def _getCasingHertzMagDipole2Deriv_z_r(srcloc,
obsloc,
freq,
sigma,
a,
b,
mu=mu_0 * np.ones(3),
eps=epsilon_0,
moment=1.):
HertzZ = _getCasingHertzMagDipole(srcloc, obsloc, freq, sigma, a, b, mu,
eps, moment)
dHertzZdr = _getCasingHertzMagDipoleDeriv_r(srcloc, obsloc, freq, sigma, a,
b, mu, eps, moment)
nobs = obsloc.shape[0]
dxyz = obsloc - np.c_[np.ones(nobs)] * np.r_[srcloc]
r2 = _r2(dxyz[:, :2])
r = np.sqrt(r2)
z = dxyz[:, 2]
sqrtr2z2 = np.sqrt(r2 + z**2)
k2 = k(freq, sigma[2], mu[2], eps)
return dHertzZdr * (-z / sqrtr2z2) * (1j * k2 + 1. / sqrtr2z2) + HertzZ * (
z * r / sqrtr2z2**3) * (1j * k2 + 2. / sqrtr2z2)
def _fastInnerProduct(self, projType, prop=None, invProp=False, invMat=False):
"""
Fast version of getFaceInnerProduct.
This does not handle the case of a full tensor prop.
:param numpy.array prop: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
:param str projType: 'E' or 'F'
:param bool returnP: returns the projection matrices
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:rtype: scipy.sparse.csr_matrix
:return: M, the inner product matrix (nF, nF)
"""
assert projType in ['F', 'E'], ("projType must be 'F' for faces or 'E'"
" for edges")
if prop is None:
prop = np.ones(self.nC)
if invProp:
prop = 1./prop
if Utils.isScalar(prop):
prop = prop*np.ones(self.nC)
# number of elements we are averaging (equals dim for regular
# meshes, but for cyl, where we use symmetry, it is 1 for edge
# variables and 2 for face variables)
if self._meshType == 'CYL':
n_elements = np.sum(getattr(self, 'vn'+projType).nonzero())
else:
n_elements = self.dim
# Isotropic? or anisotropic?
if prop.size == self.nC:
Av = getattr(self, 'ave'+projType+'2CC')
Vprop = self.vol * Utils.mkvc(prop)
M = n_elements * Utils.sdiag(Av.T * Vprop)
elif prop.size == self.nC*self.dim:
Av = getattr(self, 'ave'+projType+'2CCV')
# if cyl, then only certain components are relevant due to symmetry
# for faces, x, z matters, for edges, y (which is theta) matters
if self._meshType == 'CYL':
if projType == 'E':
prop = prop[:, 1] # this is the action of a projection mat
elif projType == 'F':
prop = prop[:, [0, 2]]
V = sp.kron(sp.identity(n_elements), Utils.sdiag(self.vol))
M = Utils.sdiag(Av.T * V * Utils.mkvc(prop))
else:
return None
if invMat:
return Utils.sdInv(M)
else:
return M
def _fastInnerProduct(self, projType, prop=None, invProp=False, invMat=False):
"""
Fast version of getFaceInnerProduct.
This does not handle the case of a full tensor prop.
:param numpy.array prop: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
:param str projType: 'E' or 'F'
:param bool returnP: returns the projection matrices
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:rtype: scipy.sparse.csr_matrix
:return: M, the inner product matrix (nF, nF)
"""
assert projType in ["F", "E"], "projType must be 'F' for faces or 'E'" " for edges"
if prop is None:
prop = np.ones(self.nC)
if invProp:
prop = 1.0 / prop
if Utils.isScalar(prop):
prop = prop * np.ones(self.nC)
# number of elements we are averaging (equals dim for regular
# meshes, but for cyl, where we use symmetry, it is 1 for edge
# variables and 2 for face variables)
if self._meshType == "CYL":
n_elements = np.sum(getattr(self, "vn" + projType).nonzero())
else:
n_elements = self.dim
# Isotropic? or anisotropic?
if prop.size == self.nC:
Av = getattr(self, "ave" + projType + "2CC")
Vprop = self.vol * Utils.mkvc(prop)
M = n_elements * Utils.sdiag(Av.T * Vprop)
elif prop.size == self.nC * self.dim:
Av = getattr(self, "ave" + projType + "2CCV")
# if cyl, then only certain components are relevant due to symmetry
# for faces, x, z matters, for edges, y (which is theta) matters
if self._meshType == "CYL":
if projType == "E":
prop = prop[:, 1] # this is the action of a projection mat
elif projType == "F":
prop = prop[:, [0, 2]]
V = sp.kron(sp.identity(n_elements), Utils.sdiag(self.vol))
M = Utils.sdiag(Av.T * V * Utils.mkvc(prop))
else:
return None
if invMat:
return Utils.sdInv(M)
else:
return M
def halfSpaceProblemAnaVMDDiff(showIt=False, waveformType="STEPOFF"):
cs, ncx, ncz, npad = 20., 25, 25, 15
hx = [(cs, ncx), (cs, npad, 1.3)]
hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)]
mesh = Mesh.CylMesh([hx, 1, hz], '00C')
sighalf = 1e-2
siginf = np.ones(mesh.nC) * 1e-8
siginf[mesh.gridCC[:, -1] < 0.] = sighalf
eta = np.ones(mesh.nC) * 0.2
tau = np.ones(mesh.nC) * 0.005
c = np.ones(mesh.nC) * 0.7
m = np.r_[siginf, eta, tau, c]
iMap = Maps.IdentityMap(nP=int(mesh.nC))
maps = [('sigmaInf', iMap), ('eta', iMap), ('tau', iMap), ('c', iMap)]
prb = ProblemATEMIP_b(mesh, mapping=maps)
if waveformType == "GENERAL":
# timeon = np.cumsum(np.r_[np.ones(10)*1e-3, np.ones(10)*5e-4, np.ones(10)*1e-4])
timeon = np.cumsum(np.r_[np.ones(10) * 1e-3,
np.ones(10) * 5e-4,
np.ones(10) * 1e-4])
timeon -= timeon.max()
timeoff = np.cumsum(np.r_[np.ones(20) * 1e-5,
np.ones(20) * 1e-4,
np.ones(20) * 1e-3])
time = np.r_[timeon, timeoff]
current_on = np.ones_like(timeon)
current_on[[0, -1]] = 0.
