def __init__(self, V, Vm, bc, bcadj, \
RHSinput=[], ObsOp=[], UD=[], Regul=[], Data=[], plot=False, \
mycomm=None):
# Define test, trial and all other functions
self.trial = TrialFunction(V)
self.test = TestFunction(V)
self.mtrial = TrialFunction(Vm)
self.mtest = TestFunction(Vm)
self.rhs = Function(V)
self.m = Function(Vm)
self.mcopy = Function(Vm)
self.srchdir = Function(Vm)
self.delta_m = Function(Vm)
self.MG = Function(Vm)
self.Grad = Function(Vm)
self.Gradnorm = 0.0
self.lenm = len(self.m.vector().array())
self.u = Function(V)
self.ud = Function(V)
self.diff = Function(V)
self.p = Function(V)
# Define weak forms to assemble A, C and E
self._wkforma()
self._wkformc()
self._wkforme()
# Store other info:
self.ObsOp = ObsOp
self.UD = UD
self.reset() # Initialize U, C and E to []
self.Data = Data
self.GN = 1.0 # GN = 0.0 => GN Hessian; = 1.0 => full Hessian
# Operators and bc
LinearOperator.__init__(self, self.delta_m.vector(), \
self.delta_m.vector())
self.bc = bc
self.bcadj = bcadj
self._assemble_solverM(Vm)
self.assemble_A()
self.assemble_RHS(RHSinput)
self.Regul = Regul
# Counters, tolerances and others
self.nbPDEsolves = 0 # Updated when solve_A called
self.nbfwdsolves = 0 # Counter for plots
self.nbadjsolves = 0 # Counter for plots
self._set_plots(plot)
# MPI:
self.mycomm = mycomm
try:
self.myrank = MPI.rank(self.mycomm)
except:
self.myrank = 0
def __init__(self, V, Vm, bc, bcadj, \
RHSinput=[], ObsOp=[], UD=[], Regul=[], Data=[], plot=False, \
mycomm=None):
# Define test, trial and all other functions
self.trial = TrialFunction(V)
self.test = TestFunction(V)
self.mtrial = TrialFunction(Vm)
self.mtest = TestFunction(Vm)
self.rhs = Function(V)
self.m = Function(Vm)
self.mcopy = Function(Vm)
self.srchdir = Function(Vm)
self.delta_m = Function(Vm)
self.MG = Function(Vm)
self.MGv = self.MG.vector()
self.Grad = Function(Vm)
self.Gradnorm = 0.0
self.lenm = len(self.m.vector().array())
self.u = Function(V)
self.ud = Function(V)
self.diff = Function(V)
self.p = Function(V)
# Store other info:
self.ObsOp = ObsOp
self.UD = UD
self.reset() # Initialize U, C and E to []
self.Data = Data
self.GN = 1.0 # GN = 0.0 => GN Hessian; = 1.0 => full Hessian
# Define weak forms to assemble A, C and E
self._wkforma()
self._wkformc()
self._wkforme()
# Operators and bc
LinearOperator.__init__(self, self.delta_m.vector(), \
self.delta_m.vector())
self.bc = bc
self.bcadj = bcadj
self._assemble_solverM(Vm)
self.assemble_A()
self.assemble_RHS(RHSinput)
self.Regul = Regul
self.regparam = 1.0
if Regul != []:
self.PD = self.Regul.isPD()
# Counters, tolerances and others
self.nbPDEsolves = 0 # Updated when solve_A called
self.nbfwdsolves = 0 # Counter for plots
self.nbadjsolves = 0 # Counter for plots
# MPI:
self.mycomm = mycomm
def __init__(self, acousticwavePDE, regularization=None):
"""
Input:
acousticwavePDE should be an instantiation from class AcousticWave
"""
self.PDE = acousticwavePDE
self.PDE.exact = None
self.fwdsource = self.PDE.ftime
self.MG = Function(self.PDE.Vl)
self.MGv = self.MG.vector()
self.Grad = Function(self.PDE.Vl)
self.Gradv = self.Grad.vector()
self.srchdir = Function(self.PDE.Vl)
self.delta_m = Function(self.PDE.Vl)
LinearOperator.__init__(self, self.MG.vector(), self.MG.vector())
self.obsop = None # Observation operator
