def limit_cycle(self):
"""
integrate the solution for one period, remembering each of time
points along the way
"""
self.ts = np.linspace(0, self.T, self.intoptions['lc_res'])
intlc = cs.Integrator('cvodes',self.model)
intlc.setOption("abstol" , self.intoptions['lc_abstol'])
intlc.setOption("reltol" , self.intoptions['lc_reltol'])
intlc.setOption("max_num_steps", self.intoptions['lc_maxnumsteps'])
intlc.setOption("tf" , self.T)
intsim = cs.Simulator(intlc, self.ts)
intsim.init()
# Input Arguments
intsim.setInput(self.y0, cs.INTEGRATOR_X0)
intsim.setInput(self.param, cs.INTEGRATOR_P)
intsim.evaluate()
self.sol = intsim.output().toArray().T
# create interpolation object
self.lc = self.interp_sol(self.ts, self.sol.T)
def int_odes(self, tf, y0=None, numsteps=10000, return_endpt=False, ts=0):
"""
This function integrates the ODEs until well past the transients.
This uses Casadi's simulator class, C++ wrapped in swig. Inputs:
tf - the final time of integration.
numsteps - the number of steps in the integration is the second argument
"""
if y0 is None: y0 = self.y0
self.integrator = cs.Integrator('cvodes', self.model)
#Set up the tolerances etc.
self.integrator.setOption("abstol", self.intoptions['int_abstol'])
self.integrator.setOption("reltol", self.intoptions['int_reltol'])
self.integrator.setOption("max_num_steps",
self.intoptions['int_maxstepcount'])
self.integrator.setOption("tf", tf)
#Let's integrate
self.integrator.init()
self.ts = np.linspace(ts, tf, numsteps, endpoint=True)
self.simulator = cs.Simulator(self.integrator, self.ts)
self.simulator.init()
self.simulator.setInput(y0, cs.INTEGRATOR_X0)
self.simulator.setInput(self.param, cs.INTEGRATOR_P)
self.simulator.evaluate()
sol = self.simulator.output().toArray().T
if return_endpt == True:
return sol[-1]
else:
return sol
def phase_of_point(self, point, error=False, tol=1E-3):
""" Finds the phase at which the distance from the point to the
limit cycle is minimized. phi=0 corresponds to the definition of
y0, returns the phase and the minimum distance to the limit
cycle """
point = np.asarray(point)
#set up integrator so we only have to once...
intr = cs.Integrator('cvodes',self.model)
intr.setOption("abstol", self.intoptions['bvp_abstol'])
intr.setOption("reltol", self.intoptions['bvp_reltol'])
intr.setOption("tf", self.T)
intr.setOption("max_num_steps",
self.intoptions['transmaxnumsteps'])
intr.setOption("disable_internal_warnings", True)
intr.init()
for i in xrange(100):
dist = cs.SX.sym("dist")
x = self.model.inputExpr(cs.DAE_X)
ode = self.model.outputExpr()[0]
dist_ode = cs.sumAll(2.*(x - point)*ode)
cat_x = cs.vertcat([x, dist])
cat_ode = cs.vertcat([ode, dist_ode])
dist_model = cs.SXFunction(
cs.daeIn(t=self.model.inputExpr(cs.DAE_T), x=cat_x,
p=self.model.inputExpr(cs.DAE_P)),
cs.daeOut(ode=cat_ode))
dist_model.setOption("name","distance model")
dist_0 = ((self.y0 - point)**2).sum()
if dist_0 < tol:
# catch the case where we start at 0
return 0.
cat_y0 = np.hstack([self.y0, dist_0])
roots_class = Oscillator(dist_model, self.param, cat_y0)
roots_class.intoptions = self.intoptions
#return roots_class
roots_class.solve_bvp()
roots_class.limit_cycle()
roots_class.roots()
phases = self._t_to_phi(roots_class.tmin[-1])
distances = roots_class.ymin[-1]
distance = np.min(distances)
if distance < tol:
phase_ind = np.argmin(distances) # for multiple minima
return phases[phase_ind]#, roots_class
intr.setInput(point, cs.INTEGRATOR_X0)
intr.setInput(self.param, cs.INTEGRATOR_P)
intr.evaluate()
point = intr.output().toArray().flatten() #advance by one cycle
raise RuntimeError("Point failed to converge to limit cycle")
def average(self):
"""
integrate the solution with quadrature to find the average
species concentration. outputs to self.avg
"""
ffcn_in = self.model.inputExpr()
ode = self.model.outputExpr()
quad = cs.vertcat([ffcn_in[cs.DAE_X], ffcn_in[cs.DAE_X]**2])
quadmodel = cs.SXFunction(ffcn_in, cs.daeOut(ode=ode[0], quad=quad))
qint = cs.Integrator('cvodes',quadmodel)
qint.setOption("abstol" , self.intoptions['lc_abstol'])
qint.setOption("reltol" , self.intoptions['lc_reltol'])
qint.setOption("max_num_steps" , self.intoptions['lc_maxnumsteps'])
qint.setOption("tf",self.T)
qint.init()
qint.setInput(self.y0, cs.INTEGRATOR_X0)
qint.setInput(self.param, cs.INTEGRATOR_P)
qint.evaluate()
quad_out = qint.output(cs.INTEGRATOR_QF).toArray().squeeze()
self.avg = quad_out[:self.neq]/self.T
self.rms = np.sqrt(quad_out[self.neq:]/self.T)
self.std = np.sqrt(self.rms**2 - self.avg**2)
def solve_ode(self):
""" Solve the ODE using casadi's CVODES wrapper to ensure that the
collocated dynamics match the error-controlled dynamics of the ODE """
self.ts.sort() # Assert ts is increasing
f_integrator = cs.SXFunction(
'ode',
cs.daeIn(t=self.dxdt.inputExpr(0),
x=self.dxdt.inputExpr(1),
p=self.dxdt.inputExpr(2)),
cs.daeOut(ode=self.dxdt.outputExpr(0)))
integrator = cs.Integrator('int', 'cvodes', f_integrator)
simulator = cs.Simulator('sim', integrator, self.ts)
simulator.setInput(self.sol[0], 'x0')
simulator.setInput(self.var.p_op, 'p')
simulator.evaluate()
x_sim = self.sol_sim = np.array(simulator.getOutput()).T
err = ((self.sol - x_sim).mean(0) / (self.sol.mean(0))).mean()
if err > 1E-3:
warn('Collocation does not match ODE Solution: \
{:.2%} Error'.format(err))
def solve_bvp_scipy(self, root_method='hybr'):
"""
Use a scipy optimize function to optimize the BVP function
"""
# Make sure inputs are the correct format
paramset = list(self.param)
# Here we create and initialize the integrator SXFunction
self.bvpint = cs.Integrator('cvodes', self.modlT)
self.bvpint.setOption('abstol', self.intoptions['bvp_abstol'])
self.bvpint.setOption('reltol', self.intoptions['bvp_reltol'])
self.bvpint.setOption('tf', 1)
self.bvpint.setOption('disable_internal_warnings', True)
self.bvpint.setOption('fsens_err_con', True)
self.bvpint.init()
def bvp_minimize_function(x):
""" Minimization objective. X = [y0,T] """
# perhaps penalize in try/catch?
if all(
[self.intoptions['constraints'] == 'positive',
np.any(x < 0)]):
return np.ones(len(x))
self.bvpint.setInput(x[:-1], cs.INTEGRATOR_X0)
self.bvpint.setInput(paramset + [x[-1]], cs.INTEGRATOR_P)
self.bvpint.evaluate()
out = x[:-1] - self.bvpint.output().toArray().flatten()
out = out.tolist()
self.modlT.setInput(x[:-1], cs.DAE_X)
self.modlT.setInput(paramset + [x[-1]], 2)
self.modlT.evaluate()
out += self.modlT.output()[0].toArray()[0].tolist()
return np.array(out)
from scipy.optimize import root
options = {}
root_out = root(bvp_minimize_function,
np.append(self.y0, self.T),
tol=self.intoptions['bvp_ftol'],
method=root_method,
options=options)
# Check solve success
if not root_out.status:
raise RuntimeError("bvpsolve: " + root_out.message)
# Check output convergence
if np.linalg.norm(root_out.qtf) > self.intoptions['bvp_ftol'] * 1E4:
raise RuntimeError("bvpsolve: nonconvergent")
# save output to self.y0
self.y0 = root_out.x[:-1]
self.T = root_out.x[-1]
def _initialize_polynomial_coefs(self):
""" Setup radau polynomials and initialize the weight factor matricies
"""
self.col_vars['tau_root'] = cs.collocationPoints(self.d, "radau")
# Dimensionless time inside one control interval
tau = cs.SX.sym("tau")
# For all collocation points
L = [[]]*(self.d+1)
for j in range(self.d+1):
# Construct Lagrange polynomials to get the polynomial basis at the
# collocation point
L[j] = 1
for r in range(self.d+1):
if r != j:
L[j] *= (
(tau - self.col_vars['tau_root'][r]) /
(self.col_vars['tau_root'][j] -
self.col_vars['tau_root'][r]))
self.col_vars['lfcn'] = lfcn = cs.SXFunction(
'lfcn', [tau], [cs.vertcat(L)])
# Evaluate the polynomial at the final time to get the coefficients of
# the continuity equation
# Coefficients of the continuity equation
self.col_vars['D'] = lfcn([1.0])[0].toArray().squeeze()
# Evaluate the time derivative of the polynomial at all collocation
# points to get the coefficients of the continuity equation
tfcn = lfcn.tangent()
# Coefficients of the collocation equation
self.col_vars['C'] = np.zeros((self.d+1, self.d+1))
for r in range(self.d+1):
self.col_vars['C'][:,r] = tfcn([self.col_vars['tau_root'][r]]
)[0].toArray().squeeze()
# Find weights for gaussian quadrature: approximate int_0^1 f(x) by
# Sum(
xtau = cs.SX.sym("xtau")
Phi = [[]] * (self.d+1)
for j in range(self.d+1):
tau_f_integrator = cs.SXFunction('ode', cs.daeIn(t=tau, x=xtau),
cs.daeOut(ode=L[j]))
tau_integrator = cs.Integrator(
"integrator", "cvodes", tau_f_integrator, {'t0':0., 'tf':1})
Phi[j] = np.asarray(tau_integrator({'x0' : 0})['xf'])[0][0]
self.col_vars['Phi'] = np.array(Phi)
def solve_bvp_casadi(self):
"""
Uses casadi's interface to sundials to solve the boundary value
problem using a single-shooting method with automatic differen-
tiation.
Related to PCSJ code.
