def transcription_function(self, weight):
"""
Returns a function that can be used with Collocation's
'minimize_f', such that total transcription is minimized with
constant weight 'weight'
"""
x = cs.vertcat(self.states)
p = cs.vertcat(self.params)
txn = [
rxn.rate for rxn in self.reactions if type(rxn) is TranscriptionRxn
]
txn = weight * cs.sumAll(cs.vertcat(txn))
t = cs.ssym('t')
fn = cs.SXFunction([x, p], [txn])
fn.init()
def return_func(x, p):
""" Function to return for Collocation """
try:
fn.setInput(x, 0)
fn.setInput(p, 1)
fn.evaluate()
return float(fn.output().toArray())
except Exception:
return fn.call([x, p])[0]
return return_func
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 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)
for i in xrange(100):
dist = cs.ssym("dist")
x = self.model.inputSX(cs.DAE_X)
ode = self.model.outputSX()
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.inputSX(cs.DAE_T), x=cat_x,
p=self.model.inputSX(cs.DAE_P)),
cs.daeOut(ode=cat_ode))
dist_model.setOption("name","distance model")
dist_0 = ((self.y0[:-1] - point)**2).sum()
cat_y0 = np.hstack([self.y0[:-1], dist_0, self.y0[-1]])
roots_class = pBase(dist_model, self.paramset, cat_y0)
# roots_class.solveBVP()
roots_class.roots()
phase = self._t_to_phi(roots_class.Tmin[-1])
distance = roots_class.Ymin[-1]
if distance < tol: return phase, distance
intr = cs.CVodesIntegrator(self.model)
intr.setOption("abstol", self.intoptions['transabstol'])
intr.setOption("reltol", self.intoptions['transreltol'])
intr.setOption("tf", self.y0[-1])
intr.setOption("max_num_steps",
self.intoptions['transmaxnumsteps'])
intr.setOption("disable_internal_warnings", True)
intr.init()
intr.setInput(point, cs.INTEGRATOR_X0)
intr.setInput(self.paramset, cs.INTEGRATOR_P)
intr.evaluate()
point = intr.output().toArray().flatten()
raise RuntimeError("Point failed to converge to limit cycle")
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
, 0.316039689643
, -0.073559821379
, 0.945889986864
, 0.940484536806
, -0.106993361072
, -0.322554269411
, 0.000000000000
, 0.000000000000
, 0.000000000000
, 0.137035790811
, 3.664945343102
, -1.249768772258
, 3.874600000000
, 0.0
])
x0=C.veccat([x0,C.sqrt(C.sumAll(x0[0:2]*x0[0:2])),0,0,0])
def setupOcp(dae,conf,nk=50,nicp=1,deg=4):
ocp = rawe.collocation.Coll(dae, nk=nk,nicp=nicp,deg=deg)
ocp.setupCollocation(ocp.lookup('endTime'))
# constrain invariants
def constrainInvariantErrs():
dcm = ocp.lookup('dcm',timestep=0)
rawekite.kiteutils.makeOrthonormal(ocp, dcm)
ocp.constrain(ocp.lookup('c',timestep=0), '==', 0)
ocp.constrain(ocp.lookup('cdot',timestep=0), '==', 0)
constrainInvariantErrs()
# constraint line angle
for k in range(0,nk):
def main():
nSteps = 15
print "creating model"
dae = models.carousel(zt, rArm, nSteps)
print "setting up OCP"
ocp = MultipleShootingStage(dae, nSteps)
# make the integrator
print "setting up dynamics constraints"
integratorOptions = [
("reltol", 1e-7),
("abstol", 1e-9),
("t0", 0),
