def __init__(self, regul, param, isprint=False):
"""
Arguments:
regul = regularization for inversion parameters
param = inversion parameters (either 'a' or 'b')
isprint = boolean
"""
self.param = param
if self.param == 'a':
self.regul1 = regul
self.regul2 = ZeroRegularization(regul.Vm)
elif self.param == 'b':
self.regul1 = ZeroRegularization(regul.Vm)
self.regul2 = regul
else:
if isprint:
print "[SingleRegularization] *** Error: argument 'param' must be 'a' or 'b'"
sys.exit(1)
self.isprint = isprint
Vm = regul.Vm
self.VmVm = createMixedFS(Vm, Vm)
self.ab = Function(self.VmVm)
bd = BlockDiagonal(Vm, Vm, Vm.mesh().mpi_comm())
self.saa = bd.saa
if isprint:
print '[SingleRegularization] inversion parameter {}'.format(
self.param)
if self.isPD():
print '[SingleRegularization] Using primal-dual TV'
class ObjectiveAcoustic(LinearOperator):
"""
Computes data misfit, gradient and Hessian evaluation for the seismic
inverse problem using acoustic wave data
"""
#TODO: add support for multiple sources
# CONSTRUCTORS:
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 copy(self):
"""(hard) copy constructor"""
newobj = self.__class__(self.PDE.copy())
setfct(newobj.MG, self.MG)
setfct(newobj.srchdir, self.srchdir)
newobj.obsop = self.obsop
return newobj
# FORWARD PROBLEM + COST:
def solvefwd(self, cost=False):
self.PDE.set_fwd()
self.PDE.ftime = self.fwdsource
self.solfwd,_ = self.PDE.solve()
# observations:
self.Bp = np.zeros((len(self.obsop.PtwiseObs.Points),len(self.solfwd)))
for index, sol in enumerate(self.solfwd):
setfct(self.p, sol[0])
self.Bp[:,index] = self.obsop.obs(self.p)
if cost:
assert not self.dd == None, "Provide observations"
self.misfit = self.obsop.costfct(self.Bp, self.dd, self.PDE.times)
self.cost_reg = self.regularization.cost(self.PDE.lam)
self.cost = self.misfit + self.alpha_reg*self.cost_reg
def solvefwd_cost(self): self.solvefwd(True)
# ADJOINT PROBLEM + GRAD:
#@profile
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 solveadj_constructgrad(self): self.solveadj(True)
# HESSIAN:
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 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 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))
# SETTERS + UPDATE:
def update_PDE(self, parameters): self.PDE.update(parameters)
def update_m(self, lam): self.update_PDE({'lambda':lam})
def set_abc(self, mesh, class_bc_abc, lumpD):
self.PDE.set_abc(mesh, class_bc_abc, lumpD)
def backup_m(self): self.lam_bkup = self.getmarray()
def restore_m(self): self.update_m(self.lam_bkup)
def setsrcterm(self, ftime): self.PDE.ftime = ftime
# GETTERS:
def getmcopyarray(self): return self.lam_bkup
def getmarray(self): return self.PDE.lam.vector().array()
def getMGarray(self): return self.MGv.array()
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)
class ObjectiveAcoustic(LinearOperator):
"""
Computes data misfit, gradient and Hessian evaluation for the seismic
inverse problem using acoustic wave data
"""
# CONSTRUCTORS:
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)
def copy(self):
"""(hard) copy constructor"""
newobj = self.__class__(self.PDE.copy())
setfct(newobj.MG, self.MG)
setfct(newobj.Grad, self.Grad)
setfct(newobj.srchdir, self.srchdir)
newobj.obsop = self.obsop
newobj.dd = self.dd
newobj.fwdsource = self.fwdsource
newobj.srcindex = self.srcindex
newobj.tsteps = self.tsteps
return newobj
# FORWARD PROBLEM + COST:
#@profile
def solvefwd(self, cost=False):
self.PDE.set_fwd()
self.solfwd, self.solpfwd, self.solppfwd = [], [], []
