def run_example():
#initial values
t0 = 0
y0 = np.array([0., -0.10344, -0.65, 0., 0. , 0., -0.628993, 0.047088]) #|phi_s| <= 0.1034 rad, |phi_b| <= 0.12 rad
yd0 = np.array([0., 0., 0., 0., 0., 0., 0., 0.])
sw = [False, True, False]
#problem
model = Implicit_Problem(pecker, y0, yd0, t0, sw0=sw)
model.state_events = state_events #from woodpecker.py
model.handle_event = handle_event #from woodpecker.py
model.name = 'Woodpeckermodel'
sim = IDA(model) #create IDA solver
tfinal = 2.0 #final time
ncp = 500 #number control points
sim.suppress_alg = True
sim.rtol=1.e-6
sim.atol[6:8] = 1e6
sim.algvar[6:8] = 0
t, y, yd = sim.simulate(tfinal, ncp) #simulate
#plot
fig, ax = P.subplots()
ax.plot(t, y[:, 0], label='z')
legend = ax.legend(loc='upper center', shadow=True)
P.grid()
P.figure(1)
fig2, ax2 = P.subplots()
ax2.plot(t, y[:, 1], label='phi_s')
ax2.plot(t, y[:, 2], label='phi_b')
legend = ax2.legend(loc='upper center', shadow=True)
P.grid()
P.figure(2)
fig3, ax3 = P.subplots()
ax3.plot(t, y[:, 4], label='phi_sp')
ax3.plot(t, y[:, 5], label='phi_bp')
legend = ax3.legend(loc='upper center', shadow=True)
P.grid()
P.figure(3)
fig4, ax4 = P.subplots()
ax4.plot(t, y[:, 6], label='lambda_1')
ax4.plot(t, y[:, 7], label='lambda_2')
legend = ax4.legend(loc='upper right', shadow=True)
P.grid()
#event data
sim.print_event_data()
#show plots
P.show()
print("...")
P.show()
def solve_squeezer(self):
model = Implicit_Problem(self.squeezer_func, self.y, self.yp, self.t)
sim = IDA(model)
tfinal = 10.0
ncp = 1000
sim.atol = 1.0e-6
sim.suppress_alg = True
for i in range(sim.algvar.size):
if i > 14:
sim.algvar[i] = 0
print(sim.algvar)
t, y, yd = sim.simulate(tfinal, ncp)
sim.plot()
def run_example(index="ind1", with_plots=True, with_test=False):
my_pend_sys = pendulum()
my_pend = my_pend_sys.generate_problem(index)
my_pend.name = 'Index = {}'.format(index)
dae_pend = IDA(my_pend) if index not in ('ovstab2',
'ovstab1') else ODASSL(my_pend)
dae_pend.atol = 1.e-6
dae_pend.rtol = 1.e-6
dae_pend.suppress_alg = True
t, y, yd = dae_pend.simulate(10., 100)
final_residual = my_pend.res(0., dae_pend.y, dae_pend.yd)
print(my_pend.name + " Residuals after the integration run\n")
print(final_residual, 'Norm: ', sl.norm(final_residual))
if with_test:
assert (sl.norm(final_residual) < 1.5e-1)
if with_plots:
dae_pend.plot(mask=[1, 1] + (len(my_pend.y0) - 2) * [0])
return my_pend, dae_pend
def buildsim(self, ):
"""
Setup the assimulo IDA simulator.
"""
# Create an Assimulo implicit solver (IDA)
imp_sim = IDA(self.imp_mod) # Create a IDA solver
# Sets the paramters
# 1e-4 #Default 1e-6
imp_sim.atol = self.p.RunInput['TIMESTEPPING']['SOLVER_TOL']
# 1e-4 #Default 1e-6
imp_sim.rtol = self.p.RunInput['TIMESTEPPING']['SOLVER_TOL']
# Suppres the algebraic variables on the error test
imp_sim.suppress_alg = True
imp_sim.display_progress = False
imp_sim.verbosity = 50
imp_sim.report_continuously = True
imp_sim.time_limit = 10.