"""
self.bvpint = cs.Integrator('cvodes', self.modlT)
self.bvpint.setOption('abstol', self.intoptions['bvp_abstol'])
self.bvpint.setOption('reltol', self.intoptions['bvp_reltol'])
self.bvpint.setOption('tf', 1)
self.bvpint.setOption('disable_internal_warnings', True)
self.bvpint.setOption('fsens_err_con', True)
self.bvpint.init()
# Vector of unknowns [y0, T]
V = cs.MX.sym("V", self.neq + 1)
y0 = V[:-1]
T = V[-1]
param = cs.vertcat([self.param, T])
yf = self.bvpint.call(cs.integratorIn(x0=y0, p=param))[0]
fout = self.modlT.call(cs.daeIn(t=T, x=y0, p=param))[0]
# objective: continuity
obj = (yf -
y0)**2 # yf and y0 are the same ..i.e. 2 ends of periodic fcn
obj.append(
fout[0]) # y0 is a peak for state 0, i.e. fout[0] is slope state 0
#set up the matrix we want to solve
F = cs.MXFunction([V], [obj])
F.init()
guess = np.append(self.y0, self.T)
solver = cs.ImplicitFunction('kinsol', F)
solver.setOption('abstol', self.intoptions['bvp_ftol'])
solver.setOption('strategy', 'linesearch')
solver.setOption('exact_jacobian', False)
solver.setOption('pretype', 'both')
solver.setOption('use_preconditioner', True)
if self.intoptions['constraints'] == 'positive':
solver.setOption('constraints', (2, ) * (self.neq + 1))
solver.setOption('linear_solver_type', 'dense')
solver.init()
solver.setInput(guess)
solver.evaluate()
sol = solver.output().toArray().squeeze()
self.y0 = sol[:-1]
self.T = sol[-1]
def first_order_sensitivity(self):
"""
Function to calculate the first order period sensitivity
matricies using the direct method. See Wilkins et al. 2009. Only
calculates initial conditions and period sensitivities.
"""
self.check_monodromy()
monodromy = self.monodromy
integrator = cs.Integrator('cvodes',self.model)
integrator.setOption("abstol", self.intoptions['sensabstol'])
integrator.setOption("reltol", self.intoptions['sensreltol'])
integrator.setOption("max_num_steps",
self.intoptions['sensmaxnumsteps'])
integrator.setOption("sensitivity_method",
self.intoptions['sensmethod']);
integrator.setOption("t0", 0)
integrator.setOption("tf", self.T)
integrator.setOption("fsens_err_con", 1)
integrator.setOption("fsens_abstol", self.intoptions['sensabstol'])
integrator.setOption("fsens_reltol", self.intoptions['sensreltol'])
integrator.init()
integrator.setInput(self.y0,cs.INTEGRATOR_X0)
integrator.setInput(self.param,cs.INTEGRATOR_P)
intdyfdp = integrator.jacobian(cs.INTEGRATOR_P, cs.INTEGRATOR_XF)
intdyfdp.init()
intdyfdp.setInput(self.y0,"x0")
intdyfdp.setInput(self.param,"p")
intdyfdp.evaluate()
s0 = intdyfdp.output().toArray()
self.model.init()
self.model.setInput(self.y0,cs.DAE_X)
self.model.setInput(self.param,cs.DAE_P)
self.model.evaluate()
ydot0 = self.model.output().toArray().squeeze()
LHS = np.zeros([(self.neq + 1), (self.neq + 1)])
LHS[:-1,:-1] = monodromy - np.eye(len(monodromy))
LHS[-1,:-1] = self.dfdy(self.y0)[0]
LHS[:-1,-1] = ydot0
RHS = np.zeros([(self.neq + 1), self.np])
RHS[:-1] = -s0
RHS[-1] = self.dfdp(self.y0)[0]
unk = np.linalg.solve(LHS,RHS)
self.S0 = unk[:-1]
self.dTdp = unk[-1]
self.reldTdp = self.dTdp*self.param/self.T
def findARC_whole(self, res=100, trans=3):
""" Calculate entire sARC matrix, which will be faster than
calcualting for each parameter """
# Calculate necessary quantities
if not hasattr(self, 'avg'): self.average()
if not hasattr(self, 'sPRC'): self.find_prc(res)
# Set up quadrature integrator
self.sarc_int = cs.Integrator(
'cvodes', self._create_ARC_model(numstates=self.neq))
self.sarc_int.setOption("abstol", self.intoptions['sensabstol'])
self.sarc_int.setOption("reltol", self.intoptions['sensreltol'])
self.sarc_int.setOption("max_num_steps",
self.intoptions['sensmaxnumsteps'])
self.sarc_int.setOption("t0", 0)
self.sarc_int.setOption("tf", trans * self.T)
#self.sarc_int.setOption("numeric_jacobian", True)
self.sarc_int.init()
self.arc_ts = np.linspace(0, self.T, res)
amp_change = []
for t in self.arc_ts:
# Initialize model and sensitivity states
x0 = np.zeros(self.neq * (self.neq + 1))
x0[:self.neq] = self.lc(t)
x0[self.neq:] = np.eye(self.neq).flatten()
# Add dphi/dt from seed perturbation
param = np.zeros(self.np + self.neq)
param[:self.np] = self.param
param[self.np:] = self.sPRC_interp(t)
# Evaluate model
self.sarc_int.setInput(x0, cs.INTEGRATOR_X0)
self.sarc_int.setInput(param, cs.INTEGRATOR_P)
self.sarc_int.evaluate()
out = self.sarc_int.output(cs.INTEGRATOR_QF).toArray()
# amp_change += [out]
amp_change += [out * 2 * np.pi / self.T]
#[time, state_out, state_in]
self.sARC = np.array(amp_change)
dfdp = np.array([self.dfdp(self.lc(t)) for t in self.arc_ts])
self.pARC = np.array([
self.sARC[i].dot(self._phi_to_t(dfdp[i]))
for i in xrange(len(self.sARC))
])
self.rel_pARC = (np.array(self.param) * self.pARC /
np.atleast_2d(self.avg).T)
def fwd_simulation(self,
dE_start,
condition,
detail=True,
reltol=1e-6,
abstol=1e-8):
Tem = condition.Temperature
time = condition.TimeGrid
opts = {}
opts['abstol'] = abstol
opts['reltol'] = reltol
opts['disable_internal_warnings'] = True
opts['max_num_steps'] = 1e5
P_dae = np.hstack([dE_start, Tem])
# Partial Pressure
Pinlet = np.zeros(self.ngas)
for idx, spe in enumerate(self.specieslist):
if spe.phase == 'gaseous':
Pinlet[idx] = condition.PartialPressure[str(spe)]
x0 = Pinlet.tolist() + [0] * (self.nsurf - 1) + [1]
# print(x0)
Fint = cas.Integrator('Fint', 'cvodes', self._dae_, opts)
Fsim = cas.Simulator('Fsim', Fint, time)
Fsim.setInput(x0, 'x0')
Fsim.setInput(P_dae, 'p')
Fsim.evaluate()
# Evalu
out = Fsim.getOutput().full()
tor_list = {}
for i, spe in enumerate(self.specieslist):
if spe.phase == 'gaseous':
nt = int(condition.Ntime / 2)
slope, intercept, r_value, p_value, std_err = stats.linregress(
condition.TimeGrid[nt:], out[i, nt:])
tor_list[spe.name] = slope
return out, tor_list
def check_monodromy(self):
"""
Check the stability of the limit cycle by finding the
eigenvalues of the monodromy matrix
"""
integrator = cs.Integrator('cvodes', self.model)
integrator.setOption("abstol", self.intoptions['sensabstol'])
integrator.setOption("reltol", self.intoptions['sensreltol'])
integrator.setOption("max_num_steps",
self.intoptions['int_maxstepcount'])
integrator.setOption("sensitivity_method",
self.intoptions['sensmethod'])
integrator.setOption("t0", 0)
integrator.setOption("tf", self.T)
integrator.setOption("fsens_err_con", 1)
integrator.setOption("fsens_abstol", self.intoptions['sensabstol'])
integrator.setOption("fsens_reltol", self.intoptions['sensreltol'])
integrator.init()
integrator.setInput(self.y0, cs.INTEGRATOR_X0)
integrator.setInput(self.param, cs.INTEGRATOR_P)
intdyfdy0 = integrator.jacobian(cs.INTEGRATOR_X0, cs.INTEGRATOR_XF)
intdyfdy0.init()
intdyfdy0.setInput(self.y0, "x0")
intdyfdy0.setInput(self.param, "p")
intdyfdy0.evaluate()
monodromy = intdyfdy0.output().toArray()
self.monodromy = monodromy
# Calculate Floquet Multipliers, check if all (besides n_0 = 1)
# are inside unit circle
eigs = np.linalg.eigvals(monodromy)
self.floquet_multipliers = np.abs(eigs)
#self.floquet_multipliers.sort()
idx = (np.abs(self.floquet_multipliers - 1.0)).argmin()
f = self.floquet_multipliers.tolist()
f.pop(idx)
return np.all(np.array(f) < 1)
def _findARC_seed(self, seeds, res=100, trans=3):
# Calculate necessary quantities
if not hasattr(self, 'avg'): self.average()
if not hasattr(self, 'sPRC'): self.find_prc(res)
# Set up quadrature integrator
self.sarc_int = cs.Integrator('cvodes',self._create_ARC_model())
self.sarc_int.setOption("abstol", self.intoptions['sensabstol'])
self.sarc_int.setOption("reltol", self.intoptions['sensreltol'])
self.sarc_int.setOption("max_num_steps",
self.intoptions['sensmaxnumsteps'])
self.sarc_int.setOption("t0", 0)
self.sarc_int.setOption("tf", trans*self.T)
#self.sarc_int.setOption("numeric_jacobian", True)
self.sarc_int.init()
t_arc = np.linspace(0, self.yT, res)
arc = np.array([self._sarc_single_time(t, seed) for t, seed in
zip(t_arc, seeds)]).squeeze()
return t_arc, arc
def fwd_simulation(self,
dE_start,
condition,
detail=True,
reltol=1e-6,
abstol=1e-8):
# reevaluate the reaction condition
condition._calSim()
condition._calGrid()
time = condition.TimeGrid
T0 = condition.T0
beta = condition.Beta
opts = {}
opts['abstol'] = abstol
opts['reltol'] = reltol
