def simulate(self, Tend, nIntervals, gridWidth):
problem = Implicit_Problem(self.rhs, self.y0, self.yd0)
problem.name = 'IDA'
# solver.rhs = self.right_hand_side
problem.handle_result = self.handle_result
problem.state_events = self.state_events
problem.handle_event = self.handle_event
problem.time_events = self.time_events
problem.finalize = self.finalize
# Create IDA object and set additional parameters
simulation = IDA(problem)
simulation.atol = self.atol
simulation.rtol = self.rtol
simulation.verbosity = self.verbosity
if hasattr(simulation, 'continuous_output'):
simulation.continuous_output = False # default 0, if one step approach should be used
elif hasattr(simulation, 'report_continuously'):
simulation.report_continuously = False # default 0, if one step approach should be used
simulation.tout1 = self.tout1
simulation.lsoff = self.lsoff
# Calculate nOutputIntervals:
if gridWidth <> None:
nOutputIntervals = int((Tend - self.t0) / gridWidth)
else:
nOutputIntervals = nIntervals
# Check for feasible input parameters
if nOutputIntervals == 0:
print 'Error: gridWidth too high or nIntervals set to 0! Continue with nIntervals=1'
nOutputIntervals = 1
# Perform simulation
simulation.simulate(Tend, nOutputIntervals) # to get the values: t_new, y_new, yd_new = simulation.simulate
def test_ordinary_dae(self):
"""
This tests a simulation using JMIDAESens without any parameters.
"""
self.m_DAE = JMUModel('Pendulum_pack_Pendulum.jmu')
self.DAE = JMIDAESens(self.m_DAE)
sim = IDA(self.DAE)
sim.simulate(1.0)
nose.tools.assert_almost_equal(sim.y_sol[-1][0], 0.15420124, 4)
nose.tools.assert_almost_equal(sim.y_sol[-1][1], 0.11721253, 4)
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 test_input_simulation(self):
"""
This tests that input simulation works.
"""
self.m_SENS = JMUModel('QuadTankSens.jmu')
self.SENS = JMIDAESens(self.m_SENS)
path_result = os.path.join(get_files_path(), 'Results',
'qt_par_est_data.mat')
data = loadmat(path_result,appendmat=False)
# Extract data series
t_meas = data['t'][6000::100,0]-60
u1 = data['u1_d'][6000::100,0]
u2 = data['u2_d'][6000::100,0]
# Build input trajectory matrix for use in simulation
u_data = N.transpose(N.vstack((t_meas,u1,u2)))
u_traj = TrajectoryLinearInterpolation(u_data[:,0],
u_data[:,1:])
input_object = (['u1','u2'], u_traj)
qt_mod = JMIDAESens(self.m_SENS, input_object)
qt_sim = IDA(qt_mod)
#Store data continuous during the simulation, important when solving a
#problem with sensitivites.
qt_sim.report_continuously = True
#Value used when IDA estimates the tolerances on the parameters
qt_sim.pbar = qt_mod.p0
#Let Sundials find consistent initial conditions by use of 'IDA_YA_YDP_INIT'
qt_sim.make_consistent('IDA_YA_YDP_INIT')
#Simulate
qt_sim.simulate(60) #Simulate 4 seconds with 400 communication points
#write_data(qt_sim)
res = ResultDymolaTextual('QuadTankSens_result.txt')
dx1da1 = res.get_variable_data('dx1/da1')
dx1da2 = res.get_variable_data('dx1/da2')
dx4da1 = res.get_variable_data('dx4/da1')
nose.tools.assert_almost_equal(dx1da2.x[0], 0.000000, 4)
nose.tools.assert_almost_equal(dx1da2.x[-1], 0.00000, 4)
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()
np.real(b_par_x_min), \
np.imag(b_par_x_min), \
np.real(u_perp_x_min), \
np.imag(u_perp_x_min) ))
dU_x_min = np.concatenate(( \
np.real(dux_x_min), \
np.imag(dux_x_min), \
np.real(db_par_x_min), \
np.imag(db_par_x_min), \
np.real(du_perp_x_min), \
np.imag(du_perp_x_min) ))
model = Implicit_Problem(residual, U_x_min, dU_x_min, x_min)
model.name = 'Pendulum'
sim = IDA(model)
# x,U,dU = sim.simulate(x_max, nx)
# sim.plot()
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(x, vA(x, 0))
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(x, np.real(ux_ana(x, 0)))
ax.plot(x, np.imag(ux_ana(x, 0)))
fig = plt.figure()
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
ux_x_min = ux_ana(x_min)
b_par_x_min = b_par_ana(x_min)
u_perp_x_min = u_perp_ana(x_min)
dux_x_min = dux_ana(x_min)
db_par_x_min = 0
du_perp_x_min = du_perp_ana(x_min)
U_x_min = np.array([
np.real(ux_x_min), \
np.imag(ux_x_min), \
np.real(b_par_x_min), \
np.imag(b_par_x_min), \
np.real(u_perp_x_min), \
np.imag(u_perp_x_min) ])
dU_x_min = np.array([ \
np.real(dux_x_min), \
np.imag(dux_x_min), \
np.real(db_par_x_min), \
np.imag(db_par_x_min), \
np.real(du_perp_x_min), \
np.imag(du_perp_x_min) ])
model = Implicit_Problem(residual, U_x_min, dU_x_min, x_min)
model.name = 'Pendulum'
sim = IDA(model)
x, U, dU = sim.simulate(x_min + 0.0000001, nx)
sim.plot()
def __init__(self, residual_eval, solution, solution_dot, bc_eval, jacobian_eval, set_time):
self.residual_eval = residual_eval
self.solution = solution
self.solution_dot = solution_dot
self.bc_eval = bc_eval
self.jacobian_eval = jacobian_eval
self.set_time = set_time
# We should be solving a square system
self.sample_residual = residual_eval(0, self.solution, self.solution_dot)
self.sample_jacobian = jacobian_eval(0, self.solution, self.solution_dot, 0.)
assert self.sample_jacobian.M == self.sample_jacobian.N
assert self.sample_jacobian.N == self.sample_residual.N
# Storage for current BC
self.current_bc = None
# Define an Assimulo Implicit problem
def _store_solution_and_solution_dot(t, solution, solution_dot):
self.solution.vector()[:] = solution
self.solution_dot.vector()[:] = solution_dot
# Update current bc
if self.bc_eval is not None:
bcs_t = self.bc_eval(t)
assert isinstance(bcs_t, (tuple, dict))
if isinstance(bcs_t, tuple):
self.current_bc = DirichletBC(bcs_t)
elif isinstance(bcs_t, dict):
self.current_bc = DirichletBC(bcs_t, self.sample_residual._component_name_to_basis_component_index, self.solution.vector().N)
else:
raise TypeError("Invalid bc in _LinearSolver.__init__().")
def _assimulo_residual_eval(t, solution, solution_dot):
# Store current time
self.set_time(t)
# Convert to a matrix with one column, rather than an array
_store_solution_and_solution_dot(t, solution, solution_dot)
# Compute residual
residual_vector = self.residual_eval(t, self.solution, self.solution_dot)
# Apply BCs, if necessary
if self.bc_eval is not None:
self.current_bc.apply_to_vector(residual_vector, self.solution.vector())
# Convert to an array, rather than a matrix with one column, and return
return residual_vector.__array__()
def _assimulo_jacobian_eval(solution_dot_coefficient, t, solution, solution_dot):
# Store current time
self.set_time(t)
# Convert to a matrix with one column, rather than an array
_store_solution_and_solution_dot(t, solution, solution_dot)
# Compute jacobian
jacobian_matrix = self.jacobian_eval(t, self.solution, self.solution_dot, solution_dot_coefficient)
# Apply BCs, if necessary
if self.bc_eval is not None:
self.current_bc.apply_to_matrix(jacobian_matrix)
# Return
return jacobian_matrix.__array__()
self.problem = Implicit_Problem(_assimulo_residual_eval, self.solution.vector(), self.solution_dot.vector())
self.problem.jac = _assimulo_jacobian_eval
# Define an Assimulo IDA solver
self.solver = IDA(self.problem)
self.solver.display_progress = False
self.solver.verbosity = 50
# Additional storage which will be setup by set_parameters
self._final_time = None
self._initial_time = 0.
self._max_time_steps = None
self._monitor = None
self._time_step_size = None
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 main():
SV_0 = solver_inputs.SV_0
SV_dot_0 = np.zeros_like(SV_0)
algvar = solver_inputs.algvar
# Close any open pyplot objects:
plt.close('all')
atol = np.ones_like(SV_0)*1e-8
rtol = 1e-4
# Start a timer:
t_count = time.time()
# Calculate the time span, which should be enough to charge or discharge fully
# (i.e. 3600 seconds divided by the C-rate):
t_0 = 0
t_f = 3600/Inputs.C_rate
rate_tag = str(Inputs.C_rate)+"C"
"""----------Figures----------"""
if Inputs.plot_profiles_flag:
fig1, axes1, fig2, axes2, fig3, axes3 = setup_plots(plt, rate_tag)
for cycle in np.arange(0, Inputs.n_cycles):
"""----------Equilibration----------"""
# Equilibrate by integrating at zero current:
print('\nEquilibrating...')
