def test_transforms_logMap_reciprocalMap(self):
# Note that log/reciprocal maps can be kinda finicky, so we are being
# explicit about the random seed.
v2 = np.r_[0.40077291, 0.1441044, 0.58452314, 0.96323738, 0.01198519,
0.79754415]
dv2 = np.r_[0.80653921, 0.13132446, 0.4901117, 0.03358737, 0.65473762,
0.44252488]
v3 = np.r_[0.96084865, 0.34385186, 0.39430044, 0.81671285, 0.65929109,
0.2235217, 0.87897526, 0.5784033, 0.96876393, 0.63535864,
0.84130763, 0.22123854]
dv3 = np.r_[0.96827838, 0.26072111, 0.45090749, 0.10573893, 0.65276365,
0.15646586, 0.51679682, 0.23071984, 0.95106218, 0.14201845,
0.25093564, 0.3732866]
maps = Maps.LogMap(self.mesh2)
self.assertTrue(maps.test(v2, dx=dv2))
maps = Maps.LogMap(self.mesh3)
self.assertTrue(maps.test(v3, dx=dv3))
maps = Maps.ReciprocalMap(self.mesh2)
self.assertTrue(maps.test(v2, dx=dv2))
maps = Maps.ReciprocalMap(self.mesh3)
self.assertTrue(maps.test(v3, dx=dv3))
def run(plotIt=True):
nC = 40
de = 1.
h = np.ones(nC) * de / nC
M = Mesh.TensorMesh([h, h])
y = np.linspace(M.vectorCCy[0], M.vectorCCx[-1], int(np.floor(nC / 4)))
rlocs = np.c_[0 * y + M.vectorCCx[-1], y]
rx = StraightRay.Rx(rlocs, None)
srcList = [
StraightRay.Src(loc=np.r_[M.vectorCCx[0], yi], rxList=[rx]) for yi in y
]
# phi model
phi0 = 0
phi1 = 0.65
phitrue = Utils.ModelBuilder.defineBlock(M.gridCC, [0.4, 0.6], [0.6, 0.4],
[phi1, phi0])
knownVolume = np.sum(phitrue * M.vol)
print('True Volume: {}'.format(knownVolume))
# Set up true conductivity model and plot the model transform
sigma0 = np.exp(1)
sigma1 = 1e4
if plotIt:
fig, ax = plt.subplots(1, 1)
sigmaMapTest = Maps.SelfConsistentEffectiveMedium(nP=1000,
sigma0=sigma0,
sigma1=sigma1,
rel_tol=1e-1,
maxIter=150)
testphis = np.linspace(0., 1., 1000)
sigetest = sigmaMapTest * testphis
ax.semilogy(testphis, sigetest)
ax.set_title('Model Transform')
ax.set_xlabel('$\\varphi$')
ax.set_ylabel('$\sigma$')
sigmaMap = Maps.SelfConsistentEffectiveMedium(M,
sigma0=sigma0,
sigma1=sigma1)
# scale the slowness so it is on a ~linear scale
slownessMap = Maps.LogMap(M) * sigmaMap
# set up the true sig model and log model dobs
sigtrue = sigmaMap * phitrue
# modt = Model.BaseModel(M);
slownesstrue = slownessMap * phitrue # true model (m = log(sigma))
# set up the problem and survey
survey = StraightRay.Survey(srcList)
problem = StraightRay.Problem(M, slownessMap=slownessMap)
problem.pair(survey)
if plotIt:
fig, ax = plt.subplots(1, 1)
cb = plt.colorbar(M.plotImage(phitrue, ax=ax)[0], ax=ax)
survey.plot(ax=ax)
cb.set_label('$\\varphi$')
# get observed data
dobs = survey.makeSyntheticData(phitrue, std=0.03, force=True)
dpred = survey.dpred(np.zeros(M.nC))
# objective function pieces
reg = Regularization.Tikhonov(M)
dmis = DataMisfit.l2_DataMisfit(survey)
dmisVol = Volume(mesh=M, knownVolume=knownVolume)
beta = 0.25
maxIter = 15
# without the volume regularization
opt = Optimization.ProjectedGNCG(maxIter=maxIter, lower=0.0, upper=1.0)
opt.remember('xc')
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=beta)
inv = Inversion.BaseInversion(invProb)
mopt1 = inv.run(np.zeros(M.nC) + 1e-16)
print('\nTotal recovered volume (no vol misfit term in inversion): '
'{}'.format(dmisVol(mopt1)))
# with the volume regularization
vol_multiplier = 9e4
reg2 = reg
dmis2 = dmis + vol_multiplier * dmisVol
opt2 = Optimization.ProjectedGNCG(maxIter=maxIter, lower=0.0, upper=1.0)
opt2.remember('xc')
invProb2 = InvProblem.BaseInvProblem(dmis2, reg2, opt2, beta=beta)
inv2 = Inversion.BaseInversion(invProb2)
mopt2 = inv2.run(np.zeros(M.nC) + 1e-16)
print('\nTotal volume (vol misfit term in inversion): {}'.format(
dmisVol(mopt2)))
# plot results
if plotIt:
fig, ax = plt.subplots(1, 1)
ax.plot(dobs)
ax.plot(dpred)
ax.plot(survey.dpred(mopt1), 'o')
ax.plot(survey.dpred(mopt2), 's')
ax.legend(['dobs', 'dpred0', 'dpred w/o Vol', 'dpred with Vol'])
fig, ax = plt.subplots(1, 3, figsize=(16, 4))
cb0 = plt.colorbar(M.plotImage(phitrue, ax=ax[0])[0], ax=ax[0])
cb1 = plt.colorbar(M.plotImage(mopt1, ax=ax[1])[0], ax=ax[1])
cb2 = plt.colorbar(M.plotImage(mopt2, ax=ax[2])[0], ax=ax[2])
for cb in [cb0, cb1, cb2]:
cb.set_clim([0., phi1])
ax[0].set_title('true, vol: {:1.3e}'.format(knownVolume))
ax[1].set_title('recovered(no Volume term), vol: {:1.3e} '.format(
dmisVol(mopt1)))
ax[2].set_title('recovered(with Volume term), vol: {:1.3e} '.format(
dmisVol(mopt2)))
plt.tight_layout()
# Create a flat topo
topoXYZ = Utils.ndgrid(mesh.vectorNx, mesh.vectorNy, np.r_[-1.])
actv = sigma != 1e-8
nC = int(actv.sum())
midLocs = survey.srcList[0].rxList[0].locs[0] + survey.srcList[0].rxList[
0].locs[1]
midLocs /= 2
idenMap = Maps.IdentityMap(nP=nC)
expmap = Maps.ExpMap(mesh)
actmap = Maps.InjectActiveCells(mesh, actv, np.log(1e-8))
mapping = expmap * actmap
logmap = Maps.LogMap(mesh)
m0 = np.log(np.ones_like(sigma) * 1e-3)[actv]
mref = np.log(np.ones_like(sigma) * mref_val)
problem = DC.Problem3D_N(mesh, sigmaMap=mapping, storeJ=True)
problem.Solver = PardisoSolver
problem.pair(survey)
mtrue = np.log(sigma[actv])
# Depth weight
#depth = 1./(abs(mesh.gridCC[:,2]))**1.5
#depth = depth/depth.max()
d0 = survey.dpred(m0)
dobs = survey.makeSyntheticData(mtrue, std=0.02)