("tf", 1),
('name', 'integrator'),
("linear_solver_creator", C.CSparse)
# , ("linear_solver_creator",C.LapackLUDense)
,
("linear_solver", "user_defined")
]
ocp.setIdasIntegrator(integratorOptions)
# constrain invariants
def invariantErrs():
dcm = C.horzcat([
C.veccat([dae.x('e11'), dae.x('e21'),
dae.x('e31')]),
C.veccat([dae.x('e12'), dae.x('e22'),
dae.x('e32')]),
C.veccat([dae.x('e13'), dae.x('e23'),
dae.x('e33')])
]).trans()
err = C.mul(dcm.trans(), dcm)
dcmErr = C.veccat([
err[0, 0] - 1, err[1, 1] - 1, err[2, 2] - 1, err[0, 1], err[0, 2],
err[1, 2]
])
f = C.SXFunction(
[dae.xVec(), dae.uVec(), dae.pVec()],
[dae.output('c'), dae.output('cdot'), dcmErr])
f.setOption('name', 'invariant errors')
f.init()
return f
[c0, cdot0, dcmError0] = invariantErrs().call(
[ocp.states[:, 0], ocp.actions[:, 0], ocp.params])
ocp.addConstraint(c0, '==', 0)
ocp.addConstraint(cdot0, '==', 0)
ocp.addConstraint(dcmError0, '==', 0)
# bounds
ocp.setBound('aileron', (-0.04, 0.04))
ocp.setBound('elevator', (-0.1, 0.1))
ocp.setBound('x', (0, 4))
ocp.setBound('y', (-3, 3))
ocp.setBound('z', (-2, 3))
ocp.setBound('r', (1, 2))
ocp.setBound('dr', (-1, 1))
ocp.setBound('ddr', (0, 0))
ocp.setBound('r', (1.2, 1.2), timestep=0)
for e in ['e11', 'e21', 'e31', 'e12', 'e22', 'e32', 'e13', 'e23', 'e33']:
ocp.setBound(e, (-1.1, 1.1))
for d in ['dx', 'dy', 'dz']:
ocp.setBound(d, (-50, 50))
for w in ['w1', 'w2', 'w3']:
ocp.setBound(w, (-8 * pi, 8 * pi))
ocp.setBound('delta', (-0.01, 1.01 * 2 * pi))
ocp.setBound('ddelta', (-pi / 4, 8 * pi))
ocp.setBound('tc', (-200, 600))
# ocp.setBound('tc',(389.970797939731,389.970797939731))
ocp.setBound('endTime', (0.5, 2.0))
# ocp.setBound('endTime',(1.6336935276077966,1.6336935276077966))
ocp.setBound('w0', (10, 10))
# boundary conditions
ocp.setBound('delta', (0, 0), timestep=0)
ocp.setBound('delta', (2 * pi, 2 * pi), timestep=nSteps - 1)
# make it periodic
ocp.addConstraint(ocp.states[:18, 0], '==', ocp.states[:18, -1])
ocp.addConstraint(ocp.states[19, 0], '==', ocp.states[19, -1])
ocp.addConstraint(ocp.actions[:, 0], '==', ocp.actions[:, -1])
# make the solver
# objective function
tc0 = 390
obj = (C.sumAll(ocp.actions[0:2, :] * ocp.actions[0:2, :]) +
1e-10 * C.sumAll((ocp.actions[2, :] - tc0) *
(ocp.actions[2, :] - tc0))) * ocp.lookup('endTime')
ocp.setObjective(obj)
# zero mq setup
context = zmq.Context(1)
publisher = context.socket(zmq.PUB)
publisher.bind("tcp://*:5563")
# callback function
class MyCallback:
def __init__(self):
self.iter = 0
def __call__(self, f, *args):
self.iter = self.iter + 1
xOpt = f.input(C.NLP_X_OPT)
xs, us, p = ocp.getTimestepsFromDvs(xOpt)
kiteProtos = [
kiteproto.toKiteProto(xs[k], us[k], p, rArm, zt)
for k in range(0, nSteps)
]
mc = kite_pb2.KiteOpt()
mc.horizon.extend(list(kiteProtos))
xup = ocp.devectorize(xOpt)
mc.messages.append("endTime: " + str(xup['endTime']))
mc.messages.append("w0: " + str(xup['w0']))
mc.messages.append("iter: " + str(self.iter))
publisher.send_multipart(