# Create problem instance
current.set_i_ext(0)
battery_eq = li_ion(li_ion.res_fun, SV_0, SV_dot_0, t_0)
battery_eq.external_event_detection = True
battery_eq.algvar = algvar
# Simulation parameters
sim_eq = IDA(battery_eq) # Create simulation instance
sim_eq.atol = atol # Solver absolute tolerance
sim_eq.rtol = rtol # Solver relative tolerance
sim_eq.verbosity = 50
sim_eq.make_consistent('IDA_YA_YDP_INIT')
t_eq, SV_eq, SV_dot_eq = sim_eq.simulate(0.1*t_f)
# Put solution into pandas dataframe with labeled columns
SV_eq_df = Label_Columns(t_eq, SV_eq, an.npoints, sep.npoints,
cat.npoints)
# Obtain tag strings for dataframe columns
tags = tag_strings(SV_eq_df)
print('Done equilibrating\n')
"""------------Charging-------------"""
print('\nCharging...')
# New initial conditions are the final equilibrium conditions
t_0 = 0
SV_0 = SV_eq[-1, :]
SV_dot_0 = SV_dot_eq[-1 :]
# Charge the battery
current.set_i_ext(current.i_ext_set)
# Create problem instance
battery_ch = li_ion(li_ion.res_fun, SV_0, SV_dot_0, t_0)
battery_ch.external_event_detection = True
battery_ch.algvar = algvar
# Simulation parameters
sim_ch = IDA(battery_ch)
sim_ch.atol = atol
sim_ch.rtol = rtol
sim_ch.verbosity = 50
sim_ch.make_consistent('IDA_YA_YDP_INIT')
t_ch, SV_ch, SV_dot_ch = sim_ch.simulate(t_f)
SV_ch_df = Label_Columns(t_ch, SV_ch, an.npoints,
sep.npoints, cat.npoints)
if Inputs.plot_potential_profiles == 1:
plot_potential(tags['Phi_an'], tags['Phi_cat'], SV_ch_df,
'Charging', 0, fig1, axes1)
if Inputs.plot_electrode_profiles == 1:
plot_electrode(tags['X_an'], tags['X_cat'], SV_ch_df,
'Charging', 0, fig2, axes2)
if Inputs.plot_elyte_profiles == 1:
plot_elyte(tags['X_el_an'], tags['X_el_cat'], tags['X_el_sep'], SV_ch_df,
'Charging', 0, fig3, axes3)
print('Done charging\n')
"""------------Re_equilibrating-------------"""
if Inputs.flag_re_equil == 1:
# New initial conditions are the final charge conditions
SV_0 = SV_ch[-2, :]
SV_dot_0 = SV_dot_ch[-2, :]
# Equilibrate again. Note - this is a specific choice to reflect
# equilibration after the charging steps. We may want, at times, to
# simulate a situation where the battery is not equilibrated between
# charge and discharge, or is equilibrated for a shorter amount of time.
print('\nRe-equilibrating...')
current.set_i_ext(0)
battery_req = li_ion(li_ion.res_fun, SV_0, SV_dot_0, t_0)
battery_req.external_event_detection = True
battery_req.algvar = algvar
# Simulation parameters
sim_req = IDA(battery_req)
sim_req.atol = atol
sim_req.rtol = rtol
sim_req.verbosity = 50
sim_req.make_consistent('IDA_YA_YDP_INIT')
t_req, SV_req, SV_dot_req = sim_req.simulate(t_f)
SV_req_df = Label_Columns(t_req, SV_req, an.npoints, sep.npoints,
cat.npoints)
if Inputs.plot_potential_profiles*Inputs.phi_time == 1:
plot_potential(tags['Phi_an'], tags['Phi_cat'], SV_req_df,
'Re-equilibrating', 1, None, fig1, axes1)
if Inputs.plot_electrode_profiles == 1:
plot_electrode(tags['X_an'], tags['X_cat'], SV_req_df,
'Re-equilibrating', 1, fig2, axes2)
if Inputs.plot_elyte_profiles == 1:
plot_elyte(tags['X_el_an'], tags['X_el_cat'], tags['X_el_sep'], SV_req_df,
'Re-equilibrating', 1, fig3, axes3)
print('Done re-equilibrating\n')
else:
SV_req = SV_ch
SV_dot_req = SV_dot_ch
SV_req_df = SV_req
"""------------Discharging-------------"""
print('\nDischarging...')
SV_0 = SV_req[-1, :]
SV_dot_0 = SV_dot_req[-1, :]
current.set_i_ext(-current.i_ext_set)
battery_dch = li_ion(li_ion.res_fun, SV_0, SV_dot_0, t_0)
battery_dch.external_event_detection = True
battery_dch.algvar = algvar
# Simulation parameters
sim_dch = IDA(battery_dch)
sim_dch.atol = atol
sim_dch.rtol = rtol
sim_dch.verbosity = 50
sim_dch.make_consistent('IDA_YA_YDP_INIT')
t_dch, SV_dch, SV_dot_dch = sim_dch.simulate(t_f)
SV_dch_df = Label_Columns(t_dch, SV_dch, an.npoints, sep.npoints,
cat.npoints)
if Inputs.plot_potential_profiles == 1:
plot_potential(tags['Phi_an'], tags['Phi_cat'], SV_dch_df,
'Discharging', 1+(Inputs.flag_re_equil*Inputs.phi_time), fig1, axes1)
if Inputs.plot_electrode_profiles == 1:
plot_electrode(tags['X_an'], tags['X_cat'], SV_dch_df,
'Discharging', 1+Inputs.flag_re_equil, fig2, axes2)
if Inputs.plot_elyte_profiles == 1:
plot_elyte(tags['X_el_an'], tags['X_el_cat'], tags['X_el_sep'], SV_dch_df,
'Discharging', 1+Inputs.flag_re_equil, fig3, axes3)
print('Done discharging\n')
"""---------------------------------"""
SV_0 = SV_dch[-1, :]
SV_dot_0 = np.zeros_like(SV_0)
# %% Plot capacity if flagged
plt.show('all')
plot_cap(SV_ch_df, SV_dch_df, rate_tag, current.i_ext_set,
Inputs.plot_cap_flag, tags)
elapsed = time.time() - t_count
print('t_cpu=', elapsed, '\n')
plt.show()
return SV_eq_df, SV_ch_df, SV_req_df, SV_dch_df
def solve(self):
# Setup IDA
assert self._initial_time is not None
problem = Implicit_Problem(self._residual_vector_eval,
self.solution.vector(),
self.solution_dot.vector(),
self._initial_time)
problem.jac = self._jacobian_matrix_eval
problem.handle_result = self._monitor
# Define an Assimulo IDA solver
solver = IDA(problem)
# Setup options
assert self._time_step_size is not None
solver.inith = self._time_step_size
if self._absolute_tolerance is not None:
solver.atol = self._absolute_tolerance
if self._max_time_steps is not None:
solver.maxsteps = self._max_time_steps
if self._relative_tolerance is not None:
solver.rtol = self._relative_tolerance
if self._report:
solver.verbosity = 10
solver.display_progress = True
solver.report_continuously = True
else:
solver.display_progress = False
solver.verbosity = 50
# Assert consistency of final time and time step size
assert self._final_time is not None
final_time_consistency = (
self._final_time - self._initial_time) / self._time_step_size
assert isclose(
round(final_time_consistency), final_time_consistency
), ("Final time should be occuring after an integer number of time steps"
)
# Prepare monitor computation if not provided by parameters
if self._monitor_initial_time is None:
self._monitor_initial_time = self._initial_time
assert isclose(
round(self._monitor_initial_time / self._time_step_size),
self._monitor_initial_time / self._time_step_size
), ("Monitor initial time should be a multiple of the time step size"
)
if self._monitor_time_step_size is None:
self._monitor_time_step_size = self._time_step_size
assert isclose(
round(self._monitor_time_step_size / self._time_step_size),
self._monitor_time_step_size / self._time_step_size
), ("Monitor time step size should be a multiple of the time step size"
)
monitor_t = arange(
self._monitor_initial_time,
self._final_time + self._monitor_time_step_size / 2.,
self._monitor_time_step_size)
# Solve
solver.simulate(self._final_time, ncp_list=monitor_t)
def run_demo(with_plots=True):
"""
Model predicitve control of the Hicks-Ray CSTR reactor. This example
demonstrates how to use the blocking factor feature of the collocation
algorithm.
This example also shows how to use classes for initialization, simulation
and optimization directly rather than calling then through the high-level
classes 'initialialize', 'simulate' and 'optimize'.
"""
curr_dir = os.path.dirname(os.path.abspath(__file__))
# Compile the stationary initialization model into a JMU
jmu_name = compile_jmu("CSTR.CSTR_Init",
os.path.join(curr_dir, "files", "CSTR.mop"))
# Load a JMUModel instance
init_model = JMUModel(jmu_name)
# Create DAE initialization object.
init_nlp = NLPInitialization(init_model)
# Create an Ipopt solver object for the DAE initialization system
init_nlp_ipopt = InitializationOptimizer(init_nlp)
def compute_stationary(Tc_stat):
init_model.set('Tc', Tc_stat)
# Solve the DAE initialization system with Ipopt
init_nlp_ipopt.init_opt_ipopt_solve()
return (init_model.get('c'), init_model.get('T'))
# Set inputs for Stationary point A
Tc_0_A = 250
c_0_A, T_0_A = compute_stationary(Tc_0_A)
# Print some data for stationary point A
print(' *** Stationary point A ***')
print('Tc = %f' % Tc_0_A)
print('c = %f' % c_0_A)
print('T = %f' % T_0_A)
# Set inputs for Stationary point B
Tc_0_B = 280
c_0_B, T_0_B = compute_stationary(Tc_0_B)
# Print some data for stationary point B
print(' *** Stationary point B ***')
print('Tc = %f' % Tc_0_B)
print('c = %f' % c_0_B)
print('T = %f' % T_0_B)
jmu_name = compile_jmu("CSTR.CSTR_Opt_MPC",
os.path.join(curr_dir, "files", "CSTR.mop"))
cstr = JMUModel(jmu_name)
cstr.set('Tc_ref', Tc_0_B)
cstr.set('c_ref', c_0_B)
cstr.set('T_ref', T_0_B)
cstr.set('cstr.c_init', c_0_A)
cstr.set('cstr.T_init', T_0_A)
