# RBComb Simulation Framework
This project aims at developing a framework that can be used to simulate any project
that is to be undertaken on the RBComb platform. It is designed in modular fashion,
such that it is flexible enough to adapt easily to any given situation.

## Structure
The code is structured in an object oriented approach. The classes that likely will
not need to be adapted for a new situation are found in the `lib` folder. They are
described in the following. Note that qualifiers, references and the like are discarded
where it improves legibility. Consult the source files for more information.

### Template Type `Vec2` (vec2.hpp), 2-vector utility class
1. Template arguments
   - `value_t`: type of vector entries
2. Members
   - Access
     - `value_t x()`
       - returns x entry
     - `value_t y()`
       - returns y entry
     - `Vec2 normalized()`
       - returns normalized version of vector
     - `value_t r()`
       - returns length
     - `value_t phi()`
       - returns angle (`std::atan2` version of it)
   - Member functions
     - `value_t r_wrt(Vec2)`
       - returns length with origin at argument
     - `value_t phi_wrt(Vec2)`
       - returns angle with origin at argument
     - `value_t norm()`
       - returns norm
     - `value_t norm_sq()`
       - returns square of norm
   - Modifiers
     - `Vec2 normalize()`
       - normalizes the vector and returns it
     - `Vec2 rotate(Vec2, value_t)`
       - rotates the vector and returns it
   - Supported Operators, All of these work as one would expect
     - `*` with `Vec2` (inner product) and `value_t`
     - `/` with `value_t`
     - `+, -` with `Vec2`
     - All versions of `op=` of the above
     - `[]` with `std::size_t`
     - `<<` with `std::ostream`

### Type `Diagonalizer` (diagonalizer.hpp), class to diagonalize symmetric Matrices
1. Member functions
   - `std::vector<double> ev(std::vector<double> mat, size_t N)`
     - returns eigenvalues of the symmetric matrix mat of linear size N
     - throws upon diagonalization failure
   - `std::pair<std::vector<double>, std::vector<double> > evv(std::vector<double> mat, size_t N)`
     - returns pair of (eigenvalues, eigenvectors) of the symmetric matrix mat of size N
     - throws upon diagonalization failure
2. Further developments
   - Only finding eigenvectors and -values in a certain range may be added later on

### Template Type `Drum` (drum.hpp), represents a single drum top resonator
1. Template arguments
   - `value_t`: Scalar type
   - `params_t`: Drum parameters container type
   - `vars_t`: Drum variables container type
   - `sbuffer_t`: Stepper buffer container type
2. Access
   - `params_t get_parameters()`
     - returns the parameters, const and reference versions implemented
   - `vars_t get_variables()`
     - returns the variables, const and reference versions implemented
   - `sbuffer_t get_sbuffer()`
     - returns the stepper buffer, const and reference versions implemented
3. Modifiers
   - `void set_coupling_0(value_t)`
     - Sets coupling 0
   - `void set_coupling_1(value_t)`
     - Sets coupling 1
   - `void set_coupling_2(value_t)`
     - Sets coupling 2
   - `void set_drive(value_t)`
     - Sets central electrode coupling
4. Description
A drum is described by a set of (static) parameters (stiffness, mass, x-y position, etc),
which are to be stored in a container of type `params_t`. The variables (displacement, velocity,
electrode charges, etc.) are stored in a container of type `vars_t`. Example classes for
these two types are `lib/drum_parameters.hpp` and `lib/drum_variables.hpp`.
However, these containers likely need to be adapted to the situation at hand.
When time evolving, the stepper will use the container of
type `sbuffer_t` to store its intermediate results. Note that the default constructor of
this class is `delete`'d. It should be constructed from an object of type `params_t`.
5. Further developments
Abstract interfaces for `params_t` and `vars_t` could be added, but they would
be trivial.

### Interface template type `Force` (force.hpp), force functional
1. Template arguments
   - `value_t`: Scalar type
   - `params_t`: Drum parameters type
   - `vars_t`: Drum variables type
   - `buffer_t`: Stepper buffer type
2. Virtual functions
   - `value_t operator()(drum_t drum, drum_t n1, drum_t n2, drum_t n3, value_t time)`
     - Returns force on `drum` at `time`, given its three neighbours `n1`, `n2`, `n3`
3. Description
This interface is a guide to complete implementation of a force functional. Any force
functional should derive from this class, but the child type should then be used in
order to avoid the vtable penalty.

The type `drum_t` is a `Drum` with the given
template arguments. Typically, this functional would make heavy use of the `Drum`
access members `get_parameters()` and `get_variables()`. The `time` argument of the
functional exists to fit special cases as well. The file `include/force_simple.hpp`
showcases how a real force functional could be written.

