYezV2wZYOzZZSSqMQYjSwDHgVJQilCoEQYhZqoDleSnmTpWwy8Chw0VJtkpRy2fUY\nHhoaSnR0NBcvXrx65SqAu7s7oaGhjjajypOXns6qrybiuWAtI5Mlpjo1qfXGk/jfMxQnDw9Hm1e2\nmPPgn3UQtR0GfgQul71o9H5TbV8wTq3nmaD+bWo5RGfgq0rYIgQuQggXYCjwhZTSJISwpZ9iNvAF\n8ONl5Z9IKT+8NjOLMcrFhfDwKtI01zicvJQULv38M+d/+I4GqVlcaOiP9+svEtr/HoTB4Gjzyp4T\ny+HX0SDzwC8Mbh5zZR2vQOj0KKz+j1o3nleTyDwCwE+/lFQlbBGCb4AI4ACwUQhRHzBebScp5UYh\nRIMbMU6jsTem+HguzZ7DpV/nQUYmhxoLEp/qwTNjv6raXY5/v6tEAKDTOHB2Lb5e58chOxX2/ggx\neywpJYfoCKNVjKsKgZTyc+DzQkWRQogbmT0yQQgxBtiNcj9NuoFjaTTXRc65cyTOnEXKH39gzstl\nR0sXVnUPYOCdTzK++ciKIwI5GTCzj0rp2P/9snkAZxlVXuF8Gt9Zcl1nN+j1f9B8IHx7h0oo3/vN\nG7dBU6GwZbA4EHgT6AZIYDPwNpB4HeebAbxjOc47wEfAIyWc9zHgMYB69bSXqqZsyDpxgsRvv8O4\nfDkYDGwDnjwDAAAgAElEQVRoY+B/ncwENW7B9O7TSwwA5zAuHoO4w+rvlkchqMn1Hys3B9a9BxdP\nqAHfjo+o7p7gVlffN6StGkwOvwP8KnGMJE2x2NI19CuwERhuWR8NzAdKeY0oHillXP6yEOI7oMRk\npVLKb4FvATp27Kh9JzU3RMbefSR++y1p69cjPdw5eVczfmh1kX9ck2kR0JIven9BkEeQo828koTT\n1uVTq6xCcH4/xB6A9mNsbyVEbVfzAwA8A6HvFHCxcQBcCBj+ve12ayoVtghBgJTynULr7wohriuo\nvhAiREoZa1m9BxWuQqOxC1JKMrZtI2HG12Ts2oWTvx9Hh7Vler3DmH2iaRPUhg86vUyzgGaONtVK\nZjKcXKk8eFoOgcTTKrqnf304tRq6PKXqzRsFqefVm32Hh9SnUzGD2mYzHF4Abj6QfE6V9XgNWg61\nXQQ0VR5bhGCdEOI+4DfL+r+AKyabXY4QYh7QAwgSQkSjupd6CCHaobqGIoDHr8NmjaZUpJSkb9lK\nwpdfkrlvHxn+Hhwd2YalrXM4mn6UEU1H8lKnl/BwrmAPQrMZPmquQjeA6rs/vQZqhKs++p3fQlo8\nZKUoEQBYMVEJRNQOGDEb9vwASREqLHRKDGRegj2zVd2QduDuB3e8qgd7NUUQV5uxKoRIBbwAM+oB\nbgDSLZullNLXrhaiuoZ2795t79NoKjlSStI3bSLhy6/IPHCAjBoe/NIpm3VtBSZnQbBnMC93epl+\nDfo52tTiuXQWPi9molbvNyDsVpg9wFrm5gsPLYW590BGwtWPbXCDvGyo1wUeWVF2NmsqNEKIPVLK\nK+PkX4YtXkM+ZWOSRmMfpJSkbdhAwldfkXXwEJmB3iwbWpMFTS4xrOV9LGr1EFFpUbQKbIWfm5+j\nzS2e9ASrCHSZANu+UB46o3+HBt3VG3zrEXDod1Wn7X0Q0kY91A/8CrVawopJ0KSP6kraO8d67Nqt\n1TyB5S9Dt+fL/7tpKjy2eA0J1ABxuJTyHSFEGBAipdxpd+s0mlKQUhK/agnxX36J88lIEvwN/K+/\nExtaZ9KyVhM+aj2ZXvVUwpQK5w2UT3YamDJhayEP7Tb3KiHo8Ro07GEtH/YdnNsOKVFQ52ZVFtQE\nelsmfN1k8efISVepI9e+Dbc9ox7+ngHQdqTqGtJoLsOWMYKvUN1CvVAun2nAl0AnO9ql0ZSIlBLj\n6tWc/OQ9vM/Gk+APiwY6k3tXV+r412NxywcJ86lgD/7MZPh5hPLUCSt06/z8Lzi3DVwsid/r3Kxc\nNV84fmUuACHAO1gJQe02JZ/L1UvlErjtWTWAnD8eoEVAUwK2CEFnKWV7IcQ+ACllkhCihGmIGo39\nkFIStWoR8Z99htc/F0itAdseaE7nh17m3eA2eLt6O9pERcJpCGxkfQDn5aqZudE7VbiG4d+riWIB\n4UoEQAV/e+4Q+FvmzPiGFH/sYd/B/p8huOXV7TBU0twImnLHlivFJIQwoAaKEULURLUQNJpywSzN\n/PX7VLx+WETo2VTS/GH2QCe6j3udJ5v9CxeDi6NNtHJ2E8wZBF414YEFgIBf7lVhngGSo+CzdmA2\nqclZ+dw52SoCpRHYSA0eazRliC1C8DnwJxAshHgP5T76H7tapdFYmL/gHdxmLqDZP9kk+sBPg7yp\nN+ohxjfoSctAG96Ky5M8E5xerZbTL8Kat1R/vTlXPbzNeWpmbz5nN6hkMP+apd05NQ7FFq+hn4UQ\ne4DegACGSimP2d0yTbUlPiOeqD0bSfzvF7Q5GEe6tzOXHhtCm0dfopWLgRruNcrfqMitsOMbcPOG\ngR+rGDyFSU+Az2+GbKPy9snLgTNr1bb+H1iDtxUWAlAx/rUIaByMLV5Dc6WUDwLHiynTaMoEKSWb\nYjaxcfMv1Pl1I12OS6Q7HB/RgQGvfImbj4MHOlf+H5y3ZOvq8DCEXuaavXuWEgGAoTMgJw0WPwsI\nuPkBVe7mA/f+CFu/gAbdVMyeoKbl9hU0mpKwpWuoSEQqy3hBB/uYo6mOmKWZ1xc8Tuj8LdxzWJLn\n5kzyqJ40e/JlOgZXEO+f/D5+gISTViFIPgc7v1PunwENoe0o1d0jzZCbrUJDuHpZ9205RP1pNBWI\nEoVACPEaMAnwEELk5x8QQA6WYHAazY2Sl5LCqneeYOTy/TgLAwFjRlPz8cdxDghwtGkKKSHhlBKC\nPu8o3/yEk9btW7+And+o5bs/g/Dulg1OqjtIo6kElJa8fiowVQgxVUr5WjnapKkGmLOzufTTT8TO\n+IJ6aVlEdqnHne/MxLWipePc/hWsnKSWw24BnxDY/IkK+dCsn3L/bHA7DJ8JPrUca6tGc5042VBn\niRDCC0AI8YAQ4mNLljKN5pqReXkk/7mQE3f14eL0DzkUnM3cV9rSZ+aSiicCAEcWWpdrt4aeFlH4\n+13Y8AFcOKjy+GoR0FRibBkjmAG0FUK0BV4BZqLyEN9R6l4aTSHyA8JdmD4d06nTnA0xsHCsPwNH\nTOS9hoMwFBdC2dGsm6ImgeXj6gXtRqmInisnQdwhaNQLbtZ+E5rKjS1CkCullEKIIcBnUsqZQoix\n9jZMU3U4u3MNkVPeptbxi1zwh3lDnLjYuRFvdnuLdsHFRNusCERshg3vW9cHfWJdrtfFunz/73oG\nr6bSY8sVnGoZOH4A6G7xGqpAUzk1FRVTfDwR06eQs2QlHu7wx6AAao4azdjabbmtzm0VJy9wcWyf\nYV1u2k+ldcyndmv1GdhYi4CmSmDLVTwSuB8YJ6W8IISoB0y3r1mayow5K4tLs+eQ8M03mHKyWNPF\nnbve+IbX6nfESdgyLOVgEk6phDCd/q2if4beUnS7wQWe3KoGjjWaKkBp7qNCKi4AH+eXSynPocYI\nCurY30xNZUBKSery5cR9+CG552PZ3dyZOT2ceGnIVFo1uOXqB6gIJJ+DLyxzBELaQYu7i69Xy4aE\n7xpNJaG0FsE6IcQCYJHl4Q+AJfJoN2AssA6YbVcLNZWCzIMHiZs6jcx9+7gU5sfn9zvh3qk9U2+e\nQKfalShi+fFl1uX8LiCNpopTmhD0Ax4B5gkhwoFkwB2VqnIV8ImUcr/9TdRUZExxccR99CGpfy0h\n3ceFHwc4sb51Gg1qNOKHO2fgmR9nv7JwfIn6NLhBzeaOtUWjKSdKm1CWhUpK85UQwgUIAjKllMnl\nZZym4iJzcoid9R0JM2Ygc/NYcptgW++a/Kvtg0xtNgJXgysuTpXMpyDjEkRugdtfsmb90miqATa5\nPEgpTUDsVStqqjy55lzW/fEpnv+dR0BcBgeaCCIfvpPOHQbzalhPnJ0qsRfN0UUqRlCLQY62RKMp\nVyrxXaspT6SU7D+8hrPvvkmLA0nEBxhY8mQ7+o/+Px4MusnR5pUN+3+Bmi3UILFGU43QQqAplYTM\nBGbu+RoxfzF91htpBCQ8eBddX5zGHe4ejjav7MgyQvQuuONVnR9AU+2wSQgssYWaSCnXCCE8AGcp\nZap9TdM4mszcTP779Tju+P0UIZckqV1a0WzyNPzqN3a0aWVPzB5AqsByGk01w5bENI8CjwEBQCMg\nFPgalbFMU8WQUhJpjGTt/v/h/eVv3HcwFVOdIMK+m4r37d0ca9yG6Soa6J2T4Z910HcK+Na5sWNK\nqTyFdnwDiCsTzmg01QBbWgRPAbcAOwCklKeEEMF2tUrjEDJMGTy79hm8Vmxj9HozbibIeGgIN7/w\nNk6uro42D478oQK+LX5GrUuzyvh1I+z5AZY8r5brdQF3B2dC02gcgC1CkC2lzMmPCyOEcAb0bOIq\nxv74/Xzw2wRGLEykeTRkt2lC42kf49mwgnQD5eYUTQgDcGIFZKVc38N70QRIjlThJDwCIKgJ9Hm7\nbGzVaCoZtgjBBiFEfqayPsB4YLF9zdKUF1JK5h2YQ/QXn/LatmwMXt6ETJmE3z1DK1ZQuISTYM6F\ne75RsX5y0uGvp+H4Umh3/7Ufb99c6/Ldn0MHHVBXU32xRQgmAuOAQ8DjwDLge3sapSkfpJT89NOr\n1P1qMTcngfOAOwl//a2KkyayMPkzfkM7QWAj1be/biosfBI8akCz/sXvl54AGz+EWx5V+wGkJxat\nU9K+Gk01wRYh8ABmSSm/g4Lk9R5Ahj0N09iXf2KOcGjyi3TcFElqsDdhMz/Fu2tXR5tVPGazShDf\ntL/1YS4EhHaAY+dh3n3w3GHwLybR/d/vwJ7ZcHIFPLNP7ZffxdTjNfAMBG895KWp3tgSE3gt6sGf\njwewxj7maMqDVfPfJ+aeETTeHEnkoJu5ecX6iisCAHGHISMBWg0tWt79FZU7WBhg/ugr90s4DXvn\ngrM7JJ1Vg8wHf4P5D6jt7UarloJGU82xRQjcpZRp+SuW5UoWSUwDEBlzlHkPdiXszdkID3f8fviS\nfh/+gounl6NNK52ji9RnePei5SFtYNxK6DERYg9AdlrR7eveVSLw+Ca1vvdH+ONRJSq3PVN8C0Kj\nqYbY0jWULoRoL6XcCyCE6ABk2tcsTVlzeul8Et96lzapuZwb0pGek7/G1aOCCYCUV87qNcbCpo9U\nXoCS5gzUbKY+986BlkPg4gkIbglH/oTbX4SaTWHSefh5hBpPGP49uFShWdEazQ1iixA8B/wuhDhv\nWQ9BZS3TVAJykpPYM+kp/P/eR2pNJ3Lee4W+fR52tFlFSY1TD+ilz0PkVtWXn8/F44CEWx4vef8g\nixCsnKT+wJpjuPGd6tPVCx5aqsNHaDTFcFUhkFLuEkI0B5oBAjhuiUZaKkKIWcAgIF5KeZOlLACY\nDzQAIoB7pZRJ1229plTStm3jxAtP4ZOcyYbeNRk+5Vdq+t3gTNyyxhgLn7eD3CxrWXoCeAWp5aQI\n9VmjQcnHCGh4ZVn+JLHCOQW0CGg0xWJrAtlOQBvgZmCUEGKMDfvMRiW3KcxEYK2UsglqEHqijefX\nXAPm7GwuTJtG1MOPkCwy2TF5KP/+798VTwQADv2mRKBw/t+ondblpAgwuJYeSsLZFcbvgJdOw4AP\noc191m2eFdAVVqOpYNgSa2guKsbQfiDPUiyx5C0uCSnlRiFEg8uKhwA9LMtzgPXAq7Yaq7k6WSdO\ncOrZ8ThHnGflzYKoMT2Z3u+9ipk0Pi8Xds1Unj8PL4fYfTCrP0RshuYDVJ2ks+BfD5wMpR8r2PLm\nf8uj0H6Mcgn1qmlf+zWaKoItYwQdgZZllKS+lpQyFkBKGVsdYhaZ8sz0+XgDL/dtzsA2IVff4TqR\nZjP/fP0pWV/NJM1dsuiRMNoOfpjHGg2pmCIAsOF9Feah7xRwcoK6HaD+bXB6DTAFkqPg5Cpodc+1\nHdfZDe56xy4mazQlcfd/NzOyUxgP3Frf0aZcM7YIwWGgNuWcoUwI8Rgq6in16tUrz1OXKUkZOUQk\nZnDkfIrdhCD7Qixnnn8ase8Iu5sKDv/7dl67ayoB7hW4W8Rshm1fKm+g5gOt5Y17w6rX1djBlk9B\n5kHP1xxnp0ZjA6Y8M4diUriprq+jTbkubBGCIOCoEGInkJ1fKKUcfB3nixNChFhaAyFAfEkVpZTf\nAt8CdOzYsdIGuUvJUOPqyZlXHV+/LmJXLeH8a6/hlJPL3EFuPPraPMYGtrDLucoUYzSY0qFRr6KD\nuHUtYaBPr4F9P0Hb+1TXkEZTgUmx3N/JGfa5z+2NLUIwuQzP9xcwFphm+VxUhseukOQLQEoZXyAy\nJ4fdbz2P94K/uRgsiH7rPl7q8Sh1vCvggHBxXLSEeSjs1QNQ+yZAwF8T1Odtz5a3ZRrNNZMvAFVW\nCKSUG67nwEKIeaiB4SAhRDTwJkoAfhNCjAPOASOu59iViYILJDOnzI6ZExXFgfFj8T4Vy+bO3nSb\nNpN+IW3K7PjlwsVj6vNyIXDzgYBwuPQPtBwMQRUkDLZGUwoplvvbXi1/e2OL19CtwH+BFoArYADS\npZSldoZJKUeVsKlaZTZLyrBcIGX0ppC4bDGxr/8HkZfN6sduZvxzP+LsVElST5/fD+e2AUKNA/jX\nL9698+7PYON06DGp3E3UaK6HpPT8ln/ZvfCVJ7Y8Qb4A7gN+R3kQjQGa2NOoqkRKGTUZZU4OJya/\nhvxjGWfqwOIxTfj4/q8rjwiYzTCzD+QVulGCWxZfN7z7lXGFNJoKTH5LoMq2CACklKeFEAYpZR7w\ngxBiq53tqjLkdwml3MAFYoqL48xTTyAPH2fprc7UfuElvmx1H24Gt7Iy0/7E7isqAgBddf+/pmqQ\nbGkJZOTkkZ2bh5vzVea9VDBsEYIMIYQrsF8I8QHKjbSCRSurmByOSeHoeSMAadm55OSacXW+Np/+\nDX99hfc73yCyc5hzry8vvPQb9X3Lxk85NiWTqEuZZJryuKOpnSdfRe9Rn88egDyTSg2p0VQSNp68\niLuLgbAAD0L8igYsPBmXyv6o5IL1lAwTwb5VTwgeRIWimAA8D4QBw+xpVFVh0H83F1lPyTRR08e2\nt3gpJRs/fJnAWUuJCxDMfrg2b42eWWYiANBj+nqyc80ArH6+O01q+dz4QXd8o5LH5Ad7yydmD3jX\nUuMCOuaPphJxOj6VMbNU2BMXg+DUewOKbL/rk41F1pMzTQT7upebfWWBLUIwVEr5GZAFvAUghHgW\n+MyehlVFUjJzbBKC6PjTHH/5GeruOMvJtoH0+WYhvfwCyzyHcL4IABizyqBvMzcblr+ilienqM/E\nM5ASpZLLhLTVIqCpdBTu1jXlXX1KU2V0IbVFCMZy5UP/oWLKNIXIzs0rWHZ1diIn13zVCyTDlMGi\nzd8R+Ma31E0ws3dYK0a8/Quuzq72NpfMHPPVK12N8/uty2Yz/DLCEi4CEE7QoNuNn0OjKWdsvTes\n93nl8xwqUQiEEKOA+4FwIcRfhTb5AonF76XJp/BbRP0AT07Fp5UqBEcSjvDRrH/z+LxkXHEmZ/rL\n3D9wbJm3AkqiTOY5RBeKGrrhfasIAEhz6aGkNZoKSmn3hinPKhIF93kl9BwqrUWwFTUwHAR8VKg8\nFThoT6OqAoVnEtcP9Cr1AjmSeIS5Hz3C838ZcQqpTePvZuEWHl5epgJl1JyNP2Zd3jBNRRUdsxDe\nq63KtBBoKiGl3RuFX/hCa3hwKj6tzKMIlAclurBIKSOllOuBO4FNlhnGsUAoKkGNphQKP/TDApSX\nQXFNxmMXj7DylQcZ+6cRl5vb0nzBwtJFYO9cmN4Y4o5A9G6V3vE6uDyY7I24txYQfwzC77CuD/xQ\npYQMaafWdcwgTSXk8nuj8L1TWCR83F0wOIkyjSJQXtjiy7gRcBdC1EUlk3kYlXRGUwqFLxA/Dxec\nxJUX1P6I7ez79yj6b8nEefggmv0wF4OfX+kH3vU9pF+EGbfB971VhM7rICMnr8j6DfdrpkTD+b0Q\n3AJ6va6iitZurbaN/h36vFPyBDKNpgJz+b2RXujeSSn00BcC/D1cquxgsZBSZljiA/1XSvmBEGLf\nVfeq5hS+eJyEwO+yC2T7kZUkTniBthfMeLz8NA3GjbftwK6WKRxdn1PhGtZPgzYjS8/gVQxJl13c\nSTdy8SafgxmWgeA67aHtZSmtvYOh6zPXf3yNxoFc/mBPzsjB28252G1+ni6VcozAlhaBEEJ0AUYD\nSy1llSSuwZWY8sw8++s+TlxItds5ft8dxQcrTxSsuxic8Pd05X97opm2/Bhrtswl89/PE5og8f90\nmm0iICUsewUit6hUjH3egmHfgjkXtnymuol+HQ3ZaTbZeOXFfQMX76lVkJ0CD/4Jbe4tKJ6x/gwL\n9kTbfJjlh2L5eNWJK8q3nkngjUWHr9++CkaeWfLC/P0cjlEuticupPLsr/uKDDzam+zcPJ76ZS//\nXLTteqnOXP5gz79XVhyO5Y1FRwrK3Zyd8PdwuWKM4LM1p1h84DzHYo089+s+csvx/2wrtgjBc8Br\nwJ9SyiNCiIbAOvuaZT/OJ2eyaP95Np68aLdzvPy/g1xMVakbxnSpz5gu9fHzcCHTlM3mDe/g/fQU\nfHIM1Jn1HXX7DrHtoEcXwc5v1HJ+q6BGAxWvf8fXqpvo+BLY/hWcWqMSu+Rz4RBE7SpyuPxuqm6N\ng/DzcCnSxL1m4o+Bmy807FlknsC8nedYuD/G5sMsPnieudsjryhfdSSOH7dFkpNb8W6g6yE+NYs/\n9sWwwXINbjgZz6L954lNzio3G84mpLP0YCxbzmgHwKuRnJGDv6cL3RoHWdbVvfPET3uJSc4EYNjN\ndXm1X3P8PV2vaG3/tCOSxQfOs+HkRRbuP09sSvn9n23F1jDUGwqt/wNU2na+PcJCl0SglytvD7kJ\nAF9P6Gb+lBeXXyDL140Wc3/Hq2EJYRa2z1D5dlOioUkf2PwJHPrduj2/7x3gjolq4Pi8pbduy2eQ\nkwZ+9WDCTpUF7G9L2sb8SV5Yf4f/DGrJp2tOcjr+Bt4M44+rcNKXubrm30C2kpxhIiXThNkscXKy\nHitftK5lZnZFxhq7vmhk2uTMHOrhWa4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ZGS6l65fP0t30uvvjfOrXKqXFGbPG5rjtGdET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\nH7t/HSteO8jS//oLsXjKlt3C7I2XcQSIs+irK3h+59Ec4TBphOierVD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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x107eca438>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x110bd8cf8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "### Bernoulli\n",
+ "n_steps = 500\n",
+ "n_walks = 1000\n",
+ "n = np.arange(n_steps) +1\n",
+ "\n",
+ "W = [] # Final distance\n",
+ "A = [] # Running average over whole set\n",
+ "T = 0\n",
+ "for idx in range(n_walks):\n",
+ " w = np.abs(random_walk(n_steps))\n",
+ " W.append(w[-1])\n",
+ " T += w**2\n",
+ " A.append(np.sqrt(T/(idx+1)))\n",
+ " \n",
+ "plt.figure()\n",
+ "plt.plot(n, np.array(A).transpose()[:,[0,20,-1]])\n",
+ "plt.plot(n, np.sqrt(n))\n",
+ "plt.legend(['0', '20', '1000', r'$\\sqrt{N}$'])\n",
+ "plt.xlabel('Step #')\n",
+ "plt.ylabel('Distance (steps)')\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.hist(np.array(W), normed=True)\n",
+ "plt.axvline(np.sqrt(n_steps), color='r') # Expected distance\n",
+ "plt.xlabel('Dist D')\n",
+ "plt.show()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Now consider the case $p \\ne 0.5$, where the \"person\" is more likely to step in one direction than another. Find again analytically the expectation and the variance for the (rms) distance travelled in terms of $N$ and $p$.\n",
+ "\n",
+ "Expectation: $N \\left|1-2p \\right|$\n",
+ "\n",
+ "Variance: $N$\n",
+ "\n",
+ "* Modify the random_walk function to account for the unequal probability between the directions."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Run a series of random walks as before, and plot again the histogram of distances travelled. On top of this, plot the Gaussian PDF with the $\\mu$ and $\\sigma$ parameters as determined above."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x11072d6d8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot histogram\n",
+ "n_steps = 2000\n",
+ "n_trials = 5000\n",
+ "p = 0.4\n",
+ "\n",
+ "V = []\n",
+ "for n in range(n_trials):\n",
+ " V.append(np.abs(np.sum(2*(np.random.binomial(size=n_steps, n=1, p=p)-0.5))))\n",
+ " \n",
+ "plt.figure()\n",
+ "plt.hist(V, 40, normed=True)\n",
+ "plt.plot(range(500), stats.norm.pdf(range(500), loc=n_steps*np.abs(1-2*p), scale=np.sqrt(n_steps)))\n",
+ "plt.axvline(n_steps*(np.abs(1-2*p)))\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 3. Small sample sizes: t-distribution\n",
+ "### 3.1 Compare to normal distribution\n",
+ "\n",
+ "Student's t-distributions are interesting for cases where you have few samples and the population variance is unknown, but the underlying distribution of the means can be assumed normal. They are parameterised by the degrees of freedom (\"df\"), which is usually equal the number of samples minus one. As the number of degrees of freedom increases, the t-distribution converges to the normal distribution.\n",
+ "\n",
+ "* Plot the standard t-distribution for several increasing degrees of freedom and compare this to the normal PDF.\n",
+ "* Plot and compare the cumulative distribution functions\n",
+ "* Plot the variance of the t-distribution as a function of degrees of freedom. Compare to the standard normal variance (=1)\n",
+ "* (optional) make a Q-Q plot (see Wiki) and compare the distributions\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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6JY65+XNZvms5/pAfgMEZg3E73K2WjvAFfUw+20tKCmzd2ilhGGOMMXGLJ+nK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\nEEII0Qsk6RJCCCGE6AWSdAkhhBBC9AJJuoQQQgghekGfmzIiOztbjxg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XAAAg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\nXXRJSgM3A0cBLcALklaY2bpui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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1a11a96b38>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x = np.linspace(-5, 5, 200)\n",
+ "df_all = [1,2,5,10,30]\n",
+ "\n",
+ "fh, ax = plt.subplots(2,2, figsize=(10,8))\n",
+ "\n",
+ "# PDF\n",
+ "for df in df_all:\n",
+ " c = 1/df\n",
+ " ax[0,0].plot(x, stats.t.pdf(x, df), 'g', alpha=c)\n",
+ " #plt.axhline(stats.t.pdf(0, df), color='g', alpha=c)\n",
+ "ax[0,0].plot(x, stats.norm.pdf(x), '--', color='b')\n",
+ "\n",
+ "# CDF\n",
+ "for df in [1,2,5,10,30]:\n",
+ " c = 1/df\n",
+ " ax[1,0].plot(x, stats.t.cdf(x, df), 'g', alpha=c)\n",
+ "ax[1,0].plot(x, stats.norm.cdf(x), '--', color='b')\n",
+ "\n",
+ "# Variance vs degrees of freedom\n",
+ "ax[0,1].semilogx(range(1,30), stats.t.var(range(1,30)), 'o')\n",
+ "ax[0,1].axhline(1) # Gaussian\n",
+ "ax[0,1].set_xlabel('DOF')\n",
+ "ax[0,1].set_ylabel('Var(T)')\n",
+ "\n",
+ "# Q-Q plot (optional)\n",
+ "for df in [1,2,5,10,30]:\n",
+ " c = 1/df\n",
+ " ax[1,1].plot(stats.norm.cdf(x), stats.t.cdf(x, df), 'g', alpha=c)\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 3.2 Eggs\n",
+ "An egg producer claims to supply eggs with an average egg weight of 63 g. In a box of 12, the following weights were measured (all in g):\n",
+ "\n",
+ " 62.75, 56.98, 53.30, 62.65, 57.63, 57.23, 56.65, 64.89, 57.87, 60.42, 57.01, 63.65\n",
+ " \n",
+ "* Calculate the sample mean and (adjusted) sample standard deviation.\n",
+ "\n",
+ "* What is the probability of obtaining this average weight or lighter, given the supplier's claim?\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Probability of this sample mean (59.25) against claimed mean (63.00): 15.58 %\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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TeUTnlla52fAZZJ1jfNZN5w3dV/6vdmgZhrSvy+Qt6Zy74jbY/LXnDYQqkQpS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\niEQaYzrk105HcJcg6VkuRk3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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x11061bf60>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "s = [62.75, 56.98, 53.30, 62.65, 57.63, 57.23, 56.65, 64.89, 57.87, 60.42, 57.01, 63.65]\n",
+ "n_samples = len(s)\n",
+ "dof = n_samples-1\n",
+ "mu_samp = np.mean(s)\n",
+ "sig_samp = np.std(s, ddof=1) #/np.sqrt(n_samples-1)\n",
+ "mu_claim = 63\n",
+ "\n",
+ "x = np.linspace(mu_claim-10, mu_claim+10, 500)\n",
+ "fill_sel = x <= mu_samp\n",
+ "\n",
+ "t_pdf = stats.t.pdf(x, dof, loc=mu_claim, scale=sig_samp)\n",
+ "p = stats.t.cdf(mu_samp, dof, loc=mu_claim, scale=sig_samp)\n",
+ "\n",
+ "print('Probability of this sample mean ({:.2f}) against claimed mean ({:.2f}): {:.2f} %'.format(\n",
+ " mu_samp, mu_claim, p*100))\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.plot(x, t_pdf)\n",
+ "plt.plot(x, stats.norm.pdf(x, mu_claim, sig_samp))\n",
+ "plt.fill_between(x[fill_sel], t_pdf[fill_sel])\n",
+ "plt.text(59, 0.01, '{:.1f} %'.format(100*p), color='white', horizontalalignment='right')\n",
+ "plt.axvline(mu_samp)\n",
+ "plt.xlabel('Egg weight (g) (W)')\n",
+ "plt.ylabel('P(W)')\n",
+ "\n",
+ "plt.show()\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Within what range would 95% of samples follow? And how would this compare with an equivalent normal distribution?\n",
+ "* Plot again the two distributions, marking the 95% intervals"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Normal: 57.19 to 68.81\n",
+ "T: 56.66 to 69.34\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.text.Text at 0x1a1193cc88>"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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jys/ad8HdizfOdsHP250R7WrbnUgVA38fD+5uX5t5O89wptE91pHFKb2hsTQr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\nYDCw1BhjRKQy8B3wtDFmtQs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OQCAQ7/wa4Hwe4OJcJWH/yitXSdi/fperJOxfuT7/SaB2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\nwgAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x110cb36a0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "t_ppf = lambda pc : stats.t.ppf(pc, dof, loc=mu_claim, scale=sig_samp)\n",
+ "norm_ppf = lambda pc : stats.norm.ppf(pc, loc=mu_claim, scale=sig_samp)\n",
+ "\n",
+ "def print_CI(dist, dfunc, cl=0.05, cu=0.95):\n",
+ " print('{}: {:.2f} to {:.2f}'.format(dist, dfunc(cl), dfunc(cu)))\n",
+ "print_CI('Normal', norm_ppf)\n",
+ "print_CI('T', t_ppf)\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.plot(x, t_pdf)\n",
+ "plt.axvline(t_ppf(0.05))\n",
+ "plt.axvline(t_ppf(0.95))\n",
+ "\n",
+ "plt.plot(x, stats.norm.pdf(x, mu_claim, sig_samp))\n",
+ "plt.axvline(norm_ppf(0.05), color='darkorange')\n",
+ "plt.axvline(norm_ppf(0.95), color='darkorange')\n",
+ "\n",
+ "plt.text(59, 0.01, '{:.1f} %'.format(100*p), color='white', horizontalalignment='right')\n",
+ "plt.xlabel('Egg weight (g) (W)')\n",
+ "plt.ylabel('P(W)')\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Bonus\n",
+ "A pair of independent, standard normal random variables can be generated by sampling a uniform distribution. One approach to this is the Box-Muller transform (see https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform).\n",
+ "\n",
+ "* Generate a long sequence of numbers drawn from U(0,1)\n",
+ "* Use the Box-Muller transform to convert these to normal random variables\n",
+ "* Plot the normal samples on a scatter plot - verify they are not correlated\n",
+ "* Plot the histograms, and superimpose the normal PDF\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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hxSqkMDaVpNZdY5mQZlMryl2CO8izqAugWDrk4HJNXzsrqUm63xPiWCD0CUGL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\nK4D/ldLxO0K32SVV45XJR15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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1106b9eb8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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Y540x0fbDFbTNV7CcMWajMeZgJ7Ml296lNowxYWDPUhuWMsa8Qhfz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\nlVIqA2lxV0qpDPT/AbNcQ8vwJSyaAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x11049de80>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Box Muller method\n",
+ "u1 = np.random.rand(1000)\n",
+ "u2 = np.random.rand(1000)\n",
+ "x = np.sqrt(-2*np.log(u1))*np.cos(2*np.pi*u2)\n",
+ "y = np.sqrt(-2*np.log(u1))*np.sin(2*np.pi*u2)\n",
+ "\n",
+ "z = np.linspace(-4,4,500)\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.scatter(x, y)\n",
+ "plt.xlabel('u1')\n",
+ "plt.ylabel('u2')\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.hist(x, 50, normed=True, label='n1')\n",
+ "plt.hist(y, 50, normed=True, label='n2')\n",
+ "plt.plot(z, stats.norm.pdf(z), label='Normal PDF')\n",
+ "plt.legend()\n",
+ "\n",
+ "plt.show()\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Improbable events\n",
+ "In this example, we tabulate the amplitude deviation against the probability, odds (inverse probability), and equivalent timescale (once in 10 thousand years). Modify the code and try with different distributions - especially those which look similar to the normal distribution, but carry a fatter tail."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<div>\n",
+ "<style>\n",
+ " .dataframe thead tr:only-child th {\n",
+ " text-align: right;\n",
+ " }\n",
+ "\n",
+ " .dataframe thead th {\n",
+ " text-align: left;\n",
+ " }\n",
+ "\n",
+ " .dataframe tbody tr th {\n",
+ " vertical-align: top;\n",
+ " }\n",
+ "</style>\n",
+ "<table border=\"1\" class=\"dataframe\">\n",
+ " <thead>\n",
+ " <tr style=\"text-align: right;\">\n",
+ " <th></th>\n",
+ " <th>|X| ($\\sigma)$</th>\n",
+ " <th>p</th>\n",
+ " <th>1 in</th>\n",
+ " <th>time equivalent</th>\n",
+ " </tr>\n",
+ " </thead>\n",
+ " <tbody>\n",
+ " <tr>\n",
+ " <th>0</th>\n",
+ " <td>1</td>\n",
+ " <td>3.173105e-01</td>\n",
+ " <td>3.151487e+00</td>\n",
+ " <td>3 days</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1</th>\n",
+ " <td>2</td>\n",
+ " <td>4.550026e-02</td>\n",
+ " <td>2.197789e+01</td>\n",
+ " <td>3 weeks</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2</th>\n",
+ " <td>3</td>\n",
+ " <td>2.699796e-03</td>\n",
+ " <td>3.703983e+02</td>\n",
+ " <td>1.0 years</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3</th>\n",
+ " <td>4</td>\n",
+ " <td>6.334248e-05</td>\n",
+ " <td>1.578719e+04</td>\n",
+ " <td>43.3 years</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>4</th>\n",
+ " <td>5</td>\n",
+ " <td>5.733031e-07</td>\n",
+ " <td>1.744278e+06</td>\n",
+ " <td>4.8 millenia</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>5</th>\n",
+ " <td>6</td>\n",
+ " <td>1.973175e-09</td>\n",
+ " <td>5.067973e+08</td>\n",
+ " <td>1.4 million years</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>6</th>\n",
+ " <td>7</td>\n",
+ " <td>2.559730e-12</td>\n",
+ " <td>3.906662e+11</td>\n",
+ " <td>1.1 billion years</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ " |X| ($\\sigma)$ p 1 in time equivalent\n",
+ "0 1 3.173105e-01 3.151487e+00 3 days\n",
+ "1 2 4.550026e-02 2.197789e+01 3 weeks\n",
+ "2 3 2.699796e-03 3.703983e+02 1.0 years\n",
+ "3 4 6.334248e-05 1.578719e+04 43.3 years\n",
+ "4 5 5.733031e-07 1.744278e+06 4.8 millenia\n",
+ "5 6 1.973175e-09 5.067973e+08 1.4 million years\n",
+ "6 7 2.559730e-12 3.906662e+11 1.1 billion years"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "from IPython.display import display\n",
+ "import pandas as pd\n",
+ "\n",
+ "def format_days(d):\n",
+ " if d < 365:\n",
+ " if d > 90:\n",
+ " return '{:1.0f} months'.format(d/30)\n",
+ " elif d > 7:\n",
+ " return '{:1.0f} weeks'.format(d/7)\n",
+ " else:\n",
+ " return '{:1.0f} days'.format(d)\n",
+ " d /= 365\n",
+ " \n",
+ " if d > 1e9:\n",
+ " return '{:1.1f} billion years'.format(d*1e-9)\n",
+ " elif d > 1e6:\n",
+ " return '{:1.1f} million years'.format(d*1e-6)\n",
+ " elif d > 1e3:\n",
+ " return '{:1.1f} millenia'.format(d*1e-3)\n",
+ " else:\n",
+ " return '{:1.1f} years'.format(d)\n",
+ "\n",
+ "\n",
+ "z = np.linspace(0, 10, 500)\n",
+ "\n",
+ "data = []\n",
+ "for n in range(1,8):\n",
+ " p = 2*(1-stats.norm.cdf(n))\n",
+ " data.append([n, p, 1/p, format_days(1/p)])\n",
+ " \n",
+ "display(pd.DataFrame(data, columns=[r'|X| ($\\sigma)$', 'p', '1 in', 'time equivalent']))\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Code to generate \"egg\" distribution"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "55.30, 56.10, 52.49, 61.32, 50.20, 61.86, 61.05, 62.20, 59.52, 60.16, 56.32, 57.61\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Generate small dataset for T-dist question\n",
+ "# True parameters:\n",
+ "sig = 3\n",
+ "mu = 58\n",
+ "n_samples = 12\n",
+ "\n",
+ "s = stats.norm.rvs(size=n_samples, loc=mu, scale=sig)\n",
+ "print(('{:.2f}, '*n_samples).format(*s)[:-2])\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Solutions4/Solutions_4.ipynb b/exercises/Solutions4/Solutions_4.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..364e34d7a8c1b97d37bd14014b47f2aeec661d6b
--- /dev/null
+++ b/exercises/Solutions4/Solutions_4.ipynb
@@ -0,0 +1,788 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 4 Solutions\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function # For Python < 3\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "import scipy.stats as stats\n",
+ "\n",
+ "%matplotlib inline \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1. Approximations to the binomial\n",
+ "\n",
+ "For np < 10, large n, the Poisson distribution is a good approximation for the binomial.\n",
+ "\n",
+ "* Show analytically that the binomial distribution converges to the Poisson distribution in the limit of large n. (Hint: $e = \\lim_{n\\to\\infty}(1+\\frac{1}{x})^x$)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$P(x=k) = \\binom{n}{k}p^k (1-p)^{n-k}$\n",
+ "\n",
+ "$\\lambda = np$\n",
+ "\n",
+ "$\\lim_{n\\to\\infty} \\frac{n!}{(n-k)!k!} \\frac{\\lambda}{n}^k (1-\\frac{\\lambda}{n})^{n-k}$\n",
+ "\n",
+ "$\\lim_{n\\to\\infty} \\frac{n}{n} \\frac{n-1}{n} \\bigl ( ... \\bigr ) \\frac{n-k+1}{n} (1-\\frac{\\lambda}{n})^{n} (1-\\frac{\\lambda}{n})^{-k}$\n",
+ "\n",
+ "Remembering $e = \\lim_{n\\to\\infty}(1+\\frac{1}{x})^x$\n",
+ "\n",
+ "$\\frac{\\lambda}{k!}e^{-\\lambda}$\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Keeping $n p$ fixed, plot the binomial probability mass function for an increasing number of observations $n$, comparing in each case to the equivalent Poisson distribution ($\\lambda=n p$). For convenience, you should use the relevant functions in ```scipy.stat```."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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ntfec1/7JdF4raeasVLd0KJEPRcQuSccC90n6c/JJbj1zXquT81qmKmmkX7a3\ndIiIXcnf54GfkftqWw7+Q9K7AJK/z5c4ns44r73nvPZD1vNaSUU/ze0gBp2kIyQd2fEcOAvY0n2v\nQZN/e4x5wM9LGEtXnNfec177yHklNzFDpTyAjwP/DjwFfLXU8SQxTQAeTR5bSxUXcCfwHPAmuVHW\nfGAUuasAnkz+vrPU/17Oq/PqvJY2r74Ng5lZhlTS4R0zM+snF30zswxx0TczyxAXfTOzDHHRNzPL\nEBd9M7MMcdE3M8uQ/w/eiXuGcmEQ6wAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x107ecaf60>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "n_trials = [5, 10, 100]\n",
+ "p0 = 0.8\n",
+ "n_p = n_trials[0] * p0\n",
+ "x = range(12)\n",
+ "\n",
+ "fh, ax = plt.subplots(1,3, sharey=True)\n",
+ "for idx, nt in enumerate(n_trials):\n",
+ " p = n_p / nt\n",
+ " ax[idx].bar(x, stats.binom.pmf(x, nt, p), width=1, alpha=1, label='Binomial')\n",
