diff --git a/notebooks/leastSquaresFits_gauss.ipynb b/notebooks/leastSquaresFits_gauss.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..19a98b729f00f06d14621f8af3a8b4d3e36d3c52 --- /dev/null +++ b/notebooks/leastSquaresFits_gauss.ipynb @@ -0,0 +1,247 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Least squares Fit\n", + "\n", + "A couple of examples to show how to use: \n", + "- scipy.optimize.curve_fit \n", + "\n" + ] + }, + { + "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 gaussian\n", + "Consider a Gaussian. 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": 2, + "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": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 360x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Create sample\n", + "## SAMPLE SIZE\n", + "sample_size = 5000\n", + "##################\n", + "\n", + "# Prepare toy 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, 1580, 101)\n", + "bins = 10\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 = hist[0]/normalization\n", + "y_errors = np.sqrt( (np.sqrt(hist[0]) / normalization) **2) #sqrt(x^2) just to take the positive value\n", + "\n", + "# Plot our toy 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": 4, + "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": 5, + "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": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Fit Results:\n", + "mu = 1539.8 +- 0.2\n", + "sigma = 11.2 +- 0.1\n" + ] + } + ], + "source": [ + "# Perform the fit minimizing least squares\n", + "initial_values = [1545, 9]\n", + "p_opt, p_cov = curve_fit(model_function, x, y, p0=initial_values, sigma=y_error, absolute_sigma=True, check_finite=True)\n", + "p_err = np.sqrt(np.diag(p_cov))\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]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Plot the result" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 360x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x_arr = np.linspace(1500, 1580, 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_values), '-', color='grey', label='initial_values')\n", + "plt.plot(x_arr, model_function(x_arr, *p_opt), '-', color='black', label='fit')\n", + "plt.legend()\n", + "plt.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What happens if you reduce significantly the number of events or increase the number of bins ? (mind empty bins!)" + ] + }, + { + "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": "3.8.5" + }, + "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/notebooks/leastSquaresFits_straightLine.ipynb b/notebooks/leastSquaresFits_straightLine.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..d5d477c1b23cd74c419215890d6dc6ac22745911 --- /dev/null +++ b/notebooks/leastSquaresFits_straightLine.ipynb @@ -0,0 +1,313 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Least squares Fit\n", + "\n", + "A couple of examples to show how to use: \n", + "- numpy.polyfit \n", + "\n" + ] + }, + { + "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.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 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": 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 = 0.005\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", + " Return fit parameters' best estimate, covariance matrix, \n", + " residuals, chi-squared and degrees of freedom.