def ftimeincradj(self, tt):
""" Compute rhs for incremental adjoint at time tt """
try:
indexf = int(np.where(isequal(self.PDE.times, tt, 1e-14))[0])
indexa = int(np.where(isequal(self.PDE.times[::-1], tt, 1e-14))[0])
except:
print 'Error in ftimeincradj at time {}'.format(tt)
print np.min(np.abs(self.PDE.times-tt))
sys.exit(0)
# B* B phat
# assert isequal(tt, self.solincrfwd[indexf][1], 1e-16)
setfct(self.phat, self.solincrfwd[indexf][0])
self.qhat.vector().zero()
self.qhat.vector().axpy(1.0, self.obsop.incradj(self.phat, tt))
if not self.GN:
# bhat: bhat*grad(ptilde).grad(v)
# assert isequal(tt, self.soladji[indexa][1], 1e-16)
setfct(self.q, self.soladji[indexa][0])
self.qhat.vector().axpy(1.0, self.C*self.q.vector())
# ahat: ahat*ptilde*q'':
setfct(self.q, self.solppadji[indexa][0])
self.qhat.vector().axpy(1.0, self.get_incra(self.q.vector()))
# ABC:
if self.PDE.parameters['abc']:
setfct(self.phat, self.solpadji[indexa][0])
self.qhat.vector().axpy(-0.5, self.Dp*self.phat.vector())
return -1.0*self.qhat.vector()
def mult(self, lamhat, y):
"""
mult(self, lamhat, y): return y = Hessian * lamhat
inputs:
y, lamhat = Function(V).vector()
"""
self.regularization.assemble_hessian(lamhat)
setfct(self.lamhat, lamhat)
self.C = assemble(self.wkformrhsincr)
if self.PDE.abc: self.Dp = assemble(self.wkformDprime)
# solve for phat
self.PDE.set_fwd()
self.PDE.ftime = self.ftimeincrfwd
self.solincrfwd,_ = self.PDE.solve()
# solve for vhat
self.PDE.set_adj()
self.PDE.ftime = self.ftimeincradj
self.solincradj,_ = self.PDE.solve()
# Compute Hessian*lamhat
y.zero()
index = 0
if self.PDE.abc:
self.vD.vector().zero(); self.vhatD.vector().zero();
self.p1D.vector().zero(); self.p2D.vector().zero();
self.p1hatD.vector().zero(); self.p2hatD.vector().zero();
for fwd, adj, incrfwd, incradj, fact in \
zip(self.solfwd, reversed(self.soladj), \
self.solincrfwd, reversed(self.solincradj), self.factors):
ttf, tta, ttf2 = incrfwd[1], incradj[1], fwd[1]
assert isequal(ttf, tta, 1e-16), 'tfwd={}, tadj={}, reldiff={}'.\
format(ttf, tta, abs(ttf-tta)/ttf)
assert isequal(ttf, ttf2, 1e-16), 'tfwd={}, tadj={}, reldiff={}'.\
format(ttf, ttf2, abs(ttf-ttf2)/ttf)
setfct(self.p, fwd[0])
setfct(self.v, adj[0])
setfct(self.phat, incrfwd[0])
setfct(self.vhat, incradj[0])
y.axpy(fact, assemble(self.wkformhess))
if self.PDE.abc:
if index%2 == 0:
self.p2D.vector().axpy(1.0, self.p.vector())
self.p2hatD.vector().axpy(1.0, self.phat.vector())
setfct(self.dp, self.p2D)
setfct(self.dph, self.p2hatD)
y.axpy(1.0*0.5*self.invDt, assemble(self.wkformhessD))
setfct(self.p2D, -1.0*self.p.vector())
setfct(self.p2hatD, -1.0*self.phat.vector())
else:
self.p1D.vector().axpy(1.0, self.p.vector())
self.p1hatD.vector().axpy(1.0, self.phat.vector())
setfct(self.dp, self.p1D)
setfct(self.dph, self.p1hatD)
y.axpy(1.0*0.5*self.invDt, assemble(self.wkformhessD))
setfct(self.p1D, -1.0*self.p.vector())
setfct(self.p1hatD, -1.0*self.phat.vector())