current = np.r_[current_on, np.zeros_like(timeoff)]
wave = np.c_[time, current]
prb.waveformType = "GENERAL"
prb.currentwaveform(wave)
prb.t0 = time.min()
elif waveformType == "STEPOFF":
prb.timeSteps = [(1e-5, 20), (1e-4, 20), (1e-3, 10)]
offset = 20.
tobs = np.logspace(-4, -2, 21)
rx = EM.TDEM.RxTDEM(np.array([[offset, 0., 0.]]), tobs, "bz")
src = EM.TDEM.SrcTDEM_VMD_MVP([rx],
np.array([[0., 0., 0.]]),
waveformType=waveformType)
survey = EM.TDEM.SurveyTDEM([src])
prb.Solver = MumpsSolver
prb.pair(survey)
out = survey.dpred(m)
bz_ana = mu_0 * hzAnalyticDipoleT_CC(
offset, rx.times, sigmaInf=sighalf, eta=eta[0], tau=tau[0], c=c[0])
err = np.linalg.norm(bz_ana - out) / np.linalg.norm(bz_ana)
print '>> Relative error = ', err
if showIt:
plt.loglog(rx.times, abs(bz_ana), 'k')
plt.loglog(rx.times, abs(out), 'b.')
plt.show()
return err
def _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
Kc1 = getKc(freq,sigma[1],a,b,mu[1],eps)
nobs = obsloc.shape[0]
dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
r2 = _r2(dxyz[:,:2])
sqrtr2z2 = np.sqrt(r2 + dxyz[:,2]**2)
k2 = k(freq,sigma[2],mu[2],eps)
return Kc1 * moment / (4.*np.pi) *np.exp(-1j*k2*sqrtr2z2) / sqrtr2z2
def _getCasingHertzMagDipoleDeriv_z(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
nobs = obsloc.shape[0]
dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
r2z2 = _r2(dxyz)
sqrtr2z2 = np.sqrt(r2z2)
k2 = k(freq,sigma[2],mu[2],eps)
return -HertzZ*dxyz[:,2] /sqrtr2z2 * (1j*k2 + 1./sqrtr2z2)
def test_derivs(self):
Tests.checkDerivative(CasingMagDipoleDeriv_r,
np.ones(n) * 10 + np.random.randn(n),
plotIt=False)
Tests.checkDerivative(CasingMagDipoleDeriv_z,
np.random.randn(n),
plotIt=False)
Tests.checkDerivative(CasingMagDipole2Deriv_z_r,
np.ones(n) * 10 + np.random.randn(n),
plotIt=False)
Tests.checkDerivative(CasingMagDipole2Deriv_z_z,
np.random.randn(n),
plotIt=False)
def _getCasingHertzMagDipole2Deriv_z_z(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
dHertzZdz = _getCasingHertzMagDipoleDeriv_z(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
nobs = obsloc.shape[0]
dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
r2 = _r2(dxyz[:,:2])
r = np.sqrt(r2)
z = dxyz[:,2]
sqrtr2z2 = np.sqrt(r2 + z**2)
k2 = k(freq,sigma[2],mu[2],eps)
return (dHertzZdz*z + HertzZ)/sqrtr2z2*(-1j*k2 - 1./sqrtr2z2) + HertzZ*z/sqrtr2z2**3*(1j*k2*z + 2.*z/sqrtr2z2)
def edge(self):
"""Construct edge legnths of the 3D model as 1d array."""
if getattr(self, '_edge', None) is None:
# Ensure that we are working with column vectors
vh = self.h
# The number of cell centers in each direction
n = self.vnC
# Compute edge lengths
if (self.dim == 1):
self._edge = Utils.mkvc(vh[0])
elif (self.dim == 2):
l1 = np.outer(vh[0], np.ones(n[1] + 1))
l2 = np.outer(np.ones(n[0] + 1), vh[1])
self._edge = np.r_[Utils.mkvc(l1), Utils.mkvc(l2)]
elif (self.dim == 3):
l1 = np.outer(
vh[0],
Utils.mkvc(np.outer(np.ones(n[1] + 1), np.ones(n[2] + 1))))
l2 = np.outer(np.ones(n[0] + 1),
Utils.mkvc(np.outer(vh[1], np.ones(n[2] + 1))))
l3 = np.outer(np.ones(n[0] + 1),
Utils.mkvc(np.outer(np.ones(n[1] + 1), vh[2])))
self._edge = np.r_[Utils.mkvc(l1),
Utils.mkvc(l2),
Utils.mkvc(l3)]
return self._edge
def setUp(self):
# Define inducing field and sphere parameters
H0 = (50000., 60., 270.)
self.b0 = PF.MagAnalytics.IDTtoxyz(-H0[1], H0[2], H0[0])
self.rad = 2.
self.chi = 0.01
# Define a mesh
cs = 0.2
hxind = [(cs, 21)]
hyind = [(cs, 21)]
hzind = [(cs, 21)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Get cells inside the sphere
sph_ind = PF.MagAnalytics.spheremodel(mesh, 0., 0., 0., self.rad)
# Adjust susceptibility for volume difference
Vratio = (4. / 3. * np.pi * self.rad**3.) / (np.sum(sph_ind) * cs**3.)