self.Bp = []
#TODO: make fwdsource iterable to return source term
Ricker = self.fwdsource[0]
srcv = self.fwdsource[2]
for sii in self.srcindex:
ptsrc = self.fwdsource[1][sii]
def srcterm(tt):
srcv.zero()
srcv.axpy(Ricker(tt), ptsrc)
return srcv
self.PDE.ftime = srcterm
solfwd, solpfwd, solppfwd,_ = self.PDE.solve()
self.solfwd.append(solfwd)
self.solpfwd.append(solpfwd)
self.solppfwd.append(solppfwd)
self.PDEcount += 1
#TODO: come back and parallellize this too (over time steps)
Bp = np.zeros((len(self.obsop.PtwiseObs.Points),len(solfwd)))
for index, sol in enumerate(solfwd):
setfct(self.p, sol[0])
Bp[:,index] = self.obsop.obs(self.p)
self.Bp.append(Bp)
if cost:
assert not self.dd == None, "Provide data observations to compute cost"
self.cost_misfit_local = 0.0
for Bp, dd in izip(self.Bp, self.dd):
self.cost_misfit_local += self.obsop.costfct(\
Bp[:,self.tsteps], dd[:,self.tsteps],\
self.PDE.times[self.tsteps], self.factors[self.tsteps])
self.cost_misfit = MPI.sum(self.mpicomm_global, self.cost_misfit_local)
self.cost_misfit /= len(self.fwdsource[1])
self.cost_reg = self.regularization.costab(self.PDE.a, self.PDE.b)
self.cost = self.cost_misfit + self.alpha_reg*self.cost_reg
if DEBUG:
print 'cost_misfit={}, cost_reg={}'.format(\
self.cost_misfit, self.cost_reg)
def solvefwd_cost(self): self.solvefwd(True)
# ADJOINT PROBLEM + GRADIENT:
#@profile
def solveadj(self, grad=False):
self.PDE.set_adj()
self.soladj, self.solpadj, self.solppadj = [], [], []
for Bp, dd in zip(self.Bp, self.dd):
self.obsop.assemble_rhsadj(Bp, dd, self.PDE.times, self.PDE.bc)
self.PDE.ftime = self.obsop.ftimeadj
soladj,solpadj,solppadj,_ = self.PDE.solve()
self.soladj.append(soladj)
self.solpadj.append(solpadj)
self.solppadj.append(solppadj)
self.PDEcount += 1
if grad:
self.MG.vector().zero()
MGa_local, MGb_local = self.MG.split(deepcopy=True)
MGav_local, MGbv_local = MGa_local.vector(), MGb_local.vector()
t0, t1 = self.tsteps[0], self.tsteps[-1]+1
for solfwd, solpfwd, solppfwd, soladj in \
izip(self.solfwd, self.solpfwd, self.solppfwd, self.soladj):
for fwd, fwdp, fwdpp, adj, fact in \
izip(solfwd[t0:t1], solpfwd[t0:t1], solppfwd[t0:t1],\
soladj[::-1][t0:t1], self.factors[t0:t1]):
setfct(self.q, adj[0])
if self.inverta:
# gradient a
setfct(self.p, fwdpp[0])
MGav_local.axpy(fact, self.get_gradienta())
if self.invertb:
# gradient b
setfct(self.p, fwd[0])
assemble(form=self.wkformgradb, tensor=self.wkformgradbout)
MGbv_local.axpy(fact, self.wkformgradbout)
if self.PDE.parameters['abc']:
setfct(self.p, fwdp[0])
if self.inverta:
assemble(form=self.wkformgradaABC, tensor=self.wkformgradaABCout)
MGav_local.axpy(0.5*fact, self.wkformgradaABCout)
if self.invertb:
assemble(form=self.wkformgradbABC, tensor=self.wkformgradbABCout)
MGbv_local.axpy(0.5*fact, self.wkformgradbABCout)
MGa, MGb = self.MG.split(deepcopy=True)
MPIAllReduceVector(MGav_local, MGa.vector(), self.mpicomm_global)
MPIAllReduceVector(MGbv_local, MGb.vector(), self.mpicomm_global)
setfct(MGa, MGa.vector()/len(self.fwdsource[1]))
setfct(MGb, MGb.vector()/len(self.fwdsource[1]))
self.MG.vector().zero()
if self.inverta:
assign(self.MG.sub(0), MGa)
if self.invertb:
assign(self.MG.sub(1), MGb)
if DEBUG:
print 'grad_misfit={}, grad_reg={}'.format(\
self.MG.vector().norm('l2'),\
self.regularization.gradab(self.PDE.a, self.PDE.b).norm('l2'))
self.MG.vector().axpy(self.alpha_reg, \
self.regularization.gradab(self.PDE.a, self.PDE.b))
try:
self.solverM.solve(self.Grad.vector(), self.MG.vector())
except:
# if |G|<<1, first residuals may diverge
# caveat: Hope that ALL processes throw an exception
pseudoGradnorm = np.sqrt(self.MGv.inner(self.MGv))
if pseudoGradnorm < 1e-8:
print '*** Warning: Increasing divergence_limit for Mass matrix solver'
self.solverM.parameters["divergence_limit"] = 1e6
self.solverM.solve(self.Grad.vector(), self.MG.vector())
else:
print '*** Error: Problem with Mass matrix solver'
sys.exit(1)
def solveadj_constructgrad(self): self.solveadj(True)
def get_gradienta_lumped(self):
return self.Mprime.get_gradient(self.p.vector(), self.q.vector())
def get_gradienta_full(self):
return assemble(self.wkformgrada)
# HESSIAN:
#@profile
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()
#@profile
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 get_incra_full(self, pvector):
return self.E*pvector
def get_incra_lumped(self, pvector):
return self.Mprime.get_incremental(self.ahat.vector(), pvector)
#@profile
def mult(self, abhat, y):
"""
mult(self, abhat, y): return y = Hessian * abhat
inputs:
y, abhat = Function(V).vector()
"""
setfct(self.ab, abhat)
ahat, bhat = self.ab.split(deepcopy=True)
setfct(self.ahat, ahat)
setfct(self.bhat, bhat)
if not self.inverta:
self.ahat.vector().zero()
if not self.invertb:
self.bhat.vector().zero()
self.C = assemble(self.wkformrhsincrb)
if not self.PDE.parameters['lumpM']: self.E = assemble(self.wkformrhsincra)
if self.PDE.parameters['abc']: self.Dp = assemble(self.wkformincrrhsABC)
t0, t1 = self.tsteps[0], self.tsteps[-1]+1
# Compute Hessian*abhat
self.ab.vector().zero()
yaF_local, ybF_local = self.ab.split(deepcopy=True)
ya_local, yb_local = yaF_local.vector(), ybF_local.vector()
# iterate over sources:
for self.solfwdi, self.solpfwdi, self.solppfwdi, \
self.soladji, self.solpadji, self.solppadji \
in izip(self.solfwd, self.solpfwd, self.solppfwd, \
self.soladj, self.solpadj, self.solppadj):
# incr. fwd
self.PDE.set_fwd()
self.PDE.ftime = self.ftimeincrfwd
self.solincrfwd,solpincrfwd,self.solppincrfwd,_ = self.PDE.solve()
self.PDEcount += 1
# incr. adj
self.PDE.set_adj()
self.PDE.ftime = self.ftimeincradj
solincradj,_,_,_ = self.PDE.solve()
self.PDEcount += 1
# assemble Hessian-vect product:
for fwd, adj, fwdp, incrfwdp, \
fwdpp, incrfwdpp, incrfwd, incradj, fact \
in izip(self.solfwdi[t0:t1], self.soladji[::-1][t0:t1],\
self.solpfwdi[t0:t1], solpincrfwd[t0:t1], \
self.solppfwdi[t0:t1], self.solppincrfwd[t0:t1],\
self.solincrfwd[t0:t1], solincradj[::-1][t0:t1], self.factors[t0:t1]):
# 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.q, adj[0])
setfct(self.qhat, incradj[0])
if self.invertb:
# Hessian b
setfct(self.p, fwd[0])
setfct(self.phat, incrfwd[0])
if self.GN:
yb_local.axpy(fact, assemble(self.wkformhessbGN))
else:
yb_local.axpy(fact, assemble(self.wkformhessb))
if self.inverta:
# Hessian a
setfct(self.p, fwdpp[0])
setfct(self.phat, incrfwdpp[0])
ya_local.axpy(fact, self.get_hessiana())
if self.PDE.parameters['abc']:
if not self.GN:
setfct(self.p, incrfwdp[0])
if self.inverta:
ya_local.axpy(0.5*fact, assemble(self.wkformgradaABC))
if self.invertb:
yb_local.axpy(0.5*fact, assemble(self.wkformgradbABC))
setfct(self.p, fwdp[0])
setfct(self.q, incradj[0])
if self.inverta:
ya_local.axpy(0.5*fact, assemble(self.wkformgradaABC))
if self.invertb:
yb_local.axpy(0.5*fact, assemble(self.wkformgradbABC))
if not self.GN:
setfct(self.q, adj[0])
if self.inverta:
ya_local.axpy(0.25*fact, assemble(self.wkformhessaABC))
if self.invertb:
yb_local.axpy(0.25*fact, assemble(self.wkformhessbABC))
yaF, ybF = self.ab.split(deepcopy=True)
