def solveBVP_casadi(self):
"""
Uses casadi's interface to sundials to solve the boundary value
problem using a single-shooting method with automatic differen-
tiation.
"""
# Here we create and initialize the integrator SXFunction
self.bvpint = cs.CVodesIntegrator(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.msym("V",self.NEQ+1)
y0 = V[:-1]
T = V[-1]
t = cs.msym('t')
param = cs.vertcat([self.paramset, 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]
obj = (yf - y0)**2
obj.append(fout[0])
F = cs.MXFunction([V],[obj])
F.init()
solver = cs.KinsolSolver(F)
solver.setOption('abstol',self.intoptions['bvp_ftol'])
solver.setOption('ad_mode', "forward")
solver.setOption('strategy','linesearch')
solver.setOption('numeric_jacobian', True)
solver.setOption('exact_jacobian', False)
solver.setOption('pretype', 'both')
solver.setOption('use_preconditioner', True)
solver.setOption('numeric_hessian', True)
solver.setOption('constraints', (2,)*(self.NEQ+1))
solver.setOption('verbose', False)
solver.setOption('sparse', False)
solver.setOption('linear_solver', 'dense')
solver.init()
solver.output().set(self.y0)
solver.solve()
self.y0 = solver.output().toArray().squeeze()
def __init__(self,dae,nk):
self.dae = dae
self.nk = nk
self._gaussNewtonObjF = []
mapSize = len(self.dae.xNames())*(self.nk+1) + len(self.dae.pNames())
V = C.msym('dvs',mapSize)
self._dvMap = nmheMaps.VectorizedReadOnlyNmheMap(self.dae,self.nk,V)
self._boundMap = nmheMaps.WriteableNmheMap(self.dae,self.nk)
self._guessMap = nmheMaps.WriteableNmheMap(self.dae,self.nk)
self._U = C.msym('u',self.nk,len(self.dae.uNames()))
self._outputMapGenerator = nmheMaps.NmheOutputMapGenerator(self,self._U)
self._outputMap = nmheMaps.NmheOutputMap(self._outputMapGenerator, self._dvMap.vectorize(), self._U)
self._constraints = Constraints()
def __init__(self,dae,nk):
self.dae = dae
self.nk = nk
self._gaussNewtonObjF = []
mapSize = len(self.dae.xNames())*(self.nk+1) + len(self.dae.pNames())
V = C.msym('dvs',mapSize)
self._dvMap = nmheMaps.VectorizedReadOnlyNmheMap(self.dae,self.nk,V)
self._boundMap = nmheMaps.WriteableNmheMap(self.dae,self.nk)
self._guessMap = nmheMaps.WriteableNmheMap(self.dae,self.nk)
self._U = C.msym('u',self.nk,len(self.dae.uNames()))
self._outputMapGenerator = nmheMaps.NmheOutputMapGenerator(self,self._U)
self._outputMap = nmheMaps.NmheOutputMap(self._outputMapGenerator, self._dvMap.vectorize(), self._U)
self._constraints = Constraints()
def __init__(self, dae, nSteps):
# check inputs
assert(isinstance(dae, Dae))
assert(isinstance(nSteps, int))
# make sure dae has everything
assert(hasattr(dae,'_odeRes'))
assert(hasattr(dae,'_algRes'))
assert(hasattr(dae,'stateDotDummy'))
self.dae = dae
self.dae._freeze('MultipleShootingStage(dae)')
# set up design vars
self.nSteps = nSteps
self.states = C.msym("x" ,self.nStates(),self.nSteps)
self.actions = C.msym("u",self.nActions(),self.nSteps)
self.params = C.msym("p",self.nParams())
# self._dvs = C.msym("dv",self.nStates()*self.nSteps+self.nActions()*self.nSteps+self.nParams())
#
# numXVars = self.nStates()*self.nSteps
# numUVars = self.nActions()*self.nSteps
# numPVars = self.nParams()
#
# self.states = C.reshape(self._dvs[:numXVars], [self.nStates(), self.nSteps])
# self.actions = C.reshape(self._dvs[numXVars:numXVars+numUVars], [self.nActions(), self.nSteps])
# self.params = self._dvs[numXVars+numUVars:]
#
# assert( self.states.size() == numXVars )
# assert( self.actions.size() == numUVars )
# assert( self.params.size() == numPVars )
# set up interface
self._constraints = Constraints()
self._bounds = Bounds(self.dae._xNames, self.dae._uNames, self.dae._pNames, self.nSteps)
