# set up plots:
filename, ext = splitext(sys.argv[0])
if isdir(filename + '/'): rmtree(filename + '/')
myplot = PlotFenics(filename + str(Nxy))
myplot.set_varname('a_target')
myplot.plot_vtk(a_target_fn)
# define objective function:
regul = LaplacianPrior({
'Vm': Vm,
'gamma': 5e-4,
'beta': 5e-4,
'm0': a_target_fn
})
waveobj = ObjectiveAcoustic(wavepde, mysrc, 'a', regul)
waveobj.obsop = obsop
# noisy data
print 'generate noisy data'
waveobj.solvefwd()
skip = 20
myplot.plot_timeseries(waveobj.solfwd[0], 'pd', 0, skip, dl.Function(V))
DD = waveobj.Bp[:]
noiselevel = 0.1 # = 10%
for ii, dd in enumerate(DD):
np.random.seed(11)
nbobspt, dimsol = dd.shape
sigmas = np.sqrt((dd**2).sum(axis=1) / dimsol) * noiselevel
rndnoise = np.random.randn(nbobspt * dimsol).reshape((nbobspt, dimsol))
DD[ii] = dd + sigmas.reshape((len(sigmas), 1)) * rndnoise
mpilocalrank = MPI.rank(mpicomm_local)
mpiglobalrank = MPI.rank(mpicomm_global)
mpiworldsize = MPI.size(dl.mpi_comm_world())
print 'mpiworldrank={}, mpiglobalrank={}, mpilocalrank={}, sources={}, timestep=[{},{}]'.format(\
mpiworldrank, mpiglobalrank, mpilocalrank, sources,\
timesteps[0], timesteps[-1])
# observation operator:
obspts = [[ii * float(X) / float(Nxy), Y] for ii in range(1, Nxy)]
tfilterpts = [t0, t1, t2, tf]
obsop = TimeObsPtwise({'V': V, 'Points': obspts}, tfilterpts)
# define objective function:
if FDGRAD:
waveobj = ObjectiveAcoustic(mpicomm_global, Wave, [Ricker, Pt, srcv],\
sources, timesteps, PARAM)
else:
# REGULARIZATION:
amg = 'hypre_amg'
#regul = V_TV(Vl, {'k':k, 'eps':eps, 'amg':amg,\
#'print':PRINT, 'GNhessian':False})
regul = V_TVPD(Vl, {'k':k, 'eps':eps, 'amg':amg,\
'rescaledradiusdual':1.0, 'print':PRINT, 'PCGN':False})
waveobj = ObjectiveAcoustic(mpicomm_global, Wave, [Ricker, Pt, srcv],\
sources, timesteps, PARAM, regul)
waveobj.obsop = obsop
#waveobj.GN = True
# Generate synthetic observations
if PRINT: print 'generate noisy data'
waveobj.solvefwd()
Wave.update({'b':bt, 'a':at, 't0':0.0, 'tf':tf, 'Dt':Dt,\
'u0init':dl.Function(V), 'utinit':dl.Function(V)})
# observation operator:
obspts = [[0.0, ii/10.] for ii in range(1,10)] + \
[[1.0, ii/10.] for ii in range(1,10)] + \
[[ii/10., 0.0] for ii in range(1,10)] + \
[[ii/10., 1.0] for ii in range(1,10)]
tfilterpts = [t0, t1, t2, tf]
obsop = TimeObsPtwise({'V':V, 'Points':obspts}, tfilterpts)
# Regularization
regula = LaplacianPrior({'Vm':Vl, 'gamma':1e-4, 'beta':1e-4, 'm0':at})
regulab = SingleRegularization(regula, 'a', (not mpirank))
# define objective function:
waveobjab = ObjectiveAcoustic(Wave, [Ricker, Pt, srcv], 'a', regulab)
waveobjabnoregul = ObjectiveAcoustic(Wave, [Ricker, Pt, srcv], 'a')
waveobjab.obsop = obsop
waveobjabnoregul.obsop = obsop
# Generate synthetic observations
if mpirank == 0: print 'generate noisy data'
waveobjab.solvefwd()
DD = waveobjab.Bp[:]
if NOISE:
SNRdB = 20.0 # [dB], i.e, log10(mu/sigma) = SNRdB/10
np.random.seed(11)
for ii, dd in enumerate(DD):
if mpirank == 0: print 'source {}'.format(ii)
nbobspt, dimsol = dd.shape
#mu = np.abs(dd).mean(axis=1)
