def simulate(self, tmax, nout=500, maxsteps=5000, rtol=1e-8, verbose=False, test_jac_args=None):
if not hasattr(self, 't0'):
self.assemble(verbose)
if test_jac_args is not None:
self.test_jacobian(*test_jac_args)
sim = IDA(self)
flag, _, _ = sim.make_consistent('IDA_YA_YDP_INIT')
translation = {0:'SUCCESS', 1:'TSTOP_RETURN', 2:'ROOT_RETURN',
99:'WARNING', -1 :'TOO_MUCH_WORK', -2 :'TOO_MUCH_ACC',
-3 :'ERR_FAIL', -4 :'CONV_FAIL', -5 :'LINIT_FAIL',
-6 :'LSETUP_FAIL', -7 :'LSOLVE_FAIL', -8 :'RES_FAIL',
-9 :'REP_RES_ERR', -10:'RTFUNC_FAIL', -11:'CONSTR_FAIL',
-12:'FIRST_RES_FAIL', -13:'LINESEARCH_FAIL', -14:'NO_RECOVERY',
-20:'MEM_NULL', -21:'MEM_FAIL', -22:'ILL_INPUT', -23:'NO_MALLOC',
-24:'BAD_EWT', -25:'BAD_K', -26:'BAD_T', -27:'BAD_DKY'}
if flag < 0:
raise ArithmeticError('make_consistent failed with flag = IDA_%s' % translation[flag])
if flag != 0:
warn('make_consistent returned IDA_%s' % translation[flag])
sim.rtol = rtol
sim.maxsteps = maxsteps
T,Y,Yd = sim.simulate(tmax, nout)
ncnt = len(self.nodes)
nterm = len(self.terminals)
self.T = T
Vs = Y [:, :ncnt]
dVsdt = Yd[:, :ncnt]
Is = Y [:, ncnt:(ncnt+nterm)]
dIsdt = Yd[:, ncnt:(ncnt+nterm)]
Qs = Y [:, (ncnt+nterm):]
dQsdt = Yd[:, (ncnt+nterm):]
for i,node in enumerate(self.nodes):
for term in node:
term.V = Vs[:, i]
term.dVdt = dVsdt[:, i]
for i,term in enumerate(self.terminals):
term.I = Is[:, i]
term.dIdt = dIsdt[:, i]
for i,state in enumerate(self.states):
state.val = Qs[:, i]
state.der = dQsdt[:, i]
def run_example(with_plots=True):
#Create an instance of the problem
iter_mod = Extended_Problem() #Create the problem
iter_sim = IDA(iter_mod) #Create the solver
iter_sim.verbosity = 0
iter_sim.continuous_output = True
#Simulate
t, y, yd = iter_sim.simulate(
10.0, 1000) #Simulate 10 seconds with 1000 communications points
#Basic test
nose.tools.assert_almost_equal(y[-1][0], 8.0)
nose.tools.assert_almost_equal(y[-1][1], 3.0)
nose.tools.assert_almost_equal(y[-1][2], 2.0)
#Plot
if with_plots:
P.plot(t, y)
P.show()
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
"""
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)
#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.continuous_output = 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.plot(t, y)
P.show()
def run_example(with_plots=True):
"""
This is the same example from the Sundials package (idasRoberts_FSA_dns.c)
This simple example problem for IDA, due to Robertson,
is from chemical kinetics, and consists of the following three
equations::
dy1/dt = -p1*y1 + p2*y2*y3
dy2/dt = p1*y1 - p2*y2*y3 - p3*y2**2
0 = y1 + y2 + y3 - 1
"""
def f(t, y, yd, p):
res1 = -p[0] * y[0] + p[1] * y[1] * y[2] - yd[0]
res2 = p[0] * y[0] - p[1] * y[1] * y[2] - p[2] * y[1]**2 - yd[1]
res3 = y[0] + y[1] + y[2] - 1
return N.array([res1, res2, res3])
#The initial conditons
y0 = [1.0, 0.0, 0.0] #Initial conditions for y
yd0 = [0.1, 0.0, 0.0] #Initial conditions for dy/dt
p0 = [0.040, 1.0e4, 3.0e7] #Initial conditions for parameters
#Create an Assimulo implicit problem
imp_mod = Implicit_Problem(f, y0, yd0, p0=p0)
#Create an Assimulo implicit solver (IDA)
imp_sim = IDA(imp_mod) #Create a IDA solver
#Sets the paramters
imp_sim.atol = N.array([1.0e-8, 1.0e-14, 1.0e-6])
imp_sim.algvar = [1.0, 1.0, 0.0]
imp_sim.suppress_alg = False #Suppres the algebraic variables on the error test
imp_sim.continuous_output = True #Store data continuous during the simulation
imp_sim.pbar = p0
imp_sim.suppress_sens = False #Dont suppress the sensitivity variables in the error test.
