def setUp(self):
mesh = Mesh.TensorMesh([np.ones(n) * 5 for n in [10, 11, 12]],
[0, 0, -30])
x = np.linspace(5, 10, 3)
XYZ = Utils.ndgrid(x, x, np.r_[0.])
srcLoc = np.r_[0, 0, 0.]
rxList0 = Survey.BaseRx(XYZ, 'exi')
Src0 = Survey.BaseSrc([rxList0], loc=srcLoc)
rxList1 = Survey.BaseRx(XYZ, 'bxi')
Src1 = Survey.BaseSrc([rxList1], loc=srcLoc)
rxList2 = Survey.BaseRx(XYZ, 'bxi')
Src2 = Survey.BaseSrc([rxList2], loc=srcLoc)
rxList3 = Survey.BaseRx(XYZ, 'bxi')
Src3 = Survey.BaseSrc([rxList3], loc=srcLoc)
Src4 = Survey.BaseSrc([rxList0, rxList1, rxList2, rxList3], loc=srcLoc)
srcList = [Src0, Src1, Src2, Src3, Src4]
survey = Survey.BaseSurvey(srcList=srcList)
prob = Problem.BaseTimeProblem(mesh, timeSteps=[(10., 3), (20., 2)])
survey.pair(prob)
def alias(b, srcInd, timeInd):
return self.F.mesh.edgeCurl.T * b + timeInd
self.F = Problem.TimeFields(mesh,
survey,
knownFields={'b': 'F'},
aliasFields={'e': ['b', 'E', alias]})
self.Src0 = Src0
self.Src1 = Src1
self.mesh = mesh
self.XYZ = XYZ
def test_aliasFunction(self):
def alias(e, ind):
self.assertTrue(ind[0] is self.Src0)
return self.F.mesh.edgeCurl * e
F = Problem.Fields(self.F.mesh,
self.F.survey,
knownFields={'e': 'E'},
aliasFields={'b': ['e', 'F', alias]})
e = np.random.rand(F.mesh.nE, 1)
F[self.Src0, 'e'] = e
F[self.Src0, 'b']
def alias(e, ind):
self.assertTrue(type(ind) is list)
self.assertTrue(ind[0] is self.Src0)
self.assertTrue(ind[1] is self.Src1)
return self.F.mesh.edgeCurl * e
F = Problem.Fields(self.F.mesh,
self.F.survey,
knownFields={'e': 'E'},
aliasFields={'b': ['e', 'F', alias]})
e = np.random.rand(F.mesh.nE, 2)
F[[self.Src0, self.Src1], 'e'] = e
F[[self.Src0, self.Src1], 'b']
def setUp(self):
mesh = Mesh.TensorMesh([np.ones(n) * 5 for n in [10, 11, 12]],
[0, 0, -30])
x = np.linspace(5, 10, 3)
XYZ = Utils.ndgrid(x, x, np.r_[0.])
srcLoc = np.r_[0., 0., 0.]
rxList0 = Survey.BaseRx(XYZ, 'exi')
Src0 = Survey.BaseSrc([rxList0], loc=srcLoc)
rxList1 = Survey.BaseRx(XYZ, 'bxi')
Src1 = Survey.BaseSrc([rxList1], loc=srcLoc)
rxList2 = Survey.BaseRx(XYZ, 'bxi')
Src2 = Survey.BaseSrc([rxList2], loc=srcLoc)
rxList3 = Survey.BaseRx(XYZ, 'bxi')
Src3 = Survey.BaseSrc([rxList3], loc=srcLoc)
Src4 = Survey.BaseSrc([rxList0, rxList1, rxList2, rxList3], loc=srcLoc)
srcList = [Src0, Src1, Src2, Src3, Src4]
survey = Survey.BaseSurvey(srcList=srcList)
self.D = Survey.Data(survey)
self.F = Problem.Fields(mesh,
survey,
knownFields={
'phi': 'CC',
'e': 'E',
'b': 'F'
},
dtype={
"phi": float,
"e": complex,
"b": complex
})
self.Src0 = Src0
self.Src1 = Src1
self.mesh = mesh
self.XYZ = XYZ
def setUp(self):
mesh = Mesh.TensorMesh([np.ones(n) * 5 for n in [10, 11, 12]],
[0, 0, -30])
x = np.linspace(5, 10, 3)
XYZ = Utils.ndgrid(x, x, np.r_[0.])
