# 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
waveobj.dd = DD
waveobj.solvefwd_cost()
print 'noise misfit={}, regul cost={}, ratio={}'.format(waveobj.cost_misfit, \
waveobj.cost_reg, waveobj.cost_misfit/waveobj.cost_reg)
######### Media for gradient and Hessian checks
#Medium = np.zeros((5, Vm.dim()))
# 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))
# fig.savefig(filename + '/observations.eps')
# perturbate medium
V = np.linspace(1.0, 3.0, 20)
MISFIT = []
for ii, eps in enumerate(V):
for index, pp in enumerate(sol):
setfct(solp, pp[0])
Bp[:, index] = myObs.obs(solp)
mytimes[index] = pp[1]
Bpf = Bp * mytf.evaluate(mytimes)
# Plots:
try:
boolplot = int(sys.argv[1])
except:
boolplot = 20
if boolplot > 0:
filename, ext = splitext(sys.argv[0])
if myrank == 0:
if isdir(filename + '/'): rmtree(filename + '/')
if PARALLEL: MPI.barrier(mycomm)
myplot = PlotFenics(filename)
plotp = Function(V)
myplot.plot_timeseries(sol, 'p', 0, boolplot, plotp)
# Plot medium
myplot.set_varname('lambda')
myplot.plot_vtk(lambda_target_fn)
# Plot observations
fig = plt.figure()
for ii in range(Bp.shape[0]):
ax = fig.add_subplot(2, 2, ii + 1)
ax.plot(mytimes, Bp[ii, :], 'b')
ax.plot(mytimes, Bpf[ii, :], 'r--')
ax.set_title('Plot' + str(ii))
fig.savefig(filename + '/observations_p' + str(myrank) + '.eps')
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)
"""
# Plots:
try:
boolplot = int(sys.argv[1])
except:
boolplot = 20
if boolplot > 0:
filename, ext = splitext(sys.argv[0])
#filename = filename + '0'
if myrank == 0:
if isdir(filename + '/'): rmtree(filename + '/')
if not mycomm == None: MPI.barrier(mycomm)
myplot = PlotFenics(filename)
plotp = Function(V)
myplot.plot_timeseries(sol, 'p', 0, boolplot, plotp)
# myplot.set_varname('p')
# for index, pp in enumerate(sol):
# if index%boolplot == 0:
# setfct(plotp, pp[0])
# myplot.plot_vtk(plotp, index)
# myplot.gather_vtkplots()
# Plot medium
myplot.set_varname('lambda')
myplot.plot_vtk(lambda_target_fn)
# Plot observations
fig = plt.figure()
for ii in range(Bp.shape[0]):
ax = fig.add_subplot(2,2,ii+1)
ax.plot(mytimes, Bp[ii,:], 'b')
ax.plot(mytimes, Bpf[ii,:], 'r--')
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)
