def DerivProjfieldsTest(inputSetup, comp="All", freq=False):
survey, simulation = nsem.utils.test_utils.setupSimpegNSEM_ePrimSec(
inputSetup, comp, freq)
print(
"Derivative test of data projection for eFormulation primary/secondary\n"
)
# simulation.mapping = maps.ExpMap(simulation.mesh)
# Initate things for the derivs Test
src = survey.source_list[0]
np.random.seed(1983)
u0x = np.random.randn(
survey.mesh.nE) + np.random.randn(survey.mesh.nE) * 1j
u0y = np.random.randn(
survey.mesh.nE) + np.random.randn(survey.mesh.nE) * 1j
u0 = np.vstack((mkvc(u0x, 2), mkvc(u0y, 2)))
f0 = simulation.fieldsPair(survey.mesh, survey)
# u0 = np.hstack((mkvc(u0_px,2),mkvc(u0_py,2)))
f0[src, "e_pxSolution"] = u0[:len(u0) / 2] # u0x
f0[src, "e_pySolution"] = u0[len(u0) / 2::] # u0y
def fun(u):
f = simulation.fieldsPair(survey.mesh, survey)
f[src, "e_pxSolution"] = u[:len(u) / 2]
f[src, "e_pySolution"] = u[len(u) / 2::]
return (
rx.eval(src, survey.mesh, f),
lambda t: rx.evalDeriv(src, survey.mesh, f0, mkvc(t, 2)),
)
return tests.checkDerivative(fun, u0, num=4, plotIt=False, eps=FLR)
def test_ana_forward(self):
# Compute 3-component mag data
self.survey.pair(self.prob_xyz)
d = self.prob_xyz.fields(self.model)
ndata = self.locXyz.shape[0]
dbx = d[0:ndata]
dby = d[ndata:2 * ndata]
dbz = d[2 * ndata:]
# Compute tmi mag data
self.survey.pair(self.prob_tmi)
dtmi = self.prob_tmi.fields(self.model)
# Compute analytical response from a magnetized sphere
bxa, bya, bza = PF.MagAnalytics.MagSphereFreeSpace(
self.locXyz[:, 0], self.locXyz[:, 1], self.locXyz[:, 2], self.rad,
0, 0, 0, self.chi, self.b0)
# Projection matrix
Ptmi = mkvc(self.b0) / np.sqrt(np.sum(self.b0**2.))
btmi = mkvc(Ptmi.dot(np.vstack((bxa, bya, bza))))
err_xyz = (np.linalg.norm(d - np.r_[bxa, bya, bza]) /
np.linalg.norm(np.r_[bxa, bya, bza]))
err_tmi = np.linalg.norm(dtmi - btmi) / np.linalg.norm(btmi)
self.assertTrue(err_xyz < 0.005 and err_tmi < 0.005)
def S_eDeriv_m(self, problem, v, adjoint=False):
'''
Get the derivative of S_e wrt to sigma (m)
'''
# Need to deal with
if problem.mesh.dim == 1:
# Need to use the faceInnerProduct
ePri = self.ePrimary(problem)[:, 1]
MsigmaDeriv = (
problem.mesh.getFaceInnerProductDeriv(problem.sigma)(ePri) *
problem.sigmaDeriv)
# MsigmaDeriv = ( MsigmaDeriv * MsigmaDeriv.T)**2
if adjoint:
#
return MsigmaDeriv.T * v
else:
# v should be nC size
return MsigmaDeriv * v
if problem.mesh.dim == 2:
raise NotImplementedError('The NSEM 2D problem is not implemented')
if problem.mesh.dim == 3:
# Need to take the derivative of both u_px and u_py
# And stack them to be of the correct size
e_p = self.ePrimary(problem)
if adjoint:
return sp.hstack((
problem.MeSigmaDeriv(e_p[:, 0]).T,
problem.MeSigmaDeriv(e_p[:, 1]).T)) * v
else:
return np.hstack((
mkvc(problem.MeSigmaDeriv(e_p[:, 0]) * v, 2),
mkvc(problem.MeSigmaDeriv(e_p[:, 1]) * v, 2)))
def S_eDeriv_m(self, problem, v, adjoint=False):
"""
Get the derivative of S_e wrt to sigma (m)
"""
# Need to deal with
if problem.mesh.dim == 1:
# Need to use the faceInnerProduct
MsigmaDeriv = (
problem.mesh.getFaceInnerProductDeriv(problem.curModel.sigma)(self.ePrimary(problem)[:, 1])
* problem.curModel.sigmaDeriv
)
# MsigmaDeriv = ( MsigmaDeriv * MsigmaDeriv.T)**2
if problem.mesh.dim == 2:
pass
if problem.mesh.dim == 3:
# Need to take the derivative of both u_px and u_py
ePri = self.ePrimary(problem)
# MsigmaDeriv = problem.MeSigmaDeriv(ePri[:,0]) + problem.MeSigmaDeriv(ePri[:,1])
# MsigmaDeriv = problem.MeSigmaDeriv(np.sum(ePri,axis=1))
if adjoint:
return sp.hstack((problem.MeSigmaDeriv(ePri[:, 0]).T, problem.MeSigmaDeriv(ePri[:, 1]).T)) * v
else:
return np.hstack(
(mkvc(problem.MeSigmaDeriv(ePri[:, 0]) * v, 2), mkvc(problem.MeSigmaDeriv(ePri[:, 1]) * v, 2))
)
if adjoint:
#
return MsigmaDeriv.T * v
else:
# v should be nC size
return MsigmaDeriv * v
def getADeriv(self, freq, u, v, adjoint=False):
"""
Calculate the derivative of A wrt m.
:param float freq: Frequency
:param SimPEG.EM.NSEM.FieldsNSEM u: NSEM Fields object
:param numpy.ndarray v: vector of size (nU,) (adjoint=False)
and size (nP,) (adjoint=True)
:rtype: numpy.ndarray
:return: Calculated derivative (nP,) (adjoint=False) and (nU,)[NOTE return as a (nU/2,2)
columnwise polarizations] (adjoint=True) for both polarizations
"""
# Fix u to be a matrix nE,2
# This considers both polarizations and returns a nE,2 matrix for each polarization
# The solution types
sol0, sol1 = self._solutionType
if adjoint:
dMe_dsigV = (
self.MeSigmaDeriv(u[sol0], v[:self.mesh.nE], adjoint) +
self.MeSigmaDeriv(u[sol1], v[self.mesh.nE:], adjoint)
)
else:
# Need a nE,2 matrix to be returned
dMe_dsigV = np.hstack(
(
mkvc(self.MeSigmaDeriv(u[sol0], v, adjoint), 2),
mkvc(self.MeSigmaDeriv(u[sol1], v, adjoint), 2)
)
)
return 1j * omega(freq) * dMe_dsigV
def test_ana_forward(self):
# Compute 3-component mag data
self.survey.pair(self.prob_xyz)
d = self.prob_xyz.fields(self.model)
ndata = self.locXyz.shape[0]
dbx = d[0:ndata]
dby = d[ndata:2*ndata]
dbz = d[2*ndata:]
# Compute tmi mag data
self.survey.pair(self.prob_tmi)
dtmi = self.prob_tmi.fields(self.model)
# Compute analytical response from a magnetized sphere
bxa, bya, bza = PF.MagAnalytics.MagSphereFreeSpace(self.locXyz[:, 0],
self.locXyz[:, 1],
self.locXyz[:, 2],
self.rad, 0, 0, 0,
self.chi, self.b0)
# Projection matrix
Ptmi = mkvc(self.b0)/np.sqrt(np.sum(self.b0**2.))
btmi = mkvc(Ptmi.dot(np.vstack((bxa, bya, bza))))
err_xyz = (np.linalg.norm(d-np.r_[bxa, bya, bza]) /
np.linalg.norm(np.r_[bxa, bya, bza]))
err_tmi = np.linalg.norm(dtmi-btmi)/np.linalg.norm(btmi)
self.assertTrue(err_xyz < 0.005 and err_tmi < 0.005)
def test_basic_inversion(self):
"""
Test to see if inversion recovers model
"""
h = [(2, 30)]
meshObj = Mesh.TensorMesh((h, h, [(2, 10)]), x0='CCN')
mod = 0.00025 * np.ones(meshObj.nC)
mod[(meshObj.gridCC[:, 0] > -4.) & (meshObj.gridCC[:, 1] > -4.) &
(meshObj.gridCC[:, 0] < 4.) & (meshObj.gridCC[:, 1] < 4.)] = 0.001
times = np.logspace(-4, -2, 5)
waveObj = VRM.WaveformVRM.SquarePulse(0.02)
x, y = np.meshgrid(np.linspace(-17, 17, 16), np.linspace(-17, 17, 16))
x, y, z = mkvc(x), mkvc(y), 0.5 * np.ones(np.size(x))
rxList = [VRM.Rx.Point(np.c_[x, y, z], times, 'dbdt', 'z')]
txNodes = np.array([[-20, -20, 0.001], [20, -20,
0.001], [20, 20, 0.001],
[-20, 20, 0.01], [-20, -20, 0.001]])
txList = [VRM.Src.LineCurrent(rxList, txNodes, 1., waveObj)]
Survey = VRM.Survey(txList)
Problem = VRM.Problem_Linear(meshObj, refFact=2)
Problem.pair(Survey)
Survey.makeSyntheticData(mod)
Survey.eps = 1e-11
dmis = DataMisfit.l2_DataMisfit(Survey)
W = mkvc((np.sum(np.array(Problem.A)**2, axis=0)))**0.25
reg = Regularization.Simple(meshObj,
alpha_s=0.01,
alpha_x=1.,
alpha_y=1.,
alpha_z=1.,
cell_weights=W)
opt = Optimization.ProjectedGNCG(maxIter=20,
lower=0.,
upper=1e-2,
maxIterLS=20,
tolCG=1e-4)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
directives = [
Directives.BetaSchedule(coolingFactor=2, coolingRate=1),
Directives.TargetMisfit()
]
inv = Inversion.BaseInversion(invProb, directiveList=directives)
m0 = 1e-6 * np.ones(len(mod))
mrec = inv.run(m0)
dmis_final = np.sum(
(dmis.W.diagonal() * (Survey.dobs - Problem.fields(mrec)))**2)
mod_err_2 = np.sqrt(np.sum((mrec - mod)**2)) / np.size(mod)
mod_err_inf = np.max(np.abs(mrec - mod))
self.assertTrue(dmis_final < Survey.nD and mod_err_2 < 5e-6
and mod_err_inf < np.max(mod))
def test_basic_inversion(self):
"""
Test to see if inversion recovers model
"""
h = [(2, 30)]
meshObj = Mesh.TensorMesh((h, h, [(2, 10)]), x0='CCN')
mod = 0.00025*np.ones(meshObj.nC)
mod[(meshObj.gridCC[:, 0] > -4.) &
(meshObj.gridCC[:, 1] > -4.) &
(meshObj.gridCC[:, 0] < 4.) &
(meshObj.gridCC[:, 1] < 4.)] = 0.001
times = np.logspace(-4, -2, 5)
waveObj = VRM.WaveformVRM.SquarePulse(delt=0.02)
x, y = np.meshgrid(np.linspace(-17, 17, 16), np.linspace(-17, 17, 16))
x, y, z = mkvc(x), mkvc(y), 0.5*np.ones(np.size(x))
rxList = [VRM.Rx.Point(np.c_[x, y, z], times=times, fieldType='dbdt', fieldComp='z')]
txNodes = np.array([[-20, -20, 0.001],
[20, -20, 0.001],
[20, 20, 0.001],
[-20, 20, 0.01],
[-20, -20, 0.001]])
txList = [VRM.Src.LineCurrent(rxList, txNodes, 1., waveObj)]
Survey = VRM.Survey(txList)
Survey.t_active = np.zeros(Survey.nD, dtype=bool)
Survey.set_active_interval(-1e6, 1e6)
Problem = VRM.Problem_Linear(meshObj, ref_factor=2)
Problem.pair(Survey)
Survey.makeSyntheticData(mod)
Survey.eps = 1e-11
dmis = DataMisfit.l2_DataMisfit(Survey)
W = mkvc((np.sum(np.array(Problem.A)**2, axis=0)))**0.25
reg = Regularization.Simple(
meshObj, alpha_s=0.01, alpha_x=1., alpha_y=1., alpha_z=1., cell_weights=W
)
opt = Optimization.ProjectedGNCG(
maxIter=20, lower=0., upper=1e-2, maxIterLS=20, tolCG=1e-4
)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
directives = [
Directives.BetaSchedule(coolingFactor=2, coolingRate=1),
Directives.TargetMisfit()
]
inv = Inversion.BaseInversion(invProb, directiveList=directives)
m0 = 1e-6*np.ones(len(mod))
mrec = inv.run(m0)
dmis_final = np.sum((dmis.W.diagonal()*(Survey.dobs - Problem.fields(mrec)))**2)
mod_err_2 = np.sqrt(np.sum((mrec-mod)**2))/np.size(mod)
mod_err_inf = np.max(np.abs(mrec-mod))
self.assertTrue(dmis_final < Survey.nD and mod_err_2 < 5e-6 and mod_err_inf < np.max(mod))
def getADeriv(self, freq, u, v, adjoint=False):
"""
Calculate the derivative of A wrt m.