# Initialize the mesh
n_e = 50 # Number of elements
hs = N.ones(n_e) * 1. / n_e # Equidistant points
n_cp = 3
# Number of collocation points in each element
# Create an NLP object
# The length of the optimization interval is 50s and the
# number of elements is 50, which gives a blocking factor
# vector of 2*ones(n_e/2) to match the sampling interval
# of 2s.
nlp = ipopt.NLPCollocationLagrangePolynomials(cstr,
n_e,
hs,
n_cp,
blocking_factors=2 *
N.ones(n_e / 2, dtype=N.int))
# Create an Ipopt NLP object
nlp_ipopt = ipopt.CollocationOptimizer(nlp)
nlp_ipopt.opt_coll_ipopt_set_int_option("max_iter", 500)
h = 2. # Sampling interval
T_final = 180. # Final time of simulation
t_mpc = N.linspace(0, T_final, T_final / h + 1)
n_samples = N.size(t_mpc)
ref_mpc = N.zeros(n_samples)
ref_mpc[0:3] = N.ones(3) * Tc_0_A
ref_mpc[3:] = N.ones(n_samples - 3) * Tc_0_B
cstr.set('cstr.c_init', c_0_A)
cstr.set('cstr.T_init', T_0_A)
# Compile the simulation model into a DLL
jmu_name = compile_jmu("CSTR.CSTR",
os.path.join(curr_dir, "files", "CSTR.mop"))
# Load a model instance into Python
sim_model = JMUModel(jmu_name)
sim_model.set('c_init', c_0_A)
sim_model.set('T_init', T_0_A)
global cstr_mod
global cstr_sim
cstr_mod = JMIDAE(sim_model) # Create an Assimulo problem
cstr_sim = IDA(cstr_mod) # Create an IDA solver
i = 0
if with_plots:
plt.figure(4)
plt.clf()
for t in t_mpc[0:-1]:
Tc_ref = ref_mpc[i]
c_ref, T_ref = compute_stationary(Tc_ref)
cstr.set('Tc_ref', Tc_ref)
cstr.set('c_ref', c_ref)
cstr.set('T_ref', T_ref)
# Solve the optimization problem
nlp_ipopt.opt_coll_ipopt_solve()
# Write to file.
nlp.export_result_dymola()
# Load the file we just wrote to file
res = ResultDymolaTextual('CSTR_CSTR_Opt_MPC_result.txt')
# Extract variable profiles
c_res = res.get_variable_data('cstr.c')
T_res = res.get_variable_data('cstr.T')
Tc_res = res.get_variable_data('cstr.Tc')
# Get the first Tc sample
Tc_ctrl = Tc_res.x[0]
# Set the value to the model
sim_model.set('Tc', Tc_ctrl)
# Simulate
cstr_sim.simulate(t_mpc[i + 1])
t_T_sim = cstr_sim.t_sol
# Set terminal values of the states
cstr.set('cstr.c_init', cstr_sim.y[0])
cstr.set('cstr.T_init', cstr_sim.y[1])
sim_model.set('c_init', cstr_sim.y[0])
sim_model.set('T_init', cstr_sim.y[1])
if with_plots:
plt.figure(4)
plt.subplot(3, 1, 1)
plt.plot(t_T_sim, N.array(cstr_sim.y_sol)[:, 0], 'b')
plt.subplot(3, 1, 2)
plt.plot(t_T_sim, N.array(cstr_sim.y_sol)[:, 1], 'b')
if t_mpc[i] == 0:
plt.subplot(3, 1, 3)
plt.plot([t_mpc[i], t_mpc[i + 1]], [Tc_ctrl, Tc_ctrl], 'b')
else:
plt.subplot(3, 1, 3)
plt.plot([t_mpc[i], t_mpc[i], t_mpc[i + 1]],
[Tc_ctrl_old, Tc_ctrl, Tc_ctrl], 'b')
Tc_ctrl_old = Tc_ctrl
i = i + 1
assert N.abs(Tc_ctrl - 279.097186038194) < 1e-6
assert N.abs(N.array(cstr_sim.y_sol)[:, 0][-1] - 350.89028563) < 1e-6
assert N.abs(N.array(cstr_sim.y_sol)[:, 1][-1] - 283.15229948) < 1e-6
if with_plots:
plt.figure(4)
plt.subplot(3, 1, 1)
plt.ylabel('c')
plt.plot([0, T_final], [c_0_B, c_0_B], '--')
plt.grid()
plt.subplot(3, 1, 2)
plt.ylabel('T')
plt.plot([0, T_final], [T_0_B, T_0_B], '--')
plt.grid()
plt.subplot(3, 1, 3)
plt.ylabel('Tc')
plt.plot([0, T_final], [Tc_0_B, Tc_0_B], '--')
plt.grid()
plt.xlabel('t')
plt.show()
def run_demo(with_plots=True):
"""
Model predicitve control of the Hicks-Ray CSTR reactor. This example
demonstrates how to use the blocking factor feature of the collocation
algorithm.
This example also shows how to use classes for initialization, simulation
and optimization directly rather than calling then through the high-level
classes 'initialialize', 'simulate' and 'optimize'.
"""
curr_dir = os.path.dirname(os.path.abspath(__file__));
# Compile the stationary initialization model into a JMU
jmu_name = compile_jmu("CSTR.CSTR_Init", os.path.join(curr_dir, "files", "CSTR.mop"))
# Load a JMUModel instance
init_model = JMUModel(jmu_name)
# Create DAE initialization object.
init_nlp = NLPInitialization(init_model)
# Create an Ipopt solver object for the DAE initialization system
init_nlp_ipopt = InitializationOptimizer(init_nlp)
def compute_stationary(Tc_stat):
init_model.set('Tc',Tc_stat)
# Solve the DAE initialization system with Ipopt
init_nlp_ipopt.init_opt_ipopt_solve()
return (init_model.get('c'),init_model.get('T'))
# Set inputs for Stationary point A
Tc_0_A = 250
c_0_A, T_0_A = compute_stationary(Tc_0_A)
# Print some data for stationary point A
print(' *** Stationary point A ***')
print('Tc = %f' % Tc_0_A)
print('c = %f' % c_0_A)
print('T = %f' % T_0_A)
# Set inputs for Stationary point B
Tc_0_B = 280
c_0_B, T_0_B = compute_stationary(Tc_0_B)
# Print some data for stationary point B
print(' *** Stationary point B ***')
print('Tc = %f' % Tc_0_B)
print('c = %f' % c_0_B)
print('T = %f' % T_0_B)
jmu_name = compile_jmu("CSTR.CSTR_Opt_MPC", os.path.join(curr_dir, "files", "CSTR.mop"))
cstr = JMUModel(jmu_name)
cstr.set('Tc_ref',Tc_0_B)
cstr.set('c_ref',c_0_B)
cstr.set('T_ref',T_0_B)
cstr.set('cstr.c_init',c_0_A)
cstr.set('cstr.T_init',T_0_A)
# Initialize the mesh
n_e = 50 # Number of elements
hs = N.ones(n_e)*1./n_e # Equidistant points
n_cp = 3; # Number of collocation points in each element
# Create an NLP object
# The length of the optimization interval is 50s and the
# number of elements is 50, which gives a blocking factor
# vector of 2*ones(n_e/2) to match the sampling interval
# of 2s.
nlp = ipopt.NLPCollocationLagrangePolynomials(
cstr, n_e, hs, n_cp, blocking_factors=2*N.ones(n_e/2,dtype=N.int))
# Create an Ipopt NLP object
nlp_ipopt = ipopt.CollocationOptimizer(nlp)
nlp_ipopt.opt_coll_ipopt_set_int_option("max_iter",500)
h = 2. # Sampling interval
T_final = 180. # Final time of simulation
t_mpc = N.linspace(0,T_final,T_final/h+1)
n_samples = N.size(t_mpc)
ref_mpc = N.zeros(n_samples)
ref_mpc[0:3] = N.ones(3)*Tc_0_A
ref_mpc[3:] = N.ones(n_samples-3)*Tc_0_B
cstr.set('cstr.c_init',c_0_A)
cstr.set('cstr.T_init',T_0_A)
# Compile the simulation model into a DLL
jmu_name = compile_jmu("CSTR.CSTR", os.path.join(curr_dir, "files", "CSTR.mop"))
# Load a model instance into Python
sim_model = JMUModel(jmu_name)
sim_model.set('c_init',c_0_A)
sim_model.set('T_init',T_0_A)
global cstr_mod
global cstr_sim
cstr_mod = JMIDAE(sim_model) # Create an Assimulo problem
cstr_sim = IDA(cstr_mod) # Create an IDA solver
i = 0
if with_plots:
plt.figure(4)
plt.clf()
for t in t_mpc[0:-1]:
Tc_ref = ref_mpc[i]
c_ref, T_ref = compute_stationary(Tc_ref)
cstr.set('Tc_ref',Tc_ref)
cstr.set('c_ref',c_ref)
cstr.set('T_ref',T_ref)
# Solve the optimization problem
nlp_ipopt.opt_coll_ipopt_solve()