model = np.ones(mesh.nC) * self.chi * Vratio
self.model = model[sph_ind]
# Creat reduced identity map for Linear Pproblem
idenMap = Maps.IdentityMap(nP=int(sum(sph_ind)))
# Create plane of observations
xr = np.linspace(-20, 20, 21)
yr = np.linspace(-20, 20, 21)
X, Y = np.meshgrid(xr, yr)
# Move obs plane 2 radius away from sphere
Z = np.ones((xr.size, yr.size)) * 2. * self.rad
self.locXyz = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
rxLoc = PF.BaseMag.RxObs(self.locXyz)
srcField = PF.BaseMag.SrcField([rxLoc], param=H0)
self.survey = PF.BaseMag.LinearSurvey(srcField)
self.prob_xyz = PF.Magnetics.MagneticIntegral(mesh,
mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='xyz')
self.prob_tmi = PF.Magnetics.MagneticIntegral(mesh,
mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='tmi')
def halfSpaceProblemAnaVMDDiff(showIt=False, waveformType="STEPOFF"):
cs, ncx, ncz, npad = 20., 25, 25, 15
hx = [(cs,ncx), (cs,npad,1.3)]
hz = [(cs,npad,-1.3), (cs,ncz), (cs,npad,1.3)]
mesh = Mesh.CylMesh([hx,1,hz], '00C')
sighalf = 1e-2
siginf = np.ones(mesh.nC)*1e-8
siginf[mesh.gridCC[:,-1]<0.] = sighalf
eta = np.ones(mesh.nC)*0.2
tau = np.ones(mesh.nC)*0.005
c = np.ones(mesh.nC)*0.7
m = np.r_[siginf, eta, tau, c]
iMap = Maps.IdentityMap(nP=int(mesh.nC))
maps = [('sigmaInf', iMap), ('eta', iMap), ('tau', iMap), ('c', iMap)]
prb = ProblemATEMIP_b(mesh, mapping = maps)
if waveformType =="GENERAL":
# timeon = np.cumsum(np.r_[np.ones(10)*1e-3, np.ones(10)*5e-4, np.ones(10)*1e-4])
timeon = np.cumsum(np.r_[np.ones(10)*1e-3, np.ones(10)*5e-4, np.ones(10)*1e-4])
timeon -= timeon.max()
timeoff = np.cumsum(np.r_[np.ones(20)*1e-5, np.ones(20)*1e-4, np.ones(20)*1e-3])
time = np.r_[timeon, timeoff]
current_on = np.ones_like(timeon)
current_on[[0,-1]] = 0.
current = np.r_[current_on, np.zeros_like(timeoff)]
wave = np.c_[time, current]
prb.waveformType = "GENERAL"
prb.currentwaveform(wave)
prb.t0 = time.min()
elif waveformType =="STEPOFF":
prb.timeSteps = [(1e-5, 20), (1e-4, 20), (1e-3, 10)]
offset = 20.
tobs = np.logspace(-4, -2, 21)
rx = EM.TDEM.RxTDEM(np.array([[offset, 0., 0.]]), tobs, "bz")
src = EM.TDEM.SrcTDEM_VMD_MVP([rx], np.array([[0., 0., 0.]]), waveformType=waveformType)
survey = EM.TDEM.SurveyTDEM([src])
prb.Solver = MumpsSolver
prb.pair(survey)
out = survey.dpred(m)
bz_ana = mu_0*hzAnalyticDipoleT_CC(offset, rx.times, sigmaInf=sighalf, eta=eta[0], tau=tau[0], c=c[0])
err = np.linalg.norm(bz_ana-out)/np.linalg.norm(bz_ana)
print '>> Relative error = ', err
if showIt:
plt.loglog(rx.times, abs(bz_ana), 'k')
plt.loglog(rx.times, abs(out), 'b.')
plt.show()
return err
def makeModelFile():
"""
Loads in a triangulated surface from Gocad (*.ts) and use VTK to transfer onto
a 3D mesh.
New scripts to be added to basecode
"""
#%%
work_dir = ''
mshfile = 'MEsh_TEst.msh'
# Load mesh file
mesh = Mesh.TensorMesh.readUBC(work_dir+mshfile)
# Load in observation file
#[B,M,dobs] = PF.BaseMag.readUBCmagObs(obsfile)
# Read in topo surface
topsurf = work_dir+'CDED_Lake_Coarse.ts'
geosurf = [[work_dir+'Till.ts',True,True],
[work_dir+'XVK.ts',True,True],
[work_dir+'PK1.ts',True,True],
[work_dir+'PK2.ts',True,True],
[work_dir+'PK3.ts',True,True],
[work_dir+'HK1.ts',True,True],
[work_dir+'VK.ts',True,True]
]
# Background density
bkgr = 1e-4
airc = 1e-8
# Units
vals = np.asarray([1e-2,3e-2,5e-2,2e-2,2e-2,1e-3,5e-3])
#%% Script starts here
# # Create a grid of observations and offset the z from topo
model= np.ones(mesh.nC) * bkgr
# Load GOCAD surf
#[vrtx, trgl] = PF.BaseMag.read_GOCAD_ts(tsfile)
# Find active cells from surface
for ii in range(len(geosurf)):
tin = tm.time()
print "Computing indices with VTK: " + geosurf[ii][0]
indx = gocad2simpegMeshIndex(geosurf[ii][0],mesh)
print "VTK operation completed in " + str(tm.time() - tin) + " sec"
model[indx] = vals[ii]
indx = gocad2simpegMeshIndex(topsurf,mesh)
actv = np.zeros(mesh.nC)
actv[indx] = 1
model[actv==0] = airc
Mesh.TensorMesh.writeModelUBC(mesh,'VTKout.dat',model)
def setUp(self):
cs = 25.
hx = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
hy = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
hz = [(cs,7, -1.3),(cs,20)]
mesh = Mesh.TensorMesh([hx, hy, hz],x0="CCN")
sigma = np.ones(mesh.nC)*1e-2
x = mesh.vectorCCx[(mesh.vectorCCx>-155.)&(mesh.vectorCCx<155.)]
y = mesh.vectorCCx[(mesh.vectorCCy>-155.)&(mesh.vectorCCy<155.)]
Aloc = np.r_[-200., 0., 0.]
Bloc = np.r_[200., 0., 0.]
M = Utils.ndgrid(x-25.,y, np.r_[0.])