+ " ax[idx].bar(x, stats.poisson.pmf(x, n_p), fill=False, width=1, alpha=1, label='Poisson')\n",
+ " \n",
+ " ax[idx].set_title('n={}'.format(nt))\n",
+ "\n",
+ " if idx==2:\n",
+ " plt.legend()\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "For np > 10, n(1-p) > 10, the discrete binomial distribution can be reasonably approximated by the continuous normal distribution.\n",
+ "\n",
+ "* Choose a large n (> 30, with p close to 0.5). To start with, choose n=100 and p=0.45. Plot the binomial pmf, and, with equivalent parameters, the normal pdf \n",
+ "* Calculate the probability that X >= 55 for each. Don't forget to apply the continuity correction\n",
+ "* What happens to the relative difference as n increases?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Binomial (exact): 0.4911796759527426\n",
+ "Gaussian (approximate): 0.48595290935296537\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x10d046d30>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "n_trials = 100\n",
+ "p0 = 0.45\n",
+ "mu = n_trials * p0\n",
+ "std = np.sqrt(stats.binom.stats(n_trials, p0, moments='v'))\n",
+ "\n",
+ "xd = np.arange(int(mu), int(1.5*mu))\n",
+ "x = np.linspace(xd[0], xd[-1], 200)\n",
+ "\n",
+ "x_ch = 55\n",
+ "sel_d = xd >= 55\n",
+ "sel_cont = x >= 55\n",
+ "p_bin = stats.binom.cdf(x_ch, n_trials, p0)/2\n",
+ "p_gauss = stats.norm.cdf(x_ch-0.5, mu, std)/2\n",
+ "\n",
+ "print('Binomial (exact):', p_bin)\n",
+ "print('Gaussian (approximate):', p_gauss)\n",
+ "\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.bar(xd, stats.binom.pmf(xd, n_trials, p0), width=1)\n",
+ "plt.bar(xd[sel_d], stats.binom.pmf(xd[sel_d], n_trials, p0), width=1, color='g')\n",
+ "plt.plot(x, stats.norm.pdf(x, mu, std), 'r')\n",
+ "plt.show()\n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 2. Random walk\n",
+ "\n",
+ "Consider a simple 1D random walk. A person starts at the position $x=0$. With equal probability $p=0.5$, they may take one step forwards or one step backwards, corresponding to a displacement of +1 and -1 respectively.\n",
+ "\n",
+ "* Show that for an N step walk, the expected absolute distance from the starting position is given by $\\sqrt{N}$.\n",
+ "\n",
+ "* Write a function to simulate such a random walk, parameterised by the number of steps. The output should be an array, with the displacement at each step index.\n",
+ "\n",
+ "* Plot a single walk."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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6exvy3gH5zzuA3rfzq7e3S8Q5HAqgwIHPvizjwrgXQ261tZx+DT/9TQkuhw2X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\nThAEYRFI0AmCICwCCTpBEIRF+P86OddqGMrfTgAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x107eca2e8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "def random_walk(n_steps, p=0.5):\n",
+ " return np.cumsum(2*(np.random.binomial(size=n_steps, n=1, p=0.5)-0.5)) # Bernoulli\n",
+ "\n",
+ "n_steps = 100\n",
+ "w = random_walk(n_steps)\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.plot(range(n_steps), w)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Simulate ~1000 random walks of 500 steps.\n",
+ "\n",
+ "* Plot the average distance (rms) of these over the whole set with respect to step index (time). Does the average converge to the expected distance?\n",
+ "\n",
+ "* (Optional) sample and plot the running average to show how the convergence improves with number of walks."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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2kC+MH0rLMU8WJH2pNBxfokQAIDcLNn2kQj4UJwan16gw0kHN4Nbx0G60Ch2h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\nHitftK5lZnZFxhq7vmhk2uTMHOrhWa4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ZGS6l65fP0t30uvvjfOrXKqXFGbPG5rjtGdET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\nH7t/HSteO8jS//oLsXjKlt3C7I2XcQSIs+irK3h+59Ec4TBphOierVD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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x107eca438>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x110bd8cf8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "### Bernoulli\n",
+ "n_steps = 500\n",
+ "n_walks = 1000\n",
+ "n = np.arange(n_steps) +1\n",
+ "\n",
+ "W = [] # Final distance\n",
+ "A = [] # Running average over whole set\n",
+ "T = 0\n",
+ "for idx in range(n_walks):\n",
+ " w = np.abs(random_walk(n_steps))\n",
+ " W.append(w[-1])\n",
+ " T += w**2\n",
+ " A.append(np.sqrt(T/(idx+1)))\n",
+ " \n",
+ "plt.figure()\n",
+ "plt.plot(n, np.array(A).transpose()[:,[0,20,-1]])\n",
+ "plt.plot(n, np.sqrt(n))\n",
+ "plt.legend(['0', '20', '1000', r'$\\sqrt{N}$'])\n",
+ "plt.xlabel('Step #')\n",
+ "plt.ylabel('Distance (steps)')\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.hist(np.array(W), normed=True)\n",
+ "plt.axvline(np.sqrt(n_steps), color='r') # Expected distance\n",
+ "plt.xlabel('Dist D')\n",
+ "plt.show()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Now consider the case $p \\ne 0.5$, where the \"person\" is more likely to step in one direction than another. Find again analytically the expectation and the variance for the (rms) distance travelled in terms of $N$ and $p$.\n",
+ "\n",
+ "Expectation: $N \\left|1-2p \\right|$\n",
+ "\n",
+ "Variance: $N$\n",
+ "\n",
+ "* Modify the random_walk function to account for the unequal probability between the directions."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Run a series of random walks as before, and plot again the histogram of distances travelled. On top of this, plot the Gaussian PDF with the $\\mu$ and $\\sigma$ parameters as determined above."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x11072d6d8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Plot histogram\n",
+ "n_steps = 2000\n",
+ "n_trials = 5000\n",
+ "p = 0.4\n",
+ "\n",
+ "V = []\n",
+ "for n in range(n_trials):\n",
+ " V.append(np.abs(np.sum(2*(np.random.binomial(size=n_steps, n=1, p=p)-0.5))))\n",
+ " \n",
+ "plt.figure()\n",
+ "plt.hist(V, 40, normed=True)\n",
+ "plt.plot(range(500), stats.norm.pdf(range(500), loc=n_steps*np.abs(1-2*p), scale=np.sqrt(n_steps)))\n",
+ "plt.axvline(n_steps*(np.abs(1-2*p)))\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 3. Small sample sizes: t-distribution\n",
+ "### 3.1 Compare to normal distribution\n",
+ "\n",
+ "Student's t-distributions are interesting for cases where you have few samples and the population variance is unknown, but the underlying distribution of the means can be assumed normal. They are parameterised by the degrees of freedom (\"df\"), which is usually equal the number of samples minus one. As the number of degrees of freedom increases, the t-distribution converges to the normal distribution.\n",
+ "\n",
+ "* Plot the standard t-distribution for several increasing degrees of freedom and compare this to the normal PDF.\n",
+ "* Plot and compare the cumulative distribution functions\n",
+ "* Plot the variance of the t-distribution as a function of degrees of freedom. Compare to the standard normal variance (=1)\n",
+ "* (optional) make a Q-Q plot (see Wiki) and compare the distributions\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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6JY65+XNZvms5/pAfgMEZg3E73K2WjvAFfUw+20tKCmzd2ilhGGOMMXGLJ+nK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\nEEII0Qsk6RJCCCGE6AWSdAkhhBBC9AJJuoQQQgghekGfmzIiOztbjxg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XAAAg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\nXXRJSgM3A0cBLcALklaY2bpui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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1a11a96b38>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x = np.linspace(-5, 5, 200)\n",
+ "df_all = [1,2,5,10,30]\n",
+ "\n",
+ "fh, ax = plt.subplots(2,2, figsize=(10,8))\n",
+ "\n",
+ "# PDF\n",
+ "for df in df_all:\n",
+ " c = 1/df\n",
+ " ax[0,0].plot(x, stats.t.pdf(x, df), 'g', alpha=c)\n",
+ " #plt.axhline(stats.t.pdf(0, df), color='g', alpha=c)\n",
+ "ax[0,0].plot(x, stats.norm.pdf(x), '--', color='b')\n",
+ "\n",
+ "# CDF\n",
+ "for df in [1,2,5,10,30]:\n",
+ " c = 1/df\n",
+ " ax[1,0].plot(x, stats.t.cdf(x, df), 'g', alpha=c)\n",
+ "ax[1,0].plot(x, stats.norm.cdf(x), '--', color='b')\n",
+ "\n",
+ "# Variance vs degrees of freedom\n",
+ "ax[0,1].semilogx(range(1,30), stats.t.var(range(1,30)), 'o')\n",
+ "ax[0,1].axhline(1) # Gaussian\n",
+ "ax[0,1].set_xlabel('DOF')\n",
+ "ax[0,1].set_ylabel('Var(T)')\n",
+ "\n",
+ "# Q-Q plot (optional)\n",
+ "for df in [1,2,5,10,30]:\n",
+ " c = 1/df\n",
+ " ax[1,1].plot(stats.norm.cdf(x), stats.t.cdf(x, df), 'g', alpha=c)\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 3.2 Eggs\n",
+ "An egg producer claims to supply eggs with an average egg weight of 63 g. In a box of 12, the following weights were measured (all in g):\n",
+ "\n",
+ " 62.75, 56.98, 53.30, 62.65, 57.63, 57.23, 56.65, 64.89, 57.87, 60.42, 57.01, 63.65\n",
+ " \n",
+ "* Calculate the sample mean and (adjusted) sample standard deviation.\n",
+ "\n",
+ "* What is the probability of obtaining this average weight or lighter, given the supplier's claim?\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Probability of this sample mean (59.25) against claimed mean (63.00): 15.58 %\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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TeUTnlla52fAZZJ1jfNZN5w3dV/6vdmgZhrSvy+Qt6Zy74jbY/LXnDYQqkQpS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\niEQaYzrk105HcJcg6VkuRk3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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x11061bf60>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "s = [62.75, 56.98, 53.30, 62.65, 57.63, 57.23, 56.65, 64.89, 57.87, 60.42, 57.01, 63.65]\n",
+ "n_samples = len(s)\n",
+ "dof = n_samples-1\n",
+ "mu_samp = np.mean(s)\n",
+ "sig_samp = np.std(s, ddof=1) #/np.sqrt(n_samples-1)\n",
+ "mu_claim = 63\n",
+ "\n",
+ "x = np.linspace(mu_claim-10, mu_claim+10, 500)\n",
+ "fill_sel = x <= mu_samp\n",
+ "\n",
+ "t_pdf = stats.t.pdf(x, dof, loc=mu_claim, scale=sig_samp)\n",
+ "p = stats.t.cdf(mu_samp, dof, loc=mu_claim, scale=sig_samp)\n",
+ "\n",
+ "print('Probability of this sample mean ({:.2f}) against claimed mean ({:.2f}): {:.2f} %'.format(\n",
+ " mu_samp, mu_claim, p*100))\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.plot(x, t_pdf)\n",
+ "plt.plot(x, stats.norm.pdf(x, mu_claim, sig_samp))\n",
+ "plt.fill_between(x[fill_sel], t_pdf[fill_sel])\n",
+ "plt.text(59, 0.01, '{:.1f} %'.format(100*p), color='white', horizontalalignment='right')\n",
+ "plt.axvline(mu_samp)\n",
+ "plt.xlabel('Egg weight (g) (W)')\n",
+ "plt.ylabel('P(W)')\n",
+ "\n",
+ "plt.show()\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Within what range would 95% of samples follow? And how would this compare with an equivalent normal distribution?\n",
+ "* Plot again the two distributions, marking the 95% intervals"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Normal: 57.19 to 68.81\n",
+ "T: 56.66 to 69.34\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.text.Text at 0x1a1193cc88>"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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jys/ad8HdizfOdsHP250R7WrbnUgVA38fD+5uX5t5O89wptE91pHFKb2hsTQr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\nYDCw1BhjRKQy8B3wtDFmtQs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OQCAQ7/wa4Hwe4OJcJWH/yitXSdi/fperJOxfuT7/SaB2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\nwgAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x110cb36a0>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "t_ppf = lambda pc : stats.t.ppf(pc, dof, loc=mu_claim, scale=sig_samp)\n",
+ "norm_ppf = lambda pc : stats.norm.ppf(pc, loc=mu_claim, scale=sig_samp)\n",
+ "\n",
+ "def print_CI(dist, dfunc, cl=0.05, cu=0.95):\n",
+ " print('{}: {:.2f} to {:.2f}'.format(dist, dfunc(cl), dfunc(cu)))\n",
+ "print_CI('Normal', norm_ppf)\n",
+ "print_CI('T', t_ppf)\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.plot(x, t_pdf)\n",
+ "plt.axvline(t_ppf(0.05))\n",
+ "plt.axvline(t_ppf(0.95))\n",
+ "\n",
+ "plt.plot(x, stats.norm.pdf(x, mu_claim, sig_samp))\n",
+ "plt.axvline(norm_ppf(0.05), color='darkorange')\n",
+ "plt.axvline(norm_ppf(0.95), color='darkorange')\n",
+ "\n",
+ "plt.text(59, 0.01, '{:.1f} %'.format(100*p), color='white', horizontalalignment='right')\n",
+ "plt.xlabel('Egg weight (g) (W)')\n",
+ "plt.ylabel('P(W)')\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Bonus\n",
+ "A pair of independent, standard normal random variables can be generated by sampling a uniform distribution. One approach to this is the Box-Muller transform (see https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform).\n",
+ "\n",
+ "* Generate a long sequence of numbers drawn from U(0,1)\n",
+ "* Use the Box-Muller transform to convert these to normal random variables\n",
+ "* Plot the normal samples on a scatter plot - verify they are not correlated\n",
+ "* Plot the histograms, and superimpose the normal PDF\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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hxSqkMDaVpNZdY5mQZlMryl2CO8izqAugWDrk4HJNXzsrqUm63xPiWCD0CUGL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\nK4D/ldLxO0K32SVV45XJR15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+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x1106b9eb8>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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Y540x0fbDFbTNV7CcMWajMeZgJ7Ml296lNowxYWDPUhuWMsa8Qhfz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\nlVIqA2lxV0qpDPT/AbNcQ8vwJSyaAAAAAElFTkSuQmCC\n",
+ "text/plain": [
+ "<matplotlib.figure.Figure at 0x11049de80>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Box Muller method\n",
+ "u1 = np.random.rand(1000)\n",
+ "u2 = np.random.rand(1000)\n",
+ "x = np.sqrt(-2*np.log(u1))*np.cos(2*np.pi*u2)\n",
+ "y = np.sqrt(-2*np.log(u1))*np.sin(2*np.pi*u2)\n",
+ "\n",
+ "z = np.linspace(-4,4,500)\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.scatter(x, y)\n",
+ "plt.xlabel('u1')\n",
+ "plt.ylabel('u2')\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.hist(x, 50, normed=True, label='n1')\n",
+ "plt.hist(y, 50, normed=True, label='n2')\n",
+ "plt.plot(z, stats.norm.pdf(z), label='Normal PDF')\n",
+ "plt.legend()\n",
+ "\n",
+ "plt.show()\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Improbable events\n",
+ "In this example, we tabulate the amplitude deviation against the probability, odds (inverse probability), and equivalent timescale (once in 10 thousand years). Modify the code and try with different distributions - especially those which look similar to the normal distribution, but carry a fatter tail."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<div>\n",
+ "<style>\n",
+ " .dataframe thead tr:only-child th {\n",
+ " text-align: right;\n",
+ " }\n",
+ "\n",
+ " .dataframe thead th {\n",
+ " text-align: left;\n",
+ " }\n",
+ "\n",
+ " .dataframe tbody tr th {\n",
+ " vertical-align: top;\n",
+ " }\n",
+ "</style>\n",
+ "<table border=\"1\" class=\"dataframe\">\n",
+ " <thead>\n",
+ " <tr style=\"text-align: right;\">\n",
+ " <th></th>\n",
+ " <th>|X| ($\\sigma)$</th>\n",
+ " <th>p</th>\n",
+ " <th>1 in</th>\n",
+ " <th>time equivalent</th>\n",
+ " </tr>\n",
+ " </thead>\n",
+ " <tbody>\n",
+ " <tr>\n",
+ " <th>0</th>\n",
+ " <td>1</td>\n",
+ " <td>3.173105e-01</td>\n",
+ " <td>3.151487e+00</td>\n",
+ " <td>3 days</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1</th>\n",
+ " <td>2</td>\n",
+ " <td>4.550026e-02</td>\n",
+ " <td>2.197789e+01</td>\n",
+ " <td>3 weeks</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2</th>\n",
+ " <td>3</td>\n",
+ " <td>2.699796e-03</td>\n",
+ " <td>3.703983e+02</td>\n",
+ " <td>1.0 years</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3</th>\n",
+ " <td>4</td>\n",
+ " <td>6.334248e-05</td>\n",
+ " <td>1.578719e+04</td>\n",
+ " <td>43.3 years</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>4</th>\n",
+ " <td>5</td>\n",
+ " <td>5.733031e-07</td>\n",
+ " <td>1.744278e+06</td>\n",
+ " <td>4.8 millenia</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>5</th>\n",
+ " <td>6</td>\n",
+ " <td>1.973175e-09</td>\n",
+ " <td>5.067973e+08</td>\n",
+ " <td>1.4 million years</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>6</th>\n",
+ " <td>7</td>\n",
+ " <td>2.559730e-12</td>\n",
+ " <td>3.906662e+11</td>\n",
+ " <td>1.1 billion years</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ " |X| ($\\sigma)$ p 1 in time equivalent\n",
+ "0 1 3.173105e-01 3.151487e+00 3 days\n",
+ "1 2 4.550026e-02 2.197789e+01 3 weeks\n",
+ "2 3 2.699796e-03 3.703983e+02 1.0 years\n",
+ "3 4 6.334248e-05 1.578719e+04 43.3 years\n",
+ "4 5 5.733031e-07 1.744278e+06 4.8 millenia\n",
+ "5 6 1.973175e-09 5.067973e+08 1.4 million years\n",
+ "6 7 2.559730e-12 3.906662e+11 1.1 billion years"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "from IPython.display import display\n",
+ "import pandas as pd\n",
+ "\n",
+ "def format_days(d):\n",
+ " if d < 365:\n",
+ " if d > 90:\n",
+ " return '{:1.0f} months'.format(d/30)\n",
+ " elif d > 7:\n",
+ " return '{:1.0f} weeks'.format(d/7)\n",
+ " else:\n",
+ " return '{:1.0f} days'.format(d)\n",
+ " d /= 365\n",
+ " \n",
+ " if d > 1e9:\n",
+ " return '{:1.1f} billion years'.format(d*1e-9)\n",
+ " elif d > 1e6:\n",
+ " return '{:1.1f} million years'.format(d*1e-6)\n",
+ " elif d > 1e3:\n",
+ " return '{:1.1f} millenia'.format(d*1e-3)\n",
+ " else:\n",
+ " return '{:1.1f} years'.format(d)\n",
+ "\n",
+ "\n",
+ "z = np.linspace(0, 10, 500)\n",
+ "\n",
+ "data = []\n",
+ "for n in range(1,8):\n",
+ " p = 2*(1-stats.norm.cdf(n))\n",
+ " data.append([n, p, 1/p, format_days(1/p)])\n",
+ " \n",
+ "display(pd.DataFrame(data, columns=[r'|X| ($\\sigma)$', 'p', '1 in', 'time equivalent']))\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Code to generate \"egg\" distribution"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "55.30, 56.10, 52.49, 61.32, 50.20, 61.86, 61.05, 62.20, 59.52, 60.16, 56.32, 57.61\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Generate small dataset for T-dist question\n",
+ "# True parameters:\n",
+ "sig = 3\n",
+ "mu = 58\n",
+ "n_samples = 12\n",
+ "\n",
+ "s = stats.norm.rvs(size=n_samples, loc=mu, scale=sig)\n",
+ "print(('{:.2f}, '*n_samples).format(*s)[:-2])\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.7"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Solutions4/Solutions_4.pdf b/exercises/Solutions4/Solutions_4.pdf
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diff --git a/exercises/Solutions6/.ipynb_checkpoints/Exercise_6_Solutions-checkpoint.ipynb b/exercises/Solutions6/.ipynb_checkpoints/Exercise_6_Solutions-checkpoint.ipynb
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--- /dev/null
+++ b/exercises/Solutions6/.ipynb_checkpoints/Exercise_6_Solutions-checkpoint.ipynb
@@ -0,0 +1,1767 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 6: Arbitrary distributions, moving averages, and Monte-Carlo\n",
+ "## Solutions\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import datetime\n",
+ "import scipy.stats as stats\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1. Sampling from an arbitrary distribution\n",
+ "As seen in exercise 4, you can use uniformly distributed random variables, which are in principle themselves simple to generate, to draw samples from the normal distribution via the Box-Muller transform. A more general approach is to sample according to the inverse of the cumulative distribution function (CDF).\n",
+ "\n",
+ "A simple example is to generate numbers from the exponential distribution.\n",
+ "\n",
+ "$$ f(t;\\lambda) = \\lambda e^{-\\lambda t} $$\n",
+ "\n",
+ "* Write the CDF $F(T,\\lambda)$ and find its inverse ($T=...$)\n",
+ "* Write a function to compute this, and compare your result to that from scipy (hint: sometimes called percent-point function or quantile function)\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "C:\\Users\\Matt\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:5: RuntimeWarning: divide by zero encountered in log\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Quantile function\n",
+ "def exp_quantile(p, l):\n",
+ " p[p<0] = 0\n",
+ " p[p>=1] = 1\n",
+ " return -np.log(1-p)/l # scipy equivalent: stats.expon.ppf(p,0,1/l)\n",
+ "\n",
+ "p = np.linspace(0, 1, 100)\n",
+ "l = 0.2\n",
+ "plt.figure()\n",
+ "plt.plot(p, exp_quantile(p, l))\n",
+ "plt.plot(p, stats.expon.ppf(p,0,1/l))\n",
+ "plt.xlabel('x')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Now draw N samples from the uniform distribution $[0,1]$. For each sample, calculate $F^{-1}(u,\\lambda)$\n",
+ "* Plot a histogram and compare the distribution of points to the exponential pdf\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Actual: 0.2\n",
+ "Estimated: 0.19919715788379894\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "def logfit(x, y):\n",
+ " good = y > 0\n",
+ " ly = np.log(y[good])\n",
+ " return np.polyfit(x[good], ly, 1, w=np.sqrt(y[good]))\n",
+ "\n",
+ "N = 1000\n",
+ "l = 0.2\n",
+ "x = np.random.rand(N)\n",
+ "y = exp_quantile(x, l)\n",
+ "\n",
+ "hist, bins = np.histogram(y, bins=10, normed=True)\n",
+ "bc = 0.5*(bins[:-1] + bins[1:])\n",
+ "\n",
+ "popt = logfit(bc, hist)\n",
+ "\n",
+ "print('Actual:', l)\n",
+ "print('Estimated: ', -popt[0])\n",
+ "\n",
+ "q = np.linspace(0, bc[-1], 200)\n",
+ "\n",
+ "\n",
+ "# Check the fit\n",
+ "valid = hist>0\n",
+ "plt.figure()\n",
+ "plt.scatter(bc[valid], np.log(hist[valid]), marker='o')\n",
+ "plt.plot(q, np.polyval(popt, q))\n",
+ "\n",
+ "# Plot histogram, fit, and calculated pdf\n",
+ "plt.figure()\n",
+ "plt.bar(bc, hist)\n",
+ "plt.plot(q, np.exp(np.polyval(popt, q)))\n",
+ "plt.plot(q, stats.expon.pdf(q, scale=1/l))\n",
+ "plt.show()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 2. Smoothing data\n",
+ "## 2.1 Moving average\n",
+ "The moving average, or rolling mean, is a simple technique which can be used to remove short term or periodic (e.g. seasonal) variations in time series data, for example. It can be viewed as a \"smoothing\", and can ease trend spotting, for instance. One has to be careful when interpreting and using the result; for instance, it is generally improper to fit on such data.\n",
+ "\n",
+ "The simplest moving average can be computed using a \"sliding window\" of length $N$, with all weights equal. For example, for a 3 point moving average, the window would be $\\frac{1}{3}[1,1,1]$.\n",
+ "\n",
+ "* Write a function to compute the $N$ point moving average of a data series"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def moving_average(y, length):\n",
+ " return np.convolve(np.ones(length)/length, y, 'same')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The following line of code loads a dataset (into a ```pandas DataFrame```) containing monthly measurements of variation in the global surface temperature, stretching back as far as 1750. (More data like this can be found on http://berkeleyearth.org)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
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+ "<table border=\"1\" class=\"dataframe\">\n",
+ " <thead>\n",
+ " <tr style=\"text-align: right;\">\n",
+ " <th></th>\n",
+ " <th>Year</th>\n",
+ " <th>Month</th>\n",
+ " <th>MDiff</th>\n",
+ " <th>MUnc</th>\n",
+ " <th>YDiff</th>\n",
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+ " <th>Date</th>\n",
+ " </tr>\n",
+ " </thead>\n",
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+ " <tr>\n",
+ " <th>0</th>\n",
+ " <td>1750</td>\n",
+ " <td>1</td>\n",
+ " <td>-0.121</td>\n",
+ " <td>4.187</td>\n",
+ " <td>-0.687</td>\n",
+ " <td>2.557</td>\n",
+ " <td>-0.364</td>\n",
+ " <td>0.897</td>\n",
+ " <td>-0.160</td>\n",
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+ " <td>NaN</td>\n",
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+ " <th>1</th>\n",
+ " <td>1750</td>\n",
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+ " <td>3.177</td>\n",
+ " <td>-0.691</td>\n",
+ " <td>1.733</td>\n",
+ " <td>-0.381</td>\n",
+ " <td>0.904</td>\n",
+ " <td>-0.169</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-02-15</td>\n",
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+ " <th>2</th>\n",
+ " <td>1750</td>\n",
+ " <td>3</td>\n",
+ " <td>0.112</td>\n",
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+ " <td>-0.721</td>\n",
+ " <td>1.568</td>\n",
+ " <td>-0.401</td>\n",
+ " <td>0.918</td>\n",
+ " <td>-0.164</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-03-15</td>\n",
+ " </tr>\n",
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+ " <th>3</th>\n",
+ " <td>1750</td>\n",
+ " <td>4</td>\n",
+ " <td>0.026</td>\n",
+ " <td>2.862</td>\n",
+ " <td>-0.734</td>\n",
+ " <td>1.609</td>\n",
+ " <td>-0.452</td>\n",
+ " <td>0.951</td>\n",
+ " <td>-0.168</td>\n",
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+ " <th>4</th>\n",
+ " <td>1750</td>\n",
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+ " <td>-1.420</td>\n",
+ " <td>2.611</td>\n",
+ " <td>-1.043</td>\n",
+ " <td>1.553</td>\n",
+ " <td>-0.439</td>\n",
+ " <td>1.022</td>\n",
+ " <td>-0.167</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>5</th>\n",
+ " <td>1750</td>\n",
+ " <td>6</td>\n",
+ " <td>-1.029</td>\n",
+ " <td>3.379</td>\n",
+ " <td>-1.004</td>\n",
+ " <td>1.271</td>\n",
+ " <td>-0.414</td>\n",
+ " <td>1.060</td>\n",
+ " <td>-0.176</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>6</th>\n",
+ " <td>1750</td>\n",
+ " <td>7</td>\n",
+ " <td>-0.262</td>\n",
+ " <td>2.722</td>\n",
+ " <td>-1.049</td>\n",
+ " <td>1.026</td>\n",
+ " <td>-0.411</td>\n",
+ " <td>1.023</td>\n",
+ " <td>-0.183</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-07-15</td>\n",
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+ " <tr>\n",
+ " <th>7</th>\n",
+ " <td>1750</td>\n",
+ " <td>8</td>\n",
+ " <td>0.290</td>\n",
+ " <td>3.219</td>\n",
+ " <td>-1.137</td>\n",
+ " <td>0.792</td>\n",
+ " <td>-0.466</td>\n",
+ " <td>0.933</td>\n",
+ " <td>-0.210</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-08-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>8</th>\n",
+ " <td>1750</td>\n",
+ " <td>9</td>\n",
+ " <td>-0.851</td>\n",
+ " <td>2.121</td>\n",
+ " <td>-1.107</td>\n",
+ " <td>0.775</td>\n",
+ " <td>-0.375</td>\n",
+ " <td>0.945</td>\n",
+ " <td>-0.230</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-09-15</td>\n",
+ " </tr>\n",
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+ " <th>9</th>\n",
+ " <td>1750</td>\n",
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+ " <td>-1.448</td>\n",
+ " <td>3.078</td>\n",
+ " <td>-1.167</td>\n",
+ " <td>0.826</td>\n",
+ " <td>-0.394</td>\n",