# Write to file.
nlp.export_result_dymola()
# Load the file we just wrote to file
res = ResultDymolaTextual('CSTR_CSTR_Opt_MPC_result.txt')
# Extract variable profiles
c_res = res.get_variable_data('cstr.c')
T_res = res.get_variable_data('cstr.T')
Tc_res = res.get_variable_data('cstr.Tc')
# Get the first Tc sample
Tc_ctrl = Tc_res.x[0]
# Set the value to the model
sim_model.set('Tc',Tc_ctrl)
# Simulate
cstr_sim.simulate(t_mpc[i+1])
t_T_sim = cstr_sim.t_sol
# Set terminal values of the states
cstr.set('cstr.c_init',cstr_sim.y[0])
cstr.set('cstr.T_init',cstr_sim.y[1])
sim_model.set('c_init',cstr_sim.y[0])
sim_model.set('T_init',cstr_sim.y[1])
if with_plots:
plt.figure(4)
plt.subplot(3,1,1)
plt.plot(t_T_sim,N.array(cstr_sim.y_sol)[:,0],'b')
plt.subplot(3,1,2)
plt.plot(t_T_sim,N.array(cstr_sim.y_sol)[:,1],'b')
if t_mpc[i]==0:
plt.subplot(3,1,3)
plt.plot([t_mpc[i],t_mpc[i+1]],[Tc_ctrl,Tc_ctrl],'b')
else:
plt.subplot(3,1,3)
plt.plot(
[t_mpc[i],t_mpc[i],t_mpc[i+1]],
[Tc_ctrl_old,Tc_ctrl,Tc_ctrl],
'b')
Tc_ctrl_old = Tc_ctrl
i = i+1
assert N.abs(Tc_ctrl - 279.097186038194) < 1e-6
assert N.abs(N.array(cstr_sim.y_sol)[:,0][-1] - 350.89028563) < 1e-6
assert N.abs(N.array(cstr_sim.y_sol)[:,1][-1] - 283.15229948) < 1e-6
if with_plots:
plt.figure(4)
plt.subplot(3,1,1)
plt.ylabel('c')
plt.plot([0,T_final],[c_0_B,c_0_B],'--')
plt.grid()
plt.subplot(3,1,2)
plt.ylabel('T')
plt.plot([0,T_final],[T_0_B,T_0_B],'--')
plt.grid()
plt.subplot(3,1,3)
plt.ylabel('Tc')
plt.plot([0,T_final],[Tc_0_B,Tc_0_B],'--')
plt.grid()
plt.xlabel('t')
plt.show()
class ReactorSolverAssimulo(ReactorSolverBase):
def __init__(self,reactor,**params):
#Initialize base solver class
ReactorSolverBase.__init__(self,reactor,**params)
#### SOLVER PARAMETERS ####:
self.iter = params.get('iter','Newton') #Iteration method (Newton or FixedPoint)
self.discr = params.get('discr','BDF') #Discretization method (BDF or Adams)
#Set up the linear solver from the following list:
# ['DENSE'(= default) or 'SPGMR']
self.linear_solver = params.get('linear_solver','DENSE')
#Boolean value to turn OFF Sundials LineSearch when calculating
#initial conditions (IDA only)
self.lsoff = params.get('lsoff',False)
def solve_ode(self):
#Get initial conditions vector
self.init_conditions()
#Instantiate reactor as ODE class
self._rode = AssimuloODE(self._r,self._r.z_in,self.y0)
#Define the CVode solver
self.solver = CVode(self._rode)
#Solver parameters
self.solver.atol = self.atol
self.solver.rtol = self.rtol
self.solver.iter = self.iter
self.solver.discr = self.discr
self.solver.linear_solver = self.linear_solver
self.solver.maxord = self.order
self.solver.maxsteps = self.max_steps
self.solver.inith = self.first_step_size
self.solver.minh = self.min_step_size
self.solver.maxh = self.max_step_size
self.solver.maxncf = self.max_conv_fails
self.solver.maxnef = self.max_nonlin_iters
self.solver.stablimdet = self.bdf_stability
self.solver.verbosity = 50
#Solve the equations
z, self.values = self.solver.simulate(self._r.z_out,self.grid-1)
#Convert axial coordinates list to array
self._z = np.array(z)
def solve_dae(self):
#Get initial conditions vector
self.init_conditions()
#Initial derivatives vector
self.yd0 = np.zeros(len(self.y0))
#Instantiate reactor as DAE class
self._rdae = AssimuloDAE(self._r,self._r.z_in,
self.y0,self.yd0)
#Get list of differential and algebraic variables
varlist = np.ones(len(self.y0))
#Set algebraic variables
varlist[self._rdae.p1:] = 0.0
#Set up the solver and its parameters
self.solver = IDA(self._rdae)
self.solver.atol = self.atol
self.solver.rtol = self.rtol
self.solver.linear_solver = self.linear_solver
self.solver.maxord = self.order
self.solver.maxsteps = self.max_steps
self.solver.inith = self.first_step_size
self.solver.maxh = self.max_step_size
self.solver.algvar = varlist
self.solver.make_consistent('IDA_YA_YDP_INIT')
self.solver.tout1 = 1e-06
self.solver.suppress_alg = self.exclude_algvar_from_error
self.solver.lsoff = self.lsoff
self.solver.verbosity = 50
#Solve the DAE equation system
z, self.values, self.valuesd = self.solver.simulate(self._r.z_out,
self.grid-1)
#Convert axial coordinates list to array
self._z = np.array(z)
def initialize_ode_solver(self, y_0, yd_0, t_0):
model = Implicit_Problem(self.residual, y_0, yd_0, t_0)
#model.state_events = self.state_events
#model.handle_events = self.handle_event
model.handle_result = self.handle_result
solver = IDA(model)
solver.rtol = self.solver_rtol
solver.atol = self.solver_atol #* np.array([100, 10, 1e-4, 1e-4])
solver.inith = 0.1 #self.wind.R_g / const.C
solver.maxh = self.dt * self.wind.R_g / const.C
solver.report_continuously = True
solver.display_progress = False
solver.verbosity = 50 # 50 = quiet
solver.maxsteps = self.max_steps
solver.num_threads = 3
#solver.display_progress = True
return solver
from sei_1d_functions import residual
from sei_1d_functions import df_2spec2var
import cantera as ct
from assimulo.solvers import IDA
from assimulo.problem import Implicit_Problem
print('\n Importing inputs and intializing.')
from sei_1d_init import SV_0, SV_dot_0, SVptr, times, objs, params, \
voltage_lookup
print('\n Running simulation\n')
# Set up problem instance
SEI_1D = Implicit_Problem(residual, SV_0, SV_dot_0)
# Define simulation parameters
simulation = IDA(SEI_1D) # Create simulation instance
simulation.atol = 1e-7 # Solver absolute tolerance
simulation.rtol = 1e-4 # Solver relative tolerance
#simulation.maxh = 0.1 # Solver max step size
# Set simulation end time, slope flag (for anode voltage cycle), and run simulation
t_f = times[-1]
#ncp_list = np.arange(0, t_f, 0.15)
#ncp = 10000
# Run simulation
t, SV, SV_dot = simulation.simulate(t_f)
# %% Organize data and plot
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()
# State IV => State III
if solver.sw[3]:
solver.sw[3] = not solver.sw[3]
solver.sw[2] = not solver.sw[2]
y0,yp0 = init_woodpecker()
t0 = 0.0
sw0 = np.array([1,0,0,0])
model = Implicit_Problem(woodpecker,y0,yp0,t0,sw0)
model.state_events = state_events
model.handle_event = handle_event
solver = IDA(model)
solver.simulate(3)
def run_example(with_plots=True):
r"""
An example for IDA with scaled preconditioned GMRES method
as a special linear solver.
Note, how the operation Jacobian times vector is provided.
ODE:
.. math::
\dot y_1 - y_2 &= 0\\
\dot y_2 -9.82 &= 0
on return:
- :dfn:`imp_mod` problem instance
- :dfn:`imp_sim` solver instance
"""
#Defines the residual
def res(t, y, yd):
res_0 = yd[0] - y[1]
res_1 = yd[1] + 9.82
return N.array([res_0, res_1])
#Defines the Jacobian*vector product
def jacv(t, y, yd, res, v, c):
jy = N.array([[0, -1.], [0, 0]])
jyd = N.array([[1, 0.], [0, 1]])
j = jy + c * jyd
return N.dot(j, v)
#Initial conditions
y0 = [1.0, 0.0]
yd0 = [0.0, -9.82]
#Defines an Assimulo implicit problem
imp_mod = Implicit_Problem(
res, y0, yd0, name='Example using the Jacobian Vector product')
imp_mod.jacv = jacv #Sets the jacobian
imp_sim = IDA(imp_mod) #Create an IDA solver instance
#Set the parameters
imp_sim.atol = 1e-5 #Default 1e-6
imp_sim.rtol = 1e-5 #Default 1e-6
imp_sim.linear_solver = 'SPGMR' #Change linear solver
#imp_sim.options["usejac"] = False
#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], -121.75000000, 4)
nose.tools.assert_almost_equal(y[-1][1], -49.100000000)
#Plot
if with_plots:
P.plot(t, y)
P.xlabel('Time')
P.ylabel('State')
P.title(imp_mod.name)
P.show()
return imp_mod, imp_sim
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)
yp[5] = -f[5] / Iv
# Check Jacobian
g = jac(0.1, t, y, yp)
isNotValid = isnan(g).any()
if isNotValid == True:
raise ValueError('Please check initial conditions. Jacobian has NaN.\n')
# Create an Assimulo implicit problem
imp_mod = Implicit_Problem(res, y, yp)
imp_mod.jac = jac # Sets the jacobian
# Sets the options to the problem
# Create an Assimulo implicit solver (IDA)
imp_sim = IDA(imp_mod) # Create a IDA solver
imp_sim.algvar = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
imp_sim.suppress_alg = True
# Let Sundials find consistent initial conditions by use of 'IDA_YA_YDP_INIT'
imp_sim.make_consistent('IDA_YA_YDP_INIT')
# Simulate 4*pi seconds with 1000 communication points
endtime = eval(params['endtime'])
N = params['timepoints']
t_sol, y_sol, yd_sol = imp_sim.simulate(endtime, N)
t = array(t_sol)
# Save results
outputfile = params['Output'] # Output file name
y0 = numpy.array([0.5, 0,0, -0, w0, w0,-1e-4,0]) yd0 = numpy.array([-0, w0, w0,-g, 1e-12, 0, 0, 0]) #y0 = numpy.array([4.83617428e-01, -3.00000000e-02, -2.16050178e-01, 1.67315232e-16, -5.39725367e-14, -1.31300925e+01, -7.20313572e-02, -6.20545138e-02]) #yd0 = numpy.array([1.55140566e-17, -5.00453439e-15, -1.31302838e+01, 6.62087352e-13, -2.13577297e-10, 2.21484026e+02, -4.67637454e+00, -2.89824658e+00]) #startsw = [0,1, 0, 0] problem = Implicit_Problem(res, y0, yd0, t0, sw0=startsw) problem.state_events = state_events problem.handle_event = handle_event problem.name = 'Woodpecker' phipIndex = [4, 5] lambdaIndex = [6, 7] sim = IDA(problem) sim.rtol = 1e-6 sim.atol[phipIndex] = 1e8 sim.algvar[phipIndex] = 1 sim.atol[lambdaIndex] = 1e8 sim.algvar[lambdaIndex] = 1 sim.suppress_alg = True ncp = 500 tfinal = 2 t, y, yd = sim.simulate(tfinal, ncp) y = y[:,[ 0, ]] plt.plot(t, y) plt.legend(["z", "phi_s", "phi_b", "zp", "phip_s", "phip_b", "lambda_2", "lambda_2"], loc = 'lower left')
def main():
res_class = eval(inputs.test_type)
# plt.close('all')
t_count = time.time()
SV_0 = sol_init.SV_0
SV_dot_0 = np.zeros_like(SV_0)
t_0 = 0.