:param float freq: Frequency
:param SimPEG.EM.NSEM.FieldsNSEM u: NSEM Fields object
:param numpy.ndarray v: vector of size (nU,) (adjoint=False)
and size (nP,) (adjoint=True)
:rtype: numpy.ndarray
:return: Calculated derivative (nP,) (adjoint=False) and (nU,)[NOTE return as a (nU/2,2)
columnwise polarizations] (adjoint=True) for both polarizations
"""
# Fix u to be a matrix nE,2
# This considers both polarizations and returns a nE,2 matrix for each polarization
# The solution types
sol0, sol1 = self._solutionType
if adjoint:
dMe_dsigV = sp.hstack((self.MeSigmaDeriv(
u[sol0]).T, self.MeSigmaDeriv(u[sol1]).T)) * v
else:
# Need a nE,2 matrix to be returned
dMe_dsigV = np.hstack(
(mkvc(self.MeSigmaDeriv(u[sol0]) * v,
2), mkvc(self.MeSigmaDeriv(u[sol1]) * v, 2)))
return 1j * omega(freq) * dMe_dsigV
def getInputs():
"""
Function that returns Mesh, freqs, rx_loc, elev.
"""
# Make a mesh
M = discretize.TensorMesh(
[
[(200, 6, -1.5), (200.0, 4), (200, 6, 1.5)],
[(200, 6, -1.5), (200.0, 4), (200, 6, 1.5)],
[(200, 8, -1.5), (200.0, 8), (200, 8, 1.5)],
],
x0=["C", "C", "C"],
) # Setup the model
# Set the frequencies
freqs = np.logspace(1, -3, 5)
elev = 0
# Setup the the survey object
# Receiver locations
rx_x, rx_y = np.meshgrid(np.arange(-350, 350, 200),
np.arange(-350, 350, 200))
rx_loc = np.hstack((mkvc(rx_x, 2), mkvc(rx_y, 2), elev + np.zeros(
(np.prod(rx_x.shape), 1))))
return M, freqs, rx_loc, elev
def S_eDeriv_m(self, problem, v, adjoint=False):
'''
Get the derivative of S_e wrt to sigma (m)
'''
# Need to deal with
if problem.mesh.dim == 1:
# Need to use the faceInnerProduct
MsigmaDeriv = (
problem.mesh.getFaceInnerProductDeriv(
problem.sigma)(self.ePrimary(problem)[:, 1]) *
problem.sigmaDeriv)
# MsigmaDeriv = ( MsigmaDeriv * MsigmaDeriv.T)**2
if problem.mesh.dim == 2:
pass
if problem.mesh.dim == 3:
# Need to take the derivative of both u_px and u_py
ePri = self.ePrimary(problem)
if adjoint:
return sp.hstack((
problem.MeSigmaDeriv(ePri[:, 0]).T,
problem.MeSigmaDeriv(ePri[:, 1]).T)) * v
else:
return np.hstack((
mkvc(problem.MeSigmaDeriv(ePri[:, 0]) * v, 2),
mkvc(problem.MeSigmaDeriv(ePri[:, 1]) * v, 2) ))
if adjoint:
#
return MsigmaDeriv.T * v
else:
# v should be nC size
return MsigmaDeriv * v
def S_eDeriv_m(self, problem, v, adjoint = False):
'''
Get the derivative of S_e wrt to sigma (m)
'''
# Need to deal with
if problem.mesh.dim == 1:
# Need to use the faceInnerProduct
ePri = self.ePrimary(problem)[:,1]
MsigmaDeriv = problem.mesh.getFaceInnerProductDeriv(problem.sigma)(ePri) * problem.sigmaDeriv
# MsigmaDeriv = ( MsigmaDeriv * MsigmaDeriv.T)**2
if adjoint:
#
return MsigmaDeriv.T * v
else:
# v should be nC size
return MsigmaDeriv * v
if problem.mesh.dim == 2:
raise NotImplementedError('The NSEM 2D problem is not implemented')
if problem.mesh.dim == 3:
# Need to take the derivative of both u_px and u_py
# And stack them to be of the correct size
e_p = self.ePrimary(problem)
if adjoint:
return sp.hstack(( problem.MeSigmaDeriv(e_p[:,0]).T, problem.MeSigmaDeriv(e_p[:,1]).T ))*v
else:
return np.hstack(( mkvc(problem.MeSigmaDeriv(e_p[:,0]) * v,2), mkvc(problem.MeSigmaDeriv(e_p[:,1])*v,2) ))
def importFiles(self):
"""
Function to import EDI files into a object.
"""
# Constants that are needed for convertion of units
# Temp lists
tmpStaList = []
tmpCompList = ['freq','x','y','z']
tmpCompList.extend(self.comps)
# Make the outarray
dtRI = [(compS.lower().replace('.',''),float) for compS in tmpCompList]
# Loop through all the files
for nrEDI, EDIfile in enumerate(self.filesList):
# Read the file into a list of the lines
with open(EDIfile,'r') as fid:
EDIlines = fid.readlines()
# Find the location
latD, longD, elevM = _findLatLong(EDIlines)
# Transfrom coordinates
transCoord = self._transfromPoints(longD,latD)
# Extract the name of the file (station)
EDIname = EDIfile.split(os.sep)[-1].split('.')[0]
# Arrange the data
staList = [EDIname, EDIfile, transCoord[0], transCoord[1], elevM[0]]
# Add to the station list
tmpStaList.extend(staList)
# Read the frequency data
freq = _findEDIcomp('>FREQ',EDIlines)
# Make the temporary rec array.
tArrRec = ( np.nan*np.ones( (len(freq),len(dtRI)) ) ).view(dtRI) #np.concatenate((freq*np.ones((locs.shape[0],1)),locs,np.nan*np.ones((locs.shape[0],8))),axis=1).view(dtRI)
# Add data to the array
tArrRec['freq'] = mkvc(freq,2)
tArrRec['x'] = mkvc(np.ones((len(freq),1))*transCoord[0],2)
tArrRec['y'] = mkvc(np.ones((len(freq),1))*transCoord[1],2)
tArrRec['z'] = mkvc(np.ones((len(freq),1))*elevM[0],2)
for comp in self.comps:
# Deal with converting units of the impedance tensor
if 'Z' in comp:
unitConvert = self._impUnitEDI2SI
else:
unitConvert = 1
# Rotate the data since EDI x is *north, y *east but Simpeg uses x *east, y *north (* means internal reference frame)
key = [comp.lower().replace('.','').replace(s,t) for s,t in [['xx','yy'],['xy','yx'],['yx','xy'],['yy','xx']] if s in comp.lower()][0]
tArrRec[key] = mkvc(unitConvert*_findEDIcomp('>'+comp,EDIlines),2)
# Make a masked array
mArrRec = np.ma.MaskedArray(rec2ndarr(tArrRec),mask=np.isnan(rec2ndarr(tArrRec))).view(dtype=tArrRec.dtype)
try:
outTemp = recFunc.stack_arrays((outTemp,mArrRec))
except NameError as e:
outTemp = mArrRec
# Assign the data
self._data = outTemp
def importFiles(self):
"""
Function to import EDI files into a object.
"""
# Constants that are needed for convertion of units
# Temp lists
tmpStaList = []
tmpCompList = ['freq','x','y','z']
tmpCompList.extend(self.comps)
# Make the outarray
dtRI = [(compS.lower().replace('.',''),float) for compS in tmpCompList]
# Loop through all the files
for nrEDI, EDIfile in enumerate(self.filesList):
# Read the file into a list of the lines
with open(EDIfile,'r') as fid:
EDIlines = fid.readlines()
# Find the location
latD, longD, elevM = _findLatLong(EDIlines)
# Transfrom coordinates
transCoord = self._transfromPoints(longD,latD)
# Extract the name of the file (station)
EDIname = EDIfile.split(os.sep)[-1].split('.')[0]
# Arrange the data
staList = [EDIname, EDIfile, transCoord[0], transCoord[1], elevM[0]]
# Add to the station list
tmpStaList.extend(staList)
# Read the frequency data
freq = _findEDIcomp('>FREQ',EDIlines)
# Make the temporary rec array.
tArrRec = ( np.nan*np.ones( (len(freq),len(dtRI)) ) ).view(dtRI) #np.concatenate((freq*np.ones((locs.shape[0],1)),locs,np.nan*np.ones((locs.shape[0],8))),axis=1).view(dtRI)
# Add data to the array
tArrRec['freq'] = mkvc(freq,2)
tArrRec['x'] = mkvc(np.ones((len(freq),1))*transCoord[0],2)
tArrRec['y'] = mkvc(np.ones((len(freq),1))*transCoord[1],2)
tArrRec['z'] = mkvc(np.ones((len(freq),1))*elevM[0],2)
for comp in self.comps:
# Deal with converting units of the impedance tensor
if 'Z' in comp:
unitConvert = self._impUnitEDI2SI
else:
unitConvert = 1
# Rotate the data since EDI x is *north, y *east but Simpeg uses x *east, y *north (* means internal reference frame)
key = [comp.lower().replace('.','').replace(s,t) for s,t in [['xx','yy'],['xy','yx'],['yx','xy'],['yy','xx']] if s in comp.lower()][0]
tArrRec[key] = mkvc(unitConvert*_findEDIcomp('>'+comp,EDIlines),2)
# Make a masked array
mArrRec = np.ma.MaskedArray(rec2ndarr(tArrRec),mask=np.isnan(rec2ndarr(tArrRec))).view(dtype=tArrRec.dtype)
try:
outTemp = recFunc.stack_arrays((outTemp,mArrRec))
except NameError as e:
outTemp = mArrRec
# Assign the data
self._data = outTemp
def Jtvec(self, m, v, u=None):
"""
Function to calculate the transpose of the data sensitivities (dD/dm)^T times a vector.