setfct(self.vD, self.v)
setfct(self.vhatD, self.vhat)
index += 1
# add regularization term
y.axpy(self.alpha_reg, self.regularization.hessian(lamhat))
def solve(self):
""" General solver method """
if self.timestepper == 'backward':
def iterate(tt): self.iteration_backward(tt)
elif self.timestepper == 'centered':
def iterate(tt): self.iteration_centered(tt)
else:
print "Time stepper not implemented"
sys.exit(1)
if self.verbose: print 'Compute solution'
solout = [] # Store computed solution
# u0:
tt = self.get_tt(0)
if self.verbose: print 'Compute solution -- time {}'.format(tt)
setfct(self.u0, self.u0init)
solout.append([self.u0.vector().array(), tt])
# Compute u1:
if not self.u1init == None: self.u1 = self.u1init
else:
assert(not self.utinit == None)
setfct(self.rhs, self.ftime(tt))
self.rhs.vector().axpy(-self.fwdadj, self.D*self.utinit.vector())
self.rhs.vector().axpy(-1.0, self.K*self.u0.vector())
if not self.bc == None: self.bc.apply(self.rhs.vector())
self.solverM.solve(self.sol.vector(), self.rhs.vector())
setfct(self.u1, self.u0)
self.u1.vector().axpy(self.fwdadj*self.Dt, self.utinit.vector())
self.u1.vector().axpy(0.5*self.Dt**2, self.sol.vector())
tt = self.get_tt(1)
if self.verbose: print 'Compute solution -- time {}'.format(tt)
solout.append([self.u1.vector().array(), tt])
# Iteration
for nn in xrange(2, self.Nt+1):
iterate(tt)
# Advance to next time step
setfct(self.u0, self.u1)
setfct(self.u1, self.u2)
tt = self.get_tt(nn)
if self.verbose:
print 'Compute solution -- time {}, rhs {}'.\
format(tt, np.max(np.abs(self.ftime(tt))))
solout.append([self.u1.vector().array(),tt])
if self.fwdadj > 0.0:
assert isequal(tt, self.Tf, 1e-16), \
'tt={}, Tf={}, reldiff={}'.format(tt, self.Tf, abs(tt-self.Tf)/self.Tf)
else:
assert isequal(tt, self.t0, 1e-16), \
'tt={}, t0={}, reldiff={}'.format(tt, self.t0, abs(tt-self.t0))
return solout, self.computeerror()
def ftimeincrfwd(self, tt):
""" Compute rhs for incremental forward at time tt """
try:
index = int(np.where(isequal(self.PDE.times, tt, 1e-14))[0])
except:
print 'Error in ftimeincrfwd at time {}'.format(tt)
print np.min(np.abs(self.PDE.times-tt))
sys.exit(0)
# bhat: bhat*grad(p).grad(qtilde)
# assert isequal(tt, self.solfwdi[index][1], 1e-16)
setfct(self.p, self.solfwdi[index][0])
self.q.vector().zero()
self.q.vector().axpy(1.0, self.C*self.p.vector())
# ahat: ahat*p''*qtilde:
setfct(self.p, self.solppfwdi[index][0])
self.q.vector().axpy(1.0, self.get_incra(self.p.vector()))
# ABC:
if self.PDE.parameters['abc']:
setfct(self.phat, self.solpfwdi[index][0])
self.q.vector().axpy(0.5, self.Dp*self.phat.vector())
return -1.0*self.q.vector()
def ftimeincrfwd(self, tt):
""" Compute rhs for incremental forward at time tt """
try:
index = int(np.where(isequal(self.PDE.times, tt, 1e-14))[0])
except:
print 'Error in ftimeincrfwd at time {}'.format(tt)
print np.min(np.abs(self.PDE.times-tt))
sys.exit(0)