MPIAllReduceVector(ya_local, yaF.vector(), self.mpicomm_global)
MPIAllReduceVector(yb_local, ybF.vector(), self.mpicomm_global)
self.ab.vector().zero()
if self.inverta:
assign(self.ab.sub(0), yaF)
if self.invertb:
assign(self.ab.sub(1), ybF)
y.zero()
y.axpy(1.0/len(self.fwdsource[1]), self.ab.vector())
if DEBUG:
print 'Hess_misfit={}, Hess_reg={}'.format(\
y.norm('l2'),\
self.regularization.hessianab(self.ahat.vector(),\
self.bhat.vector()).norm('l2'))
y.axpy(self.alpha_reg, \
self.regularization.hessianab(self.ahat.vector(), self.bhat.vector()))
def get_hessiana_full(self):
if self.GN:
return assemble(self.wkformhessaGN)
else:
return assemble(self.wkformhessa)
def get_hessiana_lumped(self):
if self.GN:
return self.Mprime.get_gradient(self.p.vector(), self.qhat.vector())
else:
return self.Mprime.get_gradient(self.phat.vector(), self.q.vector()) +\
self.Mprime.get_gradient(self.p.vector(), self.qhat.vector())
def assemble_hessian(self):
self.regularization.assemble_hessianab(self.PDE.a, self.PDE.b)
# SETTERS + UPDATE:
def update_PDE(self, parameters): self.PDE.update(parameters)
def update_m(self, medparam):
""" medparam contains both med parameters """
setfct(self.ab, medparam)
a, b = self.ab.split(deepcopy=True)
self.update_PDE({'a':a, 'b':b})
def backup_m(self):
""" back-up current value of med param a and b """
assign(self.m_bkup.sub(0), self.PDE.a)
assign(self.m_bkup.sub(1), self.PDE.b)
def restore_m(self):
""" restore backed-up values of a and b """
a, b = self.m_bkup.split(deepcopy=True)
self.update_PDE({'a':a, 'b':b})
def mediummisfit(self, target_medium):
"""
Compute medium misfit at current position
"""
assign(self.ab.sub(0), self.PDE.a)
assign(self.ab.sub(1), self.PDE.b)
try:
diff = self.ab.vector() - target_medium.vector()
except:
diff = self.ab.vector() - target_medium
Md = self.Mass*diff
self.ab.vector().zero()
self.ab.vector().axpy(1.0, Md)
Mda, Mdb = self.ab.split(deepcopy=True)
self.ab.vector().zero()
self.ab.vector().axpy(1.0, diff)
da, db = self.ab.split(deepcopy=True)
medmisfita = np.sqrt(da.vector().inner(Mda.vector()))
medmisfitb = np.sqrt(db.vector().inner(Mdb.vector()))
return medmisfita, medmisfitb
def compare_ab_global(self):
"""
Check that med param (a, b) are the same across all proc
"""
assign(self.ab.sub(0), self.PDE.a)
assign(self.ab.sub(1), self.PDE.b)
ab_recv = self.ab.vector().copy()
normabloc = np.linalg.norm(self.ab.vector().array())
MPIAllReduceVector(self.ab.vector(), ab_recv, self.mpicomm_global)
ab_recv /= MPI.size(self.mpicomm_global)
diff = ab_recv - self.ab.vector()
reldiff = np.linalg.norm(diff.array())/normabloc
assert reldiff < 2e-16, 'Diff in (a,b) across proc: {:.2e}'.format(reldiff)
# GETTERS:
def getmbkup(self): return self.m_bkup.vector()
def getMG(self): return self.MGv
def getprecond(self):
if self.PC == 'prior':
return self.regularization.getprecond()
elif self.PC == 'bfgs':
return self.bfgsop
else:
print 'Wrong keyword for choice of preconditioner'
sys.exit(1)
# SOLVE INVERSE PROBLEM
#@profile
def inversion(self, initial_medium, target_medium, parameters_in=[], \
boundsLS=None, myplot=None):
"""
Solve inverse problem with that objective function
parameters:
solverNS = solver for Newton system ('steepest', 'Newton', 'BFGS')
retolgrad = relative tolerance for stopping criterion (grad)
abstolgrad = absolute tolerance for stopping criterion (grad)
tolcost = tolerance for stopping criterion (cost)
maxiterNewt = max nb of Newton iterations
nbGNsteps = nb of Newton steps with GN Hessian