["multi-carousel", mc.SerializeToString()])
def makeCallback():
nd = ocp.getDesignVars().size()
nc = ocp._constraints.getG().size()
c = C.PyFunction(
MyCallback(),
C.nlpsolverOut(x_opt=C.sp_dense(nd, 1),
cost=C.sp_dense(1, 1),
lambda_x=C.sp_dense(nd, 1),
lambda_g=C.sp_dense(nc, 1),
g=C.sp_dense(nc, 1)), [C.sp_dense(1, 1)])
c.init()
return c
# solver
solverOptions = [("iteration_callback", makeCallback()),
("linear_solver", "ma57")
# , ("max_iter",5)
]
ocp.setSolver(C.IpoptSolver, solverOptions=solverOptions)
#ocp.setBounds()
# initial conditions
ocp.setXGuess(x0)
for k in range(0, nSteps):
val = 2 * pi * k / (nSteps - 1)
ocp.setGuess('delta', val, timestep=k, quiet=True)
ocp.setGuess('aileron', 0)
ocp.setGuess('elevator', 0)
ocp.setGuess('tc', 389.970797939731)
ocp.setGuess('endTime', 1.6336935276077966)
ocp.setGuess('ddr', 0)
ocp.setGuess('w0', 0)
ocp.solve()
def setupOcp(dae,conf,publisher,nk=50,nicp=1,deg=4):
ocp = Coll(dae, nk=nk,nicp=nicp,deg=deg)
# constrain invariants
def invariantErrs():
dcm = C.horzcat( [ C.veccat([dae.x('e11'), dae.x('e21'), dae.x('e31')])
, C.veccat([dae.x('e12'), dae.x('e22'), dae.x('e32')])
, C.veccat([dae.x('e13'), dae.x('e23'), dae.x('e33')])
] ).trans()
err = C.mul(dcm.trans(), dcm)
dcmErr = C.veccat([ err[0,0]-1, err[1,1]-1, err[2,2]-1, err[0,1], err[0,2], err[1,2] ])
f = C.SXFunction( [dae.xVec(),dae.uVec(),dae.pVec()]
, [dae.output('c'),dae.output('cdot'),dcmErr]
)
f.setOption('name','invariant errors')
f.init()
return f
[c0,cdot0,dcmError0] = invariantErrs().call([ocp.xVec(0),ocp.uVec(0),ocp.pVec()])
ocp.constrain(c0,'==',0)
ocp.constrain(cdot0,'==',0)
ocp.constrain(dcmError0,'==',0)
# constrain line angle
for k in range(0,nk+1):
ocp.constrain(kiteutils.getCosLineAngle(ocp,k),'>=',C.cos(55*pi/180))
# constrain airspeed
def constrainAirspeedAlphaBeta():
f = C.SXFunction( [dae.xVec(),dae.uVec(),dae.pVec()]
, [dae.output('airspeed'),dae.output('alpha(deg)'),dae.output('beta(deg)')]
)
f.setOption('name','airspeed/alpha/beta')
f.init()
for k in range(0,nk):
[airspeed,alphaDeg,betaDeg] = f.call([ocp.xVec(k),ocp.uVec(k),ocp.pVec()])
ocp.constrainBnds(airspeed,(10,50))
ocp.constrainBnds(alphaDeg,(-5,10))
ocp.constrainBnds(betaDeg,(-10,10))
constrainAirspeedAlphaBeta()
# make it periodic
for name in [ #"x" # state 0
"y" # state 1
, "z" # state 2
# , "e11" # state 3
# , "e12" # state 4
# , "e13" # state 5
# , "e21" # state 6
# , "e22" # state 7
# , "e23" # state 8
# , "e31" # state 9
# , "e32" # state 10
# , "e33" # state 11
# , "dx" # state 12
, "dy" # state 13
, "dz" # state 14
, "w1" # state 15
, "w2" # state 16
, "w3" # state 17
, "r" # state 20
, "dr" # state 21
]:
ocp.constrain(ocp.lookup(name,timestep=0),'==',ocp.lookup(name,timestep=-1))
# periodic attitude
kiteutils.periodicDcm(ocp)
# bounds
ocp.bound('aileron',(-0.04,0.04))
ocp.bound('elevator',(-0.1,0.1))
ocp.bound('x',(-2,200))
ocp.bound('y',(-200,200))
ocp.bound('z',(0.5,200))
ocp.bound('r',(1,30))
ocp.bound('dr',(-10,10))