# myplot.set_varname('perturb_medium')
# myplot.plot_vtk(PerturbMed)
# observation operator:
obspts = [[x / 10.0, 1.0] for x in range(1, 10)]
obsop = TimeObsPtwise({"V": V, "Points": obspts})
# define pde operator:
wavepde = AcousticWave({"V": V, "Vl": Vl, "Vr": Vl})
wavepde.timestepper = "backward"
wavepde.lump = True
wavepde.set_abc(mesh, ABC(), True)
wavepde.update(
{"lambda": TargetMed, "rho": 1.0, "t0": t0, "tf": tf, "Dt": Dt, "u0init": dl.Function(V), "utinit": dl.Function(V)}
)
wavepde.ftime = mysrc
# define objective function:
waveobj = ObjectiveAcoustic(wavepde)
waveobj.obsop = obsop
# data
print "generate data"
waveobj.solvefwd()
myplot.plot_timeseries(waveobj.solfwd, "pd", 0, 40, fctV)
dd = waveobj.Bp.copy()
waveobj.dd = dd
# Plot observations
# fig = plt.figure()
# for ii in range(len(obspts)):
# ax = fig.add_subplot(3,3,ii+1)
# ax.plot(waveobj.times, waveobj.dd[ii,:], 'k--')
# ax.plot(waveobj.times, waveobj.Bp[ii,:], 'r--')
# ax.set_title('recv '+str(ii+1))
def run_test(fpeak, lambdamin, lambdamax, Nxy, tfilterpts, r, Dt, skip):
h = 1. / Nxy
checkdt(Dt, h, r, np.sqrt(lambdamax), True)
mesh = dl.UnitSquareMesh(Nxy, Nxy)
Vl = dl.FunctionSpace(mesh, 'Lagrange', 1)
V = dl.FunctionSpace(mesh, 'Lagrange', r)
fctV = dl.Function(V)
# set up plots:
filename, ext = splitext(sys.argv[0])
if isdir(filename + '/'): rmtree(filename + '/')
myplot = PlotFenics(filename)
# source:
Ricker = RickerWavelet(fpeak, 1e-10)
Pt = PointSources(V, [[0.5, 0.5]])
mydelta = Pt[0].array()
def mysrc(tt):
return Ricker(tt) * mydelta
# target medium:
lambda_target = dl.Expression('lmin + x[0]*(lmax-lmin)', \
lmin=lambdamin, lmax=lambdamax)
lambda_target_fn = dl.interpolate(lambda_target, Vl)
myplot.set_varname('lambda_target')
myplot.plot_vtk(lambda_target_fn)
# initial medium:
lambda_init = dl.Constant(lambdamin)
lambda_init_fn = dl.interpolate(lambda_init, Vl)
myplot.set_varname('lambda_init')
myplot.plot_vtk(lambda_init_fn)
# observation operator:
#obspts = [[0.2, 0.5], [0.5, 0.2], [0.5, 0.8], [0.8, 0.5]]
obspts = [[0.2, ii/10.] for ii in range(2,9)] + \
[[0.8, ii/10.] for ii in range(2,9)] + \
[[ii/10., 0.2] for ii in range(3,8)] + \
[[ii/10., 0.8] for ii in range(3,8)]
obsop = TimeObsPtwise({'V': V, 'Points': obspts}, tfilterpts)
# define pde operator:
wavepde = AcousticWave({'V': V, 'Vl': Vl, 'Vr': Vl})
wavepde.timestepper = 'backward'
wavepde.lump = True
wavepde.set_abc(mesh, LeftRight(), True)
wavepde.update({'lambda':lambda_target_fn, 'rho':1.0, \
't0':t0, 'tf':tf, 'Dt':Dt, 'u0init':dl.Function(V), 'utinit':dl.Function(V)})
wavepde.ftime = mysrc
# define objective function:
waveobj = ObjectiveAcoustic(wavepde)
waveobj.obsop = obsop
# data
print 'generate data'
waveobj.solvefwd()
myplot.plot_timeseries(waveobj.solfwd, 'pd', 0, skip, fctV)
dd = waveobj.Bp.copy()
# gradient
print 'generate observations'
waveobj.dd = dd
waveobj.update_m(lambda_init_fn)
waveobj.solvefwd_cost()
cost1 = waveobj.misfit
print 'misfit = {}'.format(waveobj.misfit)
myplot.plot_timeseries(waveobj.solfwd, 'p', 0, skip, fctV)
# Plot data and observations
fig = plt.figure()
if len(obspts) > 9: fig.set_size_inches(20., 15.)