self.imp_sim = imp_sim
def main():
y0 = [1.0, 0.0, 0.0, 0.0, 5]
yd0 = [0.0, 0.0, 0.0, -9.82, 0.0]
# tout = [1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0]
tout = np.linspace(0.0, 10.0, 500)
implicit_model = Implicit_Problem(res, y0, yd0, name="Example problem")
# implicit_model.jac = jac
implicit_model.algvar = [1.0, 1.0, 1.0, 1.0, 0.0]
implicit_solver = IDA(implicit_model)
implicit_solver.atol = 1E-6
implicit_solver.rtol = 1E-6
implicit_solver.suppress_alg = True
implicit_solver.make_consistent("IDA_YA_YDP_INIT")
t, y, yd = implicit_solver.simulate(10.0, ncp=500)
plt.plot(t, y, linestyle="dashed", marker="o")
plt.xlabel("Time")
plt.ylabel("State")
plt.title(implicit_model.name)
plt.show()
def run_example(with_plots=True):
r"""
Example for demonstrating the use of a user supplied Jacobian
ODE:
.. math::
\dot y_1-y_3 &= 0 \\
\dot y_2-y_4 &= 0 \\
\dot y_3+y_5 y_1 &= 0 \\
\dot y_4+y_5 y_2+9.82&= 0 \\
y_3^2+y_4^2-y_5(y_1^2+y_2^2)-9.82 y_2&= 0
on return:
- :dfn:`imp_mod` problem instance
- :dfn:`imp_sim` solver instance
"""
#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[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,
name='Example using an analytic Jacobian')
#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
#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:
import pylab as P
P.plot(t, y, linestyle="dashed", marker="o") #Plot the solution
P.xlabel('Time')
P.ylabel('State')
P.title(imp_mod.name)
P.show()
return imp_mod, imp_sim
def run_example(with_plots=True):
r"""
This is the same example from the Sundials package (cvsRoberts_FSA_dns.c)
Its purpose is to demonstrate the use of parameters in the differential equation.
This simple example problem for IDA, due to Robertson
see http://www.dm.uniba.it/~testset/problems/rober.php,
is from chemical kinetics, and consists of the system:
.. math::
\dot y_1 -( -p_1 y_1 + p_2 y_2 y_3)&=0 \\
\dot y_2 -(p_1 y_1 - p_2 y_2 y_3 - p_3 y_2^2)&=0 \\
\dot y_3 -( p_3 y_ 2^2)&=0
on return:
- :dfn:`imp_mod` problem instance
- :dfn:`imp_sim` solver instance
"""
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 = N.array([1.0, 0.0, 0.0]) # Initial conditions for y
yd0 = N.array([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.report_continuously = 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.title(imp_mod.name)
P.xlabel('Time')
P.ylabel('State')
P.show()
return imp_mod, imp_sim
#plt.show()
#print z_out
#Sets the options to the problem
#imp_mod.jac = jac #Sets the jacobian
imp_mod.algvar = [1.0 for i in range(N)] + [0.0 for i in range(N+Na+Nc)] #Set the algebraic components
#imp_mod.algvar = [1.0 for i in range(N)] + [0.0 for i in range(N)] #Set the algebraic components
#Create an Assimulo implicit solver (IDA)
imp_sim = IDA(imp_mod) #Create a IDA solver
#Sets the paramters
imp_sim.atol = 1e-5 #Default 1e-6
imp_sim.rtol = 1e-5 #Default 1e-6
imp_sim.suppress_alg = True #Suppres the algebraic variables on the error test
### Simulate
imp_mod.set_j_vec( I_app )
#res_test = imp_mod.res( 0.0, y0, yd0 )
#jac_test = imp_mod.jac( 2, 0.0, y0, yd0 )
#Let Sundials find consistent initial conditions by use of 'IDA_YA_YDP_INIT'
imp_sim.make_consistent('IDA_YA_YDP_INIT')
# Sim step 1
t1, y1, yd1 = imp_sim.simulate(100,100)
#t1, y1, yd1 = imp_sim.simulate(1000,1000)
imp_mod.set_j_vec( 0.0 )
def DAE_integration_assimulo(self, **kwargs):
"""
Perform time integration for DAEs with the assimulo package
"""
assert self.set_time_setting == 1, 'Time discretization must be specified first'
if self.tclose > 0:
close = True
else:
close = False
# Control vector
self.U = interpolate(self.boundary_cntrl_space, self.Vb).vector()[self.bndr_i_b]
if self.discontinous_boundary_values == 1:
self.U[self.Corner_indices] = self.U[self.Corner_indices]/2
# Definition of the sparse solver for the DAE res function to
# be defined next M should be invertible !!
my_solver = factorized(csc_matrix(self.M))
rhs = self.my_mult(self.J, self.my_mult(self.Q,self.A0)) + self.my_mult(self.Bext,self.U* self.boundary_cntrl_time(0.,self.tclose))
self.AD0 = my_solver(rhs)
# Definition of the rhs function required in assimulo
def res(t,y,yd):
"""
Definition of the residual function required in the DAE part of assimulo
"""
if close:
if t < self.tclose:
z = self.my_mult(self.M,yd) - self.my_mult(self.J, self.my_mult(self.Q,y)) - self.my_mult(self.Bext,self.U* self.boundary_cntrl_time(t,self.tclose))
else:
z = self.my_mult(self.M,yd) - self.my_mult((self.J - self.R), self.my_mult(self.Q,y))
else:
z = self.my_mult(self.M,yd) - self.my_mult(self.J, self.my_mult(self.Q,y)) - self.my_mult(self.Bext,self.U* self.boundary_cntrl_time(t,self.tclose))
return z
# Definition of the jacobian function required in assimulo
def jac(c,t,y,yd):
"""
Definition of the Jacobian matrix required in the DAE part of assimulo
"""
Matrix = csr_matrix(self.my_mult(self.J,self.Q))
if close and t > self.tclose:
Matrix = csr_matrix(self.my_mult(self.J - self.R, self.Q))
return c*csr_matrix(self.M) - Matrix
# Definition of the jacobian matrix vector function required in assimulo
def jacv(t,y,yd,res,v,c):
"""
Jacobian matrix-vector product required in the DAE part of assimulo
"""
w = self.my_mult(self.Q, v)
z = self.my_mult(self.J, w)
if close and t > self.tclose:
z -= self.my_mult(self.R, w)
return c*self.my_mult(self.M,v) - z
print('DAE Integration using assimulo built-in functions:')
model = Implicit_Problem(res,self.A0,self.AD0,self.tinit)
model.jacv = jacv
#sim = Radau5DAE(model,**kwargs)
#
# IDA method from Assimulo
#
sim = IDA(model,**kwargs)
sim.algvar = [1 for i in range(self.M.shape[0])]
sim.atol = 1.e-6
sim.rtol = 1.e-6
sim.report_continuously = True
ncp = self.Nt
sim.usejac = True
sim.suppress_alg = True
sim.inith = self.dt
sim.maxord = 5
#sim.linear_solver = 'SPGMR'
time_span, DAE_y, DAE_yd = sim.simulate(self.tfinal,ncp)
#print(sim.get_options())
print(sim.print_statistics())
A_dae = DAE_y.transpose()
# Hamiltonian
self.Nt = A_dae.shape[1]
self.tspan = np.array(time_span)
Ham_dae = np.zeros(self.Nt)
for k in range(self.Nt):
#Ham_dae[k] = 1/2 * A_dae[:,k] @ self.M @ self.Q @ A_dae[:,k]
Ham_dae[k] = 1/2 * self.my_mult(A_dae[:,k].T, \
self.my_mult(self.M, self.my_mult(self.Q, A_dae[:,k])))
# Get q variables
Aq_dae = A_dae[:self.Nq,:]
# Get p variables
Ap_dae = A_dae[self.Nq:,:]
# Get Deformation
Rho = np.zeros(self.Np)
for i in range(self.Np):
Rho[i] = self.rho(self.coord_p[i])
W_dae = np.zeros((self.Np,self.Nt))
theta = .5
for k in range(self.Nt-1):
W_dae[:,k+1] = W_dae[:,k] + self.dt * 1/Rho[:] * ( theta * Ap_dae[:,k+1] + (1-theta) * Ap_dae[:,k] )
self.Ham_dae = Ham_dae
return Aq_dae, Ap_dae, Ham_dae, W_dae, np.array(time_span)
def run_example(with_plots=True):
r"""