opts['disable_internal_warnings'] = True
opts['max_num_steps'] = 1e5
x0 = self.init_condition(condition)
P_dae = np.hstack([dE_start, T0, beta])
# print(x0)
# print(P_dae)
# print(time)
# opts['tf'] = 2
# Fint = cas.Integrator('Fint', 'cvodes', self._dae_, opts)
# F_sim = Fint(x0=x0, p=P_dae)
Fint = cas.Integrator('Fint', 'cvodes', self._dae_, opts)
Fsim = cas.Simulator('Fsim', Fint, time)
Fsim.setInput(x0, 'x0')
Fsim.setInput(P_dae, 'p')
Fsim.evaluate()
# Evaluate
out = Fsim.getOutput().full()
out[:self.ngas, :] *= self.pump_ratio
return out
def eval_likeli(self, dE, conditionlist, evidence_info={}):
reltol = evidence_info.get('reltol', 1e-12)
abstol = evidence_info.get('abstol', 1e-12)
err = evidence_info.get('peak_err', 10)
opts = {}
opts['abstol'] = abstol
opts['reltol'] = reltol
opts['disable_internal_warnings'] = True
opts['max_num_steps'] = 1e5
# Initialize simulator
evidence = 0
for condition in conditionlist:
time = condition.TimeGrid
T0 = condition.T0
beta = condition.Beta
x0 = self.init_condition(condition)
P_dae = np.hstack([dE, T0, beta])
Fint = cas.Integrator('Fint', 'cvodes', self._dae_, opts)
Fsim = cas.Simulator('Fsim', Fint, time)
Fsim.setInput(x0, 'x0')
Fsim.setInput(P_dae, 'p')
Fsim.evaluate()
out = Fsim.getOutput().full()
# Find the peak
for spe, peak_exp in condition.PeakPosition.items():
idx = get_index_species(spe, self.specieslist)
des = out[idx, :]
idx_peak = np.argmax(des)
peak_sim = condition.TemGrid[idx_peak]
dev = peak_sim - peak_exp
evidence += (dev * dev) / err**2
return -evidence
def solve_ode(self):
""" Solve the ODE using casadi's CVODES wrapper to ensure that the
collocated dynamics match the error-controlled dynamics of the ODE """
f_integrator = cs.SXFunction(
'ode',
cs.daeIn(t=self.model.inputExpr(0),
x=self.model.inputExpr(1),
p=self.model.inputExpr(2)),
cs.daeOut(ode=self.model.outputExpr(0)))
integrator = cs.Integrator('int', 'cvodes', f_integrator)
simulator = cs.Simulator('sim', integrator, self._tgrid)
simulator.setInput(self._output['x_opt'][0], 'x0')
simulator.setInput(self._output['p_opt'], 'p')
simulator.evaluate()
x_sim = self._output['x_sim'] = np.array(simulator.getOutput()).T
err = ((self._output['x_opt'] - x_sim).mean(0) /
(self._output['x_opt'].mean(0))).mean()
if err > 1E-3:
warn('Collocation does not match ODE Solution: \
{:.2f}% Error'.format(100 * err))
def test_X(self):
self.message("Extensive integrator tests")
num=self.num
tstart = SX.sym("tstart")
tend = SX.sym("tstart")
for Integrator, features, options in integrators:
self.message(Integrator)
def variations(p_features, din, dout, rdin, rdout, *args):
if "ode" in p_features:
p_features_ = copy.copy(p_features)
p_features_[p_features.index("ode")] = "dae"
din_ = copy.copy(din)
dout_ = copy.copy(dout)
rdin_ = copy.copy(rdin)
rdout_ = copy.copy(rdout)
z = SX.sym("x", din_["x"].shape)
din_["z"] = z
dout_["ode"] = z
dout_["alg"] = ( dout["ode"] - z) * (-0.8)
if len(rdin_)>0:
rz = SX.sym("rx", rdin_["rx"].shape)
rdin_["rz"] = rz
rdin_["z"] = z
rdout_["ode"] = rz
rdout_["alg"] = ( rdout["ode"] - rz) * (-0.7)
yield (p_features, din, dout, rdin, rdout) + tuple(args)
yield (p_features_, din_, dout_, rdin_, rdout_) + tuple(args)
else:
yield (p_features, din, dout, rdin, rdout) + tuple(args)
def checks():
x0=num['q0']
p_=num['p']
rx0_= 0.13
t=SX.sym("t")
x=SX.sym("x")
rx=SX.sym("rx")
p=SX.sym("p")
dp=SX.sym("dp")
z=SX.sym("z")
rz=SX.sym("rz")
rp=SX.sym("rp")
si = {'x0':x, 'p': p, 'rx0': rx,'rp' : rp}
pointA = {'x0':x0,'p': p_, 'rx0': rx0_, 'rp': 0.127}
ti = (0.2,num['tend'])
yield (["ode"],{'x':x},{'ode': 0},{},{},si,{'xf':x},pointA,ti)
yield (["ode"],{'x':x},{'ode': 1},{},{},si,{'xf':x+(tend-tstart)},pointA,ti)
yield (["ode"],{'x':x},{'ode': x},{},{},si,{'xf':x*exp(tend-tstart)},pointA,ti)
yield (["ode"],{'x':x,'t':t},{'ode': t},{},{},si,{'xf':x+(tend**2/2-tstart**2/2)},pointA,ti)
yield (["ode"],{'x':x,'t':t},{'ode': x*t},{},{},si,{'xf':x*exp(tend**2/2-tstart**2/2)},pointA,ti)
yield (["ode"],{'x':x,'p':p},{'ode': x/p},{},{},si,{'xf':x*exp((tend-tstart)/p)},pointA,ti)
if not(args.run_slow): return
yield (["ode"],{'x':x},{'ode': x,'quad':0},{},{},si,{'qf':0},pointA,ti)
yield (["ode"],{'x':x},{'ode': x,'quad':1},{},{},si,{'qf':(tend-tstart)},pointA,ti)
yield (["ode"],{'x':x},{'ode': 0,'quad':x},{},{},si,{'qf':x*(tend-tstart)},pointA,ti)
#yield ({'x':x},{'ode': 1,'quad':x},{'qf':(x-tstart)*(tend-tstart)+(tend**2/2-tstart**2/2)}), # bug in cvodes quad_err_con
yield (["ode"],{'x':x},{'ode': x,'quad':x},{},{},si,{'qf':x*(exp(tend-tstart)-1)},pointA,ti)
yield (["ode"],{'x':x,'t':t},{'ode': x,'quad':t},{},{},si,{'qf':(tend**2/2-tstart**2/2)},pointA,ti)
yield (["ode"],{'x':x,'t':t},{'ode': x,'quad':x*t},{},{},si,{'qf':x*(exp(tend-tstart)*(tend-1)-(tstart-1))},pointA,ti)
yield (["ode"],{'x':x,'p':p},{'ode': x,'quad':x/p},{},{},si,{'qf':x*(exp((tend-tstart))-1)/p},pointA,ti)
yield (["ode"],{'x':x},{'ode':x},{'x':x,'rx':rx},{'ode':0},si,{'rxf': rx},pointA,ti)
yield (["ode"],{'x':x},{'ode':x},{'x':x,'rx':rx},{'ode':1},si,{'rxf': rx+tend-tstart},pointA,ti)
yield (["ode"],{'x':x,'t':t},{'ode':x},{'x':x,'rx':rx,'t':t},{'ode':t},si,{'rxf': rx+tend**2/2-tstart**2/2},pointA,ti)
yield (["ode"],{'x':x},{'ode':x},{'x':x,'rx':rx},{'ode':rx},si,{'rxf': rx*exp(tend-tstart)},pointA,ti)
yield (["ode"],{'x':x},{'ode':x},{'x':x,'rx':rx},{'ode':x},si,{'rxf': rx+x*(exp(tend-tstart)-1)},pointA,ti)
yield (["ode"],{'x':x,'t':t},{'ode':x},{'x':x,'rx':rx,'t':t},{'ode':x*t},si,{'rxf': rx+x*(exp(tend-tstart)*(tend-1)-(tstart-1))},pointA,ti)
yield (["ode"],{'x':x,'t':t},{'ode':x},{'x':x,'rx':rx,'t':t},{'ode':rx*t},si,{'rxf': rx*exp(tend**2/2-tstart**2/2)},pointA,ti)
yield (["ode"],{'x':x},{'ode':x},{'x':x,'rx':rx},{'ode':rx, 'quad': 0},si,{'rqf': 0},pointA,ti)
yield (["ode"],{'x':x},{'ode':x},{'x':x,'rx':rx},{'ode':rx, 'quad': 1},si,{'rqf': (tend-tstart)},pointA,ti)
yield (["ode"],{'x':x},{'ode':x},{'x':x,'rx':rx},{'ode':rx, 'quad': rx},si,{'rqf': rx*(exp(tend-tstart)-1)},pointA,ti)
yield (["ode"],{'x':x},{'ode':x},{'x':x,'rx':rx},{'ode':rx, 'quad': x},si,{'rqf': x*(exp(tend-tstart)-1)},pointA,ti)
yield (["ode"],{'x':x,'t':t},{'ode':x},{'x':x,'rx':rx,'t':t},{'ode':rx, 'quad': t},si,{'rqf': (tend**2/2-tstart**2/2)},pointA,ti)
yield (["ode"],{'x':x,'t':t},{'ode':x},{'x':x,'rx':rx,'t':t},{'ode':rx, 'quad': x*t},si,{'rqf': x*(exp(tend-tstart)*(tend-1)-(tstart-1))},pointA,ti)
yield (["ode"],{'x':x,'t':t},{'ode':x},{'x':x,'rx':rx,'t':t},{'ode':rx, 'quad': rx*t},si,{'rqf': rx*(exp(tend-tstart)*(tstart+1)-(tend+1))},pointA,ti) # this one is special: integrate(t*rx*exp(tf-t),t,t0,tf)
yield (["ode"],{'x':x,'p':p},{'ode':x},{'x':x,'rx':rx,'p':p},{'ode':rx, 'quad': p},si,{'rqf': p*(tend-tstart)},pointA,ti)
yield (["ode"],{'x':x,'p':p},{'ode':x},{'x':x,'rx':rx,'p':p,'rp':rp},{'ode':rx, 'quad': rp},si,{'rqf': rp*(tend-tstart)},pointA,ti)
yield (["ode"],{'x':x,'t':t},{'ode':x},{'x':x,'rx':rx,'t':t},{'ode':rx*t},si,{'rxf': rx*exp(tend**2/2-tstart**2/2)},pointA,ti)
yield (["ode"],{'x':x,'t':t},{'ode':x},{'x':x,'rx':rx,'t':t},{'ode':x*t},si,{'rxf': rx+x*(exp(tend-tstart)*(tend-1)-(tstart-1))},pointA,ti)
yield (["dae"],{'x':x,'z':z},{'ode':z,'alg': -0.8*(z-x),'quad': z},{},{},si,{'qf':x*(exp(tend-tstart)-1)},pointA,ti)
yield (["dae"],{'x':x,'z':z},{'ode':z,'alg': -0.8*(z-x)},{'x':x,'rx':rx,'rz': rz,'z':z},{'ode':rz, 'alg': -0.7*(rz-rx), 'quad': rz},si,{'rqf': rx*(exp(tend-tstart)-1)},pointA,ti)
yield (["dae"],{'x':x,'z':z},{'ode':z,'alg': -0.8*(z-x)},{'x':x,'rx':rx,'rz': rz,'z':z},{'ode':rz, 'alg': -0.7*(rz-rx), 'quad': z},si,{'rqf': x*(exp(tend-tstart)-1)},pointA,ti)
A=array([1,0.1])
p0 = 1.13
q=SX.sym("y",2,1)
y0=q[0]
yc0=dy0=q[1]
p=SX.sym("p",1,1)
s1=(2*y0-log(yc0**2/p+1))/2-log(cos(arctan(yc0/sqrt(p))+sqrt(p)*(tend-tstart)))
s2=sqrt(p)*tan(arctan(yc0/sqrt(p))+sqrt(p)*(tend-tstart))
yield (["ode"],{'x':q,'p':p},{'ode': vertcat([q[1],p[0]+q[1]**2 ])},{},{},{'x0':q, 'p': p} ,{'xf': vertcat([s1,s2])},{'x0': A, 'p': p0},(0,0.4) )
for tt in checks():
print tt
for p_features, din, dout, rdin, rdout, solutionin, solution, point, (tstart_, tend_) in variations(*tt):
if p_features[0] in features:
message = "%s: %s => %s, %s => %s, explicit (%s) tstart = %f" % (Integrator,str(din),str(dout),str(rdin),str(rdout),str(solution),tstart_)