for ii in range(len(obspts)):
if len(obspts) == 4: ax = fig.add_subplot(2, 2, ii + 1)
else: ax = fig.add_subplot(4, 6, ii + 1)
ax.plot(waveobj.PDE.times, waveobj.dd[ii, :], 'k--')
ax.plot(waveobj.PDE.times, waveobj.Bp[ii, :], 'b')
ax.set_title('Plot' + str(ii))
fig.savefig(filename + '/observations.eps')
print 'compute gradient'
waveobj.solveadj_constructgrad()
myplot.plot_timeseries(waveobj.soladj, 'v', 0, skip, fctV)
MG = waveobj.MGv.array().copy()
myplot.set_varname('grad')
myplot.plot_vtk(waveobj.Grad)
"""
# set up plots:
filename, ext = splitext(sys.argv[0])
#if mpirank == 0 and isdir(filename + '/'): rmtree(filename + '/')
#MPI.barrier(mpicomm)
myplot = PlotFenics(filename + str(Nxy))
myplot.set_varname('b_target')
myplot.plot_vtk(b_target_fn)
# define objective function:
regul = LaplacianPrior({
'Vm': Vm,
'gamma': 5e-4,
'beta': 5e-4,
'm0': a_target_fn
})
waveobj = ObjectiveAcoustic(wavepde, mysrc, 'b', regul)
waveobj.obsop = obsop
# noisy data
#TODO: to be fixed for parallel computation
if mpirank == 0: print 'generate noisy data'
waveobj.solvefwd()
skip = 20
myplot.plot_timeseries(waveobj.solfwd[0], 'pd', 0, skip, dl.Function(V))
DD = waveobj.Bp[:]
noiselevel = 0.1 # = 10%
for ii, dd in enumerate(DD):
np.random.seed(11)
nbobspt, dimsol = dd.shape
sigmas = np.sqrt((dd**2).sum(axis=1) / dimsol) * noiselevel
rndnoise = np.random.randn(nbobspt * dimsol).reshape((nbobspt, dimsol))
def run_test(fpeak, lambdamin, lambdamax, Nxy, tfilterpts, r, Dt, skip):
h = 1./Nxy
checkdt(Dt, h, r, np.sqrt(lambdamax), True)
mesh = dl.UnitSquareMesh(Nxy, Nxy)
Vl = dl.FunctionSpace(mesh, 'Lagrange', 1)
V = dl.FunctionSpace(mesh, 'Lagrange', r)
fctV = dl.Function(V)
# set up plots:
filename, ext = splitext(sys.argv[0])
if isdir(filename + '/'): rmtree(filename + '/')
myplot = PlotFenics(filename)
# source:
Ricker = RickerWavelet(fpeak, 1e-10)
Pt = PointSources(V, [[0.5,0.5]])
mydelta = Pt[0].array()
def mysrc(tt):
return Ricker(tt)*mydelta
# target medium:
lambda_target = dl.Expression('lmin + x[0]*(lmax-lmin)', \
lmin=lambdamin, lmax=lambdamax)
lambda_target_fn = dl.interpolate(lambda_target, Vl)
myplot.set_varname('lambda_target')
myplot.plot_vtk(lambda_target_fn)
# initial medium:
lambda_init = dl.Constant(lambdamin)
lambda_init_fn = dl.interpolate(lambda_init, Vl)
myplot.set_varname('lambda_init')
myplot.plot_vtk(lambda_init_fn)
# observation operator:
#obspts = [[0.2, 0.5], [0.5, 0.2], [0.5, 0.8], [0.8, 0.5]]
obspts = [[0.2, ii/10.] for ii in range(2,9)] + \
[[0.8, ii/10.] for ii in range(2,9)] + \
[[ii/10., 0.2] for ii in range(3,8)] + \
[[ii/10., 0.8] for ii in range(3,8)]
obsop = TimeObsPtwise({'V':V, 'Points':obspts}, tfilterpts)
# define pde operator:
wavepde = AcousticWave({'V':V, 'Vl':Vl, 'Vr':Vl})
wavepde.timestepper = 'centered'
wavepde.lump = True
wavepde.set_abc(mesh, LeftRight(), True)
wavepde.update({'lambda':lambda_target_fn, 'rho':1.0, \
't0':t0, 'tf':tf, 'Dt':Dt, 'u0init':dl.Function(V), 'utinit':dl.Function(V)})
wavepde.ftime = mysrc
# define objective function:
waveobj = ObjectiveAcoustic(wavepde)
waveobj.obsop = obsop
# data
print 'generate noisy data'
waveobj.solvefwd()
myplot.plot_timeseries(waveobj.solfwd, 'pd', 0, skip, fctV)
dd = waveobj.Bp.copy()
nbobspt, dimsol = dd.shape
noiselevel = 0.1 # = 10%
sigmas = np.sqrt((dd**2).sum(axis=1)/dimsol)*noiselevel
rndnoise = np.random.randn(nbobspt*dimsol).reshape((nbobspt, dimsol))
waveobj.dd = dd + sigmas.reshape((len(sigmas),1))*rndnoise
# gradient
print 'generate observations'
waveobj.update_m(lambda_init_fn)
waveobj.solvefwd_cost()
cost1 = waveobj.misfit
print 'misfit = {}'.format(waveobj.misfit)
myplot.plot_timeseries(waveobj.solfwd, 'p', 0, skip, fctV)
# Plot data and observations
fig = plt.figure()
if len(obspts) > 9: fig.set_size_inches(20., 15.)