Example for demonstrating the use of a user supplied Jacobian
ODE:
.. math::
\dot y_1-y_3 &= 0 \\
\dot y_2-y_4 &= 0 \\
\dot y_3+y_5 y_1 &= 0 \\
\dot y_4+y_5 y_2+9.82&= 0 \\
y_3^2+y_4^2-y_5(y_1^2+y_2^2)-9.82 y_2&= 0
on return:
- :dfn:`imp_mod` problem instance
- :dfn:`imp_sim` solver instance
"""
global order
order = []
#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[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])
def handle_result(solver, t, y, yd):
global order
order.append(solver.get_last_order())
solver.t_sol.extend([t])
solver.y_sol.extend([y])
solver.yd_sol.extend([yd])
#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,
name='Example for plotting used order')
imp_mod.handle_result = handle_result
#Sets the options to the problem
imp_mod.algvar = [1.0, 1.0, 1.0, 1.0, 0.0] #Set the algebraic components
#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
imp_sim.report_continuously = True
#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) #Simulate 5 seconds
#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)
nose.tools.assert_almost_equal(order[-1], 5, places=4)
#Plot
if with_plots:
P.figure(1)
P.plot(t, y, linestyle="dashed", marker="o") #Plot the solution
P.xlabel('Time')
P.ylabel('State')
P.title(imp_mod.name)
P.figure(2)
P.plot([0] + N.add.accumulate(N.diff(t)).tolist(), order)
P.title("Used order during the integration")
P.xlabel("Time")
P.ylabel("Order")
P.show()
return imp_mod, imp_sim
from assimulo.problem import Implicit_Problem
from assimulo.solvers import IDA
import matplotlib.pyplot as P
import numpy as N
t0 = 0.0
tfinal = 2.0
y0, yd0, switches0 = init_woodpecker()
model = Implicit_Problem(res, y0, yd0, t0, sw0=switches0)
model.state_events = state_event
model.handle_event = handle_event
sim = IDA(model)
sim.algvar = [1, 1, 1, 0, 0, 0, 0, 0]
sim.suppress_alg = True
sim.atol = [1e-5, 1e-5, 1e-5, 1e15, 1e15, 1e15, 1e15, 1e15]
t, y, yd = sim.simulate(tfinal)
#sim.print_event_data()
"""
Plotting
y[:,0] - plots z (height)
y[:,1] - plots sleeve angle
y[:,2] - plots bird angle
"""
# Plot z (height)
P.plot(t, y[:, 0])
P.title('Woodpecker')
from assimulo.problem import Implicit_Problem
from assimulo.solvers import IDA
from Project_2 import squeezer as sq
from Project_2 import squeezer2 as sq2
import matplotlib.pyplot as plt
t0 = 0
tfinal = 0.03
# Model 1, squeezer with index 3 constraints
y0_1,yp0_1 = sq.init_squeezer()
ncp_1 = 100
model_1 = Implicit_Problem(sq.squeezer, y0_1, yp0_1, t0)
model_1.name = 'Squeezer index 3 constraints'
sim_1 = IDA(model_1)
sim_1.suppress_alg = True
sim_1.algvar = array([1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0])
sim_1.atol = ones(20,)
for i in range(size(sim_1.atol)):
if 0 <= i <= 6:
sim_1.atol[i] = pow(10,-6)
else:
sim_1.atol[i] = pow(10,5)
t, y, yd = sim_1.simulate(tfinal, ncp_1)
plt.plot(t,y[:,14:shape(y)[1]]) # Plots the Lagrange multipliers
plt.show()
plt.plot(t,(y[:,0:7]+pi)%(2*pi)-pi) # Plots the position variables i.e beta,gamma etc, modulo 2pi.