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+ " <td>-0.211</td>\n",
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+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-10-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>10</th>\n",
+ " <td>1750</td>\n",
+ " <td>11</td>\n",
+ " <td>-3.518</td>\n",
+ " <td>1.996</td>\n",
+ " <td>-1.160</td>\n",
+ " <td>1.283</td>\n",
+ " <td>-0.423</td>\n",
+ " <td>1.094</td>\n",
+ " <td>-0.226</td>\n",
+ " <td>0.879</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-11-15</td>\n",
+ " </tr>\n",
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+ " <th>11</th>\n",
+ " <td>1750</td>\n",
+ " <td>12</td>\n",
+ " <td>-2.538</td>\n",
+ " <td>4.091</td>\n",
+ " <td>-1.210</td>\n",
+ " <td>1.458</td>\n",
+ " <td>-0.451</td>\n",
+ " <td>1.143</td>\n",
+ " <td>-0.250</td>\n",
+ " <td>0.894</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-12-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>12</th>\n",
+ " <td>1751</td>\n",
+ " <td>1</td>\n",
+ " <td>-0.659</td>\n",
+ " <td>3.318</td>\n",
+ " <td>-1.094</td>\n",
+ " <td>1.533</td>\n",
+ " <td>-0.464</td>\n",
+ " <td>1.148</td>\n",
+ " <td>-0.258</td>\n",
+ " <td>0.844</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-01-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>13</th>\n",
+ " <td>1751</td>\n",
+ " <td>2</td>\n",
+ " <td>-2.341</td>\n",
+ " <td>4.503</td>\n",
+ " <td>-1.047</td>\n",
+ " <td>1.776</td>\n",
+ " <td>-0.482</td>\n",
+ " <td>1.131</td>\n",
+ " <td>-0.231</td>\n",
+ " <td>0.914</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-02-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>14</th>\n",
+ " <td>1751</td>\n",
+ " <td>3</td>\n",
+ " <td>0.477</td>\n",
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+ " <td>1.673</td>\n",
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+ " <td>1.200</td>\n",
+ " <td>-0.201</td>\n",
+ " <td>0.952</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-03-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>15</th>\n",
+ " <td>1751</td>\n",
+ " <td>4</td>\n",
+ " <td>-0.690</td>\n",
+ " <td>2.489</td>\n",
+ " <td>-0.933</td>\n",
+ " <td>1.504</td>\n",
+ " <td>-0.492</td>\n",
+ " <td>1.245</td>\n",
+ " <td>-0.184</td>\n",
+ " <td>1.004</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>16</th>\n",
+ " <td>1751</td>\n",
+ " <td>5</td>\n",
+ " <td>-1.338</td>\n",
+ " <td>3.435</td>\n",
+ " <td>-0.771</td>\n",
+ " <td>1.606</td>\n",
+ " <td>-0.486</td>\n",
+ " <td>1.336</td>\n",
+ " <td>-0.184</td>\n",
+ " <td>1.019</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>17</th>\n",
+ " <td>1751</td>\n",
+ " <td>6</td>\n",
+ " <td>-1.637</td>\n",
+ " <td>3.336</td>\n",
+ " <td>-0.721</td>\n",
+ " <td>1.085</td>\n",
+ " <td>-0.539</td>\n",
+ " <td>1.393</td>\n",
+ " <td>-0.188</td>\n",
+ " <td>1.075</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>18</th>\n",
+ " <td>1751</td>\n",
+ " <td>7</td>\n",
+ " <td>1.130</td>\n",
+ " <td>3.753</td>\n",
+ " <td>-0.876</td>\n",
+ " <td>1.400</td>\n",
+ " <td>-0.527</td>\n",
+ " <td>1.212</td>\n",
+ " <td>-0.208</td>\n",
+ " <td>1.084</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-07-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>19</th>\n",
+ " <td>1751</td>\n",
+ " <td>8</td>\n",
+ " <td>0.858</td>\n",
+ " <td>2.757</td>\n",
+ " <td>-0.409</td>\n",
+ " <td>1.841</td>\n",
+ " <td>-0.538</td>\n",
+ " <td>1.097</td>\n",
+ " <td>-0.221</td>\n",
+ " <td>1.106</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-08-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>20</th>\n",
+ " <td>1751</td>\n",
+ " <td>9</td>\n",
+ " <td>-1.098</td>\n",
+ " <td>2.928</td>\n",
+ " <td>-0.382</td>\n",
+ " <td>1.840</td>\n",
+ " <td>-0.531</td>\n",
+ " <td>1.123</td>\n",
+ " <td>-0.225</td>\n",
+ " <td>1.119</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-09-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>21</th>\n",
+ " <td>1751</td>\n",
+ " <td>10</td>\n",
+ " <td>0.169</td>\n",
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+ " <td>-0.429</td>\n",
+ " <td>1.791</td>\n",
+ " <td>-0.446</td>\n",
+ " <td>1.151</td>\n",
+ " <td>-0.219</td>\n",
+ " <td>1.148</td>\n",
+ " <td>-0.276</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-10-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>22</th>\n",
+ " <td>1751</td>\n",
+ " <td>11</td>\n",
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+ " <td>2.326</td>\n",
+ " <td>-0.302</td>\n",
+ " <td>1.688</td>\n",
+ " <td>-0.437</td>\n",
+ " <td>1.160</td>\n",
+ " <td>-0.222</td>\n",
+ " <td>1.178</td>\n",
+ " <td>-0.286</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-11-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>23</th>\n",
+ " <td>1751</td>\n",
+ " <td>12</td>\n",
+ " <td>-1.935</td>\n",
+ " <td>3.412</td>\n",
+ " <td>-0.129</td>\n",
+ " <td>1.784</td>\n",
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+ " <td>1.293</td>\n",
+ " <td>-0.258</td>\n",
+ " <td>1.173</td>\n",
+ " <td>-0.316</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-12-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>24</th>\n",
+ " <td>1752</td>\n",
+ " <td>1</td>\n",
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+ " <td>-0.431</td>\n",
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+ " <td>1.160</td>\n",
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+ " <td>NaN</td>\n",
+ " <td>1752-01-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>25</th>\n",
+ " <td>1752</td>\n",
+ " <td>2</td>\n",
+ " <td>3.263</td>\n",
+ " <td>4.891</td>\n",
+ " <td>-0.311</td>\n",
+ " <td>1.743</td>\n",
+ " <td>-0.461</td>\n",
+ " <td>1.061</td>\n",
+ " <td>-0.216</td>\n",
+ " <td>1.213</td>\n",
+ " <td>-0.299</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-02-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>26</th>\n",
+ " <td>1752</td>\n",
+ " <td>3</td>\n",
+ " <td>0.804</td>\n",
+ " <td>3.040</td>\n",
+ " <td>-0.166</td>\n",
+ " <td>1.570</td>\n",
+ " <td>-0.480</td>\n",
+ " <td>1.053</td>\n",
+ " <td>-0.192</td>\n",
+ " <td>1.258</td>\n",
+ " <td>-0.303</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-03-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>27</th>\n",
+ " <td>1752</td>\n",
+ " <td>4</td>\n",
+ " <td>-1.259</td>\n",
+ " <td>2.243</td>\n",
+ " <td>-0.263</td>\n",
+ " <td>1.645</td>\n",
+ " <td>-0.447</td>\n",
+ " <td>1.072</td>\n",
+ " <td>-0.185</td>\n",
+ " <td>1.364</td>\n",
+ " <td>-0.295</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>28</th>\n",
+ " <td>1752</td>\n",
+ " <td>5</td>\n",
+ " <td>0.196</td>\n",
+ " <td>1.576</td>\n",
+ " <td>-0.090</td>\n",
+ " <td>1.758</td>\n",
+ " <td>-0.449</td>\n",
+ " <td>1.030</td>\n",
+ " <td>-0.178</td>\n",
+ " <td>1.431</td>\n",
+ " <td>-0.293</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>29</th>\n",
+ " <td>1752</td>\n",
+ " <td>6</td>\n",
+ " <td>0.434</td>\n",
+ " <td>3.225</td>\n",
+ " <td>0.040</td>\n",
+ " <td>1.815</td>\n",
+ " <td>-0.390</td>\n",
+ " <td>1.072</td>\n",
+ " <td>-0.179</td>\n",
+ " <td>1.504</td>\n",
+ " <td>-0.293</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>...</th>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3195</th>\n",
+ " <td>2016</td>\n",
+ " <td>4</td>\n",
+ " <td>1.796</td>\n",
+ " <td>0.111</td>\n",
+ " <td>1.454</td>\n",
+ " <td>0.042</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3196</th>\n",
+ " <td>2016</td>\n",
+ " <td>5</td>\n",
+ " <td>1.260</td>\n",
+ " <td>0.112</td>\n",
+ " <td>1.433</td>\n",
+ " <td>0.040</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3197</th>\n",
+ " <td>2016</td>\n",
+ " <td>6</td>\n",
+ " <td>0.882</td>\n",
+ " <td>0.078</td>\n",
+ " <td>1.387</td>\n",
+ " <td>0.034</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3198</th>\n",
+ " <td>2016</td>\n",
+ " <td>7</td>\n",
+ " <td>0.935</td>\n",
+ " <td>0.046</td>\n",
+ " <td>1.385</td>\n",
+ " <td>0.029</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-07-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3199</th>\n",
+ " <td>2016</td>\n",
+ " <td>8</td>\n",
+ " <td>1.433</td>\n",
+ " <td>0.102</td>\n",
+ " <td>1.348</td>\n",
+ " <td>0.028</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-08-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3200</th>\n",
+ " <td>2016</td>\n",
+ " <td>9</td>\n",
+ " <td>1.058</td>\n",
+ " <td>0.082</td>\n",
+ " <td>1.321</td>\n",
+ " <td>0.027</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-09-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3201</th>\n",
+ " <td>2016</td>\n",
+ " <td>10</td>\n",
+ " <td>1.019</td>\n",
+ " <td>0.062</td>\n",
+ " <td>1.280</td>\n",
+ " <td>0.031</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-10-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3202</th>\n",
+ " <td>2016</td>\n",
+ " <td>11</td>\n",
+ " <td>1.079</td>\n",
+ " <td>0.095</td>\n",
+ " <td>1.278</td>\n",
+ " <td>0.031</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-11-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3203</th>\n",
+ " <td>2016</td>\n",
+ " <td>12</td>\n",
+ " <td>1.259</td>\n",
+ " <td>0.077</td>\n",
+ " <td>1.271</td>\n",
+ " <td>0.035</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-12-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3204</th>\n",
+ " <td>2017</td>\n",
+ " <td>1</td>\n",
+ " <td>1.569</td>\n",
+ " <td>0.082</td>\n",
+ " <td>1.275</td>\n",
+ " <td>0.038</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-01-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3205</th>\n",
+ " <td>2017</td>\n",
+ " <td>2</td>\n",
+ " <td>1.746</td>\n",
+ " <td>0.062</td>\n",
+ " <td>1.244</td>\n",
+ " <td>0.039</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-02-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3206</th>\n",
+ " <td>2017</td>\n",
+ " <td>3</td>\n",
+ " <td>1.831</td>\n",
+ " <td>0.052</td>\n",
+ " <td>1.231</td>\n",
+ " <td>0.037</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-03-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3207</th>\n",
+ " <td>2017</td>\n",
+ " <td>4</td>\n",
+ " <td>1.301</td>\n",
+ " <td>0.144</td>\n",
+ " <td>1.253</td>\n",
+ " <td>0.038</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3208</th>\n",
+ " <td>2017</td>\n",
+ " <td>5</td>\n",
+ " <td>1.235</td>\n",
+ " <td>0.132</td>\n",
+ " <td>1.249</td>\n",
+ " <td>0.036</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3209</th>\n",
+ " <td>2017</td>\n",
+ " <td>6</td>\n",
+ " <td>0.803</td>\n",
+ " <td>0.089</td>\n",
+ " <td>1.268</td>\n",
+ " <td>0.040</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3210</th>\n",
+ " <td>2017</td>\n",
+ " <td>7</td>\n",
+ " <td>0.973</td>\n",
+ " <td>0.079</td>\n",
+ " <td>1.235</td>\n",
+ " <td>0.038</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-07-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3211</th>\n",
+ " <td>2017</td>\n",
+ " <td>8</td>\n",
+ " <td>1.066</td>\n",
+ " <td>0.086</td>\n",
+ " <td>1.180</td>\n",
+ " <td>0.039</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-08-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3212</th>\n",
+ " <td>2017</td>\n",
+ " <td>9</td>\n",
+ " <td>0.906</td>\n",
+ " <td>0.093</td>\n",
+ " <td>1.142</td>\n",
+ " <td>0.042</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-09-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3213</th>\n",
+ " <td>2017</td>\n",
+ " <td>10</td>\n",
+ " <td>1.275</td>\n",
+ " <td>0.048</td>\n",
+ " <td>1.145</td>\n",
+ " <td>0.041</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-10-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3214</th>\n",
+ " <td>2017</td>\n",
+ " <td>11</td>\n",
+ " <td>1.035</td>\n",
+ " <td>0.080</td>\n",
+ " <td>1.138</td>\n",
+ " <td>0.040</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-11-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3215</th>\n",
+ " <td>2017</td>\n",
+ " <td>12</td>\n",
+ " <td>1.487</td>\n",
+ " <td>0.073</td>\n",
+ " <td>1.161</td>\n",
+ " <td>0.040</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-12-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3216</th>\n",
+ " <td>2018</td>\n",
+ " <td>1</td>\n",
+ " <td>1.171</td>\n",
+ " <td>0.093</td>\n",
+ " <td>1.172</td>\n",
+ " <td>0.038</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-01-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3217</th>\n",
+ " <td>2018</td>\n",
+ " <td>2</td>\n",
+ " <td>1.093</td>\n",
+ " <td>0.102</td>\n",
+ " <td>1.166</td>\n",
+ " <td>0.035</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-02-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3218</th>\n",
+ " <td>2018</td>\n",
+ " <td>3</td>\n",
+ " <td>1.366</td>\n",
+ " <td>0.091</td>\n",
+ " <td>1.158</td>\n",
+ " <td>0.042</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-03-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3219</th>\n",
+ " <td>2018</td>\n",
+ " <td>4</td>\n",
+ " <td>1.342</td>\n",
+ " <td>0.112</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3220</th>\n",
+ " <td>2018</td>\n",
+ " <td>5</td>\n",
+ " <td>1.147</td>\n",
+ " <td>0.170</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3221</th>\n",
+ " <td>2018</td>\n",
+ " <td>6</td>\n",
+ " <td>1.078</td>\n",
+ " <td>0.122</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3222</th>\n",
+ " <td>2018</td>\n",
+ " <td>7</td>\n",
+ " <td>1.112</td>\n",
+ " <td>0.039</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-07-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3223</th>\n",
+ " <td>2018</td>\n",
+ " <td>8</td>\n",
+ " <td>0.991</td>\n",
+ " <td>0.107</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-08-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3224</th>\n",
+ " <td>2018</td>\n",
+ " <td>9</td>\n",
+ " <td>0.804</td>\n",
+ " <td>0.161</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-09-15</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "<p>3225 rows × 13 columns</p>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ " Year Month MDiff MUnc YDiff YUnc 5YDiff 5YUnc 10YDiff 10YUnc \\\n",
+ "0 1750 1 -0.121 4.187 -0.687 2.557 -0.364 0.897 -0.160 NaN \n",
+ "1 1750 2 -1.278 3.177 -0.691 1.733 -0.381 0.904 -0.169 NaN \n",
+ "2 1750 3 0.112 3.550 -0.721 1.568 -0.401 0.918 -0.164 NaN \n",
+ "3 1750 4 0.026 2.862 -0.734 1.609 -0.452 0.951 -0.168 NaN \n",
+ "4 1750 5 -1.420 2.611 -1.043 1.553 -0.439 1.022 -0.167 NaN \n",
+ "5 1750 6 -1.029 3.379 -1.004 1.271 -0.414 1.060 -0.176 NaN \n",
+ "6 1750 7 -0.262 2.722 -1.049 1.026 -0.411 1.023 -0.183 NaN \n",
+ "7 1750 8 0.290 3.219 -1.137 0.792 -0.466 0.933 -0.210 NaN \n",
+ "8 1750 9 -0.851 2.121 -1.107 0.775 -0.375 0.945 -0.230 NaN \n",
+ "9 1750 10 -1.448 3.078 -1.167 0.826 -0.394 1.023 -0.211 NaN \n",
+ "10 1750 11 -3.518 1.996 -1.160 1.283 -0.423 1.094 -0.226 0.879 \n",
+ "11 1750 12 -2.538 4.091 -1.210 1.458 -0.451 1.143 -0.250 0.894 \n",
+ "12 1751 1 -0.659 3.318 -1.094 1.533 -0.464 1.148 -0.258 0.844 \n",
+ "13 1751 2 -2.341 4.503 -1.047 1.776 -0.482 1.131 -0.231 0.914 \n",
+ "14 1751 3 0.477 2.778 -1.068 1.673 -0.488 1.200 -0.201 0.952 \n",
+ "15 1751 4 -0.690 2.489 -0.933 1.504 -0.492 1.245 -0.184 1.004 \n",
+ "16 1751 5 -1.338 3.435 -0.771 1.606 -0.486 1.336 -0.184 1.019 \n",
+ "17 1751 6 -1.637 3.336 -0.721 1.085 -0.539 1.393 -0.188 1.075 \n",
+ "18 1751 7 1.130 3.753 -0.876 1.400 -0.527 1.212 -0.208 1.084 \n",
+ "19 1751 8 0.858 2.757 -0.409 1.841 -0.538 1.097 -0.221 1.106 \n",
+ "20 1751 9 -1.098 2.928 -0.382 1.840 -0.531 1.123 -0.225 1.119 \n",
+ "21 1751 10 0.169 4.986 -0.429 1.791 -0.446 1.151 -0.219 1.148 \n",
+ "22 1751 11 -1.577 2.326 -0.302 1.688 -0.437 1.160 -0.222 1.178 \n",
+ "23 1751 12 -1.935 3.412 -0.129 1.784 -0.426 1.293 -0.258 1.173 \n",
+ "24 1752 1 -2.523 4.962 -0.154 1.757 -0.431 1.296 -0.262 1.160 \n",
+ "25 1752 2 3.263 4.891 -0.311 1.743 -0.461 1.061 -0.216 1.213 \n",
+ "26 1752 3 0.804 3.040 -0.166 1.570 -0.480 1.053 -0.192 1.258 \n",
+ "27 1752 4 -1.259 2.243 -0.263 1.645 -0.447 1.072 -0.185 1.364 \n",
+ "28 1752 5 0.196 1.576 -0.090 1.758 -0.449 1.030 -0.178 1.431 \n",
+ "29 1752 6 0.434 3.225 0.040 1.815 -0.390 1.072 -0.179 1.504 \n",
+ "... ... ... ... ... ... ... ... ... ... ... \n",
+ "3195 2016 4 1.796 0.111 1.454 0.042 NaN NaN NaN NaN \n",
+ "3196 2016 5 1.260 0.112 1.433 0.040 NaN NaN NaN NaN \n",
+ "3197 2016 6 0.882 0.078 1.387 0.034 NaN NaN NaN NaN \n",
+ "3198 2016 7 0.935 0.046 1.385 0.029 NaN NaN NaN NaN \n",
+ "3199 2016 8 1.433 0.102 1.348 0.028 NaN NaN NaN NaN \n",
+ "3200 2016 9 1.058 0.082 1.321 0.027 NaN NaN NaN NaN \n",
+ "3201 2016 10 1.019 0.062 1.280 0.031 NaN NaN NaN NaN \n",
+ "3202 2016 11 1.079 0.095 1.278 0.031 NaN NaN NaN NaN \n",
+ "3203 2016 12 1.259 0.077 1.271 0.035 NaN NaN NaN NaN \n",
+ "3204 2017 1 1.569 0.082 1.275 0.038 NaN NaN NaN NaN \n",
+ "3205 2017 2 1.746 0.062 1.244 0.039 NaN NaN NaN NaN \n",
+ "3206 2017 3 1.831 0.052 1.231 0.037 NaN NaN NaN NaN \n",
+ "3207 2017 4 1.301 0.144 1.253 0.038 NaN NaN NaN NaN \n",
+ "3208 2017 5 1.235 0.132 1.249 0.036 NaN NaN NaN NaN \n",
+ "3209 2017 6 0.803 0.089 1.268 0.040 NaN NaN NaN NaN \n",
+ "3210 2017 7 0.973 0.079 1.235 0.038 NaN NaN NaN NaN \n",
+ "3211 2017 8 1.066 0.086 1.180 0.039 NaN NaN NaN NaN \n",
+ "3212 2017 9 0.906 0.093 1.142 0.042 NaN NaN NaN NaN \n",
+ "3213 2017 10 1.275 0.048 1.145 0.041 NaN NaN NaN NaN \n",
+ "3214 2017 11 1.035 0.080 1.138 0.040 NaN NaN NaN NaN \n",
+ "3215 2017 12 1.487 0.073 1.161 0.040 NaN NaN NaN NaN \n",
+ "3216 2018 1 1.171 0.093 1.172 0.038 NaN NaN NaN NaN \n",
+ "3217 2018 2 1.093 0.102 1.166 0.035 NaN NaN NaN NaN \n",
+ "3218 2018 3 1.366 0.091 1.158 0.042 NaN NaN NaN NaN \n",
+ "3219 2018 4 1.342 0.112 NaN NaN NaN NaN NaN NaN \n",
+ "3220 2018 5 1.147 0.170 NaN NaN NaN NaN NaN NaN \n",
+ "3221 2018 6 1.078 0.122 NaN NaN NaN NaN NaN NaN \n",
+ "3222 2018 7 1.112 0.039 NaN NaN NaN NaN NaN NaN \n",
+ "3223 2018 8 0.991 0.107 NaN NaN NaN NaN NaN NaN \n",
+ "3224 2018 9 0.804 0.161 NaN NaN NaN NaN NaN NaN \n",
+ "\n",
+ " 20YDiff 20YUnc Date \n",
+ "0 NaN NaN 1750-01-15 \n",
+ "1 NaN NaN 1750-02-15 \n",
+ "2 NaN NaN 1750-03-15 \n",
+ "3 NaN NaN 1750-04-15 \n",
+ "4 NaN NaN 1750-05-15 \n",
+ "5 NaN NaN 1750-06-15 \n",
+ "6 NaN NaN 1750-07-15 \n",
+ "7 NaN NaN 1750-08-15 \n",
+ "8 NaN NaN 1750-09-15 \n",
+ "9 NaN NaN 1750-10-15 \n",
+ "10 NaN NaN 1750-11-15 \n",
+ "11 NaN NaN 1750-12-15 \n",
+ "12 NaN NaN 1751-01-15 \n",
+ "13 NaN NaN 1751-02-15 \n",
+ "14 NaN NaN 1751-03-15 \n",
+ "15 NaN NaN 1751-04-15 \n",
+ "16 NaN NaN 1751-05-15 \n",
+ "17 NaN NaN 1751-06-15 \n",
+ "18 NaN NaN 1751-07-15 \n",
+ "19 NaN NaN 1751-08-15 \n",
+ "20 NaN NaN 1751-09-15 \n",
+ "21 -0.276 NaN 1751-10-15 \n",
+ "22 -0.286 NaN 1751-11-15 \n",
+ "23 -0.316 NaN 1751-12-15 \n",
+ "24 -0.299 NaN 1752-01-15 \n",
+ "25 -0.299 NaN 1752-02-15 \n",
+ "26 -0.303 NaN 1752-03-15 \n",
+ "27 -0.295 NaN 1752-04-15 \n",
+ "28 -0.293 NaN 1752-05-15 \n",
+ "29 -0.293 NaN 1752-06-15 \n",
+ "... ... ... ... \n",
+ "3195 NaN NaN 2016-04-15 \n",
+ "3196 NaN NaN 2016-05-15 \n",
+ "3197 NaN NaN 2016-06-15 \n",
+ "3198 NaN NaN 2016-07-15 \n",
+ "3199 NaN NaN 2016-08-15 \n",
+ "3200 NaN NaN 2016-09-15 \n",
+ "3201 NaN NaN 2016-10-15 \n",
+ "3202 NaN NaN 2016-11-15 \n",
+ "3203 NaN NaN 2016-12-15 \n",
+ "3204 NaN NaN 2017-01-15 \n",
+ "3205 NaN NaN 2017-02-15 \n",
+ "3206 NaN NaN 2017-03-15 \n",
+ "3207 NaN NaN 2017-04-15 \n",
+ "3208 NaN NaN 2017-05-15 \n",
+ "3209 NaN NaN 2017-06-15 \n",
+ "3210 NaN NaN 2017-07-15 \n",
+ "3211 NaN NaN 2017-08-15 \n",
+ "3212 NaN NaN 2017-09-15 \n",
+ "3213 NaN NaN 2017-10-15 \n",
+ "3214 NaN NaN 2017-11-15 \n",
+ "3215 NaN NaN 2017-12-15 \n",
+ "3216 NaN NaN 2018-01-15 \n",
+ "3217 NaN NaN 2018-02-15 \n",
+ "3218 NaN NaN 2018-03-15 \n",
+ "3219 NaN NaN 2018-04-15 \n",
+ "3220 NaN NaN 2018-05-15 \n",
+ "3221 NaN NaN 2018-06-15 \n",
+ "3222 NaN NaN 2018-07-15 \n",
+ "3223 NaN NaN 2018-08-15 \n",
+ "3224 NaN NaN 2018-09-15 \n",
+ "\n",
+ "[3225 rows x 13 columns]"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "df = pd.read_csv('Material/Complete_TAVG_complete.txt', skipinitialspace=True, delimiter=' ', comment='%')\n",
+ "df['Date'] = df.apply(lambda row: datetime.datetime(\n",
+ " int(row['Year']), int(row['Month']), 15), axis=1)\n",
+ "df"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Plot the data. To plot the monthly differences, for example, you can directly write ```df2['MDiff'].plot()```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# For example...\n",
+ "df.query('Year>1980 & Year<2000').plot(x='Date', y='MDiff')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Apply your moving average filter to the monthly data ```MDiff```. Try (for example) 6 months, 5 years, 10 years. Plot these on top of cuts of the original data to compare."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "df['6MA'] = moving_average(df['MDiff'], 6)\n",
+ "df['5Y'] = moving_average(df['MDiff'], 60)\n",
+ "df['20Y'] = moving_average(df['MDiff'], 240)\n",
+ "\n",
+ "df.plot(x='Date', y=['6MA', '5Y', '20Y'])\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 2.2 Electronic response of RC circuit\n",
+ "\n",
+ "In general, the response of a linearly time invariant system is found to be the convolution of the its impulse response $h(t)$ and the input voltage. Consider a resistor and capacitor connected in series, driven by a time-varying voltage $u(t)$. The impulse response for such a circuit is:\n",
+ "\n",
+ "$$h_c(t) = \\frac{1}{RC} e^{-t/RC} u(t)$$\n",
+ "\n",
+ "* Write a function to calculate the impulse response as a function of time, the resistance, and the capacitance, and input. Take care to normalise the integral.\n",
+ "\n",
+ "* Now consider a noisy sinusoidal input voltage $u_N(t) = u(t) + \\epsilon(t)$, where $\\epsilon$ is a vector comprising samples draw from $N~(0,1)$. Plot the noisy signal and superimpose the clean signal.\n",
+ "\n",
+ "* Calculate the circuit response for your signal and compare the result to the noisy signal and the clean, original signal\n",
+ "\n",
+ "Play with the RC time constant and see the effect on the signal.\n",
+ "\n",
+ "\n",
+ "Note: this first order low pass filter is exactly equivalent to an exponential moving average. The \"memory\" of the output is effectively determined by the time constant.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Cutoff: 0.0005\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "def rc_impulse(t, R, C):\n",
+ " RC = R*C\n",
+ " return 1/RC * np.exp(-t/RC)\n",
+ "\n",
+ "def rc_response(t, u, R, C):\n",
+ " return np.convolve(rc_impulse(t, R, C), u)[:len(t)]*dt\n",
+ "\n",
+ "t = np.linspace(0, 0.1, 5000)\n",
+ "dt = t[1]-t[0]\n",
+ "R = 5e3\n",
+ "C = 100e-9\n",
+ "tc = R*C\n",
+ "\n",
+ "fw = 200\n",
+ "u = np.sin(2*np.pi*fw*t) + np.cos(2*np.pi*0.1*fw*t)\n",
+ "un = u + np.random.randn(len(u))\n",
+ "\n",
+ "print('Cutoff: ', tc)\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.plot(t, un)\n",
+ "plt.plot(t, rc_response(t, un, R, C))\n",
+ "plt.plot(t, u)\n",
+ "plt.xlabel('Time (s)')\n",
+ "\n",
+ "# Try different cutoffs (remove noise, fast ripple, then whole thing)\n",
+ "plt.figure()\n",
+ "plt.plot(t, un)\n",
+ "plt.plot(t, rc_response(t, un, R, C))\n",
+ "plt.plot(t, rc_response(t, un, 20*R, C))\n",
+ "plt.plot(t, rc_response(t, un, 200*R, C))\n",
+ "plt.xlabel('Time (s)')\n",
+ "plt.show()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 3. Monte Carlo methods\n",
+ "### 3.1. Particle propagation\n",
+ "The elementary processes of particle absorption and scattering are random in their nature. Propagation of particles through a slab of material with multiple scattering events may be impossible to calculate analytically, but can easily be simulated with Monte Carlo methods.\n",
+ "\n",
+ "* Consider a beam of photons propagating through an absorbing medium with absorption coefficient $\\alpha=0.2$ per unit length. What is the probability of a photon being absorbed in a unit length slab of material?\n",
+ "\n",
+ "* Now take a piece of 1D material made up of 100 slices, each unit length. Starting at x=0, propagate a beam of 1000 photons through the material, slice-by-slice. At each interface, you should \"measure\" each photon to determine whether it has been transmitted or absorbed (hint: uniform distribution, $P(abs)$)\n",
+ "\n",
+ "* Plot the number of photons which are transmitted at the end of each slice, and compare that to the Beer-Lambert-Bouger law\n",
+ "\n",
+ "* Plot a histogram of the distance travelled before absorption for each photon (free paths).\n",
+ "\n",
+ "$I(x) = I_{0}e^{-\\alpha x }$ , where $\\alpha$ is absorption coefficient"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Generated absorption probability (mean) = 0.18105\n",
+ "Fraction of escaped particles = 0.0\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "C:\\Users\\Matt\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
+ " warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "4.577\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "N_slices = 100 # Slices of material\n",
+ "N_particles = 1000 # Number of particles to simulate\n",
+ "alpha = 0.2 # absorption coefficient\n",
+ "P_abs = 1 - np.exp(-alpha) # Absorption probability in a slice\n",
+ "\n",
+ "# Generate N_slices x N_particles matrix of uniformly distributed random numbers. \n",
+ "# Transform it into a matrix of absorption events, where True = absorption, False = no absorption, \n",
+ "# mean(ABs_events) = P_abs\n",
+ "Abs_events = np.random.uniform(0,1,(N_slices,N_particles)) < P_abs \n",
+ "Abs_c = np.cumprod(Abs_events == False, axis=0) # Propagate the absorbed state (False propagates)\n",
+ "\n",
+ "free_path = np.sum(Abs_c, axis=0) # Number of \"True\" (i.e. _not_ absorbed) until absorbed\n",
+ "N_transmitted = np.append([N_particles], np.sum(Abs_c, axis=1))\n",
+ "N_escaped_final = np.sum(free_path == N_slices)\n",
+ "\n",
+ "print('Generated absorption probability (mean) = ', np.mean(Abs_events))\n",
+ "print('Fraction of escaped particles = ',N_escaped_final/N_particles)\n",
+ "\n",
+ "x = np.linspace(0,N_slices);\n",
+ "plt.plot(x,N_particles*np.exp(-x*alpha), label = 'Beer-Lambert-Bouguer law') \n",
+ "plt.plot(N_transmitted, label = 'Simulation')\n",
+ "plt.legend()\n",
+ "plt.xlabel('Propagation distance (slice #)')\n",
+ "plt.ylabel('# of transmitted particles')\n",
+ "plt.title('Transmission of %i particles' %N_particles)\n",
+ "plt.show()\n",
+ "#plt.hist(free_path[free_path!=np.inf],30,normed='True')\n",
+ "ax = plt.figure()\n",
+ "plt.hist(free_path,int(N_particles/5),normed='True')\n",
+ "plt.xlabel('Free propagation distance')\n",
+ "plt.ylabel('#')\n",
+ "plt.title('Histogram distribution of free paths')\n",
+ "plt.show()\n",
+ "print(np.mean(free_path))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 3.2. Monte-Carlo integration: estimate $\\pi$\n",
