#!/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 IDA
from assimulo.problem import Implicit_Problem
[docs]def run_example(with_plots=True):
"""
This example show how to use Assimulo and IDA for simulating sensitivities
for initial conditions.::
0 = dy1/dt - -(k01+k21+k31)*y1 - k12*y2 - k13*y3 - b1
0 = dy2/dt - k21*y1 + (k02+k12)*y2
0 = dy3/dt - k31*y1 + k13*y3
y1(0) = p1, y2(0) = p2, y3(0) = p3
p1=p2=p3 = 0
See http://sundials.2283335.n4.nabble.com/Forward-sensitivities-for-initial-conditions-td3239724.html
on return:
- :dfn:`imp_mod` problem instance
- :dfn:`imp_sim` solver instance
"""
def f(t, y, yd,p):
y1,y2,y3 = y
yd1,yd2,yd3 = yd
k01 = 0.0211
k02 = 0.0162
k21 = 0.0111
k12 = 0.0124
k31 = 0.0039
k13 = 0.000035
b1 = 49.3
res_0 = -yd1 -(k01+k21+k31)*y1+k12*y2+k13*y3+b1
res_1 = -yd2 + k21*y1-(k02+k12)*y2
res_2 = -yd3 + k31*y1-k13*y3
return N.array([res_0,res_1,res_2])
#The initial conditions
y0 = [0.0,0.0,0.0] #Initial conditions for y
yd0 = [49.3,0.,0.]
p0 = [0.0, 0.0, 0.0] #Initial conditions for parameters
yS0 = N.array([[1,0,0],[0,1,0],[0,0,1.]])
#Create an Assimulo implicit problem
imp_mod = Implicit_Problem(f,y0,yd0,p0=p0,name='Example: Computing Sensitivities')
#Sets the options to the problem
imp_mod.yS0=yS0
#Create an Assimulo explicit solver (IDA)
imp_sim = IDA(imp_mod)
#Sets the paramters
imp_sim.rtol = 1e-7
imp_sim.atol = 1e-6
imp_sim.pbar = [1,1,1] #pbar is used to estimate the tolerances for the parameters
imp_sim.report_continuously = True #Need to be able to store the result using the interpolate methods
imp_sim.sensmethod = 'SIMULTANEOUS' #Defines the sensitvity method used
imp_sim.suppress_sens = False #Dont suppress the sensitivity variables in the error test.
#Simulate
t, y, yd = imp_sim.simulate(400) #Simulate 400 seconds
#Basic test
nose.tools.assert_almost_equal(y[-1][0], 1577.6552477,3)
nose.tools.assert_almost_equal(y[-1][1], 611.9574565, 3)
nose.tools.assert_almost_equal(y[-1][2], 2215.88563217, 3)
nose.tools.assert_almost_equal(imp_sim.p_sol[0][1][0], 1.0)
#Plot
if with_plots:
P.figure(1)
P.subplot(221)
P.plot(t, N.array(imp_sim.p_sol[0])[:,0],
t, N.array(imp_sim.p_sol[0])[:,1],
t, N.array(imp_sim.p_sol[0])[:,2])
P.title("Parameter p1")
P.legend(("p1/dy1","p1/dy2","p1/dy3"))
P.subplot(222)
P.plot(t, N.array(imp_sim.p_sol[1])[:,0],
t, N.array(imp_sim.p_sol[1])[:,1],
t, N.array(imp_sim.p_sol[1])[:,2])
P.title("Parameter p2")
P.legend(("p2/dy1","p2/dy2","p2/dy3"))
P.subplot(223)
P.plot(t, N.array(imp_sim.p_sol[2])[:,0],
t, N.array(imp_sim.p_sol[2])[:,1],
t, N.array(imp_sim.p_sol[2])[:,2])
P.title("Parameter p3")
P.legend(("p3/dy1","p3/dy2","p3/dy3"))
P.subplot(224)
P.title('ODE Solution')
P.plot(t, y)
P.suptitle(imp_mod.name)
P.show()
return imp_mod, imp_sim
if __name__=='__main__':
mod,sim = run_example()