:param numpy.ndarray m (nC, 1) - conductive model
:param numpy.ndarray v (nD, 1) - vector
:param MTfields object u (optional) - MT fields object, if not given it is calculated
:rtype: MTdata object
:return: Data sensitivities wrt m
"""
if u is None:
u = self.fields(m)
self.curModel = m
# Ensure v is a data object.
if not isinstance(v, self.dataPair):
v = self.dataPair(self.survey, v)
Jtv = np.zeros(m.size)
for freq in self.survey.freqs:
AT = self.getA(freq).T
ATinv = self.Solver(AT, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
ftype = self._fieldType + 'Solution'
u_src = u[src, :]
for rx in src.rxList:
# Get the adjoint evalDeriv
# PTv needs to be nE,
PTv = rx.evalDeriv(src, self.mesh, u, mkvc(v[src, rx],2), adjoint=True) # wrt u, need possibility wrt m
# Get the
dA_duIT = ATinv * PTv
dA_dmT = self.getADeriv_m(freq, u_src, mkvc(dA_duIT), adjoint=True)
dRHS_dmT = self.getRHSDeriv_m(freq, mkvc(dA_duIT), adjoint=True)
# Make du_dmT
if dRHS_dmT is None:
du_dmT = -dA_dmT
else:
du_dmT = -dA_dmT + dRHS_dmT
# Select the correct component
# du_dmT needs to be of size nC,
real_or_imag = rx.projComp
if real_or_imag == 'real':
Jtv += du_dmT.real
elif real_or_imag == 'imag':
Jtv += -du_dmT.real
else:
raise Exception('Must be real or imag')
# Clean the factorization, clear memory.
ATinv.clean()
return Jtv
def Jtvec(self, m, v, f=None):
"""
Function to calculate the transpose of the data sensitivities (dD/dm)^T times a vector.
:param numpy.ndarray m: inversion model (nP,)
:param numpy.ndarray v: vector which we take adjoint product with (nP,)
:param SimPEG.EM.NSEM.FieldsNSEM f (optional): NSEM fields object, if not given it is calculated
:rtype: numpy.ndarray
:return: Jtv (nP,) Data sensitivities wrt m
"""
if f is None:
f = self.fields(m)
self.model = m
# Ensure v is a data object.
if not isinstance(v, self.dataPair):
v = self.dataPair(self.survey, v)
Jtv = np.zeros(m.size)
for freq in self.survey.freqs:
AT = self.getA(freq).T
ATinv = self.Solver(AT, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
# u_src needs to have both polarizations
u_src = f[src, :]
for rx in src.rxList:
# Get the adjoint evalDeriv
# PTv needs to be nE,2
PTv = rx.evalDeriv(
src, self.mesh, f, mkvc(v[src, rx]),
adjoint=True) # wrt f, need possibility wrt m
# Get the
dA_duIT = mkvc(ATinv * PTv) # Force (nU,) shape
dA_dmT = self.getADeriv(freq, u_src, dA_duIT, adjoint=True)
dRHS_dmT = self.getRHSDeriv(freq, dA_duIT, adjoint=True)
# Make du_dmT
du_dmT = -dA_dmT + dRHS_dmT
# Select the correct component
# du_dmT needs to be of size (nP,) number of model parameters
real_or_imag = rx.component
if real_or_imag == 'real':
Jtv += np.array(du_dmT, dtype=complex).real
elif real_or_imag == 'imag':
Jtv += -np.array(du_dmT, dtype=complex).real
else:
raise Exception('Must be real or imag')
# Clean the factorization, clear memory.
ATinv.clean()
return Jtv
def getADeriv(self, freq, u, v, adjoint=False):
"""
The derivative of A wrt sigma
"""
u_src = u['e_1dSolution']
dMfSigma_dm = self.MfSigmaDeriv(u_src)
if adjoint:
return 1j * omega(freq) * mkvc(dMfSigma_dm.T * v, )
# Note: output has to be nN/nF, not nC/nE.
# v should be nC
return 1j * omega(freq) * mkvc(dMfSigma_dm * v, )
def getADeriv(self, freq, u, v, adjoint=False):
"""
The derivative of A wrt sigma
"""
u_src = u['e_1dSolution']
dMfSigma_dm = self.MfSigmaDeriv(u_src)
if adjoint:
return 1j * omega(freq) * mkvc(dMfSigma_dm.T * v,)
# Note: output has to be nN/nF, not nC/nE.
# v should be nC
return 1j * omega(freq) * mkvc(dMfSigma_dm * v,)
def Jtvec(self, m, v, f=None):
"""
Function to calculate the transpose of the data sensitivities (dD/dm)^T times a vector.
:param numpy.ndarray m: inversion model (nP,)
:param numpy.ndarray v: vector which we take adjoint product with (nP,)
:param SimPEG.EM.NSEM.FieldsNSEM f (optional): NSEM fields object, if not given it is calculated
:rtype: numpy.ndarray
:return: Jtv (nP,) Data sensitivities wrt m
"""
if f is None:
f = self.fields(m)
self.model = m
# Ensure v is a data object.
if not isinstance(v, self.dataPair):
v = self.dataPair(self.survey, v)
Jtv = np.zeros(m.size)
for freq in self.survey.freqs:
AT = self.getA(freq).T
ATinv = self.Solver(AT, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
# u_src needs to have both polarizations
u_src = f[src, :]
for rx in src.rxList:
# Get the adjoint evalDeriv
# PTv needs to be nE,2
PTv = rx.evalDeriv(src, self.mesh, f, mkvc(v[src, rx]), adjoint=True) # wrt f, need possibility wrt m
# Get the
dA_duIT = mkvc(ATinv * PTv) # Force (nU,) shape
dA_dmT = self.getADeriv(freq, u_src, dA_duIT, adjoint=True)
dRHS_dmT = self.getRHSDeriv(freq, dA_duIT, adjoint=True)
# Make du_dmT
du_dmT = -dA_dmT + dRHS_dmT
# Select the correct component
# du_dmT needs to be of size (nP,) number of model parameters
real_or_imag = rx.component
if real_or_imag == 'real':
Jtv += np.array(du_dmT, dtype=complex).real
elif real_or_imag == 'imag':
Jtv += -np.array(du_dmT, dtype=complex).real
else:
raise Exception('Must be real or imag')
# Clean the factorization, clear memory.
ATinv.clean()
return Jtv
def Jtvec(self, m, v, u=None):
if u is None:
u = self.fields(m)
self.curModel = m
# Ensure v is a data object.
if not isinstance(v, self.dataPair):
v = self.dataPair(self.survey, v)
Jtv = np.zeros(m.size)
for freq in self.survey.freqs:
AT = self.getA(freq).T
ATinv = self.Solver(AT, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
ftype = self._fieldType + 'Solution'
u_src = u[src, :]
for rx in src.rxList:
# Get the adjoint projectFieldsDeriv
# PTv needs to be nE,
PTv = rx.projectFieldsDeriv(
src, self.mesh, u, mkvc(v[src, rx], 2),
adjoint=True) # wrt u, need possibility wrt m
# Get the
dA_duIT = ATinv * PTv
dA_dmT = self.getADeriv_m(freq,
u_src,
mkvc(dA_duIT),
adjoint=True)
dRHS_dmT = self.getRHSDeriv_m(freq,
mkvc(dA_duIT),
adjoint=True)
# Make du_dmT
if dRHS_dmT is None:
du_dmT = -dA_dmT
else:
du_dmT = -dA_dmT + dRHS_dmT
# Select the correct component
# du_dmT needs to be of size nC,
real_or_imag = rx.projComp
if real_or_imag == 'real':
Jtv += du_dmT.real
elif real_or_imag == 'imag':
Jtv += -du_dmT.real
else:
raise Exception('Must be real or imag')
return Jtv
def _getSubsetAcolumns(self, xyzc, xyzh, pp, qq, refFlag):
"""
This method returns the refined sensitivities for columns that will be
replaced in the A matrix for source pp and refinement factor qq.
..
.. INPUTS:
..
.. xyzc -- Cell centers of topo mesh cells N X 3 array
..
.. xyzh -- Cell widths of topo mesh cells N X 3 array
..
.. pp -- Source ID
..
.. qq -- Mesh refinement factor
..
.. refFlag -- refinement factors for all topo mesh cells
..
.. OUTPUTS:
..
.. Acols -- Columns containing replacement sensitivities
"""
# GET SUBMESH GRID
n = 2**qq
[nx, ny, nz] = np.meshgrid(
np.linspace(1, n, n) - 0.5,
np.linspace(1, n, n) - 0.5,
np.linspace(1, n, n) - 0.5)
nxyz_sub = np.c_[mkvc(nx), mkvc(ny), mkvc(nz)]
xyzh_sub = xyzh[refFlag == qq, :] # Get widths of cells to be refined
xyzc_sub = xyzc[refFlag == qq, :] - xyzh[
refFlag ==
qq, :] / 2 # Get bottom southwest corners of cells to be refined
m = np.shape(xyzc_sub)[0]
xyzc_sub = np.kron(xyzc_sub, np.ones(
(n**3, 1))) # Kron for n**3 refined cells
xyzh_sub = np.kron(xyzh_sub / n, np.ones(
(n**3, 1))) # Kron for n**3 refined cells with widths h/n
nxyz_sub = np.kron(np.ones((m, 1)),
nxyz_sub) # Kron for n**3 refined cells
xyzc_sub = xyzc_sub + xyzh_sub * nxyz_sub
# GET SUBMESH A MATRIX AND COLLAPSE TO COLUMNS
G = self._getGeometryMatrix(xyzc_sub, xyzh_sub, pp)
H0 = self._getH0matrix(xyzc_sub, pp)
Acols = (G * H0) * sp.kron(sp.diags(np.ones(m)), np.ones((n**3, 1)))
return Acols
def Jvec(self, m, v, f=None):
"""
Function to calculate the data sensitivities dD/dm times a vector.
:param numpy.ndarray m: conductivity model (nP,)
:param numpy.ndarray v: vector which we take sensitivity product with (nP,)
:param SimPEG.EM.NSEM.FieldsNSEM (optional) u: NSEM fields object, if not given
it is calculated
:rtype: numpy.ndarray
:return: Jv (nData,) Data sensitivities wrt m
"""
# Calculate the fields if not given as input
if f is None:
f = self.fields(m)
# Set current model
self.curModel = m
# Initiate the Jv object
Jv = self.dataPair(self.survey)
# Loop all the frequenies
for freq in self.survey.freqs:
# Get the system
A = self.getA(freq)
# Factor
Ainv = self.Solver(A, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
# We need fDeriv_m = df/du*du/dm + df/dm
# Construct du/dm, it requires a solve
# NOTE: need to account for the 2 polarizations in the derivatives.
u_src = f[
src, :] # u should be a vector by definition. Need to fix this...
