if mpirank == 0:
print 'Check gradient and Hessian against finite-difference'
InvPb.update_m(mtrueVm) #InvPb.update_m(1.0)
InvPb.Regul.update_Parameters({
'Vm': Vm,
'gamma': 0.0,
'beta': 0.0,
'm0': 1.0
})
InvPb.solvefwd_cost()
InvPb.solveadj_constructgrad()
nbcheck = 5
MedPert = np.zeros((nbcheck, InvPb.m.vector().local_size()))
for ii in range(nbcheck):
smoothperturb = dl.Expression('sin(n*pi*x[0])*sin(n*pi*x[1])',
n=ii + 1)
smoothperturb_fn = dl.interpolate(smoothperturb, Vm)
MedPert[ii, :] = smoothperturb_fn.vector().array()
checkgradfd_med(InvPb, MedPert, 1e-6, [1e-4, 1e-5, 1e-6], True, mpicomm)
print ''
checkhessfd_med(InvPb, MedPert, 1e-6, [1e-4, 1e-5, 1e-6], True, mpicomm)
sys.exit(0)
# Solve inverse problem
if mpirank == 0: print 'Solve inverse problem'
InvPb.inversion(1.0, mtrueVm, mpicomm, {'maxnbNewtiter': 200}, myplot=myplot)
dl.Expression('sin(pi*x[0])*sin(pi*x[1])', degree=10),
dl.Expression('x[1]', degree=10),
dl.Expression('x[0]', degree=10),
dl.Expression('sin(3*pi*x[0])*sin(3*pi*x[1])', degree=10)
]
if ALL:
Medium = []
tmp = dl.Function(Vl * Vl)
for ii in range(nbtest):
tmp.vector().zero()
dl.assign(tmp.sub(0), dl.interpolate(MPa[ii], Vl))
dl.assign(tmp.sub(1), dl.interpolate(MPb[ii], Vl))
Medium.append(tmp.vector().copy())
if PRINT: print 'check gradient with FD'
checkgradfd_med(waveobj, Medium, PRINT, 1e-6, [1e-5, 1e-6, 1e-7], True)
if PRINT: print '\ncheck Hessian with FD'
checkhessabfd_med(waveobj, Medium, PRINT, 1e-6, [1e-5, 1e-6, 1e-7],
True, 'all')
else:
Mediuma, Mediumb = [], []
tmp = dl.Function(Vl * Vl)
for ii in range(nbtest):
tmp.vector().zero()
dl.assign(tmp.sub(0), dl.interpolate(MPa[ii], Vl))
Mediuma.append(tmp.vector().copy())
tmp.vector().zero()
dl.assign(tmp.sub(1), dl.interpolate(MPb[ii], Vl))
Mediumb.append(tmp.vector().copy())
if PRINT: print 'check a-gradient with FD'
if 'a' in PARAM:
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)