# lamhat * grad(p).grad(vtilde)
assert isequal(tt, self.solfwd[index][1], 1e-16)
setfct(self.p, self.solfwd[index][0])
setfct(self.v, self.C*self.p.vector())
# D'.dot(p)
if self.PDE.abc and index > 0:
setfct(self.p, \
self.solfwd[index+1][0] - self.solfwd[index-1][0])
self.v.vector().axpy(.5*self.invDt, self.Dp*self.p.vector())
return -1.0*self.v.vector().array()
def ftimeadj(self, tt):
""" Evaluate source term for adj eqn at time tt """
try:
index = int(np.where(isequal(self.times, tt, 1e-14))[0])
except:
print 'Error in ftimeadj at time {}'.format(tt)
print np.min(np.abs(self.times-tt))
sys.exit(0)
dd = self.diff[:, index]
self.PtwiseObs.BTdotvec(dd, self.outvec)
if not self.bcadj == None: self.bcadj.apply(self.outvec.vector())
return -1.0*self.st(tt)*self.outvec.array()
def ftimeincradj(self, tt):
""" Compute rhs for incremental adjoint at time tt """
try:
indexf = int(np.where(isequal(self.PDE.times, tt, 1e-14))[0])
indexa = int(np.where(isequal(self.PDE.times[::-1], tt, 1e-14))[0])
except:
print 'Error in ftimeincradj at time {}'.format(tt)
print np.min(np.abs(self.PDE.times-tt))
sys.exit(0)
# lamhat * grad(ptilde).grad(v)
assert isequal(tt, self.soladj[indexa][1], 1e-16)
setfct(self.v, self.soladj[indexa][0])
setfct(self.vhat, self.C*self.v.vector())
# B* B phat
assert isequal(tt, self.solincrfwd[indexf][1], 1e-16)
setfct(self.phat, self.solincrfwd[indexf][0])
self.vhat.vector().axpy(1.0, self.obsop.incradj(self.phat, tt))
# D'.dot(v)
if self.PDE.abc and indexa > 0:
setfct(self.v, \
self.soladj[indexa-1][0] - self.soladj[indexa+1][0])
self.vhat.vector().axpy(-.5*self.invDt, self.Dp*self.v.vector())
return -1.0*self.vhat.vector().array()
def solveadj(self, grad=False):
self.PDE.set_adj()
self.obsop.assemble_rhsadj(self.Bp, self.dd, self.PDE.times, self.PDE.bc)
self.PDE.ftime = self.obsop.ftimeadj
self.soladj,_ = self.PDE.solve()
if grad:
self.MGv.zero()
if self.PDE.abc:
self.vD.vector().zero(); self.pD.vector().zero();
self.p1D.vector().zero(); self.p2D.vector().zero();
index = 0
for fwd, adj, fact in \
zip(self.solfwd, reversed(self.soladj), self.factors):
ttf, tta = fwd[1], adj[1]
assert isequal(ttf, tta, 1e-16), \
'tfwd={}, tadj={}, reldiff={}'.format(ttf, tta, abs(ttf-tta)/ttf)
setfct(self.p, fwd[0])
setfct(self.v, adj[0])
self.MGv.axpy(fact, assemble(self.wkformgrad))
# self.MGv.axpy(fact, assemble(self.wkformgrad, \
# form_compiler_parameters={'optimize':True,\
# 'representation':'quadrature'}))
if self.PDE.abc:
if index%2 == 0:
self.p2D.vector().axpy(1.0, self.p.vector())
setfct(self.pD, self.p2D)
#self.MGv.axpy(1.0*0.5*self.invDt, assemble(self.wkformgradD))
self.MGv.axpy(fact*0.5*self.invDt, assemble(self.wkformgradD))
setfct(self.p2D, -1.0*self.p.vector())
setfct(self.vD, self.v)
else:
self.p1D.vector().axpy(1.0, self.p.vector())
setfct(self.pD, self.p1D)
#self.MGv.axpy(1.0*0.5*self.invDt, assemble(self.wkformgradD))