N = Utils.ndgrid(x+25.,y, np.r_[0.])
phiA = EM.Analytics.DCAnalyticHalf(Aloc, [M,N], 1e-2, earth_type="halfspace")
phiB = EM.Analytics.DCAnalyticHalf(Bloc, [M,N], 1e-2, earth_type="halfspace")
data_anal = phiA-phiB
rx = DC.Rx.Dipole(M, N)
src = DC.Src.Dipole([rx], Aloc, Bloc)
survey = DC.Survey([src])
self.survey = survey
self.mesh = mesh
self.sigma = sigma
self.data_anal = data_anal
try:
from pymatsolver import PardisoSolver
self.Solver = PardisoSolver
except ImportError:
self.Solver = SolverLU
def setUp(self):
cs = 25.
hx = [(cs, 0, -1.3), (cs, 21), (cs, 0, 1.3)]
hy = [(cs, 0, -1.3), (cs, 21), (cs, 0, 1.3)]
hz = [(cs, 0, -1.3), (cs, 20)]
mesh = Mesh.TensorMesh([hx, hy, hz], x0="CCN")
blkind0 = Utils.ModelBuilder.getIndicesSphere(
np.r_[-100., -100., -200.], 75., mesh.gridCC
)
blkind1 = Utils.ModelBuilder.getIndicesSphere(
np.r_[100., 100., -200.], 75., mesh.gridCC
)
sigma = np.ones(mesh.nC)*1e-2
eta = np.zeros(mesh.nC)
tau = np.ones_like(sigma)*1.
eta[blkind0] = 0.1
eta[blkind1] = 0.1
tau[blkind0] = 0.1
tau[blkind1] = 0.01
x = mesh.vectorCCx[(mesh.vectorCCx > -155.) & (mesh.vectorCCx < 155.)]
y = mesh.vectorCCx[(mesh.vectorCCy > -155.) & (mesh.vectorCCy < 155.)]
Aloc = np.r_[-200., 0., 0.]
Bloc = np.r_[200., 0., 0.]
M = Utils.ndgrid(x-25., y, np.r_[0.])
N = Utils.ndgrid(x+25., y, np.r_[0.])
times = np.arange(10)*1e-3 + 1e-3
rx = SIP.Rx.Dipole(M, N, times)
src = SIP.Src.Dipole([rx], Aloc, Bloc)
survey = SIP.Survey([src])
wires = Maps.Wires(('eta', mesh.nC), ('taui', mesh.nC))
problem = SIP.Problem3D_N(
mesh,
sigma=sigma,
etaMap=wires.eta,
tauiMap=wires.taui
)
problem.Solver = Solver
problem.pair(survey)
mSynth = np.r_[eta, 1./tau]
survey.makeSyntheticData(mSynth)
# Now set up the problem to do some minimization
dmis = DataMisfit.l2_DataMisfit(survey)
reg = Regularization.Tikhonov(mesh)
opt = Optimization.InexactGaussNewton(
maxIterLS=20, maxIter=10, tolF=1e-6,
tolX=1e-6, tolG=1e-6, maxIterCG=6
)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e4)
inv = Inversion.BaseInversion(invProb)
self.inv = inv
self.reg = reg
self.p = problem
self.mesh = mesh
self.m0 = mSynth
self.survey = survey
self.dmis = dmis
def setUp(self):
cs = 12.5
npad = 2
hx = [(cs, npad, -1.3), (cs, 21), (cs, npad, 1.3)]
hy = [(cs, npad, -1.3), (cs, 21), (cs, npad, 1.3)]
hz = [(cs, npad, -1.3), (cs, 20)]
mesh = Mesh.TensorMesh([hx, hy, hz], x0="CCN")
x = mesh.vectorCCx[(mesh.vectorCCx > -80.) & (mesh.vectorCCx < 80.)]
y = mesh.vectorCCx[(mesh.vectorCCy > -80.) & (mesh.vectorCCy < 80.)]
Aloc = np.r_[-100., 0., 0.]
Bloc = np.r_[100., 0., 0.]
M = Utils.ndgrid(x - 12.5, y, np.r_[0.])
N = Utils.ndgrid(x + 12.5, y, np.r_[0.])
radius = 50.
xc = np.r_[0., 0., -100]
blkind = Utils.ModelBuilder.getIndicesSphere(xc, radius, mesh.gridCC)
sigmaInf = np.ones(mesh.nC) * 1e-2
eta = np.zeros(mesh.nC)
eta[blkind] = 0.1
sigma0 = sigmaInf * (1. - eta)
rx = DC.Rx.Dipole(M, N)
src = DC.Src.Dipole([rx], Aloc, Bloc)
surveyDC = DC.Survey([src])
self.surveyDC = surveyDC
self.mesh = mesh
self.sigmaInf = sigmaInf
self.sigma0 = sigma0
self.src = src
self.eta = eta
def test_ana_forward(self):
survey = PF.BaseMag.BaseMagSurvey()
Inc = 45.
Dec = 45.
Btot = 51000
b0 = PF.MagAnalytics.IDTtoxyz(Inc, Dec, Btot)
survey.setBackgroundField(Inc, Dec, Btot)
xr = np.linspace(-300, 300, 41)
yr = np.linspace(-300, 300, 41)
X, Y = np.meshgrid(xr, yr)
Z = np.ones((xr.size, yr.size))*150
rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
survey.rxLoc = rxLoc
self.prob.pair(survey)
u = self.prob.fields(self.chi)
B = u['B']
bxa, bya, bza = PF.MagAnalytics.MagSphereAnaFunA(rxLoc[:, 0], rxLoc[:, 1], rxLoc[:, 2], 100., 0., 0., 0., 0.01, b0, 'secondary')
dpred = survey.projectFieldsAsVector(B)
err = np.linalg.norm(dpred-np.r_[bxa, bya, bza])/np.linalg.norm(np.r_[bxa, bya, bza])
self.assertTrue(err < 0.08)
def setUp(self):
cs = 12.5
hx = [(cs,7, -1.3),(cs,61),(cs,7, 1.3)]
hy = [(cs,7, -1.3),(cs,20)]
mesh = Mesh.TensorMesh([hx, hy],x0="CN")
sighalf = 1e-2
sigma = np.ones(mesh.nC)*sighalf
x = np.linspace(-135, 250., 20)
M = Utils.ndgrid(x-12.5, np.r_[0.])
N = Utils.ndgrid(x+12.5, np.r_[0.])
A0loc = np.r_[-150, 0.]
