# Tutorial¶

## Model Building¶

Consider a simple system of chemical reactions given by:

$\begin{split}A \xrightarrow[]{k_1} B\\ B \xrightarrow[]{k_2} C \\\end{split}$

Suppose k1 = 1, k2 1 and there are initiall 100 units of A. Then we have the following variable definitions

k1, k2 = 1.0, 1.0
A0, B0, C0 = 100, 0, 0


Then to build the model we have the following variable definitions:

import numpy as np
V_r = np.array([[1, 0], [0, 1], [0, 0]])
V_p = np.array([[0, 0], [1, 0], [0, 1]])
X0 = np.array([A0, B0, C0])
k = np.array([k1, k2])


## Running Simulations¶

Suppose we want to run 10 runs of the system for earlier of 1000 time steps / 150 time units each, we have

from pyssa.simulation import Simulation

sim = Simulation(V_r, V_p, X0, k)
sim.simulate(max_t=150, max_iter=1000, chem_flag=True, n_rep=10)


Note that the chem_flag is set to True since we are dealing with a chemical system.

## Plotting¶

To plot the results on the screen, we simply have

sim.plot() To plot only A and B, we use the species indices ([0,1])

sim.plot(plot_indices = [0, 1]) To not display the plot on the screen and retrieve the figure and axis objects, we have

fig, ax = sim.plot(disp = False)


## Accessing the results¶

The results of the simulation can be retrieved by accessing the Results object as

results = sim.results

<Results n_rep=10 algorithm=direct seed=[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]>


The Results object provides abstractions for easy retrieval and iteration over the simulation results. For example you can iterate over every run of the simulation using

for x, t, status in results:
pass


You can access the results of the n th run by

nth_result = results[n]


You can also access the final states of all the simulation runs by

final_times, final_states = results.final

#final_times
array([ 7.59679567,  6.370443  ,  8.62018373,  6.44826162,  6.42278186,
4.66472231,  6.15595516,  5.87319502,  9.13955542, 11.12529717])
#final_states
array([[  0.,   0., 100.],
[  0.,   0., 100.],
[  0.,   0., 100.],
[  0.,   0., 100.],
[  0.,   0., 100.],
[  0.,   0., 100.],
[  0.,   0., 100.],
[  0.,   0., 100.],
[  0.,   0., 100.],
[  0.,   0., 100.]])


## Algorithms¶

The Simulation class currently supports the following algorithms:

1. Direct

2. Tau leaping

You can change the algorithm used to perform a simulation using the simulation flag

sim.simulate(max_t=150, max_iter=1000, chem_flag=True, n_rep=10, algorithm="tau_leaping")