t_f = 3600. / inputs.C_rate #63006.69900049 93633
algvar = sol_init.algvar
atol = np.ones_like(SV_0) * 1e-6
atol[cat.ptr_vec['eps_S8']] = 1e-15
atol[cat.ptr_vec['eps_Li2S']] = 1e-15
atol[cat.ptr_vec['rho_k_el']] = 1e-16 # 1e-16 for Bessler
rtol = 1e-6
sim_output = 50
rtol_ch = 1e-6
atol_ch = np.ones_like(SV_0) * 1e-6
atol_ch[cat.ptr_vec['eps_S8']] = 1e-15
atol_ch[cat.ptr_vec['eps_Li2S']] = 1e-15
atol_ch[cat.ptr_vec['rho_k_el']] = 1e-30
rate_tag = str(inputs.C_rate) + "C"
# if 'cascade' in inputs.ctifile:
# ncols = 2 + inputs.flag_req
# else:
ncols = 1 + inputs.flag_req
fig, axes = plt.subplots(sharey="row",
figsize=(9, 12),
nrows=3,
ncols=(ncols) * inputs.n_cycles,
num=1)
plt.subplots_adjust(wspace=0.15, hspace=0.4)
fig.text(0.35,
0.85,
rate_tag,
fontsize=20,
bbox=dict(facecolor='white', alpha=0.5))
# Set up user function to build figures based on inputs
"----------Equilibration----------"
print('\nEquilibrating...')
# Set external current to 0 for equilibration
cat.set_i_ext(0)
# cat.nucleation_flag = 1
# Create problem object
bat_eq = res_class(res_class.res_fun, SV_0, SV_dot_0, t_0)
bat_eq.external_event_detection = True
bat_eq.algvar = algvar
# Create simulation object
sim_eq = IDA(bat_eq)
sim_eq.atol = atol
sim_eq.rtol = rtol
sim_eq.verbosity = sim_output
sim_eq.make_consistent('IDA_YA_YDP_INIT')
t_eq, SV_eq, SV_dot_eq = sim_eq.simulate(t_f)
# Put solution into pandas dataframe with labeled columns
SV_eq_df = label_columns(t_eq, SV_eq, an.npoints, sep.npoints, cat.npoints)
# Obtain tag strings for dataframe columns
tags = tag_strings(SV_eq_df)
# plot_sim(tags, SV_eq_df, 'Equilibrating', 0, fig, axes)
t_equilibrate = time.time() - t_count
print("Equilibration time = ", t_equilibrate, '\n')
print('Done equilibrating\n')
for cycle_num in np.arange(0, inputs.n_cycles):
"------------Discharging-------------"
print('Discharging...')
# cat.np_L = inputs.np_Li2S_init
cat.nucleation_flag = np.zeros((inputs.npoints_cathode, 1))
# New initial conditions from previous simulation
if cycle_num == 0:
# SV_0 = SV_0
SV_0 = SV_eq[-1, :]
# SV_dot_0 = SV_dot_0
SV_dot_0 = SV_dot_eq[-1, :]
else:
SV_0 = SV_0_cycle
SV_dot_0 = SV_dot_0_cycle
# Set external current
cat.set_i_ext(cat.i_ext_amp)
# Update problem instance initial conditions
bat_dch = res_class(res_class.res_fun, SV_0, SV_dot_0, t_0)
bat_dch.external_event_detection = True
bat_dch.algvar = algvar
# Re-initialize simulation object
sim_dch = IDA(bat_dch)
sim_dch.atol = atol
sim_dch.rtol = rtol
# sim_dch.maxh = 57
sim_dch.verbosity = sim_output
sim_dch.make_consistent('IDA_YA_YDP_INIT')
t_dch, SV_dch, SV_dot_dch = sim_dch.simulate(131865.32)
SV_dch_df = label_columns(t_dch, SV_dch, an.npoints, sep.npoints,
cat.npoints)
# Obtain tag strings for dataframe columns
tags = tag_strings(SV_dch_df)
plot_sim(tags, SV_dch_df, 'Discharging', 0 + 2 * cycle_num, fig, axes)
# plot_meanPS(SV_dch_df, tags, 'Discharging')
print('Done Discharging\n')
"--------Re-equilibration---------"
if inputs.flag_req == 1:
print('Re-equilibrating...')
# New initial conditions from previous simulation
SV_0 = SV_dch[-1, :]
SV_dot_0 = SV_dot_dch[-1, :]
# Set external current
cat.set_i_ext(0)
# Update problem instance initial conditions
bat_req = res_class(res_class.res_fun, SV_0, SV_dot_0, t_0)
bat_req.external_event_detection = True
bat_req.algvar = algvar
# Re-initialize simulation object
sim_req = IDA(bat_req)
sim_req.atol = atol
sim_req.rtol = rtol
sim_req.verbosity = sim_output
sim_req.make_consistent('IDA_YA_YDP_INIT')
t_req, SV_req, SV_dot_req = sim_req.simulate(t_f)
SV_req_df = label_columns(t_req, SV_req, an.npoints, sep.npoints,
cat.npoints)
# plot_sim(tags, SV_req_df, 'Re-Equilibrating', 1, fig, axes)
print('Done re-equilibrating\n')
else:
SV_req = SV_dch
SV_dot_req = SV_dot_dch
"-----------Charging-----------"
if 'dog' in inputs.ctifile:
print('Charging...')