A1loc = np.r_[-130, 0.]
rxloc = [np.c_[M, np.zeros(20)], np.c_[N, np.zeros(20)]]
data_anal = EM.Analytics.DCAnalyticHalf(np.r_[A0loc, 0.], rxloc, sighalf, earth_type="halfspace")
rx = DC.Rx.Dipole_ky(M, N)
src0 = DC.Src.Pole([rx], A0loc)
survey = DC.Survey_ky([src0])
self.survey = survey
self.mesh = mesh
self.sigma = sigma
self.data_anal = data_anal
try:
from pymatsolver import MumpsSolver
self.Solver = MumpsSolver
except ImportError, e:
self.Solver = SolverLU
def setUp(self):
cs = 25.
hx = [(cs, 7, -1.3), (cs, 21), (cs, 7, 1.3)]
hy = [(cs, 7, -1.3), (cs, 21), (cs, 7, 1.3)]
hz = [(cs, 7, -1.3), (cs, 20), (cs, 7, -1.3)]
mesh = Mesh.TensorMesh([hx, hy, hz], x0="CCC")
sigma = np.ones(mesh.nC) * 1e-2
x = mesh.vectorCCx[(mesh.vectorCCx > -155.) & (mesh.vectorCCx < 155.)]
y = mesh.vectorCCx[(mesh.vectorCCy > -155.) & (mesh.vectorCCy < 155.)]
Aloc = np.r_[-200., 0., 0.]
Bloc = np.r_[200., 0., 0.]
M = Utils.ndgrid(x - 25., y, np.r_[0.])
N = Utils.ndgrid(x + 25., y, np.r_[0.])
phiA = EM.Analytics.DCAnalytic_Pole_Dipole(Aloc, [M, N],
1e-2,
earth_type="wholespace")
phiB = EM.Analytics.DCAnalytic_Pole_Dipole(Bloc, [M, N],
1e-2,
earth_type="wholespace")
data_anal = phiA - phiB
rx = DC.Rx.Dipole(M, N)
src = DC.Src.Dipole([rx], Aloc, Bloc)
survey = DC.Survey([src])
self.survey = survey
self.mesh = mesh
self.sigma = sigma
self.data_anal = data_anal
def unpackdx(fid,nrows):
for ii in range(nrows):
line = fid.readline()
var = np.array(line.split(),dtype=float)
if ii==0:
x0= var[0]
xvec = np.ones(int(var[2])) * (var[1] - var[0]) / int(var[2])
xend = var[1]
else:
xvec = np.hstack((xvec,np.ones(int(var[1])) * (var[0] - xend) / int(var[1])))
xend = var[0]
return x0, xvec
def __init__(self, h_in, x0_in=None):
assert type(h_in) in [list, tuple], 'h_in must be a list'
assert len(h_in) in [1,2,3], 'h_in must be of dimension 1, 2, or 3'
h = range(len(h_in))
for i, h_i in enumerate(h_in):
if Utils.isScalar(h_i) and type(h_i) is not np.ndarray:
# This gives you something over the unit cube.
h_i = self._unitDimensions[i] * np.ones(int(h_i))/int(h_i)
elif type(h_i) is list:
h_i = Utils.meshTensor(h_i)
assert isinstance(h_i, np.ndarray), ("h[%i] is not a numpy array." % i)
assert len(h_i.shape) == 1, ("h[%i] must be a 1D numpy array." % i)
h[i] = h_i[:] # make a copy.
x0 = np.zeros(len(h))
if x0_in is not None:
assert len(h) == len(x0_in), "Dimension mismatch. x0 != len(h)"
for i in range(len(h)):
x_i, h_i = x0_in[i], h[i]
if Utils.isScalar(x_i):
x0[i] = x_i
elif x_i == '0':
x0[i] = 0.0
elif x_i == 'C':
x0[i] = -h_i.sum()*0.5
elif x_i == 'N':
x0[i] = -h_i.sum()
else:
raise Exception("x0[%i] must be a scalar or '0' to be zero, 'C' to center, or 'N' to be negative." % i)
BaseRectangularMesh.__init__(self, np.array([x.size for x in h]), x0)
# Ensure h contains 1D vectors
self._h = [Utils.mkvc(x.astype(float)) for x in h]
def test_ana_forward(self):
survey = PF.BaseMag.BaseMagSurvey()
Inc = 45.0
Dec = 45.0
Btot = 51000
b0 = PF.MagAnalytics.IDTtoxyz(Inc, Dec, Btot)
survey.setBackgroundField(Inc, Dec, Btot)
xr = np.linspace(-300, 300, 41)
yr = np.linspace(-300, 300, 41)
X, Y = np.meshgrid(xr, yr)
Z = np.ones((xr.size, yr.size)) * 150
rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
survey.rxLoc = rxLoc
self.prob.pair(survey)
u = self.prob.fields(self.chi)
B = u["B"]
bxa, bya, bza = PF.MagAnalytics.MagSphereAnaFunA(
rxLoc[:, 0], rxLoc[:, 1], rxLoc[:, 2], 100.0, 0.0, 0.0, 0.0, 0.01, b0, "secondary"
)
dpred = survey.projectFieldsAsVector(B)
err = np.linalg.norm(dpred - np.r_[bxa, bya, bza]) / np.linalg.norm(np.r_[bxa, bya, bza])
self.assertTrue(err < 0.08)
def setUp(self):
cs = 12.5
hx = [(cs, 7, -1.3), (cs, 61), (cs, 7, 1.3)]
hy = [(cs, 7, -1.3), (cs, 20)]
mesh = Mesh.TensorMesh([hx, hy], x0="CN")
sighalf = 1e-2
sigma = np.ones(mesh.nC) * sighalf
x = np.linspace(-135, 250., 20)
M = Utils.ndgrid(x - 12.5, np.r_[0.])
N = Utils.ndgrid(x + 12.5, np.r_[0.])
A0loc = np.r_[-150, 0.]