# dA_dm and dRHS_dm should be of size nE,2, so that we can multiply by Ainv.
# The 2 columns are each of the polarizations.
dA_dm_v = self.getADeriv(
freq, u_src, v) # Size: nE,2 (u_px,u_py) in the columns.
dRHS_dm_v = self.getRHSDeriv(
freq, v) # Size: nE,2 (u_px,u_py) in the columns.
# Calculate du/dm*v
du_dm_v = Ainv * (-dA_dm_v + dRHS_dm_v)
# Calculate the projection derivatives
for rx in src.rxList:
# Calculate dP/du*du/dm*v
Jv[src, rx] = rx.evalDeriv(
src, self.mesh, f,
mkvc(du_dm_v)) # wrt uPDeriv_u(mkvc(du_dm))
Ainv.clean()
# Return the vectorized sensitivities
return mkvc(Jv)
def Jvec(self, m, v, u=None):
"""
Function to calculate the data sensitivities dD/dm times a vector.
:param numpy.ndarray (nC, 1) - conductive model
:param numpy.ndarray (nC, 1) - random vector
:param MTfields object (optional) - MT fields object, if not given it is calculated
:rtype: MTdata object
:return: Data sensitivities wrt m
"""
# Calculate the fields
if u is None:
u = self.fields(m)
# Set current model
self.curModel = m
# Initiate the Jv object
Jv = self.dataPair(self.survey)
# Loop all the frequenies
for freq in self.survey.freqs:
dA_du = self.getA(freq) #
dA_duI = self.Solver(dA_du, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
# We need fDeriv_m = df/du*du/dm + df/dm
# Construct du/dm, it requires a solve
# NOTE: need to account for the 2 polarizations in the derivatives.
u_src = u[src, :]
# dA_dm and dRHS_dm should be of size nE,2, so that we can multiply by dA_duI. The 2 columns are each of the polarizations.
dA_dm = self.getADeriv_m(
freq, u_src, v) # Size: nE,2 (u_px,u_py) in the columns.
dRHS_dm = self.getRHSDeriv_m(
freq, v) # Size: nE,2 (u_px,u_py) in the columns.
if dRHS_dm is None:
du_dm = dA_duI * (-dA_dm)
else:
du_dm = dA_duI * (-dA_dm + dRHS_dm)
# Calculate the projection derivatives
for rx in src.rxList:
# Get the projection derivative
# v should be of size 2*nE (for 2 polarizations)
PDeriv_u = lambda t: rx.projectFieldsDeriv(
src, self.mesh, u, t
) # wrt u, we don't have have PDeriv wrt m
Jv[src, rx] = PDeriv_u(mkvc(du_dm))
# Return the vectorized sensitivities
return mkvc(Jv)
def writeUBC_DCobs(fileName,Tx,Rx,d,wd, dtype):
from SimPEG import np, mkvc
import re
"""
Read UBC GIF DCIP 3D observation file and generate arrays for tx-rx location
Input:
:param fileName, path to the UBC GIF 3D obs file
Output:
:param rx, tx, d, wd
:return
Created on Mon December 7th, 2015
@author: dominiquef
"""
fid = open(fileName,'w')
fid.write('! GENERAL FORMAT\n')
for ii in range(len(Tx)):
tx = np.asarray(Tx[ii])
rx = np.asarray(Rx[ii])
nrx = rx.shape[0]
fid.write('\n')
if re.match(dtype,'2D'):
for jj in range(nrx):
fid.writelines("%e " % ii for ii in mkvc(tx))
fid.writelines("%e " % ii for ii in mkvc(rx[jj]))
fid.write('%e %e\n'% (d[ii][jj],wd[ii][jj]))
#np.savetxt(fid, np.c_[ rx ,np.asarray(d[ii]), np.asarray(wd[ii]) ], fmt='%e',delimiter=' ',newline='\n')
elif re.match(dtype,'3D'):
fid.write('\n')
fid.writelines("%e " % ii for ii in mkvc(tx))
fid.write('%i\n'% nrx)
np.savetxt(fid, np.c_[ rx ,np.asarray(d[ii]), np.asarray(wd[ii]) ], fmt='%e',delimiter=' ',newline='\n')
fid.close()
def fields(self, m=None):
"""Computes the fields at every time d(t) = G*M(t)"""
if self.ispaired is False:
AssertionError("Problem must be paired with survey to generate A matrix")
# Fields from each source
srcList = self.survey.srcList
nSrc = len(srcList)
f = []
for pp in range(0, nSrc):
rxList = srcList[pp].rxList
nRx = len(rxList)
waveObj = srcList[pp].waveform
for qq in range(0, nRx):
times = rxList[qq].times
eta = waveObj.getLogUniformDecay(
rxList[qq].fieldType, times, self.chi0, self.dchi, self.tau1, self.tau2
)
f.append(mkvc((self.A[qq] * np.matrix(eta)).T))
return np.array(np.hstack(f))
def getADeriv_m(self, freq, u, v, adjoint=False):
"""
Calculate the derivative of A wrt m.
"""
# This considers both polarizations and returns a nE,2 matrix for each polarization
if adjoint:
dMe_dsigV = sp.hstack((self.MeSigmaDeriv(u['e_pxSolution']).T,
self.MeSigmaDeriv(u['e_pySolution']).T)) * v
else:
# Need a nE,2 matrix to be returned
dMe_dsigV = np.hstack(
(mkvc(self.MeSigmaDeriv(u['e_pxSolution']) * v,
2), mkvc(self.MeSigmaDeriv(u['e_pySolution']) * v, 2)))
return 1j * omega(freq) * dMe_dsigV
def fields(self, m=None):
"""Computes the fields at every time d(t) = G*M(t)"""
if self.ispaired is False:
AssertionError(
"Problem must be paired with survey to generate A matrix")
# Fields from each source
srcList = self.survey.srcList
nSrc = len(srcList)
f = []
for pp in range(0, nSrc):
rxList = srcList[pp].rxList
nRx = len(rxList)
waveObj = srcList[pp].waveform
for qq in range(0, nRx):
times = rxList[qq].times
eta = waveObj.getLogUniformDecay(rxList[qq].fieldType, times,
self.chi0, self.dchi,
self.tau1, self.tau2)
f.append(mkvc((self.A[qq] * np.matrix(eta)).T))
return np.array(np.hstack(f))
def _aey_py_u(self, vec):
"""
"""
# vec is (nD,) and returns a (nU,)
return self.f._e_pyDeriv_u(self.src,
self.Pey.T * mkvc(vec, ),
adjoint=True)
def fields(self, m):
'''
Function to calculate all the fields for the model m.
:param np.ndarray (nC,) m: Conductivity model
:param np.ndarray (nC,) m_back: Background conductivity model
'''
self.curModel = m
# RHS, CalcFields = self.getRHS(freq,m_back), self.calcFields
F = Fields1D_e(self.mesh, self.survey)
for freq in self.survey.freqs:
if self.verbose:
startTime = time.time()
print 'Starting work for {:.3e}'.format(freq)
sys.stdout.flush()
A = self.getA(freq)
rhs, e_o = self.getRHS(freq)
Ainv = self.Solver(A, **self.solverOpts)
e_i = Ainv * rhs
e = mkvc(np.r_[e_o[0], e_i, e_o[1]], 2)
# Store the fields
Src = self.survey.getSrcByFreq(freq)
# NOTE: only store e fields
F[Src, 'e_1dSolution'] = e[:, 0]
if self.verbose:
print 'Ran for {:f} seconds'.format(time.time() - startTime)
sys.stdout.flush()
return F
def fields(self, m):
'''
Function to calculate all the fields for the model m.
:param np.ndarray (nC,) m: Conductivity model
:param np.ndarray (nC,) m_back: Background conductivity model
'''
self.curModel = m
# RHS, CalcFields = self.getRHS(freq,m_back), self.calcFields
F = FieldsMT_1D(self.mesh, self.survey)
for freq in self.survey.freqs:
if self.verbose:
startTime = time.time()
print 'Starting work for {:.3e}'.format(freq)
sys.stdout.flush()
A = self.getA(freq)
rhs, e_o = self.getRHS(freq)
Ainv = self.Solver(A, **self.solverOpts)
e_i = Ainv * rhs
e = mkvc(np.r_[e_o[0], e_i, e_o[1]],2)
# Store the fields
Src = self.survey.getSrcByFreq(freq)
# NOTE: only store e fields
F[Src, 'e_1dSolution'] = e[:,0]
if self.verbose:
print 'Ran for {:f} seconds'.format(time.time()-startTime)
sys.stdout.flush()
return F
def Jvec(self, m, v, u=None):
"""
Function to calculate the data sensitivities dD/dm times a vector.
:param numpy.ndarray m (nC, 1) - conductive model
:param numpy.ndarray v (nC, 1) - random vector
:param MTfields object (optional) - MT fields object, if not given it is calculated
:rtype: MTdata object
:return: Data sensitivities wrt m
"""
# Calculate the fields
if u is None:
u = self.fields(m)
# Set current model
self.curModel = m
# Initiate the Jv object
Jv = self.dataPair(self.survey)
# Loop all the frequenies
for freq in self.survey.freqs:
dA_du = self.getA(freq) #
dA_duI = self.Solver(dA_du, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
# We need fDeriv_m = df/du*du/dm + df/dm
# Construct du/dm, it requires a solve
# NOTE: need to account for the 2 polarizations in the derivatives.
u_src = u[src,:]
# dA_dm and dRHS_dm should be of size nE,2, so that we can multiply by dA_duI. The 2 columns are each of the polarizations.
dA_dm = self.getADeriv_m(freq, u_src, v) # Size: nE,2 (u_px,u_py) in the columns.
dRHS_dm = self.getRHSDeriv_m(freq, v) # Size: nE,2 (u_px,u_py) in the columns.
if dRHS_dm is None:
du_dm = dA_duI * ( -dA_dm )
else:
du_dm = dA_duI * ( -dA_dm + dRHS_dm )
# Calculate the projection derivatives
for rx in src.rxList:
# Get the projection derivative
# v should be of size 2*nE (for 2 polarizations)
PDeriv_u = lambda t: rx.evalDeriv(src, self.mesh, u, t) # wrt u, we don't have have PDeriv wrt m
Jv[src, rx] = PDeriv_u(mkvc(du_dm))
dA_duI.clean()
# Return the vectorized sensitivities
return mkvc(Jv)
def fun(u):
f = simulation.fieldsPair(survey.mesh, survey)
f[src, "e_pxSolution"] = u[:len(u) / 2]
f[src, "e_pySolution"] = u[len(u) / 2::]
return (
rx.eval(src, survey.mesh, f),
lambda t: rx.evalDeriv(src, survey.mesh, f0, mkvc(t, 2)),
)
def Jtvec(self, m, v, u=None):
if u is None:
u = self.fields(m)
self.curModel = m
# Ensure v is a data object.
if not isinstance(v, self.dataPair):
v = self.dataPair(self.survey, v)
Jtv = np.zeros(m.size)
for freq in self.survey.freqs:
AT = self.getA(freq).T
ATinv = self.Solver(AT, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
ftype = self._fieldType + 'Solution'
u_src = u[src, :]
for rx in src.rxList:
# Get the adjoint projectFieldsDeriv
# PTv needs to be nE,
PTv = rx.projectFieldsDeriv(src, self.mesh, u, mkvc(v[src, rx],2), adjoint=True) # wrt u, need possibility wrt m
# Get the
dA_duIT = ATinv * PTv
dA_dmT = self.getADeriv_m(freq, u_src, mkvc(dA_duIT), adjoint=True)
dRHS_dmT = self.getRHSDeriv_m(freq, mkvc(dA_duIT), adjoint=True)
# Make du_dmT
if dRHS_dmT is None:
du_dmT = -dA_dmT
else:
du_dmT = -dA_dmT + dRHS_dmT
# Select the correct component
# du_dmT needs to be of size nC,
real_or_imag = rx.projComp
if real_or_imag == 'real':
Jtv += du_dmT.real
elif real_or_imag == 'imag':
Jtv += -du_dmT.real
else:
raise Exception('Must be real or imag')
return Jtv
def Jvec(self, m, v, f=None):
"""
Function to calculate the data sensitivities dD/dm times a vector.