ocp.bound('ddr',(-2.5,2.5))
for e in ['e11','e21','e31','e12','e22','e32','e13','e23','e33']:
ocp.bound(e,(-1.1,1.1))
for d in ['dx','dy','dz']:
ocp.bound(d,(-70,70))
for w in ['w1','w2','w3']:
ocp.bound(w,(-4*pi,4*pi))
ocp.bound('endTime',(0.5,5))
ocp.bound('w0',(10,10))
ocp.bound('energy',(-1e6,1e6))
# boundary conditions
ocp.bound('energy',(0,0),timestep=0,quiet=True)
ocp.bound('y',(0,0),timestep=0,quiet=True)
# objective function
obj = 0
for k in range(nk):
u = ocp.uVec(k)
ddr = ocp.lookup('ddr',timestep=k)
aileron = ocp.lookup('aileron',timestep=k)
elevator = ocp.lookup('elevator',timestep=k)
aileronSigma = 0.1
elevatorSigma = 0.1
ddrSigma = 5.0
ailObj = aileron*aileron / (aileronSigma*aileronSigma)
eleObj = elevator*elevator / (elevatorSigma*elevatorSigma)
winchObj = ddr*ddr / (ddrSigma*ddrSigma)
obj += ailObj + eleObj + winchObj
ocp.setObjective( 1e1*C.sumAll(obj)/float(nk) + ocp.lookup('energy',timestep=-1)/ocp.lookup('endTime') )
# callback function
class MyCallback:
def __init__(self):
self.iter = 0
def __call__(self,f,*args):
self.iter = self.iter + 1
xOpt = numpy.array(f.input(C.NLP_X_OPT))
opt = ocp.devectorize(xOpt)
xup = opt['vardict']
kiteProtos = []
for k in range(0,nk):
j = nicp*(deg+1)*k
kiteProtos.append( kiteproto.toKiteProto(C.DMatrix(opt['x'][:,j]),
C.DMatrix(opt['u'][:,j]),
C.DMatrix(opt['p']),
conf['kite']['zt'],
conf['carousel']['rArm'],
zeroDelta=True) )
# kiteProtos = [kiteproto.toKiteProto(C.DMatrix(opt['x'][:,k]),C.DMatrix(opt['u'][:,k]),C.DMatrix(opt['p']), conf['kite']['zt'], conf['carousel']['rArm'], zeroDelta=True) for k in range(opt['x'].shape[1])]
mc = kite_pb2.MultiCarousel()
mc.css.extend(list(kiteProtos))
mc.messages.append("endTime: "+str(xup['endTime']))
mc.messages.append("w0: "+str(xup['w0']))
mc.messages.append("iter: "+str(self.iter))
# bounds feedback
# lbx = ocp.solver.input(C.NLP_LBX)
# ubx = ocp.solver.input(C.NLP_UBX)
# violations = boundsFeedback(xOpt,lbx,ubx,ocp.bndtags,tolerance=1e-9)
# for name in violations:
# violmsg = "violation!: "+name+": "+str(violations[name])
# mc.messages.append(violmsg)
publisher.send_multipart(["multi-carousel", mc.SerializeToString()])
# solver
solverOptions = [ ("expand_f",True)
, ("expand_g",True)
, ("generate_hessian",True)
# ,("qp_solver",C.NLPQPSolver)
# ,("qp_solver_options",{'nlp_solver': C.IpoptSolver, "nlp_solver_options":{"linear_solver":"ma57"}})
, ("linear_solver","ma57")
, ("max_iter",1000)
, ("tol",1e-9)
# , ("Timeout", 1e6)
# , ("UserHM", True)
# , ("ScaleConIter",True)
# , ("ScaledFD",True)
# , ("ScaledKKT",True)
# , ("ScaledObj",True)
# , ("ScaledQP",True)
]
# initial guess
# ocp.guessX(x0)
# for k in range(0,nk+1):
# val = 2.0*pi*k/nk
# ocp.guess('delta',val,timestep=k,quiet=True)
#
# ocp.guess('aileron',0)
# ocp.guess('elevator',0)
# ocp.guess('tc',0)
ocp.guess('endTime',5.4)
#
# ocp.guess('ddr',0)
ocp.guess('w0',10)
print "setting up collocation..."
ocp.setupCollocation(ocp.lookup('endTime'))
print "setting up solver..."