maxtolcg = max value of the tolerance for CG solver
checkab = nb of steps in-between check of param
inexactCG = [bool] inexact CG solver or exact CG
isprint = [bool] print results to screen
avgPC = [bool] average Preconditioned step over all proc in CG
PC = choice of preconditioner ('prior', or 'bfgs')
"""
parameters = {}
parameters['solverNS'] = 'Newton'
parameters['reltolgrad'] = 1e-10
parameters['abstolgrad'] = 1e-14
parameters['tolcost'] = 1e-24
parameters['maxiterNewt'] = 100
parameters['nbGNsteps'] = 10
parameters['maxtolcg'] = 0.5
parameters['checkab'] = 10
parameters['inexactCG'] = True
parameters['isprint'] = False
parameters['avgPC'] = True
parameters['PC'] = 'prior'
parameters['BFGS_damping'] = 0.2
parameters['memory_limit'] = 50
parameters['H0inv'] = 'Rinv'
parameters.update(parameters_in)
solverNS = parameters['solverNS']
isprint = parameters['isprint']
maxiterNewt = parameters['maxiterNewt']
reltolgrad = parameters['reltolgrad']
abstolgrad = parameters['abstolgrad']
tolcost = parameters['tolcost']
nbGNsteps = parameters['nbGNsteps']
checkab = parameters['checkab']
avgPC = parameters['avgPC']
if parameters['inexactCG']:
maxtolcg = parameters['maxtolcg']
else:
maxtolcg = 1e-12
if solverNS == 'BFGS':
maxtolcg = -1.0
self.PC = parameters['PC']
# BFGS (preconditioner or solver):
if self.PC == 'bfgs' or solverNS == 'BFGS':
self.bfgsop = BFGS_operator(parameters)
H0inv = self.bfgsop.parameters['H0inv']
else:
self.bfgsop = []
self.PDEcount = 0 # reset
if isprint:
print '\t{:12s} {:10s} {:12s} {:12s} {:12s} {:16s}\t\t\t {:10s} {:12s} {:10s} {:10s}'.format(\
'iter', 'cost', 'misfit', 'reg', '|G|', 'medmisf', 'a_ls', 'tol_cg', 'n_cg', 'PDEsolves')
a0, b0 = initial_medium.split(deepcopy=True)
self.update_PDE({'a':a0, 'b':b0})
self._plotab(myplot, 'init')
Mab = self.Mass*target_medium.vector()
self.ab.vector().zero()
self.ab.vector().axpy(1.0, Mab)
Ma, Mb = self.ab.split(deepcopy=True)
at, bt = target_medium.split(deepcopy=True)
atnorm = np.sqrt(at.vector().inner(Ma.vector()))
btnorm = np.sqrt(bt.vector().inner(Mb.vector()))
alpha = -1.0 # dummy value for print outputs
self.solvefwd_cost()
for it in xrange(maxiterNewt):
MGv_old = self.MGv.copy()
self.solveadj_constructgrad()
gradnorm = np.sqrt(self.MGv.inner(self.Grad.vector()))
if it == 0: gradnorm0 = gradnorm
medmisfita, medmisfitb = self.mediummisfit(target_medium)
self._plotab(myplot, str(it))
self._plotgrad(myplot, str(it))
# Stopping criterion (gradient)
if gradnorm < gradnorm0*reltolgrad or gradnorm < abstolgrad:
print '{:12d} {:12.4e} {:12.2e} {:12.2e} {:11.4e} {:10.2e} ({:4.1f}%) {:10.2e} ({:4.1f}%)'.\
format(it, self.cost, self.cost_misfit, self.cost_reg, gradnorm,\
medmisfita, 100.0*medmisfita/atnorm, medmisfitb, 100.0*medmisfitb/btnorm),
print '{:11.3f} {:12.2} {:10} {:10d}'.format(\
alpha, "", "", self.PDEcount)
if isprint:
print '\nGradient sufficiently reduced'
print 'Optimization converged'
return
# Assemble Hessian of regularization for nonlinear regularization:
self.assemble_hessian()
# Update BFGS approx (s, y, H0)
if self.PC == 'bfgs' or solverNS == 'BFGS':
if it > 0:
s = self.srchdir.vector() * alpha
y = self.MGv - MGv_old
theta = self.bfgsop.update(s, y)
else:
theta = 1.0
if H0inv == 'Rinv':
self.bfgsop.set_H0inv(self.regularization.getprecond())
elif H0inv == 'Minv':
print 'H0inv = Minv? That is not a good idea'
sys.exit(1)
# Compute search direction and plot
tolcg = min(maxtolcg, np.sqrt(gradnorm/gradnorm0))
self.GN = (it < nbGNsteps) # use GN or full Hessian?