:param numpy.ndarray m: conductivity model (nP,)
:param numpy.ndarray v: vector which we take sensitivity product with (nP,)
:param SimPEG.EM.NSEM.FieldsNSEM (optional) u: NSEM fields object, if not given
it is calculated
:rtype: numpy.ndarray
:return: Jv (nData,) Data sensitivities wrt m
"""
# Calculate the fields if not given as input
if f is None:
f = self.fields(m)
# Set current model
self.model = m
# Initiate the Jv object
Jv = self.dataPair(self.survey)
# Loop all the frequenies
for freq in self.survey.freqs:
# Get the system
A = self.getA(freq)
# Factor
Ainv = self.Solver(A, **self.solverOpts)
for src in self.survey.getSrcByFreq(freq):
# We need fDeriv_m = df/du*du/dm + df/dm
# Construct du/dm, it requires a solve
# NOTE: need to account for the 2 polarizations in the derivatives.
u_src = f[src,:] # u should be a vector by definition. Need to fix this...
# dA_dm and dRHS_dm should be of size nE,2, so that we can multiply by Ainv.
# The 2 columns are each of the polarizations.
dA_dm_v = self.getADeriv(freq, u_src, v) # Size: nE,2 (u_px,u_py) in the columns.
dRHS_dm_v = self.getRHSDeriv(freq, v) # Size: nE,2 (u_px,u_py) in the columns.
# Calculate du/dm*v
du_dm_v = Ainv * ( - dA_dm_v + dRHS_dm_v)
# Calculate the projection derivatives
for rx in src.rxList:
# Calculate dP/du*du/dm*v
Jv[src, rx] = rx.evalDeriv(src, self.mesh, f, mkvc(du_dm_v)) # wrt uPDeriv_u(mkvc(du_dm))
Ainv.clean()
# Return the vectorized sensitivities
return mkvc(Jv)
def getRHSDeriv(self, freq, v, adjoint=False):
"""
The derivative of the RHS wrt sigma
"""
Src = self.survey.getSrcByFreq(freq)[0]
S_eDeriv = mkvc(Src.S_eDeriv_m(self, v, adjoint), )
return -1j * omega(freq) * S_eDeriv
def getRHSDeriv(self, freq, v, adjoint=False):
"""
The derivative of the RHS wrt sigma
"""
Src = self.survey.getSrcByFreq(freq)[0]
S_eDeriv = mkvc(Src.S_eDeriv_m(self, v, adjoint),)
return -1j * omega(freq) * S_eDeriv
def projectFields(self, u):
"""
Predicted data.
.. math::
d_\\text{pred} = Pu(m)
"""
P = self.getP(self.prob.mesh)
return P*mkvc(u[self.srcList, 'phi_sol'])
def _getSubsetAcolumns(self, xyzc, xyzh, pp, qq, refFlag):
"""
This method returns the refined sensitivities for columns that will be
replaced in the A matrix for source pp and refinement factor qq.
..
.. INPUTS:
..
.. xyzc -- Cell centers of topo mesh cells N X 3 array
..
.. xyzh -- Cell widths of topo mesh cells N X 3 array
..
.. pp -- Source ID
..
.. qq -- Mesh refinement factor
..
.. refFlag -- refinement factors for all topo mesh cells
..
.. OUTPUTS:
..
.. Acols -- Columns containing replacement sensitivities
"""
# GET SUBMESH GRID
n = 2**qq
[nx, ny, nz] = np.meshgrid(
np.linspace(1, n, n)-0.5, np.linspace(1, n, n)-0.5, np.linspace(1, n, n)-0.5)
nxyz_sub = np.c_[mkvc(nx), mkvc(ny), mkvc(nz)]
xyzh_sub = xyzh[refFlag == qq, :] # Get widths of cells to be refined
xyzc_sub = xyzc[refFlag == qq, :] - xyzh[refFlag == qq, :]/2 # Get bottom southwest corners of cells to be refined
m = np.shape(xyzc_sub)[0]
xyzc_sub = np.kron(xyzc_sub, np.ones((n**3, 1))) # Kron for n**3 refined cells
xyzh_sub = np.kron(xyzh_sub/n, np.ones((n**3, 1))) # Kron for n**3 refined cells with widths h/n
nxyz_sub = np.kron(np.ones((m, 1)), nxyz_sub) # Kron for n**3 refined cells
xyzc_sub = xyzc_sub + xyzh_sub*nxyz_sub
# GET SUBMESH A MATRIX AND COLLAPSE TO COLUMNS
G = self._getGeometryMatrix(xyzc_sub, xyzh_sub, pp)
H0 = self._getH0matrix(xyzc_sub, pp)
Acols = (G*H0)*sp.kron(sp.diags(np.ones(m)), np.ones((n**3, 1)))
return Acols
def setup1DSurvey(sigmaHalf, tD=False, structure=False):
# Frequency
num_frequencies = 33
freqs = np.logspace(3, -3, num_frequencies)
# Make the mesh
ct = 5
air = meshTensor([(ct, 25, 1.3)])
# coreT0 = meshTensor([(ct,15,1.2)])
# coreT1 = np.kron(meshTensor([(coreT0[-1],15,1.3)]),np.ones((7,)))
core = np.concatenate((np.kron(meshTensor([(ct, 15, -1.2)]), np.ones(
(10, ))), meshTensor([(ct, 20)])))
bot = meshTensor([(core[0], 20, -1.3)])
x0 = -np.array([np.sum(np.concatenate((core, bot)))])
m1d = discretize.TensorMesh([np.concatenate((bot, core, air))], x0=x0)
# Make the model
sigma = np.zeros(m1d.nC) + sigmaHalf
sigma[m1d.gridCC > 0] = 1e-8
sigmaBack = sigma.copy()
# Add structure
if structure:
shallow = (m1d.gridCC < -200) * (m1d.gridCC > -600)
deep = (m1d.gridCC < -3000) * (m1d.gridCC > -5000)
sigma[shallow] = 1
sigma[deep] = 0.1
receiver_list = []
for rxType in ["z1d", "z1d"]:
receiver_list.append(
Point1DImpedance(mkvc(np.array([0.0]), 2).T, "real"))
receiver_list.append(
Point1DImpedance(mkvc(np.array([0.0]), 2).T, "imag"))
# Source list
source_list = []
if tD:
for freq in freqs:
source_list.append(Planewave_xy_1DhomotD(receiver_list, freq))
else:
for freq in freqs:
source_list.append(Planewave_xy_1Dprimary(receiver_list, freq))
survey = Survey(source_list)
return (survey, sigma, sigmaBack, m1d)
def toRecArray(self,returnType='RealImag'):
'''
Function that returns a numpy.recarray for a SimpegMT impedance data object.
:param str returnType: Switches between returning a rec array where the impedance is split to real and imaginary ('RealImag') or is a complex ('Complex')
'''
# Define the record fields
dtRI = [('freq',float),('x',float),('y',float),('z',float),('zxxr',float),('zxxi',float),('zxyr',float),('zxyi',float),
('zyxr',float),('zyxi',float),('zyyr',float),('zyyi',float),('tzxr',float),('tzxi',float),('tzyr',float),('tzyi',float)]
dtCP = [('freq',float),('x',float),('y',float),('z',float),('zxx',complex),('zxy',complex),('zyx',complex),('zyy',complex),('tzx',complex),('tzy',complex)]
impList = ['zxxr','zxxi','zxyr','zxyi','zyxr','zyxi','zyyr','zyyi']
for src in self.survey.srcList:
# Temp array for all the receivers of the source.
# Note: needs to be written more generally, using diffterent rxTypes and not all the data at the locaitons
# Assume the same locs for all RX
locs = src.rxList[0].locs
if locs.shape[1] == 1:
locs = np.hstack((np.array([[0.0,0.0]]),locs))
elif locs.shape[1] == 2:
locs = np.hstack((np.array([[0.0]]),locs))
tArrRec = np.concatenate((src.freq*np.ones((locs.shape[0],1)),locs,np.nan*np.ones((locs.shape[0],12))),axis=1).view(dtRI)
# np.array([(src.freq,rx.locs[0,0],rx.locs[0,1],rx.locs[0,2],np.nan ,np.nan ,np.nan ,np.nan ,np.nan ,np.nan ,np.nan ,np.nan ) for rx in src.rxList],dtype=dtRI)
# Get the type and the value for the DataMT object as a list
typeList = [[rx.rxType.replace('z1d','zyx'),self[src,rx]] for rx in src.rxList]
# Insert the values to the temp array
for nr,(key,val) in enumerate(typeList):
tArrRec[key] = mkvc(val,2)
# Masked array
mArrRec = np.ma.MaskedArray(rec2ndarr(tArrRec),mask=np.isnan(rec2ndarr(tArrRec))).view(dtype=tArrRec.dtype)
# Unique freq and loc of the masked array
uniFLmarr = np.unique(mArrRec[['freq','x','y','z']]).copy()
try:
outTemp = recFunc.stack_arrays((outTemp,mArrRec))
#outTemp = np.concatenate((outTemp,dataBlock),axis=0)
except NameError as e:
outTemp = mArrRec
if 'RealImag' in returnType:
outArr = outTemp
elif 'Complex' in returnType:
# Add the real and imaginary to a complex number
outArr = np.empty(outTemp.shape,dtype=dtCP)
for comp in ['freq','x','y','z']:
outArr[comp] = outTemp[comp].copy()
for comp in ['zxx','zxy','zyx','zyy','tzx','tzy']:
outArr[comp] = outTemp[comp+'r'].copy() + 1j*outTemp[comp+'i'].copy()
else:
raise NotImplementedError('{:s} is not implemented, as to be RealImag or Complex.')
# Return
return outArr
def Jvec(self, m, v, u=None):
"""
:param numpy.array m: model
:param numpy.array v: vector to multiply
:param numpy.array u: fields
:rtype: numpy.array
:return: Jv
.. math::
c(m,u) = A(m)u - q = G\\text{sdiag}(M(mT(m)))Du - q = 0
\\nabla_u (A(m)u - q) = A(m)
\\nabla_m (A(m)u - q) = G\\text{sdiag}(Du)\\nabla_m(M(mT(m)))
Where M() is the mass matrix and mT is the model transform.