#Let Sundials find consistent initial conditions by use of 'IDA_YA_YDP_INIT'
imp_sim.make_consistent('IDA_YA_YDP_INIT')
#Simulate
t, y, yd = imp_sim.simulate(
4, 400) #Simulate 4 seconds with 400 communication points
print imp_sim.p_sol[0][-1], imp_sim.p_sol[1][-1], imp_sim.p_sol[0][-1]
#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(
imp_sim.p_sol[0][-1][0], -1.8761,
2) #Values taken from the example in Sundials
nose.tools.assert_almost_equal(imp_sim.p_sol[1][-1][0], 2.9614e-06, 8)
nose.tools.assert_almost_equal(imp_sim.p_sol[2][-1][0], -4.9334e-10, 12)
#Plot
if with_plots:
P.plot(t, y)
P.show()
def run_example(with_plots=True):
#Defines the residual
def f(t, y, yd):
res_0 = yd[0] - y[2]
res_1 = yd[1] - y[3]
res_2 = yd[2] + y[4] * y[0]
res_3 = yd[3] + y[4] * y[1] + 9.82
#res_4 = y[0]**2+y[1]**2-1
res_4 = y[2]**2 + y[3]**2 - y[4] * (y[0]**2 + y[1]**2) - y[1] * 9.82
return N.array([res_0, res_1, res_2, res_3, res_4])
#Defines the jacobian
def jac(c, t, y, yd):
jacobian = N.zeros([len(y), len(y)])
#Derivative
jacobian[0, 0] = 1 * c
jacobian[1, 1] = 1 * c
jacobian[2, 2] = 1 * c
jacobian[3, 3] = 1 * c
#Differentiated
jacobian[0, 2] = -1
jacobian[1, 3] = -1
jacobian[2, 0] = y[4]
jacobian[3, 1] = y[4]
jacobian[4, 0] = y[0] * 2 * y[4] * -1
jacobian[4, 1] = y[1] * 2 * y[4] * -1 - 9.82
jacobian[4, 2] = y[2] * 2
jacobian[4, 3] = y[3] * 2
#Algebraic
jacobian[2, 4] = y[0]
jacobian[3, 4] = y[1]
jacobian[4, 4] = -(y[0]**2 + y[1]**2)
return jacobian
#The initial conditons
y0 = [1.0, 0.0, 0.0, 0.0, 5] #Initial conditions
yd0 = [0.0, 0.0, 0.0, -9.82, 0.0] #Initial conditions
#Create an Assimulo implicit problem
imp_mod = Implicit_Problem(f, y0, yd0)
#Sets the options to the problem
imp_mod.jac = jac #Sets the jacobian
imp_mod.algvar = [1.0, 1.0, 1.0, 1.0, 0.0] #Set the algebraic components
imp_mod.name = 'Test Jacobian'
#Create an Assimulo implicit solver (IDA)
imp_sim = IDA(imp_mod) #Create a IDA solver
#Sets the paramters
imp_sim.atol = 1e-6 #Default 1e-6
imp_sim.rtol = 1e-6 #Default 1e-6
imp_sim.suppress_alg = True #Suppres the algebraic variables on the error test
#Let Sundials find consistent initial conditions by use of 'IDA_YA_YDP_INIT'
imp_sim.make_consistent('IDA_YA_YDP_INIT')
#Simulate
t, y, yd = imp_sim.simulate(
5, 1000) #Simulate 5 seconds with 1000 communication points
#Basic tests
nose.tools.assert_almost_equal(y[-1][0], 0.9401995, places=4)
nose.tools.assert_almost_equal(y[-1][1], -0.34095124, places=4)
nose.tools.assert_almost_equal(yd[-1][0], -0.88198927, places=4)
nose.tools.assert_almost_equal(yd[-1][1], -2.43227069, places=4)
#Plot
if with_plots:
P.plot(t, y)
P.show()