# A1loc = np.r_[-130, 0.]
rxloc = [np.c_[M, np.zeros(20)], np.c_[N, np.zeros(20)]]
data_anal = EM.Analytics.DCAnalytic_Pole_Dipole(np.r_[A0loc, 0.],
rxloc,
sighalf,
earth_type="halfspace")
rx = DC.Rx.Dipole_ky(M, N)
src0 = DC.Src.Pole([rx], A0loc)
survey = DC.Survey_ky([src0])
self.survey = survey
self.mesh = mesh
self.sigma = sigma
self.data_anal = data_anal
try:
from pymatsolver import PardisoSolver
self.Solver = PardisoSolver
except ImportError:
self.Solver = SolverLU
def test_ana_boundary_computation(self):
hxind = [(0, 25, 1.3), (21, 12.5), (0, 25, 1.3)]
hyind = [(0, 25, 1.3), (21, 12.5), (0, 25, 1.3)]
hzind = [(0, 25, 1.3), (20, 12.5), (0, 25, 1.3)]
# hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)
M3 = Mesh.TensorMesh([hxind, hyind, hzind], "CCC")
indxd, indxu, indyd, indyu, indzd, indzu = M3.faceBoundaryInd
mu0 = 4*np.pi*1e-7
chibkg = 0.
chiblk = 0.01
chi = np.ones(M3.nC)*chibkg
sph_ind = PF.MagAnalytics.spheremodel(M3, 0, 0, 0, 100)
chi[sph_ind] = chiblk
mu = (1.+chi)*mu0
Bbc, const = PF.MagAnalytics.CongruousMagBC(M3, np.array([1., 0., 0.]), chi)
flag = 'secondary'
Box = 1.
H0 = Box/mu_0
Bbcxx, Bbcxy, Bbcxz = PF.MagAnalytics.MagSphereAnaFun(M3.gridFx[(indxd|indxu),0], M3.gridFx[(indxd|indxu),1], M3.gridFx[(indxd|indxu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
Bbcyx, Bbcyy, Bbcyz = PF.MagAnalytics.MagSphereAnaFun(M3.gridFy[(indyd|indyu),0], M3.gridFy[(indyd|indyu),1], M3.gridFy[(indyd|indyu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
Bbczx, Bbczy, Bbczz = PF.MagAnalytics.MagSphereAnaFun(M3.gridFz[(indzd|indzu),0], M3.gridFz[(indzd|indzu),1], M3.gridFz[(indzd|indzu),2], 100, 0., 0., 0., mu_0, mu_0*(1+chiblk), H0, flag)
Bbc_ana = np.r_[Bbcxx, Bbcyy, Bbczz]
if plotIt:
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1,1, figsize = (10, 10))
ax.plot(Bbc_ana)
ax.plot(Bbc)
plt.show()
err = np.linalg.norm(Bbc-Bbc_ana) / np.linalg.norm(Bbc_ana)
assert err < 0.1, 'Mag Boundary computation is wrong!!, err = {}'.format(err)
def unpackdx(fid,nrows):
for ii in range(nrows):
line = fid.readline()
var = np.array(line.split(),dtype=float)
if ii==0:
x0= var[0]
xvec = np.ones(int(var[2])) * (var[1] - var[0]) / int(var[2])
xend = var[1]
else:
xvec = np.hstack((xvec,np.ones(int(var[1])) * (var[0] - xend) / int(var[1])))
xend = var[0]
return x0, xvec
def setUp(self):
# Define inducing field and sphere parameters
H0 = (50000., 60., 270.)
self.b0 = PF.MagAnalytics.IDTtoxyz(-H0[1], H0[2], H0[0])
self.rad = 2.
self.chi = 0.01
# Define a mesh
cs = 0.2
hxind = [(cs, 21)]
hyind = [(cs, 21)]
hzind = [(cs, 21)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Get cells inside the sphere
sph_ind = PF.MagAnalytics.spheremodel(mesh, 0., 0., 0., self.rad)
# Adjust susceptibility for volume difference
Vratio = (4./3.*np.pi*self.rad**3.) / (np.sum(sph_ind)*cs**3.)
model = np.ones(mesh.nC)*self.chi*Vratio
self.model = model[sph_ind]
# Creat reduced identity map for Linear Pproblem
idenMap = Maps.IdentityMap(nP=int(sum(sph_ind)))
# Create plane of observations
xr = np.linspace(-20, 20, 21)
yr = np.linspace(-20, 20, 21)
X, Y = np.meshgrid(xr, yr)
# Move obs plane 2 radius away from sphere
Z = np.ones((xr.size, yr.size))*2.*self.rad
self.locXyz = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
rxLoc = PF.BaseMag.RxObs(self.locXyz)
srcField = PF.BaseMag.SrcField([rxLoc], param=H0)
self.survey = PF.BaseMag.LinearSurvey(srcField)
self.prob_xyz = PF.Magnetics.MagneticIntegral(mesh, mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='xyz')
self.prob_tmi = PF.Magnetics.MagneticIntegral(mesh, mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='tmi')
def setUp(self):
# Define sphere parameters
self.rad = 2.
self.rho = 0.1
# Define a mesh
cs = 0.2
hxind = [(cs, 21)]
hyind = [(cs, 21)]
hzind = [(cs, 21)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Get cells inside the sphere
sph_ind = PF.MagAnalytics.spheremodel(mesh, 0., 0., 0., self.rad)
# Adjust density for volume difference
Vratio = (4. / 3. * np.pi * self.rad**3.) / (np.sum(sph_ind) * cs**3.)
model = np.ones(mesh.nC) * self.rho * Vratio
self.model = model[sph_ind]
# Create reduced identity map for Linear Pproblem
idenMap = Maps.IdentityMap(nP=int(sum(sph_ind)))
# Create plane of observations
xr = np.linspace(-20, 20, 21)
yr = np.linspace(-20, 20, 21)
X, Y = np.meshgrid(xr, yr)
# Move obs plane 2 radius away from sphere
Z = np.ones((xr.size, yr.size)) * 2. * self.rad
self.locXyz = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
rxLoc = PF.BaseGrav.RxObs(self.locXyz)
srcField = PF.BaseGrav.SrcField([rxLoc])
self.survey = PF.BaseGrav.LinearSurvey(srcField)
self.prob_xyz = PF.Gravity.GravityIntegral(mesh,
mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='xyz')
self.prob_z = PF.Gravity.GravityIntegral(mesh,
mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='z')
def __init__(self, h_in, x0=None):
assert type(h_in) is list, 'h_in must be a list'
assert len(h_in) > 1, "len(h_in) must be greater than 1"
h = range(len(h_in))
for i, h_i in enumerate(h_in):
if type(h_i) in [int, long, float]:
# This gives you something over the unit cube.
h_i = np.ones(int(h_i))/int(h_i)
assert isinstance(h_i, np.ndarray), ("h[%i] is not a numpy array." % i)
assert len(h_i.shape) == 1, ("h[%i] must be a 1D numpy array." % i)
h[i] = h_i[:] # make a copy.