srcLoc = np.r_[0, 0, 0.]
rxList0 = Survey.BaseRx(XYZ, 'exi')
Src0 = Survey.BaseSrc([rxList0], loc=srcLoc)
rxList1 = Survey.BaseRx(XYZ, 'bxi')
Src1 = Survey.BaseSrc([rxList1], loc=srcLoc)
rxList2 = Survey.BaseRx(XYZ, 'bxi')
Src2 = Survey.BaseSrc([rxList2], loc=srcLoc)
rxList3 = Survey.BaseRx(XYZ, 'bxi')
Src3 = Survey.BaseSrc([rxList3], loc=srcLoc)
Src4 = Survey.BaseSrc([rxList0, rxList1, rxList2, rxList3], loc=srcLoc)
srcList = [Src0, Src1, Src2, Src3, Src4]
survey = Survey.BaseSurvey(srcList=srcList)
self.F = Problem.Fields(
mesh,
survey,
knownFields={'e': 'E'},
aliasFields={
'b': ['e', 'F', (lambda e, ind: self.F.mesh.edgeCurl * e)]
})
self.Src0 = Src0
self.Src1 = Src1
self.mesh = mesh
self.XYZ = XYZ
def test_aliasFunction(self):
nT = self.F.survey.prob.nT + 1
count = [0]
def alias(e, srcInd, timeInd):
count[0] += 1
self.assertTrue(srcInd[0] is self.Src0)
return self.F.mesh.edgeCurl * e
F = Problem.TimeFields(self.F.mesh,
self.F.survey,
knownFields={'e': 'E'},
aliasFields={'b': ['e', 'F', alias]})
e = np.random.rand(F.mesh.nE, 1, nT)
F[self.Src0, 'e', :] = e
F[self.Src0, 'b', :]
# ensure that this is called for every time separately.
self.assertTrue(count[0] == nT)
e = np.random.rand(F.mesh.nE, 1, 1)
F[self.Src0, 'e', 1] = e
count[0] = 0
F[self.Src0, 'b', 1]
self.assertTrue(count[0] == 1) # ensure that this is called only once.
def alias(e, srcInd, timeInd):
count[0] += 1
self.assertTrue(type(srcInd) is list)
self.assertTrue(srcInd[0] is self.Src0)
self.assertTrue(srcInd[1] is self.Src1)
return self.F.mesh.edgeCurl * e
F = Problem.TimeFields(self.F.mesh,
self.F.survey,
knownFields={'e': 'E'},
aliasFields={'b': ['e', 'F', alias]})
e = np.random.rand(F.mesh.nE, 2, nT)
F[[self.Src0, self.Src1], 'e', :] = e
count[0] = 0
F[[self.Src0, self.Src1], 'b', :]
# ensure that this is called for every time separately.
self.assertTrue(count[0] == nT)
e = np.random.rand(F.mesh.nE, 2, 1)
F[[self.Src0, self.Src1], 'e', 1] = e
count[0] = 0
F[[self.Src0, self.Src1], 'b', 1]
self.assertTrue(count[0] == 1) # ensure that this is called only once.
def run(N=100, plotIt=True):
np.random.seed(1)
mesh = Mesh.TensorMesh([N])
nk = 20
jk = np.linspace(1., 60., nk)
p = -0.25
q = 0.25
def g(k):
return (np.exp(p * jk[k] * mesh.vectorCCx) *
np.cos(np.pi * q * jk[k] * mesh.vectorCCx))
G = np.empty((nk, mesh.nC))
for i in range(nk):
G[i, :] = g(i)
mtrue = np.zeros(mesh.nC)
mtrue[mesh.vectorCCx > 0.3] = 1.
mtrue[mesh.vectorCCx > 0.45] = -0.5
mtrue[mesh.vectorCCx > 0.6] = 0
prob = Problem.LinearProblem(mesh, G=G)
survey = Survey.LinearSurvey()
survey.pair(prob)
survey.makeSyntheticData(mtrue, std=0.01)
M = prob.mesh
reg = Regularization.Tikhonov(mesh, alpha_s=1., alpha_x=1.)