plt.show()
# Model 2, squeezer with index 2 constraints
y0_2,yp0_2 = sq2.init_squeezer()
def DAE_integration_assimulo_lagrangian(self, **kwargs):
"""
Perform time integration for DAEs with the assimulo package
Lagrangian variant
"""
assert self.set_time_setting == 1, 'Time discretization must be specified first'
if self.tclose > 0:
close = True
else:
close = False
# Control vector
self.U = interpolate(self.boundary_cntrl_space, self.Vl).vector()[self.bndr_i_l]
if self.discontinous_boundary_values == 1:
self.U[self.Corner_indices] = self.U[self.Corner_indices]/2
self.UU = np.zeros(self.Nb)
for i in range(self.Nb):
self.UU[i] = self.boundary_cntrl_space(self.coord_b[i])
# Definition of the sparse solver for the DAE res function to
# be defined next M should be invertible !!
#my_solver = factorized(csc_matrix(self.M))
#rhs = self.my_mult(self.J, self.my_mult(self.Q,self.A0)) + self.my_mult(self.Bext,self.U* self.boundary_cntrl_time(0.,self.tclose))
#self.AD0 = my_solver(rhs)
# Definition of the rhs function required in assimulo
def res(t,y,yd):
"""
Definition of the residual function required in the DAE part of assimulo
"""
z = np.zeros(self.Np+self.Nl)
z[0:self.Np] = self.my_mult(self.M_class, yd[0:self.Np]) + self.my_mult(self.D_class, y[0:self.Np]) - self.my_mult(self.C_class, y[self.Np:])
z[self.Np:self.Np+self.Nl] = self.my_mult(self.C_class.T, y[0:self.Np]) - self.L_class * self.boundary_cntrl_time(t,self.tclose)
return z
# Definition of the jacobian function required in assimulo
def jac(c,t,y,yd):
"""
Definition of the Jacobian matrix required in the DAE part of assimulo
"""
#Matrix = csr_matrix(self.my_mult(self.J,self.Q))
#if close and t > self.tclose:
# Matrix = csr_matrix(self.my_mult(self.J - self.R, self.Q))
#return c*csr_matrix(self.M) - Matrix
return None
# Definition of the jacobian matrix vector function required in assimulo
def jacv(t,y,yd,res,v,c):
"""
Jacobian matrix-vector product required in the DAE part of assimulo
"""
#w = self.my_mult(self.Q, v)
#z = self.my_mult(self.J, w)
#if close and t > self.tclose:
# z -= self.my_mult(self.R, w)
#return c*self.my_mult(self.M,v) - z
return None
print('DAE Integration using assimulo built-in functions:')
#def handle_result(solver, t ,y, yd):
# global order
# order.append(solver.get_last_order())
#
# solver.t_sol.extend([t])
# solver.y_sol.extend([y])
# solver.yd_sol.extend([yd])
# The initial conditons
y0 = np.concatenate(( self.Tp0, np.zeros(self.Nl) ))
yd0 = np.zeros(self.Np + self.Nl)
model = Implicit_Problem(res,y0,yd0,self.tinit)
#model.handle_result = handle_result
#model.jacv = jacv
#sim = Radau5DAE(model,**kwargs)
#
# IDA method from Assimulo
#
sim = IDA(model,**kwargs)
sim.algvar = list(np.concatenate((np.ones(self.Np), np.zeros(self.Nl) )) )
sim.atol = 1.e-6
sim.rtol = 1.e-6
sim.report_continuously = True
ncp = self.Nt
#sim.usejac = True
sim.suppress_alg = True
sim.inith = self.dt
sim.maxord = 5
#sim.linear_solver = 'SPGMR'