self.h = h
if x0 is None:
x0 = np.zeros(self.dim)
else:
assert type(x0) in [list, np.ndarray], 'x0 must be a numpy array or a list'
x0 = np.array(x0, dtype=float)
assert len(x0) == self.dim, 'x0 must have the same dimensions as the mesh'
# TODO: this has a lot of stuff which doesn't work for this style of mesh...
BaseMesh.__init__(self, np.array([x.size for x in h]), x0)
# set the sets for holding the cells, nodes, faces, and edges
self.cells = set()
self.nodes = set()
self.faces = set()
self.facesX = set()
self.facesY = set()
if self.dim == 3:
self.facesZ = set()
self.edges = set()
self.edgesX = set()
self.edgesY = set()
self.edgesZ = set()
self.children = np.empty([hi.size for hi in h],dtype=TreeCell)
if self.dim == 2:
for i in range(h[0].size):
for j in range(h[1].size):
fXm = None if i is 0 else self.children[i-1][j].fXp
fYm = None if j is 0 else self.children[i][j-1].fYp
x0i = (np.r_[x0[0], h[0][:i]]).sum()
x0j = (np.r_[x0[1], h[1][:j]]).sum()
self.children[i][j] = TreeCell(self, x0=[x0i, x0j], depth=0, sz=[h[0][i], h[1][j]], fXm=fXm, fYm=fYm)
elif self.dim == 3:
for i in range(h[0].size):
for j in range(h[1].size):
for k in range(h[2].size):
fXm = None if i is 0 else self.children[i-1][j][k].fXp
fYm = None if j is 0 else self.children[i][j-1][k].fYp
fZm = None if k is 0 else self.children[i][j][k-1].fZp
x0i = (np.r_[x0[0], h[0][:i]]).sum()
x0j = (np.r_[x0[1], h[1][:j]]).sum()
x0k = (np.r_[x0[2], h[2][:k]]).sum()
self.children[i][j][k] = TreeCell(self, x0=[x0i, x0j, x0k], depth=0, sz=[h[0][i], h[1][j], h[2][k]], fXm=fXm, fYm=fYm, fZm=fZm)
def run(plotIt=True):
"""
PF: Magnetics: Analytics
========================
Comparing the magnetics field in Vancouver to Seoul
"""
xr = np.linspace(-300, 300, 41)
yr = np.linspace(-300, 300, 41)
X, Y = np.meshgrid(xr, yr)
Z = np.ones((np.size(xr), np.size(yr)))*150
# Bz component in Korea
inckr = -8. + 3./60
deckr = 54. + 9./60
btotkr = 50898.6
Bokr = PF.MagAnalytics.IDTtoxyz(inckr, deckr, btotkr)
bx, by, bz = PF.MagAnalytics.MagSphereAnaFunA(
X, Y, Z, 100., 0., 0., 0., 0.01, Bokr, 'secondary'
)
Bzkr = np.reshape(bz, (np.size(xr), np.size(yr)), order='F')
# Bz component in Canada
incca = 16. + 49./60
decca = 70. + 19./60
btotca = 54692.1
Boca = PF.MagAnalytics.IDTtoxyz(incca, decca, btotca)
bx, by, bz = PF.MagAnalytics.MagSphereAnaFunA(
X, Y, Z, 100., 0., 0., 0., 0.01, Boca, 'secondary'
)
Bzca = np.reshape(bz, (np.size(xr), np.size(yr)), order='F')
if plotIt:
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1 import make_axes_locatable
fig = plt.figure(figsize=(14, 5))
ax1 = plt.subplot(121)
dat1 = plt.imshow(Bzkr, extent=[min(xr), max(xr), min(yr), max(yr)])
divider = make_axes_locatable(ax1)
cax1 = divider.append_axes("right", size="5%", pad=0.05)
ax1.set_xlabel('East-West (m)')
ax1.set_ylabel('South-North (m)')
plt.colorbar(dat1, cax=cax1)
ax1.set_title('$B_z$ field at Seoul, South Korea')
ax2 = plt.subplot(122)
dat2 = plt.imshow(Bzca, extent=[min(xr), max(xr), min(yr), max(yr)])
divider = make_axes_locatable(ax2)
cax2 = divider.append_axes("right", size="5%", pad=0.05)
ax2.set_xlabel('East-West (m)')
ax2.set_ylabel('South-North (m)')
plt.colorbar(dat2, cax=cax2)
ax2.set_title('$B_z$ field at Vancouver, Canada')
plt.show()
def mref(self):
if getattr(self, '_mref', None) is None:
if isinstance(self._mrefInput, float):
self._mref = np.ones(self.nC) * self._mrefInput
else:
self._mref = Mesh.TensorMesh.readModelUBC(self.mesh, self.basePath + self._mrefInput)
self._mref = self._mref[self.activeCells]
return self._mref
def getFields(timeStep, method):
timeSteps = np.ones(360/timeStep)*timeStep
prob = Richards.RichardsProblem(
M, mapping=E, timeSteps=timeSteps,
boundaryConditions=bc, initialConditions=h,
doNewton=False, method=method
)
return prob.fields(params['Ks'])
def halfSpaceProblemAnaVMDDiff(showIt=False, waveformType="STEPOFF"):
cs, ncx, ncz, npad = 20., 25, 25, 15
hx = [(cs, ncx), (cs, npad, 1.3)]
hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)]
mesh = Mesh.CylMesh([hx, 1, hz], '00C')
prb = ProblemATEM_b(mesh)
if waveformType == "GENERAL":
timeon = np.cumsum(np.r_[np.ones(10) * 1e-3,
np.ones(10) * 5e-4,
np.ones(10) * 1e-4])
timeon -= timeon.max()
timeoff = np.cumsum(np.r_[np.ones(10) * 5e-5,
np.ones(10) * 1e-4,
np.ones(10) * 5e-4,
np.ones(10) * 1e-3,
np.ones(10) * 5e-3])
time = np.r_[timeon, timeoff]
current_on = np.ones_like(timeon)
current_on[[0, -1]] = 0.