self.MGv.axpy(fact*0.5*self.invDt, assemble(self.wkformgradD))
setfct(self.p1D, -1.0*self.p.vector())
setfct(self.vD, self.v)
index += 1
self.MGv.axpy(self.alpha_reg, self.regularization.grad(self.PDE.lam))
self.solverM.solve(self.Gradv, self.MGv)
def update(self, parameters_m):
assert not self.timestepper == None, "You need to set a time stepping method"
# Time options:
if parameters_m.has_key('t0'): self.t0 = parameters_m['t0']
if parameters_m.has_key('tf'): self.tf = parameters_m['tf']
if parameters_m.has_key('Dt'): self.Dt = parameters_m['Dt']
if parameters_m.has_key('t0') or parameters_m.has_key('tf') or parameters_m.has_key('Dt'):
self.Nt = int(round((self.tf-self.t0)/self.Dt))
self.Tf = self.t0 + self.Dt*self.Nt
self.times = np.linspace(self.t0, self.Tf, self.Nt+1)
assert isequal(self.times[1]-self.times[0], self.Dt, 1e-16), "Dt modified"
self.Dt = self.times[1] - self.times[0]
assert isequal(self.Tf, self.tf, 1e-2), "Final time differs by more than 1%"
if not isequal(self.Tf, self.tf, 1e-12):
print 'Final time modified from {} to {} ({}%)'.\
format(self.tf, self.Tf, abs(self.Tf-self.tf)/self.tf)
# Initial conditions:
if parameters_m.has_key('u0init'): self.u0init = parameters_m['u0init']
if parameters_m.has_key('utinit'): self.utinit = parameters_m['utinit']
if parameters_m.has_key('u1init'): self.u1init = parameters_m['u1init']
if parameters_m.has_key('um1init'): self.um1init = parameters_m['um1init']
# Medium parameters:
setfct(self.lam, parameters_m['lambda'])
if self.verbose: print 'lambda updated '
if self.elastic == True:
setfct(self.mu, parameters_m['mu'])
if self.verbose: print 'mu updated'
if self.verbose: print 'assemble K',
self.K = assemble(self.weak_k)
if self.verbose: print ' -- K assembled'
if parameters_m.has_key('rho'):
setfct(self.rho, parameters_m['rho'])
# Mass matrix:
if self.verbose: print 'rho updated\nassemble M',
Mfull = assemble(self.weak_m)
if self.lump:
self.solverM = LumpedMatrixSolverS(self.V)
self.solverM.set_operator(Mfull, self.bc)
self.M = self.solverM
else:
if mpisize == 1:
self.solverM = LUSolver()
self.solverM.parameters['reuse_factorization'] = True
self.solverM.parameters['symmetric'] = True
else:
self.solverM = KrylovSolver('cg', 'amg')
self.solverM.parameters['report'] = False
self.M = Mfull
if not self.bc == None: self.bc.apply(Mfull)
self.solverM.set_operator(Mfull)
if self.verbose: print ' -- M assembled'
# Matrix D for abs BC
if self.abc == True:
if self.verbose: print 'assemble D',
Mfull = assemble(self.weak_m)
Dfull = assemble(self.weak_d)
if self.lumpD:
self.D = LumpedMatrixSolverS(self.V)
self.D.set_operator(Dfull, None, False)
if self.lump:
self.solverMplD = LumpedMatrixSolverS(self.V)
self.solverMplD.set_operators(Mfull, Dfull, .5*self.Dt, self.bc)
self.MminD = LumpedMatrixSolverS(self.V)
self.MminD.set_operators(Mfull, Dfull, -.5*self.Dt, self.bc)
else:
self.D = Dfull
if self.verbose: print ' -- D assembled'
else: self.D = 0.0