sim.make_consistent('IDA_YA_YDP_INIT')
#time_span, DAE_y, DAE_yd = sim.simulate(self.tfinal,ncp, self.tspan)
time_span, DAE_y, DAE_yd = sim.simulate(self.tfinal, 0, self.tspan)
#print(sim.get_options())
print(sim.print_statistics())
A_dae = DAE_y[:,0:self.Np].transpose()
# Hamiltonian
self.Nt = A_dae.shape[1]
self.tspan = np.array(time_span)
Ham_dae = np.zeros(self.Nt)
for k in range(self.Nt):
Ham_dae[k] = 1/2 * self.my_mult(A_dae[:,k].T, \
self.my_mult(self.Mp_rho_Cv, A_dae[:,k]))
self.Ham_dae = Ham_dae
return Ham_dae, np.array(time_span)
def run_example():
def residual(t,y,yd):
return squeezer(t, y, yd)
def residual2(t,y,yd):
return squeezer2(t, y, yd)
#The initial conditons
t0 = 0
y0, yd0 = init_squeezer()
model = Implicit_Problem(residual, y0, yd0, t0) #Create an Assimulo problem
model2 = Implicit_Problem(residual2, y0, yd0, t0) #Create an Assimulo problem
sim = IDA(model) #Create the IDA solver
sim2 = IDA(model2) #Create the IDA solver
# index 3
sim.algvar = 7*[True] + 7*[False] + 6*[False]
sim.suppress_alg = True
sim.atol = 7*[1e-6] + 7*[1e5] + 6*[1e5]
# index 2
sim2.algvar = 7*[True] + 7*[True] + 6*[False]
sim2.suppress_alg = True
sim2.atol = 7*[1e-6] + 7*[1e-6] + 6*[1e5]
tfinal = 0.03 #Specify the final time
ncp = 500 #Number of communcation points (number of return points)
t,y,yd = sim.simulate(tfinal, ncp) #Use the .simulate method to simulate and provide the final time and ncp (optional)
t2,y2,yd2 = sim2.simulate(tfinal, ncp) #Use the .simulate method to simulate and provide the final time and ncp (optional)
print("500####################")
print("####################")
fig, ax = P.subplots()
P.title('IDA, difference between index 3 and index 2 formulation')
P.xlabel('Time')
P.ylabel('Angle')
#P.ylabel('Step size')
#P.axis([0, tfinal + 0.01, -0.7, 0.7])
#P.plot(t[1:], np.diff(t))
#P.plot(t, y[:, 0], label='beta')
#P.plot(t, y[:, 1], label='theta')
#P.plot(t, y[:, 2], label='gamma')
#P.plot(t, y[:, 3], label='phi')
#P.plot(t, y[:, 4], label='delta')
#P.plot(t, y[:, 5], label='omega')
#P.plot(t, y[:, 6], label='epsilon')
P.plot(t, y[:, 0] - y2[:, 0], label='beta')
P.plot(t, y[:, 1] - y2[:, 1], label='theta')
P.plot(t, y[:, 2] - y2[:, 2], label='gamma')
P.plot(t, y[:, 3] - y2[:, 3], label='phi')
P.plot(t, y[:, 4] - y2[:, 4], label='delta')
P.plot(t, y[:, 5] - y2[:, 5], label='omega')
#P.plot(t, y[:, 6], label='epsilon')
legend = ax.legend(shadow=True, loc = 'upper left')
'''
P.plot(t, y[:, 14])
P.plot(t, y[:, 15])
P.plot(t, y[:, 16])
P.plot(t, y[:, 17])
P.plot(t, y[:, 18])
P.plot(t, y[:, 19])
P.axis([0, tfinal, -100, 200])
'''
P.grid()
P.show()
def dae_solver(residual,
y0,
yd0,
t0,
p0=None,
jac=None,
name='DAE',
solver='IDA',
algvar=None,
atol=1e-6,
backward=False,
display_progress=True,
pbar=None,
report_continuously=False,
rtol=1e-6,
sensmethod='STAGGERED',
suppress_alg=False,
suppress_sens=False,
usejac=False,
usesens=False,
verbosity=30,
tfinal=10.,
ncp=500):
'''
DAE solver.
