Source code for assimulo.examples.cvode_with_parameters_modified
#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Copyright (C) 2010 Modelon AB
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, version 3 of the License.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import numpy as N
import pylab as P
import nose
from assimulo.solvers import CVode
from assimulo.problem import Explicit_Problem
[docs]def run_example(with_plots=True):
"""
This is the same example from the Sundials package (cvsRoberts_FSA_dns.c)
This simple example problem for CVode, due to Robertson,
is from chemical kinetics, and consists of the following three
equations:
.. math::
\dot y_1 &= -p_1 y_1 + p_2 y_2 y_3 \\
\dot y_2 &= p_1 y_1 - p_2 y_2 y_3 - p_3 y_2^2 \\
\dot y_3 &= p_3 y_2^2
on return:
- :dfn:`exp_mod` problem instance
- :dfn:`exp_sim` solver instance
"""
def f(t, y, p):
p3 = 3.0e7
yd_0 = -p[0]*y[0]+p[1]*y[1]*y[2]
yd_1 = p[0]*y[0]-p[1]*y[1]*y[2]-p3*y[1]**2
yd_2 = p3*y[1]**2
return N.array([yd_0,yd_1,yd_2])
#The initial conditions
y0 = [1.0,0.0,0.0] #Initial conditions for y
#Create an Assimulo explicit problem
exp_mod = Explicit_Problem(f,y0, name='Sundials test example: Chemical kinetics')
#Sets the options to the problem
exp_mod.p0 = [0.040, 1.0e4] #Initial conditions for parameters
exp_mod.pbar = [0.040, 1.0e4]
#Create an Assimulo explicit solver (CVode)
exp_sim = CVode(exp_mod)
#Sets the paramters
exp_sim.iter = 'Newton'
exp_sim.discr = 'BDF'
exp_sim.rtol = 1.e-4
exp_sim.atol = N.array([1.0e-8, 1.0e-14, 1.0e-6])
exp_sim.sensmethod = 'SIMULTANEOUS' #Defines the sensitvity method used
exp_sim.suppress_sens = False #Dont suppress the sensitivity variables in the error test.
exp_sim.report_continuously = True
#Simulate
t, y = exp_sim.simulate(4,400) #Simulate 4 seconds with 400 communication points
#Basic test
nose.tools.assert_almost_equal(y[-1][0], 9.05518032e-01, 4)
nose.tools.assert_almost_equal(y[-1][1], 2.24046805e-05, 4)
nose.tools.assert_almost_equal(y[-1][2], 9.44595637e-02, 4)
nose.tools.assert_almost_equal(exp_sim.p_sol[0][-1][0], -1.8761, 2) #Values taken from the example in Sundials
nose.tools.assert_almost_equal(exp_sim.p_sol[1][-1][0], 2.9614e-06, 8)
#Plot
if with_plots:
P.plot(t, y)
P.xlabel('Time')
P.ylabel('State')
P.title(exp_mod.name)
P.show()
return exp_mod, exp_sim
if __name__=='__main__':
mod,sim = run_example()