print message
g = Function()
if len(rdin)>1:
g = SXFunction(rdaeIn(**rdin),rdaeOut(**rdout))
g.init()
f = SXFunction(daeIn(**din),daeOut(**dout))
f.init()
for k in solution.keys():
solution[k] = substitute(solution[k],vertcat([tstart,tend]),vertcat([tstart_,tend_]))
fs = SXFunction(integratorIn(**solutionin),integratorOut(**solution))
fs.init()
integrator = c.Integrator(Integrator,f,g)
integrator.setOption(options)
integrator.setOption("t0",tstart_)
if integrator.hasOption("abstol"):
integrator.setOption("abstol",1e-9)
if integrator.hasOption("reltol"):
integrator.setOption("reltol",1e-9)
integrator.setOption("tf",tend_)
if integrator.hasOption("init_xdot"):
integrator.setOption("init_xdot",list(DMatrix(point["x0"])))
integrator.setOption("calc_icB",True)
integrator.setOption("augmented_options", {"init_xdot":None, "abstol":1e-9,"reltol":1e-9})
#if "dae" in p_features and integrator.hasOption("init_z"):
# integrator.setOption("init_z",[0.1])
# integrator.setOption("augmented_options", {"init_z":GenericType(),"init_xdot":GenericType()})
integrator.init()
# reproduce = """
#from casadi import *
#t=SX.sym("t")
#x=SX.sym("x")
#rx=SX.sym("rx")
#p=SX.sym("p")
#dp=SX.sym("dp")
#z=SX.sym("z")
#rz=SX.sym("rz")
#rp=SX.sym("rp")
#f = SXFunction(daeIn(**{din}),daeOut(**{dout}))
#f.init()
#g = SXFunction(rdaeIn(**{rdin}),rdaeOut(**{rdout}))
#g.init()
#integrator = {intclass.__name__}(f,g)
#integrator.setOption({options})
#integrator.init()
#integrator.setInput({x0},"x0")
#if not integrator.input("p").isEmpty():
# integrator.setInput({p_},"p")
#if not integrator.input("rx0").isEmpty():
# integrator.setInput(0.13,"rx0")
#if not integrator.input("rp").isEmpty():
# integrator.setInput(0.127,"rp")
# """.format(din=din,dout=dout,rdin=rdin,rdout=rdout,x0=x0,p_=p_,intclass=Integrator,options=integrator.dictionary())
# message+="\nTo reproduce:\n" + reproduce
for ff in [fs,integrator]:
for k,v in point.items():
i = getattr(casadi,('integrator_'+k).upper())
if not ff.input(i).isEmpty():
ff.setInput(v,i)
integrator.evaluate()
self.checkfunction(integrator,fs,gradient=False,hessian=False,sens_der=False,evals=False,digits=4,digits_sens=4,failmessage=message,verbose=False)
def test_jac(self):
self.message("Test exact jacobian #536")
# This test is not automized, but works by inspection only.
# To activate, recompile after ucnommenting the printout lines in cvodes.c, near "Used for validating casadi#536"
#return
DMatrix.setPrecision(18)
tstart = SX.sym("tstart")
tend = SX.sym("tend")
integrators = [
("idas",["dae","ode"],{"abstol": 1e-9,"reltol":1e-9,"fsens_err_con": True,"calc_ic":True,"calc_icB":True}),
("cvodes",["ode"],{"abstol": 1e-5,"reltol":1e-5,"fsens_err_con": False,"quad_err_con": False})
]
def variations(p_features, din, dout, rdin, rdout, *args):
if "ode" in p_features:
p_features_ = copy.copy(p_features)
p_features_[p_features.index("ode")] = "dae"
din_ = copy.copy(din)
dout_ = copy.copy(dout)
rdin_ = copy.copy(rdin)
rdout_ = copy.copy(rdout)
z = SX.sym("x", din_["x"].shape)
din_["z"] = z
dout_["ode"] = z
dout_["alg"] = ( dout["ode"] - z) * (-0.8)
if len(rdin_)>0:
rz = SX.sym("rx", rdin_["rx"].shape)
rdin_["rz"] = rz
rdin_["z"] = z
rdout_["ode"] = rz
rdout_["alg"] = ( rdout["ode"] - rz) * (-0.7)
yield (p_features, din, dout, rdin, rdout) + tuple(args)
yield (p_features_, din_, dout_, rdin_, rdout_) + tuple(args)
else:
yield (p_features, din, dout, rdin, rdout) + tuple(args)
def checks():
Ns = 1
x = SX.sym("x")
rx = SX.sym("rx")
t = SX.sym("t")
ti = (0,0.9995)
pointA = {'x0': 1, 'rx0': 1}
si = {'x0':x, 'rx0': rx}
#sol = {'rxf': 1.0/(1-tend)}
sol = {'rxf': rx*exp(tend), 'xf': x*exp(tend)}
yield (["ode"],{'x':x,'t':t},{'ode':x},{'x':x,'rx':rx,'t':t},{'ode': rx},si,sol,pointA,ti)
refXF = refRXF = None
for tt in checks():
for p_features, din, dout, rdin, rdout, solutionin, solution, point, (tstart_, tend_) in variations(*tt):
for Integrator, features, options in integrators:
self.message(Integrator)
dummyIntegrator = c.Integrator(Integrator,c.SXFunction())
if p_features[0] in features:
g = Function()
if len(rdin)>1:
g = SXFunction(rdaeIn(**rdin),rdaeOut(**rdout))
g.init()
f = SXFunction(daeIn(**din),daeOut(**dout))
f.init()
for k in solution.keys():
solution[k] = substitute(solution[k],vertcat([tstart,tend]),vertcat([tstart_,tend_]))
fs = SXFunction(integratorIn(**solutionin),integratorOut(**solution))
fs.init()
def itoptions(post=""):
yield {"iterative_solver"+post: "gmres"}
yield {"iterative_solver"+post: "bcgstab"}
yield {"iterative_solver"+post: "tfqmr", "use_preconditionerB": True, "linear_solverB" : "csparse"} # Bug in Sundials? Preconditioning seems to be needed
def solveroptions(post=""):
yield {"linear_solver_type" +post: "dense" }
allowedOpts = list(dummyIntegrator.getOptionAllowed("linear_solver_type" +post))
#allowedOpts.remove("iterative") # disabled, see #1231
if "iterative" in allowedOpts:
for it in itoptions(post):
d = {"linear_solver_type" +post: "iterative" }
d.update(it)
yield d
if "banded" in allowedOpts:
yield {"linear_solver_type" +post: "banded" }
yield {"linear_solver_type" +post: "user_defined", "linear_solver"+post: "csparse" }
for a_options in solveroptions("B"):
for f_options in solveroptions():
message = "f_options: %s , a_options: %s" % (str(f_options) , str(a_options))
print message
integrator = c.Integrator(Integrator,f,g)
integrator.setOption("exact_jacobianB",True)
integrator.setOption("gather_stats",True)
#integrator.setOption("verbose",True)
#integrator.setOption("monitor",["djacB","resB","djac","res"])
integrator.setOption("t0",tstart_)
integrator.setOption("tf",tend_)
integrator.setOption(options)
integrator.setOption(f_options)
integrator.setOption(a_options)
integrator.init()
for ff in [fs,integrator]:
for k,v in point.items():
i = getattr(casadi,('integrator_'+k).upper())
if not ff.getInput(i).isEmpty():
ff.setInput(v,i)
integrator.evaluate()
fs.evaluate()
print "res=",integrator.getOutput("xf")-fs.getOutput("xf"), fs.getOutput("xf")
print "Rres=",integrator.getOutput("rxf")-fs.getOutput("rxf"), fs.getOutput("rxf")
# self.checkarray(integrator.getOutput("rxf"),fs.getOutput("rxf"),digits=4)
stats = integrator.getStats()
print stats
self.assertTrue(stats["nsteps"]<1500)
self.assertTrue(stats["nstepsB"]<2500)
self.assertTrue(stats["nlinsetups"]<100)
self.assertTrue(stats["nlinsetupsB"]<250)
def test_lsolvers(self):
self.message("Test different linear solvers")
tstart = SX.sym("tstart")
tend = SX.sym("tend")
integrators = [
("idas",["dae","ode"],{"abstol": 1e-9,"reltol":1e-9,"fsens_err_con": True,"calc_ic":True,"calc_icB":True}),
("cvodes",["ode"],{"abstol": 1e-15,"reltol":1e-15,"fsens_err_con": True,"quad_err_con": False})
]
def checks():
t=SX.sym("t")
x=SX.sym("x")
rx=SX.sym("rx")
p=SX.sym("p")
dp=SX.sym("dp")
z=SX.sym("z")
rz=SX.sym("rz")
rp=SX.sym("rp")
solutionin = {'x0':x, 'p': p, 'rx0': rx,'rp' : rp}
pointA = {'x0':7.1,'p': 2, 'rx0': 0.13, 'rp': 0.127}
ti = (0.2,2.3)
yield (["dae"],{'x': x, 'z': z},{'alg': x-z, 'ode': z},{'x': x, 'z': z, 'rx': rx, 'rz': rz},{'alg': x-rz, 'ode': rz},solutionin,{'rxf': rx+x*(exp(tend-tstart)-1), 'xf':x*exp(tend-tstart)},pointA,ti)
if not(args.run_slow): return
yield (["dae"],{'x': x, 'z': z},{'alg': x-z, 'ode': z},{'x': x, 'z': z, 'rx': rx, 'rz': rz},{'alg': rx-rz, 'ode': rz},solutionin,{'rxf': rx*exp(tend-tstart), 'xf':x*exp(tend-tstart)},pointA,ti)
yield (["ode"],{'x': x},{'ode': x},{'x': x,'rx': rx},{'ode': x},solutionin,{'rxf': rx+x*(exp(tend-tstart)-1), 'xf':x*exp(tend-tstart)},pointA,ti)
yield (["ode"],{'x': x},{'ode': x},{'x': x,'rx': rx},{'ode': rx},solutionin,{'rxf': rx*exp(tend-tstart), 'xf':x*exp(tend-tstart)},pointA,ti)
A=array([1,0.1])
p0 = 1.13
q=SX.sym("y",2,1)
y0=q[0]
yc0=dy0=q[1]
p=SX.sym("p",1,1)
s1=(2*y0-log(yc0**2/p+1))/2-log(cos(arctan(yc0/sqrt(p))+sqrt(p)*(tend-tstart)))
s2=sqrt(p)*tan(arctan(yc0/sqrt(p))+sqrt(p)*(tend-tstart))
yield (["ode"],{'x':q,'p':p},{'ode': vertcat([q[1],p[0]+q[1]**2 ])},{},{},{'x0':q, 'p': p} ,{'xf': vertcat([s1,s2])},{'x0': A, 'p': p0},(0,0.4) )
for p_features, din, dout, rdin, rdout, solutionin, solution, point, (tstart_, tend_) in checks():
for Integrator, features, options in integrators:
self.message(Integrator)
dummyIntegrator = c.Integrator(Integrator,SXFunction())
if p_features[0] in features:
g = Function()
if len(rdin)>1:
g = SXFunction(rdaeIn(**rdin),rdaeOut(**rdout))
g.init()
f = SXFunction(daeIn(**din),daeOut(**dout))
f.init()
for k in solution.keys():
solution[k] = substitute(solution[k],vertcat([tstart,tend]),vertcat([tstart_,tend_]))
fs = SXFunction(integratorIn(**solutionin),integratorOut(**solution))
fs.init()
def itoptions(post=""):
yield {"iterative_solver"+post: "gmres"}
yield {"iterative_solver"+post: "bcgstab"}
yield {"iterative_solver"+post: "tfqmr", "use_preconditionerB": True, "linear_solverB" : "csparse"} # Bug in Sundials? Preconditioning seems to be needed
def solveroptions(post=""):
yield {"linear_solver_type" +post: "dense" }
allowedOpts = list(dummyIntegrator.getOptionAllowed("linear_solver_type" +post))
#allowedOpts.remove("iterative") # disabled, see #1231
if "iterative" in allowedOpts:
for it in itoptions(post):
d = {"linear_solver_type" +post: "iterative" }
d.update(it)
yield d
if "banded" in allowedOpts:
yield {"linear_solver_type" +post: "banded" }
yield {"linear_solver_type" +post: "user_defined", "linear_solver"+post: "csparse" }
for a_options in solveroptions("B"):
for f_options in solveroptions():
message = "f_options: %s , a_options: %s" % (str(f_options) , str(a_options))
print message
integrator = c.Integrator(Integrator,f,g)
integrator.setOption("exact_jacobianB",True)
integrator.setOption("t0",tstart_)
integrator.setOption("tf",tend_)
integrator.setOption(options)
integrator.setOption(f_options)
integrator.setOption(a_options)
integrator.init()
for ff in [fs,integrator]:
for k,v in point.items():
i = getattr(casadi,('integrator_'+k).upper())
if not ff.input(i).isEmpty():
ff.setInput(v,i)
integrator.evaluate()
self.checkfunction(integrator,fs,gradient=False,hessian=False,sens_der=False,evals=False,digits=4,digits_sens=4,failmessage=message,verbose=False)
def defineOCP(self,
ocp,
DT=20,
controlCost=0,
xOpt=[],
uOpt=[],
finalStateCost=1,
deltaUCons=[]):
self.ocp = ocp
ocp = self.ocp
self.DT = DT
self.n_k = int(self.ocp.tf / self.DT)
self.controlCost = controlCost
stateScaling = C.vertcat([
ocp.variable(ocp.x[k].getName()).nominal
for k in range(ocp.x.size())
])
algStateScaling = C.vertcat([
ocp.variable(ocp.z[k].getName()).nominal
for k in range(ocp.z.size())
])
controlScaling = C.vertcat([
ocp.variable(ocp.u[k].getName()).nominal
for k in range(ocp.u.size())
])
xOpt = xOpt / stateScaling
uOpt = uOpt / controlScaling
self.xOpt = xOpt
self.uOpt = uOpt
self.stateScaling = C.vertcat([
ocp.variable(ocp.x[k].getName()).nominal
for k in range(ocp.x.size())
])
self.algStateScaling = C.vertcat([
ocp.variable(ocp.z[k].getName()).nominal
for k in range(ocp.z.size())
])
self.controlScaling = C.vertcat([
ocp.variable(ocp.u[k].getName()).nominal
for k in range(ocp.u.size())
])
odeS = C.substitute(
ocp.ode(ocp.x), C.vertcat([ocp.x, ocp.z, ocp.u]),
C.vertcat([
stateScaling * ocp.x, algStateScaling * ocp.z,
controlScaling * ocp.u
])) / stateScaling
algS = C.substitute(
ocp.alg, C.vertcat([ocp.x, ocp.z, ocp.u]),
C.vertcat([
stateScaling * ocp.x, algStateScaling * ocp.z,
controlScaling * ocp.u
]))
ltermS = C.substitute(
ocp.lterm, C.vertcat([ocp.x, ocp.z, ocp.u]),
C.vertcat([
stateScaling * ocp.x, algStateScaling * ocp.z,
controlScaling * ocp.u
]))
sysIn = C.daeIn(x=ocp.x, z=ocp.z, p=ocp.u, t=ocp.t)
sysOut = C.daeOut(ode=odeS, alg=algS, quad=ltermS)
odeF = C.SXFunction(sysIn, sysOut)
odeF.init()
C.Integrator.loadPlugin("idas")
G = C.Integrator("idas", odeF)
G.setOption("reltol", self.INTG_REL_TOL) #for CVODES and IDAS
G.setOption("abstol", self.INTG_ABS_TOL) #for CVODES and IDAS
G.setOption("max_multistep_order", 5) #for CVODES and IDAS
G.setOption("max_step_size", self.IDAS_MAX_STEP_SIZE) #for IDAS only
G.setOption("tf", self.DT)
self.G = G
#==============================================================================
# G.setOption('verbose',True)
# G.addMonitor('res')
# G.addMonitor('inputs')
# G.addMonitor('outputs')
#G.addMonitor('djacB')
# G.addMonitor('bjacB')
# G.addMonitor('jtimesB')
# G.addMonitor('psetup')
# G.addMonitor('psetupB')
# G.addMonitor('psolveB')
# G.addMonitor('resB')
# G.addMonitor('resS')
# G.addMonitor('rhsQB')
#==============================================================================
G.init()
self.n_u = self.ocp.u.size()
self.n_x = self.ocp.x.size()
self.n_v = self.n_u * self.n_k + self.n_x * self.n_k
self.V = C.MX.sym("V", int(self.n_v), 1)
self.U, self.X = self.splitVariables(self.V)
uMin = C.vertcat([
self.ocp.variable(self.ocp.u[i].getName()).min.getValue()
for i in range(self.n_u)
]) / controlScaling
uMax = C.vertcat([
self.ocp.variable(self.ocp.u[i].getName()).max.getValue()
for i in range(self.n_u)
]) / controlScaling
UMIN = C.vertcat([uMin for k in range(self.n_k)])
UMAX = C.vertcat([uMax for k in range(self.n_k)])
xMin = C.vertcat([
self.ocp.variable(self.ocp.x[i].getName()).min.getValue()
for i in range(self.n_x)
]) / stateScaling
xMax = C.vertcat([
self.ocp.variable(self.ocp.x[i].getName()).max.getValue()
for i in range(self.n_x)
]) / stateScaling
XMIN = C.vertcat([xMin for k in range(self.n_k)])
XMAX = C.vertcat([xMax for k in range(self.n_k)])
if len(deltaUCons) > 0:
addDeltaUCons = True
deltaUCons = deltaUCons / self.controlScaling
else:
addDeltaUCons = False
pathIn = C.daeIn(x=ocp.x, z=ocp.z, p=ocp.u, t=ocp.t)
pathVarNames = [sv.getName() for sv in ocp.beq(ocp.path)]
pathScaling = C.vertcat([ocp.nominal(pv) for pv in pathVarNames])
pathS = C.substitute(
ocp.beq(ocp.beq(ocp.path)), C.vertcat([ocp.x, ocp.z, ocp.u]),
C.vertcat([
stateScaling * ocp.x, algStateScaling * ocp.z,
controlScaling * ocp.u
])) / pathScaling
pathConstraints = C.SXFunction(pathIn, [pathS])
pathMax = C.vertcat([
ocp.variable(pathVarNames[i]).max.getValue()
for i in range(ocp.path.size())
]) / pathScaling
pathMin = C.vertcat([
ocp.variable(pathVarNames[i]).min.getValue()
for i in range(ocp.path.size())
]) / pathScaling
pathConstraints.setOption("name", "PATH")
pathConstraints.init()
pathConstraints.setInput(xOpt, 'x')
pathConstraints.setInput([], 'z')
pathConstraints.setInput(uOpt, 'p')
pathConstraints.setInput(0, 't')
pathConstraints.evaluate()
pathOpt = pathConstraints.getOutput()
optimalValues = {}
print 'min <= (name,optimal,nominal) <= max'
for i in range(self.n_x):
print ocp.variable(
ocp.x[i].getName()).min.getValue(), ' <= (', ocp.x[i].getName(
), ',', xOpt[i] * stateScaling[i], ',', stateScaling[
i], ') <= ', ocp.variable(
ocp.x[i].getName()).max.getValue()
optimalValues[ocp.x[i].getName()] = xOpt[i] * stateScaling[i]
for i in range(self.n_u):
print ocp.variable(
ocp.u[i].getName()).min.getValue(), ' <= (', ocp.u[i].getName(
), ',', uOpt[i] * controlScaling[i], ',', controlScaling[
i], ') <= ', ocp.variable(
ocp.u[i].getName()).max.getValue()
if addDeltaUCons:
print -deltaUCons[i] * controlScaling[i], ' <= (Delta(', ocp.u[
i].getName(), ')/DTMPC,', 0, ',', controlScaling[
i], ') <= ', deltaUCons[i] * controlScaling[i]
optimalValues[ocp.u[i].getName()] = uOpt[i] * controlScaling[i]
for i in range(len(pathVarNames)):
print ocp.variable(pathVarNames[i]).min.getValue(
), ' <= (', pathVarNames[i], ',', pathOpt[i] * pathScaling[
i], ',', pathScaling[i], ') <= ', ocp.variable(
pathVarNames[i]).max.getValue()
optimalValues[pathVarNames[i]] = pathOpt[i] * pathScaling[i]
plotTags = [ocp.x[i].getName() for i in range(ocp.x.size())]
plotTags = plotTags + [ocp.u[i].getName() for i in range(ocp.u.size())]
plotTags = plotTags + [sv.getName() for sv in ocp.beq(ocp.path)]
self.plotTags = plotTags
self.optimalValues = optimalValues
# Constraint functions
g = []
g_min = []
g_max = []
self.XU0 = C.MX.sym("XU0", self.n_x + self.n_u, 1)
Z = self.XU0[0:self.n_x]
U0 = self.XU0[self.n_x:self.n_x + self.n_u]
# Build up a graph of integrator calls
obj = 0
zf = C.vertcat([
ocp.variable(ocp.z[k].getName()).start for k in range(ocp.z.size())
]) / algStateScaling
for k in range(self.n_k):
Z, QF, zf = C.integratorOut(
G(C.integratorIn(x0=Z, p=self.U[k], z0=zf)), "xf", "qf", "zf")
errU = self.U[k] - U0
obj = obj + QF + C.mul(C.mul(errU.T, controlCost), errU)
U0 = self.U[k]