ocp.setupSolver( solverOpts=solverOptions,
callback=MyCallback() )
return ocp
def main():
nSteps = 15
print "creating model"
dae = models.carousel(zt,rArm,nSteps)
print "setting up OCP"
ocp = MultipleShootingStage(dae, nSteps)
# make the integrator
print "setting up dynamics constraints"
integratorOptions = [ ("reltol",1e-7)
, ("abstol",1e-9)
, ("t0",0)
, ("tf",1)
, ('name','integrator')
, ("linear_solver_creator",C.CSparse)
# , ("linear_solver_creator",C.LapackLUDense)
, ("linear_solver","user_defined")
]
ocp.setIdasIntegrator(integratorOptions)
# constrain invariants
def invariantErrs():
dcm = C.horzcat( [ C.veccat([dae.x('e11'), dae.x('e21'), dae.x('e31')])
, C.veccat([dae.x('e12'), dae.x('e22'), dae.x('e32')])
, C.veccat([dae.x('e13'), dae.x('e23'), dae.x('e33')])
] ).trans()
err = C.mul(dcm.trans(), dcm)
dcmErr = C.veccat([ err[0,0]-1, err[1,1]-1, err[2,2]-1, err[0,1], err[0,2], err[1,2] ])
f = C.SXFunction( [dae.xVec(),dae.uVec(),dae.pVec()]
, [dae.output('c'),dae.output('cdot'),dcmErr]
)
f.setOption('name','invariant errors')
f.init()
return f
[c0,cdot0,dcmError0] = invariantErrs().call([ocp.states[:,0],ocp.actions[:,0],ocp.params])
ocp.addConstraint(c0,'==',0)
ocp.addConstraint(cdot0,'==',0)
ocp.addConstraint(dcmError0,'==',0)
# bounds
ocp.setBound('aileron',(-0.04,0.04))
ocp.setBound('elevator',(-0.1,0.1))
ocp.setBound('x',(0,4))
ocp.setBound('y',(-3,3))
ocp.setBound('z',(-2,3))
ocp.setBound('r',(1,2))
ocp.setBound('dr',(-1,1))
ocp.setBound('ddr',(0,0))
ocp.setBound('r',(1.2,1.2),timestep=0)
for e in ['e11','e21','e31','e12','e22','e32','e13','e23','e33']:
ocp.setBound(e,(-1.1,1.1))
for d in ['dx','dy','dz']:
ocp.setBound(d,(-50,50))
for w in ['w1','w2','w3']:
ocp.setBound(w,(-8*pi,8*pi))
ocp.setBound('delta',(-0.01,1.01*2*pi))
ocp.setBound('ddelta',(-pi/4,8*pi))
ocp.setBound('tc',(-200,600))
# ocp.setBound('tc',(389.970797939731,389.970797939731))
ocp.setBound('endTime',(0.5,2.0))
# ocp.setBound('endTime',(1.6336935276077966,1.6336935276077966))
ocp.setBound('w0',(10,10))
# boundary conditions
ocp.setBound('delta',(0,0),timestep=0)
ocp.setBound('delta',(2*pi,2*pi),timestep=nSteps-1)
# make it periodic
ocp.addConstraint(ocp.states[:18,0],'==',ocp.states[:18,-1])
ocp.addConstraint(ocp.states[19,0],'==',ocp.states[19,-1])
ocp.addConstraint(ocp.actions[:,0],'==',ocp.actions[:,-1])
# make the solver
# objective function
tc0 = 390
obj = (C.sumAll(ocp.actions[0:2,:]*ocp.actions[0:2,:]) + 1e-10*C.sumAll((ocp.actions[2,:]-tc0)*(ocp.actions[2,:]-tc0)))*ocp.lookup('endTime')
ocp.setObjective(obj)
# zero mq setup
context = zmq.Context(1)
publisher = context.socket(zmq.PUB)
publisher.bind("tcp://*:5563")
# callback function
class MyCallback:
def __init__(self):
self.iter = 0
def __call__(self,f,*args):
self.iter = self.iter + 1
xOpt = f.input(C.NLP_X_OPT)
xs,us,p = ocp.getTimestepsFromDvs(xOpt)
kiteProtos = [kiteproto.toKiteProto(xs[k],us[k],p,rArm,zt) for k in range(0,nSteps)]
mc = kite_pb2.KiteOpt()
mc.horizon.extend(list(kiteProtos))
xup = ocp.devectorize(xOpt)
mc.messages.append("endTime: "+str(xup['endTime']))
mc.messages.append("w0: "+str(xup['w0']))
mc.messages.append("iter: "+str(self.iter))
publisher.send_multipart(["multi-carousel", mc.SerializeToString()])
def makeCallback():
nd = ocp.getDesignVars().size()
nc = ocp._constraints.getG().size()
c = C.PyFunction( MyCallback(), C.nlpsolverOut(x_opt=C.sp_dense(nd,1), cost=C.sp_dense(1,1), lambda_x=C.sp_dense(nd,1), lambda_g = C.sp_dense(nc,1), g = C.sp_dense(nc,1) ), [C.sp_dense(1,1)] )
c.init()
return c
# solver
solverOptions = [ ("iteration_callback",makeCallback())
, ("linear_solver","ma57")
# , ("max_iter",5)
]
ocp.setSolver( C.IpoptSolver, solverOptions=solverOptions )
#ocp.setBounds()
# initial conditions
ocp.setXGuess(x0)
for k in range(0,nSteps):
val = 2*pi*k/(nSteps-1)
ocp.setGuess('delta',val,timestep=k,quiet=True)
ocp.setGuess('aileron',0)
ocp.setGuess('elevator',0)
ocp.setGuess('tc',389.970797939731)
ocp.setGuess('endTime',1.6336935276077966)
ocp.setGuess('ddr',0)
ocp.setGuess('w0',0)
ocp.solve()
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 sum_squares(a): if type(a)==casadi.SXMatrix: return casadi.sumAll(a*a) else: return (a*a).reshape(-1).sum()
def fx_polybasis(u,t):
f = casadi.sumAll(casadi.polyval(u,t-.5))
return f
def normalize_casadi(x): n = casadi.sumAll(x*x) n = casadi.sqrt(n) nx = x/n return nx
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()
def parameter_estimation(self):
"""
Again, borrow from PSJ. Gets a decent estimate of the parameters
initial values by looking at slopes. I think.