SV_0 = SV_req[-1, :]
SV_dot_0 = SV_dot_req[-1, :]
SV_0[cat.ptr_vec['eps_S8']] = cat.eps_cutoff
cat.set_i_ext(-cat.i_ext_amp)
# Update problem instance initial conditions
bat_ch = res_class(res_class.res_fun, SV_0, SV_dot_0, t_0)
bat_ch.external_event_detection = True
bat_ch.algvar = algvar
# Re-initialize simulation object
sim_ch = IDA(bat_ch)
sim_ch.atol = atol_ch
sim_ch.rtol = rtol_ch
if cycle_num > 0:
sim_ch.maxh = 0.1
sim_ch.verbosity = sim_output
sim_ch.make_consistent('IDA_YA_YDP_INIT')
t_ch, SV_ch, SV_dot_ch = sim_ch.simulate(t_f)
SV_ch_df = label_columns(t_ch, SV_ch, an.npoints, sep.npoints,
cat.npoints)
plot_sim(tags, SV_ch_df, 'Charging',
1 + inputs.flag_req + 2 * cycle_num, fig, axes)
plot_meanPS(SV_ch_df, tags, 'Charging')
SV_ch_df = 0
#
# print('Max S_8(e) concentration = ', max(SV_ch[:, 6]))
# SV_0_cycle = SV_ch[-1, :]
# SV_dot_0_cycle = SV_ch[-1, :]
print('Done Charging\n')
exp_data_01C = pd.read_csv(r'0.1C Data.csv', header=None)
exp_data_05C = pd.read_csv(r'0.5C Data.csv', header=None)
exp_data_1C = pd.read_csv(r'1C Data.csv', header=None)
Bessler = pd.read_csv(r'Bessler Dennis Data.csv', header=None)
SV_copy = SV_dch_df.copy()
SV_copy.loc[:, 'Time'] *= -cat.i_ext_amp * inputs.A_cat / 3600 / (
cat.m_S_tot_0)
"Set up your figure"
fig = plt.figure(3)
ax = fig.add_axes([0.2, 0.2, 0.6, 0.75])
fig.set_size_inches((10., 5.0))
# ax2 = ax.twinx()
"Formatting for the figure:"
fs = 20 #font size for plots
lw = 3.0 #line width for plots
# font = plt.matplotlib.font_manager.FontProperties(family='Times New Roman',size=fs-1)
for tick in ax.xaxis.get_major_ticks():
tick.label1.set_fontsize(fs)
tick.label1.set_fontname('Times New Roman')
for tick in ax.yaxis.get_major_ticks():
tick.label1.set_fontsize(fs)
tick.label1.set_fontname('Times New Roman')
color = matplotlib.cm.plasma(inputs.C_rate)
p1, = plt.plot(SV_copy.loc[:, 'Time'],
SV_copy.loc[:, 'Phi_ed1'],
'k-',
linewidth=lw)
# p2, = plt.plot(exp_data_01C.iloc[:,0], exp_data_01C.iloc[:,1], 'ro')
# p3, = plt.plot(exp_data_05C.iloc[:,0], exp_data_05C.iloc[:,1], 'co')
# p4, = plt.plot(exp_data_1C.iloc[:,0], exp_data_1C.iloc[:,1], 'ko')
p5, = plt.plot(Bessler.iloc[:, 0], Bessler.iloc[:, 1], 'mo', ms=4)
plt.xlim((0, 1700))
plt.xticks([0, 400, 800, 1200, 1600])
plt.ylim((1.8, 2.6))
plt.ylabel(r'Cell Voltage $[\mathrm{V}]$',
fontstyle='normal',
fontname='Times new Roman',
fontsize=fs + 2,
labelpad=5.0)
plt.xlabel(
r'Capacity $[\mathrm{Ah} \hspace{0.5} \mathrm{kg}^{-1}_{\mathrm{sulfur}}]$',
fontstyle='normal',
fontname='Times new Roman',
fontsize=fs + 2,
labelpad=5.0)
# plt.legend(["Discharge", "Charge"])
file_name_dch = 'dch' + str(inputs.C_rate) + "C_" + inputs.mech + '.csv'
SV_dch = SV_dch_df.copy()
SV_dch.loc[:,
'Time'] *= -cat.i_ext_amp * inputs.A_cat / 3600 / (cat.m_S_0 +
cat.m_S_el)
SV_dch.to_csv(file_name_dch, index=False, header=True)
t_elapsed = time.time() - t_count
print('t_cpu=', t_elapsed, '\n')
return SV_eq_df, SV_dch_df, SV_ch_df, tags
posIndex = list(range(0,7))
velocityIndex = list(range(7,14))
lambdaIndex = list(range(14,20))
algvar = numpy.ones(numpy.size(y0))
indexNumber = 1
#1 - expl runge - index1 solution
#2 - index2
#3 - index3
if indexNumber == 3:
problem = Implicit_Problem(squeezer3, y0, yd0, t0)
algvar[lambdaIndex] = 0
algvar[velocityIndex] = 0
sim = IDA(problem)
sim.atol = numpy.ones(numpy.size(y0))*1e-7
sim.atol[lambdaIndex] = 1e-1
sim.atol[velocityIndex] = 1e-5
elif indexNumber == 2:
problem = Implicit_Problem(squeezer2, y0, yd0, t0)
algvar[lambdaIndex] = 0
algvar[velocityIndex] = 1
sim = IDA(problem)
sim.atol = numpy.ones(numpy.size(y0))*1e-7
sim.atol[lambdaIndex] = 1e-5
sim.atol[velocityIndex] = 1e-5
elif indexNumber == 1:
problem = Explicit_Problem(squeezer1, y0[0:14], t0)
sim = RungeKutta34(problem)
sim.atol = numpy.ones(14)*1e-7
class _AssimuloIDA(object):
def __init__(self, residual_eval, solution, solution_dot, bc_eval, jacobian_eval, set_time):
self.residual_eval = residual_eval
self.solution = solution
self.solution_dot = solution_dot
self.bc_eval = bc_eval
self.jacobian_eval = jacobian_eval
self.set_time = set_time
# We should be solving a square system
self.sample_residual = residual_eval(0, self.solution, self.solution_dot)
self.sample_jacobian = jacobian_eval(0, self.solution, self.solution_dot, 0.)
assert self.sample_jacobian.M == self.sample_jacobian.N
assert self.sample_jacobian.N == self.sample_residual.N
# Storage for current BC
self.current_bc = None
# Define an Assimulo Implicit problem
def _store_solution_and_solution_dot(t, solution, solution_dot):
self.solution.vector()[:] = solution
self.solution_dot.vector()[:] = solution_dot
# Update current bc
if self.bc_eval is not None:
bcs_t = self.bc_eval(t)
assert isinstance(bcs_t, (tuple, dict))
if isinstance(bcs_t, tuple):
self.current_bc = DirichletBC(bcs_t)
elif isinstance(bcs_t, dict):
self.current_bc = DirichletBC(bcs_t, self.sample_residual._component_name_to_basis_component_index, self.solution.vector().N)
else:
raise TypeError("Invalid bc in _LinearSolver.__init__().")
def _assimulo_residual_eval(t, solution, solution_dot):
# Store current time
self.set_time(t)
# Convert to a matrix with one column, rather than an array
_store_solution_and_solution_dot(t, solution, solution_dot)
# Compute residual
residual_vector = self.residual_eval(t, self.solution, self.solution_dot)
# Apply BCs, if necessary
if self.bc_eval is not None:
self.current_bc.apply_to_vector(residual_vector, self.solution.vector())
# Convert to an array, rather than a matrix with one column, and return
return residual_vector.__array__()
def _assimulo_jacobian_eval(solution_dot_coefficient, t, solution, solution_dot):
# Store current time
self.set_time(t)
# Convert to a matrix with one column, rather than an array
_store_solution_and_solution_dot(t, solution, solution_dot)
# Compute jacobian
jacobian_matrix = self.jacobian_eval(t, self.solution, self.solution_dot, solution_dot_coefficient)
# Apply BCs, if necessary
if self.bc_eval is not None:
self.current_bc.apply_to_matrix(jacobian_matrix)
# Return
return jacobian_matrix.__array__()
self.problem = Implicit_Problem(_assimulo_residual_eval, self.solution.vector(), self.solution_dot.vector())
self.problem.jac = _assimulo_jacobian_eval
# Define an Assimulo IDA solver
self.solver = IDA(self.problem)
self.solver.display_progress = False
self.solver.verbosity = 50
# Additional storage which will be setup by set_parameters
self._final_time = None
self._initial_time = 0.
self._max_time_steps = None
self._monitor = None
self._time_step_size = None
def set_parameters(self, parameters):
for (key, value) in parameters.items():
if key == "absolute_tolerance":
self.solver.atol = value
elif key == "final_time":
self._final_time = value
elif key == "initial_time":
self._initial_time = value
elif key == "integrator_type":
assert value == "ida"
elif key == "max_time_steps":
self.solver.maxsteps = value
self._max_time_steps = value
elif key == "monitor":
self._monitor = value
elif key == "nonlinear_solver":
for (key_nonlinear, value_nonlinear) in value.items():
if key_nonlinear == "absolute_tolerance":
self.solver.atol = value_nonlinear
elif key_nonlinear == "line_search":
raise NotImplementedError("This feature has not been implemented in IDA.")
elif key_nonlinear == "maximum_iterations":
raise NotImplementedError("This feature has not been implemented in IDA.")
elif key_nonlinear == "relative_tolerance":
self.solver.rtol = value
elif key_nonlinear == "report":
raise NotImplementedError("This feature has not been implemented in IDA.")
elif key_nonlinear == "solution_tolerance":
raise NotImplementedError("This feature has not been implemented in IDA.")
else:
raise ValueError("Invalid paramater passed to _AssimuloIDA object.")
elif key == "problem_type":
pass
elif key == "relative_tolerance":
self.solver.rtol = value
elif key == "report":
self.solver.verbosity = 10
self.solver.display_progress = True
self.solver.report_continuously = True
elif key == "time_step_size":
self.solver.inith = value
self._time_step_size = value
else:
raise ValueError("Invalid paramater passed to _AssimuloIDA object.")
def solve(self):
assert self._max_time_steps is not None or self._time_step_size is not None
if self._time_step_size is not None:
all_t = [0]
all_t_arange = self._time_step_size + arange(self._initial_time, self._final_time, self._time_step_size)
all_t.extend(all_t_arange.tolist())
elif self._max_time_steps is not None:
all_t = linspace(self._initial_time, self._final_time, num=self._max_time_steps+1)
all_t = all_t.tolist()
for ida_trial in range(5):
try:
all_times, all_solutions, all_solutions_dot = self.solver.simulate(self._final_time, ncp_list=all_t)
except IDAError as error:
if str(error) == "'Error test failures occurred too many times during one internal time step or minimum step size was reached. At time 0.000000.'":
# There is no way to increase the number of error test failures in the assimulo interface, try again with smaller inith
self.solver.inith /= 10.
else:
# There was an error, but we cannot handle it. Raise it again
raise
else:
break
# Convert all_solutions to a list of Function
all_solutions_as_functions = list()
all_solutions_dot_as_functions = list()
for (t, solution) in zip(all_times, all_solutions):
self.solution.vector()[:] = solution
all_solutions_as_functions.append(function_copy(self.solution))
if len(all_solutions_as_functions) > 1: # monitor is being called at t > 0.