.. math::
J = - P \left( \\nabla_u c(m, u) \\right)^{-1} \\nabla_m c(m, u)
J(v) = - P ( A(m)^{-1} ( G\\text{sdiag}(Du)\\nabla_m(M(mT(m))) v ) )
"""
# Set current model; clear dependent property $\mathbf{A(m)}$
self.curModel = m
sigma = self.curModel.transform # $\sigma = \mathcal{M}(\m)$
if u is None:
# Run forward simulation if $u$ not provided
u = self.fields(self.curModel)[self.survey.srcList, 'phi_sol']
else:
u = u[self.survey.srcList, 'phi_sol']
D = self.mesh.faceDiv
G = self.mesh.cellGrad
# Derivative of model transform, $\deriv{\sigma}{\m}$
dsigdm_x_v = self.curModel.transformDeriv * v
# Take derivative of $C(m,u)$ w.r.t. $m$
dCdm_x_v = np.empty_like(u)
# loop over fields for each source
for i in range(self.survey.nSrc):
# Derivative of inner product, $\left(\mathbf{M}_{1/\sigma}^f\right)^{-1}$
dAdsig = D * self.dMdsig( G * u[:,i] )
dCdm_x_v[:, i] = dAdsig * dsigdm_x_v
# Take derivative of $C(m,u)$ w.r.t. $u$
dA_du = self.A
# Solve for $\deriv{u}{m}$
# dCdu_inv = self.Solver(dCdu, **self.solverOpts)
if self.Ainv is None:
self.Ainv = self.Solver(dA_du, **self.solverOpts)
P = self.survey.getP(self.mesh)
Jv = - P * mkvc( self.Ainv * dCdm_x_v )
return Jv
def readUBC_DC2DModel(fileName):
from SimPEG import np, mkvc
"""
Read UBC GIF 2DTensor model and generate 2D Tensor model in simpeg
Input:
:param fileName, path to the UBC GIF 2D model file
Output:
:param SimPEG TensorMesh 2D object
:return
Created on Thu Nov 12 13:14:10 2015
@author: dominiquef
"""
# Open fileand skip header... assume that we know the mesh already
obsfile = np.genfromtxt(fileName,delimiter=' \n',dtype=np.str,comments='!')
dim = np.array(obsfile[0].split(),dtype=float)
temp = np.array(obsfile[1].split(),dtype=float)
if len(temp) > 1:
model = np.zeros(dim)
for ii in range(len(obsfile)-1):
mm = np.array(obsfile[ii+1].split(),dtype=float)
model[:,ii] = mm
model = model[:,::-1]
else:
if len(obsfile[1:])==1:
mm = np.array(obsfile[1:].split(),dtype=float)
else:
mm = np.array(obsfile[1:],dtype=float)
# Permute the second dimension to flip the order
model = mm.reshape(dim[1],dim[0])
model = model[::-1,:]
model = np.transpose(model, (1, 0))
model = mkvc(model)
return model
def S_eDeriv_m(self, problem, v, adjoint=False):
'''
Get the derivative of S_e wrt to sigma (m)
'''
# Need to deal with
if problem.mesh.dim == 1:
# Need to use the faceInnerProduct
MsigmaDeriv = (
problem.mesh.getFaceInnerProductDeriv(
problem.sigma)(self.ePrimary(problem)[:, 1]) *
problem.sigmaDeriv)
# MsigmaDeriv = ( MsigmaDeriv * MsigmaDeriv.T)**2
if problem.mesh.dim == 2:
pass
if problem.mesh.dim == 3:
# Need to take the derivative of both u_px and u_py
ePri = self.ePrimary(problem)
if adjoint:
return (
problem.MeSigmaDeriv(
ePri[:, 0], v[:int(v.shape[0]/2)], adjoint
) +
problem.MeSigmaDeriv(
ePri[:, 1], v[int(v.shape[0]/2):], adjoint
)
)
# return sp.hstack((
# problem.MeSigmaDeriv(ePri[:, 0]).T,
# problem.MeSigmaDeriv(ePri[:, 1]).T)) * v
else:
return np.hstack((
mkvc(problem.MeSigmaDeriv(ePri[:, 0], v, adjoint), 2),
mkvc(problem.MeSigmaDeriv(ePri[:, 1], v, adjoint), 2)
))
if adjoint:
#
return MsigmaDeriv.T * v
else:
# v should be nC size
return MsigmaDeriv * v
def readUBC_DC2DModel(fileName):
"""
Read UBC GIF 2DTensor model and generate 2D Tensor model in simpeg
Input:
:param fileName, path to the UBC GIF 2D model file
Output:
:param SimPEG TensorMesh 2D object
:return
Created on Thu Nov 12 13:14:10 2015
@author: dominiquef
"""
from SimPEG import np, mkvc
# Open fileand skip header... assume that we know the mesh already
obsfile = np.genfromtxt(fileName,delimiter=' \n',dtype=np.str,comments='!')
dim = np.array(obsfile[0].split(),dtype=float)
temp = np.array(obsfile[1].split(),dtype=float)
if len(temp) > 1:
model = np.zeros(dim)
for ii in range(len(obsfile)-1):
mm = np.array(obsfile[ii+1].split(),dtype=float)
model[:,ii] = mm
model = model[:,::-1]
else:
if len(obsfile[1:])==1:
mm = np.array(obsfile[1:].split(),dtype=float)
else:
mm = np.array(obsfile[1:],dtype=float)
# Permute the second dimension to flip the order
model = mm.reshape(dim[1],dim[0])
model = model[::-1,:]
model = np.transpose(model, (1, 0))
model = mkvc(model)
return model
def getRHS(self, freq):
"""
Function to return the right hand side for the system.
:param float freq: Frequency
:rtype: numpy.ndarray
:return: RHS for 1 polarizations, primary fields (nF, 1)
"""
# Get sources for the frequncy(polarizations)
Src = self.survey.getSrcByFreq(freq)[0]
# Only select the yx polarization
S_e = mkvc(Src.S_e(self)[:, 1], 2)
return -1j * omega(freq) * S_e
def getADeriv_m(self, freq, u, v, adjoint=False):
# Nee to account for both the polarizations
# dMe_dsig = (self.MeSigmaDeriv( u['e_pxSolution'] ) + self.MeSigmaDeriv( u['e_pySolution'] ))
# dMe_dsig = (self.MeSigmaDeriv( u['e_pxSolution'] + u['e_pySolution'] ))
# # dMe_dsig = self.MeSigmaDeriv( u )
# if adjoint:
# return 1j * omega(freq) * ( dMe_dsig.T * v ) # As in simpegEM
# return 1j * omega(freq) * ( dMe_dsig * v ) # As in simpegEM
# This considers both polarizations and returns a nE,2 matrix for each polarization
if adjoint:
dMe_dsigV = sp.hstack((self.MeSigmaDeriv(u['e_pxSolution']).T,
self.MeSigmaDeriv(u['e_pySolution']).T)) * v
else:
# Need a nE,2 matrix to be returned
dMe_dsigV = np.hstack(
(mkvc(self.MeSigmaDeriv(u['e_pxSolution']) * v,
2), mkvc(self.MeSigmaDeriv(u['e_pySolution']) * v, 2)))
return 1j * omega(freq) * dMe_dsigV
def getRHS(self, freq):
"""
Function to return the right hand side for the system.
:param float freq: Frequency
:rtype: numpy.ndarray
:return: RHS for 1 polarizations, primary fields (nF, 1)
"""
# Get sources for the frequncy(polarizations)
Src = self.survey.getSrcByFreq(freq)[0]
# Only select the yx polarization
S_e = mkvc(Src.S_e(self)[:, 1], 2)
return -1j * omega(freq) * S_e
def getADeriv_m(self, freq, u, v, adjoint=False):
"""
Calculate the derivative of A wrt m.
"""
# This considers both polarizations and returns a nE,2 matrix for each polarization
if adjoint:
dMe_dsigV = sp.hstack(( self.MeSigmaDeriv( u['e_pxSolution'] ).T, self.MeSigmaDeriv(u['e_pySolution'] ).T ))*v
else:
# Need a nE,2 matrix to be returned
dMe_dsigV = np.hstack(( mkvc(self.MeSigmaDeriv( u['e_pxSolution'] )*v,2), mkvc( self.MeSigmaDeriv(u['e_pySolution'] )*v,2) ))
return 1j * omega(freq) * dMe_dsigV
def fields(self, m):
"""Computes the fields d = T*A*m"""
assert self.ispaired, "Problem must be paired with survey to predict data"
self.model = m # Initiates/updates model and initiates mapping
# Project to active mesh cells
# m = np.matrix(self.xiMap * m).T
m = np.matrix(self.xiMap * m).T
# Must return as a numpy array
return mkvc(sp.coo_matrix.dot(self.T, np.dot(self.A, m)))
def grid_survey(spacing,width, x0 = (0,0,0), topo=None):
"""
grid_survey(spacing,width)
Generate concentric grid surveys centered at the origin
:grid: List of grid spacing
:width: Grid width
return: rxLoc an n-by-3 receiver locations
"""
rxLoc = []
if len(spacing)!=len(width):
raise 'Number of elements in spacing different than grid width'
ii = -1
for dx in spacing:
ii += 1
# Define survey grids centered at [0,0]
# Number of grid points that fits in the width
nC = int(width[ii]/dx)
rxVec = -width[ii]/2. + dx/2. + np.asarray(range(nC))*dx
rxGridx, rxGridy = np.meshgrid(rxVec,rxVec)
rxGridx += x0[0]
rxGridy += x0[1]
if topo is not None:
rxGridz = scipy.interpolate.griddata(topo[:,:2], topo[:,2], (rxGridx, rxGridy),
method='linear') + x0[2]
else:
rxGridz = np.zeros_like(rxGridx) + x0[2]
# Remove points if already inside inner grid
if ii > 0:
indx = np.logical_and(np.logical_and(rxGridy<rxLoc[:,1].max(), rxGridy>rxLoc[:,1].min()),np.logical_and(rxGridx>rxLoc[:,0].min(), rxGridx<rxLoc[:,0].max()))
indx = indx.reshape(rxGridx.shape)
rxGridx = rxGridx[indx==0]
rxGridy = rxGridy[indx==0]
rxGridz = rxGridz[indx==0]
rxLoc = np.vstack([rxLoc, np.c_[mkvc(rxGridx),mkvc(rxGridy),mkvc(rxGridz)]])
else:
rxLoc = np.c_[mkvc(rxGridx),mkvc(rxGridy),mkvc(rxGridz)]
return rxGridx, rxGridy, rxGridz
def fields(self, m):
"""Computes the fields d = T*A*m"""
if self.ispaired is False:
AssertionError(
"Problem must be paired with survey to generate A matrix")
self.model = m # Initiates/updates model and initiates mapping
# Project to active mesh cells
# m = np.matrix(self.xiMap * m).T
m = np.matrix(self.xiMap * m).T
# Must return as a numpy array
return mkvc(sp.coo_matrix.dot(self.T, np.dot(self.A, m)))
def fields(self, m):
"""Computes the fields d = T*A*m"""
if self.ispaired is False:
AssertionError("Problem must be paired with survey to generate A matrix")
self.model = m # Initiates/updates model and initiates mapping
# Project to active mesh cells
# m = np.matrix(self.xiMap * m).T
m = np.matrix(self.xiMap * m).T
# Must return as a numpy array
return mkvc(sp.coo_matrix.dot(self.T, np.dot(self.A, m)))
def dataMis_AnalyticPrimarySecondary(sigmaHalf):
# Make the survey
# Primary secondary
survey, sig, sigBG, mesh = nsem.utils.test_utils.setup1DSurvey(
sigmaHalf, False, structure=True)
# Analytic data
simulation = nsem.Simulation1DPrimarySecondary(mesh,
sigmaPrimary=sig,
sigma=sig,
survey=survey)
dataAnaObj = calculateAnalyticSolution(survey.source_list, mesh, sig)
data = simulation.dpred()
dataAna = mkvc(dataAnaObj)
return np.all((data - dataAna) / dataAna < 2.0)
def Jvec(self, m, v, f=None):
"""Compute Pd*T*A*dxidm*v"""
if self.ispaired is False:
AssertionError("Problem must be paired with survey to generate A matrix")
# Jacobian of xi wrt model
dxidm = self.xiMap.deriv(m)
# dxidm*v
v = np.matrix(dxidm*v).T
# Dot product with A
v = self.A*v
# Get active time rows of T
T = self.T.tocsr()[self.survey.t_active, :]
# Must return an array
return mkvc(sp.csr_matrix.dot(T, v))
def Jtvec(self, m, v, f=None):
"""Compute (Pd*T*A*dxidm)^T * v"""
if self.ispaired is False:
AssertionError("Problem must be paired with survey to generate A matrix")
# Define v as a column vector
v = np.matrix(v).T
# Get T'*Pd'*v
T = self.T.tocsr()[self.survey.t_active, :]
v = sp.csc_matrix.dot(T.transpose(), v)
# Multiply by A'
v = (np.dot(v.T, self.A)).T
# Jacobian of xi wrt model
dxidm = self.xiMap.deriv(m)
# Must return an array
return mkvc(dxidm.T*v)
def _hx(self):
return self.Pbx * mkvc(self.f[self.src, 'b_1d'], 2) / mu_0
def eval(self, src, mesh, f):
'''
Project the fields to natural source data.