\n", + " \"\"\"\n", + " \n", + " fit, cov = np.polyfit(x, y, degree, w=weight, cov=True)\n", + " \n", + " chisq = np.sum((y - np.polyval(fit, x))**2 / y_error**2)\n", + "\n", + " dof = x.shape[0] - degree\n", + " chisqndof = chisq / (dof)\n", + " \n", + " return fit, cov, chisq, chisqndof, dof\n", + " \n", + "# Fit straight line\n", + "fit_1, cov_1, chisq_1, chisqndof_1, dof_1 = fit_polynomial(x, y, 1, 1/y_error) \n", + "\n", + "# Fit parabola\n", + "fit, cov, chisq, chisqndof, dof = fit_polynomial(x, y, 2, 1/y_error) " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Fit with a straight line\n", + "a = -0.1028 +/- 0.0064\n", + "b = 1.0186 +/- 0.0037\n", + "Fit with a parabola\n", + "a = -0.0951 +/- 0.0094\n", + "b = -0.0077 +/- 0.0097\n", + "c = 1.0035 +/- 0.0021\n" + ] + } + ], + "source": [ + "# Get the fitted parameters and their uncertainties\n", + "\n", + "print (\"Fit with a straight line\")\n", + "errPars_1 = np.sqrt(np.diag(cov_1))\n", + "print ('a = {:.4f}'.format(fit_1[0]), ' +/- {:.4f}'.format(errPars_1[0]))\n", + "print ('b = {:.4f}'.format(fit_1[1]), ' +/- {:.4f}'.format(errPars_1[1]))\n", + "\n", + "print (\"Fit with a parabola\")\n", + "errPars = np.sqrt(np.diag(cov))\n", + "print ('a = {:.4f}'.format(fit[0]), ' +/- {:.4f}'.format(errPars[0]))\n", + "print ('b = {:.4f}'.format(fit[1]), ' +/- {:.4f}'.format(errPars[1]))\n", + "print ('c = {:.4f}'.format(fit[2]), ' +/- {:.4f}'.format(errPars[2]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Compare the fitted parameters with the true ones you defined at the beginning" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Reduced chi^2, dof:\n", + "straight line: 59.5775 ; dof= 20\n", + "parabola: 8.8565 ; dof= 19\n" + ] + } + ], + "source": [ + "print ('Reduced chi^2, dof:')\n", + "print ('straight line: {:.4f}'.format(chisq_1), \" ; dof=\",dof_1) \n", + "print ('parabola: {:.4f}' .format(chisq ), \" ; dof=\",dof) " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# p-value for test \\alpha for confidence interval\n", + "def evaluate_chisq(chisq, dof):\n", + " return chi2.sf(chisq, dof)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Chi^2 p-values\n", + "straight line: chi2=59.5775 ; dof= 20 ; p-value=0.0000082774\n", + "parabola: chi2=8.8565 ; dof= 19 ; p-value=0.9757873149\n" + ] + } + ], + "source": [ + "print('Chi^2 p-values')\n", + "print ('straight line: chi2={:.4f}'.format(chisq_1),' ; dof=', dof_1, ' ; p-value={:.10f}'.format(evaluate_chisq(chisq_1, dof_1)))\n", + "print ('parabola: chi2={:.4f}'.format(chisq) ,' ; dof=', dof , ' ; p-value={:.10f}'.format(evaluate_chisq(chisq, dof)))" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 360x540 with 3 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "f, ax = plt.subplots(3,1, figsize=(5, 7.5))\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--',label='truth') # true parabola\n", + "ax[0].plot(x, np.polyval(fit_1, x), label='line', color='green')\n", + "ax[0].plot(x, np.polyval(fit, x), label='parabola', color='blue')\n", + "ax[0].legend()\n", + "\n", + "ax[1].errorbar(x,y - np.polyval(fit_1, x), yerr=y_error, fmt='.', color='green')\n", + "ax[1].errorbar(x,y - np.polyval(fit, x), yerr=y_error, fmt='.', color='blue')\n", + "ax[1].set_title('residuals')\n", + "ax[1].plot(x,np.polyval([0,0], x), label='line', color='red')\n", + "\n", + "ax[2].errorbar(x,(y - np.polyval(fit_1, x))/y_error, yerr=y_error, fmt='.', color='green')\n", + "ax[2].errorbar(x,(y - np.polyval(fit, x))/y_error, yerr=y_error, fmt='.', color='blue')\n", + "ax[2].set_title('pulls')\n", + "\n", + "band = np.ones(x.size) #draw a grey band showing sigma = 1\n", + "ax[2].fill_between(ax[1].get_xlim(), -1, 1, color='grey', alpha=0.4, label=r'$1\\sigma$')\n", + "ax[2].plot(x,np.polyval([0,0], x), label='line', color='red')\n", + "\n", + "ax[1].legend()\n", + "f.tight_layout()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 504x360 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Draw the plot form lecture notes \n", + "plt.figure(figsize=(7, 5))\n", + "chisq_arr = np.linspace(0, 100, 1001)\n", + "plt.ylabel(r'p-value for test $\\alpha$ for confidence interval') \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.xlim(1, 100)\n", + "\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": [] + } + ], + "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": "3.8.5" + }, + "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 +}