self._initialGuess = InitialGuess(self.dae._xNames, self.dae._uNames, self.dae._pNames, self.nSteps)
self._designVars = DesignVars((self.dae._xNames,self.states),
(self.dae._uNames,self.actions),
(self.dae._pNames,self.params),
self.nSteps)
def __init__(self, dae, nSteps):
# check inputs
assert isinstance(dae, Dae)
assert isinstance(nSteps, int)
# make sure dae has everything
assert hasattr(dae, '_residual')
self.dae = dae
self.dae._freeze('MultipleShootingStage(dae)')
# set up design vars
self.nSteps = nSteps
self.states = C.msym("x", self.nStates(), self.nSteps)
self.actions = C.msym("u", self.nActions(), self.nSteps)
self.params = C.msym("p", self.nParams())
# self._dvs = C.msym("dv",self.nStates()*self.nSteps+self.nActions()*self.nSteps+self.nParams())
#
# numXVars = self.nStates()*self.nSteps
# numUVars = self.nActions()*self.nSteps
# numPVars = self.nParams()
#
# self.states = C.reshape(self._dvs[:numXVars], [self.nStates(), self.nSteps])
# self.actions = C.reshape(self._dvs[numXVars:numXVars+numUVars], [self.nActions(), self.nSteps])
# self.params = self._dvs[numXVars+numUVars:]
#
# assert self.states.size() == numXVars
# assert self.actions.size() == numUVars
# assert self.params.size() == numPVars
# set up interface
self._constraints = Constraints()
self._bounds = Bounds(self.dae._xNames, self.dae._uNames,
self.dae._pNames, self.nSteps)
self._initialGuess = InitialGuess(self.dae._xNames, self.dae._uNames,
self.dae._pNames, self.nSteps)
self._designVars = DesignVars(
(self.dae._xNames, self.states), (self.dae._uNames, self.actions),
(self.dae._pNames, self.params), self.nSteps)
def mkParallelG():
gs = [C.MXFunction([self.getDesignVars()],[gg]) for gg in self._constraints._g]
for gg in gs:
gg.init()
pg = C.Parallelizer(gs)
# pg.setOption("parallelization","openmp")
pg.setOption("parallelization","serial")
# pg.setOption("parallelization","expand")
pg.init()
dvsDummy = C.msym('dvs',(self.nStates()+self.nActions())*self.nSteps+self.nParams())
g_ = C.MXFunction([dvsDummy],[C.veccat(pg.call([dvsDummy]*len(gs)))])
g_.init()
return g_
def mkParallelG():
gs = [C.MXFunction([self.getDesignVars()],[gg]) for gg in self._constraints._g]
for gg in gs:
gg.init()
pg = C.Parallelizer(gs)
# pg.setOption("parallelization","openmp")
pg.setOption("parallelization","serial")
# pg.setOption("parallelization","expand")
pg.init()
dvsDummy = C.msym('dvs',(self.nStates()+self.nActions())*self.nSteps+self.nParams())
g_ = C.MXFunction([dvsDummy],[C.veccat(pg.call([dvsDummy]*len(gs)))])
g_.init()
return g_
def inverse_parameterization(R, parameterizationFunction):
angle1 = ssym('angle1')
angle2 = ssym('angle2')
angle3 = ssym('angle3')
Restimated = parameterizationFunction(angle1,angle2,angle3)
E = R - Restimated;
e = casadi.sumAll(E*E)
f = SXFunction([casadi.vertcat([angle1,angle2,angle3])], [e])
f.init()
anglerange = numpy.linspace(-1*numpy.pi,1*numpy.pi,25)
best_eTemp = 9999999999999
best_angle1 = numpy.nan
best_angle2 = numpy.nan
best_angle3 = numpy.nan
for i in xrange(len(anglerange)):
for j in xrange(len(anglerange)):
for k in xrange(len(anglerange)):
r = anglerange[i]
p = anglerange[j]
y = anglerange[k]
f.setInput([r,p,y])
f.evaluate()
eTemp = f.output(0)
if eTemp<best_eTemp:
best_eTemp = eTemp
best_angle1 = r
best_angle2 = p
best_angle3 = y
if 0:
V = msym("V",(3,1))
fval = f.call([V])
fmx = MXFunction([V],fval)
nlp_solver = IpoptSolver(fmx)
else:
nlp_solver = IpoptSolver(f)
nlp_solver.setOption('generate_hessian',True)
nlp_solver.setOption('expand_f',True)
nlp_solver.setOption('expand_g',True)
nlp_solver.init()
