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 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 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 initialize_ode_solver(self, y_0, yd_0, t_0):
model = Implicit_Problem(self.residual, y_0, yd_0, t_0)
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.num_threads = 3
# solver.display_progress = True
return solver
def test_handle_result(self):
"""
This function tests the handle result.
"""
f = lambda t,x,xd: x**0.25-xd
def handle_result(solver, t ,y, yd):
assert solver.t == t
prob = Implicit_Problem(f, [1.0],[1.0])
prob.handle_result = handle_result
sim = IDA(prob)
sim.continuous_output = True
sim.simulate(10.)
def test_handle_result(self):
"""
This function tests the handle result.
"""
f = lambda t,x,xd: x**0.25-xd
def handle_result(solver, t ,y, yd):
assert solver.t == t
prob = Implicit_Problem(f, [1.0],[1.0])
prob.handle_result = handle_result
sim = IDA(prob)
sim.report_continuously = True
sim.simulate(10.)
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
def simulate(model, init_cond, start_time=0., final_time=1., input=(lambda t: []), ncp=500, blt=True,
causalization_options=sp.CausalizationOptions(), expand_to_sx=True, suppress_alg=False,
tol=1e-8, solver="IDA"):
"""
Simulate model from CasADi Interface using CasADi.
init_cond is a dictionary containing initial conditions for all variables.
"""
if blt:
t_0 = timing.time()
blt_model = sp.BLTModel(model, causalization_options)
blt_time = timing.time() - t_0
print("BLT analysis time: %.3f s" % blt_time)
blt_model._model = model
model = blt_model
if causalization_options['closed_form']:
solved_vars = model._solved_vars
solved_expr = model._solved_expr
#~ for (var, expr) in itertools.izip(solved_vars, solved_expr):
#~ print('%s := %s' % (var.getName(), expr))
return model
dh() # This is not a debug statement!
# Extract model variables
model_states = [var for var in model.getVariables(model.DIFFERENTIATED) if not var.isAlias()]
model_derivatives = [var for var in model.getVariables(model.DERIVATIVE) if not var.isAlias()]
model_algs = [var for var in model.getVariables(model.REAL_ALGEBRAIC) if not var.isAlias()]
model_inputs = [var for var in model.getVariables(model.REAL_INPUT) if not var.isAlias()]
states = [var.getVar() for var in model_states]
derivatives = [var.getMyDerivativeVariable().getVar() for var in model_states]
algebraics = [var.getVar() for var in model_algs]
inputs = [var.getVar() for var in model_inputs]
n_x = len(states)
n_y = len(states) + len(algebraics)
n_w = len(algebraics)
n_u = len(inputs)
# Create vectorized model variables
t = model.getTimeVariable()
y = MX.sym("y", n_y)
yd = MX.sym("yd", n_y)
u = MX.sym("u", n_u)
# Extract the residuals and substitute the (x,z) variables for the old variables
scalar_vars = states + algebraics + derivatives + inputs
vector_vars = [y[k] for k in range(n_y)] + [yd[k] for k in range(n_x)] + [u[k] for k in range(n_u)]
[dae] = substitute([model.getDaeResidual()], scalar_vars, vector_vars)
# Fix parameters
if not blt:
# Sort parameters
par_kinds = [model.BOOLEAN_CONSTANT,
model.BOOLEAN_PARAMETER_DEPENDENT,
model.BOOLEAN_PARAMETER_INDEPENDENT,
model.INTEGER_CONSTANT,
model.INTEGER_PARAMETER_DEPENDENT,
model.INTEGER_PARAMETER_INDEPENDENT,
model.REAL_CONSTANT,
model.REAL_PARAMETER_INDEPENDENT,
model.REAL_PARAMETER_DEPENDENT]
pars = reduce(list.__add__, [list(model.getVariables(par_kind)) for
par_kind in par_kinds])
# Get parameter values
model.calculateValuesForDependentParameters()
par_vars = [par.getVar() for par in pars]
par_vals = [model.get_attr(par, "_value") for par in pars]
# Eliminate parameters
[dae] = casadi.substitute([dae], par_vars, par_vals)
# Extract initial conditions
y0 = [init_cond[var.getName()] for var in model_states] + [init_cond[var.getName()] for var in model_algs]
yd0 = [init_cond[var.getName()] for var in model_derivatives] + n_w * [0.]