:param SrcMT src: The source of the fields to project
:param SimPEG.Mesh mesh:
:param FieldsMT f: Natural source fields object to project
'''
## NOTE: Assumes that e is on t
if self.projType is 'Z1D':
Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
ex = Pex*mkvc(f[src,'e_1d'],2)
bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
# Note: Has a minus sign in front, to comply with quadrant calculations.
# Can be derived from zyx case for the 3D case.
f_part_complex = -ex/bx
# elif self.projType is 'Z2D':
elif self.projType is 'Z3D':
## NOTE: Assumes that e is on edges and b on the faces. Need to generalize that or use a prop of fields to determine that.
if self.locs.ndim == 3:
eFLocs = self.locs[:,:,0]
bFLocs = self.locs[:,:,1]
else:
eFLocs = self.locs
bFLocs = self.locs
# Get the projection
Pex = mesh.getInterpolationMat(eFLocs,'Ex')
Pey = mesh.getInterpolationMat(eFLocs,'Ey')
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
# Get the fields at location
# px: x-polaration and py: y-polaration.
ex_px = Pex*f[src,'e_px']
ey_px = Pey*f[src,'e_px']
ex_py = Pex*f[src,'e_py']
ey_py = Pey*f[src,'e_py']
hx_px = Pbx*f[src,'b_px']/mu_0
hy_px = Pby*f[src,'b_px']/mu_0
hx_py = Pbx*f[src,'b_py']/mu_0
hy_py = Pby*f[src,'b_py']/mu_0
# Make the complex data
if 'zxx' in self.rxType:
f_part_complex = ( ex_px*hy_py - ex_py*hy_px)/(hx_px*hy_py - hx_py*hy_px)
elif 'zxy' in self.rxType:
f_part_complex = (-ex_px*hx_py + ex_py*hx_px)/(hx_px*hy_py - hx_py*hy_px)
elif 'zyx' in self.rxType:
f_part_complex = ( ey_px*hy_py - ey_py*hy_px)/(hx_px*hy_py - hx_py*hy_px)
elif 'zyy' in self.rxType:
f_part_complex = (-ey_px*hx_py + ey_py*hx_px)/(hx_px*hy_py - hx_py*hy_px)
elif self.projType is 'T3D':
if self.locs.ndim == 3:
horLoc = self.locs[:,:,0]
vertLoc = self.locs[:,:,1]
else:
horLoc = self.locs
vertLoc = self.locs
Pbx = mesh.getInterpolationMat(horLoc,'Fx')
Pby = mesh.getInterpolationMat(horLoc,'Fy')
Pbz = mesh.getInterpolationMat(vertLoc,'Fz')
bx_px = Pbx*f[src,'b_px']
by_px = Pby*f[src,'b_px']
bz_px = Pbz*f[src,'b_px']
bx_py = Pbx*f[src,'b_py']
by_py = Pby*f[src,'b_py']
bz_py = Pbz*f[src,'b_py']
if 'tzx' in self.rxType:
f_part_complex = (- by_px*bz_py + by_py*bz_px)/(bx_px*by_py - bx_py*by_px)
if 'tzy' in self.rxType:
f_part_complex = ( bx_px*bz_py - bx_py*bz_px)/(bx_px*by_py - bx_py*by_px)
else:
NotImplementedError('Projection of {:s} receiver type is not implemented.'.format(self.rxType))
# Get the real or imag component
real_or_imag = self.projComp
f_part = getattr(f_part_complex, real_or_imag)
# print f_part
return f_part
def evalDeriv(self, src, mesh, f, v, adjoint=False):
"""
The derivative of the projection wrt u
:param MTsrc src: MT source
:param TensorMesh mesh: Mesh defining the topology of the problem
:param MTfields f: MT fields object of the source
:param numpy.ndarray v: Random vector of size
"""
real_or_imag = self.projComp
if not adjoint:
if self.projType is 'Z1D':
Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
# ex = Pex*mkvc(f[src,'e_1d'],2)
# bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
dP_de = -mkvc(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))*(Pex*v),2)
dP_db = mkvc( Utils.sdiag(Pex*mkvc(f[src,'e_1d'],2))*(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)).T*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)))*(Pbx*f._bDeriv_u(src,v)/mu_0),2)
PDeriv_complex = np.sum(np.hstack((dP_de,dP_db)),1)
elif self.projType is 'Z2D':
raise NotImplementedError('Has not been implement for 2D impedance tensor')
elif self.projType is 'Z3D':
if self.locs.ndim == 3:
eFLocs = self.locs[:,:,0]
bFLocs = self.locs[:,:,1]
else:
eFLocs = self.locs
bFLocs = self.locs
# Get the projection
Pex = mesh.getInterpolationMat(eFLocs,'Ex')
Pey = mesh.getInterpolationMat(eFLocs,'Ey')
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
# Get the fields at location
# px: x-polaration and py: y-polaration.
ex_px = Pex*f[src,'e_px']
ey_px = Pey*f[src,'e_px']
ex_py = Pex*f[src,'e_py']
ey_py = Pey*f[src,'e_py']
hx_px = Pbx*f[src,'b_px']/mu_0
hy_px = Pby*f[src,'b_px']/mu_0
hx_py = Pbx*f[src,'b_py']/mu_0
hy_py = Pby*f[src,'b_py']/mu_0
# Derivatives as lambda functions
# The size of the diratives should be nD,nU
ex_px_u = lambda vec: Pex*f._e_pxDeriv_u(src,vec)
ey_px_u = lambda vec: Pey*f._e_pxDeriv_u(src,vec)
ex_py_u = lambda vec: Pex*f._e_pyDeriv_u(src,vec)
ey_py_u = lambda vec: Pey*f._e_pyDeriv_u(src,vec)
# NOTE: Think b_p?Deriv_u should return a 2*nF size matrix
hx_px_u = lambda vec: Pbx*f._b_pxDeriv_u(src,vec)/mu_0
hy_px_u = lambda vec: Pby*f._b_pxDeriv_u(src,vec)/mu_0
hx_py_u = lambda vec: Pbx*f._b_pyDeriv_u(src,vec)/mu_0
hy_py_u = lambda vec: Pby*f._b_pyDeriv_u(src,vec)/mu_0
# Update the input vector
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
# Define the components of the derivative
Hd = sDiag(1./(sDiag(hx_px)*hy_py - sDiag(hx_py)*hy_px))
Hd_uV = sDiag(hy_py)*hx_px_u(v) + sDiag(hx_px)*hy_py_u(v) - sDiag(hx_py)*hy_px_u(v) - sDiag(hy_px)*hx_py_u(v)
# Calculate components
if 'zxx' in self.rxType:
Zij = sDiag(Hd*( sDiag(ex_px)*hy_py - sDiag(ex_py)*hy_px ))
ZijN_uV = sDiag(hy_py)*ex_px_u(v) + sDiag(ex_px)*hy_py_u(v) - sDiag(ex_py)*hy_px_u(v) - sDiag(hy_px)*ex_py_u(v)
elif 'zxy' in self.rxType:
Zij = sDiag(Hd*(-sDiag(ex_px)*hx_py + sDiag(ex_py)*hx_px ))
ZijN_uV = -sDiag(hx_py)*ex_px_u(v) - sDiag(ex_px)*hx_py_u(v) + sDiag(ex_py)*hx_px_u(v) + sDiag(hx_px)*ex_py_u(v)
elif 'zyx' in self.rxType:
Zij = sDiag(Hd*( sDiag(ey_px)*hy_py - sDiag(ey_py)*hy_px ))
ZijN_uV = sDiag(hy_py)*ey_px_u(v) + sDiag(ey_px)*hy_py_u(v) - sDiag(ey_py)*hy_px_u(v) - sDiag(hy_px)*ey_py_u(v)
elif 'zyy' in self.rxType:
Zij = sDiag(Hd*(-sDiag(ey_px)*hx_py + sDiag(ey_py)*hx_px ))
ZijN_uV = -sDiag(hx_py)*ey_px_u(v) - sDiag(ey_px)*hx_py_u(v) + sDiag(ey_py)*hx_px_u(v) + sDiag(hx_px)*ey_py_u(v)
# Calculate the complex derivative
PDeriv_complex = Hd * (ZijN_uV - Zij * Hd_uV )
elif self.projType is 'T3D':
if self.locs.ndim == 3:
eFLocs = self.locs[:,:,0]
bFLocs = self.locs[:,:,1]
else:
eFLocs = self.locs
bFLocs = self.locs
# Get the projection
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
Pbz = mesh.getInterpolationMat(bFLocs,'Fz')