nlp_solver.setInput([best_angle1,best_angle2,best_angle3],NLP_X_INIT)
nlp_solver.solve()
sol = nlp_solver.output(NLP_X_OPT).toArray()
sol = nlp_solver.output(NLP_X_OPT).toArray()
return sol
def __init__(self, dae, nk=None, nicp=1, deg=4, collPoly='RADAU'):
assert nk is not None
assert isinstance(dae, Dae)
self.dae = dae
self.nk = nk
self.nicp = nicp
self.deg = deg
self.collPoly = collPoly
self._bounds = BoundsMap(self,"bounds")
self._guess = collmaps.WriteableCollMap(self,"guess")
self._constraints = Constraints()
# setup NLP variables
self._dvMap = collmaps.VectorizedReadOnlyCollMap(self,"design var map",CS.msym("V",self.getNV()))
# quadratures
self._quadratureManager = collmaps.QuadratureManager(self)
def _bvp_setup(self):
""" Set up the casadi ipopt solver for the bvp solution """
# Define some variables
deg = self.deg
nk = self.nk
NV = nk * (deg + 1) * self.NEQ
# NLP variable vector
V = cs.msym("V", NV)
XD = np.resize(np.array([], dtype=cs.MX), (nk, deg + 1))
P = cs.msym("P", self.NP * self.nk)
PK = P.reshape((self.nk, self.NP))
offset = 0
for k in range(nk):
for j in range(deg + 1):
XD[k][j] = V[offset:offset + self.NEQ]
offset += self.NEQ
# Constraint function for the NLP
g = []
lbg = []
ubg = []
# For all finite elements
for k in range(nk):
# For all collocation points
for j in range(1, deg + 1):
# Get an expression for the state derivative at the
# collocation point
xp_jk = 0
for j2 in range(deg + 1):
# get the time derivative of the differential states
# (eq 10.19b)
xp_jk += self.coll_setup_dict['C'][j2][j] * XD[k][j2]
# Generate parameter set, accounting for variable
#
# Add collocation equations to the NLP
[fk] = self.rfmod.call(
[0., xp_jk / self.h, XD[k][j], PK[k, :].T])
# impose system dynamics (for the differential states
# (eq
# 10.19b))
g += [fk[:self.NEQ]]
lbg.append(np.zeros(self.NEQ)) # equality constraints
ubg.append(np.zeros(self.NEQ)) # equality constraints
# Get an expression for the state at the end of the finite
# element
xf_k = 0
for j in range(deg + 1):
xf_k += self.coll_setup_dict['D'][j] * XD[k][j]
# Add continuity equation to NLP
# End = Beginning of next
if k + 1 != nk:
g += [XD[k + 1][0] - xf_k]
# At the last segment, periodicity constraints
else:
g += [XD[0][0] - xf_k]
lbg.append(np.zeros(self.NEQ))
ubg.append(np.zeros(self.NEQ))
# Nonlinear constraint function
gfcn = cs.MXFunction([V, P], [cs.vertcat(g)])
# Objective function (periodicity)
ofcn = cs.MXFunction([V, P], [cs.sumAll(g[-1]**2)])
## ----
## SOLVE THE NLP
## ----
# Allocate an NLP solver
self.solver = cs.IpoptSolver(ofcn, gfcn)
# Set options
self.solver.setOption("expand_f", True)
self.solver.setOption("expand_g", True)
self.solver.setOption("generate_hessian", True)
self.solver.setOption("max_iter", 1000)
self.solver.setOption("tol", self.int_opt['bvp_tol'])
self.solver.setOption("constr_viol_tol",
self.int_opt['bvp_constr_tol'])
self.solver.setOption("linear_solver",
self.int_opt['bvp_linear_solver'])
self.solver.setOption('parametric', True)
self.solver.setOption('print_level', self.int_opt['bvp_print_level'])
# initialize the self.solver
self.solver.init()
self.lbg = lbg
self.ubg = ubg
self.need_bvp_setup = False
def CollocationSetup(self, warmstart=False):
"""
Sets up NLP for collocation solution. Constructs initial guess
arrays, constructs constraint and objective functions, and
otherwise passes arguments to the correct places. This looks
really inefficient and is likely unneccessary to run multiple
times for repeated runs with new data. Not sure how much time it
takes compared to the NLP solution.
Run immediately before CollocationSolve.