# include MS constraints!
g.append(Z - self.X[k])
g_min.append(NP.zeros(self.n_x))
g_max.append(NP.zeros(self.n_x))
Z = self.X[k]
[pathCons] = pathConstraints.call(
C.daeIn(t=[], x=self.X[k], z=zf, p=self.U[k]))
g.append(pathCons) ## be carefull on giving all inputs
g_max.append(pathMax)
g_min.append(pathMin)
if addDeltaUCons:
g.append(errU)
g_max.append(deltaUCons * DT)
g_min.append(-deltaUCons * DT)
#errU = (self.U[-1]-uOpt)
#errX = self.X[-1]-xOpt
#obj = obj + finalStateCost*C.mul((errX).trans(),(errX))+C.mul(C.mul(errU.T,controlCost),errU)
self.obj = obj
### Constrains
g = C.vertcat(g)
nlp = C.MXFunction(C.nlpIn(x=self.V, p=self.XU0), C.nlpOut(f=obj, g=g))
nlp.init()
self.odeF = odeF
self.nlp = nlp
solver = C.NlpSolver('ipopt', nlp)
# remove the comment to implement the hessian
solver.setOption('hessian_approximation',
'limited-memory') # comment for exact hessian
solver.setOption('print_user_options', 'no')
solver.setOption("tol", self.IPOPT_tol) # IPOPT tolerance
solver.setOption("dual_inf_tol",
self.IPOPT_dual_inf_tol) # dual infeasibility
solver.setOption("constr_viol_tol",
self.IPOPT_constr_viol_tol) # primal infeasibility
solver.setOption("compl_inf_tol",
self.IPOPT_compl_inf_tol) # complementarity
# solver.setOption("acceptable_tol",0.01)
# solver.setOption("acceptable_obj_change_tol",1e-6)
# solver.setOption("acceptable_constr_viol_tol",1e-6)
solver.setOption("max_iter",
self.IPOPT_max_iter) # IPOPT maximum iterations
solver.setOption("print_level", self.IPOPT_print_level)
solver.setOption("max_cpu_time",
self.IPOPT_max_cpu_time) # IPOPT maximum iterations
solver.init()
### Variable Bounds and initial guess
solver.setInput(C.vertcat([UMIN, XMIN]), 'lbx') # u_L
solver.setInput(C.vertcat([UMAX, XMAX]), 'ubx') # u_U
solver.setInput(C.vertcat(g_min), 'lbg') # g_L
solver.setInput(C.vertcat(g_max), 'ubg') # g_U
self.solver = solver
u0N = C.vertcat([
self.ocp.variable(self.ocp.u[i].getName()).initialGuess.getValue()
for i in range(self.n_u)
]) / controlScaling
x0N = C.vertcat([
self.ocp.variable(self.ocp.x[i].getName()).initialGuess.getValue()
for i in range(self.n_x)
]) / stateScaling
USOL, XSOL = self.forwardSimulation(x0N, u0N)
self.USOL = USOL
self.XSOL = XSOL
def plotNLP(self, x0, DTplot=10, additionalplottags=None):
plotH = []
plotAdd = []
plotT = []
plotTags = self.plotTags
ocp = self.ocp
algStateScaling = self.algStateScaling
controlScaling = self.controlScaling
stateScaling = self.stateScaling
DT = self.DT
Z = x0 / self.stateScaling
odeF = self.odeF
xOpt = self.xOpt
uOpt = self.uOpt
C.Integrator.loadPlugin("idas")
G = C.Integrator("idas", odeF)
G.setOption("reltol", self.INTG_REL_TOL) #for CVODES and IDAS
G.setOption("abstol", self.INTG_ABS_TOL) #for CVODES and IDAS
G.setOption("max_multistep_order", 5) #for CVODES and IDAS
G.setOption("max_step_size", self.IDAS_MAX_STEP_SIZE) #for IDAS only
G.setOption("tf", DTplot)
G.init()
pathIn = C.daeIn(x=ocp.x, z=ocp.z, p=ocp.u, t=ocp.t)
if additionalplottags is None:
Config = ConfigParser.ConfigParser()
Config.read('config.ini')
additionalplottags = Config.get('MultipleShooting',
'additionalplottags')
additionalplottags = additionalplottags.split(',')
self.additionalplottags = additionalplottags
addTagScale = C.vertcat([ocp.nominal(pv) for pv in additionalplottags])
tagsFsx = C.substitute(
C.vertcat([ocp.beq(sv) for sv in additionalplottags]),
C.vertcat([ocp.x, ocp.z, ocp.u]),
C.vertcat([
stateScaling * ocp.x, algStateScaling * ocp.z,
controlScaling * ocp.u
]))
tagsF = C.SXFunction(pathIn, [tagsFsx])
tagsF.init()
tagsF.setInput(xOpt, 'x')
tagsF.setInput([], 'z')
tagsF.setInput(uOpt, 'p')
tagsF.setInput(0, 't')
tagsF.evaluate()
addTagsOpt = tagsF.getOutput()
for i in range(len(additionalplottags)):
self.optimalValues[additionalplottags[i]] = addTagsOpt[i]
sxPlotTags = C.vertcat([ocp.beq(tag) for tag in plotTags])
pathS = C.substitute(
sxPlotTags, C.vertcat([ocp.x, ocp.z, ocp.u]),
C.vertcat([
stateScaling * ocp.x, algStateScaling * ocp.z,
controlScaling * ocp.u
]))
pathF = C.SXFunction(pathIn, [pathS, tagsFsx])
pathF.init()
nPlot = NP.int(NP.round(self.DT / DTplot))
zf = C.vertcat([
ocp.variable(ocp.z[k].getName()).start for k in range(ocp.z.size())
]) / algStateScaling
for k in range(self.n_k):
try:
for jp in range(nPlot):
#Z,QF,zf = C.integratorOut(G(C.integratorIn(x0=Z,p=self.USOL[k],z0=zf)),"xf","qf","zf")
G.setInput(Z, 'x0')
G.setInput(self.USOL[k], 'p')
G.evaluate()
Z = G.getOutput('xf')
QF = G.getOutput('qf')
zf = G.getOutput('zf')
pathF.setInput(Z, 'x')
pathF.setInput(zf, 'z')
pathF.setInput(self.USOL[k], 'p')
t = k * DT + jp * DTplot
pathF.setInput(t, 't')
pathF.evaluate()
p = pathF.getOutput(0)
pAdd = pathF.getOutput(1)
plotH.append(p)
plotAdd.append(pAdd)
plotT.append(t)
Z = self.XSOL[k]
except:
print 'something bad happened', sys.exc_info()[0]
break
plotDic = {}
plotDic['t'] = plotT
for si in range(len(plotTags)):
plotDic[plotTags[si]] = [i[si] for i in plotH]
for si in range(len(additionalplottags)):
plotDic[additionalplottags[si]] = [i[si] for i in plotAdd]
self.plotDic = plotDic
def fwd_simulation(self,
dE_start,
condition,
detail=True,
reltol=1e-8,
abstol=1e-10,
DRX=False,
drc_opt={}):
TotalPressure = condition.TotalPressure
TotalFlow = condition.TotalFlow
Tem = condition.Temperature
tf = condition.SimulationTime
opts = {}
opts['tf'] = tf # Simulation time
opts['abstol'] = abstol
opts['reltol'] = reltol
opts['disable_internal_warnings'] = True
opts['max_num_steps'] = 1e8
if py == 2:
Fint = cas.Integrator('Fint', 'cvodes', self._dae_, opts)
elif py == 3:
Fint = cas.integrator('Fint', 'cvodes', self._dae_, opts)
if condition.InitCoverage == {}:
x0 = [0] * (self.nspe - 1) + [1]
else:
# Construct Coverage
x0 = [0] * (self.nspe - 1) + [1]
for spe, cov in condition.InitCoverage.items():
idx = get_index_species(spe, self.specieslist)
x0[idx - self.ngas] = cov
x0[-1] -= cov
# Partial Pressure
Pinlet = np.zeros(self.ngas)
for idx, spe in enumerate(self.specieslist):
if spe.phase == 'gaseous':
Pinlet[idx] = condition.PartialPressure[str(spe)] if str(
spe) in condition.PartialPressure.keys() else 0
P_dae = np.hstack([dE_start, Pinlet, Tem, TotalFlow])
F_sim = Fint(x0=x0, p=P_dae)
tor = {}
for idx, spe in enumerate(self.specieslist):
if spe.phase == 'gaseous':
tor[str(spe)] = float(F_sim['xf'][idx] -
Pinlet[idx] / TotalPressure * TotalFlow)
# Detailed Reaction network data
# Evaluate partial pressure and surface coverage
self.pressure_value = list(
(F_sim['xf'][:self.ngas] / TotalFlow * TotalPressure).full().T[0])
self.coverage_value = list(F_sim['xf'][self.ngas:].full().T[0])
# Evaluate Reaction Rate automatically save to Rate attribute
x = self._x
p = self._p
if py == 2:
rate_fxn = cas.SXFunction('rate_fxn', [x, p],
[self._rate, self._rfor, self._rrev])
rate_fxn.setInput(F_sim['xf'], 'i0')
rate_fxn.setInput(P_dae, 'i1')
rate_fxn.evaluate()
self.rate_value = {}
self.rate_value['rnet'] = rate_fxn.getOutput(
'o0').full().T[0].tolist()
self.rate_value['rfor'] = rate_fxn.getOutput(
'o1').full().T[0].tolist()
self.rate_value['rrev'] = rate_fxn.getOutput(
'o2').full().T[0].tolist()
# Evaluate Reaction Energy
ene_fxn = cas.SXFunction('ene_fxn', [x, p], [
self._reaction_energy_expression['activation'],
self._reaction_energy_expression['enthalpy']
])
ene_fxn.setInput(F_sim['xf'], 'i0')
ene_fxn.setInput(P_dae, 'i1')
ene_fxn.evaluate()
self.energy_value = {}
self.energy_value['activation'] = list(
ene_fxn.getOutput('o0').full().T[0])
self.energy_value['enthalpy'] = list(
ene_fxn.getOutput('o1').full().T[0])
# Evaluate Equilibrium Constant and Rate Constant
k_fxn = cas.SXFunction('k_fxn', [x, p],
[self._Keq, self._Qeq, self._kf, self._kr])
k_fxn.setInput(F_sim['xf'], 'i0')
k_fxn.setInput(P_dae, 'i1')
k_fxn.evaluate()
self.equil_rate_const_value = {}
self.equil_rate_const_value['Keq'] = list(