# most time spent here:
if avgPC:
cgiter, cgres, cgid = compute_searchdirection(self,
{'method':solverNS, 'tolcg':tolcg,\
'max_iter':250+1250*(self.GN==False)},\
comm=self.mpicomm_global, BFGSop=self.bfgsop)
else:
cgiter, cgres, cgid = compute_searchdirection(self,
{'method':solverNS, 'tolcg':tolcg,\
'max_iter':250+1250*(self.GN==False)}, BFGSop=self.bfgsop)
# addt'l safety: zero-out entries of 'srchdir' corresponding to
# param that are not inverted for
if not self.inverta*self.invertb:
srcha, srchb = self.srchdir.split(deepcopy=True)
if not self.inverta:
srcha.vector().zero()
assign(self.srchdir.sub(0), srcha)
if not self.invertb:
srchb.vector().zero()
assign(self.srchdir.sub(1), srchb)
self._plotsrchdir(myplot, str(it))
if isprint:
print '{:12d} {:12.4e} {:12.2e} {:12.2e} {:11.4e} {:10.2e} ({:4.1f}%) {:10.2e} ({:4.1f}%)'.\
format(it, self.cost, self.cost_misfit, self.cost_reg, gradnorm,\
medmisfita, 100.0*medmisfita/atnorm, medmisfitb, 100.0*medmisfitb/btnorm),
print '{:11.3f} {:12.2e} {:10d} {:10d}'.format(\
alpha, tolcg, cgiter, self.PDEcount)
# Backtracking line search
cost_old = self.cost
statusLS, LScount, alpha = bcktrcklinesearch(self, parameters, boundsLS)
cost = self.cost
# Perform line search for dual variable (TV-PD):
if self.PD:
self.regularization.update_w(self.srchdir.vector(), alpha)
if it%checkab == 0:
self.compare_ab_global()
# Stopping criterion (LS)
if not statusLS:
if isprint:
print '\nLine search failed'
print 'Optimization aborted'
return
# Stopping criterion (cost)
if np.abs(cost-cost_old)/np.abs(cost_old) < tolcost:
if isprint:
print '\nCost function stagnates'
print 'Optimization aborted'
return
if isprint:
print '\nMaximum number of Newton iterations reached'
print 'Optimization aborted'
# PLOTS:
def _plotab(self, myplot, index):
""" plot media during inversion """
if not myplot == None:
if self.invparam == 'a' or self.invparam == 'ab':
myplot.set_varname('a'+index)
myplot.plot_vtk(self.PDE.a)
if self.invparam == 'b' or self.invparam == 'ab':
myplot.set_varname('b'+index)
myplot.plot_vtk(self.PDE.b)
def _plotgrad(self, myplot, index):
""" plot grad during inversion """
if not myplot == None:
if self.invparam == 'a':
myplot.set_varname('Grad_a'+index)
myplot.plot_vtk(self.Grad)
elif self.invparam == 'b':
myplot.set_varname('Grad_b'+index)
myplot.plot_vtk(self.Grad)
elif self.invparam == 'ab':
Ga, Gb = self.Grad.split(deepcopy=True)
myplot.set_varname('Grad_a'+index)
myplot.plot_vtk(Ga)
myplot.set_varname('Grad_b'+index)
myplot.plot_vtk(Gb)
def _plotsrchdir(self, myplot, index):
""" plot srchdir during inversion """
if not myplot == None:
if self.invparam == 'a':
myplot.set_varname('srchdir_a'+index)
myplot.plot_vtk(self.srchdir)
elif self.invparam == 'b':
myplot.set_varname('srchdir_b'+index)
myplot.plot_vtk(self.srchdir)
elif self.invparam == 'ab':
Ga, Gb = self.srchdir.split(deepcopy=True)