"""
# Dimensions of the problem
nx = self.NVAR # total number of states
ndiff = nx # number of differential states
nalg = 0 # number of algebraic states
nu = 0 # number of controls
# Collocated variables
NXD = self.NICP * self.NK * (self.DEG +
1) * ndiff # differential states
NXA = self.NICP * self.NK * self.DEG * nalg # algebraic states
NU = self.NK * nu # Parametrized controls
NV = NXD + NXA + NU + self.NP + self.NMP # Total variables
self.NV = NV
# NLP variable vector
V = cs.msym("V", NV)
# All variables with bounds and initial guess
vars_lb = np.zeros(NV)
vars_ub = np.zeros(NV)
vars_init = np.zeros(NV)
offset = 0
#
# Split NLP vector into useable slices
#
# Get the parameters
P = V[offset:offset + self.NP]
vars_init[offset:offset + self.NP] = self.NLPdata['p_init']
vars_lb[offset:offset + self.NP] = self.NLPdata['p_min']
vars_ub[offset:offset + self.NP] = self.NLPdata['p_max']
offset += self.NP # indexing variable
# Get collocated states and parametrized control
XD = np.resize(np.array([], dtype=cs.MX),
(self.NK, self.NICP, self.DEG + 1))
# NB: same name as above
XA = np.resize(np.array([], dtype=cs.MX),
(self.NK, self.NICP, self.DEG))
# NB: same name as above
U = np.resize(np.array([], dtype=cs.MX), self.NK)
# Prepare the starting data matrix vars_init, vars_ub, and
# vars_lb, by looping over finite elements, states, etc. Also
# groups the variables in the large unknown vector V into XD and
# XA(unused) for later indexing
for k in range(self.NK):
# Collocated states
for i in range(self.NICP):
#
for j in range(self.DEG + 1):
# Get the expression for the state vector
XD[k][i][j] = V[offset:offset + ndiff]
if j != 0:
XA[k][i][j - 1] = V[offset + ndiff:offset + ndiff +
nalg]
# Add the initial condition
index = (self.DEG + 1) * (self.NICP * k + i) + j
if k == 0 and j == 0 and i == 0:
vars_init[offset:offset+ndiff] = \
self.NLPdata['xD_init'][index,:]
vars_lb[offset:offset+ndiff] = \
self.NLPdata['xDi_min']
vars_ub[offset:offset+ndiff] = \
self.NLPdata['xDi_max']
offset += ndiff
else:
if j != 0:
vars_init[offset:offset+nx] = \
np.append(self.NLPdata['xD_init'][index,:],
self.NLPdata['xA_init'][index,:])
vars_lb[offset:offset+nx] = \
np.append(self.NLPdata['xD_min'],
self.NLPdata['xA_min'])
vars_ub[offset:offset+nx] = \
np.append(self.NLPdata['xD_max'],
self.NLPdata['xA_max'])
offset += nx
else:
vars_init[offset:offset+ndiff] = \
self.NLPdata['xD_init'][index,:]
vars_lb[offset:offset+ndiff] = \
self.NLPdata['xD_min']
vars_ub[offset:offset+ndiff] = \
self.NLPdata['xD_max']
offset += ndiff
# Parametrized controls (unused here)
U[k] = V[offset:offset + nu]
# Attach these initial conditions to external dictionary
self.NLPdata['v_init'] = vars_init
self.NLPdata['v_ub'] = vars_ub
self.NLPdata['v_lb'] = vars_lb
# Setting up the constraint function for the NLP. Over each
# collocated state, ensure continuitity and system dynamics
g = []
lbg = []
ubg = []
# For all finite elements
for k in range(self.NK):
for i in range(self.NICP):
# For all collocation points
for j in range(1, self.DEG + 1):
# Get an expression for the state derivative
# at the collocation point
xp_jk = 0
for j2 in range(self.DEG + 1):
# get the time derivative of the differential
# states (eq 10.19b)
xp_jk += self.C[j2][j] * XD[k][i][j2]
# Add collocation equations to the NLP
[fk] = self.rfmod.call([
0., xp_jk / self.h, XD[k][i][j], XA[k][i][j - 1], U[k],
P
])
# impose system dynamics (for the differential
# states (eq 10.19b))
g += [fk[:ndiff]]
lbg.append(np.zeros(ndiff)) # equality constraints
ubg.append(np.zeros(ndiff)) # equality constraints
# impose system dynamics (for the algebraic states
# (eq 10.19b)) (unused)
g += [fk[ndiff:]]
lbg.append(np.zeros(nalg)) # equality constraints