# Get the fields at location
# px: x-polaration and py: y-polaration.
bx_px = Pbx*f[src,'b_px']
by_px = Pby*f[src,'b_px']
bz_px = Pbz*f[src,'b_px']
bx_py = Pbx*f[src,'b_py']
by_py = Pby*f[src,'b_py']
bz_py = Pbz*f[src,'b_py']
# Derivatives as lambda functions
# NOTE: Think b_p?Deriv_u should return a 2*nF size matrix
bx_px_u = lambda vec: Pbx*f._b_pxDeriv_u(src,vec)
by_px_u = lambda vec: Pby*f._b_pxDeriv_u(src,vec)
bz_px_u = lambda vec: Pbz*f._b_pxDeriv_u(src,vec)
bx_py_u = lambda vec: Pbx*f._b_pyDeriv_u(src,vec)
by_py_u = lambda vec: Pby*f._b_pyDeriv_u(src,vec)
bz_py_u = lambda vec: Pbz*f._b_pyDeriv_u(src,vec)
# Update the input vector
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
# Define the components of the derivative
Hd = sDiag(1./(sDiag(bx_px)*by_py - sDiag(bx_py)*by_px))
Hd_uV = sDiag(by_py)*bx_px_u(v) + sDiag(bx_px)*by_py_u(v) - sDiag(bx_py)*by_px_u(v) - sDiag(by_px)*bx_py_u(v)
if 'tzx' in self.rxType:
Tij = sDiag(Hd*( - sDiag(by_px)*bz_py + sDiag(by_py)*bz_px ))
TijN_uV = -sDiag(by_px)*bz_py_u(v) - sDiag(bz_py)*by_px_u(v) + sDiag(by_py)*bz_px_u(v) + sDiag(bz_px)*by_py_u(v)
elif 'tzy' in self.rxType:
Tij = sDiag(Hd*( sDiag(bx_px)*bz_py - sDiag(bx_py)*bz_px ))
TijN_uV = sDiag(bz_py)*bx_px_u(v) + sDiag(bx_px)*bz_py_u(v) - sDiag(bx_py)*bz_px_u(v) - sDiag(bz_px)*bx_py_u(v)
# Calculate the complex derivative
PDeriv_complex = Hd * (TijN_uV - Tij * Hd_uV )
# Extract the real number for the real/imag components.
Pv = np.array(getattr(PDeriv_complex, real_or_imag))
elif adjoint:
# Note: The v vector is real and the return should be complex
if self.projType is 'Z1D':
Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
# ex = Pex*mkvc(f[src,'e_1d'],2)
# bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
dP_deTv = -mkvc(Pex.T*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)).T*v,2)
db_duv = Pbx.T/mu_0*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))*(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))).T*Utils.sdiag(Pex*mkvc(f[src,'e_1d'],2)).T*v
dP_dbTv = mkvc(f._bDeriv_u(src,db_duv,adjoint=True),2)
PDeriv_real = np.sum(np.hstack((dP_deTv,dP_dbTv)),1)
elif self.projType is 'Z2D':
raise NotImplementedError('Has not be implement for 2D impedance tensor')
elif self.projType is 'Z3D':
if self.locs.ndim == 3:
eFLocs = self.locs[:,:,0]
bFLocs = self.locs[:,:,1]
else:
eFLocs = self.locs
bFLocs = self.locs
# Get the projection
Pex = mesh.getInterpolationMat(eFLocs,'Ex')
Pey = mesh.getInterpolationMat(eFLocs,'Ey')
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
# Get the fields at location
# px: x-polaration and py: y-polaration.
aex_px = mkvc(mkvc(f[src,'e_px'],2).T*Pex.T)
aey_px = mkvc(mkvc(f[src,'e_px'],2).T*Pey.T)
aex_py = mkvc(mkvc(f[src,'e_py'],2).T*Pex.T)
aey_py = mkvc(mkvc(f[src,'e_py'],2).T*Pey.T)
ahx_px = mkvc(mkvc(f[src,'b_px'],2).T/mu_0*Pbx.T)
ahy_px = mkvc(mkvc(f[src,'b_px'],2).T/mu_0*Pby.T)
ahx_py = mkvc(mkvc(f[src,'b_py'],2).T/mu_0*Pbx.T)
ahy_py = mkvc(mkvc(f[src,'b_py'],2).T/mu_0*Pby.T)
# Derivatives as lambda functions
aex_px_u = lambda vec: f._e_pxDeriv_u(src,Pex.T*vec,adjoint=True)
aey_px_u = lambda vec: f._e_pxDeriv_u(src,Pey.T*vec,adjoint=True)
aex_py_u = lambda vec: f._e_pyDeriv_u(src,Pex.T*vec,adjoint=True)
aey_py_u = lambda vec: f._e_pyDeriv_u(src,Pey.T*vec,adjoint=True)
ahx_px_u = lambda vec: f._b_pxDeriv_u(src,Pbx.T*vec,adjoint=True)/mu_0
ahy_px_u = lambda vec: f._b_pxDeriv_u(src,Pby.T*vec,adjoint=True)/mu_0
ahx_py_u = lambda vec: f._b_pyDeriv_u(src,Pbx.T*vec,adjoint=True)/mu_0
ahy_py_u = lambda vec: f._b_pyDeriv_u(src,Pby.T*vec,adjoint=True)/mu_0
# Update the input vector
# Define shortcuts
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
sVec = lambda t: Utils.sp.csr_matrix(mkvc(t,2))
# Define the components of the derivative
aHd = sDiag(1./(sDiag(ahx_px)*ahy_py - sDiag(ahx_py)*ahy_px))
aHd_uV = lambda x: ahx_px_u(sDiag(ahy_py)*x) + ahx_px_u(sDiag(ahy_py)*x) - ahy_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(ahy_px)*x)
# Need to fix this to reflect the adjoint
if 'zxx' in self.rxType:
Zij = sDiag(aHd*( sDiag(ahy_py)*aex_px - sDiag(ahy_px)*aex_py))
ZijN_uV = lambda x: aex_px_u(sDiag(ahy_py)*x) + ahy_py_u(sDiag(aex_px)*x) - ahy_px_u(sDiag(aex_py)*x) - aex_py_u(sDiag(ahy_px)*x)
elif 'zxy' in self.rxType:
Zij = sDiag(aHd*(-sDiag(ahx_py)*aex_px + sDiag(ahx_px)*aex_py))
ZijN_uV = lambda x:-aex_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(aex_px)*x) + ahx_px_u(sDiag(aex_py)*x) + aex_py_u(sDiag(ahx_px)*x)
elif 'zyx' in self.rxType:
Zij = sDiag(aHd*( sDiag(ahy_py)*aey_px - sDiag(ahy_px)*aey_py))
ZijN_uV = lambda x: aey_px_u(sDiag(ahy_py)*x) + ahy_py_u(sDiag(aey_px)*x) - ahy_px_u(sDiag(aey_py)*x) - aey_py_u(sDiag(ahy_px)*x)
elif 'zyy' in self.rxType:
Zij = sDiag(aHd*(-sDiag(ahx_py)*aey_px + sDiag(ahx_px)*aey_py))
ZijN_uV = lambda x:-aey_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(aey_px)*x) + ahx_px_u(sDiag(aey_py)*x) + aey_py_u(sDiag(ahx_px)*x)
# Calculate the complex derivative
PDeriv_real = ZijN_uV(aHd*v) - aHd_uV(Zij.T*aHd*v)#
# NOTE: Need to reshape the output to go from 2*nU array to a (nU,2) matrix for each polarization
# PDeriv_real = np.hstack((mkvc(PDeriv_real[:len(PDeriv_real)/2],2),mkvc(PDeriv_real[len(PDeriv_real)/2::],2)))
PDeriv_real = PDeriv_real.reshape((2,mesh.nE)).T
elif self.projType is 'T3D':
if self.locs.ndim == 3:
bFLocs = self.locs[:,:,1]
else:
bFLocs = self.locs
# Get the projection
Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
Pby = mesh.getInterpolationMat(bFLocs,'Fy')
Pbz = mesh.getInterpolationMat(bFLocs,'Fz')
# Get the fields at location
# px: x-polaration and py: y-polaration.
abx_px = mkvc(mkvc(f[src,'b_px'],2).T*Pbx.T)
aby_px = mkvc(mkvc(f[src,'b_px'],2).T*Pby.T)
abz_px = mkvc(mkvc(f[src,'b_px'],2).T*Pbz.T)
abx_py = mkvc(mkvc(f[src,'b_py'],2).T*Pbx.T)
aby_py = mkvc(mkvc(f[src,'b_py'],2).T*Pby.T)
abz_py = mkvc(mkvc(f[src,'b_py'],2).T*Pbz.T)
# Derivatives as lambda functions
abx_px_u = lambda vec: f._b_pxDeriv_u(src,Pbx.T*vec,adjoint=True)
aby_px_u = lambda vec: f._b_pxDeriv_u(src,Pby.T*vec,adjoint=True)
abz_px_u = lambda vec: f._b_pxDeriv_u(src,Pbz.T*vec,adjoint=True)
abx_py_u = lambda vec: f._b_pyDeriv_u(src,Pbx.T*vec,adjoint=True)
aby_py_u = lambda vec: f._b_pyDeriv_u(src,Pby.T*vec,adjoint=True)
abz_py_u = lambda vec: f._b_pyDeriv_u(src,Pbz.T*vec,adjoint=True)
# Update the input vector
# Define shortcuts
sDiag = lambda t: Utils.sdiag(mkvc(t,2))
sVec = lambda t: Utils.sp.csr_matrix(mkvc(t,2))
# Define the components of the derivative
aHd = sDiag(1./(sDiag(abx_px)*aby_py - sDiag(abx_py)*aby_px))
aHd_uV = lambda x: abx_px_u(sDiag(aby_py)*x) + abx_px_u(sDiag(aby_py)*x) - aby_px_u(sDiag(abx_py)*x) - abx_py_u(sDiag(aby_px)*x)
# Need to fix this to reflect the adjoint
if 'tzx' in self.rxType:
Tij = sDiag(aHd*( -sDiag(abz_py)*aby_px + sDiag(abz_px)*aby_py))
TijN_uV = lambda x: -abz_py_u(sDiag(aby_px)*x) - aby_px_u(sDiag(abz_py)*x) + aby_py_u(sDiag(abz_px)*x) + abz_px_u(sDiag(aby_py)*x)
elif 'tzy' in self.rxType:
Tij = sDiag(aHd*( sDiag(abz_py)*abx_px - sDiag(abz_px)*abx_py))
TijN_uV = lambda x: abx_px_u(sDiag(abz_py)*x) + abz_py_u(sDiag(abx_px)*x) - abx_py_u(sDiag(abz_px)*x) - abz_px_u(sDiag(abx_py)*x)
# Calculate the complex derivative
PDeriv_real = TijN_uV(aHd*v) - aHd_uV(Tij.T*aHd*v)#
# NOTE: Need to reshape the output to go from 2*nU array to a (nU,2) matrix for each polarization
# PDeriv_real = np.hstack((mkvc(PDeriv_real[:len(PDeriv_real)/2],2),mkvc(PDeriv_real[len(PDeriv_real)/2::],2)))
PDeriv_real = PDeriv_real.reshape((2,mesh.nE)).T
# Extract the data
if real_or_imag == 'imag':
Pv = 1j*PDeriv_real
elif real_or_imag == 'real':
Pv = PDeriv_real.astype(complex)
return Pv