Parameters
----------
residual: function
Implicit DAE model.
y0: List[float]
Initial model state.
yd0: List[float]
Initial model state derivatives.
t0: float
Initial simulation time.
p0: List[float]
Parameters for which sensitivites are to be calculated.
jac: function
Model jacobian.
name: string
Model name.
solver: string
DAE solver.
algvar: List[bool]
A list for defining which variables are differential and which are algebraic.
The value True(1.0) indicates a differential variable and the value False(0.0) indicates an algebraic variable.
atol: float
Absolute tolerance.
backward: bool
Specifies if the simulation is done in reverse time.
display_progress: bool
Actives output during the integration in terms of that the current integration is periodically printed to the stdout.
Report_continuously needs to be activated.
pbar: List[float]
An array of positive floats equal to the number of parameters. Default absolute values of the parameters.
Specifies the order of magnitude for the parameters. Useful if IDAS is to estimate tolerances for the sensitivity solution vectors.
report_continuously: bool
Specifies if the solver should report the solution continuously after steps.
rtol: float
Relative tolerance.
sensmethod: string
Specifies the sensitivity solution method.
Can be either ‘SIMULTANEOUS’ or ‘STAGGERED’. Default is 'STAGGERED'.
suppress_alg: bool
Indicates that the error-tests are suppressed on algebraic variables.
suppress_sens: bool
Indicates that the error-tests are suppressed on the sensitivity variables.
usejac: bool
Sets the option to use the user defined jacobian.
usesens: bool
Aactivates or deactivates the sensitivity calculations.
verbosity: int
Determines the level of the output.
QUIET = 50 WHISPER = 40 NORMAL = 30 LOUD = 20 SCREAM = 10
tfinal: float
Simulation final time.
ncp: int
Number of communication points (number of return points).
Returns
-------
sol: solution [time, model states], List[float]
'''
if usesens is True: # parameter sensitivity
model = Implicit_Problem(residual, y0, yd0, t0, p0=p0)
else:
model = Implicit_Problem(residual, y0, yd0, t0)
model.name = name
if usejac is True: # jacobian
model.jac = jac
if algvar is not None: # differential or algebraic variables
model.algvar = algvar
if solver == 'IDA': # solver
from assimulo.solvers import IDA
sim = IDA(model)
sim.atol = atol
sim.rtol = rtol
sim.backward = backward # backward in time
sim.report_continuously = report_continuously
sim.display_progress = display_progress
sim.suppress_alg = suppress_alg
sim.verbosity = verbosity
if usesens is True: # sensitivity
sim.sensmethod = sensmethod
sim.pbar = np.abs(p0)
sim.suppress_sens = suppress_sens
# Simulation
# t, y, yd = sim.simulate(tfinal, ncp=(ncp - 1))
ncp_list = np.linspace(t0, tfinal, num=ncp, endpoint=True)
t, y, yd = sim.simulate(tfinal, ncp=0, ncp_list=ncp_list)
