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#!/usr/bin/env python | ||
# -*- coding: utf-8 -*- | ||
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# Copyright (C) 2021 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/>. | ||
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import numpy as N | ||
import scipy.sparse as SP | ||
import nose | ||
from assimulo.solvers import Radau5ODE | ||
from assimulo.problem import Explicit_Problem | ||
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def run_example(with_plots=True, solver = 'c'): | ||
r""" | ||
Example for demonstrating the use of a user supplied Jacobian (sparse). | ||
Based on the SUNDIALS example cvRoberts_sps.c | ||
ODE: | ||
.. math:: | ||
\dot y_1 &= -0.04y_1 + 1e4 y_2 y_3 \\ | ||
\dot y_2 &= - \dot y_1 - \dot y_3 \\ | ||
\dot y_3 &= 3e7 y_2^2 | ||
on return: | ||
- :dfn:`exp_mod` problem instance | ||
- :dfn:`exp_sim` solver instance | ||
""" | ||
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#Defines the rhs | ||
def f(t,y): | ||
yd_0 = -0.04*y[0] + 1e4*y[1]*y[2] | ||
yd_2 = 3e7*y[1]*y[1] | ||
yd_1 = -yd_0 - yd_2 | ||
return N.array([yd_0,yd_1,yd_2]) | ||
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#Defines the Jacobian | ||
def jac(t,y): | ||
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colptrs = [0,3,6,9] | ||
rowvals = [0, 1, 2, 0, 1, 2, 0, 1, 2] | ||
data = [-0.04, 0.04, 0.0, 1e4*y[2], -1e4*y[2]-6e7*y[1], 6e7*y[1], 1e4*y[1], -1e4*y[1], 0.0] | ||
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J = SP.csc_matrix((data, rowvals, colptrs)) | ||
return J | ||
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#Defines an Assimulo explicit problem | ||
y0 = [1.0, 0.0, 0.0] #Initial conditions | ||
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exp_mod = Explicit_Problem(f, y0, name = 'Example using analytic (sparse) Jacobian') | ||
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exp_mod.jac = jac #Sets the Jacobian | ||
exp_mod.jac_nnz = 9 | ||
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exp_sim = Radau5ODE(exp_mod) #Create a Radau5 solver | ||
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#Set the parameters | ||
exp_sim.atol = [1e-8,1e-14,1e-6] #Default 1e-6 | ||
exp_sim.rtol = 1e-4 #Default 1e-6 | ||
exp_sim.solver = solver | ||
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#Simulate | ||
t, y = exp_sim.simulate(0.4) #Simulate 0.4 seconds | ||
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#Plot | ||
if with_plots: | ||
import pylab as P | ||
P.plot(t,y[:,1],linestyle="dashed",marker="o") #Plot the solution | ||
P.xlabel('Time') | ||
P.ylabel('State') | ||
P.title(exp_mod.name) | ||
P.show() | ||
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#Basic tests | ||
nose.tools.assert_almost_equal(y[-1][0],0.9851,3) | ||
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return exp_mod, exp_sim | ||
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if __name__=='__main__': | ||
mod,sim = run_example() |
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