ubg.append(np.zeros(nalg)) # equality constraints
# Get an expression for the state at the end of the finite
# element
xf_k = 0
for j in range(self.DEG + 1):
xf_k += self.D[j] * XD[k][i][j]
# if i==self.NICP-1:
# Add continuity equation to NLP
if k + 1 != self.NK: # End = Beginning of next
g += [XD[k + 1][0][0] - xf_k]
lbg.append(-self.NLPdata['CONtol'] * np.ones(ndiff))
ubg.append(self.NLPdata['CONtol'] * np.ones(ndiff))
else: # At the last segment
# Periodicity constraints (only for NEQ)
g += [XD[0][0][0][:self.NEQ] - xf_k[:self.NEQ]]
lbg.append(-self.NLPdata['CONtol'] * np.ones(self.NEQ))
ubg.append(self.NLPdata['CONtol'] * np.ones(self.NEQ))
# else:
# g += [XD[k][i+1][0] - xf_k]
# Flatten contraint arrays for last addition
lbg = np.concatenate(lbg).tolist()
ubg = np.concatenate(ubg).tolist()
# Constraint to protect against fixed point solutions
if self.NLPdata['FPgaurd'] is True:
fout = self.model.call(
cs.daeIn(t=self.tgrid[0],
x=XD[0, 0, 0][:self.NEQ],
p=V[:self.NP]))[0]
g += [cs.MX(cs.sumAll(fout**2))]
lbg.append(np.array(self.NLPdata['FPTOL']))
ubg.append(np.array(cs.inf))
elif self.NLPdata['FPgaurd'] is 'all':
fout = self.model.call(
cs.daeIn(t=self.tgrid[0],
x=XD[0, 0, 0][:self.NEQ],
p=V[:self.NP]))[0]
g += [cs.MX(fout**2)]
lbg += [self.NLPdata['FPTOL']] * self.NEQ
ubg += [cs.inf] * self.NEQ
# Nonlinear constraint function
gfcn = cs.MXFunction([V], [cs.vertcat(g)])
# Minimize derivative of first state variable at t=0
xp_0 = 0
for j in range(self.NLPdata['DEG'] + 1):
# get the time derivative of the differential
# states (eq 10.19b)
xp_0 += self.C[j][0] * XD[0][j][0]
obj = xp_0
ofcn = cs.MXFunction([V], [obj])
self.CollocationSolver = cs.IpoptSolver(ofcn, gfcn)
for opt, val in self.IpoptOpts.iteritems():
self.CollocationSolver.setOption(opt, val)
self.CollocationSolver.setOption('obj_scaling_factor', len(vars_init))
if warmstart:
self.CollocationSolver.setOption('warm_start_init_point', 'yes')
# initialize the self.CollocationSolver
self.CollocationSolver.init()
# Initial condition
self.CollocationSolver.setInput(vars_init, cs.NLP_X_INIT)
# Bounds on x
self.CollocationSolver.setInput(vars_lb, cs.NLP_LBX)
self.CollocationSolver.setInput(vars_ub, cs.NLP_UBX)
# Bounds on g
self.CollocationSolver.setInput(np.array(lbg), cs.NLP_LBG)
self.CollocationSolver.setInput(np.array(ubg), cs.NLP_UBG)
if warmstart:
self.CollocationSolver.setInput( \
self.WarmStartData['NLP_X_OPT'],cs.NLP_X_INIT)
self.CollocationSolver.setInput( \
self.WarmStartData['NLP_LAMBDA_G'],cs.NLP_LAMBDA_INIT)
self.CollocationSolver.setOutput( \
self.WarmStartData['NLP_LAMBDA_X'],cs.NLP_LAMBDA_X)
def _setupDesignVars(self):
## set these:
# self._V = V
# self._XD = XD
# self._XA = XA
# self._U = U
# self._P = P
ndiff = len(self.dae.xNames())
nalg = len(self.dae.zNames())
nu = len(self.dae.uNames())
NP = len(self.dae.pNames())
nx = ndiff + nalg
# Total number of variables
NXD = self.nicp*self.nk*(self.deg+1)*ndiff # Collocated differential states
NXA = self.nicp*self.nk*self.deg*nalg # Collocated algebraic states
NU = self.nk*nu # Parametrized controls
NXF = ndiff # Final state (only the differential states)
NV = NXD+NXA+NU+NXF+NP
# NLP variable vector
V = CS.msym("V",NV)
offset = 0
# Get the parameters
P = V[offset:offset+NP]
offset += NP
# Get collocated states and parametrized control
XD = np.resize(np.array([],dtype=CS.MX),(self.nk+1,self.nicp,self.deg+1)) # NB: same name as above
XA = np.resize(np.array([],dtype=CS.MX),(self.nk,self.nicp,self.deg)) # NB: same name as above
U = np.resize(np.array([],dtype=CS.MX),self.nk)
for k in range(self.nk):
# Collocated states
for i in range(self.nicp):
for j in range(self.deg+1):
# Get the expression for the state vector
XD[k][i][j] = V[offset:offset+ndiff]