k_fxn.getOutput('o0').full().T[0])
self.equil_rate_const_value['Qeq'] = list(
k_fxn.getOutput('o1').full().T[0])
self.equil_rate_const_value['kf'] = list(
k_fxn.getOutput('o2').full().T[0])
self.equil_rate_const_value['kr'] = list(
k_fxn.getOutput('o3').full().T[0])
elif py == 3:
rate_fxn = cas.Function('rate_fxn', [x, p],
[self._rate, self._rfor, self._rrev])
outs = rate_fxn(F_sim['xf'], P_dae)
self.rate_value = {}
self.rate_value['rnet'] = outs[0].full().T[0].tolist()
self.rate_value['rfor'] = outs[1].full().T[0].tolist()
self.rate_value['rrev'] = outs[2].full().T[0].tolist()
# Evaluate Reaction Energy
ene_fxn = cas.Function('ene_fxn', [x, p], [
self._reaction_energy_expression['activation'],
self._reaction_energy_expression['enthalpy']
])
outs = ene_fxn(F_sim['xf'], P_dae)
self.energy_value = {}
self.energy_value['activation'] = list(outs[0].full().T[0])
self.energy_value['enthalpy'] = list(outs[1].full().T[0])
# Evaluate Equilibrium Constant and Rate Constant
k_fxn = cas.Function('k_fxn', [x, p],
[self._Keq, self._Qeq, self._kf, self._kr])
outs = k_fxn(F_sim['xf'], P_dae)
self.equil_rate_const_value = {}
self.equil_rate_const_value['Keq'] = list(outs[0].full().T[0])
self.equil_rate_const_value['Qeq'] = list(outs[1].full().T[0])
self.equil_rate_const_value['kf'] = list(outs[2].full().T[0])
self.equil_rate_const_value['kr'] = list(outs[3].full().T[0])
xrc, xtrc = [], []
# TODO: degree of rate control
if DRX:
delG = drc_opt.get('delG', 1)
ref_species = drc_opt.get('ref', 'H2(g)')
numer = drc_opt.get('numer', 'fwd')
tor0 = tor[ref_species]
if numer == 'ad':
opts = fwd_sensitivity_option(tf=tf, reltol=1e-8, abstol=1e-16)
Fint = cas.Integrator('Fint', 'cvodes', self._dae_, opts)
Pnlp = self._Pnlp
P_dae = cas.vertcat([Pnlp, Pinlet, Tem, TotalFlow])
F_sim = Fint(x0=x0, p=P_dae)
ii = [
ii for ii, spe in enumerate(self.specieslist)
if str(spe) == ref_species
][0]
tor_ad = F_sim['xf'][
ii] - Pinlet[ii] / TotalPressure * TotalFlow
# define the jacobian and MX function
jac = cas.jacobian(tor_ad, Pnlp)
# evaluate the jacobian
fjac = cas.MXFunction('fjac', [Pnlp], [jac])
xrc = fjac([np.copy(dE_start)])[0]
xrc = xrc / tor0 * (_const.Rg * Tem) / (-1000)
xrc = xrc.full()[0].tolist()[:len(self.dEa_index)]
for idx, j in enumerate(self.dEa_index):
dP = np.copy(dE_start)
dP[idx] += delG
# Partial Pressure
P_dae = np.hstack([dP, Pinlet, Tem, TotalFlow])
F_sim = Fint(x0=x0, p=P_dae)
for ii, spe in enumerate(self.specieslist):
if str(spe) == ref_species:
tor_p = float(F_sim['xf'][ii] -
Pinlet[ii] / TotalPressure * TotalFlow)
if numer == 'cent':
dP = np.copy(dE_start)
dP[idx] -= delG
# Partial Pressure
P_dae = np.hstack([dP, Pinlet, Tem, TotalFlow])
F_sim = Fint(x0=x0, p=P_dae)
for ii, spe in enumerate(self.specieslist):
if str(spe) == ref_species:
tor_n = float(F_sim['xf'][ii] - Pinlet[ii] /
TotalPressure * TotalFlow)
if numer == 'fwd':
xrc.append((tor_p - tor0) / tor0 / (-delG * 1000 /
(_const.Rg * Tem)))
# xrc.append((np.log(np.abs(tor_p)) - np.log(np.abs(tor0)))/(-delG * 1000 /(_const.Rg * Tem)))
if numer == 'cent':
xrc.append((tor_p - tor_n) / tor0 / (-2 * delG * 1000 /
(_const.Rg * Tem)))
# xrc.append((np.log(np.abs(tor_p)) - np.log(np.abs(tor_n)))/(-2 * delG * 1000 /(_const.Rg * Tem)))
# XTRC
for idx, j in enumerate(self.dBE_index):
spe = self.reactionlist[idx]
dP = np.copy(dE_start)
deltaE = np.zeros(self.nspe)
deltaE[j] += delG
# propagate through stoichiomatric
deltaEa = self.stoimat.dot(deltaE)
# dP[:len(self.dEa_index)] -= deltaEa
dP[len(self.dEa_index):] += deltaE[self.dBE_index]
# Partial Pressure
P_dae = np.hstack([dP, Pinlet, Tem, TotalFlow])
F_sim = Fint(x0=x0, p=P_dae)
for ii, spe in enumerate(self.specieslist):
if str(spe) == ref_species:
tor_p = float(F_sim['xf'][ii] -
Pinlet[ii] / TotalPressure * TotalFlow)
if numer == 'fwd':
xtrc.append((tor_p - tor0) / tor0 / (-delG * 1000 /
(_const.Rg * Tem)))
# xrc.append((np.log(np.abs(tor_p)) - np.log(np.abs(tor0)))/(-delG * 1000 /(_const.Rg * Tem)))
if numer == 'cent':
dP = np.copy(dE_start)
deltaE = np.zeros(self.nspe)
deltaE[j] -= delG
# propagate through stoichiomatric
deltaEa = self.stoimat.dot(deltaE)
# dP[:len(self.dEa_index)] -= deltaEa
dP[len(self.dEa_index):] += deltaE[self.dBE_index]
# Partial Pressure
P_dae = np.hstack([dP, Pinlet, Tem, TotalFlow])
F_sim = Fint(x0=x0, p=P_dae)
for ii, spe in enumerate(self.specieslist):
if str(spe) == ref_species:
tor_n = float(F_sim['xf'][ii] - Pinlet[ii] /
TotalPressure * TotalFlow)
xtrc.append((tor_p - tor_n) / tor0 / (-2 * delG * 1000 /
(_const.Rg * Tem)))
# RESULT
result = {}
result['pressure'] = self.pressure_value
result['coverage'] = self.coverage_value
result['rate'] = self.rate_value
result['energy'] = self.energy_value
result['equil_rate'] = self.equil_rate_const_value
result['xrc'] = xrc
result['xtrc'] = xtrc
self.xrc = xrc
return tor, result
def init(self, ocp, DT, measuremntsList):
measurementScaling = C.vertcat(
[ocp.variable(k).nominal for k in measuremntsList])
stateScaling = C.vertcat([
ocp.variable(ocp.x[k].getName()).nominal
for k in range(ocp.x.size())
])
algStateScaling = C.vertcat([
ocp.variable(ocp.z[k].getName()).nominal
for k in range(ocp.z.size())
])
controlScaling = C.vertcat([
ocp.variable(ocp.u[k].getName()).nominal
for k in range(ocp.u.size())
])
odeS = C.substitute(
ocp.ode(ocp.x), C.vertcat([ocp.x, ocp.z, ocp.u]),
C.vertcat([
stateScaling * ocp.x, algStateScaling * ocp.z,
controlScaling * ocp.u
])) / stateScaling
algS = C.substitute(
ocp.alg, C.vertcat([ocp.x, ocp.z, ocp.u]),
C.vertcat([
stateScaling * ocp.x, algStateScaling * ocp.z,
controlScaling * ocp.u
]))
sysIn = C.daeIn(x=ocp.x, z=ocp.z, p=ocp.u, t=ocp.t)
sysOut = C.daeOut(ode=odeS, alg=algS)
odeF = C.SXFunction(sysIn, sysOut)
odeF.init()
C.Integrator.loadPlugin("idas")
G = C.Integrator("idas", odeF)
G.setOption("reltol", 1e-8) #for IDAS
G.setOption("abstol", 1e-8) #for IDAS
G.setOption("max_multistep_order", 5) #for IDAS
G.setOption("tf", DT)
G.init()
mSX = C.vertcat([
ocp.variable(measuremntsList[k]).beq
for k in range(len(measuremntsList))
])
mSX = C.substitute(
mSX, C.vertcat([ocp.x, ocp.z, ocp.u]),
C.vertcat([
stateScaling * ocp.x, algStateScaling * ocp.z,
controlScaling * ocp.u
])) / measurementScaling
mSXF = C.SXFunction(sysIn, [mSX])
mSXF.init()
self.measurementScaling = measurementScaling
self.stateScaling = stateScaling
self.algStateScaling = algStateScaling
self.controlScaling = controlScaling
self.ocp = ocp
self.DT = DT
self.measurmentList = measuremntsList
self.mSXF = mSXF
self.G = G
self.z0 = C.vertcat([
ocp.variable(ocp.z[k].getName()).start for k in range(ocp.z.size())
]) / algStateScaling
self.x0 = C.vertcat([
ocp.variable(ocp.x[k].getName()).initialGuess.getValue()
for k in range(ocp.x.size())
]) / stateScaling
def find_prc(self, res=100, num_cycles=20):
""" Function to calculate the phase response curve with
specified resolution """
# Make sure the lc object exists
if not hasattr(self, 'lc'): self.limit_cycle()
# Get a state that is not at a local max/min (0 should be at
# max)
state_ind = 1
while np.abs(self.dydt(self.y0)[state_ind]) < 1E-5: state_ind += 1
integrator = cs.Integrator('cvodes',self.model)
integrator.setOption("abstol", self.intoptions['sensabstol'])
integrator.setOption("reltol", self.intoptions['sensreltol'])
integrator.setOption("max_num_steps",
self.intoptions['sensmaxnumsteps'])
integrator.setOption("sensitivity_method",
self.intoptions['sensmethod']);
integrator.setOption("t0", 0)
integrator.setOption("tf", num_cycles*self.T)
#integrator.setOption("numeric_jacobian", True)
integrator.setOption("fsens_err_con", 1)
integrator.setOption("fsens_abstol", self.intoptions['sensabstol'])
integrator.setOption("fsens_reltol", self.intoptions['sensreltol'])
integrator.init()
seed = np.zeros(self.neq)
seed[state_ind] = 1.