self.dd = None # observations
if regularization == None: self.regularization = ZeroRegularization()
else: self.regularization = regularization
self.alpha_reg = 1.0
# gradient
self.lamtest, self.lamtrial = TestFunction(self.PDE.Vl), TrialFunction(self.PDE.Vl)
self.p, self.v = Function(self.PDE.V), Function(self.PDE.V)
self.wkformgrad = inner(self.lamtest*nabla_grad(self.p), nabla_grad(self.v))*dx
# incremental rhs
self.lamhat = Function(self.PDE.Vl)
self.ptrial, self.ptest = TrialFunction(self.PDE.V), TestFunction(self.PDE.V)
self.wkformrhsincr = inner(self.lamhat*nabla_grad(self.ptrial), nabla_grad(self.ptest))*dx
# Hessian
self.phat, self.vhat = Function(self.PDE.V), Function(self.PDE.V)
self.wkformhess = inner(self.lamtest*nabla_grad(self.phat), nabla_grad(self.v))*dx \
+ inner(self.lamtest*nabla_grad(self.p), nabla_grad(self.vhat))*dx
# Mass matrix:
weak_m = inner(self.lamtrial,self.lamtest)*dx
Mass = assemble(weak_m)
self.solverM = LUSolver()
self.solverM.parameters['reuse_factorization'] = True
self.solverM.parameters['symmetric'] = True
self.solverM.set_operator(Mass)
# Time-integration factors
self.factors = np.ones(self.PDE.times.size)
self.factors[0], self.factors[-1] = 0.5, 0.5
self.factors *= self.PDE.Dt
self.invDt = 1./self.PDE.Dt
# Absorbing BCs
if self.PDE.abc:
#TODO: should probably be tested in other situations
if self.PDE.lumpD:
print '*** Warning: Damping matrix D is lumped. ',\
'Make sure gradient is consistent.'
self.vD, self.pD, self.p1D, self.p2D = Function(self.PDE.V), \
Function(self.PDE.V), Function(self.PDE.V), Function(self.PDE.V)
self.wkformgradD = inner(0.5*sqrt(self.PDE.rho/self.PDE.lam)\
*self.pD, self.vD*self.lamtest)*self.PDE.ds(1)
self.wkformDprime = inner(0.5*sqrt(self.PDE.rho/self.PDE.lam)\
*self.lamhat*self.ptrial, self.ptest)*self.PDE.ds(1)
self.dp, self.dph, self.vhatD = Function(self.PDE.V), \
Function(self.PDE.V), Function(self.PDE.V)
self.p1hatD, self.p2hatD = Function(self.PDE.V), Function(self.PDE.V)
self.wkformhessD = inner(-0.25*sqrt(self.PDE.rho)/(self.PDE.lam*sqrt(self.PDE.lam))\
*self.lamhat*self.dp, self.vD*self.lamtest)*self.PDE.ds(1) \
+ inner(0.5*sqrt(self.PDE.rho/self.PDE.lam)\
*self.dph, self.vD*self.lamtest)*self.PDE.ds(1)\
+ inner(0.5*sqrt(self.PDE.rho/self.PDE.lam)\
*self.dp, self.vhatD*self.lamtest)*self.PDE.ds(1)
def __init__(self, mpicomm_global, acousticwavePDE, sources, \
sourcesindex, timestepsindex, \
invparam='ab', regularization=None):
"""
Input:
acousticwavePDE should be an instantiation from class AcousticWave
"""
self.mpicomm_global = mpicomm_global
self.PDE = acousticwavePDE
self.PDE.exact = None
self.obsop = None # Observation operator
self.dd = None # observations
self.fwdsource = sources
self.srcindex = sourcesindex
self.tsteps = timestepsindex
self.PDEcount = 0
self.inverta = False
self.invertb = False
if 'a' in invparam:
self.inverta = True
if 'b' in invparam:
self.invertb = True
assert self.inverta + self.invertb > 0
Vm = self.PDE.Vm
V = self.PDE.V
VmVm = createMixedFS(Vm, Vm)
self.ab = Function(VmVm) # used for conversion (Vm,Vm)->VmVm
self.invparam = invparam
self.MG = Function(VmVm)
self.MGv = self.MG.vector()
self.Grad = Function(VmVm)
self.srchdir = Function(VmVm)
self.delta_m = Function(VmVm)
self.m_bkup = Function(VmVm)