if j !=0:
XA[k][i][j-1] = V[offset+ndiff:offset+ndiff+nalg]
# Add the initial condition
index = (self.deg+1)*(self.nicp*k+i) + j
if k==0 and j==0 and i==0:
offset += ndiff
else:
if j!=0:
offset += nx
else:
offset += ndiff
# Parametrized controls
U[k] = V[offset:offset+nu]
offset += nu
# State at end time
XD[self.nk][0][0] = V[offset:offset+ndiff]
offset += ndiff
assert(offset==NV)
self._V = V
self._XD = XD
self._XA = XA
self._U = U
self._P = P
def collocation_solver_setup(self, warmstart=False):
"""
Sets up NLP for collocation solution. Constructs initial guess
arrays, constructs constraint and objective functions, and
otherwise passes arguments to the correct places. This looks
really inefficient and is likely unneccessary to run multiple
times for repeated runs with new data. Not sure how much time it
takes compared to the NLP solution.
Run immediately before CollocationSolve.
"""
# Dimensions of the problem
nx = self.NVAR # total number of states
ndiff = nx # number of differential states
nalg = 0 # number of algebraic states
nu = 0 # number of controls
# Collocated variables
NXD = self.nk*(self.deg+1)*ndiff # differential states
NXA = self.nk*self.deg*nalg # algebraic states
NU = self.nk*nu # Parametrized controls
NV = NXD+NXA+NU+self.ParamCount+self.NMP # Total variables
self.NV = NV
# NLP variable vector
V = cs.msym("V",NV)
# All variables with bounds and initial guess
vars_lb = np.zeros(NV)
vars_ub = np.zeros(NV)
vars_init = np.zeros(NV)
offset = 0
## I AM HERE ##
#
# Split NLP vector into useable slices
#
# Get the parameters
P = V[offset:offset+self.ParamCount]
vars_init[offset:offset+self.ParamCount] = self.NLPdata['p_init']
vars_lb[offset:offset+self.ParamCount] = self.NLPdata['p_min']
vars_ub[offset:offset+self.ParamCount] = self.NLPdata['p_max']
# Initial conditions for measurement adjustment
MP = V[self.NV-self.NMP:]
vars_init[self.NV-self.NMP:] = np.ones(self.NMP)
vars_lb[self.NV-self.NMP:] = 0.1*np.ones(self.NMP)
vars_ub[self.NV-self.NMP:] = 10*np.ones(self.NMP)
pdb.set_trace()
offset += self.np # indexing variable
# Get collocated states and parametrized control
XD = np.resize(np.array([], dtype=cs.MX), (self.nk, self.points_per_interval,
self.deg+1))
# NB: same name as above
XA = np.resize(np.array([],dtype=cs.MX),(self.nk,self.points_per_interval,self.deg))
# NB: same name as above
U = np.resize(np.array([],dtype=cs.MX),self.nk)
# Prepare the starting data matrix vars_init, vars_ub, and
# vars_lb, by looping over finite elements, states, etc. Also
# groups the variables in the large unknown vector V into XD and
# XA(unused) for later indexing
for k in range(self.nk):
# Collocated states
for i in range(self.points_per_interval):
#
for j in range(self.deg+1):
# Get the expression for the state vector
XD[k][i][j] = V[offset:offset+ndiff]
if j !=0:
XA[k][i][j-1] = V[offset+ndiff:offset+ndiff+nalg]
# Add the initial condition
index = (self.deg+1)*(self.points_per_interval*k+i) + j
if k==0 and j==0 and i==0:
vars_init[offset:offset+ndiff] = \
self.NLPdata['xD_init'][index,:]
vars_lb[offset:offset+ndiff] = \
self.NLPdata['xDi_min']
vars_ub[offset:offset+ndiff] = \
self.NLPdata['xDi_max']
offset += ndiff
else:
if j!=0:
vars_init[offset:offset+nx] = \
np.append(self.NLPdata['xD_init'][index,:],
self.NLPdata['xA_init'][index,:])
vars_lb[offset:offset+nx] = \
np.append(self.NLPdata['xD_min'],
self.NLPdata['xA_min'])
vars_ub[offset:offset+nx] = \
np.append(self.NLPdata['xD_max'],
self.NLPdata['xA_max'])
offset += nx
else:
vars_init[offset:offset+ndiff] = \
self.NLPdata['xD_init'][index,:]
vars_lb[offset:offset+ndiff] = \
self.NLPdata['xD_min']
vars_ub[offset:offset+ndiff] = \
self.NLPdata['xD_max']
offset += ndiff
# Parametrized controls (unused here)
U[k] = V[offset:offset+nu]