Here we will set up an NLP to estimate the initial parameter
guess (potentially along with unmeasured state variables) by
minimizing the difference between the calculated slope at each
shooting node (a function of the parameters) and the measured
slope (using a spline interpolant)
"""
# Here we must interpolate the x_init data using a spline. We
# will differentiate this spline to get intial values for
# the parameters
node_ts = self.tgrid.reshape((self.nk, self.deg+1))[:,0]
try:
f_init = self.sx(self.tgrid,1).T
except AttributeError:
# Create interpolation object
sx = fnlist([])
def flat_factory(x):
""" Protects against nan's resulting from flat trajectories
in spline curve """
return lambda t, d: (np.array([x] * len(t)) if d is 0 else
np.array([0] * len(t)))
for x in np.array(self.x_init).T:
tvals = list(node_ts)
tvals.append(tvals[0] + self.tf)
xvals = list(x.reshape((self.nk, self.deg+1))[:,0])
## here ##
xvals.append(x[0])
if np.linalg.norm(xvals - xvals[0]) < 1E-8:
# flat profile
sx += [flat_factory(xvals[0])]
else: sx += [spline(tvals, xvals, 0)]
f_init = sx(self.tgrid,1).T
# set initial guess for parameters
logmax = np.log10(np.array(self.PARMAX))
logmin = np.log10(np.array(self.PARMIN))
p_init = 10**(logmax - (logmax - logmin)/2)
f = self.model
V = cs.MX("V", self.ParamCount)
par = V
# Allocate the initial conditions
pvars_init = np.ones(self.ParamCount)
pvars_lb = np.array(self.PARMIN)
pvars_ub = np.array(self.PARMAX)
pvars_init = p_init
xin = []
fin = []
# For each state, add the (variable or constant) MX
# representation of the measured x and f value to the input
# variable list.
for state in xrange(self.neq):
xin += [cs.MX(self.x_init[:,state])]
fin += [cs.MX(f_init[:,state])]
xin = cs.horzcat(xin)
fin = cs.horzcat(fin)
# For all nodes
res = []
xmax = self.x_init.max(0)
for ii in xrange((self.deg+1)*self.nk):
f_out = f.call(cs.daeIn(t=self.tgrid[ii],
x=xin[ii,:].T, p=par))[0]
res += [cs.sumAll(((f_out - fin[ii,:].T) / xmax)**2)]
F = cs.MXFunction([V],[cs.sumAll(cs.vertcat(res))])
F.init()
parsolver = cs.IpoptSolver(F)
for opt,val in self.IpoptOpts.iteritems():
if not opt == "expand_g":
parsolver.setOption(opt,val)
parsolver.init()
parsolver.setInput(pvars_init,cs.NLP_X_INIT)
parsolver.setInput(pvars_lb,cs.NLP_LBX)
parsolver.setInput(pvars_ub,cs.NLP_UBX)
parsolver.solve()
success = parsolver.getStat('return_status') == 'Solve_Succeeded'
assert success, "Parameter Estimation Failed"
self.pcost = float(parsolver.output(cs.NLP_COST))
pvars_opt = np.array(parsolver.output( \
cs.NLP_X_OPT)).flatten()
if success: return pvars_opt
else: return False