dmis = DataMisfit.l2_DataMisfit(survey)
opt = Optimization.InexactGaussNewton(maxIter=60)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
directives = [
Directives.BetaEstimate_ByEig(beta0_ratio=1e-2),
Directives.TargetMisfit()
]
inv = Inversion.BaseInversion(invProb, directiveList=directives)
m0 = np.zeros_like(survey.mtrue)
mrec = inv.run(m0)
if plotIt:
fig, axes = plt.subplots(1, 2, figsize=(12 * 1.2, 4 * 1.2))
for i in range(prob.G.shape[0]):
axes[0].plot(prob.G[i, :])
axes[0].set_title('Columns of matrix G')
axes[1].plot(M.vectorCCx, survey.mtrue, 'b-')
axes[1].plot(M.vectorCCx, mrec, 'r-')
axes[1].legend(('True Model', 'Recovered Model'))
axes[1].set_ylim([-2, 2])
return prob, survey, mesh, mrec
def get_problem_survey(self):
prob = Problem.LinearProblem(self.mesh, G=self.G)
survey = Survey.LinearSurvey()
survey.pair(prob)
return survey, prob
def setUp(self):
mesh = Mesh.TensorMesh([10, 10])
self.prob = Problem.BaseTimeProblem(mesh)
def run(N=100, plotIt=True):
np.random.seed(1)
std_noise = 1e-2
mesh = Mesh.TensorMesh([N])
m0 = np.ones(mesh.nC) * 1e-4
mref = np.zeros(mesh.nC)
nk = 20
jk = np.linspace(1., 60., nk)
p = -0.25
q = 0.25
def g(k):
return (np.exp(p * jk[k] * mesh.vectorCCx) *
np.cos(np.pi * q * jk[k] * mesh.vectorCCx))
G = np.empty((nk, mesh.nC))
for i in range(nk):
G[i, :] = g(i)
mtrue = np.zeros(mesh.nC)
mtrue[mesh.vectorCCx > 0.3] = 1.
mtrue[mesh.vectorCCx > 0.45] = -0.5
mtrue[mesh.vectorCCx > 0.6] = 0
prob = Problem.LinearProblem(mesh, G=G)
survey = Survey.LinearSurvey()
survey.pair(prob)
survey.dobs = prob.fields(mtrue) + std_noise * np.random.randn(nk)
wd = np.ones(nk) * std_noise
# Distance weighting
wr = np.sum(prob.G**2., axis=0)**0.5
wr = wr / np.max(wr)
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.Wd = 1. / wd
betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e-2)
reg = Regularization.Sparse(mesh)
reg.mref = mref
reg.cell_weights = wr
reg.mref = np.zeros(mesh.nC)
opt = Optimization.ProjectedGNCG(maxIter=100,
lower=-2.,
upper=2.,
maxIterLS=20,
maxIterCG=10,
tolCG=1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
update_Jacobi = Directives.Update_lin_PreCond()
# Set the IRLS directive, penalize the lowest 25 percentile of model values
# Start with an l2-l2, then switch to lp-norms
norms = [0., 0., 2., 2.]
IRLS = Directives.Update_IRLS(norms=norms,
prctile=25,
maxIRLSiter=15,
minGNiter=3)
inv = Inversion.BaseInversion(invProb,
directiveList=[IRLS, betaest, update_Jacobi])
# Run inversion
mrec = inv.run(m0)
print("Final misfit:" + str(invProb.dmisfit.eval(mrec)))
if plotIt:
fig, axes = plt.subplots(1, 2, figsize=(12 * 1.2, 4 * 1.2))
for i in range(prob.G.shape[0]):
axes[0].plot(prob.G[i, :])
axes[0].set_title('Columns of matrix G')
axes[1].plot(mesh.vectorCCx, mtrue, 'b-')
axes[1].plot(mesh.vectorCCx, reg.l2model, 'r-')
# axes[1].legend(('True Model', 'Recovered Model'))
axes[1].set_ylim(-1.0, 1.25)
axes[1].plot(mesh.vectorCCx, mrec, 'k-', lw=2)
axes[1].legend(('True Model', 'Smooth l2-l2',
'Sparse lp: {0}, lqx: {1}'.format(*reg.norms)),
fontsize=12)
return prob, survey, mesh, mrec
def run(N=100, plotIt=True):
np.random.seed(1)
std_noise = 1e-2
mesh = Mesh.TensorMesh([N])
m0 = np.ones(mesh.nC) * 1e-4
mref = np.zeros(mesh.nC)
nk = 20
jk = np.linspace(1., 60., nk)
p = -0.25
q = 0.25
def g(k):
return (
np.exp(p*jk[k]*mesh.vectorCCx) *
np.cos(np.pi*q*jk[k]*mesh.vectorCCx)
)
G = np.empty((nk, mesh.nC))
for i in range(nk):
G[i, :] = g(i)
mtrue = np.zeros(mesh.nC)
mtrue[mesh.vectorCCx > 0.3] = 1.