myplot.set_varname('srchdir_a'+index)
myplot.plot_vtk(Ga)
myplot.set_varname('srchdir_b'+index)
myplot.plot_vtk(Gb)
# SHOULD BE REMOVED:
def set_abc(self, mesh, class_bc_abc, lumpD):
self.PDE.set_abc(mesh, class_bc_abc, lumpD)
def init_vector(self, x, dim):
self.Mass.init_vector(x, dim)
def getmcopyarray(self): return self.getmcopy().array()
def getMGarray(self): return self.MGv.array()
def setsrcterm(self, ftime): self.PDE.ftime = ftime
class SingleRegularization():
"""
Implement regularization for a single parameter
Used to solve single inverse problem with code for joint inverse problem
Parameter fixed has zero cost, zero gradient, and zero Hessian, but identity
preconditioner
"""
def __init__(self, regul, param, isprint=False):
"""
Arguments:
regul = regularization for inversion parameters
param = inversion parameters (either 'a' or 'b')
isprint = boolean
"""
self.param = param
if self.param == 'a':
self.regul1 = regul
self.regul2 = ZeroRegularization(regul.Vm)
elif self.param == 'b':
self.regul1 = ZeroRegularization(regul.Vm)
self.regul2 = regul
else:
if isprint:
print "[SingleRegularization] *** Error: argument 'param' must be 'a' or 'b'"
sys.exit(1)
self.isprint = isprint
Vm = regul.Vm
self.VmVm = createMixedFS(Vm, Vm)
self.ab = Function(self.VmVm)
bd = BlockDiagonal(Vm, Vm, Vm.mesh().mpi_comm())
self.saa = bd.saa
if isprint:
print '[SingleRegularization] inversion parameter {}'.format(
self.param)
if self.isPD():
print '[SingleRegularization] Using primal-dual TV'
def isTV(self):
return self.regul1.isTV() or self.regul2.isTV()
def isPD(self):
return self.regul1.isPD() or self.regul2.isPD()
def costab(self, m1, m2):
return self.regul1.cost(m1) + self.regul2.cost(m2)
def costabvect(self, m1, m2):
return self.regul1.costvect(m1) + self.regul2.costvect(m2)
def gradab(self, m1, m2):
grad1 = self.regul1.grad(m1)
grad2 = self.regul2.grad(m2)
return self.saa.assign(grad1, grad2)
def gradabvect(self, m1, m2):
""" relies on gradvect method from regularization instead of grad
gradvect takes a Vector() as input argument """
grad1 = self.regul1.gradvect(m1)
grad2 = self.regul2.gradvect(m2)
return self.saa.assign(grad1, grad2)
def assemble_hessianab(self, m1, m2):
self.regul1.assemble_hessian(m1)
self.regul2.assemble_hessian(m2)
def hessianab(self, m1, m2):
Hx1 = self.regul1.hessian(m1)
Hx2 = self.regul2.hessian(m2)
return self.saa.assign(Hx1, Hx2)
def getprecond(self):
if self.param == 'a':
precondsolver = self.regul1.getprecond()
elif self.param == 'b':
precondsolver = self.regul2.getprecond()
return PrecondPlusIdentity(precondsolver, self.param, self.VmVm)
def update_w(self, mhat, alphaLS, compute_what=True):
""" update dual variable in direction what
and update re-scaled version """
mhat1, mhat2 = self.saa.split(mhat)
self.regul1.update_w(mhat1, alphaLS, compute_what)
self.regul2.update_w(mhat2, alphaLS, compute_what)