+ "\n",
+ "In a so-called ’hit-and-miss’ approach, or ’simple sampling’, one can estimate the integral\n",
+ "of an arbitrary, well-behaved function over some interval by scattering many points over\n",
+ "some rectangular area A. The probability of a point landing below the curve is proportional\n",
+ "to the function’s integral.\n",
+ "A classic problem is to determine the value of π.\n",
+ "\n",
+ "* Uniformly distribute N points over a unit area. Plot these on top of a unit circle (or quarter circle)\n",
+ "* Calculate the proportion that are within the bounds of your shape for some number of samples N (for large N, it would be unwise to plot)\n",
+ "* Repeat the exercise for increasing N. For each run, you should compute and store the error $\\epsilon = \\bar{\\pi} - \\pi$\n",
+ "* Plot log-log the convergence of your estimate to the actual value (to machine precision) of $\\pi$, i.e. $\\epsilon$ vs the number of points $N$. Compare this to the expected rate of convergence $(1/\\sqrt N)$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Helper functions...\n",
+ "def mc_integrate_1d(f, dist_x, dist_y, n_iter):\n",
+ " # Hit and miss version\n",
+ " #\n",
+ " # f: function to be evaluated\n",
+ " # dist_x, dist_y: distributions from which to draw (x,y)\n",
+ " # Does not handle -ve y\n",
+ " x = dist_x(n_iter)\n",
+ " y = dist_y(n_iter)\n",
+ " h = f(x)\n",
+ " return np.cumsum(y < f(x)) / np.arange(1,n_iter+1)\n",
+ "\n",
+ "def mc_integrate_1d_2(f, dist_x, n_iter):\n",
+ " # Sampling\n",
+ " x = dist_x(n_iter)\n",
+ " return np.cumsum(f(x))/np.arange(1,n_iter+1)\n",
+ "\n",
+ "def plot_convergence(est, sol):\n",
+ " x = np.arange(1,len(est)+1)\n",
+ " plt.figure()\n",
+ " plt.loglog(x, np.abs(est-sol)/sol, 'b', x, 1/np.sqrt(x), 'r')\n",
+ " plt.legend(('Result', '1/sqrt(N)'))\n",
+ " plt.xlabel('N iterations')\n",
+ " plt.ylabel('Fractional error')\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Pi estimate: 3.124\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "C:\\Users\\Matt\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:12: MatplotlibDeprecationWarning: axes.hold is deprecated.\n",
+ " See the API Changes document (http://matplotlib.org/api/api_changes.html)\n",
+ " for more details.\n"
+ ]
+ },
+ {
+ "data": {
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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "N_trials = int(1e3)\n",
+ "p = np.random.uniform(0,1,size=(N_trials, 2))\n",
+ "r = np.sqrt(np.sum(p**2, 1))\n",
+ "\n",
+ "print('Pi estimate:', 4 * np.sum(r<=1) / N_trials)\n",
+ "\n",
+ "sel = (r<=1, r>1)\n",
+ "\n",
+ "def plot_pi(p, r, sel):\n",
+ " x = np.linspace(0,1,200)\n",
+ " fh, ax = plt.subplots()\n",
+ " ax.hold(True)\n",
+ " ax.scatter(p[sel[0],0], p[sel[0],1], c='r', marker='x')\n",
+ " ax.scatter(p[sel[1],0], p[sel[1],1], c='b', marker='x')\n",
+ " ax.plot(x, np.sqrt(1-x**2), 'k', linewidth=2)\n",
+ " ax.set_xlim([0, 1])\n",
+ " ax.set_ylim([0, 1])\n",
+ "\n",
+ "if N_trials <= 1e4:\n",
+ " plot_pi(p,r,sel)\n",
+ "\n",
+ "x = np.arange(1,N_trials+1)\n",
+ "c_est = 4*np.cumsum(sel[0])/x\n",
+ "c_err = np.abs(c_est-np.pi)/np.pi\n",
+ "\n",
+ "# Std: sqrt(1/N(N-1) sum{(x_i-pi)^2})\n",
+ "plot_convergence(c_est, np.pi)\n",
+ "plt.tight_layout()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Solutions6/Exercise_6_Solutions.ipynb b/exercises/Solutions6/Exercise_6_Solutions.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..8af7b8165bbc86a6749275794c87ecdf4f8656ec
--- /dev/null
+++ b/exercises/Solutions6/Exercise_6_Solutions.ipynb
@@ -0,0 +1,1767 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Exercise 6: Arbitrary distributions, moving averages, and Monte-Carlo\n",
+ "## Solutions\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import datetime\n",
+ "import scipy.stats as stats\n",
+ "import matplotlib.pyplot as plt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1. Sampling from an arbitrary distribution\n",
+ "As seen in exercise 4, you can use uniformly distributed random variables, which are in principle themselves simple to generate, to draw samples from the normal distribution via the Box-Muller transform. A more general approach is to sample according to the inverse of the cumulative distribution function (CDF).\n",
+ "\n",
+ "A simple example is to generate numbers from the exponential distribution.\n",
+ "\n",
+ "$$ f(t;\\lambda) = \\lambda e^{-\\lambda t} $$\n",
+ "\n",
+ "* Write the CDF $F(T,\\lambda)$ and find its inverse ($T=...$)\n",
+ "* Write a function to compute this, and compare your result to that from scipy (hint: sometimes called percent-point function or quantile function)\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "C:\\Users\\Matt\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:5: RuntimeWarning: divide by zero encountered in log\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Quantile function\n",
+ "def exp_quantile(p, l):\n",
+ " p[p<0] = 0\n",
+ " p[p>=1] = 1\n",
+ " return -np.log(1-p)/l # scipy equivalent: stats.expon.ppf(p,0,1/l)\n",
+ "\n",
+ "p = np.linspace(0, 1, 100)\n",
+ "l = 0.2\n",
+ "plt.figure()\n",
+ "plt.plot(p, exp_quantile(p, l))\n",
+ "plt.plot(p, stats.expon.ppf(p,0,1/l))\n",
+ "plt.xlabel('x')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Now draw N samples from the uniform distribution $[0,1]$. For each sample, calculate $F^{-1}(u,\\lambda)$\n",
+ "* Plot a histogram and compare the distribution of points to the exponential pdf\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Actual: 0.2\n",
+ "Estimated: 0.19919715788379894\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "def logfit(x, y):\n",
+ " good = y > 0\n",
+ " ly = np.log(y[good])\n",
+ " return np.polyfit(x[good], ly, 1, w=np.sqrt(y[good]))\n",
+ "\n",
+ "N = 1000\n",
+ "l = 0.2\n",
+ "x = np.random.rand(N)\n",
+ "y = exp_quantile(x, l)\n",
+ "\n",
+ "hist, bins = np.histogram(y, bins=10, normed=True)\n",
+ "bc = 0.5*(bins[:-1] + bins[1:])\n",
+ "\n",
+ "popt = logfit(bc, hist)\n",
+ "\n",
+ "print('Actual:', l)\n",
+ "print('Estimated: ', -popt[0])\n",
+ "\n",
+ "q = np.linspace(0, bc[-1], 200)\n",
+ "\n",
+ "\n",
+ "# Check the fit\n",
+ "valid = hist>0\n",
+ "plt.figure()\n",
+ "plt.scatter(bc[valid], np.log(hist[valid]), marker='o')\n",
+ "plt.plot(q, np.polyval(popt, q))\n",
+ "\n",
+ "# Plot histogram, fit, and calculated pdf\n",
+ "plt.figure()\n",
+ "plt.bar(bc, hist)\n",
+ "plt.plot(q, np.exp(np.polyval(popt, q)))\n",
+ "plt.plot(q, stats.expon.pdf(q, scale=1/l))\n",
+ "plt.show()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 2. Smoothing data\n",
+ "## 2.1 Moving average\n",
+ "The moving average, or rolling mean, is a simple technique which can be used to remove short term or periodic (e.g. seasonal) variations in time series data, for example. It can be viewed as a \"smoothing\", and can ease trend spotting, for instance. One has to be careful when interpreting and using the result; for instance, it is generally improper to fit on such data.\n",
+ "\n",
+ "The simplest moving average can be computed using a \"sliding window\" of length $N$, with all weights equal. For example, for a 3 point moving average, the window would be $\\frac{1}{3}[1,1,1]$.\n",
+ "\n",
+ "* Write a function to compute the $N$ point moving average of a data series"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def moving_average(y, length):\n",
+ " return np.convolve(np.ones(length)/length, y, 'same')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The following line of code loads a dataset (into a ```pandas DataFrame```) containing monthly measurements of variation in the global surface temperature, stretching back as far as 1750. (More data like this can be found on http://berkeleyearth.org)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
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+ "<table border=\"1\" class=\"dataframe\">\n",
+ " <thead>\n",
+ " <tr style=\"text-align: right;\">\n",
+ " <th></th>\n",
+ " <th>Year</th>\n",
+ " <th>Month</th>\n",
+ " <th>MDiff</th>\n",
+ " <th>MUnc</th>\n",
+ " <th>YDiff</th>\n",
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+ " <th>Date</th>\n",
+ " </tr>\n",
+ " </thead>\n",
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+ " <tr>\n",
+ " <th>0</th>\n",
+ " <td>1750</td>\n",
+ " <td>1</td>\n",
+ " <td>-0.121</td>\n",
+ " <td>4.187</td>\n",
+ " <td>-0.687</td>\n",
+ " <td>2.557</td>\n",
+ " <td>-0.364</td>\n",
+ " <td>0.897</td>\n",
+ " <td>-0.160</td>\n",
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+ " <td>NaN</td>\n",
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+ " <th>1</th>\n",
+ " <td>1750</td>\n",
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+ " <td>3.177</td>\n",
+ " <td>-0.691</td>\n",
+ " <td>1.733</td>\n",
+ " <td>-0.381</td>\n",
+ " <td>0.904</td>\n",
+ " <td>-0.169</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-02-15</td>\n",
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+ " <th>2</th>\n",
+ " <td>1750</td>\n",
+ " <td>3</td>\n",
+ " <td>0.112</td>\n",
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+ " <td>-0.721</td>\n",
+ " <td>1.568</td>\n",
+ " <td>-0.401</td>\n",
+ " <td>0.918</td>\n",
+ " <td>-0.164</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-03-15</td>\n",
+ " </tr>\n",
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+ " <th>3</th>\n",
+ " <td>1750</td>\n",
+ " <td>4</td>\n",
+ " <td>0.026</td>\n",
+ " <td>2.862</td>\n",
+ " <td>-0.734</td>\n",
+ " <td>1.609</td>\n",
+ " <td>-0.452</td>\n",
+ " <td>0.951</td>\n",
+ " <td>-0.168</td>\n",
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+ " <th>4</th>\n",
+ " <td>1750</td>\n",
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+ " <td>-1.420</td>\n",
+ " <td>2.611</td>\n",
+ " <td>-1.043</td>\n",
+ " <td>1.553</td>\n",
+ " <td>-0.439</td>\n",
+ " <td>1.022</td>\n",
+ " <td>-0.167</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>5</th>\n",
+ " <td>1750</td>\n",
+ " <td>6</td>\n",
+ " <td>-1.029</td>\n",
+ " <td>3.379</td>\n",
+ " <td>-1.004</td>\n",
+ " <td>1.271</td>\n",
+ " <td>-0.414</td>\n",
+ " <td>1.060</td>\n",
+ " <td>-0.176</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>6</th>\n",
+ " <td>1750</td>\n",
+ " <td>7</td>\n",
+ " <td>-0.262</td>\n",
+ " <td>2.722</td>\n",
+ " <td>-1.049</td>\n",
+ " <td>1.026</td>\n",
+ " <td>-0.411</td>\n",
+ " <td>1.023</td>\n",
+ " <td>-0.183</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-07-15</td>\n",
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+ " <tr>\n",
+ " <th>7</th>\n",
+ " <td>1750</td>\n",
+ " <td>8</td>\n",
+ " <td>0.290</td>\n",
+ " <td>3.219</td>\n",
+ " <td>-1.137</td>\n",
+ " <td>0.792</td>\n",
+ " <td>-0.466</td>\n",
+ " <td>0.933</td>\n",
+ " <td>-0.210</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-08-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>8</th>\n",
+ " <td>1750</td>\n",
+ " <td>9</td>\n",
+ " <td>-0.851</td>\n",
+ " <td>2.121</td>\n",
+ " <td>-1.107</td>\n",
+ " <td>0.775</td>\n",
+ " <td>-0.375</td>\n",
+ " <td>0.945</td>\n",
+ " <td>-0.230</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-09-15</td>\n",
+ " </tr>\n",
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+ " <th>9</th>\n",
+ " <td>1750</td>\n",
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+ " <td>-1.448</td>\n",
+ " <td>3.078</td>\n",
+ " <td>-1.167</td>\n",
+ " <td>0.826</td>\n",
+ " <td>-0.394</td>\n",
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+ " <td>-0.211</td>\n",
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+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-10-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>10</th>\n",
+ " <td>1750</td>\n",
+ " <td>11</td>\n",
+ " <td>-3.518</td>\n",
+ " <td>1.996</td>\n",
+ " <td>-1.160</td>\n",
+ " <td>1.283</td>\n",
+ " <td>-0.423</td>\n",
+ " <td>1.094</td>\n",
+ " <td>-0.226</td>\n",
+ " <td>0.879</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-11-15</td>\n",
+ " </tr>\n",
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+ " <th>11</th>\n",
+ " <td>1750</td>\n",
+ " <td>12</td>\n",
+ " <td>-2.538</td>\n",
+ " <td>4.091</td>\n",
+ " <td>-1.210</td>\n",
+ " <td>1.458</td>\n",
+ " <td>-0.451</td>\n",
+ " <td>1.143</td>\n",
+ " <td>-0.250</td>\n",
+ " <td>0.894</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1750-12-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>12</th>\n",
+ " <td>1751</td>\n",
+ " <td>1</td>\n",
+ " <td>-0.659</td>\n",
+ " <td>3.318</td>\n",
+ " <td>-1.094</td>\n",
+ " <td>1.533</td>\n",
+ " <td>-0.464</td>\n",
+ " <td>1.148</td>\n",
+ " <td>-0.258</td>\n",
+ " <td>0.844</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-01-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>13</th>\n",
+ " <td>1751</td>\n",
+ " <td>2</td>\n",
+ " <td>-2.341</td>\n",
+ " <td>4.503</td>\n",
+ " <td>-1.047</td>\n",
+ " <td>1.776</td>\n",
+ " <td>-0.482</td>\n",
+ " <td>1.131</td>\n",
+ " <td>-0.231</td>\n",
+ " <td>0.914</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-02-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>14</th>\n",
+ " <td>1751</td>\n",
+ " <td>3</td>\n",
+ " <td>0.477</td>\n",
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+ " <td>1.673</td>\n",
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+ " <td>1.200</td>\n",
+ " <td>-0.201</td>\n",
+ " <td>0.952</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-03-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>15</th>\n",
+ " <td>1751</td>\n",
+ " <td>4</td>\n",
+ " <td>-0.690</td>\n",
+ " <td>2.489</td>\n",
+ " <td>-0.933</td>\n",
+ " <td>1.504</td>\n",
+ " <td>-0.492</td>\n",
+ " <td>1.245</td>\n",
+ " <td>-0.184</td>\n",
+ " <td>1.004</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>16</th>\n",
+ " <td>1751</td>\n",
+ " <td>5</td>\n",
+ " <td>-1.338</td>\n",
+ " <td>3.435</td>\n",
+ " <td>-0.771</td>\n",
+ " <td>1.606</td>\n",
+ " <td>-0.486</td>\n",
+ " <td>1.336</td>\n",
+ " <td>-0.184</td>\n",
+ " <td>1.019</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>17</th>\n",
+ " <td>1751</td>\n",
+ " <td>6</td>\n",
+ " <td>-1.637</td>\n",
+ " <td>3.336</td>\n",
+ " <td>-0.721</td>\n",
+ " <td>1.085</td>\n",
+ " <td>-0.539</td>\n",
+ " <td>1.393</td>\n",
+ " <td>-0.188</td>\n",
+ " <td>1.075</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>18</th>\n",
+ " <td>1751</td>\n",
+ " <td>7</td>\n",
+ " <td>1.130</td>\n",
+ " <td>3.753</td>\n",
+ " <td>-0.876</td>\n",
+ " <td>1.400</td>\n",
+ " <td>-0.527</td>\n",
+ " <td>1.212</td>\n",
+ " <td>-0.208</td>\n",
+ " <td>1.084</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-07-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>19</th>\n",
+ " <td>1751</td>\n",
+ " <td>8</td>\n",
+ " <td>0.858</td>\n",
+ " <td>2.757</td>\n",
+ " <td>-0.409</td>\n",
+ " <td>1.841</td>\n",
+ " <td>-0.538</td>\n",
+ " <td>1.097</td>\n",
+ " <td>-0.221</td>\n",
+ " <td>1.106</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-08-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>20</th>\n",
+ " <td>1751</td>\n",
+ " <td>9</td>\n",
+ " <td>-1.098</td>\n",
+ " <td>2.928</td>\n",
+ " <td>-0.382</td>\n",
+ " <td>1.840</td>\n",
+ " <td>-0.531</td>\n",
+ " <td>1.123</td>\n",
+ " <td>-0.225</td>\n",
+ " <td>1.119</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-09-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>21</th>\n",
+ " <td>1751</td>\n",
+ " <td>10</td>\n",
+ " <td>0.169</td>\n",
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+ " <td>-0.429</td>\n",
+ " <td>1.791</td>\n",
+ " <td>-0.446</td>\n",
+ " <td>1.151</td>\n",
+ " <td>-0.219</td>\n",
+ " <td>1.148</td>\n",
+ " <td>-0.276</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-10-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>22</th>\n",
+ " <td>1751</td>\n",
+ " <td>11</td>\n",
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+ " <td>2.326</td>\n",
+ " <td>-0.302</td>\n",
+ " <td>1.688</td>\n",
+ " <td>-0.437</td>\n",
+ " <td>1.160</td>\n",
+ " <td>-0.222</td>\n",
+ " <td>1.178</td>\n",
+ " <td>-0.286</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-11-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>23</th>\n",
+ " <td>1751</td>\n",
+ " <td>12</td>\n",
+ " <td>-1.935</td>\n",
+ " <td>3.412</td>\n",
+ " <td>-0.129</td>\n",
+ " <td>1.784</td>\n",
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+ " <td>1.293</td>\n",
+ " <td>-0.258</td>\n",
+ " <td>1.173</td>\n",
+ " <td>-0.316</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1751-12-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>24</th>\n",
+ " <td>1752</td>\n",
+ " <td>1</td>\n",
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+ " <td>-0.431</td>\n",
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+ " <td>1.160</td>\n",
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+ " <td>NaN</td>\n",
+ " <td>1752-01-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>25</th>\n",
+ " <td>1752</td>\n",
+ " <td>2</td>\n",
+ " <td>3.263</td>\n",
+ " <td>4.891</td>\n",
+ " <td>-0.311</td>\n",
+ " <td>1.743</td>\n",
+ " <td>-0.461</td>\n",
+ " <td>1.061</td>\n",
+ " <td>-0.216</td>\n",
+ " <td>1.213</td>\n",
+ " <td>-0.299</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-02-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>26</th>\n",
+ " <td>1752</td>\n",
+ " <td>3</td>\n",
+ " <td>0.804</td>\n",
+ " <td>3.040</td>\n",
+ " <td>-0.166</td>\n",
+ " <td>1.570</td>\n",
+ " <td>-0.480</td>\n",
+ " <td>1.053</td>\n",
+ " <td>-0.192</td>\n",
+ " <td>1.258</td>\n",
+ " <td>-0.303</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-03-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>27</th>\n",
+ " <td>1752</td>\n",
+ " <td>4</td>\n",
+ " <td>-1.259</td>\n",
+ " <td>2.243</td>\n",
+ " <td>-0.263</td>\n",
+ " <td>1.645</td>\n",
+ " <td>-0.447</td>\n",
+ " <td>1.072</td>\n",
+ " <td>-0.185</td>\n",
+ " <td>1.364</td>\n",
+ " <td>-0.295</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>28</th>\n",
+ " <td>1752</td>\n",
+ " <td>5</td>\n",
+ " <td>0.196</td>\n",
+ " <td>1.576</td>\n",
+ " <td>-0.090</td>\n",
+ " <td>1.758</td>\n",
+ " <td>-0.449</td>\n",
+ " <td>1.030</td>\n",
+ " <td>-0.178</td>\n",
+ " <td>1.431</td>\n",
+ " <td>-0.293</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>29</th>\n",
+ " <td>1752</td>\n",
+ " <td>6</td>\n",
+ " <td>0.434</td>\n",
+ " <td>3.225</td>\n",
+ " <td>0.040</td>\n",
+ " <td>1.815</td>\n",
+ " <td>-0.390</td>\n",
+ " <td>1.072</td>\n",
+ " <td>-0.179</td>\n",
+ " <td>1.504</td>\n",
+ " <td>-0.293</td>\n",
+ " <td>NaN</td>\n",
+ " <td>1752-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>...</th>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " <td>...</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3195</th>\n",
+ " <td>2016</td>\n",
+ " <td>4</td>\n",
+ " <td>1.796</td>\n",
+ " <td>0.111</td>\n",
+ " <td>1.454</td>\n",
+ " <td>0.042</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3196</th>\n",
+ " <td>2016</td>\n",
+ " <td>5</td>\n",
+ " <td>1.260</td>\n",
+ " <td>0.112</td>\n",
+ " <td>1.433</td>\n",
+ " <td>0.040</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3197</th>\n",
+ " <td>2016</td>\n",
+ " <td>6</td>\n",
+ " <td>0.882</td>\n",
+ " <td>0.078</td>\n",
+ " <td>1.387</td>\n",
+ " <td>0.034</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3198</th>\n",
+ " <td>2016</td>\n",
+ " <td>7</td>\n",
+ " <td>0.935</td>\n",
+ " <td>0.046</td>\n",
+ " <td>1.385</td>\n",
+ " <td>0.029</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-07-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3199</th>\n",
+ " <td>2016</td>\n",
+ " <td>8</td>\n",
+ " <td>1.433</td>\n",
+ " <td>0.102</td>\n",
+ " <td>1.348</td>\n",
+ " <td>0.028</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-08-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3200</th>\n",
+ " <td>2016</td>\n",
+ " <td>9</td>\n",
+ " <td>1.058</td>\n",
+ " <td>0.082</td>\n",
+ " <td>1.321</td>\n",
+ " <td>0.027</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-09-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3201</th>\n",
+ " <td>2016</td>\n",
+ " <td>10</td>\n",
+ " <td>1.019</td>\n",
+ " <td>0.062</td>\n",
+ " <td>1.280</td>\n",
+ " <td>0.031</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-10-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3202</th>\n",
+ " <td>2016</td>\n",
+ " <td>11</td>\n",
+ " <td>1.079</td>\n",
+ " <td>0.095</td>\n",
+ " <td>1.278</td>\n",
+ " <td>0.031</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-11-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3203</th>\n",
+ " <td>2016</td>\n",
+ " <td>12</td>\n",
+ " <td>1.259</td>\n",
+ " <td>0.077</td>\n",
+ " <td>1.271</td>\n",
+ " <td>0.035</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2016-12-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3204</th>\n",
+ " <td>2017</td>\n",
+ " <td>1</td>\n",
+ " <td>1.569</td>\n",
+ " <td>0.082</td>\n",
+ " <td>1.275</td>\n",
+ " <td>0.038</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-01-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3205</th>\n",
+ " <td>2017</td>\n",
+ " <td>2</td>\n",
+ " <td>1.746</td>\n",
+ " <td>0.062</td>\n",
+ " <td>1.244</td>\n",
+ " <td>0.039</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-02-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3206</th>\n",
+ " <td>2017</td>\n",
+ " <td>3</td>\n",
+ " <td>1.831</td>\n",
+ " <td>0.052</td>\n",
+ " <td>1.231</td>\n",
+ " <td>0.037</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-03-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3207</th>\n",
+ " <td>2017</td>\n",
+ " <td>4</td>\n",
+ " <td>1.301</td>\n",
+ " <td>0.144</td>\n",
+ " <td>1.253</td>\n",
+ " <td>0.038</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3208</th>\n",
+ " <td>2017</td>\n",
+ " <td>5</td>\n",
+ " <td>1.235</td>\n",
+ " <td>0.132</td>\n",
+ " <td>1.249</td>\n",
+ " <td>0.036</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3209</th>\n",
+ " <td>2017</td>\n",
+ " <td>6</td>\n",
+ " <td>0.803</td>\n",
+ " <td>0.089</td>\n",
+ " <td>1.268</td>\n",
+ " <td>0.040</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3210</th>\n",
+ " <td>2017</td>\n",
+ " <td>7</td>\n",
+ " <td>0.973</td>\n",
+ " <td>0.079</td>\n",
+ " <td>1.235</td>\n",
+ " <td>0.038</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-07-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3211</th>\n",
+ " <td>2017</td>\n",
+ " <td>8</td>\n",
+ " <td>1.066</td>\n",
+ " <td>0.086</td>\n",
+ " <td>1.180</td>\n",
+ " <td>0.039</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-08-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3212</th>\n",
+ " <td>2017</td>\n",
+ " <td>9</td>\n",
+ " <td>0.906</td>\n",
+ " <td>0.093</td>\n",
+ " <td>1.142</td>\n",
+ " <td>0.042</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-09-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3213</th>\n",
+ " <td>2017</td>\n",
+ " <td>10</td>\n",
+ " <td>1.275</td>\n",
+ " <td>0.048</td>\n",
+ " <td>1.145</td>\n",
+ " <td>0.041</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-10-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3214</th>\n",
+ " <td>2017</td>\n",
+ " <td>11</td>\n",
+ " <td>1.035</td>\n",
+ " <td>0.080</td>\n",
+ " <td>1.138</td>\n",
+ " <td>0.040</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-11-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3215</th>\n",
+ " <td>2017</td>\n",
+ " <td>12</td>\n",
+ " <td>1.487</td>\n",
+ " <td>0.073</td>\n",
+ " <td>1.161</td>\n",
+ " <td>0.040</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2017-12-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3216</th>\n",
+ " <td>2018</td>\n",
+ " <td>1</td>\n",
+ " <td>1.171</td>\n",
+ " <td>0.093</td>\n",
+ " <td>1.172</td>\n",
+ " <td>0.038</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-01-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3217</th>\n",
+ " <td>2018</td>\n",
+ " <td>2</td>\n",
+ " <td>1.093</td>\n",
+ " <td>0.102</td>\n",
+ " <td>1.166</td>\n",
+ " <td>0.035</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-02-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3218</th>\n",
+ " <td>2018</td>\n",
+ " <td>3</td>\n",
+ " <td>1.366</td>\n",
+ " <td>0.091</td>\n",
+ " <td>1.158</td>\n",
+ " <td>0.042</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-03-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3219</th>\n",
+ " <td>2018</td>\n",
+ " <td>4</td>\n",
+ " <td>1.342</td>\n",
+ " <td>0.112</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-04-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3220</th>\n",
+ " <td>2018</td>\n",
+ " <td>5</td>\n",
+ " <td>1.147</td>\n",
+ " <td>0.170</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-05-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3221</th>\n",
+ " <td>2018</td>\n",
+ " <td>6</td>\n",
+ " <td>1.078</td>\n",
+ " <td>0.122</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-06-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3222</th>\n",
+ " <td>2018</td>\n",
+ " <td>7</td>\n",
+ " <td>1.112</td>\n",
+ " <td>0.039</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-07-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3223</th>\n",
+ " <td>2018</td>\n",
+ " <td>8</td>\n",
+ " <td>0.991</td>\n",
+ " <td>0.107</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-08-15</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3224</th>\n",
+ " <td>2018</td>\n",
+ " <td>9</td>\n",
+ " <td>0.804</td>\n",
+ " <td>0.161</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>NaN</td>\n",
+ " <td>2018-09-15</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "<p>3225 rows × 13 columns</p>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ " Year Month MDiff MUnc YDiff YUnc 5YDiff 5YUnc 10YDiff 10YUnc \\\n",
+ "0 1750 1 -0.121 4.187 -0.687 2.557 -0.364 0.897 -0.160 NaN \n",
+ "1 1750 2 -1.278 3.177 -0.691 1.733 -0.381 0.904 -0.169 NaN \n",
+ "2 1750 3 0.112 3.550 -0.721 1.568 -0.401 0.918 -0.164 NaN \n",
+ "3 1750 4 0.026 2.862 -0.734 1.609 -0.452 0.951 -0.168 NaN \n",
+ "4 1750 5 -1.420 2.611 -1.043 1.553 -0.439 1.022 -0.167 NaN \n",
+ "5 1750 6 -1.029 3.379 -1.004 1.271 -0.414 1.060 -0.176 NaN \n",
+ "6 1750 7 -0.262 2.722 -1.049 1.026 -0.411 1.023 -0.183 NaN \n",
+ "7 1750 8 0.290 3.219 -1.137 0.792 -0.466 0.933 -0.210 NaN \n",
+ "8 1750 9 -0.851 2.121 -1.107 0.775 -0.375 0.945 -0.230 NaN \n",
+ "9 1750 10 -1.448 3.078 -1.167 0.826 -0.394 1.023 -0.211 NaN \n",
+ "10 1750 11 -3.518 1.996 -1.160 1.283 -0.423 1.094 -0.226 0.879 \n",
+ "11 1750 12 -2.538 4.091 -1.210 1.458 -0.451 1.143 -0.250 0.894 \n",
+ "12 1751 1 -0.659 3.318 -1.094 1.533 -0.464 1.148 -0.258 0.844 \n",