# Plot
# sim.plot()
# plt.figure()
# plt.subplot(221)
# plt.plot(t, y[:, 0], 'b.-')
# plt.legend([r'$\lambda$'])
# plt.subplot(222)
# plt.plot(t, y[:, 1], 'r.-')
# plt.legend([r'$\dot{\lambda}$'])
# plt.subplot(223)
# plt.plot(t, y[:, 2], 'k.-')
# plt.legend([r'$\eta$'])
# plt.subplot(224)
# plt.plot(t, y[:, 3], 'm.-')
# plt.legend([r'$\dot{\eta}$'])
# plt.figure()
# plt.subplot(221)
# plt.plot(t, yd[:, 0], 'b.-')
# plt.legend([r'$\dot{\lambda}$'])
# plt.subplot(222)
# plt.plot(t, yd[:, 1], 'r.-')
# plt.legend([r'$\ddot{\lambda}$'])
# plt.subplot(223)
# plt.plot(t, yd[:, 2], 'k.-')
# plt.legend([r'$\dot{\eta}$'])
# plt.subplot(224)
# plt.plot(t, yd[:, 3], 'm.-')
# plt.legend([r'$\ddot{\eta}$'])
# plt.figure()
# plt.subplot(121)
# plt.plot(y[:, 0], y[:, 1])
# plt.xlabel(r'$\lambda$')
# plt.ylabel(r'$\dot{\lambda}$')
# plt.subplot(122)
# plt.plot(y[:, 2], y[:, 3])
# plt.xlabel(r'$\eta$')
# plt.ylabel(r'$\dot{\eta}$')
# plt.figure()
# plt.subplot(121)
# plt.plot(yd[:, 0], yd[:, 1])
# plt.xlabel(r'$\dot{\lambda}$')
# plt.ylabel(r'$\ddot{\lambda}$')
# plt.subplot(122)
# plt.plot(yd[:, 2], yd[:, 3])
# plt.xlabel(r'$\dot{\eta}$')
# plt.ylabel(r'$\ddot{\eta}$')
# plt.figure()
# plt.subplot(121)
# plt.plot(y[:, 0], y[:, 2])
# plt.xlabel(r'$\lambda$')
# plt.ylabel(r'$\eta$')
# plt.subplot(122)
# plt.plot(y[:, 1], y[:, 3])
# plt.xlabel(r'$\dot{\lambda}$')
# plt.ylabel(r'$\dot{\eta}$')
# plt.figure()
# plt.subplot(121)
# plt.plot(yd[:, 0], yd[:, 2])
# plt.xlabel(r'$\dot{\lambda}$')
# plt.ylabel(r'$\dot{\eta}$')
# plt.subplot(122)
# plt.plot(yd[:, 1], yd[:, 3])
# plt.xlabel(r'$\ddot{\lambda}$')
# plt.ylabel(r'$\ddot{\eta}$')
# plt.show()
sol = [t, y, yd]
return sol
# -*- coding: utf-8 -*-
from __future__ import division
from scipy import *
from matplotlib.pyplot import *
import numpy as np
from assimulo.problem import Implicit_Problem
from assimulo.solvers import IDA
import squeezer
y0,yp0=squeezer.init_squeezer() # Initial values
t0 = 0 # Initial time
squeezemodel = Implicit_Problem(squeezer.squeezer, y0, yp0, t0)
algvar = 7*[1.]+13*[0.]
sim = IDA(squeezemodel) # Create solver instance
sim.algvar = algvar
sim.suppress_alg=True
sim.atol = 1e-7
tf = .03 # End time for simulation
t, y, yd = sim.simulate(tf)
sim.plot(mask=7*[1]+13*[0])
grid(1)
axis([0, .03, -1.5, 1.5])
xlabel('Time, t [s]')
ylabel('Angle, [rad]')
import squeezer_ind3
y20,yp20=squeezer_ind2.init_squeezer2() # Initial values
y30,yp30=squeezer_ind3.init_squeezer3() # Initial values
t0 = 0 # Initial time
squeezemodel2 = Implicit_Problem(squeezer_ind2.squeezer2, y20, yp20, t0)
squeezemodel3 = Implicit_Problem(squeezer_ind3.squeezer3, y30, yp30, t0)
algvar = 7*[1.]+13*[0.]
solver2 = IDA(squeezemodel2) # Create solver instance
solver3 = IDA(squeezemodel3) # Create solver instance
solver2.algvar = algvar
solver3.algvar = algvar
solver2.suppress_alg=True
solver3.suppress_alg=True
solver2.atol = 1e-7
solver3.atol = 1e-7
solver3.maxsteps = 322
print(solver3.maxsteps)
tf = .03 # End time for simulation
t2, y2, yd2 = solver2.simulate(tf)
t3, y3, yd3 = solver3.simulate(tf)
figure(1)
plot(t2,y2[:,14:16])
title('Index 2')
figure(2)