for ii in range(len(obspts)):
if len(obspts) == 4: ax = fig.add_subplot(2,2,ii+1)
else: ax = fig.add_subplot(4,6,ii+1)
ax.plot(waveobj.PDE.times, waveobj.dd[ii,:], 'k--')
ax.plot(waveobj.PDE.times, waveobj.Bp[ii,:], 'b')
ax.set_title('Plot'+str(ii))
fig.savefig(filename + '/observations.eps')
print 'compute gradient'
waveobj.solveadj_constructgrad()
myplot.plot_timeseries(waveobj.soladj, 'v', 0, skip, fctV)
MG = waveobj.MGv.array().copy()
myplot.set_varname('grad')
myplot.plot_vtk(waveobj.Grad)
print 'check gradient with FD'
Medium = np.zeros((5, Vl.dim()))
for ii in range(5):
smoothperturb = dl.Expression('sin(n*pi*x[0])*sin(n*pi*x[1])', n=ii+1)
smoothperturb_fn = dl.interpolate(smoothperturb, Vl)
Medium[ii,:] = smoothperturb_fn.vector().array()
checkgradfd_med(waveobj, Medium, 1e-6, [1e-5, 1e-4])
print 'check Hessian with FD'
checkhessfd_med(waveobj, Medium, 1e-6, [1e-1, 1e-2, 1e-3, 1e-4, 1e-5], False)
# parameters
Vm = wavepde.Vm
V = wavepde.V
lenobspts = obsop.PtwiseObs.nbPts
# set up plots:
#filename, ext = splitext(sys.argv[0])
#myplot = PlotFenics(outputdirectory + filename + str(freq))
#MPI.barrier(mpicomm)
#myplot.set_varname('b_target')
#myplot.plot_vtk(b_target_fn)
if mpirank == 0: print 'Define objective function'
# define objective function:
waveobj = ObjectiveAcoustic(wavepde, mysrc, 'b', regul)
waveobj.obsop = obsop
# noisy data
if mpirank == 0: print 'generate noisy data'
waveobj.solvefwd()
DD = waveobj.Bp[:]
noiselevel = 0.1 # = 10%
for ii, dd in enumerate(DD):
np.random.seed(11)
nbobspt, dimsol = dd.shape
sigmas = np.sqrt((dd**2).sum(axis=1)/dimsol)*noiselevel
rndnoise = np.random.randn(nbobspt*dimsol).reshape((nbobspt, dimsol))
DD[ii] = dd + sigmas.reshape((len(sigmas),1))*rndnoise
waveobj.dd = DD
waveobj.solvefwd_cost()
# source:
if mpirank == 0: print 'sources'
srcloc = [[ii / 10., 1.0] for ii in range(1, 10, 2)]
#srcloc = [[0.1, 0.9]]
Ricker = RickerWavelet(freq, 1e-10)
Pt = PointSources(V, srcloc)
src = dl.Function(V)
srcv = src.vector()
mysrc = [Ricker, Pt, srcv]
# define objective function:
wavepde.update({'a':a_target_fn, 'b':b_target_fn, \
't0':t0, 'tf':tf, 'Dt':Dt, 'u0init':dl.Function(V), 'utinit':dl.Function(V)})
regul = LaplacianPrior({'Vm': Vm, 'gamma': 1e-4, 'beta': 1e-4, 'm0': 1.0})
waveobj = ObjectiveAcoustic(wavepde, mysrc, 'b', regul)
obsop = TimeObsPtwise({'V': V, 'Points': obspts}, t0tf)
waveobj.obsop = obsop
# Save MAP point, or assemble Hessian at MAP point
if SAVE_MAP:
# noisy data
if mpirank == 0: print 'generate noisy data'
waveobj.solvefwd()
DD = waveobj.Bp[:]
noiselevel = 0.1 # = 10%
for ii, dd in enumerate(DD):
np.random.seed(11)
nbobspt, dimsol = dd.shape
sigmas = np.sqrt((dd**2).sum(axis=1) / dimsol) * noiselevel
rndnoise = np.random.randn(nbobspt * dimsol).reshape((nbobspt, dimsol))