+ "13 1751 2 -2.341 4.503 -1.047 1.776 -0.482 1.131 -0.231 0.914 \n",
+ "14 1751 3 0.477 2.778 -1.068 1.673 -0.488 1.200 -0.201 0.952 \n",
+ "15 1751 4 -0.690 2.489 -0.933 1.504 -0.492 1.245 -0.184 1.004 \n",
+ "16 1751 5 -1.338 3.435 -0.771 1.606 -0.486 1.336 -0.184 1.019 \n",
+ "17 1751 6 -1.637 3.336 -0.721 1.085 -0.539 1.393 -0.188 1.075 \n",
+ "18 1751 7 1.130 3.753 -0.876 1.400 -0.527 1.212 -0.208 1.084 \n",
+ "19 1751 8 0.858 2.757 -0.409 1.841 -0.538 1.097 -0.221 1.106 \n",
+ "20 1751 9 -1.098 2.928 -0.382 1.840 -0.531 1.123 -0.225 1.119 \n",
+ "21 1751 10 0.169 4.986 -0.429 1.791 -0.446 1.151 -0.219 1.148 \n",
+ "22 1751 11 -1.577 2.326 -0.302 1.688 -0.437 1.160 -0.222 1.178 \n",
+ "23 1751 12 -1.935 3.412 -0.129 1.784 -0.426 1.293 -0.258 1.173 \n",
+ "24 1752 1 -2.523 4.962 -0.154 1.757 -0.431 1.296 -0.262 1.160 \n",
+ "25 1752 2 3.263 4.891 -0.311 1.743 -0.461 1.061 -0.216 1.213 \n",
+ "26 1752 3 0.804 3.040 -0.166 1.570 -0.480 1.053 -0.192 1.258 \n",
+ "27 1752 4 -1.259 2.243 -0.263 1.645 -0.447 1.072 -0.185 1.364 \n",
+ "28 1752 5 0.196 1.576 -0.090 1.758 -0.449 1.030 -0.178 1.431 \n",
+ "29 1752 6 0.434 3.225 0.040 1.815 -0.390 1.072 -0.179 1.504 \n",
+ "... ... ... ... ... ... ... ... ... ... ... \n",
+ "3195 2016 4 1.796 0.111 1.454 0.042 NaN NaN NaN NaN \n",
+ "3196 2016 5 1.260 0.112 1.433 0.040 NaN NaN NaN NaN \n",
+ "3197 2016 6 0.882 0.078 1.387 0.034 NaN NaN NaN NaN \n",
+ "3198 2016 7 0.935 0.046 1.385 0.029 NaN NaN NaN NaN \n",
+ "3199 2016 8 1.433 0.102 1.348 0.028 NaN NaN NaN NaN \n",
+ "3200 2016 9 1.058 0.082 1.321 0.027 NaN NaN NaN NaN \n",
+ "3201 2016 10 1.019 0.062 1.280 0.031 NaN NaN NaN NaN \n",
+ "3202 2016 11 1.079 0.095 1.278 0.031 NaN NaN NaN NaN \n",
+ "3203 2016 12 1.259 0.077 1.271 0.035 NaN NaN NaN NaN \n",
+ "3204 2017 1 1.569 0.082 1.275 0.038 NaN NaN NaN NaN \n",
+ "3205 2017 2 1.746 0.062 1.244 0.039 NaN NaN NaN NaN \n",
+ "3206 2017 3 1.831 0.052 1.231 0.037 NaN NaN NaN NaN \n",
+ "3207 2017 4 1.301 0.144 1.253 0.038 NaN NaN NaN NaN \n",
+ "3208 2017 5 1.235 0.132 1.249 0.036 NaN NaN NaN NaN \n",
+ "3209 2017 6 0.803 0.089 1.268 0.040 NaN NaN NaN NaN \n",
+ "3210 2017 7 0.973 0.079 1.235 0.038 NaN NaN NaN NaN \n",
+ "3211 2017 8 1.066 0.086 1.180 0.039 NaN NaN NaN NaN \n",
+ "3212 2017 9 0.906 0.093 1.142 0.042 NaN NaN NaN NaN \n",
+ "3213 2017 10 1.275 0.048 1.145 0.041 NaN NaN NaN NaN \n",
+ "3214 2017 11 1.035 0.080 1.138 0.040 NaN NaN NaN NaN \n",
+ "3215 2017 12 1.487 0.073 1.161 0.040 NaN NaN NaN NaN \n",
+ "3216 2018 1 1.171 0.093 1.172 0.038 NaN NaN NaN NaN \n",
+ "3217 2018 2 1.093 0.102 1.166 0.035 NaN NaN NaN NaN \n",
+ "3218 2018 3 1.366 0.091 1.158 0.042 NaN NaN NaN NaN \n",
+ "3219 2018 4 1.342 0.112 NaN NaN NaN NaN NaN NaN \n",
+ "3220 2018 5 1.147 0.170 NaN NaN NaN NaN NaN NaN \n",
+ "3221 2018 6 1.078 0.122 NaN NaN NaN NaN NaN NaN \n",
+ "3222 2018 7 1.112 0.039 NaN NaN NaN NaN NaN NaN \n",
+ "3223 2018 8 0.991 0.107 NaN NaN NaN NaN NaN NaN \n",
+ "3224 2018 9 0.804 0.161 NaN NaN NaN NaN NaN NaN \n",
+ "\n",
+ " 20YDiff 20YUnc Date \n",
+ "0 NaN NaN 1750-01-15 \n",
+ "1 NaN NaN 1750-02-15 \n",
+ "2 NaN NaN 1750-03-15 \n",
+ "3 NaN NaN 1750-04-15 \n",
+ "4 NaN NaN 1750-05-15 \n",
+ "5 NaN NaN 1750-06-15 \n",
+ "6 NaN NaN 1750-07-15 \n",
+ "7 NaN NaN 1750-08-15 \n",
+ "8 NaN NaN 1750-09-15 \n",
+ "9 NaN NaN 1750-10-15 \n",
+ "10 NaN NaN 1750-11-15 \n",
+ "11 NaN NaN 1750-12-15 \n",
+ "12 NaN NaN 1751-01-15 \n",
+ "13 NaN NaN 1751-02-15 \n",
+ "14 NaN NaN 1751-03-15 \n",
+ "15 NaN NaN 1751-04-15 \n",
+ "16 NaN NaN 1751-05-15 \n",
+ "17 NaN NaN 1751-06-15 \n",
+ "18 NaN NaN 1751-07-15 \n",
+ "19 NaN NaN 1751-08-15 \n",
+ "20 NaN NaN 1751-09-15 \n",
+ "21 -0.276 NaN 1751-10-15 \n",
+ "22 -0.286 NaN 1751-11-15 \n",
+ "23 -0.316 NaN 1751-12-15 \n",
+ "24 -0.299 NaN 1752-01-15 \n",
+ "25 -0.299 NaN 1752-02-15 \n",
+ "26 -0.303 NaN 1752-03-15 \n",
+ "27 -0.295 NaN 1752-04-15 \n",
+ "28 -0.293 NaN 1752-05-15 \n",
+ "29 -0.293 NaN 1752-06-15 \n",
+ "... ... ... ... \n",
+ "3195 NaN NaN 2016-04-15 \n",
+ "3196 NaN NaN 2016-05-15 \n",
+ "3197 NaN NaN 2016-06-15 \n",
+ "3198 NaN NaN 2016-07-15 \n",
+ "3199 NaN NaN 2016-08-15 \n",
+ "3200 NaN NaN 2016-09-15 \n",
+ "3201 NaN NaN 2016-10-15 \n",
+ "3202 NaN NaN 2016-11-15 \n",
+ "3203 NaN NaN 2016-12-15 \n",
+ "3204 NaN NaN 2017-01-15 \n",
+ "3205 NaN NaN 2017-02-15 \n",
+ "3206 NaN NaN 2017-03-15 \n",
+ "3207 NaN NaN 2017-04-15 \n",
+ "3208 NaN NaN 2017-05-15 \n",
+ "3209 NaN NaN 2017-06-15 \n",
+ "3210 NaN NaN 2017-07-15 \n",
+ "3211 NaN NaN 2017-08-15 \n",
+ "3212 NaN NaN 2017-09-15 \n",
+ "3213 NaN NaN 2017-10-15 \n",
+ "3214 NaN NaN 2017-11-15 \n",
+ "3215 NaN NaN 2017-12-15 \n",
+ "3216 NaN NaN 2018-01-15 \n",
+ "3217 NaN NaN 2018-02-15 \n",
+ "3218 NaN NaN 2018-03-15 \n",
+ "3219 NaN NaN 2018-04-15 \n",
+ "3220 NaN NaN 2018-05-15 \n",
+ "3221 NaN NaN 2018-06-15 \n",
+ "3222 NaN NaN 2018-07-15 \n",
+ "3223 NaN NaN 2018-08-15 \n",
+ "3224 NaN NaN 2018-09-15 \n",
+ "\n",
+ "[3225 rows x 13 columns]"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "df = pd.read_csv('Material/Complete_TAVG_complete.txt', skipinitialspace=True, delimiter=' ', comment='%')\n",
+ "df['Date'] = df.apply(lambda row: datetime.datetime(\n",
+ " int(row['Year']), int(row['Month']), 15), axis=1)\n",
+ "df"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Plot the data. To plot the monthly differences, for example, you can directly write ```df2['MDiff'].plot()```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# For example...\n",
+ "df.query('Year>1980 & Year<2000').plot(x='Date', y='MDiff')\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "* Apply your moving average filter to the monthly data ```MDiff```. Try (for example) 6 months, 5 years, 10 years. Plot these on top of cuts of the original data to compare."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "df['6MA'] = moving_average(df['MDiff'], 6)\n",
+ "df['5Y'] = moving_average(df['MDiff'], 60)\n",
+ "df['20Y'] = moving_average(df['MDiff'], 240)\n",
+ "\n",
+ "df.plot(x='Date', y=['6MA', '5Y', '20Y'])\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 2.2 Electronic response of RC circuit\n",
+ "\n",
+ "In general, the response of a linearly time invariant system is found to be the convolution of the its impulse response $h(t)$ and the input voltage. Consider a resistor and capacitor connected in series, driven by a time-varying voltage $u(t)$. The impulse response for such a circuit is:\n",
+ "\n",
+ "$$h_c(t) = \\frac{1}{RC} e^{-t/RC} u(t)$$\n",
+ "\n",
+ "* Write a function to calculate the impulse response as a function of time, the resistance, and the capacitance, and input. Take care to normalise the integral.\n",
+ "\n",
+ "* Now consider a noisy sinusoidal input voltage $u_N(t) = u(t) + \\epsilon(t)$, where $\\epsilon$ is a vector comprising samples draw from $N~(0,1)$. Plot the noisy signal and superimpose the clean signal.\n",
+ "\n",
+ "* Calculate the circuit response for your signal and compare the result to the noisy signal and the clean, original signal\n",
+ "\n",
+ "Play with the RC time constant and see the effect on the signal.\n",
+ "\n",
+ "\n",
+ "Note: this first order low pass filter is exactly equivalent to an exponential moving average. The \"memory\" of the output is effectively determined by the time constant.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Cutoff: 0.0005\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "def rc_impulse(t, R, C):\n",
+ " RC = R*C\n",
+ " return 1/RC * np.exp(-t/RC)\n",
+ "\n",
+ "def rc_response(t, u, R, C):\n",
+ " return np.convolve(rc_impulse(t, R, C), u)[:len(t)]*dt\n",
+ "\n",
+ "t = np.linspace(0, 0.1, 5000)\n",
+ "dt = t[1]-t[0]\n",
+ "R = 5e3\n",
+ "C = 100e-9\n",
+ "tc = R*C\n",
+ "\n",
+ "fw = 200\n",
+ "u = np.sin(2*np.pi*fw*t) + np.cos(2*np.pi*0.1*fw*t)\n",
+ "un = u + np.random.randn(len(u))\n",
+ "\n",
+ "print('Cutoff: ', tc)\n",
+ "\n",
+ "plt.figure()\n",
+ "plt.plot(t, un)\n",
+ "plt.plot(t, rc_response(t, un, R, C))\n",
+ "plt.plot(t, u)\n",
+ "plt.xlabel('Time (s)')\n",
+ "\n",
+ "# Try different cutoffs (remove noise, fast ripple, then whole thing)\n",
+ "plt.figure()\n",
+ "plt.plot(t, un)\n",
+ "plt.plot(t, rc_response(t, un, R, C))\n",
+ "plt.plot(t, rc_response(t, un, 20*R, C))\n",
+ "plt.plot(t, rc_response(t, un, 200*R, C))\n",
+ "plt.xlabel('Time (s)')\n",
+ "plt.show()\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 3. Monte Carlo methods\n",
+ "### 3.1. Particle propagation\n",
+ "The elementary processes of particle absorption and scattering are random in their nature. Propagation of particles through a slab of material with multiple scattering events may be impossible to calculate analytically, but can easily be simulated with Monte Carlo methods.\n",
+ "\n",
+ "* Consider a beam of photons propagating through an absorbing medium with absorption coefficient $\\alpha=0.2$ per unit length. What is the probability of a photon being absorbed in a unit length slab of material?\n",
+ "\n",
+ "* Now take a piece of 1D material made up of 100 slices, each unit length. Starting at x=0, propagate a beam of 1000 photons through the material, slice-by-slice. At each interface, you should \"measure\" each photon to determine whether it has been transmitted or absorbed (hint: uniform distribution, $P(abs)$)\n",
+ "\n",
+ "* Plot the number of photons which are transmitted at the end of each slice, and compare that to the Beer-Lambert-Bouger law\n",
+ "\n",
+ "* Plot a histogram of the distance travelled before absorption for each photon (free paths).\n",
+ "\n",
+ "$I(x) = I_{0}e^{-\\alpha x }$ , where $\\alpha$ is absorption coefficient"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Generated absorption probability (mean) = 0.18105\n",
+ "Fraction of escaped particles = 0.0\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "C:\\Users\\Matt\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
+ " warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "4.577\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "N_slices = 100 # Slices of material\n",
+ "N_particles = 1000 # Number of particles to simulate\n",
+ "alpha = 0.2 # absorption coefficient\n",
+ "P_abs = 1 - np.exp(-alpha) # Absorption probability in a slice\n",
+ "\n",
+ "# Generate N_slices x N_particles matrix of uniformly distributed random numbers. \n",
+ "# Transform it into a matrix of absorption events, where True = absorption, False = no absorption, \n",
+ "# mean(ABs_events) = P_abs\n",
+ "Abs_events = np.random.uniform(0,1,(N_slices,N_particles)) < P_abs \n",
+ "Abs_c = np.cumprod(Abs_events == False, axis=0) # Propagate the absorbed state (False propagates)\n",
+ "\n",
+ "free_path = np.sum(Abs_c, axis=0) # Number of \"True\" (i.e. _not_ absorbed) until absorbed\n",
+ "N_transmitted = np.append([N_particles], np.sum(Abs_c, axis=1))\n",
+ "N_escaped_final = np.sum(free_path == N_slices)\n",
+ "\n",
+ "print('Generated absorption probability (mean) = ', np.mean(Abs_events))\n",
+ "print('Fraction of escaped particles = ',N_escaped_final/N_particles)\n",
+ "\n",
+ "x = np.linspace(0,N_slices);\n",
+ "plt.plot(x,N_particles*np.exp(-x*alpha), label = 'Beer-Lambert-Bouguer law') \n",
+ "plt.plot(N_transmitted, label = 'Simulation')\n",
+ "plt.legend()\n",
+ "plt.xlabel('Propagation distance (slice #)')\n",
+ "plt.ylabel('# of transmitted particles')\n",
+ "plt.title('Transmission of %i particles' %N_particles)\n",
+ "plt.show()\n",
+ "#plt.hist(free_path[free_path!=np.inf],30,normed='True')\n",
+ "ax = plt.figure()\n",
+ "plt.hist(free_path,int(N_particles/5),normed='True')\n",
+ "plt.xlabel('Free propagation distance')\n",
+ "plt.ylabel('#')\n",
+ "plt.title('Histogram distribution of free paths')\n",
+ "plt.show()\n",
+ "print(np.mean(free_path))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### 3.2. Monte-Carlo integration: estimate $\\pi$\n",
+ "\n",
+ "In a so-called ’hit-and-miss’ approach, or ’simple sampling’, one can estimate the integral\n",
+ "of an arbitrary, well-behaved function over some interval by scattering many points over\n",
+ "some rectangular area A. The probability of a point landing below the curve is proportional\n",
+ "to the function’s integral.\n",
+ "A classic problem is to determine the value of π.\n",
+ "\n",
+ "* Uniformly distribute N points over a unit area. Plot these on top of a unit circle (or quarter circle)\n",
+ "* Calculate the proportion that are within the bounds of your shape for some number of samples N (for large N, it would be unwise to plot)\n",
+ "* Repeat the exercise for increasing N. For each run, you should compute and store the error $\\epsilon = \\bar{\\pi} - \\pi$\n",
+ "* Plot log-log the convergence of your estimate to the actual value (to machine precision) of $\\pi$, i.e. $\\epsilon$ vs the number of points $N$. Compare this to the expected rate of convergence $(1/\\sqrt N)$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Helper functions...\n",
+ "def mc_integrate_1d(f, dist_x, dist_y, n_iter):\n",
+ " # Hit and miss version\n",
+ " #\n",
+ " # f: function to be evaluated\n",
+ " # dist_x, dist_y: distributions from which to draw (x,y)\n",
+ " # Does not handle -ve y\n",
+ " x = dist_x(n_iter)\n",
+ " y = dist_y(n_iter)\n",
+ " h = f(x)\n",
+ " return np.cumsum(y < f(x)) / np.arange(1,n_iter+1)\n",
+ "\n",
+ "def mc_integrate_1d_2(f, dist_x, n_iter):\n",
+ " # Sampling\n",
+ " x = dist_x(n_iter)\n",
+ " return np.cumsum(f(x))/np.arange(1,n_iter+1)\n",
+ "\n",
+ "def plot_convergence(est, sol):\n",
+ " x = np.arange(1,len(est)+1)\n",
+ " plt.figure()\n",
+ " plt.loglog(x, np.abs(est-sol)/sol, 'b', x, 1/np.sqrt(x), 'r')\n",
+ " plt.legend(('Result', '1/sqrt(N)'))\n",
+ " plt.xlabel('N iterations')\n",
+ " plt.ylabel('Fractional error')\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Pi estimate: 3.124\n"
+ ]
+ },
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "C:\\Users\\Matt\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:12: MatplotlibDeprecationWarning: axes.hold is deprecated.\n",
+ " See the API Changes document (http://matplotlib.org/api/api_changes.html)\n",
+ " for more details.\n"
+ ]
+ },
+ {
+ "data": {
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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "N_trials = int(1e3)\n",
+ "p = np.random.uniform(0,1,size=(N_trials, 2))\n",
+ "r = np.sqrt(np.sum(p**2, 1))\n",
+ "\n",
+ "print('Pi estimate:', 4 * np.sum(r<=1) / N_trials)\n",
+ "\n",
+ "sel = (r<=1, r>1)\n",
+ "\n",
+ "def plot_pi(p, r, sel):\n",
+ " x = np.linspace(0,1,200)\n",
+ " fh, ax = plt.subplots()\n",
+ " ax.hold(True)\n",
+ " ax.scatter(p[sel[0],0], p[sel[0],1], c='r', marker='x')\n",
+ " ax.scatter(p[sel[1],0], p[sel[1],1], c='b', marker='x')\n",
+ " ax.plot(x, np.sqrt(1-x**2), 'k', linewidth=2)\n",
+ " ax.set_xlim([0, 1])\n",
+ " ax.set_ylim([0, 1])\n",
+ "\n",
+ "if N_trials <= 1e4:\n",
+ " plot_pi(p,r,sel)\n",
+ "\n",
+ "x = np.arange(1,N_trials+1)\n",
+ "c_est = 4*np.cumsum(sel[0])/x\n",
+ "c_err = np.abs(c_est-np.pi)/np.pi\n",
+ "\n",
+ "# Std: sqrt(1/N(N-1) sum{(x_i-pi)^2})\n",
+ "plot_convergence(c_est, np.pi)\n",
+ "plt.tight_layout()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "anaconda-cloud": {},
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.7"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Solutions6/Exercise_6_Solutions.pdf b/exercises/Solutions6/Exercise_6_Solutions.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..f4f61e7025bd0ef03c1a4e4c9dcdc7920b4ca5d4
Binary files /dev/null and b/exercises/Solutions6/Exercise_6_Solutions.pdf differ
diff --git a/exercises/Solutions7/.ipynb_checkpoints/Likelihoods-checkpoint.ipynb b/exercises/Solutions7/.ipynb_checkpoints/Likelihoods-checkpoint.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..acb7876d5c7820d20ebd0504a236eb43568b774f
--- /dev/null
+++ b/exercises/Solutions7/.ipynb_checkpoints/Likelihoods-checkpoint.ipynb
@@ -0,0 +1,457 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Solutions 7\n",
+ "Maximum Likelihood method"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 205,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy.optimize import curve_fit, minimize, fsolve\n",
+ "from scipy.stats import norm, chi2, lognorm"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 151,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "measurements = np.array([97.8621, 114.105, 87.7593, 93.2134, 86.6624, 87.4629, 79.7712, \\\n",
+ "91.5024, 87.7737, 89.6926, 133.506, 91.4124, 94.4401, 97.3968, \\\n",
+ "108.424, 103.197, 88.2166, 142.217, 89.0393, 102.438, 95.7987, \\\n",
+ "94.5177, 96.8171, 90.903, 132.463, 92.3394, 84.1451, 87.3447, \\\n",
+ "92.2861, 84.4213, 124.017, 90.4941, 95.7992, 92.3484, 95.9813, \\\n",
+ "88.0641, 101.002, 97.7268, 137.379, 96.213, 140.795, 99.9332, \\\n",
+ "130.087, 108.839, 90.0145, 100.313, 87.5952, 92.995, 114.457, \\\n",
+ "90.7526, 112.181, 117.857, 95.2804, 115.922, 117.043, 104.317, \\\n",
+ "126.728, 87.8592, 89.9614, 100.377, 107.38, 88.8426, 93.3224, \\\n",
+ "138.947, 102.288, 123.431, 114.334, 88.5134, 124.7, 87.7316, 84.7141, \\\n",
+ "91.1646, 87.891, 121.257, 92.9314])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1-D Maximum likelihood fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We have a set of measurements which are distributed according to the sum of two Gaussians (e.g. this can be signal and background).\n",
+ "\n",
+ "$\\rho = \\frac{1}{3}\\frac{1}{\\sqrt{2\\pi \\sigma^2}} e^{-\\frac{1}{2}\\left(\\frac{x-p}{\\sigma}\\right)^2} + \\frac{2}{3}\\frac{1}{\\sqrt{2\\pi \\sigma_b^2}} e^{-\\frac{1}{2}\\left(\\frac{x-p_b}{\\sigma_b}\\right)^2}$ \n",
+ "\n",
+ "where for one of the two peaks the parameters are known already\n",
+ "\n",
+ "$p_b = 91.0$ \n",
+ "$\\sigma_b = 5.0$ \n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 228,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood_point(x, position, width):\n",
+ " return 1.0/3/np.sqrt(2*np.pi*width**2)*np.exp(-0.5*((x-position)/(width))**2.0) + 2.0/3/np.sqrt(2*np.pi*5**2)*np.exp(-0.5*((x-91)/(5))**2.0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First, we assume the width of the peak we want to fit is already known: $\\sigma = 15.0$.\n",
+ "Perform a 1-D Maximum Likelihood fit for the position of the peak $p$.\n",
+ "\n",
+ "Complete the functions below which return the likelihood and negative log likelihood (NLL)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 347,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood_1d(params):\n",
+ " return np.prod([likelihood_point(x, params[0], 15.0) for x in measurements])\n",
+ "\n",
+ "def nll_1d(params):\n",
+ " return -np.log(likelihood_1d(params))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the NLL and give the best-fit result, including asymetric errors and plot the NLL."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 355,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "position: 117.72333147980623\n",
+ "negative error: [3.31211666]\n",
+ "positive error: [3.39091994]\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "solution = minimize(nll_1d, [100.0], method='CG')\n",
+ "min_pos = solution.x[0]\n",
+ "min0 = solution.fun\n",
+ "scan_points = np.linspace(110.0,126.0,50)\n",
+ "plt.plot(scan_points, [nll_1d([x]) - min0 for x in scan_points])\n",
+ "\n",
+ "nll_1sigma = lambda x: nll_1d([x]) - min0 - 0.5\n",
+ "print(\"position:\", min_pos)\n",
+ "print(\"negative error:\", min_pos - fsolve(nll_1sigma, min_pos-0.5))\n",
+ "print(\"positive error:\", fsolve(nll_1sigma, min_pos+0.5) - min_pos)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 2-D Likelihood fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we perform the 2-D Maximum Likelihood fit, fitting for both $\\sigma$ and $p$ at the same time."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 350,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood(params):\n",
+ " return np.prod([likelihood_point(x, params[0], params[1]) for x in measurements])\n",
+ "\n",
+ "def nll(params):\n",
+ " return -np.log(likelihood(params))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the NLL and find the best-fit result."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 353,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "position: 118.31548192622421 width: 13.629783202046086\n"
+ ]
+ }
+ ],
+ "source": [
+ "solution = minimize(nll, [120.0, 10], method='CG')\n",
+ "print(\"position:\", solution.x[0], \"width:\", solution.x[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Create a 2D contour plot of the 1, 2 and 3 $\\sigma$ contours of the NLL and plot the best-fit solution."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 354,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "scanA = np.linspace(110.0,130.0,50)\n",
+ "scanB = np.linspace(5,20,50)\n",
+ "minValue = nll(solution.x)\n",
+ "Z = [[nll([a,b]) - minValue for b in scanB] for a in scanA]\n",
+ "p1 = plt.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute numerically the error matrix of the NLL for the 2-D fit."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 301,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[11.95694692 -3.06065748]\n",
+ " [-3.06065748 5.72672173]] \n",
+ "sigma(position): 3.4578818544955507 sigma(width): 2.3930569834299082\n"
+ ]
+ }
+ ],
+ "source": [
+ "from scipy.misc import derivative\n",
+ "\n",
+ "# compute the error matrix\n",
+ "A = np.linalg.inv([\n",
+ " [\n",
+ " derivative(lambda x: nll([x, solution.x[1]]), solution.x[0], n=2),\n",
+ " derivative(lambda y: derivative(lambda x: nll([x, y]), solution.x[0]), solution.x[1])\n",
+ " ],\n",
+ " [\n",
+ " derivative(lambda x: derivative(lambda y: nll([x, y]), solution.x[1]), solution.x[0]),\n",
+ " derivative(lambda y: nll([solution.x[0], y]), solution.x[1], n=2)\n",
+ " ]\n",
+ "])\n",
+ "print(A, \"\\nsigma(position):\", np.sqrt(A[0,0]), \"sigma(width):\", np.sqrt(A[1,1]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Binned ML fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "With the same data as above, we now perform a binned ML fit and compare with the unbinned fit.\n",
+ "First, create a histogram of the data using np.histogram."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 374,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[ 1 19 26 10 7 5 5 2 0 0]\n",
+ "[ 70. 80. 90. 100. 110. 120. 130. 140. 150. 160. 170.]\n"
+ ]
+ }
+ ],
+ "source": [
+ "nBins = 10\n",
+ "histoMax = 170\n",
+ "histoMin = 70\n",
+ "binWidth = (histoMax-histoMin)/nBins\n",
+ "h0 = np.histogram(measurements, bins=nBins, range=(histoMin, histoMax))\n",
+ "print(h0[0])\n",
+ "print(h0[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute the binned NLL:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 375,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def nll_binned(params):\n",
+ " # params is a list of [position, sigma]\n",
+ " expected = [likelihood_point(x+binWidth/2, params[0], params[1])*(binWidth/2)*sum(h0[0]) for x in h0[1]]\n",
+ " return sum([-np.log(expected[i]**h0[0][i]) for i in range(nBins)])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the binned NLL:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 376,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " fun: -138.93433719876123\n",
+ " jac: array([-1.90734863e-06, 1.90734863e-06])\n",
+ " message: 'Optimization terminated successfully.'\n",
+ " nfev: 60\n",
+ " nit: 6\n",
+ " njev: 15\n",
+ " status: 0\n",
+ " success: True\n",
+ " x: array([116.43876363, 15.33581135])\n"
+ ]
+ }
+ ],
+ "source": [
+ "solution_binned=minimize(nll_binned, [120.0, 10], method='CG')\n",
+ "print(solution_binned)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Make a contour plot of the 1,2, and 3 $\\sigma$ contours for the binned NLL and overlay it with the unbinned contours."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 377,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "scanA = np.linspace(110.0,130.0,50)\n",
+ "scanB = np.linspace(5,20,50)\n",
+ "Z_binned = [[nll_binned([a,b]) - solution_binned.fun for b in scanB] for a in scanA]\n",
+ "\n",
+ "fig1, ax2 = plt.subplots(constrained_layout=True)\n",
+ "\n",
+ "p1 = ax2.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])\n",
+ "p2 = ax2.contour(scanB, scanA, Z_binned, [0.01,0.5, 2.0, 4.5], linestyles=\"dotted\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Repeat the same for 50 bins:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 373,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "scanA = np.linspace(110.0,130.0,50)\n",
+ "scanB = np.linspace(5,20,50)\n",
+ "Z_binned = [[nll_binned([a,b]) - solution_binned.fun for b in scanB] for a in scanA]\n",
+ "\n",
+ "fig1, ax2 = plt.subplots(constrained_layout=True)\n",
+ "\n",
+ "p1 = ax2.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])\n",
+ "p2 = ax2.contour(scanB, scanA, Z_binned, [0.01,0.5, 2.0, 4.5], linestyles=\"dotted\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.7"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Solutions7/.ipynb_checkpoints/Solutions_7-checkpoint.ipynb b/exercises/Solutions7/.ipynb_checkpoints/Solutions_7-checkpoint.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..154f625cbbefa434f9e96a9c3425a47ab28bf272
--- /dev/null
+++ b/exercises/Solutions7/.ipynb_checkpoints/Solutions_7-checkpoint.ipynb
@@ -0,0 +1,457 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Solutions 7\n",
+ "Maximum Likelihood method"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 205,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy.optimize import curve_fit, minimize, fsolve\n",
+ "from scipy.stats import norm, chi2, lognorm"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 151,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "measurements = np.array([97.8621, 114.105, 87.7593, 93.2134, 86.6624, 87.4629, 79.7712, \\\n",
+ "91.5024, 87.7737, 89.6926, 133.506, 91.4124, 94.4401, 97.3968, \\\n",
+ "108.424, 103.197, 88.2166, 142.217, 89.0393, 102.438, 95.7987, \\\n",
+ "94.5177, 96.8171, 90.903, 132.463, 92.3394, 84.1451, 87.3447, \\\n",
+ "92.2861, 84.4213, 124.017, 90.4941, 95.7992, 92.3484, 95.9813, \\\n",
+ "88.0641, 101.002, 97.7268, 137.379, 96.213, 140.795, 99.9332, \\\n",
+ "130.087, 108.839, 90.0145, 100.313, 87.5952, 92.995, 114.457, \\\n",
+ "90.7526, 112.181, 117.857, 95.2804, 115.922, 117.043, 104.317, \\\n",
+ "126.728, 87.8592, 89.9614, 100.377, 107.38, 88.8426, 93.3224, \\\n",
+ "138.947, 102.288, 123.431, 114.334, 88.5134, 124.7, 87.7316, 84.7141, \\\n",
+ "91.1646, 87.891, 121.257, 92.9314])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1-D Maximum likelihood fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We have a set of measurements which are distributed according to the sum of two Gaussians (e.g. this can be signal and background).\n",