# Create residual CasADi functions
dae_res = MXFunction([t, y, yd, u], [dae])
dae_res.setOption("name", "complete_dae_residual")
dae_res.init()
###################
#~ import matplotlib.pyplot as plt
#~ h = MX.sym("h")
#~ iter_matrix_expr = dae_res.jac(2)/h + dae_res.jac(1)
#~ iter_matrix = MXFunction([t, y, yd, u, h], [iter_matrix_expr])
#~ iter_matrix.init()
#~ n = 100;
#~ hs = np.logspace(-8, 1, n);
#~ conds = [np.linalg.cond(iter_matrix.call([0, y0, yd0, input(0), hval])[0].toArray()) for hval in hs]
#~ plt.close(1)
#~ plt.figure(1)
#~ plt.loglog(hs, conds, 'b-')
#~ #plt.gca().invert_xaxis()
#~ plt.grid('on')
#~ didx = range(4, 12) + range(30, 33)
#~ aidx = [i for i in range(33) if i not in didx]
#~ didx = range(10)
#~ aidx = []
#~ F = MXFunction([t, y, yd, u], [dae[didx]])
#~ F.init()
#~ G = MXFunction([t, y, yd, u], [dae[aidx]])
#~ G.init()
#~ dFddx = F.jac(2)[:, :n_x]
#~ dFdx = F.jac(1)[:, :n_x]
#~ dFdy = F.jac(1)[:, n_x:]
#~ dGdx = G.jac(1)[:, :n_x]
#~ dGdy = G.jac(1)[:, n_x:]
#~ E_matrix = MXFunction([t, y, yd, u, h], [dFddx])
#~ E_matrix.init()
#~ E_cond = np.linalg.cond(E_matrix.call([0, y0, yd0, input(0), hval])[0].toArray())
#~ iter_matrix_expr = vertcat([horzcat([dFddx + h*dFdx, h*dFdy]), horzcat([dGdx, dGdy])])
#~ iter_matrix = MXFunction([t, y, yd, u, h], [iter_matrix_expr])
#~ iter_matrix.init()
#~ n = 100
#~ hs = np.logspace(-8, 1, n)
#~ conds = [np.linalg.cond(iter_matrix.call([0, y0, yd0, input(0), hval])[0].toArray()) for hval in hs]
#~ plt.loglog(hs, conds, 'b--')
#~ plt.gca().invert_xaxis()
#~ plt.grid('on')
#~ plt.xlabel('$h$')
#~ plt.ylabel('$\kappa$')
#~ plt.show()
#~ dh()
###################
# Expand to SX
if expand_to_sx:
dae_res = SXFunction(dae_res)
dae_res.init()
# Create DAE residual Assimulo function
def dae_residual(t, y, yd):
dae_res.setInput(t, 0)
dae_res.setInput(y, 1)
dae_res.setInput(yd, 2)
dae_res.setInput(input(t), 3)
dae_res.evaluate()
return dae_res.getOutput(0).toArray().reshape(-1)
# Set up simulator
problem = Implicit_Problem(dae_residual, y0, yd0, start_time)
if solver == "IDA":
simulator = IDA(problem)
elif solver == "Radau5DAE":
simulator = Radau5DAE(problem)
else:
raise ValueError("Unknown solver %s" % solver)
simulator.rtol = tol
simulator.atol = 1e-4 * np.array([model.get_attr(var, "nominal") for var in model_states + model_algs])
#~ simulator.atol = tol * np.ones([n_y, 1])
simulator.report_continuously = True
# Log method order
if solver == "IDA":
global order
order = []
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])
problem.handle_result = handle_result
# Suppress algebraic variables
if suppress_alg:
if isinstance(suppress_alg, bool):
simulator.algvar = n_x * [True] + (n_y - n_x) * [False]
else:
simulator.algvar = n_x * [True] + suppress_alg
simulator.suppress_alg = True
# Simulate
t_0 = timing.time()
(t, y, yd) = simulator.simulate(final_time, ncp)
simul_time = timing.time() - t_0
stats = {'time': simul_time, 'steps': simulator.statistics['nsteps']}
if solver == "IDA":
stats['order'] = order
# Generate result for time and inputs
class SimulationResult(dict):
pass
res = SimulationResult()
res.stats = stats
res['time'] = t
if u.numel() > 0:
input_names = [var.getName() for var in model_inputs]
for name in input_names:
res[name] = []
for time in t:
input_val = input(time)
for (name, val) in itertools.izip(input_names, input_val):
res[name].append(val)
# Create results for everything else
if blt:
# Iteration variables
i = 0
for var in model_states:
res[var.getName()] = y[:, i]
res[var.getMyDerivativeVariable().getName()] = yd[:, i]
i += 1
for var in model_algs:
res[var.getName()] = y[:, i]
i += 1
# Create function for computing solved algebraics
for (_, sol_alg) in model._explicit_solved_algebraics:
res[sol_alg.name] = []
alg_sol_f = casadi.MXFunction(model._known_vars + model._explicit_unsolved_vars, model._solved_expr)
alg_sol_f.init()
if expand_to_sx:
alg_sol_f = casadi.SXFunction(alg_sol_f)
alg_sol_f.init()
# Compute solved algebraics
for k in xrange(len(t)):
for (i, var) in enumerate(model._known_vars + model._explicit_unsolved_vars):
alg_sol_f.setInput(res[var.getName()][k], i)
alg_sol_f.evaluate()
for (j, sol_alg) in model._explicit_solved_algebraics:
res[sol_alg.name].append(alg_sol_f.getOutput(j).toScalar())
else:
res_vars = model_states + model_algs
for (i, var) in enumerate(res_vars):
res[var.getName()] = y[:, i]
der_var = var.getMyDerivativeVariable()
if der_var is not None:
res[der_var.getName()] = yd[:, i]
# Add results for all alias variables (only treat time-continuous variables) and convert to array
if blt:
res_model = model._model
else:
res_model = model
for var in res_model.getAllVariables():
if var.getVariability() == var.CONTINUOUS:
res[var.getName()] = np.array(res[var.getModelVariable().getName()])
res["time"] = np.array(res["time"])
res._blt_model = blt_model
return res