integrator.setInput(self.y0, cs.INTEGRATOR_X0)
integrator.setInput(self.param, cs.INTEGRATOR_P)
#adjseed = (seed, cs.INTEGRATOR_XF)
integrator.evaluate()#0, 1)
monodromy = integrator.jacobian(cs.INTEGRATOR_X0,cs.INTEGRATOR_XF)
monodromy.init()
monodromy.setInput(self.y0,"x0")
monodromy.setInput(self.param,"p")
monodromy.evaluate()
# initial state is Kcross(T,T) = I
adjsens = monodromy.getOutput().toArray().T.dot(seed)
from scipy.integrate import odeint
def adj_func(y, t):
""" t will increase, trace limit cycle backwards through -t. y
is the vector of adjoint sensitivities """
jac = self.dfdy(self.lc((-t)%self.T))
return y.dot(jac)
seed = adjsens
self.prc_ts = np.linspace(0, self.T, res)
P = odeint(adj_func, seed, self.prc_ts)[::-1] # Adjoint matrix at t
self.sPRC = self._t_to_phi(P/self.dydt(self.y0)[state_ind])
dfdp = np.array([self.dfdp(self.lc(t)) for t in self.prc_ts])
# Must rescale f to \hat{f}, inverse of rescaling t
self.pPRC = self._t_to_phi(
np.array([self.sPRC[i].dot(self._phi_to_t(dfdp[i]))
for i in xrange(len(self.sPRC))])
)
self.rel_pPRC = self.pPRC*np.array(self.param)
# Create interpolation object for the state phase response curve
self.sPRC_interp = self.interp_sol(self.prc_ts, self.sPRC.T) #phi units
self.pPRC_interp = self.interp_sol(self.prc_ts, self.pPRC.T) #phi units
def evidence_construct(self,
conditionlist,
evidence_info,
sensitivity=True):
# simulation option
reltol = evidence_info.get('reltol', 1e-6)
abstol = evidence_info.get('abstol', 1e-10)
# error value
err_type = evidence_info['type']
err = evidence_info['err']
lowSurf = evidence_info.get('lowSurf', 1e4)
lowSurf_thres = evidence_info.get('lowSurf_thres', 1e-5)
cov_err = evidence_info.get('cov_err', 0.05)
# Initialize simulator
Pnlp = self._Pnlp
if sensitivity:
# opts = fwd_sensitivity_option(reltol=reltol, adjtol=adjtol, fwdtol=fwdtol)
opts = fwd_sensitivity_option()
else:
opts = fwd_NoSensitivity_option(reltol=reltol, abstol=abstol)
print(opts)
Fint = cas.Integrator('Fint', 'cvodes', self._dae_, opts)
evidence = 0
for condition in conditionlist:
TotalPressure = condition.TotalPressure
TotalFlow = condition.TotalFlow
Tem = condition.Temperature
if condition.InitCoverage == {}:
x0 = [0] * (self.nspe - 1) + [1]
else:
# Construct Coverage
x0 = [0] * (self.nspe - 1) + [1]
for spe, cov in condition.InitCoverage.items():
idx = get_index_species(spe, self.specieslist)
x0[idx - self.ngas] = cov
x0[-1] -= cov
# construct initial partial pressure
Pinlet = np.zeros(self.ngas)
for idx, spe in enumerate(self.specieslist):
if spe.phase == 'gaseous':
Pinlet[idx] = condition.PartialPressure[str(spe)] if str(
spe) in condition.PartialPressure.keys() else 0
# run simulation
P_dae = cas.vertcat([Pnlp, Pinlet, Tem, TotalFlow])
F_sim = Fint(x0=x0, p=P_dae)
for idx, spe in enumerate(self.specieslist):
if spe.phase == 'gaseous':
# construct evidence with turnover frequency
tor = F_sim['xf'][
idx] - Pinlet[idx] / TotalPressure * TotalFlow
if str(spe) in condition.TurnOverFrequency.keys():
exp_tor = condition.TurnOverFrequency[str(spe)]
if err_type == 'abs' or abs(exp_tor) <= lowSurf_thres:
dev = tor - exp_tor
elif err_type == 'rel':
dev = 1 - tor / exp_tor
elif err_type == 'log':
dev = cas.log(tor / exp_tor)
else:
pass
# if abs(exp_tor) <= lowSurf_thres:
# evidence += (dev * dev) * lowSurf
# else:
evidence += (dev * dev) / err**2
# if spe.phase == 'surface':
# cov = F_sim['xf'][idx]
# if str(spe) in condition.Coverage.keys():
# exp_cov = condition.Coverage[str(spe)]
# dev = cas.log(cov / exp_cov)
# evidence += (dev * dev) / cov_err**2
self._evidence_ = evidence
return evidence
def run_simulation(self, \
x0 = None, tsim = None, usim = None, psim = None, method = "rk"):
r'''
:param x0: initial value for the states
:math:`x_0 \in \mathbb{R}^{n_x}`
:type x0: list, numpy,ndarray, casadi.DMatrix
:param tsim: optional, switching time points for the controls
:math:`t_{sim} \in \mathbb{R}^{L}` to be used for the
simulation
:type tsim: list, numpy,ndarray, casadi.DMatrix
:param usim: optional, control values
:math:`u_{sim} \in \mathbb{R}^{n_u \times L}`
to be used for the simulation
:type usim: list, numpy,ndarray, casadi.DMatrix
:param psim: optional, parameter set
:math:`p_{sim} \in \mathbb{R}^{n_p}`
to be used for the simulation
:type psim: list, numpy,ndarray, casadi.DMatrix
:param method: optional, CasADi integrator to be used for the
simulation
:type method: str
This function performs a simulation of the system for a given
parameter set :math:`p_{sim}`, starting from a user-provided initial
value for the states :math:`x_0`. If the argument ``psim`` is not
specified, the estimated parameter set :math:`\hat{p}` is used.
For this, a parameter
estimation using :func:`run_parameter_estimation()` has to be
done beforehand, of course.
By default, the switching time points for
the controls :math:`t_u` and the corresponding controls
:math:`u_N` will be used for simulation. If desired, other time points
:math:`t_{sim}` and corresponding controls :math:`u_{sim}`
can be passed to the function.
For the moment, the function can only be used for systems of type
:class:`pecas.systems.ExplODE`.
'''
intro.pecas_intro()
print('\n' + 27 * '-' + \
' PECas system simulation ' + 26 * '-')
print('\nPerforming system simulation, this might take some time ...')
if not type(self.pesetup.system) is systems.ExplODE:
raise NotImplementedError("Until now, this function can only " + \
"be used for systems of type ExplODE.")
if x0 == None:
raise ValueError("You have to provide an initial value x0 " + \
"to run the simulation.")
x0 = np.squeeze(np.asarray(x0))
if np.atleast_1d(x0).shape[0] != self.pesetup.nx:
raise ValueError("Wrong dimension for initial value x0.")
if tsim == None:
tsim = self.pesetup.tu
if usim == None:
usim = self.pesetup.uN
if psim == None:
try:
psim = self.phat
except AttributeError:
errmsg = '''
You have to either perform a parameter estimation beforehand to obtain a
parameter set that can be used for simulation, or you have to provide a
parameter set in the argument psim.
'''
raise AttributeError(errmsg)
else:
if not np.atleast_1d(np.squeeze(psim)).shape[0] == self.pesetup.np:
raise ValueError("Wrong dimension for parameter set psim.")
fp = ca.MXFunction("fp", \
[self.pesetup.system.t, self.pesetup.system.u, \
self.pesetup.system.x, self.pesetup.system.eps_e, \
self.pesetup.system.eps_u, self.pesetup.system.p], \
[self.pesetup.system.f])
fpeval = fp([\
self.pesetup.system.t, self.pesetup.system.u, \
self.pesetup.system.x, np.zeros(self.pesetup.neps_e), \
np.zeros(self.pesetup.neps_u), psim])[0]
fsim = ca.MXFunction("fsim", \
ca.daeIn(t = self.pesetup.system.t, \
x = self.pesetup.system.x, \
p = self.pesetup.system.u), \
ca.daeOut(ode = fpeval))
Xsim = []
Xsim.append(x0)
u0 = ca.DMatrix()
for k, e in enumerate(tsim[:-1]):
try:
integrator = ca.Integrator("integrator", method, \
fsim, {"t0": e, "tf": tsim[k+1]})
except RuntimeError as err:
errmsg = '''
It seems like you want to use an integration method that is not currently
supported by CasADi. Please refer to the CasADi documentation for a list
of supported integrators, or use the default RK4-method by not setting the
method-argument of the function.
'''
raise RuntimeError(errmsg)
if not self.pesetup.nu == 0:
u0 = usim[:, k]
Xk_end = itemgetter('xf')(integrator({'x0': x0, 'p': u0}))
Xsim.append(Xk_end)
x0 = Xk_end
self.Xsim = ca.horzcat(Xsim)
print( \
'''System simulation finished.''')
] )
# ca.mul( [ x_err.T, cost_mat, x_err ] )
dae = ca.SXFunction('dae', ca.daeIn(x=x, p=u, t=t), ca.daeOut(ode=ode))
# Create an integrator
opts = {'tf': tf / nk} # final time
if coll:
opts['number_of_finite_elements'] = 5
opts['interpolation_order'] = 5
opts['collocation_scheme'] = 'legendre'
opts['implicit_solver'] = 'kinsol'
opts['implicit_solver_options'] = {'linear_solver': 'csparse'}
opts['expand_f'] = True
integrator = ca.Integrator('integrator', 'oldcollocation', dae, opts)
else:
opts['abstol'] = 1e-1 # tolerance
opts['reltol'] = 1e-1 # tolerance
# opts['steps_per_checkpoint'] = 1000
opts['quad_err_con'] = True
opts['fsens_err_con'] = True
opts['t0'] = 0.
opts['tf'] = tf
integrator = ca.Integrator('integrator', 'cvodes', dae, opts)
integrator.setInput(x0, 'x0')
integrator.setInput(0, 'p')
integrator.evaluate()
integrator.reset()
nk = 20 # Control discretization
tf = 10.0 # End time
# Declare variables (use scalar graph)
u = ca.SX.sym("u") # control
x = ca.SX.sym("x", 2) # states
# ODE right hand side and quadratures
xdot = ca.vertcat([(1 - x[1] * x[1]) * x[0] - x[1] + u, x[0]])
qdot = x[0] * x[0] + x[1] * x[1] + u * u
# DAE residual function
dae = ca.SXFunction("dae", ca.daeIn(x=x, p=u), ca.daeOut(ode=xdot, quad=qdot))
# Create an integrator
integrator = ca.Integrator("integrator", "cvodes", dae, {"tf": tf / nk})
# All controls (use matrix graph)
x = ca.MX.sym("x", nk) # nk-by-1 symbolic variable
U = ca.vertsplit(x) # cheaper than x[0], x[1], ...
# The initial state (x_0=0, x_1=1)
X = ca.MX([0, 1])
# Objective function
f = 0
# Build a graph of integrator calls
for k in range(nk):
X, QF = itemgetter('xf', 'qf')(integrator({'x0': X, 'p': U[k]}))
f += QF