def run_example(with_plots=True):
r"""
Example for demonstrating the use of a user supplied Jacobian (sparse).
Note that this will only work if Assimulo has been configured with
Sundials + SuperLU. 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
"""
#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])
#Defines the Jacobian
def jac(t, y):
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
]
J = SP.csc_matrix((data, rowvals, colptrs))
return J
#Defines an Assimulo explicit problem
y0 = [1.0, 0.0, 0.0] #Initial conditions
exp_mod = Explicit_Problem(f,
y0,
name='Example using analytic (sparse) Jacobian')
exp_mod.jac = jac #Sets the Jacobian
exp_mod.jac_nnz = 9
exp_sim = CVode(exp_mod) #Create a CVode solver
#Set the parameters
exp_sim.iter = 'Newton' #Default 'FixedPoint'
exp_sim.discr = 'BDF' #Default 'Adams'
exp_sim.atol = [1e-8, 1e-14, 1e-6] #Default 1e-6
exp_sim.rtol = 1e-4 #Default 1e-6
exp_sim.linear_solver = "sparse"
#Simulate
t, y = exp_sim.simulate(0.4) #Simulate 0.4 seconds
#Basic tests
nose.tools.assert_almost_equal(y[-1][0], 0.9851, 3)
#Plot
if with_plots:
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()
return exp_mod, exp_sim
