Source code for assimulo.examples.cvode_basic_backward
#!/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):
"""
The same as example :doc:`EXAMPLE_cvode_basic` but now integrated backwards in time.
on return:
- :dfn:`exp_mod` problem instance
- :dfn:`exp_sim` solver instance
"""
#Define the rhs
def f(t,y):
ydot = -y[0]
return N.array([ydot])
#Define an Assimulo problem
exp_mod = Explicit_Problem(f,t0=5, y0=0.02695, name = r'CVode Test Example (reverse time): $\dot y = - y$ ')
#Define an explicit solver
exp_sim = CVode(exp_mod) #Create a CVode solver
#Sets the parameters
exp_sim.iter = 'Newton' #Default 'FixedPoint'
exp_sim.discr = 'BDF' #Default 'Adams'
exp_sim.atol = [1e-8] #Default 1e-6
exp_sim.rtol = 1e-8 #Default 1e-6
exp_sim.backward = True
#Simulate
t, y = exp_sim.simulate(0) #Simulate 5 seconds (t0=5 -> tf=0)
#print 'y(5) = {}, y(0) ={}'.format(y[0][0],y[-1][0])
#Basic test
nose.tools.assert_almost_equal(float(y[-1]), 4.00000000, 3)
#Plot
if with_plots:
P.plot(t, y, color="b")
P.title(exp_mod.name)
P.ylabel('y')
P.xlabel('Time')
P.show()
return exp_mod, exp_sim
if __name__=='__main__':
mod,sim = run_example()