### Interface template type `Driver` (driver.hpp), calculate drive of drums
1. Template arguments
   - `value_t`: Scalar type
   - `drum_t`: Drum type
2. Virtual functions
   - `void precompute(value_t t_end, value_t dt, std::vector<drum_t> drum_vec)`
     - Called once at begin of `system` lifetime
   - `void step(value_t dt)`
     - Move in time by `dt`
   - `value_t operator()(size_t drum_index)`
     - Returns drive of drum `drum_index` (wrt `drum_vec`) at current time
3. Description
This interface is a guide to complete implementation of a drive calculation class. Any driver
class should derive from this class, but the child type should then be used in
order to avoid the vtable penalty.

The purpose of this class is to set the drive of each drum at specific times.

In the `precompute` function, this class is passed all information it could need about
the system. Hence it can in principle precompute all values for all drums and all times
of the simulation.

The member `step` is called to inform the `Driver` that time is advanced by the passed argument.
Note that an rk4 scheme advances time in steps of `dt/2`.

The functional should return the current drive on the drum with index passed as argument.

An example implementation of a `Driver` is shown in `include/driver_simple.hpp`.

### Interface template type `Coupler` (coupler.hpp), calculate couplings between drums
1. Template arguments
   - `value_t`: Scalar type
   - `drum_t`: Drum type
2. Virtual functions
   - `void precompute(value_t t_end, value_t dt, std::vector<drum_t> drum_vec)`
     - Called once at begin of `system` lifetime
   - `void step(value_t dt)`
     - Move in time by `dt`
   - `value_t operator()(size_t drum_index, size_t neighbour_index)`
     - Returns coupling between drums `drum_index` and `neighbour_index` (wrt `drum_vec`) at current time
3. Description
This interface is a guide to complete implementation of a coupling calculation class. Any coupler
class should derive from this class, but the child type should then be used in
order to avoid the vtable penalty.

The purpose of this class is to set the coupling of each neighbouring pair of drums at specific times.

In the `precompute` function, this class is passed all information it could need about
the system. Hence it can in principle precompute all values for all drums and all times
of the simulation.

The member `step` is called to inform the `Coupler` that time is advanced by the passed argument.
Note that an rk4 scheme advances time in steps of `dt/2`.

The functional should return the current coupling between the two drums with indices passed as arguments.

An example implementation of a `Coupler` is shown in `include/coupler_simple.hpp`.

### Interface template type `LatticeGenerator` (lattice_generator.hpp), generates drum lattices
1. Template arguments
   - `value_t`: Scalar type
   - `params_t`: Drum parameters type
   - `vars_t`: Drum variables type
   - `sbuffer_t`: Stepper buffer type
2. Virtual functions
   - `std::pair<std::vector<drum_t>, std::vector<int> > operator()(params_t)`
     - Takes a `params_t`
     - Returns a pair that characterizes the generated lattice
       - a vector of drums `ds`
       - an adjacency vector of vectors `adj`, such that `ds[i]` and `ds[adj[i]]` are neighbours
     - All drums have the same `params_t`, except that the `position` members differ.
3. Description
An example child of the `LatticeGenerator` is shown in the file `include/rbcomb_generator.hpp`.

An important note is the __convention of neighbour ordering__. Each drum has neighbours 0 thru 3.
For drums in different sublattices, these neighbours are:
- Sublattice 'A':
  - 0, adj[0]: straight down
  - 1, adj[1]: top left
  - 2, adj[2]: top right
- Sublattice 'B':
  - 0, adj[0]: straight up
  - 1, adj[1]: bottom right
  - 2, adj[2]: bottom left
Here _adj[]_ signifies the adjacency list of the given drum. Similarly, the couplings
_t0_ thru _t2_ in objects of type `params_t` should also respect this ordering. More
generally, whenever neighbours of a specific drum are ordered in some fashion, they
are assumed to respect the above convention. Note that with this convention,
neighbours see each other as the same neighbour index (the i-th neighbour of j
  sees j as its i-th neighbour). __Never violate this convention__.
4. Further developments
In the future, there may be another overload for the functional. For example, it could either take an
`std::vector<params_t>` or an additional random number generator to construct the drums
differently.



### Template Type `Rk4Stepper` (rk4_stepper.hpp), performs timesteps using rk4 scheme
1. Template arguments
   - `value_t`: Scalar type
   - `params_t`: Drum parameters container type
   - `vars_t`: Drum variables container type
   - `buffer_t`: Stepper buffer container type
   - `force_t`: Force functional type
2. Member functions
   - `void step_1(force_t, std::vector<drum_t>, std::vector<std::vector<int> >, value_t dt, value_t time)`
   - `void step_2(force_t, std::vector<drum_t>, std::vector<std::vector<int> >, value_t dt, value_t time)`
   - `void step_3(force_t, std::vector<drum_t>, std::vector<std::vector<int> >, value_t dt, value_t time)`
     - All of the above perform one step of a timestep, between successive steps certain
     other updates need to be taken care of.
     - Arguments: Force functional, Drum vector, Adjacency vector, time step, start time of current step