mtrue[mesh.vectorCCx > 0.45] = -0.5
mtrue[mesh.vectorCCx > 0.6] = 0
prob = Problem.LinearProblem(mesh, G=G)
survey = Survey.LinearSurvey()
survey.pair(prob)
survey.dobs = prob.fields(mtrue) + std_noise * np.random.randn(nk)
wd = np.ones(nk) * std_noise
# Distance weighting
wr = np.sum(prob.getJ(m0)**2., axis=0)**0.5
wr = wr/np.max(wr)
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.W = 1./wd
betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0)
# Creat reduced identity map
idenMap = Maps.IdentityMap(nP=mesh.nC)
reg = Regularization.Sparse(mesh, mapping=idenMap)
reg.mref = mref
reg.cell_weights = wr
reg.norms = np.c_[0., 0., 2., 2.]
reg.mref = np.zeros(mesh.nC)
opt = Optimization.ProjectedGNCG(
maxIter=100, lower=-2., upper=2.,
maxIterLS=20, maxIterCG=10, tolCG=1e-3
)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
update_Jacobi = Directives.UpdatePreconditioner()
# Set the IRLS directive, penalize the lowest 25 percentile of model values
# Start with an l2-l2, then switch to lp-norms
IRLS = Directives.Update_IRLS(
maxIRLSiter=40, minGNiter=1, f_min_change=1e-4)
saveDict = Directives.SaveOutputEveryIteration(save_txt=False)
inv = Inversion.BaseInversion(
invProb,
directiveList=[IRLS, betaest, update_Jacobi, saveDict]
)
# Run inversion
mrec = inv.run(m0)
print("Final misfit:" + str(invProb.dmisfit(mrec)))
if plotIt:
fig, axes = plt.subplots(2, 2, figsize=(12*1.2, 8*1.2))
for i in range(prob.G.shape[0]):
axes[0, 0].plot(prob.G[i, :])
axes[0, 0].set_title('Columns of matrix G')
axes[0, 1].plot(mesh.vectorCCx, mtrue, 'b-')
axes[0, 1].plot(mesh.vectorCCx, invProb.l2model, 'r-')
# axes[0, 1].legend(('True Model', 'Recovered Model'))
axes[0, 1].set_ylim(-1.0, 1.25)
axes[0, 1].plot(mesh.vectorCCx, mrec, 'k-', lw=2)
axes[0, 1].legend(
(
'True Model',
'Smooth l2-l2',
'Sparse norms: {0}'.format(*reg.norms)
),
fontsize=12
)
axes[1, 1].plot(saveDict.phi_d, 'k', lw=2)
twin = axes[1, 1].twinx()
twin.plot(saveDict.phi_m, 'k--', lw=2)
axes[1, 1].plot(
np.r_[IRLS.iterStart, IRLS.iterStart],
np.r_[0, np.max(saveDict.phi_d)], 'k:'
)
axes[1, 1].text(
IRLS.iterStart, 0.,
'IRLS Start', va='bottom', ha='center',
rotation='vertical', size=12,
bbox={'facecolor': 'white'}
)
axes[1, 1].set_ylabel('$\phi_d$', size=16, rotation=0)
axes[1, 1].set_xlabel('Iterations', size=14)
axes[1, 0].axis('off')
twin.set_ylabel('$\phi_m$', size=16, rotation=0)
return prob, survey, mesh, mrec