# Attach these initial conditions to external dictionary
self.NLPdata['v_init'] = vars_init
self.NLPdata['v_ub'] = vars_ub
self.NLPdata['v_lb'] = vars_lb
# Setting up the constraint function for the NLP. Over each
# collocated state, ensure continuitity and system dynamics
g = []
lbg = []
ubg = []
# For all finite elements
for k in range(self.nk):
for i in range(self.points_per_interval):
# For all collocation points
for j in range(1,self.deg+1):
# Get an expression for the state derivative
# at the collocation point
xp_jk = 0
for j2 in range (self.deg+1):
# get the time derivative of the differential
# states (eq 10.19b)
xp_jk += self.C[j2][j]*XD[k][i][j2]
# Add collocation equations to the NLP
[fk] = self.rfmod.call([0., xp_jk/self.h,
XD[k][i][j], XA[k][i][j-1],
U[k], P])
# impose system dynamics (for the differential
# states (eq 10.19b))
g += [fk[:ndiff]]
lbg.append(np.zeros(ndiff)) # equality constraints
ubg.append(np.zeros(ndiff)) # equality constraints
# impose system dynamics (for the algebraic states
# (eq 10.19b)) (unused)
g += [fk[ndiff:]]
lbg.append(np.zeros(nalg)) # equality constraints
ubg.append(np.zeros(nalg)) # equality constraints
# Get an expression for the state at the end of the finite
# element
xf_k = 0
for j in range(self.deg+1):
xf_k += self.D[j]*XD[k][i][j]
# if i==self.points_per_interval-1:
# Add continuity equation to NLP
if k+1 != self.nk: # End = Beginning of next
g += [XD[k+1][0][0] - xf_k]
lbg.append(-self.NLPdata['CONtol']*np.ones(ndiff))
ubg.append(self.NLPdata['CONtol']*np.ones(ndiff))
else: # At the last segment
# Periodicity constraints (only for NEQ)
g += [XD[0][0][0][:self.neq] - xf_k[:self.neq]]
lbg.append(-self.NLPdata['CONtol']*np.ones(self.neq))
ubg.append(self.NLPdata['CONtol']*np.ones(self.neq))
# else:
# g += [XD[k][i+1][0] - xf_k]
# Flatten contraint arrays for last addition
lbg = np.concatenate(lbg).tolist()
ubg = np.concatenate(ubg).tolist()
# Constraint to protect against fixed point solutions
if self.NLPdata['FPgaurd'] is True:
fout = self.model.call(cs.daeIn(t=self.tgrid[0],
x=XD[0,0,0][:self.neq],
p=V[:self.np]))[0]
g += [cs.MX(cs.sumAll(fout**2))]
lbg.append(np.array(self.NLPdata['FPTOL']))
ubg.append(np.array(cs.inf))
elif self.NLPdata['FPgaurd'] is 'all':
fout = self.model.call(cs.daeIn(t=self.tgrid[0],
x=XD[0,0,0][:self.neq],
p=V[:self.np]))[0]
g += [cs.MX(fout**2)]
lbg += [self.NLPdata['FPTOL']]*self.neq
ubg += [cs.inf]*self.neq
# Nonlinear constraint function
gfcn = cs.MXFunction([V],[cs.vertcat(g)])
# Get Linear Interpolant for YDATA from TDATA
objlist = []
# xarr = np.array([V[self.np:][i] for i in \
# xrange(self.neq*self.nk*(self.deg+1))])
# xarr = xarr.reshape([self.nk,self.deg+1,self.neq])
# List of the times when each finite element starts
felist = self.tgrid.reshape((self.nk,self.deg+1))[:,0]
felist = np.hstack([felist, self.tgrid[-1]])
def z(tau, zs):
"""
Functon to calculate the interpolated values of z^K at a
given tau (0->1). zs is a matrix with the symbolic state
values within the finite element
"""
def l(j,t):
"""
Intermediate values for polynomial interpolation
"""
tau = self.NLPdata['collocation_points']\
[self.NLPdata['cp']][self.deg]
return np.prod(np.array([
(t - tau[k])/(tau[j] - tau[k])
for k in xrange(0,self.deg+1) if k is not j]))
interp_vector = []
for i in xrange(self.neq): # only state variables
interp_vector += [np.sum(np.array([l(j, tau)*zs[j][i]
for j in xrange(0, self.deg+1)]))]
return interp_vector
# Set up Objective Function by minimizing distance from
# Collocation solution to Measurement Data
# Number of measurement functions
for i in xrange(self.NM):
# Number of sampling points per measurement]
for j in xrange(len(self.tdata[i])):