self.solution_dot.vector()[:] = (all_solutions_as_functions[-1].vector() - all_solutions_as_functions[-2].vector())/self._time_step_size
else:
self.solution_dot.vector()[:] = all_solutions_dot[0]
all_solutions_dot_as_functions.append(function_copy(self.solution_dot))
if self._monitor is not None:
self._monitor(t, self.solution, self.solution_dot)
self.solution.vector()[:] = all_solutions_as_functions[-1].vector()
self.solution_dot.vector()[:] = all_solutions_dot_as_functions[-1].vector()
return all_times, all_solutions_as_functions, all_solutions_dot_as_functions
elyte_ctr = 0
SEI_ctr = 0
phi_ctr += 1
# Volume fraction of SEI per cell
res[-1] = SV_dot[-1]
return res
"""------------------------------------------------------------------------"""
# Set up problem instance
SEI_1D = Implicit_Problem(residual, SV_0, SV_dot_0, t_0)
# Define simulation parameters
simulation = IDA(SEI_1D) # Create simulation instance
simulation.atol = 1e-6 # Solver absolute tolerance
simulation.rtol = 1e-6 # Solver relative tolerance
simulation.maxh = 0.1 # Solver max step size
# Set simulation end time, slope flag (for anode voltage cycle), and run simulation
t_f = ((phi_bounds[1] - phi_anode_0)/R)*5
#ncp_list = np.arange(0, t_f, 0.15)
#ncp = 10000
# Run simulation
t, SV, SV_dot = simulation.simulate(t_f)
def main():
import numpy as np
import time
from matplotlib import pyplot as plt
from li_ion_battery_p2d_functions import Extended_Problem
from assimulo.solvers import IDA
from li_ion_battery_p2d_inputs import Inputs as inp
from li_ion_battery_p2d_init import anode, cathode, separator, SV_0, algvar
from li_ion_battery_p2d_post_process import Label_Columns, tag_strings, plot_sims
# Close any open pyplot objects:
plt.close()
# Start a timer:
t_count = time.time()
# Calculate the time span, which should be enough to charge or discharge fully
# (i.e. 3600 seconds divided by the C-rate):
t_0 = 0
t_f = 3600 / inp.C_rate
# SV_0 = anode.SV_0
# SV_0 = np.concatenate((anode.SV_0, separator.SV_0, cathode.SV_0))
#SV_0 = np.concatenate((anode.SV_0, separator.SV_0))
SV_dot_0 = np.zeros_like(SV_0)
"""----------Equilibration----------"""
# Equilibrate by integrating at zero current:
print('\nEquilibrating...')
# Create problem instance
#Battery_equil = Extended_Problem(Battery_Func, SV_0, SV_dot_0, t_0)
anode.i_ext = 0
cathode.i_ext = 0
Battery_equil = Extended_Problem.Battery_Func(t_0, SV_0, SV_dot_0, True)
Battery_equil.external_event_detection = True
# algvar = anode.algvar
# algvar = np.concatenate((anode.algvar, separator.algvar, cathode.algvar))
#algvar = np.concatenate((anode.algvar, separator.algvar))
# Battery_equil.algvar = algvar
# Simulation parameters
equil_sim = IDA(Battery_equil) # Create simulation instance
equil_sim.atol = atol1 # Solver absolute tolerance
equil_sim.rtol = rtol1 # Solver relative tolerance
equil_sim.verbosity = 50
equil_sim.make_consistent('IDA_YA_YDP_INIT')
t_eq, SV_eq, SV_dot_eq = equil_sim.simulate(t_f)
# Put solution into pandas dataframe with labeled columns
SV_eq_df = Label_Columns(t_eq, SV_eq)
# Obtain tag strings for dataframe columns
tags = tag_strings(SV_eq_df)
print('Done equilibrating\n')
"""---------------------------------"""
"""------------Charging-------------"""
print('\nCharging...')
# New initial conditions are the final equilibrium conditions
t_0 = t_eq[-1]
t_f1 = t_0 + t_f
SV_0 = SV_eq[-1, :]
SV_dot_0 = SV_dot_eq[-1:]
# Charge the battery
anode.params['i_ext'] = anode.i_ext
cathode.params['i_ext'] = -cathode.i_ext
# Create problem instance
Battery_charge = Extended_Problem(Charge, SV_0, SV_dot_0, t_0)
Battery_charge.external_event_detection = True
Battery_charge.algvar = algvar
# Simulation parameters
charge_sim = IDA(Battery_charge)
charge_sim.atol = atol2
charge_sim.rtol = rtol2
charge_sim.verbosity = 50
charge_sim.make_consistent('IDA_YA_YDP_INIT')
# charge_sim.maxh = 0.5
t_charge, SV_charge, SV_dot_charge = charge_sim.simulate(t_f1)
t_flag1 = anode.t_flag
SV_charge_df = Label_Columns(t_charge, SV_charge)
print('Done charging\n')
"""---------------------------------"""
"""------------Re_equilibrating-------------"""
# New initial conditions are the final charge conditions
t_0 = t_charge[-1] #anode.t_flag
t_f2 = t_0 + t_f
SV_0 = SV_charge[-1, :]
SV_dot_0 = SV_dot_charge[-1, :]
# Equilibrate again. Note - this is a specific choice to reflect
# equilibration after the charging steps. We may want, at times, to
# simulate a situation where the battery is not equilibrated between
# charge and discharge, or is equilibrated for a shorter amount of time.
print('\nRe-equilibrating...')
Battery_re_equil = Extended_Problem(Re_equilibrate, SV_0, SV_dot_0, t_0)
Battery_re_equil.external_event_detection = True
Battery_re_equil.algvar = algvar
# Simulation parameters
re_equil_sim = IDA(Battery_re_equil)
re_equil_sim.atol = atol3
re_equil_sim.rtol = rtol3
re_equil_sim.verbosity = 50
re_equil_sim.make_consistent('IDA_YA_YDP_INIT')
t_req, SV_req, SV_dot_req = re_equil_sim.simulate(t_f2)
SV_req_df = Label_Columns(t_req, SV_req)
print('Done re-equilibrating\n')
"""---------------------------------"""
"""------------Discharging-------------"""
print('\nDischarging...')
t_0 = t_req[-1]
t_f3 = t_f2 + t_f
SV_0 = SV_req[-1, :]
SV_dot_0 = SV_dot_req[-1, :]
anode.params['i_ext'] = -anode.i_ext
cathode.params['i_ext'] = cathode.i_ext
Battery_discharge = Extended_Problem(Discharge, SV_0, SV_dot_0, t_0)
Battery_discharge.external_event_detection = True
Battery_discharge.algvar = algvar
# Simulation parameters
Battery_discharge = IDA(Battery_discharge)
Battery_discharge.atol = atol4
Battery_discharge.rtol = rtol4
Battery_discharge.verbosity = 50
Battery_discharge.make_consistent('IDA_YA_YDP_INIT')
t_discharge, SV_discharge, SV_dot_discharge = Battery_discharge.simulate(
t_f3)
t_flag2 = anode.t_flag
SV_discharge_df = Label_Columns(t_discharge, SV_discharge)
print('Done discharging\n')
"""---------------------------------"""
SV_dict = {}
SV_dict['SV_eq'] = SV_eq_df
SV_dict['SV_charge'] = SV_charge_df
SV_dict['SV_req'] = SV_req_df
SV_dict['SV_discharge'] = SV_discharge_df
# SV_charge_df = SV_charge_df.loc[SV_charge_df['Time'] <= t_flag1]
# SV_discharge_df = SV_discharge_df.loc[SV_discharge_df['Time'] <= t_flag2]
# dt_cap = t_flag1 - t_eq[-1]
# t_80 = 0.8*dt_cap + t_eq[-1]
# elyte80_charge = SV_charge_df.loc[SV_charge_df['Time'] <= t_80]
# elyte75_charge = SV_charge_df.loc[SV_charge_df['X_an15'] <= 0.20]
# el80 = elyte80_charge[X_elyte].iloc[0]
# el80 = list(el80)
# el80.append(inp.C_rate)
# import openpyxl
# book = openpyxl.load_workbook('Elyte_depth_profiles.xlsx')
# sheet = book.active
# sheet.append(el80)
# book.save('Elyte_depth_profiles.xlsx')
# print('Elyte Li+ at 80% SOC = ', elyte75_charge, '\n')
plot_sims(tags['V_an'], tags['X_an'], tags['X_el_an'], SV_dict, t_f1, t_f3,
t_flag1, t_flag2)
# plot_sims(tags['V_cat'], tags['X_cat'], tags['X_el_cat'], SV_dict, t_f1, t_f3, t_flag1, t_flag2)
# fig, axes = plt.subplots(sharey = "row", figsize = (18, 8), nrows=1, ncols=4)
# plt.subplots_adjust(wspace=0, hspace=0.5)
#
# V_cell_plot = V_cell_eq.plot(ax = axes[0])
# V_cell_plot.set_title('Equilibration')
# V_cell_plot.set_ylabel('Cell Voltage')
# V_cell_plot.legend().set_visible(False)
#
# V_cell_plot = V_cell_charge.plot(ax = axes[1])
# V_cell_plot.set_title('Charging')
# V_cell_plot.set_ylabel('Cell Voltage')
# V_cell_plot.legend().set_visible(False)
#
# V_cell_plot = V_cell_req.plot(ax = axes[2])
# V_cell_plot.set_title('Re-Equilibration')
# V_cell_plot.set_ylabel('Cell Voltage')
# V_cell_plot.legend().set_visible(False)
#
# V_cell_plot = V_cell_discharge.plot(ax = axes[3])
# V_cell_plot.set_title('Discharge')
# V_cell_plot.set_ylabel('Cell Voltage')
# V_cell_plot.legend().set_visible(False)
"""---------------------------------"""
# Post processing
V_charge = np.array(SV_charge_df['V_dl1'])
V_discharge = np.array(SV_discharge_df['V_dl1'])
t_charge = np.array(SV_charge_df['Time'])
t_discharge = np.array(SV_discharge_df['Time'])
dt_charge = t_charge - t_charge[0]
dt_discharge = t_discharge - t_discharge[0]
# Plot charge-discharge curve
Capacity_charge = -dt_charge * anode.i_ext / 3600 # A-h/m^2
Capacity_discharge = -dt_discharge * anode.i_ext / 3600 # A-h/m^2
fig1, ax1 = plt.subplots()
ax1.plot(Capacity_charge, V_charge)
ax1.plot(Capacity_discharge, V_discharge)
# ax1.set_ylim((0, 1.2))
# ax1.set_xlim((-0.1, 18.5))
ax1.set_xlabel("Capacity [Ah/m^2]")
ax1.set_ylabel("Voltage [V]")
ax1.legend(("Charge capacity", "Discharge capacity"))