LinearOperator.__init__(self, self.MGv, self.MGv)
self.GN = False
if regularization == None:
print '[ObjectiveAcoustic] *** Warning: Using zero regularization'
self.regularization = ZeroRegularization(Vm)
else:
self.regularization = regularization
self.PD = self.regularization.isPD()
self.alpha_reg = 1.0
self.p, self.q = Function(V), Function(V)
self.phat, self.qhat = Function(V), Function(V)
self.ahat, self.bhat = Function(Vm), Function(Vm)
self.ptrial, self.ptest = TrialFunction(V), TestFunction(V)
self.mtest, self.mtrial = TestFunction(Vm), TrialFunction(Vm)
if self.PDE.parameters['lumpM']:
self.Mprime = LumpedMassMatrixPrime(Vm, V, self.PDE.M.ratio)
self.get_gradienta = self.get_gradienta_lumped
self.get_hessiana = self.get_hessiana_lumped
self.get_incra = self.get_incra_lumped
else:
self.wkformgrada = inner(self.mtest*self.p, self.q)*dx
self.get_gradienta = self.get_gradienta_full
self.wkformhessa = inner(self.phat*self.mtest, self.q)*dx \
+ inner(self.p*self.mtest, self.qhat)*dx
self.wkformhessaGN = inner(self.p*self.mtest, self.qhat)*dx
self.get_hessiana = self.get_hessiana_full
self.wkformrhsincra = inner(self.ahat*self.ptrial, self.ptest)*dx
self.get_incra = self.get_incra_full
self.wkformgradb = inner(self.mtest*nabla_grad(self.p), nabla_grad(self.q))*dx
self.wkformgradbout = assemble(self.wkformgradb)
self.wkformrhsincrb = inner(self.bhat*nabla_grad(self.ptrial), nabla_grad(self.ptest))*dx
self.wkformhessb = inner(nabla_grad(self.phat)*self.mtest, nabla_grad(self.q))*dx \
+ inner(nabla_grad(self.p)*self.mtest, nabla_grad(self.qhat))*dx
self.wkformhessbGN = inner(nabla_grad(self.p)*self.mtest, nabla_grad(self.qhat))*dx
# Mass matrix:
self.mmtest, self.mmtrial = TestFunction(VmVm), TrialFunction(VmVm)
weak_m = inner(self.mmtrial, self.mmtest)*dx
self.Mass = assemble(weak_m)
self.solverM = PETScKrylovSolver("cg", "jacobi")
self.solverM.parameters["maximum_iterations"] = 2000
self.solverM.parameters["absolute_tolerance"] = 1e-24
self.solverM.parameters["relative_tolerance"] = 1e-24
self.solverM.parameters["report"] = False
self.solverM.parameters["error_on_nonconvergence"] = True
self.solverM.parameters["nonzero_initial_guess"] = False # True?
self.solverM.set_operator(self.Mass)
# Time-integration factors
self.factors = np.ones(self.PDE.times.size)
self.factors[0], self.factors[-1] = 0.5, 0.5
self.factors *= self.PDE.Dt
self.invDt = 1./self.PDE.Dt
# Absorbing BCs
if self.PDE.parameters['abc']:
assert not self.PDE.parameters['lumpD']
self.wkformgradaABC = inner(
self.mtest*sqrt(self.PDE.b/self.PDE.a)*self.p,
self.q)*self.PDE.ds(1)
self.wkformgradbABC = inner(
self.mtest*sqrt(self.PDE.a/self.PDE.b)*self.p,
self.q)*self.PDE.ds(1)
self.wkformgradaABCout = assemble(self.wkformgradaABC)
self.wkformgradbABCout = assemble(self.wkformgradbABC)
self.wkformincrrhsABC = inner(
(self.ahat*sqrt(self.PDE.b/self.PDE.a)
+ self.bhat*sqrt(self.PDE.a/self.PDE.b))*self.ptrial,
self.ptest)*self.PDE.ds(1)
self.wkformhessaABC = inner(
(self.bhat/sqrt(self.PDE.a*self.PDE.b) -
self.ahat*sqrt(self.PDE.b/(self.PDE.a*self.PDE.a*self.PDE.a)))
*self.p*self.mtest, self.q)*self.PDE.ds(1)
self.wkformhessbABC = inner(
(self.ahat/sqrt(self.PDE.a*self.PDE.b) -
self.bhat*sqrt(self.PDE.a/(self.PDE.b*self.PDE.b*self.PDE.b)))
*self.p*self.mtest, self.q)*self.PDE.ds(1)