# the interpolating polynomial wants a tau value,
# where 0 < tau < 1, distance along current element.
# Get the index for which finite element of the tdata
# values
feind = get_ind(self.tdata[i][j],felist)[0]
# Get the starting time and tau (0->1) for the tdata
taustart = felist[feind]
tau = (self.tdata[i][j] - taustart)*(self.nk+1)/self.tf
x_interp = z(tau, XD[feind][0])
# Broken in newest numpy version, likely need to redo
# this whole file with most recent versions
y_model = self.Amatrix[i].dot(x_interp)
# Add measurement scaling
if self.mpars[i]: y_model *= MP[sum(self.mpars[:i])]
# Using relative diff's is probably messing up weights
# in Identifiability
diff = (y_model - self.ydata[i][j])
if self.NLPdata['ObjMethod'] == 'lsq':
dist = (diff**2/self.edata[i][j]**2)
elif self.NLPdata['ObjMethod'] == 'laplace':
dist = cs.fabs(diff)/np.sqrt(self.edata[i][j])
try: dist *= self.NLPdata['state_weights'][i]
except KeyError: pass
objlist += [dist]
# Minimization Objective
if self.minimize_f:
# Function integral
f_integral = 0
# For each finite element
for i in xrange(self.nk):
# For each collocation point
fvals = []
for j in xrange(self.deg+1):
fvals += [self.minimize_f(XD[i][0][j], P)]
# integrate with weights
f_integral += sum([fvals[k] * self.E[k] for k in
xrange(self.deg+1)])
objlist += [self.NLPdata['f_minimize_weight']*f_integral]
# Stability Objective (Floquet Multipliers)
if self.monodromy:
s_final = XD[-1,-1,-1][-self.neq**2:]
s_final = s_final.reshape((self.neq,self.neq))
trace = sum([s_final[i,i] for i in xrange(self.neq)])
objlist += [self.NLPdata['stability']*(trace - 1)**2]
# Objective function of the NLP
obj = cs.sumAll(cs.vertcat(objlist))
ofcn = cs.MXFunction([V], [obj])
self.CollocationSolver = cs.IpoptSolver(ofcn,gfcn)
for opt,val in self.IpoptOpts.iteritems():
self.CollocationSolver.setOption(opt,val)
self.CollocationSolver.setOption('obj_scaling_factor',
len(vars_init))
if warmstart:
self.CollocationSolver.setOption('warm_start_init_point','yes')
# initialize the self.CollocationSolver
self.CollocationSolver.init()
# Initial condition
self.CollocationSolver.setInput(vars_init,cs.NLP_X_INIT)
# Bounds on x
self.CollocationSolver.setInput(vars_lb,cs.NLP_LBX)
self.CollocationSolver.setInput(vars_ub,cs.NLP_UBX)
# Bounds on g
self.CollocationSolver.setInput(np.array(lbg),cs.NLP_LBG)
self.CollocationSolver.setInput(np.array(ubg),cs.NLP_UBG)
if warmstart:
self.CollocationSolver.setInput( \
self.WarmStartData['NLP_X_OPT'],cs.NLP_X_INIT)
self.CollocationSolver.setInput( \
self.WarmStartData['NLP_LAMBDA_G'],cs.NLP_LAMBDA_INIT)
self.CollocationSolver.setOutput( \
self.WarmStartData['NLP_LAMBDA_X'],cs.NLP_LAMBDA_X)
pdb.set_trace()