+ "\n",
+ "$\\rho = \\frac{1}{3}\\frac{1}{\\sqrt{2\\pi \\sigma^2}} e^{-\\frac{1}{2}\\left(\\frac{x-p}{\\sigma}\\right)^2} + \\frac{2}{3}\\frac{1}{\\sqrt{2\\pi \\sigma_b^2}} e^{-\\frac{1}{2}\\left(\\frac{x-p_b}{\\sigma_b}\\right)^2}$ \n",
+ "\n",
+ "where for one of the two peaks the parameters are known already\n",
+ "\n",
+ "$p_b = 91.0$ \n",
+ "$\\sigma_b = 5.0$ \n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 228,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood_point(x, position, width):\n",
+ " return 1.0/3/np.sqrt(2*np.pi*width**2)*np.exp(-0.5*((x-position)/(width))**2.0) + 2.0/3/np.sqrt(2*np.pi*5**2)*np.exp(-0.5*((x-91)/(5))**2.0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First, we assume the width of the peak we want to fit is already known: $\\sigma = 15.0$.\n",
+ "Perform a 1-D Maximum Likelihood fit for the position of the peak $p$.\n",
+ "\n",
+ "Complete the functions below which return the likelihood and negative log likelihood (NLL)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 347,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood_1d(params):\n",
+ " return np.prod([likelihood_point(x, params[0], 15.0) for x in measurements])\n",
+ "\n",
+ "def nll_1d(params):\n",
+ " return -np.log(likelihood_1d(params))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the NLL and give the best-fit result, including asymetric errors and plot the NLL."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 355,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "position: 117.72333147980623\n",
+ "negative error: [3.31211666]\n",
+ "positive error: [3.39091994]\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "solution = minimize(nll_1d, [100.0], method='CG')\n",
+ "min_pos = solution.x[0]\n",
+ "min0 = solution.fun\n",
+ "scan_points = np.linspace(110.0,126.0,50)\n",
+ "plt.plot(scan_points, [nll_1d([x]) - min0 for x in scan_points])\n",
+ "\n",
+ "nll_1sigma = lambda x: nll_1d([x]) - min0 - 0.5\n",
+ "print(\"position:\", min_pos)\n",
+ "print(\"negative error:\", min_pos - fsolve(nll_1sigma, min_pos-0.5))\n",
+ "print(\"positive error:\", fsolve(nll_1sigma, min_pos+0.5) - min_pos)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 2-D Likelihood fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we perform the 2-D Maximum Likelihood fit, fitting for both $\\sigma$ and $p$ at the same time."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 350,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood(params):\n",
+ " return np.prod([likelihood_point(x, params[0], params[1]) for x in measurements])\n",
+ "\n",
+ "def nll(params):\n",
+ " return -np.log(likelihood(params))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the NLL and find the best-fit result."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 353,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "position: 118.31548192622421 width: 13.629783202046086\n"
+ ]
+ }
+ ],
+ "source": [
+ "solution = minimize(nll, [120.0, 10], method='CG')\n",
+ "print(\"position:\", solution.x[0], \"width:\", solution.x[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Create a 2D contour plot of the 1, 2 and 3 $\\sigma$ contours of the NLL and plot the best-fit solution."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 354,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "scanA = np.linspace(110.0,130.0,50)\n",
+ "scanB = np.linspace(5,20,50)\n",
+ "minValue = nll(solution.x)\n",
+ "Z = [[nll([a,b]) - minValue for b in scanB] for a in scanA]\n",
+ "p1 = plt.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute numerically the error matrix of the NLL for the 2-D fit."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 301,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[11.95694692 -3.06065748]\n",
+ " [-3.06065748 5.72672173]] \n",
+ "sigma(position): 3.4578818544955507 sigma(width): 2.3930569834299082\n"
+ ]
+ }
+ ],
+ "source": [
+ "from scipy.misc import derivative\n",
+ "\n",
+ "# compute the error matrix\n",
+ "A = np.linalg.inv([\n",
+ " [\n",
+ " derivative(lambda x: nll([x, solution.x[1]]), solution.x[0], n=2),\n",
+ " derivative(lambda y: derivative(lambda x: nll([x, y]), solution.x[0]), solution.x[1])\n",
+ " ],\n",
+ " [\n",
+ " derivative(lambda x: derivative(lambda y: nll([x, y]), solution.x[1]), solution.x[0]),\n",
+ " derivative(lambda y: nll([solution.x[0], y]), solution.x[1], n=2)\n",
+ " ]\n",
+ "])\n",
+ "print(A, \"\\nsigma(position):\", np.sqrt(A[0,0]), \"sigma(width):\", np.sqrt(A[1,1]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Binned ML fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "With the same data as above, we now perform a binned ML fit and compare with the unbinned fit.\n",
+ "First, create a histogram of the data using np.histogram."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 374,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[ 1 19 26 10 7 5 5 2 0 0]\n",
+ "[ 70. 80. 90. 100. 110. 120. 130. 140. 150. 160. 170.]\n"
+ ]
+ }
+ ],
+ "source": [
+ "nBins = 10\n",
+ "histoMax = 170\n",
+ "histoMin = 70\n",
+ "binWidth = (histoMax-histoMin)/nBins\n",
+ "h0 = np.histogram(measurements, bins=nBins, range=(histoMin, histoMax))\n",
+ "print(h0[0])\n",
+ "print(h0[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute the binned NLL:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 375,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def nll_binned(params):\n",
+ " # params is a list of [position, sigma]\n",
+ " expected = [likelihood_point(x+binWidth/2, params[0], params[1])*(binWidth/2)*sum(h0[0]) for x in h0[1]]\n",
+ " return sum([-np.log(expected[i]**h0[0][i]) for i in range(nBins)])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the binned NLL:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 376,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " fun: -138.93433719876123\n",
+ " jac: array([-1.90734863e-06, 1.90734863e-06])\n",
+ " message: 'Optimization terminated successfully.'\n",
+ " nfev: 60\n",
+ " nit: 6\n",
+ " njev: 15\n",
+ " status: 0\n",
+ " success: True\n",
+ " x: array([116.43876363, 15.33581135])\n"
+ ]
+ }
+ ],
+ "source": [
+ "solution_binned=minimize(nll_binned, [120.0, 10], method='CG')\n",
+ "print(solution_binned)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Make a contour plot of the 1,2, and 3 $\\sigma$ contours for the binned NLL and overlay it with the unbinned contours."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 377,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "scanA = np.linspace(110.0,130.0,50)\n",
+ "scanB = np.linspace(5,20,50)\n",
+ "Z_binned = [[nll_binned([a,b]) - solution_binned.fun for b in scanB] for a in scanA]\n",
+ "\n",
+ "fig1, ax2 = plt.subplots(constrained_layout=True)\n",
+ "\n",
+ "p1 = ax2.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])\n",
+ "p2 = ax2.contour(scanB, scanA, Z_binned, [0.01,0.5, 2.0, 4.5], linestyles=\"dotted\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Repeat the same for 50 bins:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 373,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "scanA = np.linspace(110.0,130.0,50)\n",
+ "scanB = np.linspace(5,20,50)\n",
+ "Z_binned = [[nll_binned([a,b]) - solution_binned.fun for b in scanB] for a in scanA]\n",
+ "\n",
+ "fig1, ax2 = plt.subplots(constrained_layout=True)\n",
+ "\n",
+ "p1 = ax2.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])\n",
+ "p2 = ax2.contour(scanB, scanA, Z_binned, [0.01,0.5, 2.0, 4.5], linestyles=\"dotted\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Solutions7/Solutions_7.ipynb b/exercises/Solutions7/Solutions_7.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..acb7876d5c7820d20ebd0504a236eb43568b774f
--- /dev/null
+++ b/exercises/Solutions7/Solutions_7.ipynb
@@ -0,0 +1,457 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Solutions 7\n",
+ "Maximum Likelihood method"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 205,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from __future__ import print_function\n",
+ "import numpy as np\n",
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy.optimize import curve_fit, minimize, fsolve\n",
+ "from scipy.stats import norm, chi2, lognorm"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 151,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "measurements = np.array([97.8621, 114.105, 87.7593, 93.2134, 86.6624, 87.4629, 79.7712, \\\n",
+ "91.5024, 87.7737, 89.6926, 133.506, 91.4124, 94.4401, 97.3968, \\\n",
+ "108.424, 103.197, 88.2166, 142.217, 89.0393, 102.438, 95.7987, \\\n",
+ "94.5177, 96.8171, 90.903, 132.463, 92.3394, 84.1451, 87.3447, \\\n",
+ "92.2861, 84.4213, 124.017, 90.4941, 95.7992, 92.3484, 95.9813, \\\n",
+ "88.0641, 101.002, 97.7268, 137.379, 96.213, 140.795, 99.9332, \\\n",
+ "130.087, 108.839, 90.0145, 100.313, 87.5952, 92.995, 114.457, \\\n",
+ "90.7526, 112.181, 117.857, 95.2804, 115.922, 117.043, 104.317, \\\n",
+ "126.728, 87.8592, 89.9614, 100.377, 107.38, 88.8426, 93.3224, \\\n",
+ "138.947, 102.288, 123.431, 114.334, 88.5134, 124.7, 87.7316, 84.7141, \\\n",
+ "91.1646, 87.891, 121.257, 92.9314])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1-D Maximum likelihood fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We have a set of measurements which are distributed according to the sum of two Gaussians (e.g. this can be signal and background).\n",
+ "\n",
+ "$\\rho = \\frac{1}{3}\\frac{1}{\\sqrt{2\\pi \\sigma^2}} e^{-\\frac{1}{2}\\left(\\frac{x-p}{\\sigma}\\right)^2} + \\frac{2}{3}\\frac{1}{\\sqrt{2\\pi \\sigma_b^2}} e^{-\\frac{1}{2}\\left(\\frac{x-p_b}{\\sigma_b}\\right)^2}$ \n",
+ "\n",
+ "where for one of the two peaks the parameters are known already\n",
+ "\n",
+ "$p_b = 91.0$ \n",
+ "$\\sigma_b = 5.0$ \n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 228,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood_point(x, position, width):\n",
+ " return 1.0/3/np.sqrt(2*np.pi*width**2)*np.exp(-0.5*((x-position)/(width))**2.0) + 2.0/3/np.sqrt(2*np.pi*5**2)*np.exp(-0.5*((x-91)/(5))**2.0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First, we assume the width of the peak we want to fit is already known: $\\sigma = 15.0$.\n",
+ "Perform a 1-D Maximum Likelihood fit for the position of the peak $p$.\n",
+ "\n",
+ "Complete the functions below which return the likelihood and negative log likelihood (NLL)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 347,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood_1d(params):\n",
+ " return np.prod([likelihood_point(x, params[0], 15.0) for x in measurements])\n",
+ "\n",
+ "def nll_1d(params):\n",
+ " return -np.log(likelihood_1d(params))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the NLL and give the best-fit result, including asymetric errors and plot the NLL."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 355,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "position: 117.72333147980623\n",
+ "negative error: [3.31211666]\n",
+ "positive error: [3.39091994]\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "solution = minimize(nll_1d, [100.0], method='CG')\n",
+ "min_pos = solution.x[0]\n",
+ "min0 = solution.fun\n",
+ "scan_points = np.linspace(110.0,126.0,50)\n",
+ "plt.plot(scan_points, [nll_1d([x]) - min0 for x in scan_points])\n",
+ "\n",
+ "nll_1sigma = lambda x: nll_1d([x]) - min0 - 0.5\n",
+ "print(\"position:\", min_pos)\n",
+ "print(\"negative error:\", min_pos - fsolve(nll_1sigma, min_pos-0.5))\n",
+ "print(\"positive error:\", fsolve(nll_1sigma, min_pos+0.5) - min_pos)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 2-D Likelihood fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we perform the 2-D Maximum Likelihood fit, fitting for both $\\sigma$ and $p$ at the same time."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 350,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def likelihood(params):\n",
+ " return np.prod([likelihood_point(x, params[0], params[1]) for x in measurements])\n",
+ "\n",
+ "def nll(params):\n",
+ " return -np.log(likelihood(params))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the NLL and find the best-fit result."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 353,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "position: 118.31548192622421 width: 13.629783202046086\n"
+ ]
+ }
+ ],
+ "source": [
+ "solution = minimize(nll, [120.0, 10], method='CG')\n",
+ "print(\"position:\", solution.x[0], \"width:\", solution.x[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Create a 2D contour plot of the 1, 2 and 3 $\\sigma$ contours of the NLL and plot the best-fit solution."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 354,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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lwuF243S7cXk8mMWE2WTC4vsxmwSL2YzNbCYsyEZ4kI1wexBhQUGE2qx6hJh2VqVdorRUyUFEBgEPAX2UUvnFtscDGUopt4g0AhKAPac4xDxgPPBv3+Pc0sShlR/lyfB2PqsiJOZznRhOwaMU6Tl5/HUsmxTfz1/Hckg9lsPRvHyOFRaSlV9ITlFRuZRvEiEsyEZUsJ34sFCqhYcRHxbqex5KtbBQakZGUDsqAptZ9w9p5+asyUFEZgB9gTgRSQaewjs6KQhY7LtyWeUbmdQbeFZEXIAbuEUpleE7zofA+0qpNXiTwpciMgE4AFxe1h9MKz2lClCZt4D7LyTm0yrflOT2eNifkcWu9KPsTDvCrrQj7Ew/SnLmMZye/x1THhVsp2ZEOLFhITSIjSY62E5ksJ0o32NksB27xYLN4q0N2MxmbBYLNrMZi9mEx6Nwety4PQqX243Lo3B7PBS5XeQUOsgtKiKnqIicQgc5RUXkFjnIzC8gPTePbYfSWZ67jzyH439iMolQMyKcutGR1I+Jom50JPWio2gcF0OD2GgsJn27k3YyvUyo9j+UcqOy7oCiJUjUW4j9YqND8iulFPsyslh3MIX1ySlsSU1jd/pRHG43AALUj4kiIT6OBrFR1IqMoHZkBLUiw6kZGUFYkM3YDwDkORyk5+SRlptHSlY2BzKz2J95jIOZWRzIPEZmfsHf+1rNZhrHxZAQH0vTanE0qxZH02px1IgI001WlYheJlQ7L0opVPZzUPQTEv5ElUgMTrebTSmHWXvwL9YfTGV9cgoZvpNnpD2INrVrcE3D9jSNjyWhWhyN42IItloNjvrMQm02QmNtNIiNhvon/z6nsIj9mVns9tWEdqYdZfX+ZOZv3v73PrGhIbStVZ02tWrQtnYN2tWuQYTd7sdPoRlNJwftH/lToWC69wa30GuNjqbcFDid/Jq0n8Xbd7Ns1x6OFXr7BBrERNE3oSEd69aiQ51aNIqLwVQJr57D7UG0rlmd1jX/dwGZYwWF7Eo/wvbDR9iccpiNKYdYtmsvCm+NqUl8LB3r1qJr/bp0a1iX2FC99ndlppuVNACUc4d3Er2gnkjUewG10HlZyCooZOnOJBZvT2LFnv0UulxE2oPo17QRFzZtTGK92vpkdwq5RUVsSjnM+mRvrWr9wdS/O9ibVouje8O6dG9Qj8716wREk5p2aqVpVtLJQUMpJ+ro5eA5jMR9i5hijA6pTLg8Hn7ZvY+v1m9m2a49uJWiRkQYA5o1YUAzb0Kw6lE858Tl8bA1NY2Vew+wct8B1h5IweF2YxahXZ2a9EtoSN+ERiTEx+o+iwCik4NWKir3HVTuW94FeuwDjQ7nvB3MzGLWhi188+cW0nLyiAsN4dK2LRjcsimta1bXJ60yVORyse5gCiv3HuDXpP1sOeS9ZalOVAT9EhrRr2kjOterjc2iW7CNpJODds68zUkjwT4YU9RrRodTah6lWLpzD1P/2MBvew9gEqFPkwaMbt+aPgkNdQ3BTw5n57Js9x6W7tzDb3sPUORyE2Kz0i+hEcNaN6dn4/r6/8IAOjlo50Qphcq8DpzbkPjvEVPFmzldKcUvSft5Y+kKthxKo0ZEGFd2bMuodq2oHhFmdHhVWoHTyaq9B1myM4kftu8mq6CQqGA7g1s2ZXibFnSoU1PX4vxEJwftnKjCJaisW5Dwx5HQcUaHc87WHEjm9aW/sebAX9SJiuDO3t0Z2qa5vqkrADndbn5N2s/8zdv5aUcShS4XdaIiGNq6OSPatqRhbMW7MKlIdHLQSkwpB+rIMECQuPmIBPbY/eK2pB7mjWW/sXz3PuLDQrmtV1dGd2itp4ioIHKLHPy4fTfzNm9j5d6DeJSiS/06XN6hNQObJ2C36v6JsqaTg1ZiKu9TVM4LSNQkxN7P6HBKJC0nlxd/+JmFW3cSFWznph6dubpzu4C/KU07vcM5uczduJWv1m/mQOYxIu1BDG/TgjGd2tIkXq9HXlZ0ctBKRKlCVHpfsDRHoj+pEO2+P+1I4rEFi8l3OLihWyITunci3B5kdFhaGfEoxe/7DjJr/Wa+374bp9tNtwZ1Gd+1A30TGlXKmxH9SU+foZVMwTfgyUDCbg/4xFDgdPLS4uXMWLuRFtXjeW3kYBrrK8pKxyRC94b16N6wHo/lFzBr/Wamr/mTW7+YR+O4GCZ0T2RY62Z6SKwf6ZpDFaOUG3XkYjBFITFfBXRy2H4onftmLyTpSAY3dOvEvf166JNDFeJ0u1m0dRcfrlzD9sPpVAsPZXyXjlzZsY2uNZ4j3ayknZUqXITKuguJejtgJ9bzKMWU39fz6pJfiQq289KlF3NBo1PMIKdVCUopVuw5wIcr/2Dl3oOEBdkY07Et13XrSHxY6RayqWp0ctDOynN0DHiOInGLEAm80T0Ol4t7vl7ITzuTuLBpI54fNpCYkGCjw9ICxObUw3z02xoWbduF1Wzi2s4dmHhBZyKD9YyxZ6KTg3ZGyp2OSr8ACbsHCbvN6HBO4nC5uHPWApbt2ssjA/swvkuHgG720oyzPyOL/y5fxbxN2wi3B3FTj85c26W9Hrl2GqVJDvpuoaqkaJn3MSjwhq4WTwzPDOnPdV076sSgnVb9mCheHjGIOROvoVPdWry25FcG/vcTvly3CdcJq/NppaOTQxWiipaAqSZYAmvZT4fLxV3FEsOYTm2NDkmrIJpXj+f9MSOYNv5yakdG8MS3PzL0/Sks2ZlERWoVCURnTQ4i8rGIpInI5mLbXhGR7SKyUURmi0iUb/tFIrJWRDb5Hi88zTGfFpG/RGSD72dI2X0k7VSUKgLHb2DvF1BX5E63m7tmLWDprr08PeRCnRi0UkmsV4cZ113Ju1cMRxBu/WIe10/7mt3pR40OrcIqSc3hU2DQCdsWA62VUm2BncAjvu1HgGFKqTbAeODzMxz3daVUe9/PwnMLWztnzo2gChBbb6Mj+R/Pf7+Mpbv28tTgCxnbqZ3R4WgVmIjQv1lj5t18DY9f3JetqWmMmDyV15esoMDpNDq8CuesyUEptRzIOGHbD0opl+/lKqCOb/t6pVSKb/sWwC4iekByIHBu9D5aA+cEPH3Nn8xYu5EbuydyVWLgxKVVbFazmWu7dGDRbddxSetmvL9iNUPfn8Ly3fuMDq1CKYs+hxuA706xfRSwXilVdJr33eFrlvpYRE47JaOITBSRNSKyJj09vQzCrZqUcxOYaiHmwLi7ePX+ZJ7/fhl9Expy34UXGB2OVgnFhIbw0qWD+Oza0VjNZm6aMZt7v/6WI7l5RodWIZxXchCRxwAXMO2E7a2Al4CbT/PW94DGQHsgFTjtKjNKqclKqUSlVGJ8fPz5hFu1OTeDtY3RUQDehezvn72QutGRvDpiMGY9xbZWjro1qMu8iddwV5/uLN6RxCXvT2Hepm26w/osSv2tFJHxwFDgalXsX1lE6gCzgXFKqaRTvVcpdVgp5VZKeYAPgC6ljUM7O+XJAfcBxNra6FAAePWnX8jIK+DVkYP1NAiaX9gsFm7v3Y05N11Ng5hoHpyziDu/WkBmfoHRoQWsUiUHERkEPAQMV0rlF9seBXwLPKKUWnGG99cs9nIksPl0+2plwH3Q+2hpYGgYAElHMpi1YQtjE9vSumZ1o8PRqpgm8bFMv+4KHuzfi2W79nDp5Kms3HvA6LACUkmGss4AVgLNRCRZRCYA7wDhwGLfUNT3fbvfATQBnig2TLWa7zgfisjxO/Re9g133Qj0A+4t48+lFec+5H001TA2DuDNpSuwWy3c2rOr0aFoVZTZZOLGHol8ccMYgq1Wrp/6Na/+9AsOt9vo0AKKnj6jClD501DZzyDxvyLmaobFsfGvQ1z+8Qzu7N2NO/p0NywOTTsu3+HkxR+W8eX6zbSuWZ03Rg2hbnSU0WGVOT19hnZKyp0KWMEUZ2gcry35lZiQYK7r1snQODTtuBCbleeGXsTbo4eyPyOLkR9M56cdp+wqrXJ0cqgKPJlgikbEuP/uXWlHWLXvIBO6JxIWZDMsDk07lYEtEph909XUj4niti/n8d4vv1f50Uw6OVQFygFi7An5mz+3YjGZuKxdS0Pj0LTTqRsdybTxVzC0dXPeWPYb98/+rkrfWa2X1aoSHIBxycHpdjN30zb6JjQkJjTEsDiM5nK6yTySg9PhwuNWeJTC4/bg8XjwuBUIhEeGEBkdSlCwNaDmwKoq7FYLr44YRLNqsfxnyQr2ZWTy7hXDqRERbnRofqeTQ1WgHGDgLCY/797H0bx8RrVvZVgM/nIsI4+t6/aRejCD9NQs0g8d40jqMdJTs8g8klvipgpbkIWI6FAior3JIiY+nNoN46nbKJ56TapTu34sZkvgLdZUGYgIEy/oQpP4WO6f/R2jP5rOf68YTrvaNc/+5kpEJ4eqQDlBjPuvXrhlB7GhIfRq3MCwGMqL0+Fi2/r9rFuxi3W/7mL31pS/E4A9xEZ8jUjiakaRmNCM+JqRxFaPxGazYDKbMJkFk8n7aDaZ8ChFTlY+2Zn5ZGfmcSwzz/s8K4+Nq/fw09z1f5drtVmon1Cdhs1q0KRVbdp1a0y9xtV0baMMXdi0MV9eP4ZbvpjLuCmzeOeKYZXyb/h0dHKoCsQOnkJDilZK8ceBZLo3qIvVXDmudIsKnSydv56VP25l4+o9FOY7MJlNtGhfj2vuHOA9UTepRlhEcJmerAvyikjem87+3YfZt+Mwe3emsuaXnSz+Zi0A0fHhtOvamPbdGtOuW2Nq1I0ps7KrqoRqcXx5w1gmTPuGW2fO5T+XDWFgiwSjw/ILnRyqAgkFT64hRSdnZZOWk0fHerUNKb8sZR7JYcH0VSyYvorszDxq1otlwIiOdLwggbbdGhMaVr7rGAeHBpHQug4Jrev8z/ZDBzP4c1USG1Yl8eeq3SxbsAGAGnViSOzdlF6D2tAqsSFmsx5/UhqxoSFMGTeaiTPmcPfX3/LisIGMqAIDK3RyqApMoaCMmYly7cG/AOhUt5Yh5ZeFfTsPMfvTX1kybz1ul4eu/Zoz8vpetOncMCCacWrUjaFG3RguvrwzSikOJKWxYeVuNvy2m8XfrGXB9FVEx4XR46LW9BrUhtaddaI4VxF2Ox9dfRm3fzmPh+Z9T57DwdWd2xsdVrnSyaEqEG9yUEr5/WS27mAK4UFBJMQHxlTh5yJ5TzqT/72AP37eQZDdysWjOzNi/AXUaRi4swOLCPWbVKd+k+pceu0FFOQV8cfPO/hl0SZ+nL2Wb2esIio2jN5D2jJkTFfqN9HzW5VUqM3GpDEjuPfrhTy7aCmFLhcTup/TTccVik4OVYCYYlC4QWXB6ZfOKBf7MrJoEh9T4abl/uPnHbx473TMFhPj7hnIJWO6EhEdanRY5yw4NIjeQ9rSe0hbCvMd/PHzdpZ/t4mFM39n3ue/0blPM0bd0Ju2XRsFRC0o0AVZLLw5+hL+NWcRL//4C3aLpdLWIHRyqArMviYddwqY/Jsc0nPySKhWcWoNSinmfLaCD1/6lobNa/LUe+OJrxFpdFhlwh5io9fgtvQa3JZjGXl8O2MV86b+xsPjP6BJq9qMuqEXPS9ug8VaOQYOlBer2czLIwZR5HLz7KKlhNpslbIPomJdzmmlY/Z1Brv/8nvR6bl5VAurGFfcLqebt5+azeQXF9Ctf0tenXZLpUkMJ4qMCeWq2/vz2dKHueu5yyjMd/DS/TOZMPAVZn/6C4X5DqNDDGhWs5nXRw2hR8N6PDr/B5bu3GN0SGVOJ4eqwKDkUOh0kVNURFwFSA45x/J5fMJHfPfFaq68uS+PvXU19pDKPwdUkN3K4Cu6MGnhvTz13jiq1Y5m8ovfcsNFLzP38xU4Ha6zH6SKCrJYePvyYbSsWY27v17AmgP+v/gqTzo5VAUSBRKKcvt3UZOsAu8qW9Eh5TvE83y5nG6evf1ztqzbz/0vXc519w3CVMH6SM6XyWSi24UteWXqzbw6/RbqNIrn/f+bz+2Xvsn633YZHV7ACguyMXnsSGpFRnD7l/M4mJlldEhlpmp9A6ooEQFLM3Bu92u5xzuh3Z7Ant1y8osL2PzHXu59YTQDRujpxFt1asBLUyby9PvjcTrdPHr9Rzx/1zTSUirPia8sxYT0s0YwAAAgAElEQVQEM3nMCABu/WIeuUWVo0lOJ4eqwtocXNvxLtvtHzbfHdGBvMLWkrnrmT9tJZfd0IsLh3cwOpyAISJ07deCSd/ey7i7L+KPn7czcchrzHx/qW5qOoV6MVG8MeoS9hzJ4F9zFuGpBNN96+RQRYilhfdGOHey38q0+SaGc7gCMznkZhcw+d8LaN6+HjfcP8jocAKSLcjK2Nv6M2nhfST2bsZnr3/PPZf/l6RtKUaHFnC6N6zHIwP78NPOJN5attLocM5biZKDiHwsImkisrnYtldEZLuIbBSR2SISVex3j4jIbhHZISIXn+aYDUXkdxHZJSJfiBi84EBlZ23hfXRt81uRf9ccXIF5pfnFpGVkZ+Zz+5OX6hlOz6J67Wgef+sannp3HJlHc7l79DvM+vDnKr8gzomu6dye0e1b896vv/P9tordV1PSmsOnwImXVouB1kqptsBO4BEAEWkJjAFa+d7zroic6pv3EvC6UioByAQmnHP0WslZmgM2lGOd34o0m0xEBdtJyzVm6o4z8Xg8LJm7jm79W9CkVcWf98lfuvVvyaQF99K9fys+euU7nrvjc/JyjJnUMRCJCE8N7kfbWjV4fMFi/srKNjqkUitRclBKLQcyTtj2g1Lq+CXhKuD4bGCXAjOVUkVKqb3AbqBL8feK91bMC4FZvk2fASNK9Qm0EhGxgbUdOP7wa7n1Y6I4EIAjOLau209Geg69h7QzOpQKJzwqhEffvIqJjwxl9bLt3DXqbfZuTzU6rIBhs1h4beRgXB4PD8/7HrfHf/18Zams+hxuAL7zPa8NHCz2u2TftuJigaxiyeVU+wAgIhNFZI2IrElPTy+jcKsoW2dwbUX5cYbWetFRHMg45rfySuqXRZuwBVno2re50aFUSCLCyOt68tKUiRQVOLn3ynf5cc5ao8MKGPVionj84n6s3p/Mx6sq5r/LeScHEXkMcAHTjm86xW4nNkyWZB/vRqUmK6USlVKJ8fGBO+FZRSC2zoAHnBv8Vma96EhSs3MCqt/B4/Gw4vvNJPZuRnCocSvkVQatOjXgnTl30bx9PV576Cs+enkhngp6pVzWLmvXkoHNm/Dm0t/YdijN6HDO2XklBxEZDwwFrlb/9EwlA3WL7VYHOHFowxEgSuTv5clOtY9W1qwdACuqaIXfimwYG4NHKZKOZJx9Zz9JPZDB0bRsuvTRtYayEBUbxvMf3cDQq7ox66PlvPvsPJ0g8NaunrlkAFEhdh5bsLjCNS+VOjmIyCDgIWC4Uiq/2K/mAWNEJEhEGgIJwOri7/UlkqXAaN+m8cDc0sailYyYQsDWDYp+8Nsokw51vevurj0YOLk/80gOAPG1os6yp1ZSZouZ2568lNE39uHbGat0gvCJCQnmkYv6siU1jZlrNxodzjkp6VDWGcBKoJmIJIvIBOAdIBxYLCIbROR9AKXUFuBLYCuwCLhdKeX2HWehiBxf9eUh4D4R2Y23D+KjMvxc2mmIfRC4D4Jrq1/Kqx0ZQY2IMNYG0Lwzmene5BAdF25wJJWLiHDDA4N0gjjBkFZN6dGwHv9ZuoL0ABy5dzolmrJbKTX2FJtPezJXSj0PPH+K7UOKPd/DCaOYND+wD4DsJ1GFCxFrq3IvTkToVLc2fxxINmSxoVPJPOrtkI+OCzM4ksrneIIAmPXhzwDc9uTwKjdXVXEiwpODL2TYpM95afFyXh052OiQSqTq/o9VUWKKBlsPKPzOb1NpdKpXm7ScPA5kBsaopWMZ3qu38KgQgyOpnE6sQXzy6iKjQzJcw9hobuqRyPzN21lzwH+zFJwPnRyqIAke7p1Gw7nGL+X1blwfgCU7k/xS3tmEhHlHKOXn6pu3ysvxBHHJWG8ntR7mCjdf0IVq4aH8Z8mKCnFnuU4OVZF9IEgYKn/W2fctA3Wjo2hePZ7F23f7pbyzia/h7Yg+khoYNZnKSkS45bFhtOvaiLefnM2e7YEzKMEIdquF23p1Ze3BFJYn7TM6nLPSyaEKEgkG+yVQuMhvN8Rd1Kwx6w6mBESH3PFRSumHdHIobxarmYdfv4rwyBCev2talZ9qY1T71tSNjuSNpb8F/MytOjlUURI8GiiEwgV+Ke+i5gko4Mcdxtce4mt6l/5MTw28aT0qo6jYMB5+/SoOJWfyxmNfV4gmlfJiM5u5s3d3th5KC/iJ+XRyqKqsbcHSFJU/0y9f1qbVYmkYG838Tf5dcOhUouPCCQ4NYveWwBleW9m1TmzA+HsG8uv3m1j1k3+GUQeqoa2b0SAmio9XBnY/jE4OVZSIICFXee938MN0GiLCqPatWHswxfC7pc1mEx16NGHtrzur9FWsv112fS/qJ1Tn/RfmU1hQOVZLKw2zycQ1nduzMeUQG/86ZHQ4p6WTQ1Vmv9TXMT3t7PuWgRFtW2Ixmfh6w+az71zOEns3Iz31GAd2B+6cN0opdqxJ4o1bJnNf3yeZ9Z/5HEkJnGlIzpXF6r2LOu2vLL6cvMzocAw1sl1LQmxWpv7hv3nOzpVODlWYmEIh+DLvPQ/uI+VeXnxYKH0TGjJn4zbDlw7t1LMpAGt+2WFoHKeSm5XHnHe+45aOD3JHl4f58fOfycnIZdIDU7iq7i08OOAZFn28hLzs/LMfLMC07dKIvkPbM+vD5aTsL/+/uUAVFhTEZe1asXDrTo7mBeb/o04OVZyEXAU4oWCmX8q7vENrjubl86PBw1qr1YqifkJ1flu8xdA4TuXZy1/jv3d9jNli5q53b+KLlMl8sPE/fLztDa55YjRpB47w2o3vcVPr+ziwveL1m9z4ryFYrGY+/c/3RodiqKsT2+F0uwOiJn0qOjlUcWJpBEF9UflTUaqo3Mvr1bgB9aIj+fT3dYa39w8Y2Ymt6/YH3Pj76vXiCIkI5u2VLzDsloGERoYCULdZbcY9fQWf7niL15Y9g8vp4r7eT7Br3R6DIz43sdUjuGRsN1b8sJnDyRW3mex8NYqLoUOdmny7ZafRoZySTg4aEnIDeDKgYE65l2U2mbiuWyf+/OsQ65KNPSlfPCqRILuVeZ//ZmgcJ0oc1IH87AK2rz517UpEaNu7Jf9Z/hxBIUE8NeJlnA6nn6M8P8Ov6Q4izJu20uhQDDW4ZVO2H043fJDGqejkoIGtK1haofI+9st8S5e1a0lUsJ2PfjN2KF94VAgXXtqBpfM3/D2NdyDoOKANJpPwx6L1Z9yvTkJN7nr3JtKTj7L8q1V+iq5sxNeMoufFrVn05Wryc8u/xhqoBrVsigDfbQm8vi+dHDTvsNbQCeDeC0XLyr28YKuVazq356edSYavkDXqht64nO6AGj0THh1G825N+fWb38nNOvMd5Z0Htadei9rMfutbP0VXdkZe15P83CIWz/bPHF+BqHp4GJ3r1wnIpiWdHDQv+8VgroPKfQPf8hvlalyXDkQF2/n34uWG9j3UbhDHRZd1Yt7UlSRtC5y+hxF3DObgjhRubv8Afy47fad5QU4BecfyMVvMfoyubDRvV48GTWuw8seqfVPcRc2bsOdoBgcDZNbi40q0noNW+YlYIew+1LH7oHAeBI8s1/Iig+3c2ac7zy1ayk87khjQvEm5lncmEx4cwu9Lt/PGY1/zxpe3BcSJtt+YC6jRsBovjXubB/s/Q/1WdWjeuQl52fnkZReQn+1NCsfSs8nNzOWZOQ8ZHXKptOvWmEVfrsbpcGG1Vc3TUfcG3lWVf99/kLrRkQZH8w9dc9D+YR8CltaonDdQqvwnSBvTqS1N4mJ46cflOFyuci/vdMKjQrj18eHs3vIXsz/91bA4TtSiawLvrXuZEXcOxmqzsOaHPzmw7S8KcgoIjQyhYZt69Li0M49Ov4dmiY2NDrdU2nRpSFGhk52bKsYaB+WhSXwscaEhrNp70OhQ/kfVTNXaKYmYIOJhVMY1kDcFwiaWa3kWk4lHBvZlwvRv+Gz1em7q0blcyzuTXoPbsGxBSz5/azE9LmpFrfpxhsVSXHCondveuN7oMMpNm8SGAGxcvYdWnRoYG4xBRIRuDeqyat/BgFktEUpQcxCRj0UkTUQ2F9t2uYhsERGPiCQW2361bz3p4z8eEWl/imM+LSJ/FdtvyIn7aMYQWxcIuhCV9z7KfbTcy+vZuD79Ehry7i+/czjbP9OHn4qIcNtTl2Kxmnn1oS9xOY29g7uqiIgOpV6Tauz4M7Cumv2tS4M6pOcGzmqJULJmpU+BQSds2wxcBiwvvlEpNU0p1V4p1R64FtinlDrd5CGvH99XKbXwHOPWypGEPwiqEJX7ll/Ke3RgX9weDy/8sMwv5Z1OXPVI7nz2MratP8DUd340NJaqJL5GVEANJTZCixrVANhxON3gSP5x1uSglFoOZJywbZtS6mwDc8cCM84jNs0gYmkMIVdBwRcoZ/mPv64XE8XNF3Rh0bZd/GLwCll9L2nHxaMT+XLSMtavNH7tiaogKjb073W9q6qE+FgE2JkWOPNNlWeH9JWcOTncISIbfc1W0afbSUQmisgaEVmTnh44WbWyk7A7QMJROS/6ZajpTT0SaRATzbPfLaHQaVznNMAtjw2nTqN4XnnwC7KOGtfUVVVExoSSlVG1/52DrVbqxUSxM738m3JLqlySg4h0BfKVUqebUeo9oDHQHkgFXjvdsZRSk5VSiUqpxPj4+LIPVjslMUUhYXeC4zcoWlru5dksFp4eciEHMo/x/q+ry728M7GH2Hjk9avIPVbAv++bgaOoYk1NUdFExoRRVOCs0ms8ADSNj6sSNYcxnKHWoJQ6rJRyK+9cDR8AXcopDu18hIwFcyNUzgt+mZSve8N6DG/TnA9++8PwO6cbNqvBXc+N5M9VSTx/1zQcDmNrM5WZ2+Xt/DeZq/bI+rrRkaQcyzZ8Qsrjyvx/Q0RMwOXAaeeAFpGaxV6OxNvBrQUYESsS8QS4D0Dex34p87GL+xEdYufBOYsocBp7xT5gRCfufHYkq5dt54W7puHUCaJcZB7JJSwyGFsVvQnuuLiwEIpcbvIcgVGDKslQ1hnASqCZiCSLyAQRGSkiyUB34FsRKT4xe28gWSm154TjfFhs2OvLIrJJRDYC/YB7y+TTaGVOgi6AoIt8Q1tTy728qGA7/x4+iF3pR3nxh5/LvbyzGXJlV25/agS/L93Gi/dO10Ncy0HGkRyi48KNDsNwsaEhABzJDYzFf0oyWmmsUqqmUsqqlKqjlPpIKTXb9zxIKVVdKXVxsf2XKaW6neI4Nyql1vieX6uUaqOUaquUGq6UKv+zjlZqEv4wKIXKfsYvVd6ejetzY/dEvli3ie+2Gj8h2dCrunHrE8NZ+eNW/n3/DJ0gylhmeg4xcWFGh2G4uFDvuh1H8gJj5FbVbuTTSkQsdZHwu6FoiXfeJT+4p18P2tWuweMLFrM/I8svZZ7J8Gt6MPGRoaz4fjP/d+dU3UldRjweDyn7jxJXM8roUAwXHWIHIKsgMKYw18lBK5mQ68DaEZX9HMp9qNyLs5rNvH7ZJVhMJu6atcDw4a3gnWL69icv5fel23hy4qcU5AXGl7gi27MtlayjubTvXjHnhipLZvGejitth7RWOYmYkciXACfq2GN++QOuHRXByyMGsf1wOs8uWlLu5ZXE0Ku7c/9Ll7Np9R4eunYy6YcCZ7qDiuiPn7cD0KlnU4MjCQC+KZU8OjloFY1Y6iNhD4LjFyj4yi9l9mnSkFt7duXrDVuYFSALsQ8Y0Ykn3x1H8r4j3D3qbbau2290SBXWmuU7SWhdR3dIA+LLDrrmoFVMIVeBrZv3zmmXf6ZZvrNPN7o3rMuz3y1hS+phv5R5Nl37teD1L28jODSIh8ZNZsH0VQHzpa4oUg8eZduGA3S7sIXRoQSE45OxBspfkU4O2jkRMSGRLwKgsh/xy5rTZpOJ10YOISYkhDu+mk9GXmAM9avfpDpvfHU7HXo04b/PzOHlB2bqfohz8PEri7DZLQwcnXj2nauA3CLv/Q2hNpvBkXjp5KCdMzHXRsIfA8fvkD/VL2XGhobwzhXDOJKbz21fzguIDmqA8MgQnn5/POPvvZjlCzdy9+X/Zf/uwKjdBLKNq/fw6/ebuHJiX+KqB87qZ0bKyC8AICY02OBIvHRy0EoneBQE9UXlvIJy7Tn7/mWgdc3qvDJiEBuSU7l/9kLcnvKvtZSEyWRizC39eP7jCeRk5XP36HdY9NVq3cx0Gm63h0nPz6da7Sguu6G30eEEjMx8b404JkQnB60CExEk4v9A7KhjD6GUf67kB7VsyiMD+/DjjiSe/35ZQJ2A23dvwjuz76JZm7q8+fg3PHr9R6QcCJxZNgPFoi9Xs2d7Kjc+OIQgu9XocAJGRp6v5hASYnAkXjo5aKUm5mpIxNPg/BOV+x+/lTu+a0du6NaJaWv+ZNKKP/xWbknEVo/gxc9u5I6nR7Bj40FuHfo6M979SU/c57N13X4mv7iAdl0b0XNQG6PDCSgp2TlE2oOwWwNjjimdHLTzIsGXQPBYyPsQVfj92d9QRh4c0IthrZvz+tIVfL1hi9/KLQmTycQlY7sx+bv76NqvBVPeXMztw99kQxVfPCh5bzrP3PoZcTUiefiNqwJmreRAsSvtCAnVAmPtctDJQSsDEvEYWNuijj3st/4HkwgvDB9Iz0b1eWLBYpbu9E+55yKueiSPvnk1z31wPS6Xm0eu+5CXH5hZJW+cyzqayxM3fQIiPPfB9UTF6LmUilNKsTPtKAnxsUaH8jedHLTzJmJDot4CrKisO1Ee/ww1tZnNvDl6KM1rxHPP19+yPjnFL+Weq8TezXh/wb2Mve1Cflm0iQkXvcKkF+ZXmXWTC/MdPH3LZ2Sm5/DMpPHUqh84V8eB4lB2LjlFRTTVNQetshFzLSTqdXDtRmU/4beO4rAgGx+MHUn1iDBumTmX7YcCcynZILuVcXcP5MNF99NvWHvmTV3J9f1f5oN/LyAjLdvo8MrN/t2HeXj8B+zanMxDr42hebt6RocUkLYf9v7dNq2maw5aJSRBFyBhd0PhfCg40/LhZSs2NISPrroMu9XCuM+/YlNK+U8MWFrV68Rw7wujmfTtvfQc1IY5U37juv4v8+5zcytVc5PL6Wbm+0u5Y8RbpB44ysOvX0X3Aa2MDitgrdp3EJvZTOuaNYwO5W8SSEMBzyYxMVGtWbPG6DC0M1DKg8q6GYp+Q2JnINa2fiv7YOYxxk+dxbGCQj68aiQd6tTyW9mllXLgKF9OWsqPc9YhIvQY0IrBV3ahXbfGFbbDNmlbCq8/OoukrSn0HtyWW58YTlSs7mM4k2HvTyEuLJRPrhlVLscXkbVKqXO6FV0nB63MKU8W6shIQCFxsxFTtN/KTj2Ww3VTZ5GWk8eksSPoUr+O38o+H4eTM5gzZQU/zllH7rECajeIY9AVXbhoZCciY0KNDq9EHA4XM99bwpeTlxERFcLtT43ggoGtjQ4r4KXl5NLrjQ94oH9PburRuVzK0MlBCxjKuQl1dAzYuiPRkxAx+63stJxcrp/6NclZ2fz3iuH0bFzfb2WfL0eRk18XbWbhF7+zZe0+LFYzPS9uTb9hHWjfo0lArrNcmO9g1ZKtzHx/Kft3Hab/iI7c/MhQwqMC42auQDfnz608NO97Zt94NS1rViuXMsolOYjIx8BQIE0p1dq37XLgaaAF0OX48p8i0gDYBuzwvX2VUuqWUxwzBvgCaADsA65QSmWeLVidHCoWlT8Tlf0khIzDFPG4X8vOyMvn+mnfkHQkg7dGX8KFTSveYjL7dx3muy9+56e568jNLiQo2Eq7ro3p1KspnXo2pVb9WMOanlxON+t/283S+etZ+dNWCvMdVK8dzW1PXUqXPs0NiamiumXmXLYcOszPd9+EqZz+P8srOfQGcoEpxZJDC8ADTAIeOCE5LDi+3xmO+TKQoZT6t4g8DEQrpR46W7A6OVQ8nuwXIf8TJPwxJHS8X8vOKijkxunfsO1QOq+OHMzglhVzQRlHkZMNq5JY8/MO1v66k5T93ik5atSNoVPPprTr1pjGLWtRo040JlP5jTFxOd3s3JTMsgUbWP7dRo5l5BEWYafnoLb0G9ae1okNyrX8yuhoXj693/iA67p25MEBvcqtnNIkh7PWUZVSy30n/eLbtvkKPJeyirsU6Ot7/hmwDDhrctAqHgl/COVORuW8AOZaiP0iv5UdFWzn02tGMXHGHO77ZiGZ+QVcldjOb+WXFVuQlS59mv99RZ5y4CjrftnJml928tPcdXw7YxUAwaFBNGpek0YtatK4RS0at6hFzXqxhIQFnfN3NT+3iL07UknalsKebSkkbUtl385DuJxubEEWuvZrQb9h7enUu1lANnVVFPM3b8fl8TCyXUujQzlJifocTlcjEJFlnFxz2ALsBLKBx5VSv5zieFlKqahirzOVUqfstRSRicBEgHr16nXav1+vulXRKFWAyrgWnDuRmM8Rm39P0PkOJ/d98y1Ld+1lQvdOPNC/V7lV3/3N6XCxb+ch30k8laStKezZkUphvuPvfSxWMxFRIUTGhBIZE0ZkTCgR0SEoj6Ig30FhgYPCPO9jQX4RedmFpKVk/X2vSkRUCI1bepNNk9a1SezdjNAwu1EfuVIZMXkqZpOJr2+8qlzLKbcO6XNIDkFAmFLqqIh0AuYArZRS2Se8r8TJoTjdrFRxKfcRVMYVoAqQmK8Qi39HEbk8Hv5v0VJmrN3IoBYJvHTpoICZ4KyseTweUg9kkLQ1hfRDWWRn5nMsI5djGXne55l5HMvMwySCPdRGcEgQ9mAb9hAb9mAbwaFB1G0UT+OWtWjUohZx1SMq7LDaQLYx5RCXfzSDJwb145rO7cu1rHJpVjoXSqkioMj3fK2IJAFNgRPP6IdFpKZSKlVEagJpZRmHFnjEHAfRk1FHr/TeBxEzEzH5b91gi8nEU4MvpG50JC//+AuHc3J594rhxIRWvhE1JpOJ2g3iqN0gcKZi0E426dfVRNqDGNE28JqUoIzvkBaRePGNWRSRRkACcKoZ0eYBx3snxwNzyzIOLTCJpQkS9Ta49qKy7vHbGhB/ly/ChO6JvDnqErYeSuPKT2ay9+hZB8lpWpnblXaEH3ckcW2XDoQFBcayoCc6a3IQkRnASqCZiCSLyAQRGSkiyUB34FsROT5Xc29go4j8CcwCblFKZfiO86GIHK/W/Bu4SER2ARf5XmtVgAT1QCKeAccvqOznDFmsZ1DLpky59nJyixyM+WQmaw785fcYtKpt0oo/CLFay7056Xzom+A0Q3hyXoW8yRB6G6bwewyJ4WBmFjfNmENy5jEevbgvYzu11W3rWrnbdzSTwe99xnVdO/LQRf5ZJrU0fQ56ULJmCAm7H4Ivh7x3UXkfGRJD3egovrh+DN0b1eOZ75bw0NzvKXA6DYlFqxqUUvzf98sItlq5vltHo8M5I50cNEN416B+FuyDUTkvofK/MCSOyGA7k8aM4M4+3Zm3aRtXfDyTfbofQisn323dyS9J+7inXw+qhQf2ZIQ6OWiGETEjka+ArTcq+0lUwQJD4jCJcEfvbnxw1UjScnIZ9dF0ftxetZf01MpeTmERL/zwM61qVKsQN2Pq5KAZSsSGRL8N1kTUsX+hCpcaFkuvxg345saraRgbze1fzeflH5fj8ngMi0erXN5c9htHcvN4+pL+WCrANCOBH6FW6YkEI9GTwNIclXUXyrHasFhqR0UwffwVjO3Ulo9WrmXclK9Izqo8i/BoxlixZz9T/9jA1Z3b07ZW4CzocyY6OWgBQUxhSMyHYK6DyrwZ5dxkWCw2i4Wnh/Tn1RGD2ZF2hOGTpvLNn1sMGXarVXyHc3J5YPZ3NImP5YH+PY0Op8R0ctAChphikJhPwBSNyrje0AQBMKxNc+ZNvJaWNeJ5ZN4P3PnVAjLy8g2NSatYXB4PD8z+jgKnkzdGXUKw1Wp0SCWmk4MWUMRcA4meAqYIVMZ1KMefhsZTOyqCz64dzb8G9GLZ7r0Mm/Q5y3ad6qZ/TTvZ2z+vZPX+ZJ4e3J8m8bFGh3NOdHLQAo5Y6iAx07w1iMzrUI51hsZjNpmY0D2RWRPGEhMaws0z5/Lktz+S53Cc/c1albVkZxKTfl3NqPatGBGAU3KfjU4OWkASc00kZiqY4lGZEwxPEADNq8fz9YSxTOjeiS/XbWLY+5/z8669RoelBaB1B1O475uFtKxZjScG9TM6nFLRyUELWGKugcRMKZYg1hodEjaLhX8N6M3U8VcQZLEwceYc7vn6W9Jyco0OTQsQW1IPc9OM2VQPD2PymBEVqp+hOJ0ctIDmTRCfg6kaKvNGlCMw5tZKrFebuROv5q4+3flpRxJD3pvCjLV/4tEjmqq0XWlHuGHaN0Ta7Xx6zWjiwkKNDqnUdHLQAp6Yq5+QIP4wOiTAW4u4vXc35t18LS1rVuPphUu46tMv2Jl2xOjQNAPsO5rJ9dO+xmo288k1o6gZ6b/1SsqDTg5ahSDmar4EUQOVcQOq8EejQ/pbw9hoPrtmFC8Nv5i9RzMZ+cE0Xlq8nOzCQqND0/xkU8ohxn76BS6P4tNrRlE/JursbwpwOjloFYaYqyGx08HaDJV1Byr/K6ND+puIMKJdS7677TpGtG3JJ6vWctE7nzDtjw043W6jw9PK0c+79zJuyiyCbVamj7+iwg1ZPR29noNW4ShPPirrTnD8goTdB6E3B9w6DNsOpfHi4uX8vu8gjWJjeOiiXvRp0jDg4tTOzzd/buHx+YtpWi2OyWNHBOxMq6VZz0EnB61CUsqJOvYIFM6DkHFI+KOIBFZFWCnF0l17eGnx/7d35+FV1Xcex9/f3Js9kIWEnUiACBREEEWDiiii1rqvrXZ0RudxxrpUWjoOY6ejM0/7WLHt46PjVlHUti5VW607D7ZqlWUgQCBGIEiAQICsZN/u/c4f52DT7DchnHuT7+t58uTek5PDhzz33O89v3N+3/MpRRWVzH2mAUoAAA7eSURBVM/K5N7FC5g2KsPraKafAsEgv/jor6xYs5H5WZk8eu0lJMXGeh2rS1YczJCiGkRrHoT6lRB3CZL8ICLhdz/e5kCAlzfm8djHa6hubOJbM6fxvbPmMXmQDD8MNQera7j3zQ9YW7SP78ydxX9cuJAYn8/rWN0akDvBicizInJYRLa1WXatiOSLSLDNfaERkcUislFEtrrfz+tim/eLyH4R2ex+XRxKaGMARKKQYcuQpKXQ+DZaeTsarPM6VgcxPh83zZvDh3fewi05c1m9vZBvPfkCS15/h512ZVNEeTd/O5c+9SJ5+w/y00sXc//Fi8K+MPRVj0cOIrIAqAVeUNWZ7rLpQBB4Cliqqhvc5XOAQ6p6QERmAh+o6rhOtnk/UKuqD4cS1o4cTFe0/lW0+ifgn4akPon4wrctckVdPc+tzeU3GzZT39zChdOz+d7Zp9twUxiraWziv9//iLe2fsnJ40az/IpvRtQVSX05cvD3tIKqfiIiE9stK3D/wfbrbmrzNB+IE5FYVW0KJZQxoZKE65yZ1Ed+gJZfA6lPIdEzvI7VqbTEBH646CxuyZnL8+s28eL/beKDgp2cP3Uyt+acypzxY+zEdRhZv6eYe998n0PVtdy14Az+9ezTI+JmPf01kP/Dq4FN3RSGO0Ukzx22Sh3AHGaIkLhzkbSXAB9acUNYzYXoTGpCPPecO5+P7rqVOxecwfo9xXxn5Stc9+zLvL3tS7sE1mOltXXc96dV/MMLv8cfFcXv/vF67jwnZ0gUBujlCWn3yOHto8NKbZb/hTbDSm2WzwDeAi5Q1V2dbG8UUAYo8D/AGFW9pYt/+zbgNoDMzMy5e/bs6TGvGdo0cBituh1atiHDlkHCzRHxSbyuuZk/5hXwwrpciiqqGDkskRvmnsz1c2eRlhDvdbwho7apmWfXbOC5tbk0BwLcdPoc7lqQQ0JMZPZIggG8WimU4iAi44GPgH9S1c/6uu3O2DkH01uqDWjVUmhaBQk3IsPuQ6THUdSwEFTl08Iinl+fy2df7SXW7+OSmdO4ds5MZo+zIaeB0hII8GruVh77ZC0V9Q1cND2bJeeeycQRkT+wMSDnHEIMkAK8AyzrrjCIyBhVLXGfXgls62pdY/pCJB5SHkVrlkP9CjRQDMm/RKLCv99NlAjnZGdxTnYWhaXlvLB+E29tLeD1zflMTk/jmtkzuXzWdEYkJngddVBoDQZ5L38Hj36yhj0VVcw7YTw/WnQ2s8aF70UNx0NvrlZ6CVgIpAOHgP8CKoBHgQygCtisqheKyI+BZcDONpu4QFUPi8gzwJOqukFEXgRm4wwrFQH/0qZYdMmOHExfaP3LaPUD4MtEUv8X8U/xOlLIapuaee+L7by+OZ9NxSX4o6I4N3sSV8+ewdlTJg6ZcfBjqaGlhTc257Ni7Ub2V1WT7d7jeTDOZLdJcMZ0QZvXo1XfB21Ekh9C4hZ7HanPCkvLeX1LPm/mFVBeV09aQjyLpk5m8dQp5GRNIMYfGcNnXtlVVsEruXn8YcsXVDc2MWf8GP55/mmcd+IkogZZUTjKioMx3dDAQbTqTmjJg8Q7kKS7wq7lRihaAgH+snM37+Zv5+PCIuqam0mMiWFhdhbnT53MgilZJMWG34xxL1Q3NvLR9q94I+8L1hXtIzoqisXTpnDjabOZO2HsoDtSaM+KgzE9UG1yhpgaXoPYhUjyw0jUcK9j9Vtzaytrdu9j1fZCVm/fRUV9AzE+H/MmjufMrBOYPymTqSPTB/2bYFtHC8J7BTv4bNceWoJBxqUM5/o5J3H17BkRfSOeUFlxMKYXVBUafodW/xR845HUxyPyPERXAsEgufsOsGp7IZ8W7uGr8goA0hMTmD8pkzOzTiBnUiajwrSDaH+U19XzaWER7xfs4K9f7aUlEGBs8jAumn4iF30jm1ljRw+pAnmUFQdjQqDNG9Cqu0EbkOEPIPGXeR1pQJQcqeHz3Xv57Ks9fL57L5X1DQBkpiZz0tjRnDR2FCeNHcX00SNJjImsYaiSIzXk7jtAbvEB1hftY0dpOYAVhHasOBgTIuc8xBJo2Qjx1yDDfoxEDd5LRIOqfHmwlM9372XL/hK2HjhESXUN4FxCOzk9jWmjMpg6Kp2stFSyRqQyITXZ85PcrcEgeyuq2FVWQWFpOTsOl7F5fwkHjjjZE6KjmT1+DDlZE8jJymTmmFFDviC0ZcXBmD5QbUVrH4W6J8E/GUl+BInO9jrWcVNWW8e2kkNsPXCIbSWHKDhYyqGa2q9/HiXC+JThTByRyglpKYxMSiIjKYH0pEQy3K/UhPh+XenT2NJKaW0dpbV1lNXWUVpXz+GaWorKK9lVVkFReSUtweDX649LHs6scaM5ZcJYTpkwlmmjMuxy3m5YcTCmH7TpM/TIUgjWIcP/0zmSGKKfPqsbGymqqKKovJLd5ZVff99TWUV9c0uH9X0iJMfHER8dTYzfR5zfT1y0nxi/nzi/nyhx7mvR1BqguTXgPm6lORDgSEMjtU3NHbZ5tChNTh/BlIw0pqSPYHJGGpPS0yJu+MtrVhyM6ScNlDoFonkNxF3qnIuIGnwnbvujrrmZ8tp6SuvqKKutdz7p19ZT2dBAU0srja2tNLa00hxwvje2tqIKsX4f0T4fMX4fsT4/MX4fMT4fw+NjyUhMJGNYIumJiV8flaQlxOOzo4FjwvP2GcZEOvFlQOqzUPc0WvsI2rIFkh9CYk7xOlrYSIyJITEthswIup+BCZ2VZWPaEfEhSbcjaS+CBtCKGwjWPIxqx6EPYwYrKw7GdEFiTkPS/wTxVzlHEuXXoC3bvY5lzHFhxcGYbkhUElHJP0NSnoBgKVp+FVr7a1TtRjxmcLPiYEwvSNwiJP0diF2I1i5HK76Ltu71OpYxA8aKgzG9JFFpSMpjSPJD0LodLbsErVuBaqvX0Yw55qw4GBMCEUHir0DS34XY+WjNz9Hy69CWL7yOZswxZcXBmD4Q32gk5Qkk5REIlqDlVxOsWY5qo9fRjDkmrDgY00cigsR9E0l/D+KvhLpfo2WXok1rvY5mTL9ZcTCmnyQqxbmiKfV5QNHKmwhW3YsGyryOZkyfWXEw5hiR2Bwk/W1IvA0a30bLLkDrVqLasReRMeGuV8VBRJ4VkcMisq3NsmtFJF9EgiJyarv1l4lIoYhsF5ELu9hmloisE5GdIvKKiFgnLRPxROKIGrbUKRLRc9Can6HlV9hQk4k4vT1yWAlc1G7ZNuAq4JO2C0XkG8C3gRnu7zwuIr5Otvlz4Feqmg1UArf2PrYx4U38WUjqM0jK46AN7lDTPWjgoNfRjOmVXhUHVf0EqGi3rEBVO+slcDnwsqo2qepuoBCY13YFcfognwe85i56HrgixOzGhDXnhPX5SPq7SNLd0LgarXnY61jG9MpAdGUdB7Q9hi52l7U1AqjSv80e6mwdAETkNuA292mtiAxEc5t0INLOHlrmgTcAebcBvzi2m/x79jceeJGYeWqovzAQxaGzu6O0v2lEb9ZxFqo+DTzd31DdEZENofY695plHniRlhciL3Ok5YXIzRzq7wzE1UrFwIQ2z8cDB9qtUwakiIi/m3WMMcZ4ZCCKw1vAt0UkVkSygGxgfdsV1Ln93J+Ba9xFNwNvDkAWY4wxfdDbS1lfAtYAU0WkWERuFZErRaQYyAHeEZEPAFQ1H3gV+AJ4H7hD3f7GIvKuiIx1N3sv8AMRKcQ5B7HiWP7HQjSgw1YDxDIPvEjLC5GXOdLywhDJHFH3kDbGGHN82AxpY4wxHVhxMMYY08GQLw4ikiIir4nIlyJSICI5XmfqjogscduWbBORl0QkzutM7XXRbiVNRFa57VJWiUiqlxnb6yLzcvd1kScifxCRFC8zttdZ5jY/WyoiKiLpXmTrTFd5ReQut9VOvog85FW+znTxupgtImtFZLOIbBCRed1t43gSkQki8mf3vSxfRL7vLg95/xvyxQF4BHhfVacBJwMFHufpkoiMA+4GTlXVmYAPp1VJuFlJx3Yr/w6sdtulrHafh5OVdMy8CpipqrOAHcCy4x2qByvpmBkRmQAsBsLtPqYraZdXRM7F6aowS1VnAOE2hXwlHf/GDwEPqOps4Cfu83DRCvxQVacDZwB3uC2NQt7/hnRxEJHhwALcK6VUtVlVq7xN1SM/EO/OEUkgDOeHdNZuBecN4Hn3cdi1S+miRcyHbWbxr8WZjxM2uvg7A/wK+De6mFjqlS7y3g48qKpN7jqHj3uwbnSRWYHh7uNkwmgfVNUSVc11H9fgfNgdRx/2vyFdHIBJQCnwnIhsEpFnRCTR61BdUdX9OJ+s9gIlwBFV/dDbVL02SlVLwHkBAyM9zhOqW4D3vA7RExG5DNivqlu8ztJLJwJnux2aPxaR07wO1Av3AMtFZB/O/hhuR5QAiMhEYA6wjj7sf0O9OPiBU4AnVHUOUEf4DXd8zR0nvBzIAsYCiSLyXW9TDX4ich/O4fpvvc7SHRFJAO7DGeqIFH4gFWcI5EfAq25jznB2O7BEVScAS/B2jlanRCQJeB24R1Wr+7KNoV4cioFiVV3nPn8Np1iEq/OB3apaqs4dZN4A5nucqbcOicgYAPd7WA0fdEVEbgYuAW7U8J8UNBnng8MWESnCGQbLFZHRnqbqXjHwhjrWA0Gcxnbh7GacfQ/g97TrOu01EYnGKQy/VdWjOUPe/4Z0cVDVg8A+ETnasXARzszucLUXOENEEtxPV4sI4xPo7byFs1NBhLRLEZGLcGbyX6aq9V7n6YmqblXVkao6UVUn4rzxnuK+zsPVH3Ha9yMiJwIxhH/H0wPAOe7j84CdHmb5O+77wgqgQFV/2eZHoe9/qjqkv4DZwAYgD+eFmup1ph7yPgB8idP7+UUg1utMnWR8CeecSAvOG9StOC1SVuPsSKuBNK9z9iJzIbAP2Ox+Pel1zp4yt/t5EZDudc4e/sYxwG/c13MucJ7XOXuR+SxgI7AFZzx/rtc52+Q9C+eEeV6b1+3Ffdn/rH2GMcaYDob0sJIxxpjOWXEwxhjTgRUHY4wxHVhxMMYY04EVB2OMMR1YcTDGGNOBFQdjjDEd/D9zM/Z/JpXIyAAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "scanA = np.linspace(110.0,130.0,50)\n",
+ "scanB = np.linspace(5,20,50)\n",
+ "minValue = nll(solution.x)\n",
+ "Z = [[nll([a,b]) - minValue for b in scanB] for a in scanA]\n",
+ "p1 = plt.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute numerically the error matrix of the NLL for the 2-D fit."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 301,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[[11.95694692 -3.06065748]\n",
+ " [-3.06065748 5.72672173]] \n",
+ "sigma(position): 3.4578818544955507 sigma(width): 2.3930569834299082\n"
+ ]
+ }
+ ],
+ "source": [
+ "from scipy.misc import derivative\n",
+ "\n",
+ "# compute the error matrix\n",
+ "A = np.linalg.inv([\n",
+ " [\n",
+ " derivative(lambda x: nll([x, solution.x[1]]), solution.x[0], n=2),\n",
+ " derivative(lambda y: derivative(lambda x: nll([x, y]), solution.x[0]), solution.x[1])\n",
+ " ],\n",
+ " [\n",
+ " derivative(lambda x: derivative(lambda y: nll([x, y]), solution.x[1]), solution.x[0]),\n",
+ " derivative(lambda y: nll([solution.x[0], y]), solution.x[1], n=2)\n",
+ " ]\n",
+ "])\n",
+ "print(A, \"\\nsigma(position):\", np.sqrt(A[0,0]), \"sigma(width):\", np.sqrt(A[1,1]))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Binned ML fit"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "With the same data as above, we now perform a binned ML fit and compare with the unbinned fit.\n",
+ "First, create a histogram of the data using np.histogram."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 374,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[ 1 19 26 10 7 5 5 2 0 0]\n",
+ "[ 70. 80. 90. 100. 110. 120. 130. 140. 150. 160. 170.]\n"
+ ]
+ }
+ ],
+ "source": [
+ "nBins = 10\n",
+ "histoMax = 170\n",
+ "histoMin = 70\n",
+ "binWidth = (histoMax-histoMin)/nBins\n",
+ "h0 = np.histogram(measurements, bins=nBins, range=(histoMin, histoMax))\n",
+ "print(h0[0])\n",
+ "print(h0[1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Compute the binned NLL:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 375,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def nll_binned(params):\n",
+ " # params is a list of [position, sigma]\n",
+ " expected = [likelihood_point(x+binWidth/2, params[0], params[1])*(binWidth/2)*sum(h0[0]) for x in h0[1]]\n",
+ " return sum([-np.log(expected[i]**h0[0][i]) for i in range(nBins)])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Minimize the binned NLL:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 376,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " fun: -138.93433719876123\n",
+ " jac: array([-1.90734863e-06, 1.90734863e-06])\n",
+ " message: 'Optimization terminated successfully.'\n",
+ " nfev: 60\n",
+ " nit: 6\n",
+ " njev: 15\n",
+ " status: 0\n",
+ " success: True\n",
+ " x: array([116.43876363, 15.33581135])\n"
+ ]
+ }
+ ],
+ "source": [
+ "solution_binned=minimize(nll_binned, [120.0, 10], method='CG')\n",
+ "print(solution_binned)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Make a contour plot of the 1,2, and 3 $\\sigma$ contours for the binned NLL and overlay it with the unbinned contours."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 377,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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pPx3NeREJHWa1+3h3oAcHIbGvIqGXW0u7eLcElvsxqyNUZ+peBb4kJGwoAP7020CzsdWabKWz/w8kHFvU/db+6j+iFK7qg6KfrNoSzwqQaAgfZQ21CQyrqGimBGfUWOpLRnNehMJvwVYbifmPNTjbVIWVmqoHzXwIcfW2OhFIJBQtsFaYBrA3RWovL25jE1vU4V6DRrVm3QQevhGUuHcOL/UE4E8DW1FxUtOuREPOxRb9hLXBlwSuAdhCL0Xdq6xAl/cumvcBGjYMCR9TJdrpjmYCnFGlqboh7z2ry7j6rXFsEXdWi+qRqsCf/TRIBLaoRxBxoppj9ZQjMCA4cX5xbzyrGiwyiLk1KotIyBFDKA51BIJAe5+rH+JoEUh70INDIfwGJPqv1tp04deiEXdD4WQo+Aot+BoNuRCJvBcJ6VHpn+dETIAzqix1L0WzngDfTnANQqL+gjgaBjtbVZrmT0I967HFPBvY4AV8xe/b4j88Yn8zfMI4moggUQ+W2KJIzHPgaG4lfXvQjDFI9D+Q6L/hD78Ncl6yZgtKH4WGXIBE/vHINsIgMQHOqHJUi9CcVyH/A7A3QuI+sFbKNo6hnjVowXQk6jGr84DvIPiSUPUhYj8c6AyjjERCIGzY4Q32OkjcBAiU8MS3DS2aAXHjEO82NPdtNP161Hk+EvVAUNvITYAzqhT1bECzHgHvZggbhUQ9WqJnmKH+fGvAr6u/1Vbm3WZNHB1+EzgaWXfOplRmVCARF7jOP7wh5AKk1mRwtEJc/VH1Qu5L4FmPpl+LOrpZy09F3FTpQwxMgDOqBFWf1daW+zrYYpG4cYirf7CzVSWoFoG6rU4f3o1o1oNIzMsQNtSafix0SHF3cBPcjMom4gBnp8PpiDHgugDszax16nJfg9yVaNECiH4ItAgktFLGq5phAkbQqXc3mvUXq/ux6zIk5h/FM8Cf7dSfh6b2h/AbsUX9yRoD6FkJzm6mB6lRLfh9aZD7PyicFhisHge2WtgSvwNA3avB0QyxRZ/0PGUZJmD+Qoyg0oLv0LQR4N2MxLyAxL5+1gc3zX3XmvYKa4JcibiruA1SxIaE9DDBzag2bPZa2GL+hiT+ZE1YrQXg24k/+zn8vgw08x40+6ni/UuuKHHG1y63MxnGaVD14895Ac36MzhaIrWmIWEjzsoqNlUf6l5xOO3fC949h9cgi7yzSnW9NoyyEFs0tqgHrEAXNhLyJ0LqpeAaAuG3AYHJBw5cgOZ/Ui7XNAHOqHTqz0cz74O89yBsNBL/ydnd/T//I6vXmXc7ABL1d2xx/z0rg71R84k9EVvMs0itqRDSAQomQNbDaOFPqAoSeT84zwWsXsL+g0NQz/oyXeuUAU5EPhCRAyKytsS2F0Vko4isEZEpItYkaSLSVEQKRGRV4PH2Cc4ZLyKzRWRL4Ln6rYdhlIn6ktH00VA0B4l6Eol+ChFnsLNVqdR3EH/mA8WLYxI6zFqbzN4IwFQ/GmcFcbZF4j5E4sYBNjTzHsh6GEIvPbzihHrAVgvKuPJ4af6SxgODjto2G+ioqp2BzcBjJd7bpqpdA4+7T3DOvwI/qWor4KdA2qjh1LMOTbsafLuQuLeRiJvPmlKKqqKHpkayRYJnLfiTARB7LSR00FkX6A1DRBBXfyThW2uBWs9K9OBQ/NnPW0szhfTAFj8RscWe+mTHccoAp6rzgfSjts1SVW8guRg43fql4cCEwOsJwIjTPN6oZrRovlVyw4HEf3bWDQHQzPvR9DsCC1WGWut6hV0Z7GwZRpUg4kQibkUSZkHYCMh/Hz04CC38gTPp6V8edSFjgO9LpJuJyEoR+VlELjzBMXVUdT9A4LlypqM2gkILpqMZd1uT+db6EnG2CXaWKpyqGy2YyqH7QAkbioTfAAQ6jog9iLkzjKpJ7AnYYp5D4r8EW4J1Y5h5N+rbW6bzndFAbxF5AvACh7q87Acaq2qaiPQApopIB1XNPoNr3AXcBdC4sVlvqrrRvI/RnGfAeY61+KItKthZqhxF89CsvyASA6EXnXDdLcMwjiUhXaDWV9aCxrmvWZM9l0GZS3AicgswFLhBA2VIVS1S1bTA6+XANuB4ayikiEi9wHnqAQdOdB1VHaeqPVW1Z2JiYlmzawSB5n2E5vzTWpA0/v0aHdxUFS2cixbOsja4LkbiP4azrCrWMMqLiAOJGIMkfIdEPVymc5QpwInIIOBR4ApVzS+xPVECdS8i0hxoBWw/zimmAbcEXt8CfFOWfBhVlxZ8bZXcXAOtwdviCnaWKpzmvYPmTQQODcg+96zpRGMYFUXsDQLV+6fvlFWUIvIp0B9IEJEk4CmsXpMuYHbgD3hxoMdkX+CfInJojY67VTU9cJ73gLdVdRnwf8AXInI7sBu4pky5N6okLZyNZj0OIedbq0PX0N6B6t2F5r5pDXWwRUDsq1aX5mDmSZU8t4esgkIKPR7cPp/18Poo8vpw+7y4vT68fj82ERw2Gw67DbvNhtNmw2G3Y7cJIXY7US4X0aEuIkNdhNhNm6FR/Zi5KI1ypZ7f0bQbwNkaiZtQoxcmVfdqNOM2JO4dJOScCr2W1+9nf1YOe7OyScrMYm9mNml5+WTmF5BRUHjEs8fvL/frhzocRIW6ioNebHgotSMjqB0VSZ2oSGpHRVA7MpI60ZHEhYdhMyVXo5yVZS5Ks5qAUW7Ul4xm3AO2Wkjs2zUyuGnRz+Dbi4SPthrCE+dby9aUx7lVScnJZVPKQTampLIzPYOkzGz2ZmaTnJ2Dr8TNqE2E+PAwYsNCiQ0Po0l8HF3CQ4kNCyUuPIyYsFDCnU5C7HacDjshdjshh57tDhx2G6qK1+fHq37r2W89fH4/RV4vuUVucgqLyC4sIruoiNzA65yiIlKyc1m7L4W0vHyOvkV22mzUjYmiSVwsTeKtR9P4OJrEx9IgNhqnKQ0alcQEOKNcqD8PzfgDaB4S/zliTwh2liqEFkwB7w4Iu9ZqBC9jcHN7vWw6cJCNKQfZdCCVTSkH2XzgIJkFhcX7JEZG0DA2mu6N6tMwNoYGsdE0DDzqRkdViUDh8fk4mJtPSk4uKTm5HAg8783MZld6JiuT9pPndhfvbxehYVwMLRLiaVsnsfjRKC7GlPqMcmcCnHHGVH1o1kPg3WSt4+Y8XsfZ6knVDwVfWAuM2usi0f+01rI6zYUbc4vcrEraz7Lde1m2O4nVe5Nx+3wAhDudtK6dwGXtWtGmdgJt6iTSpnYCUaFVv2OO026nXkwU9WKO30NWVUnLy2dXRia70jPZlZbJzvQMtqSmMW/LDvyBUml4iLP4s7etk0Cn+nVpUzuhSgRxo/oyAc44Y5rzfGBuyb8jrr7Bzk758iej2c9BxAEk6v5Trll1SJ7bza879rBsdxJLd+1lQ/IBfKrYRWhXtzY3nNOFrg3q0a5u7RpdehEREiIjSIiMoEejBke8V+jxsiU1UIpNSWVjSirfrdvEZ8vXAFa7X8f6dejSoC7dGtane6P61Iowq7sbpWc6mRhnRAtmoFkPQPhN2KL/FuzslAtVBc+K4iVq1LPFWtLnFEEot8jNvC3bmblhC/O37qTQ6yXEbqdLg7r0bNyQno0b0LVhPSJdIZXxMaolVWVvVjZr9iazem8yq5L2sy75AJ5AabdZrTh6Nm5A72aNOb9ZY+LCw4KcY6OylKWTiQlwRpmpLxk9OBgcrZD4j2vMcADN/wLNftKaMzOk+0n3zSksYs5mK6j9sm0nbp+PxMgILmvXikvatqR7w3qEOExFyZlwe72s3X+AZbv3smLPXpbt3kdOURECdKxfhwuaN+HCFk3o0qCeqdKswUyAMyqNqqKZ90LRAiRhBuKo/tOoqfoQsaNaBAXTIOyq4y5d4/X7mbd5O1+tWsuC7bvx+HzUiYrksnatGNS+Fd0a1q+xVY5VgdfvZ+2+FBZs38XC7btYnbQfnyoRISGc17QhF7ZoyoDWzakbXXNnzjkbmQBnVBot/AHNvB+J+gsScUews3PGNP9ztOBrJP4jRI5fhZiSncuXK3/ni5VrScnJpXZUBIPbt2FQ+1Z0aVDPBLUgyS4s5LedSSzYvosF23aSlGlNfdupfh0ubtOSi9u0oEVCvJlVppozAc6oFOrPtKombXWs1QFOs0dhVaSFP6IFk5GYF46YM9OvyqLtu/ls+RrmbN6GT5U+LZowqkcX+rdqhsNmFietSlSV7WkZ/LRpKz9u2sbqvdaae03jYxnYpgWXtG1pbkaqKRPgjErhz3oKCr5Aak1GnO2DnZ0yU8968O1DQi+20qrFd/ken4+vV6/jw8Ur2JGWQVx4GFd16cB13TvROL5siy8alS8lJ5c5m7fx46Zt/LZjDx6/n7rRkQzv1I4RndvTPCE+2Fk0SskEOKPCqXc7enAIhI/CFv33YGenzFQVzbgFfAeQhOnFpVBVZdbGrbw8ZwE70zPpUK82t57XnUHtWpnOItVcdmEhP2/ZyfR1G5m/dSd+Vbo2qMeILu0Y3L4NMWGhwc6icRImwBkVzp8xFtyLkIQfEXtwJxYuq0MlNfWng/qLZ11ZvmcvL/74CyuT9tMqsRYPD+xDv5bNTNtNDXQgJ5dv125kyur1bElNI8RuZ2CbFlzZpT0XNG9iqp6rIBPgjAql7pVo+nVI5J+QyLHBzk6ZaO5bqHcrEvNicQ/J7QfTeXnOQmZv2kpiZAR/6t+bK7u0Nz9yZwFVZV3yAaauXs+3azeSWVBInahIru3eiWu6daROVPnMM2qcORPgjAqjqmj6aPDtskpvtuo5o4Tmvo16tyExz5GW5+aN+Yv5YsXvuJwO7ux9Dree153wkJoxns84PW6fj3mbt/P5yt9ZsG0XDpuNgW1aMLpnF85r0tCU5IPMrCZgVJyieeBZjkT/o9oFN1W31dbmaAgRf0CAb9du5J/fz6XA4+H6Hp0Z27eXmQbqLBdit3Npu1Zc2q4Vu9Iz+WzFGr5etY6ZG7bQvFY8N53blRGd25sboGrElOCMUvGnjQJ/CpIws9rNWOLPfATcvyEJ31PoC+HZH+bx1aq1dG9Un38NvcT0pDNOqNDj5Yf1m/l42Sp+35dCbFgoo3p04ebzuhFvpgmrVKaK0qgQ1iKmVyFRjyMRtwY7O6dNPZvBu47tuX358+QZbE5N4+4LzuWP/c837WxGqagqK5L28eGvK5i9aSvhTifX9+jMbb26U9u001UKU0VpVAjNmwASAWFXBzsrpaZaAEW/IKGXIs7WTF3v5envJxHqdPLe6Cu5sEXTYGfRqEZEhB6NGtCjUQO2pqbxzsIljP9tBR8vXcXV3Tpyx/k9aRBbupUmjMpjbl+Nk1JfChR+D2FXl9vK1ZUi7wM0834KCzfz2LRZPDptJh3r1eGbO280wa2CbEo5yM9bdxSnp6xex2vzFhWnX/ppAQ9MnlGcfmzaTMZ8Mrk4ff+X33Lbx4fTf/pqOvd/+W1x+snps3n2h7nF6bcXLOGTZauL0z9v2cHKpH3F6SKvtxw+1bFaJtbixRGXM/PeWxnRuR1frvidS9/8kMemzWJHWkaFXNMoGxPgjJPS/E8BLxJ+U7Czcnoi7mK/7TWuHr+YKavXcU+f8xh/09XUia5GQbqKWbY7ibcXLClOv/TTAvq/9l5x+uOlK3l82qzi9Oq9yczfurM4HR7iPGKpoA716tC9xBpxvZo1pm/LpsXpTvXr0rF+3eJ0REgIYc7D7b+/7tjNij2HA9q/Z//MhN9WFqeHvfMRj37zQ3H6mR/mMnX1+uL01tQ0couKSvXZj6dxfCzPDL2E2feNYVTPzsxYt5HBb03g4Snfsycjs8znNcqPaYMzTkhV0dT+4GyDLW5csLNTKlowHVwXsS2tkBsnfokA/7nyci5o3iTYWavy8txu1u0/QM/GDbCJ8PmKNbw8ZyHz/3wnLoeDt375jTfnL2b5o2NxORzM3riV1Xv389CAPogIezKyKPJ6aZkYnAkAkjKzsIlQP8aqKpy4ZCX1o6O4uG1LAEaM+5j+rZrz54t6o6p0+b//MrpnF/56ST9Ulb9Om8ng9m3o16oZAAUezxEB9VQO5ubxweLlfLJ0NT5VbjqnK/dceC7RoWaGlPJgOpkY5Uo9m9G0oUj0s0j4tcHOzimpdxfISNf5AAAgAElEQVR6cBBZ9tsZ9nE0oHxyy3U0MXNHHldKdi4zN25haIc2xEeEM3nVOh7/dhbf3XMLLRLi+XXHbmZu2MIDF11ATFgoBR4PDputRqy55vP7+WnTNhrGxtC+Xm1yCou48r1PGNOrB6N7diEjv4DzX3qbfwwZyHXdO5Pv9jB741Z6NWt0ysHfKTm5vDp3EVNWryMmLJT7+vbi+h6da8S/WzCZAGeUK819F819EUmcj9jrnvqAKiA1fT6jJ20gu9DPxzdfQ6vaCcHOUpWRlpfPR0tWcXn71rSpk8DyPXsZPf4Lxl0/gn6tmnEgJ5cNyamc06ThWT/WKyO/gEnLVjOgdXPa1a3N6r37ufaDz3jzmmFc3LYlu9IzGbdwKXf07kmzWnHHPceG5AP83+z5LN65h6bxcfzl4gsZ0Lq5GTBeRmUJcKYNzjghdc8HR5sqH9zUm4S6V5Gam8eNn24jI9/HBzeMPOuDW5HXy7iFS1m0fRcAAry7aClr9llLyHSqX5f5f76zuEqudlQk/Vo1O+uDG0BceBhj+/aiXd3aALSvW5sZd99Mr2aNAKs69MdNW/H5/QDM3bydEeM+Zk9GFmCtQt62TiLjb7yKt68bjk2Ee7+Yxi0fT2ZjSmpwPtRZ6JQBTkQ+EJEDIrK2xLYXRWSjiKwRkSkiEhvYfomILBeR3wPPA05wzqdFZK+IrAo8BpffRzLKg/pzwb0cXP2CnZVT0px/4cu4l7snfcaBnDzGjRpBh3p1gp2toJi/dSdzN28HwGm38+Hi5SzasRuA+IhwljxyD9d06whYM3eYuRZLx2m30zKxFpEuFwAXNG/C4ofupkVgkoAQh51akeEkRkYAMHHJKnq99DZ5bg8XtW7O+BtH8vglfdmUksrIdz/h2ZlzyS4sDNrnOVuUpgQ3Hhh01LbZQEdV7QxsBh4LbD8IDFPVTsAtwEcnOe8rqto18Pju9LJtVDj3YsCLVIMA5418hqcXXcnmg3n877or6N6ofrCzVGn8quws0TX9f78sZtyipQDYRJh93xgeHnhh8fsRIcdfrdw4fSJSXN14QfMmvD96JKFOa2hxh3q1ubprx+Jeo6//vJh3f13GD/feyrXdO/HRklUMenM8MzdsCVr+zwanHOitqvNFpOlR22aVSC4Grg5sX1li+zogVERcqlr2vrhGUKjnd8AOzs7BzsoJqWc9ONry7x/X8OVaB69eNYjzmzUOdrYq1b9mzmPa7xtY+MBdhDgc/OfKy6kdKEUAR3TLNyrP+c0aH/FdHNapLd0b1ScuPIynBw9kVdJ+dmVkcv9X07msbUseHNCHpidoyzPKrjxmMhkDfH6c7VcBK08S3O4TkZuBZcBDqmpGSFYlnnXgaImIK9g5OS717kHTrmVD7kgmLYvj9vN7cHn71sHOVoXbkHyAf8+ez4sjBlEnKpIRndvRvWF9CJQkGsbGBDmHxvH0atroiPQf+pyLqpKUmcXr835l1sat9GnRhHdHXYmI4FfFZjqjnLEz6mQiIk8AXuCTo7Z3AJ4H/nCCQ98CWgBdgf3ASye5xl0iskxElqWmmsbZyqCq4F0Hzg7BzsqJ2RuyXx9k7LfhnNe0EQ8O6BPsHFWYjPwCUnJyAauKcX9WNkmZVmeGTvXrMqRjG0JMF/Rq5fL2rRncoQ13XXAuX90xmvox0fyybRd3TJrChuRU+rwyzlRfloMyBzgRuQUYCtygJcYaiEhDYApws6puO96xqpqiqj5V9QPvAuee6DqqOk5Ve6pqz8TExLJm1zgd/hTwpyGO9sHOyXGpevH4fNw51Y5favHKyME1dtJkt9fLoP+N5/V5vwLW7Bmzxt5GjxIzgBjVW9s6ifz4xzH8/fIBrNizjxsmfEHjuBgaBea2XLs/hbs/m8qudDM7yukq06+CiAwCHgWuUNX8EttjgRnAY6q68CTH1yuRvBJYe6J9jSDwBKYzqoIlOPXuRA9eytTln7LtYDrPDL24xq3jtjEltXhKrBCHgycu688t53Urft+Mo6p5bCLc0LML0/5wI23rJLAyaT9vLVhCVkEhB3Pz2J6WQUyYNSPKkl1JfLVqLW6fL8i5rvpKM0zgU+BXoI2IJInI7cAbQBQwO9DN/+3A7vcBLYG/lRgCUDtwnvdE5NAgvRcCQwnWABcBD5Tz5zLOhG+n9exoEdRsHJcW4aE+7y7ex6B2rejXslmwc1TuZm/cyoeLl5NZYHUjv6JTO1qf5WP6zhaN4mL56OZreGTghczdvJ0r3/2E+PBwZo29jdhAgJu+diOvzVuEPXCjsycjE48JdsdlZjIxjuHPfg4KPkdqr6qSpYXnf5zP+MUrmH73zcXjkKozt9fLhCUr6dm4Ad0a1qfA46HI6yv+QTPOTmv2JvPnyTNIycnlkYEXcst53RARVJUDOXnUiY5EVRn2zkfUj4lm3KgRwc5yhTIzmRjlw58CtrpVKripFqF575Oac5BJS1czrGPbGhHcADx+PxOXrGTOJmuAdpjTaYKbQecGdZly5w30a9mMf8/+mXu/mEZmQSEicsSqGA8N6FNchV3k9XLTxC9ZsG1XsLJdpZgAZxzLlwxVbXquop/RnOeZueYrPD4fY/v2CnaOzsjGlFT++f0c/KpEhITwzZ038tDAmtsT1CibmLBQ3rx2GI9f2o9ftu5k5LufsHZ/SvH7IsJFrZsXr5aRnJ1LTmERtsC9aXpePsv37KU61dSVJxPgjGP5ksFWtQKchF5KeuiXPP+zmxFd2lf7FQLW7k/hu/WbSQrMXRhfwzrKGOVHRLjlvO5MuvU6/KqM+vBzJq9ad9x9m8THMuXOG4oHmX+1ah2jx3/B7sD37GxTHgO9jZrGfxDsVadTg2oBImF8vDIPr9/PPX3OC3aWyuRgbh5Jmdl0bViPq7p04NK2Lc1aYUapdW5Ql6/vGM2DU77j8W9nsSMtnQcH9DlmQHjJpoUbzulCi4T44hvCl35agAg1etxoSaYEZxzBGproAarGDCbq3Y0e6IO/8Cemrd1A72aNaRRXPWfrePSbmTzw9QzcPh8iYoKbcdriI8J5b/RIruveiXcXLeOByTMo9HhPuH9ESAgD2xzuDZ1ZUEBGfkFxel9WdoXmN9hMCc44igcAkSoyh6HYwTWQNQcS2Ju5hj/16x3sHJ0Wvyp+VRw2G09c1h+3z2dmHTHOiMNm4x+DB9IkPpYXfvyFlJxc/nftFaWq5n5m6CXF7XF7MjK57M3x/GPIQK7p1qmisx0UJsAZR1K39VxFApzYGyCxLzB5wWzCnU4uadsy2FkqNY/Px9gvvqVFQjyPXtKX5pXQ61NVycnM52BKFu4iL36f4vf78fv8+PyK3+fH77N+4CJjwoiJjyAmPoLwCFeV6jVrnJyIcPv5PWkYG8MjU7/n2g8/Y9z1I0r1HTv0/xwbFsaf+vemb2As6caUVHakZXBZu1Y1Zh5ME+CMIx0KcAQ/wGnh9+DoiJt6fL9+C5e0bVmtFuN02u00T4ijYTlXqXo9Prau38veHQc5sC+DA/uzSN2XyYH9maTuz6Qw333qkxzF4bQXB7uY+EjiE6No3KK29WhZm7qN4rHV0OnQqrPL2rWiTlQk93z+Ddd/+BlvXHsF5zZpWKpjo0Jd/KHP4VkSv1q1lqmrN9CneROiQqtGE8WZMgO9jSOoLxlN7YtEP4OEXxe8fGgBeuB8CB3KnOTbGPvFNN4fPZI+LZoELU+l9fu+ZBIiIqgXE1Vu50xNzmL5L5tY+vMmVi7aSkHe4UU6YmtFklgvltr1YwLPcSTUjcEV5sRus2GzC7Yjnq1AlZOVT1Z6XolHLlkZ1uuDyVmkpRxunwkND6F5m3o0b1eP5u3q06pjA5q3rWeCXhWxJyOLuz6dyp7MLN68ZljxKu2nw+f3syMtg5aJtQB4+rufuKhV8zKdqyKUZaC3KcEZRzq0PE6Ql/ATCYOEmYCyfPdmnHY75zap+hMMu30+/vTVDJrEx/LhjVeV+Txej4/1K3aydP5mls3fxM7NyQAk1ouh/9AudOvdimZt6pJYLxZXaMWUavNyC9m99QC7t6SwY9N+tm3cz5xpK5k+aTEA0XERdOvdku4XtKLbBa1IrFs9O//UBI3iYvj0tusY88lkxn75Lf+9eigXtW5+Wuew22zFwS2zoJDfdibRND6Ofq2aoarVsgrblOCMI6i60ZSOSOSDSOTdwc4OANd/+BkAn912fZBzUjpr96cQFxZGg8Bs8KcjP7eI7z7/janjF5B2IBu7w0bHHk3p2bcN5/RrS+OWtYP6Q6OqpCRlsH7FLlYs2sKKhVvISM0BoFHzxOJg1+W8FoSGB7+a+2yTXVjImE++ZmNyKq9ePZSL25R9Plmv34+q4rTbmbdlOxN+W8nzwy+jdlTkqQ+uAKYEZ5QDJ+BANY9g/YyqNwnNfRWJvA+PNGLd/gPceE7XIOWmdHakZbB+/wGGdGxDx3p1Tvv4zLRcvpm4kOmTfiU3u5AuvVpw95PD6HZBKyIiq85wAhGhbqN46jaKZ8Dwbqgqu7aksGLhFlYu3MIPXy7lm48W4Qpzct5F7eg/pAs9+rYhJMT81FSG6NBQPrhhJHdMmsKfvprOq1cNKXPHrJJLUOUVeSjweIgNDwOoNguymm+dcQQRQSUcDq+CVPl826BoPkT+mQ3JB3D7fHRtWO/UxwXR/35ZzK87dtOvVTMiXaUvuezfk8bXH/zCrMnL8Lh99L6kPdfc2Z82nRud+uAqQERo2rouTVvXZeRtF+Iu8rBuxS4WzlzLLz/8zvzv1hAZHcoFl3ak39CudD63OXa7aberSNGhobw/2gpyf548g5dHDuaydq3O6JxDOrZhcIfWiAhev59RH37ONd06cm33qj28wAQ441gSAZoXvMu7+kHtRYg4WJm0AqDKB7hnhlzC/uycUge3zLRc3n/xO+Z8sxKb3cbA4d24+vZ+NGxevRf1DXE56XZ+S7qd35K7nxjGykVb+XnGKuZ/t4aZXy0jLjGKAcO6MWT0edRrVCvY2a2xokJdvH/DldwxaQoPTJ7Ba1cPPeMhNoeqxnOL3NSNjiS+RGlOqJrrFJo2OOMY/oMjwJ6ILe7dSr/20Y3Z//h+DjPWbmTJI/dWel5Oxe31Mm7hUm7v3ZMwZ+k7euzamsLf7/yQ9NQcrrjxfK687UIS6tTsDhpFhR6WzNvI3G9XsmTeRtSv9B3cmWvv7E+ztlX75qU6yy1yc8ekr1m7/wDvj76S85qWf83ApGWr+WnzNl67auhp1V6cLrNcjlE+7PXAtz84187/GH/aVag/F4C03DwSIiOCk5dT+HXnHt785TeW7Eoq9TFrftvGQ9e/hcfj45XP7+XOvw6t8cENwBXq5MJBnfj7mzczYc5fGXnbhfw2ZwP3Dn+Np+4ez/oVZnmXihDpCuHt60fQJC6Ge7+YxobkA+V+DafdRpjDSUQVHKNqApxxLHt98O0LzrVtcWBvhNisnlqpeflVNsD1a9mMH+69tdSris/9dhVP3P4B8bWjeeWze2jZoeoPe6gItepEc/tfBjNh3l+56f5L2LhyNw+NeotHbnyH5b9sPmuXdqkosWGhvH/DSKJcLu78dGq5zz95TbdOvHHtMESErIJC7vx0CptSDpbrNcrKBDjjGGKvD5qL+nMq/9phQ7HFvlqcPpibR2IVW0pmX1Y2G1NSAUq1bI+q8sW4ebzw8Ge069aYlz69mzoNa8ZirWciKiac0WMHMmHuX/nD40NJ3pPOk3d8wB9H/pff5m4wga4c1Y2O4t1RIyj0eLlz0hSyCwsr5Dq70jPZfOAgfvVXyPlPlwlwxrFsgTaRSi7FqT8XVd8R2w7mVr0S3Is//sItH31Fvttzyn39fj9v/uMbPnzpB/oN6cKz799OVEzVCtjBFhoewohb+vDB7Ef487+uoiCviKfvnsCjN49j67q9wc5ejdGqdgJvXDuMXemZjP3iW9w+36kPOk2dG9Rl9n1jaFe3NgAfLVnJij1Bqg3CBDjjeOyBqjPf7kq9rOa9hab2LQ5yXr+ffI+nys2L97fLB/DKyMGlmhfz87fnMuPTxVx9e1/+8p/rzHiwk3CGOLjs6nN4Z8aDjP37cPZsS+VPV7/B2//6lvzc4M6sU1P0atqIfw27lCW7kvj3rJ8r5BqHVsso8nr5aOkqvly5tkKuUxrmr804lqMlIODdDFxSaZeVkF4gUYhYfyB2EQTw+qpGdcehwa3x4WH0bn7qOTFXLNzCR6//yEXDujLmkcurZDfqqsjhtDP0hvPpP6wrE16ZybSPFrFw1lru+dsV9L64Q7CzV+0N79yOjQdS+eDX5XSpX5cRXdpXyHVcDgdf3zEaAlNGpGTn4vZ5aRR36mr98mJKcMYxxBYB9kaoZ1PlXtd14RHTg4kITrsdTwVUpZTFxN9Wcvukr0tVNZmanMXzD31G45a1uf+fI01wK4PI6DDGPjWClz+/h6iYMJ4Z+xH/uGcCB/ZlBjtr1d5DA/pwbpOG/P27HyukZ+UhkS5X8dCBp777iRsnfonbe+IFWsubCXDG8TnagLfyApz6c1HfsX9oIQ57hbQVlEVYiINol6tUVZPjnptOUaGbJ1+/0czJeIbadmnM65P/yO1/GczKX7fyhyEv891nv5lOKGfAYbPxysjBxIaF8cevppNVUDGdTkp64rL+/HPIxYQ4rIpDn7/ia2ZMgDOOz9EGfLtQrfgvPgBF89DUPqhn4xGbQ+xVJ8Bd170zr1w15JT7rV22gwUzf+eaO6r/zCRVhcNp5+rb+/LOjAdp160J/31qCk/fM4GMg5Xf07emSIiM4LWrh5CclcMjU3/AX8E3DI3iYoqH1Py4cStXv/8pKTm5FXrNUgU4EflARA6IyNoS214UkY0iskZEpohIbIn3HhORrSKySUQuO8E5m4nIbyKyRUQ+F6kiS0gbAIizDeCHyqqmdHZGop4Ax5Gzn7scDoo8lVelcTzp+QX8umN3qX8APn59NrXqRHPV7X0rOGdnnzoN4nj2vdusacAWbmXs8NfMIPEz0K1hfR67rD8/b93Be4sqb5Yop8NOfEQYcYHpvipKaUtw44FBR22bDXRU1c7AZuAxABFpD1wPdAgc8z851GvgSM8Dr6hqKyADuP20c29UHGcX69mzqlIuJ47GSMQtiBxZ/VcnKpL92cG9S5+6ej23fjyZnWkZp9w3My2XNUt2MOiacwgNM/dsFcFmszH85gt4ffJ9hEW4ePTmcXz/xZJgZ6vaGt2jM5e1bcnr8xaxMTm1Uq7Zr2Uz3h89khC7nSKvly9Xrq2QKudSBThVnQ+kH7VtlqoeurVeDBxaJ3048JmqFqnqDmArcG7JY8VqcR8AfBXYNAEYUaZPYFQIsdcFW33Us6JSrqeezag//ZjtDeNi2JOZVSl5OJEbzunCu6OupHnCqQdnL56zHlWl9yWmt19Fa9q6Lq9+OZauvVrw+t++5r9PTcHjDm5pvzoSEZ4ecjExYaH8ddrMSm8SmLpmPU9On83qvcnlfu7yaoMbA3wfeN0A2FPivaTAtpJqAZklAuTx9gFARO4SkWUisiw1tXLuLoyAkO7gXl4pjfmacQua8/Ix2xvFxrA/KyeoPSldDgd9WzYt1b6LZq+jbsN4mrUxEwhXhqiYcJ5+51auubMf3332G4/d+p5plyuD+PAw/jHkYjakpPLOgsotDV/brROf3npd8Yoh5dkWeMYBTkSeALzAJ4c2HWe3o3Ncmn2sjarjVLWnqvZMTDQN9pVJnN3BfwB8FT+bhEQ/h4Rfd8z2RnEx+FVJDlI15StzFvL9+s2l2jcvt5CVi7bS+5L2Z/WwgLycQrIzrOWW3G4vU8YvYMMqa9KAnKx8/nztm8yZttJKZ+Zz35WvM/+7NQBkHMzh/pH/ZeEsq7k/N7uAia/NYsdGa/LvokIPW9YmUZB3eOC33W5jzMOX8+jLo9i6bi/3X/UGOzaVf2mgpru4TQuGd2rH2wuWsH5/xQ0dOJqI0L1RfQA2JqcyfNzHbDt4bG1OWZxRgBORW4ChwA16+DY/CSi5JkND4Oi5Wg4CsSLiOMk+RrCFdLeePcsr/FISehHiPHbxxIax0QDszqj8akq3z8ecLdtZuy+lVPsvm78Jr8dH70s6VnDOqg5VZe2ynWxZa62o4HZ7ufa8fzJ1wkIA7DZh3L+ns/wXq7NSaFgI4REuwgJDJ8QmJNSJITTCSttsNmITIgmLsGavyUjN4fO357J7u/WDu3dnKvdf9QZLf7bOl7wnnVce/4pdW1PoP6QLz398F36fn4dHv2U6n5TBE5f1Jy48jL9OmxmUWhOv+nE57OW37I6qluoBNAXWlkgPAtYDiUft1wFYDbiAZsB2wH6c830JXB94/TZw76ny0KNHDzUqj9/vVV/yOerLeLhir+PLVn/RKvX7co55Ly03T1v/82Udt3BJhebhRPx+vxZ6PKXad+Jrs/TyNn9Vr8dbwbkKrmXzN+nPM1YXp2/q95w+9+dPitPTJ/2qm3/fU5zOycpXv99f5ut5vb7if9Pc7AJdMOt3TTuQraqqa5Zs01G9n9FNa6zrLZ6zXod3flJv6vecXtXjKV3z2zbNzS4o87XPRrM3bNHW/3xZJ/y2IijXP/Rd8fv9uikltXg7sExLGa8OPUo7TOBT4FegjYgkicjtwBtAFDBbRFaJyNuBgLkO+CIQ/H4AxmpgckER+U5E6gdO+yjwoIhsxWqTe79MEdqoMCJ2cPWDop853FxaATxr0PRrwLvhmLfiI8JpGh/Lyj3BWZ9ORHA5SjejXWZaLlGx4dgdx+s0XH2pKqnJh0vQX70/n6kTFxSnn/zvTdzz5BXF6SGjetGqY8PidGR02BlV2drttuJ/04ioUC64pCPxiVEAdDqnOZMWPkmrjlYTfu16sVx6VU+eff92IqJC+dtdH3LNOU8Xt8sl70knZe+pe8OezQa2aUGf5k14fd6vpOflV/r1D31Xvlj5O1e++wm/7yt7dXNpe1GOUtV6qupU1Yaq+r6qtlTVRqraNfC4u8T+/1LVFqraRlW/L7F9sKruC7zerqrnBs5zjaqa2VSrIAm9BDQT3Esr7iLOdkjcu+Bofdy3uzasx6q9+yt15gq/Ktd98BmTV60r9TFZ6bnEJURWYK6C4+P//shdl79U3O714P9dw/MT7yp+v3WnhsTWCu7nPvSj2KxtPe79+3Aat6jNv8ffgSvUSWi4qzjvX70/n3uGvYrXY1W/HUzJKn5tWESExy/tR4HHwytzFwYtH0M6tOGhAX3oUK9Omc9hZjIxTs51IRCKFs2qsEuILR5x9UNsx1/ZulvD+qTl5bOnEtvhcgqLiAsPI8xZ+vnIM9PyiI2vWkv7lMWOjft54vb32bc7DYDzL27P7Y8MLg4iiXVjcFaDVRHqN0nghY//gDPEwWO3vseBfZkMv6k3f3nxOhxOq0T44sOf8+hN44qPKSxwByu7VUqLxFrcdG5Xvly5lrX7S9cGXd4iXS7GnN8Dmwjp+QVlOocJcMZJiYRZQa5wNlpBixiqLxl1L0X1+D8u3RpatdorkyqvmjImLJS3rx/O4A5tSn1MZlouMUEuyZSHyJgwUpIySA1MatyyfQOGju5VLefUbNKyDv/6YAx5OYU8duu7RESH0Wvg4dnzr7ytDyPHXAhYVbF3DnqJ957/LljZrVLGXtiL+Ihwnv1hbtDn/cwrKlsFnwlwxilJ6GXWcIGK6k1ZNBdNvwH8x58lvmViPNGhLhbvrNz16U5XUaGHEFfVL9kcz5TxC3j1CWvehcR6sbz7w0N06dXiFEdVDy3bN+CZ98aQdiCbf/3x4yMGg/ca0J4LLrV6vXo8PgZffx7dercErOEO//nL5+zaGpwSTLBFhbp44KLerEzaz0+btwc1L2VdYscEOOPUXANBwtGCqRV0/ouQuIlwgipKu81G35bNmLdlR6XMQA7w+LezGPvFtNM6plbtaNJTq+cg4/zcQrIz84t//GvaOL52XRvz4HPXsH7lLt59fsZx9wkJcTDqngH0uNBqC96xKZnf5m6gqMBaHinjYA7pB7IrLc9VwZVdOtA4LoY3fv416KW4sjABzjglsUWA6xIo/KFCVhcQe13E1QuRE6/cPbB1c9LzC1i1t3KqKVskxNOmdsJpHZNQN5q0lOrzAzhvxmo2rbEmHRp17wD+9sZN1aJtraz6Du7MyNv68O3HvxYPJD+Zjj2b8smCJ4p7aE4Zv4BbB75QPIj9bOCw2bj3wvPYkJIa9FJcWZgAZ5SKhI0AzYHCOeV+bvVnokULUf+JO5Fc2KIpTpuNOZsq54/s9vN7cn//3qd1TK06MRxMDu68maVVmO/m/Re+Y9pHiwBrgHVNK7Udz60PDqJ1p4a8+uRkUvefeuHUEJez+N/lsqvP4c/PXkV0nNWR6Itx84oHnNdkwzq1q7alOBPgjNIJ6QW2OmjhN+V/bs8mNOM2OGotuJKiQl2c27Qhc6rwXWRCnRjycgrJz626I17cbi+qSmh4CM9/dBcP/vvqYGepUjlDHDz68ih8Hh8vPPwZPl/pq7wbNE1gwPBuAHjcXmZNXsbyBYencaupEz1X51KcCXBGqYjYIewKKJqP+sp50mtneyT+U3C2P+luA1q3YHtaOttS08r3+kdJzc3j3Bf/x/S1Jw64x5NYz2pDTE6q2PyVlaryzNiP+OwtqxRev3GtGjcovTTqN67FfU9fydplO5k6YcGpDzgOZ4iDd2Y8wE1/ugSwhlbcOuB5NqysmdODDevUjkZxMby7sALHw1YAE+CMUpOwqwAfFEwu3/PaopCQHogt6qT7XdauFXYRpq45dsaT8uRy2Lm8QxvqRp88P0dr17UxAGt+q5p3ud7/Z++8w6Oovj/8nt1N74Uaeu8d6SAgIL0oIiCIoiiIBbHrV0XRn9jAiiDSRMFCEaSD9N57C70H0nu23N8fG2KEhLRtCfM+T57dnb1z5ywD9ysAACAASURBVEx2d87ce8/5HKOZ4qUD8fG3b5HJwkCH3g1p2q46v363lpjI/FWV1hv0+Ph6Wl+IUKVOWEYF96SE1EI3nXc3DDodQ5o2YP/lqxy75jgh5oKiOTiNXCOGSuDeDJX8u81z4lTqFpTx0F3bFPP1oXXlCvx16Jhdoyn9PT0Z160jTcplWcEpW0qUCSasQij7tobbybKC4eZu4Plxfen1WN7WFosqT7/endQUIz9/tbrAfVWsXpJxPwzDL8AbpRQfPDebT8bMtYGVrkOferXwMOiZt/fuv1NXQnNwGnlCvB4F8yVIs62Ej4p9G5X4c47t+tSryfX4BLafu5hjW2fQsGUVDu4841LrMcY0E1+9M58r52/m2PbC8ctMHjOTl9q8w7xPFnLDRadbbUHZysXpMagFK/7YmVGOxxao9IK3t9INlFIkxts++tjRBHh50r12dRYfOkZCauFQfNEcnEbe8OwEumBU0jybditBkxG/V3Js17F6Zfw9PVh44KhNj5+ZyMQkmnz6PX/syzmU/HYatqpKSlJaRv0zV+DC6Qg2rzzEuVNZJywb04xs+H0rr3R4n+G1XmLx9ytIjk/hp7d+ZXD5kbze5UPW/rKJ5MTCf5G+ncHPdcTH34spHy+x2ZSiTqej12Mt6fxQEwB2rDvGsI4TOHO88FcEe7RxPZLSjHlen3YWmoPTyBMi7uD1EKT+gzLbTuFB3Goi+uI5tvMwGOhaqxqrj4cTn2KfaEUPg4E+9WtSMSQoz/vWb1YZnV7H3s25K5LqCCrXLM30Na/R8oHad7x35uB5BpcfyfhHJ3L9XATDPx7ErxenMGX/58w69Q2D33mIK6eu8smQrxlQ6mnmT/zbCWdgP/wCvRnyQicO7DjDjnX2WdstVS6E1p3rUK6yVTTYbCq84s71SpekZolizNtz0Nmm5ArNwWnkGfEaAFhsOopT5suopF9zlUjev2EdUkwmFhzIvdJ/XvD1cOedLu3zvAYH1nIu9ZtXZu1f+1ziQnb1YiRKKfwCvLN8P/p6DNHXYxn24aPMCv+WR9/oS1BxazRo6coleXzcAGaFf8vn696nXrta/DB2FnM+/NORp2B3ug24jxJhQSyYscku/ZevUoIXxz+EwU1PSnIaLzz8Lct/32mXY9kbEaFfg9ocu36DMzaqum1PNAenkWfEUA48OkDy3GwFkvOM8Qgq7n0w5TzyqVu6JA3LlGLOrv12DTYx5bPv7o824+a1WKcnASclpDKy5yRmTcq+EkSd1jVw83AjPjIenS7ry4FOp6N+u9qMW/QanYa2Y9Z7vxUpJ6c36Ok+sDmHdp7l3Mn81x7LDSajmVJlgykRlvfZAVehcw2rVueq464ZTJUZzcFp5AvxHgKWKEix0ZSVeyuk2Dow1M1V86H3NeRCdCwbw8/Z5vi3MXjW74zOoxblLZp3qElIcX+WztthY6vyht6gY+Q7vWjbNfv/qYeXB3Va12DPmpynnPR6PWN/GkmHQa35edzvXD9v43xIJ9L5oSa4uRtY8ss2ux7H19+Ld74ZQqNWVQFYs2gP+7a5vqPITEl/PxqWKcXKY6ecbUqOaA5OI3+4twBDVVTibJsszovOB9GH5VouqlONKpTw82X2zn0FPnZWdK9dnc41q+ZrX71Bz4OPNGXPppNcOus8J+Dh6UaXh5tSqUbpu7Zr9EA9zh2+SOTVnCtd6/V6hv/fYBBh8fcrbWWq0wkI9qFd93r8s3ifwyIezWYLi2ZtYaGdpkbtSecaVTl6LYKL0TnLnTkTzcFp5AsRsY7iTEdtVkZHpW5GJc7OVVs3vZ7HmtZn69kLBSppnx2DmtSnX/07gzJyS49BLXBz1/P71PW2MyoP3Lgaw7ol+0lNMebYtnGnegDsWp67m4XiZUNp1acpy39aS0qS68qS5ZWeg1uSkpTGmoV2Kgt1G3q9js9/eZZXJjwCQHxMUq70MV2BzjWt05Qrj7n26FNzcBr5x6s3SCAqYbJNulOp61GJP+Q6iXxQk/oEeHrw1Xr7TCvFpaSQZspfPltgiC9dBzRj7aK9nD7m+PDwvVtO8ekr8zKKlt6Nyg0qULpKSb5+bhqLv1+ZqxF5SOlg4qMSSIjOnwqIK1Ktbhkq1yrNxuWOixD09HbPEG+e8vESXn50MilJrp9jViYwgFoli7Mh/KyzTbkrmoPTyDciXojvCEjbhEoruEad+L6AFNuISO6+lr4eHjzbuhmbTp9j6xnbagDuvnCJpp9NZveFy/nuY/DojvgFevPNewuxOKiO3S3adq3HD3+PoVS54Bzb6nQ6Jm0eT4MOdfhm9DTGPfw5cVHWunYmo4nYm3FcOX2NU3vPsH/dYVb/vIHF36+k6/COhIaF2PtUHErDFlU4eegSaak5j3xtTf+n72f4q10LTeX0ZhXKsP/SVVLzeRPoCKQw6aU1adJE7d6929lmaGRCqWTUjU6gL4sE/+rwkitpJhMPTp6Fv4cHC54ejM5Gx49LSWHOrgP0rFODskFZF2LNDf/8tY/PXvuN58f1pdujzWxim72wWCzMn7iU6W/9gsloxsPLndTkrEcTwSUDmXrwCwJC/R1spX3ZvvYo40bN5tM5I6jbtJLT7Di27zxJCakZaiiuyNoTpxn1+2LmDO1P0/Jl7H48EdmjlGqSl32KbnVDDYcg4gW+o6wh/mkbwaNdgfpTSX+gzOfQ+b2aq/buBgNj7m/FK4uWs/jQMfrUu3tFgtzi7+nJqDYFd0jtezVg1fxdzPhiOS0eqEVQaN4EnPPLzg3HQcF999fI9T46nY7+Y3vSoH1tjm0/xbWz1/EJ8MEnwBtvfy98Arwz/kpXKYmPf9a5dYWZWo3KA3Bkz3mnOTilFLMmriQ6MoHvW7zoshUfmpQLQ4Ad5y85xMHlB83BaRQcr4chcRoqfiK4t8n1FGNWKNMpMB5EKZXr0WD3OtWZsWMPk9Zt5cGa1fB0s83X2mg2c+zaDWqXKo4+mxyxnBARRr/fl5G9JjFtwjJe/WyATWzLifnTNmI2W/Lk4G5RtVElqjZy3ujFmfgH+VC+agmO7D4LtHeKDSLCO98OISkh1WWdG1i1KauXKMau85ecbUq25PirFZHpIhIhIoczbesvIkdExCIiTTJtHywi+zP9WUSkQRZ9vi8ilzO162a7U9JwNCLuiO8L1ojKlOUF68vvDXQh8/I01akT4fUH2nI1Lp6ZO/YW6PiZWXbkJP2nz+XY9YKF+pepVIz+T7Xjn8X7HJb8/b/vhvDmxEEOOVZRo2bD8hw/6Fwxb19/L4qXDgRg+ufLWfmHa9Zha1o+jP2XruZbFMHe5Oa2dCbw4G3bDgP9gI2ZNyqlflFKNVBKNQCGAOeUUvuz6XfirbZKqWV5tFvD1fDsCYbqqIQvC6Rukt/RX7MKZelUvQo/bN7Btbj4fB8/M22rVODLvt2oFJJzoEZOPDqyPRWqlWDi238SE2X/yENffy9CShSt9TFHUbx0IAmxyaS5QEUIs9nCmWNXCT+a/2Ane1KzRHFSTCYuRsc625QsyfFqopTaCETdtu2YUiqnW9GBQNEqiKSRLSJ6azUA80UooEalSpyFJfLRPCeQv96pLWaL4rO1+avSfDtB3l50r1Mdb3e3Avfl7uHGa589SnxMEl//b4Hdi2GeOnyJ36euL1JFNx1FQLA1bD8uOtHJllhz5d6dPJRR7/YGcLnPs2oxaxRt+A3XLKtkzzSBAdzdwY0WkYPpU6CFV5hN41/c24J7c1TCdyhLAUYpOn/QlwbypihRNiiAp1o24e/DxwsU3p+ZxLQ0/tx/mLOROat85ETFGqUY9nIXtq05yqo/7RsNfHj3OWZ8sYKE2GS7HqcoEhDkOg4OwN3dgIgQeT2O14ZMdao6zu1ULmad3binHJyINAOSlFLZFdSaDFQGGgBXgS/u0tcIEdktIrtv3HCdD1bjTkQE8XsVVDQq8cf89+PVF13gl9YIzTwyolVTSvn7MX7FOpsIMacaTfzv7zWsPm4b3b2+w1pTv1klfvh4Sa4KkOaXB/s3ZeH+D/ALLHqRjvbGP8j6P4uNcg0HdwtjmonI63HcvOY604E+7u6EBfjfWw4OeJS7jN6UUteVUmZllaz4EbjvLm2nKqWaKKWaFCtWzA6matgScasLnt0hcUaB68UpS97LcXi5ufHaA204dv0Gv+09VKDjAwT7eLNs5OM83bJpgfsCayj+2AmPYDDomDB2HinZ5JkVFC8fDzy9CkfCsKsREOwLuJ6DK1k2mKnLXqZBiyrONuU/VCkWwql7xcGJNUqgP5DtQoyIlMr0si/WoBWNIoL4jgHMqIRJ+e5DJf+NimiJMuVdoaRrrWo0r1CWL//ZQkR8wQM6KoYE2TSBvVipQF7+v/6EH7nMh6N/tlsww5pFe5ymhVmYMRutdfxcMUTf4KZHKcU/f+1j5Z+uEVlZJtDfZoFdtiY3aQJzgW1AdRG5JCLDRaSviFwCWgBLRSSzrHhb4JJS6sxt/UzLlFLwqYgcEpGDWJNNxtjkbDRcAjGUA++hkLwAZTyav07cm4DPSJC8T7GJCOO6dSTVZOKD5etssjA/fdsexq9cV+B+btHigdq8OP4h9m4+xadj59qlOOqhnWfZuuaIywUmuDrRkdabosAQHydbkj3/LN7HhmUHXeKzDfbxJjYllTSz8wv83k6OGbFKqYHZvLUwm/brgeZZbH8q0/MhubRPo5AiviNRyfNR8Z9A0Kw8j4BEXxLxezHfx68QEsQL97fg87WbWXjwaIEqAwDcSEjkamw8FqVsJgfW+aEmJCWkMOXjv5n0znzGfPxwtkVH88Nz7/XG3aPgEaD3GjHpDi4oxDGqM3lFRHhj4kC8fDwcLo2XFaE+1pvQ6KRkSvj5Otma/6KJLWvYBdH5W5O/07ZD6up89aGUQqXtQxnzlxz9ZPPGNC0Xxocr1hW4btVrD7Thu0d62cy53aLP460Z8kIn1izcyw8fLbHpHbnm3PLHLQcXGOpaF+vM+Pp7odfrSE5MZd9W5xYeDUl3cFGJSU61Iys0B6dhP7wHgKEaKu4jlCU/C/ZpqOgR+Y7I1Ot0TOj9IDoRXvtrZYHUFm7dKcckp9gkOjMzA0d1oN+TbVgyZxuzJq2yqZNbt2Q/o3pNwugCScuFheibCRjc9Pj4eTrblBz56bPljBs126kBMcE+1mjnm5qD07iXEHFD/D8Ay9V8BZyIeCBBUxH/9/NtQ1igP+917cDei1eYvGlHvvsBOHo1graTprLymG3vmEWEp17rRtcB9/HbD+v4+avVNnNyvv5eFCsV6LAq1Y4kLjKelTPXcfOyNYLPmGYkKT65wP+7i6cjKBFm28AiezF4dEfGTxuekZzuDAI8rTcC8SmuV/xWc3AadkXcG4H3YEiajUrLXcXo/+7fENEVbKqoV92a9KlXk+837WBnAYRha5QsxtD7GlKrZPEC2ZMVVlHmPjzYvylzJ/9js5Fc03bVGTdlGIEhrjvdlhfmfbKQ/3vsK8wmM+ePXuLzJ7/n/FHrZ3p020l6Bwxl3z/5D8o2Gc0c3HGa+s0r28pkuxIU6kedJhUA56mc3LoRsLhAwMvtaA5Ow+6I71jQlUTFvpUvnUplPIwlahjKkn81kXe7dqBcUACvLFxOVFL+1D10IrzSsQ0VQuwjvKPT6Xj+g74ZI7lpE5barFBqbFQiF09H2KQvZ2KxKCwWhd6gp0azKswO/5ZaLasDUKJ8MZ6e8BjlaoYBcPbwBVKT8zaqOH7gAslJaTRqVdXmttuTP6dt4L1nZjrFyd0a57qgf9McnIb9EZ0vEvABmE+jEibnowcPMF8A04V82+Dj7s6X/boRlZTMW4sLNjq6GB3D1C277HIx0el0jH6/Dz0fa8GCGZv5+MVfCpwMrpTi1cem8PW7C2xkpfMY9FY/3v71JQDc3N0oVakEXj7WKbKSFYrzyKu9CS0dTEpSKm90Gc9nT3yXp/73bj6FTieFZgR3C08vd/wCvElLdfxa660RnML1PJzm4DQcgni0A8/ekDgFZTyet33dqiKhaxD3+gWyoXapErz2QBvWnTrDz7uyK3KRMxvDz/H1hm2cjypYZGZ26HQ6Rr7TixFvdmfr6qO89thUoiLi8t2fiPDs2z0ZPa6vDa10LMY0I+H7zua6vae3B2OnjWTw2w8B5HokvHvjCarXL4uvf95l4pxJj8EtePWzAXh4Oj5y9lZksTaC07inEf+3QBeQPlWZtztNER1KWfKlbJKZIU0b0L5qJT5dvZGDV67lq4+HGtRh7fNP2m2qEqxOqe+wNrz73RAunonghYe/5UQBapQ1alWV8lVK2NBCx3JqzxlGNn6NFdP/yfU+93VtSMW65UlLNTLj7bkc3nzsru3PnrjGqSOXad7BNlXhnUHElRhuXLXPjVd2uEKyeXZoDk7DYYguCPH7H5gOQ9KsPO+v4t5BRQ1CqfxHBIoIn/TuQnE/X176cynR+ViP83QzZCS0JqTaN3KsecdafDH3WQwGPa8OnsKq+fmvQpCcmMo37y5k65ojNrTQMVRpWJExU56h09B2ed43PiqBP75YwuXwu9/QTP9sGb7+nnR9JFtpXJcmNcXIiK5f8OdPG3NubEPi0qMnA7w8HHrc3KA5OA3H4tkVPDqi4iehTOfytKt4DUD83gIKNg0T6OXJpIe7ExGfwMsLlmHMp8TQtxu20WvqHJKNxgLZkxOVapTm6/mjqd24AhPf+pPvP/wLkzHvNrt7GDhx6CKXzhS+qhzunu50e/oB9AZ9ngNvgksG8nfiHLoMa59tm31bT7F700kGPNuh0FZg8PB0Y+yER+g9tJVDj3vrJjHI2/WmdTUHp+FQRMSa1ybuqNh3sBaUyOW+7vURr+6IFFwEt17pkozr/gBbz15g/Mr8FQZtVqEsPWpXR7B/vpR/kA/jpz2RkRD+5hPTiL6ZN4FbvUHPpN+f45ER99vHSAdw+sA5nqo9hl0rc7+GKiIY3LJXJbRYLPz02XKKhwXS67EWtjDTabR5sC6ly4U49JgZDs5Lc3AaGoi+BOL3Bhh3QvLvedpXKYVK+h2VXPCIwIca1Obplk2Yt+cgs3bmPUevafkyvNyhNZ53uXjaEr1Bz9Ovd+e1zx/l1KFLjOw5iS2r85bzZXCz3hycPXGNGy5UVyy3FCsbQkhYMKUq5i0Xcd28LUx9dXaW761fcoDTR68wbMyDRULe7PDus2xaftBhx4tO1kZwGhr/xethcG+Bip+AMue++raIoFKWolJW2cSMlzu0plP1KnyyagP/nDydrz4OXbnGx6vyNwrMD+17NuCr+aMpViqQ8aPnMGHsPGKicl8WKDE+hVcGTebnr2zzP3Qk/sF+fLbmPcpUKw3Azx/8wV/frci2fVqqdfo4LSWNXSv33/EZxcckMXPiCqrWDqNd93r2M9yBLJi+iR8nLHXY9zEqMRmDToevh+vVH9QcnIZTsE5VjgcEFTMGpXK/jiWB3yCB+cmnuxOdCJ/2eZBapYrz8oJlHLma9yKtB69cZ9mRE1x1YE2s8lVKMPG3UTz2/ANsXnmIZ7pN5J/F+3J1UfPx8+SNLwfx1GvdHGCp/UiMS+LA+iNEnLeuKSqlWDZtLZFXrYIAP772M8/UH4tSis6P38/IL4f9R37LZDTz0Yu/EH0zgVHv9bZpJQdn8sL4fkxdNtZhUmMXomMIC/R3SWkzceUQz9tp0qSJ2r07/1FkGq6HSl6Gin0JfJ5G5/dq3va1JAJmROdfYDsi4hMYMGMeRrOFP54cSKmA3JdKsShFQmoq/p7OEec9d/Iak96Zz4kDF2narjqj3+9L8dKBudrXYrFw9UIUYRVC7Wyl/VBKISJcOH6Z4bVe4oXvnqLnyC5sXriDMwfOM/Ctvri5u92xzzfvLWT5bzt5ZcIjdOzTyEnWF366T55FueBAJg/obdfjiMgepVSTnFv+S9G4ZdEotIhXN/AaCIk/olI35Ho/pZJRNx9EJXxlEzuK+/ky5dE+JBuNjJi3KE/h/zoR/D09UUqx+fR5h+cFVahWki/mjmTEmz04uPMMz3b/ksVztmI25xzAM+PzFbzU/1uibrhmRebccGvkUK5GGNOPTaL9wNYAtO7bjKHvP3KHcwNYNGsLy3/byYBn7i9yzk0pxZ/TNrBzfd4EFfJDmtnMuagYqhZzbGBLbtEcnIbTEf83wVAdFfMaypy75GsRL8TnCcTLdneN1YqH8tVDPTh9I5IX5y/Nc3mdpUdOMPzXBWw9m39Jsfyi1+voO6w1U/4eQ81G5Zn84WKe7/s1uzeeuKvD7TawGY+PeZAgF659lhfKVg/DN/Duyvo7Nxxn2oSltOpcm6EvdXaQZY5DRFg8Zyu7NtjfwZ2PjMZksVDFRR2cNkWp4RIo02lU5ENgqIUEz0bEMZGJWfHHvkO88/caBjSqy7huHXO9tmCyWFh59BRda1ezeWHUvKCUYuPyg8z8ciXXLkZRv1klho19kBr1y911v/jYJHz9vVxyLcVWnDp8ideH/khYhVA+m/MMnt6uFxhhC1KS0hxybsuPnuSl+UtZ+NRgapWyfZWNzGhTlBqFFjFUtubHGXejEnIvkKtUGpb4L1HJS2xmS/+GdRnRsim/7T3EpPVbcz3laNDp6F6nOjoRElLTnFq+pF23+kxd9jIj/9eLc6euM+aR73nv2ZmEH806YvXaxSie6T6RRbM2O9hax2A2W/h96npefnQyPn6evPv90CLr3ACHnduhK9dw0+moFBrskOPlFc3BabgM4tUHPPtA4mRUam6Lk+ohbQfKeMimtozp0Ir+Devww+adfLtxe572vRgdQ7fJs/jr4N21D+2Nm7uBXo+1ZMaa1xj2cheO7j3P832/YfzzP3Pu5H+ngouHBXJ/9/o0al3NSdbajyvnb/La4CnM+GIFzTvU4tuFL1CsZICzzbIrO9Yd48cJS+1+nO3nLtKgTCmH5YLmFde0SuOeRfzfQxn3o2LHQuhiRHf3O0MRPQTPRsS2Ong6ET7o/gBmi+LbjdvRifBc2+a52rd0gD+tK5encjHXuKv18vFgwDPt6TGoBQtnbmLBjM1sWXWEJm2q0fOxljRpWw2dTseIN3tk7JMQl1zoFPVvRynFsnk7+HHCUtzc9Lz2+aPc36N+kZ6CvUX4kcusXbSXp1/vbrdjxCancPRqBKNz+btwBtoanIbLoYxHUZH9waMVEjgl1xckZboElsgCl9XJjNli4a0lq1h08Bhj2rfi2dZ5F+K9FcbuKsTHJLF4zlaWzttB9I14SpYNpseg5nTu1wS/QG/++nkLv09Zz6Q/Rxfakc7N67FMems+ezafpGGrqoz5+OFCey6uypoTp3nu98X88nh/mpQrY/fj5WcNThvBabgc4lYL/F5HxY+3Vh3wGZbjPkopVMwLgBFCFtvMoeh1Oj7u2RmLUkxctwWdwIhWuXdy327Yxo3EJMZ162gTe2yBX6A3g0c/wCMj7mfrmiMsmbONaROW8fNXq2nfswGN21ajZafaBBfCyEqlFBuWHuC7cYswGs08914fug9s5lI3GEWF7ecu4GkwUC+slLNNyRbNwWm4Jt5DIG0bKv4zcKuDuN/9xk1EIGA86AJtfjHT63R80qsLFgVf/LMFEeHplk1ztW+qyUyq0YTZYkHvYkoZbu4G2nWrT7tu9Tlz/ApLftnOusX7WPHHLipUK8nvU9dTu2lFSpUJplip3CWOO4sbV2NY+9c+1i7ay6WzN6jRoByvTHikUCewF4Sd64+zY90xRr3bG73e9t87pRSbws/TpFwY7vqCi5/bixwdnIhMB3oAEUqpOunb+gPvAzWB+5RSu9O3VwCOASfSd9+ulHo2iz6Dgd+ACsA54BGlVHSBzkSjSGF1WJ+gIh9BxYyGkPmIPuzu+7j9W6hSWRIQne1GIHqdjgm9u6CU4vO1m9GJMLxFzrMlYzq0QsDlRxCVapTmxQ/78eQrD7J20V42rzzM7K9WA6DT63igbyOat69JgxZV8PJxjbpfKUlpbFl1mDWL9nJg+2mUUtRpUoH+T7ejY++G6A2ue+G1N8f2nefA9tN2cW4AR69FcC4qmidbuHaSfI5rcCLSFkgAZmdycDUBCzAFeOU2B/f3rXZ36fNTIEop9YmIvAEEKaVez8lYbQ3u3kOZzljX4/SlkeB5iO7uSbwAlrgJkLYBCVmEiG3DpU0WC68uXM6yoyd5o1NbnmjeOFf7XY9L4KNV63m/aweCfQpHvbGoG/EsnbudvVtPcf7kdZITUzG46anXrBKNWlWlap0yVK5VGh9fx0mUpaYYObbvPP8s3sfmFYdITkqjZNlgHujTiA69G1KqrGsmHDsDe679frJ6A3N27mfzy88Q6OWYz98ua3BKqY3pjivztmPpB8zLsTLTG7g//fksYD2Qo4PTuPcQQyUI/AoV/RQq9lUI/BaRu9+VikdzlNjnR2fQ6fisb1cU8MnqjSSlGRnVJuc1nhuJiew8f4mTNyJpXkgcXHAxP4a80IkhL3TCmGZi8c9bOXfqGsf3X2TahGUZ7cIqhFKldhhVapWmSu0wKtcqjV9Awc8xJSmN08euEH70MuFHrH8XTt/AYrbg5eNB2271eKBvY2o3ruDyI2RnYK//idliYemRE7SpUsFhzi2/2GMNrqKI7APigHeUUpuyaFNCKXUVQCl1VUTsmwKvUagRj9bg9yYq/iNUwleI35gc2rdDPNrZzR6DTsfnfbviYdDz9YZtRCUl83aX+++qXlKnVAn+eX443lnoIhYGRIS/526nZJlgflwxluib8YQf+df5HNt/ng1LD2S0Dwr1JSDYh4Bg62NgiC8BQemPwT4gkJKYRnJSGilJqf95TIxL4dypa1w6cwOLRWX0V6V2GC061qZqnTAatqqKp1fRTdQuCFE34vn2vYX0f7odNRuWt3n/O89fIiI+kZ6dati8b1tjawd3FSinlIoUkcbAIhGp2MYFRwAAIABJREFUrZSKy2+HIjICGAFQrtzdpYY0ijDeQ8F0wpoEbqiKePXIcRdlPIhKnIEEfGLzPDmDTsf/9epCsI8307ftISoxiQm9u+BuyP4ndcu5rTx2CpPZQvc61W1qkz0xuOkZP+1JfPysd+xBoX40bVedpu3+PYe46ETCj14h/Mhlrl2KIjYqkZjIBE4fvUJsVAIJcSl3PYaXtzuePh54ebtTplIx2jxYlyq1wqhSJ4yQ4q5ZjsUViY1K5PL5mxjTTHbpf/GhY/i4u9OhWmW79G9LbOrglFKpQGr68z0ichqoBty+cHZdREqlj95KARF36XMqMBWsa3C2tFej8CAi4P8+ynQWFfsWGCoibrXvvpM5EtJ2g/kSGGz/Y9SJ8PoDbQnx9uaztZuISU7hm/4971r40aIUc3btB6Bb7WqF6qJ9KyJRKcV34/6iVqPydOjVMON9/yAfGrWqSqNWVbPc35hmIjY6kdioRETA09vqzLy8PXD3NBSZemzOpmL1kkxZ+rJd+r6ZkMjfh0/Qt34tl1UvyYxNLRSRYliDR8wiUgmoCpzJouli4HHgk/THv2xph0bRRMQdAr9FRfZDRY+EkAWIPvswcPFsDx6rETutx93iqZZNCPXx5q0lqxg6+w+mDuxDqG/WwTA6Eb7t3xNPN0Ohcm6ZSU0xcj78ep4rELi5GwgtEUBoCS3h2l5Y0itg2Otm4edd+zGazTyZy+AqZ5Pjf0FE5gLbgOoicklEhotIXxG5BLQAlorIyvTmbYGDInIA+BN4VikVld7PNBG5FQHzCdBJRE4BndJfa2jkiOhDkKDJYIlBxYxGqbS7txdrnTaVOBtlOmc3u/rUr8XkAb05ExnFwJm/cSEqJtu2AV6eeBgMpJpMfLJ6A1GJSXazyx54ernzfzOeYuCoDgBcOnODuOhEJ1ulAXBwxxkebz+Bs8ev2rzvxLQ05u4+wAPVq1AhJMjm/duDHB2cUmqgUqqUUspNKVVGKfWTUmph+nMPpVQJpVSX9LbzlVK1lVL1lVKNlFJLMvXz1K10AqVUpFKqo1KqavpjlP1OUaOoIW61kID/A+NeVNy4nFX7LZGohG9QyX/Y1a52VSsy87GHiUtJZeDM3zh6NduZdwBO34hi3p6DbD5z3q522QODmx6dTofZbOGD0T/zwXM/O616gsa/eHi5U71eGUqVt326xPz9R4hNSWV4y8IxegNNi1KjEGOJnwiJkxHflxDfUXdtq0wXQF/WIdOCp29EMvzXhcSlpPJF3660r1Yp27bX4xMo4Vf4JLEyc/zABUSE6vXKOtsUDTthsljo/N0MSvj5MnfYAKfYoNWD07inEN+XwLM3KmESKunPu7c1lENEUJaoPJTiyR+Vi4Xw2xOPUiE4kJG//cUPm3dmO7q55dyOX7/BhDUbC+UoqEb9chnObcGMTUz5eAlmk9nJVt17HNt3noS4ZLv0PXf3AS7HxDEilxJ1roLm4DQKLSKCBHwM7m1Qcf9DpazLcR8V+x4q9kWUss+F4BYl/H35ZdgjdK9dnYnrtvDS/KUkpRmzbb/h1FmWHTnBjYTCvZYVeT2WG1dj0NlJIkoja1JTjIwbNZsv37T9NHxkYhJfb9hGq0rluL9qRZv3b0+0KUqNQo+yJKKihoApHAmejbg3yL6t+QpYYv6jW2lX25Ri+vY9fL52M1WLhfDdI70oG3RnFKFSipjkFIK8C3cNNgCzyYzeoCfqRjybVx6ix6DmWgqAAwg/chlPb3fKVCxm037fXrKaRQePsviZIVR2YuVubYpS455EdD5I0I+gL46KHoEync6+rb50hnNTpqwyWGxsW7oo89SBfbgaF8/DP/3K9nMXs2wX5O2FUoofNu9k6eETWfRWOLglcrxq/m5++nQZ1y9rOur2JC3VOjNQpXaYzZ3bwSvXmL//MEPva+hU55ZfNAenUSSwpg9MB9Gjop5Cma/ftb1K3YK62Q2V8o9D7GtTuQJ/Dh9EqI83T86Zz+yd+7JcbzNaLGw+fY7NZ845xC57MuCZ+/l6/vMZAsjH9p0vlGuMrkxSQirPdJ/Ikl+22bxvi1J8uHwdob7ePNe2mc37dwSag9MoMoihnHUkp2JQ0U+jLPHZN3a/D/EdDe7NHWZf+eBAfntyIPdXrcRHK9fzxuKVd6zLuev1TB3Yl496dgYo1A5BRChftQQAJw9d4uVHJ7N0rn0DfO41lFLUbVqRyjVL27zvObv2c/DKNV7p2AZfD9cokZRXtDU4jSKHSt2Mih4B7k2QoGk5lsxRKg1UAqJzzBSMRSm+37idbzdup0JIEBP7daNmyTv1xmOTUxj1+2JGt21Oi4qFW4fVYrGwesEe2nWrj6e3OzeuxRIY7IObu+vLPbkiSimMaSbcPewj3n38+g36/zSXVpXKMXlAb5dQ3dHW4DQ0sFYfkICPIW07KvZVlLq76KyKGW2d1syhna3QiTC6XQtmDnmYxLQ0+k+fl+WUpcliIdloJM1c+EPudTodXR5uiqe3O0opPn7xF956YpqzzSq0zJ60ijcfn0ZK0t2VfPJDitHE2AXLCPDy4OOenV3CueUX7fZJo0giXn2sCibxE1C4Q8AniGRd4Vm8BlpHcOLYn0PzCmX5a8QQ3lq8ko9WrmfrmfN83KsLwemRlCE+3vw5fFBGGZ64lBT8PV27/lZuEBEeG/1ARnCEUooLpyMoX6WEky0rPFSpHUZiQgoeXrYfwU1Ys5Hwm1H8NKhfoSnOmx3aCE6jyCI+w63J4Cl/WfPklCXrdp7tEa+eACiLY1Xjgr29mDygN+90uZ/NZy7Qa8rP/4myvOXcdp2/RIevp7Pz/CWH2mcvGrepRosHrNUgNi4/yMgekzi8+6yTrXJ9biVyt+pch1H/s/3U4doTp/l19wGebN6Y1pVtX0vO0WgOTqNII76jwGcUJP+JivvgrkEbyngMdaMTKnmpAy20jmiG3NeQP558FF8Pd4b9/CcT/9mCMdPUZJViIXSsXomqxWyvMehsGreuxpOvds0oznnm+BUSE+5eO+5eZN/WUwzrMIFj++yjXXopJpa3lqyiVsnijGnf0i7HcDSag9Mo8ojvi+DzFCT/ap2yzM7JGSqDZ09wb+RYA9OpWbI4C54aTL8Gtflhy04GzvyNkxE3AQjy9mJC7wcJ8vbColSOQs6FCV9/Lx4e3ha9XofZZOaDUT/z8Yu/ONssl+HW97VyzdI0bVed8lVL2vwYcSkpPDvvLyxK8WW/bnct3FuY0KIoNe4JlFKo+A8g6RfweQ6d34s5tkclIjrnCCEvP3qSccv/ISEllZFtmjGiVVPc9NY1xCmbd/LNhm0sHfk45YMDnWKfPQk/chmTyUyN+uVISUpj8vjFPDy8LWUr3xlpWtRZOnc7+7aF8/ZXg+0W7JFiNDH81wUcuHSVHwf1ddmI3fxEURYNN62hkQMiAn7/Q6kUSPwOJV6I74hs26v4TyFtK4TMQ8Tx8llda1WjWfkyfLhiHV9v2Maq4+H8X8/O1CpVnIFN6uHv5VEknRtYAyhucfrYFTatOESXh60iv2mpxoxSPfcCJqMZY6qJ1GQjnt53T3fJV/8WC2MWLGXPhct82a+byzq3/KKN4DTuKZQyo2JfgZSliN87iM/QrNulbkCl7UZ8xyDi3Ivp6uPhjFu+lqjEZJ5u2ZRRbZvhkT6FdDE6ho3h5xjcNHv9zcJOcmIqXj7WROPZk1axbe0Rvp7/fJHMoTObzPz500aq1A6jcetqWCwWq6i4HUZvSine/ns18/cf4X8PtucxF/8OaXlwGho5IKJHAj4Fj46o+PGopHlZt/Noh85vLCI6lCXeqYoinWpU4e9nH6dX3Zr8sGUnfX/8hf2XrBWbf919kK/Wb+VmIa9CcDduOTeAyrVL06h1tQzn9sePG9iy6rCzTLMZt75fZrOFtYv2smuDVYtUp9PZzbl98c9m5u8/wqg2zVzeueUXbQSncU+iVBoq5jlI3YD4vYX4DMu6nSUaFfkIePZE5/eCY43Mgg3hZ3lv6VquxcXzWNMGjGrTjPjUtIzpSqVUoU7MzQtms4VRvSZRt2klRr/fB4A9m05Su0kFPL1sP51nL1Yv2M2CGZv5ZsHzGNz0xMcm4Rdgv/wzi1L836oNzN65j0cb1+P9rh0KxXdGG8FpaOQSEXck8Dvw6IyK/xiVMDnrUZoEgkdHxKON443MgnZVKvL3s0MY1KQ+v+w+QLcfZrPz/EUsSvH73kOM+n0xKUbHKLI4G71exw9/j2H4q10BuHzuJu88NZ3lv+0g8nocv01ZR+T1OCdbeSfxsUksmrWZ2CjrqDsgxJcyFYtl5LjZ07mZLBbeXrKK2Tv38XizhrxXSJxbftFGcBr3NEqZULFvQspf4PM04vvKXX/wynwT0Yc60MLsOXYtgg9XrGPPxSvUKVWC+8qX4UxkFN/275kRcXkvYTZbOLTzDOWrluDovvOMHz2H7/96kYo1ShF+5DIHdpzmwf734ePnWDUYs9nCyYMX8Qv0pkzFYpw9cY1RvSbx6mcD6NCrocPsSDOZeHnBclafCOf5di14rk2zQuXctBGchkYeETEgARPAayAk/oiKH5et4olKWYO62RGVtt/BVmZNzZLF+eXxR/i8T1ciEhKYvn0PgZ6exCSnkJiWVuirg+cVvV5HgxZVCAr1o1WnOszd+g7lq1nlv/ZvC2fGFyvQ6awX9DWL9vD5679jNls/68T4FMwm22h+KqVY//d+9mw+CYDFbOH1oT+y4vddAFSsXpIfV4x1qHOLS0lhxLxFrD4Rzttd7md02+aFyrnll6IXhqShkUdEdOD/Pkq8IeknlCUZAj66U5vSvQl49QNDVecYmgUiQs+6NehQvRKTN+1g5va9rDl5mtIB/iSlpbFs5OMZEZf3GoEh/+YwPvxUOzr1a5IRsBJ9I4GLpyPQ6633+D9+8je7N51kzsa3APhr9haiIxMYNqYLAFvXHCEt1cT93esD1mKuyqLo0t+avvD5a7/h6e3B6Pf7ICL88u1aylcrQeP0gJjx0574Tx6frQuT3o2L0bE8O28R56JimNCrC33qO6aavStwb37zNTRuw5on9xrofFEJX6FIgYDPEflXzFZ0gYj/e0B6iR1LDKJ3jeRjH3d3XunYhoca1OHjVevZGH6OIG9Plh05Qc+6NTHcI3ljdyMg2Cfjef+n29H/6XYZr1t3qUvVOmUyXl84HUHElZiM10vnbicxPiXDwa1fegCT0ZTh4IJC/f4jfPzxzKcIDv3XwdZrVtn2J5QLVh8P5+0lqwCYPrgfzSqUdYodzkJbg9PQuA2V+BMqfoI1uCRwEiJ3Fnu0xIwB41EkdEmO9eYcjVKKjafP8dW6rRy5FkEpfz+aVyzLRz06odccXb5ITTFiTDPh629N+jebzOgNrrvOmWoyMWH1Rn7ZfYA6pUowsV83yhVyYQC7rMGJyHQRiRCRw5m29ReRIyJiEZEmmbZ3EpE9InIo/bFDNn2+LyKXRWR/+l+3vBitoWFPxGe4daSWuhYV/RTKcmcknngPRnyecjnnBtbRaLsqFZn/1CC+ebgHiWlpLDxwlN5T57D2xOlCXSXcWXh4umU4N8ClnduZm1E8Mn0ev+w+wBPNGzH3iQGF3rnllxxHcCLSFkgAZiul6qRvqwlYgCnAK0qp3enbGwLXlVJXRKQOsFIpFZZFn+8DCUqpz/NirDaC03AkKnmxNcLSUNFaGVyftcitMoWDrgSi83OwhbkjzWTiz31HmLlzL+ejYqhdsjhjO7amZcVy90Sgwb3EwgNH+GD5OjzcDHzSqzP3V63kbJNshl1GcEqpjUDUbduOKaVOZNF2n1LqSvrLI4CnZDW/o6FRCBCvXkjQj2C+jIp8BGU8eUcbZUlCRQ1Fxb3jBAtzh7vBwKCm9Vn67FDaVK7AiYibPPnLAvpPn8uKoycxW7KOGtUoPEQlJTN2wTLeWLyKOqVL8NfTjxUp55Zf7Blk8hCwTymVms37o0VkKLAbGKuUis6qkYiMAEYAlCtXtIRANVwf8WgJwb+iop9GRQ2EoMmI+33/vq/zBv/xLhVZmR1uej3DWzSmWvEQygYGMGPHXl6cv5RyQQEMa96YfvVr4eVm+wrRGvbDbLHw5/7DTFy3lYSUVF68vyXPtGqqrbWmk6sgExGpAPx9a4oy0/b1ZJqizLS9NrAY6KyUOp1FfyWAm4ACPgRKKaWezMkObYpSw1ko8xVU1HAwX0QCv0A8u2TdLnkZeD7gkmtzt3M+KprJm3dy+kYkB69cJ8jbi8FN6jO4SX2CfeynpqFhG7advcDHqzZwMuImjcuW5v1uHalW3DVECOyBS5TLEZEywEJgaFbODUApdT1T+x+Bv21th4aGLRF9aQiZi4p+BhXzAvi/i3gP/k8blXYAFfsSot6D295zRRYcOMqa46f5+5khXIqN5adte/h243Z+3LqLPvVqMahxfWqUdFy+lkbuOBsZzYTVG1l36gxhgf589VB3utSsqq2nZoFNHZyIBAJLgTeVUlvu0q6UUupq+su+QOGXA9co8oguEIJnomJeRsWNQ5kjEN+XMi4s4l4fgmaAewsnW5o7Xrq/JQ/Vr03JAD9KBvhRPjiIVzqmMnP7HhYeOMpvew/RIKwUAxrXpWutatr0pZOJSU5h8qYdzNm1Hw+DgbEdWvN4s4b3bCJ/bshNFOVc4H4gFLgOvIc16OQboBgQA+xXSnURkXeAN4FTmbrorJSKEJFpwA9Kqd0i8jPQAOsU5TngmUwOL1u0KUoNV0ApEyrufUj+HTy7IwH/h8h/9Q2VJQaSF4L3sEJxZ73syAneWrKKn4f2p27pksQkp7Do4FF+23OIM5FR+Ht60LtuTQY0qkvVIjwN5opEJiYxY/seftl9gOQ0Iw83rMOL97ekmK9PzjsXIfIzRaklemto5AOlFCRORSV8CYbaSNBkRF/i3/cTf0LFT0RCFyGGKk60NHdExCfw07Y9vNKx9X+EmpVS7L5wmXl7DrLyeDhGs5nGZUvTv2EdOlavjL+nY4WL7yUuRsfw8679/LbnEKkmE11rVePZ1s2oXuLevMHQHJyGhoNRKWtRsWNBfJGgKYhbbet2pcAUjri5fnTl7SSlGflg+T8817YZZYP+TRCOSkxi4UHr1OX5qBjcdDpaVS7PgzWras7ORiil2Hb2ArN37mf9qTPoROhRpwbPtL6PyqHBzjbPqWgOTkPDCSjjcVT0s2CJQgI/uyPCUqVuRKVutBZWFdcP395/6Soj5i7kq4d70KLinak5SikOXrnGiqOnWHHsJFdi4zVnV0Cuxsaz7OgJFuw/QvjNKIK9vRjQqB4DG9ejhL9vzh3cA2gOTkPDSSjzTVTMKDDuR3zHgM+zGWtvlvhJkLoeCZ6D6ArHxSohNRVfD6tGw6bT52gQVgo/zzs1G7Jzds0qlKVNlQq0qVyBSiFBhWId0tFEJSWz8thJlh4+wa4LlwGoV7okg5vUp2vtalrwyG1oDk5Dw4kolYqKfQtSloBnLyTgI0Q8rNOVKhnReaOUGZBCMZIDa+Re+6+m0b1Odcb36HTXtkopDl25zvJjJ1l/8ixnIq0CSGGB/rSpbHV2zSuUxdfD9XME7UVCahprT5xm6ZETbDlzHpPFQuXQYHrUqUH32tUpf49qRuYGzcFpaDgZa/DJD6iEieDWEAn8OiP4RCmFinsTlEICPik0o5oDl69SJjCAEB9vElJT8XRzy1X5nUsxsWw6fY5N4efZdu4CSWlG3HQ6GpULo1n5MjQoU4q6pUsU6elMi1KcjLjJtrMX2HzmPLvOXyLVZKZ0gB/dalWnZ50aVC8RWmi+C85Ec3AaGi6CSlmBin0DxNtacidd3kslfAsoxPd55xqYD5RSjP5jCXEpqcwa8jC6PFyU08xm9l68wqbwc2w6fY6TETe5deWpFBJM/bCS1AsrSf2wklQrHvqfSM7ChNFs5ti1G+y6cIld5y+z9+JlYlOsaoWVQ4NpVak8XWpWpVHZ0nn6/2loDk5Dw6VQpnBU9Ggwn0f8XgHvJ/9zp67M10AXemflcBdm2ZETxCSnMKiJtfCnUipfo4/4lFQOXbnGgcvWv4NXrhGZmASAQaejevFQKoYGUykkiMqhwVQKDaZCcCDuLrIupZTialw8p25EcioiklM3bnIqIpLwm5GkmswAVAgOomn5MJqUC6NZ+bKUCnDNahOFBc3BaWi4GMqSYF2XS10BHp2tU5M6X+v2mz3AoyW6gI+dbWa+2Hn+EpPWbeHLft0o6V+wi7dSisuxcRy8fI3DV69zMiKSMzejuBz7by0+nQhlAv2pFBpMCT9fivv6UMzPh2K+1r/ivr6E+HrbpHp5mslEREIiNxISiYi/9ZhARHwi56KiOXUjkoTUtIz2xf18qFYslKrFQ6gfVoom5cLuuURse+MSWpQaGhr/IjpfCPwKkmag4j9DRT4Egd9a8+N8R4BbfWebmG/iklNINZltsoYmIpQJDKBMYADdalfP2J5sNHIuMprTN6M4czOKM5HRnI2M5uDla0QlJd/ZDxDo7YWXmwEPgwFPgwFPt/Q/g3WbXqcjzWQmzWwm1WQi1WT6z+u4lFRiklPu6FsvQqivD+WDA+ldtyZVi4dQtVgoVYuFEOBVdNcRCzPaCE5Dw0GotF2omJdAJSD+HyFePf59L2U5uLew6l0WIm5NUZotFt5dupYhTRs4TKDZaDYTmZhkHWnFJxKRkMCN+ESikpJJMZpIMZnSH42kGE2kmswkG41YlMJDr8fNoMfDYMDDoMddn/5oMODn4U5xP1/rqNDPh+K+PhT38yXI20tbN3Mi2ghOQ8OFEfemELIQFfMiKvZllHEP4vcGWGJQMa+B90DE/y1nm5knbq2/nY+KYd2pM7SoWNZhDs5Nr6ekv1+Bp0c1ii7aCE5Dw8EoZUTFfw5JM8BQHQmcCCrJ+lzuTKYuLCSkpuLj7o6IsPp4OB4GA22rVHC2WRpFhPyM4ApHtqmGRhFCxA2d/5tI4BSw3EDd7AvGI4A7SqVgiXkFZTrrbDPzjK+HByKCUooZ2/fw/abtFKYbaI2ih+bgNDSchHi2R0KWgHtTVNx7qJjnUMbjkLYVjMecbV6+ERFmPvYQXz3UAxEhITWNKZt3kmw0Ots0jXsMzcFpaDgR0RdDgqZZ1+JSN0DM8+D/EeLVDQBlSXSyhfnD3WDIEAled/IME9dt4VREpJOt0rjX0BychoaTEdEhPk8iIX+AeEPMs1jiv8CSdgh1syMqdaOzTSwQPevWYPmoYdQLKwnAooNHORlx08lWaRQWDl6+xttLVudrX83BaWi4COJWCwlZCF4PQ+IUiHsHDHXAUM3ZphWYiiFBAKQYTXy+dhPTt+1xskUahYWTN26y9ez5fO2rRVFqaLggVi3Ld0ElIr4voryfQNI2gUf7Qi/MG5OcgslsJtTXh4vRsfy0bTfPt2tBiI+3s03TcBEuRMVwLT6B+8qXQSlFktGIr4eHFkWpoVEUEM8HkdBl4NEelfA5RHZHxTwLqaucbVqBCfTyJDRdxmrPxcssOXwck9niZKs0XIk3Fq/kf3+vwWyxICL4uOevxJKW6K2h4aKIPhQCv4GUpajYcYABZboAyoxI4VTbv50+9WrxQPXKGcVV316ymkqhQQxvkacbdY0iQFRSMj7ubngYDHzUszOe6bJqBUEbwWlouDAignj1QIotA492kPAZKrI/luiRKEuMs82zCbecm8liIT4l5T8ixtFZ6E1qFD1iklPoNWU2k9ZvBaxrtraovqA5OA2NQoDoiyGB3yMBn4PpDKSuRSV8i1JFJ7fMoNPxdf+evNCuBQB7L16h7aQf2Xb2gpMt07AXUeklkgK9PHm8WSN6161p0/41B6ehUUiwjuZ6IcVWgXtbSJqNiuyHJeUfZ5tmU24F0ZTw82VA47oZ6QUHLl/l4OVrzjRNw4bM33+E9l//xKWYWACebtmUGiVsq2OaKwcnItNFJEJEDmfa1l9EjoiIRUSa3Nb+TREJF5ETItIlmz4risgOETklIr+JSP5WETU07jFEXxxd8DQk8DswR1jz5qJGoCyxzjbNpoQF+vNOl/YZAQbfbNjOSwuWYrZoASmFlcS0tIzCtq0qlWNQk/r4edhPfzW3I7iZwIO3bTsM9AP+k4UqIrWAR4Ha6ft8L1mviE8AJiqlqgLRwPDcm62hoSGenSBkERhqQtoG1M0HUclLiqz+46SHuvNd/57odTosSvHYrN9ZeOCIs83SyCUmi4U+U+cwfsU6AEr6+/F6p7Z2raWXKwenlNoIRN227ZhS6kQWzXsD85RSqUqps0A4cF/mBmKdg+gA/Jm+aRbQJ4+2a2jc8+gMpdCF/mVNENeVRMWORUU9jjLlLzHWlfH1cKdmyeIAxCan4OXuhrveGgielGZk65nzWIqocy+spJnNbAi3CocbdDpGtmnG0GYNHXZ8e6zBhQEXM72+lL4tMyFAjFLKdJc2GhoauUTcaoHvy4CAcT8q/mNnm2RXgry9+HFgX7rXsVb/Xn70JE/8soADl6862TKNzKw+Fs6IuYs4fv0GAP3q16ZhmdIOO7498uCyklm4/bYqN22sDUVGACPSXyaISFajRlsTChQVsTztXFwTO5/LIWCq/br/Ly7zuTR692VbdOMy52MDXOJcatrmc6me1x3s4eAuAWUzvS4DXLmtzU0gUEQM6aO4rNoAoJSaigN/qQAisjuvkjCuinYurol2Lq5LUTqfonYued3HHlOUi4FHRcRDRCoCVYGdmRso6yr4OuDh9E2PA3/ZwRYNDQ0NjXuU3KYJzAW2AdVF5JKIDBeRviJyCWgBLBWRlQBKqSPA78BRYAXwnFLKnN7PMhG5NQH7OvCyiIRjXZP7yZYnpqGhoaFxb5OrKUql1MBs3lqYTfuPgI+y2N4t0/Mz3BZd6UI4dErUzmjn4ppo5+K6FKXzuafPpVABge8oAAAEN0lEQVSVy9HQ0NDQ0MgtmlSXhoaGhkaRRHNwmRCRQBH5U0SOi8gxEWnhbJvyi4iMSZdSOywic0XEfnIBdiAbebhgEVmdLu+2WkSCnGljbsnmXD5L/54dFJGFIhLoTBtzS1bnkum9V0REiUioM2zLK9mdi4g8ny4zeEREPnWWfXklm+9ZAxHZLiL7RWS3iLjqslAGIlJWRNalX4OPiMiL6dvz/PvXHNx/+QpYoZSqAdQHjjnZnnwhImHAC0ATpVQdQI9VPq0wMZM75eHeANamy7utTX9dGJjJneeyGqijlKoHnATedLRR+WQmd54LIlIW6AQUJun/mdx2LiLSHqsaUz2lVG3gcyfYlV9mcudn8ykwTinVAHg3/bWrYwLGKqVqAs2B59IlIPP8+9ccXDoi4g+0JT2aUymVppQqzAW3DICXiBgAb7LJM3RVspKHw3rhmZX+vNDIu2Ujdbcqk5LPdqy5oC5PNp8LwETgNbIRbHBFsjmXkcAnSqnU9DYRDjcsn2RzPgrwT38eQCG4Diilriql9qY/j8c60AgjH79/zcH9SyXgBjBDRPaJyDQR8XG2UflBKXUZ653nBeAqEKuUWuVcq2xCCaXUVbD+CIDiTrbHVjwJLHe2EflFRHoBl5VSB5xtiw2oBrRJr3Ty/+3dvWsUURTG4d8LMUK0iYioIEQEaxMRRAJCYiEi+gcopLCySwqrVNaCrTZWGgQ/gqRPYRnRYGKhoGAwQRQ7QRvBY3FmyQcpsrPCzQzvA8PuMrCcy+6ZM5yZufelpDOlA+rRJHBH0ip5TGhKpwAASUPAMLBAjfx3gVvXB4wA9yJiGPhFc1pgm1S96avAceAosE/S9bJR2XYkTZMtmZnSsdQhaQCYJttfbdAHDJKtsVvAE3UWqGumm8BURBwDpmjQ88aS9gPPgcmI+FnnO1zg1q0BaxGxUH1+Rha8JroAfI6IH5FLPs8C5wrH9D98l3QEoHptTPtoO5ImgMvAtWju8zonyBOpJUkrZKt1UdLholHVtwbMRnoF/CXnc2yqCTL/AZ6ye5893kTSHrK4zUREJ/6u898FrhIR34BVSZ0JPcfJ2Via6AtwVtJAdfY5TkNvmNlijkxYaPj0bpIukrP5XImI36XjqSsi3kXEoYgYioghskCMVPnURC/IpbyQdBLoZxdMVtyDr8D56v0Y8LFgLDtSHbMeAO8j4u6GXd3nf0R4qzbgFPAaWCb/6IOlY+phLLeBD+TCtA+BvaVj6jL+x+T1wz/kQfMGOaXbPJmk88CB0nH2MJZP5LJSb6vtfuk4645ly/4V4GDpOHv4XfqBR1XeLAJjpePscTyjwBtgibyOdbp0nDsYxyh5c8zyhvy4VCf/PZOJmZm1kluUZmbWSi5wZmbWSi5wZmbWSi5wZmbWSi5wZmbWSi5wZmbWSi5wZmbWSi5wZmbWSv8AwxgeuO82f7YAAAAASUVORK5CYII=\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "scanA = np.linspace(110.0,130.0,50)\n",
+ "scanB = np.linspace(5,20,50)\n",
+ "Z_binned = [[nll_binned([a,b]) - solution_binned.fun for b in scanB] for a in scanA]\n",
+ "\n",
+ "fig1, ax2 = plt.subplots(constrained_layout=True)\n",
+ "\n",
+ "p1 = ax2.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])\n",
+ "p2 = ax2.contour(scanB, scanA, Z_binned, [0.01,0.5, 2.0, 4.5], linestyles=\"dotted\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Repeat the same for 50 bins:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 373,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 432x288 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "scanA = np.linspace(110.0,130.0,50)\n",
+ "scanB = np.linspace(5,20,50)\n",
+ "Z_binned = [[nll_binned([a,b]) - solution_binned.fun for b in scanB] for a in scanA]\n",
+ "\n",
+ "fig1, ax2 = plt.subplots(constrained_layout=True)\n",
+ "\n",
+ "p1 = ax2.contour(scanB, scanA, Z, [0.01,0.5, 2.0, 4.5])\n",
+ "p2 = ax2.contour(scanB, scanA, Z_binned, [0.01,0.5, 2.0, 4.5], linestyles=\"dotted\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.7"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/exercises/Solutions7/Solutions_7.pdf b/exercises/Solutions7/Solutions_7.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..c77d5b460e9f6514ad5bc44d36ea1cba3630ab64
Binary files /dev/null and b/exercises/Solutions7/Solutions_7.pdf differ