# Calculate battery energy storage/recovery and calculate round-trip
# efficiency. Anode voltage is referenced to its initial equilibrium
# value (i.e. in the discharged state).
# NOTE: This is in W-h/m^2, per unit area of battery. For the specific
# capacity, you want W-h/g of anode material.
# E_stored = 0
# E_recovered = 0
# for k in np.arange(1, len(t_charge)):
# E_stored = (E_stored - (anode.V_cathode - 0.5*(V_charge[k] + V_charge[k-1]))
# *ep.i_ext*(dt_charge[k] - dt_charge[k-1]))
#
# for k in np.arange(1, len(t_discharge)):
# E_recovered = (E_recovered - (ep.V_cathode -
# 0.5*(V_discharge[k] + V_discharge[k-1]))
# *ep.i_ext*(dt_discharge[k] - dt_discharge[k-1]))
#
# Cap_recovered = Capacity_discharge[-1]
# Eta_RT = E_recovered/E_stored
# print('Cap_recovered = ', Cap_recovered, '\n')
# print(E_stored, '\n')
# print(E_recovered, '\n')
# print('Eta_RT = ', Eta_RT, '\n')
elapsed = time.time() - t_count
print('t_cpu=', elapsed, '\n')
plt.show()
return t_req, SV_req, SV_dot_req
pc_centered
]) #Initial conditions
yd0 = [0.0 for i in range(N + Na + Nc + Na + Nc + N + Na + Nc)
] #Initial conditions
#Create an Assimulo implicit problem
imp_mod = MyProblem(Na, Ns, Nc, X, cell_coated_area, bsp_dir, y0, yd0,
'Example using an analytic Jacobian')
#Sets the options to the problem
imp_mod.algvar = [1.0 for i in range(N + Na + Nc)] + [
0.0 for i in range(Na + Nc + N + Na + Nc)
] #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_iapp( I_app/10. )
#imp_sim.make_consistent('IDA_YA_YDP_INIT')
#ta, ya, yda = imp_sim.simulate(0.1,5)
##
#imp_mod.set_iapp( I_app/2. )
#imp_sim.make_consistent('IDA_YA_YDP_INIT')
#tb, yb, ydb = imp_sim.simulate(0.2,5)
#ax[1].plot( imp_mod.x_m, z_out[:imp_mod.N,:-1] )
#ax[2].plot( imp_mod.x_m_a, z_out[imp_mod.N:imp_mod.N+imp_mod.Na,:-1] )
#ax[2].plot( imp_mod.x_m_c, z_out[-imp_mod.Nc:,:-1] )
#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')
from scipy import *
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
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
from state_event_woodpecker import state_event
from handle_event_woodpecker import handle_event
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)
resid12 = -lambda_2 - g * m - lambda_3(z1 - z2)
resid13 = (x1 * du[6] + x1_dot**2) + (y1 * du[7] + y1_dot**2) - du[8]
resid14 = (x1 * du[9] + x1_dot**2) + (y1 * du[10] + y1_dot**2) - du[11]
resid15 = (x1 - x2) * (du[6] - du[9]) + (x1_dot - x2_dot) * (x1_dot -
x2_dot)
resid16 = (y1 - y2) * (du[7] - du[10]) + (y1_dot - y2_dot) * (y1_dot -
y2_dot)
resid17 = (z1 - z2) * (du[8] - du[11]) + (z1_dot - z2_dot) * (z1_dot -
z2_dot)
return np.array([
resid1, resid2, resid3, resid4, resid5, resid6, resid7, resid8, resid9,
resid10, resid11, resid12, resid13, resid14, resid15, resid16, resid17
])
#initial conditions
t0 = 0.0
u0 = [1.0, 1.0, 1.0, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0, 0, 0]
du0 = [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0, 0, 0]
model = Implicit_Problem(residual, u0, du0, t0)
model.name = 'masses linked on surface'
sim = IDA(model)
tfinal = 10.0 #Specify the final time
ncp = 500 #Number of communication points (number of return points)
t, y, yd = sim.simulate(tfinal, ncp)
sim.plot()
r[7] = u_b - phip_b
return r
def res3(self,t,y,yp,sw):
print('res2')
if sw[0]:
return motion_state1(t,y,yp)
elif sw[1]:
return motion_state2(t,y,yp)
elif sw[2]:
return motion_state3(t,y,yp)
else:
print('wrong sw in res')
return -1
t0 = 0;
sw0 = [1,0,0,0]
y0 = numpy.array([5, 0,0, 0, 0, 1,0,0])
yd0 = numpy.array([0, 0, 1,-9.82, 1e-12, 0, 0, 0])
problem = Woodpecker(res, y0, yd0, t0, sw0)
#problem.res=res
sim = IDA(problem)
problem.name = 'Woodpecker'
ncp = 500
tfinal = 2
t, y, yd = sim.simulate(tfinal, ncp)
plt.plot(t, y)
plt.legend(["z", "phi_s", "phi_b", "zp", "phip_s", "phip_b", "lambda_1", "lambda_2"], loc = 'lower left')
plt.show()
import numpy as np from assimulo.problem import Implicit_Problem from assimulo.solvers import IDA import squeezer_ind2 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)
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
#Plot
if with_plots:
import pylab as P
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()
#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)
return imp_mod, imp_sim
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
def simulate(self, Tend, nIntervals, gridWidth):
problem = Implicit_Problem(self.rhs, self.y0, self.yd0)
problem.name = 'IDA'
# solver.rhs = self.right_hand_side
problem.handle_result = self.handle_result
problem.state_events = self.state_events
problem.handle_event = self.handle_event
problem.time_events = self.time_events
problem.finalize = self.finalize
# Create IDA object and set additional parameters
simulation = IDA(problem)
simulation.atol = self.atol
simulation.rtol = self.rtol
simulation.verbosity = self.verbosity
if hasattr(simulation, 'continuous_output'):
simulation.continuous_output = False # default 0, if one step approach should be used
elif hasattr(simulation, 'report_continuously'):
simulation.report_continuously = False # default 0, if one step approach should be used
simulation.tout1 = self.tout1
simulation.lsoff = self.lsoff
# Calculate nOutputIntervals:
if gridWidth <> None:
nOutputIntervals = int((Tend - self.t0) / gridWidth)
else:
nOutputIntervals = nIntervals
# Check for feasible input parameters
if nOutputIntervals == 0:
print 'Error: gridWidth too high or nIntervals set to 0! Continue with nIntervals=1'
nOutputIntervals = 1
# Perform simulation
simulation.simulate(Tend, nOutputIntervals) # to get the values: t_new, y_new, yd_new = simulation.simulate
# -*- 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]')
np.real(b_par_x_min), \
np.imag(b_par_x_min), \
np.real(u_perp_x_min), \
np.imag(u_perp_x_min) ])
dU_x_min = np.array([ \
np.real(dux_x_min), \
np.imag(dux_x_min), \
np.real(db_par_x_min), \
np.imag(db_par_x_min), \
np.real(du_perp_x_min), \
np.imag(du_perp_x_min) ])
model = Implicit_Problem(residual, U_x_min, dU_x_min, x_min)
model.name = 'Resonant absorption'
sim = IDA(model)
x, U, dU = sim.simulate(x_max, nx)
x = np.array(x)
ux_r = U[:, 0]
ux_i = U[:, 1]
b_par_r = U[:, 2]
b_par_i = U[:, 3]
u_perp_r = U[:, 4]
u_perp_i = U[:, 5]
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(x, ux_r)
res[0:ct.nz] = np.real(dux + 1j * ct.omega * b_par + nabla_perp_u_perp)
res[ct.nz:2 * ct.nz] = np.imag(dux + 1j * ct.omega * b_par +
nabla_perp_u_perp)
res[2 * ct.nz:3 * ct.nz] = np.real(db_par + 1j / ct.omega * L_ux)
res[3 * ct.nz:4 * ct.nz] = np.imag(db_par + 1j / ct.omega * L_ux)
res[4 * ct.nz:5 * ct.nz] = np.real(L_u_perp -
1j * ct.omega * nabla_perp_b_par)
res[5 * ct.nz:] = np.imag(L_u_perp - 1j * ct.omega * nabla_perp_b_par)
return res
model = Implicit_Problem(residual, ct.U_x_min, ct.dU_x_min, ct.x_min)
model.name = 'Resonant abosprotion'
sim = IDA(model)
x, U, dU = sim.simulate(ct.x_max, ct.nx)
# sim.plot()
# fig = plt.figure()
# ax = fig.add_subplot(111)
# ax.plot(ct.z, ct.dU_perp_x_min[0:ct.nz])
# ax.plot(ct.z, np.real(ct.du_perp_ana(ct.x_min,ct.z)))
# fig = plt.figure()
# ax = fig.add_subplot(111)
# ax.plot(ct.z, ct.dU_perp_x_min[ct.nz:])
# ax.plot(ct.z, np.imag(ct.du_perp_ana(ct.x_min,ct.z)))
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