current = np.r_[current_on, np.zeros_like(timeoff)]
wave = np.c_[time, current]
prb.waveformType = "GENERAL"
prb.currentwaveform(wave)
prb.t0 = time.min()
elif waveformType == "STEPOFF":
prb.timeSteps = [(1e-5, 10), (5e-5, 10), (1e-4, 10), (5e-4, 10),
(1e-3, 10), (5e-3, 10)]
offset = 20.
tobs = np.logspace(-4, -2, 21)
rx = EM.TDEM.RxTDEM(np.array([[offset, 0., 0.]]), tobs, "bz")
src = EM.TDEM.SrcTDEM_VMD_MVP([rx],
np.array([[0., 0., 0.]]),
waveformType=waveformType)
survey = EM.TDEM.SurveyTDEM([src])
prb.Solver = MumpsSolver
sigma = np.ones(mesh.nC) * 1e-8
active = mesh.gridCC[:, 2] < 0.
sig_half = 1e-2
sigma[active] = sig_half
prb.pair(survey)
out = survey.dpred(sigma)
bz_ana = mu_0 * hzAnalyticDipoleT(offset, rx.times, sig_half)
err = np.linalg.norm(bz_ana - out) / np.linalg.norm(bz_ana)
print '>> Relative error = ', err
if showIt:
plt.loglog(rx.times, bz_ana, 'k')
plt.loglog(rx.times, out, 'b.')
plt.show()
return err
def test_sub2ind(self):
x = np.ones((5,2))
self.assertTrue(np.all(sub2ind(x.shape, [0,0]) == [0]))
self.assertTrue(np.all(sub2ind(x.shape, [4,0]) == [4]))
self.assertTrue(np.all(sub2ind(x.shape, [0,1]) == [5]))
self.assertTrue(np.all(sub2ind(x.shape, [4,1]) == [9]))
self.assertTrue(np.all(sub2ind(x.shape, [[4,1]]) == [9]))
self.assertTrue(np.all(sub2ind(x.shape, [[0,0],[4,0],[0,1],[4,1]]) == [0,4,5,9]))
def mref(self):
if getattr(self, '_mref', None) is None:
if isinstance(self._mrefInput, float):
self._mref = np.ones(self.nC) * self._mrefInput
else:
self._mref = Mesh.TensorMesh.readModelUBC(self.mesh, self.basePath + self._mrefInput)
self._mref = self._mref[self.activeCells]
return self._mref
def setUp(self):
# Define sphere parameters
self.rad = 2.
self.rho = 0.1
# Define a mesh
cs = 0.2
hxind = [(cs, 21)]
hyind = [(cs, 21)]
hzind = [(cs, 21)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Get cells inside the sphere
sph_ind = PF.MagAnalytics.spheremodel(mesh, 0., 0., 0., self.rad)
# Adjust density for volume difference
Vratio = (4./3.*np.pi*self.rad**3.) / (np.sum(sph_ind)*cs**3.)
model = np.ones(mesh.nC)*self.rho*Vratio
self.model = model[sph_ind]
# Create reduced identity map for Linear Pproblem
idenMap = Maps.IdentityMap(nP=int(sum(sph_ind)))
# Create plane of observations
xr = np.linspace(-20, 20, 21)
yr = np.linspace(-20, 20, 21)
X, Y = np.meshgrid(xr, yr)
# Move obs plane 2 radius away from sphere
Z = np.ones((xr.size, yr.size))*2.*self.rad
self.locXyz = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
rxLoc = PF.BaseGrav.RxObs(self.locXyz)
srcField = PF.BaseGrav.SrcField([rxLoc])
self.survey = PF.BaseGrav.LinearSurvey(srcField)
self.prob_xyz = PF.Gravity.GravityIntegral(mesh, mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='xyz')
self.prob_z = PF.Gravity.GravityIntegral(mesh, mapping=idenMap,
actInd=sph_ind,
forwardOnly=True,
rtype='z')
def _fastInnerProduct(self,
projType,
prop=None,
invProp=False,
invMat=False):
"""
Fast version of getFaceInnerProduct.
This does not handle the case of a full tensor prop.
:param numpy.array prop: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
:param str projType: 'E' or 'F'
:param bool returnP: returns the projection matrices
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:rtype: scipy.csr_matrix
:return: M, the inner product matrix (nF, nF)
"""
assert projType in [
'F', 'E'
], "projType must be 'F' for faces or 'E' for edges"
if prop is None:
prop = np.ones(self.nC)
if invProp:
prop = 1. / prop
if Utils.isScalar(prop):
prop = prop * np.ones(self.nC)
if prop.size == self.nC:
Av = getattr(self, 'ave' + projType + '2CC')
Vprop = self.vol * Utils.mkvc(prop)
M = self.dim * Utils.sdiag(Av.T * Vprop)
elif prop.size == self.nC * self.dim:
Av = getattr(self, 'ave' + projType + '2CCV')
V = sp.kron(sp.identity(self.dim), Utils.sdiag(self.vol))
M = Utils.sdiag(Av.T * V * Utils.mkvc(prop))
else:
return None
if invMat:
return Utils.sdInv(M)
else:
return M
def m0(self):
if getattr(self, '_m0', None) is None:
if isinstance(self.mstart, float):
self._m0 = np.ones(self.nC) * self.mstart
else:
self._m0 = Mesh.TensorMesh.readModelUBC(
self.mesh, self.basePath + self.mstart)
return self._m0
def m0(self):
if getattr(self, '_m0', None) is None:
if isinstance(self.mstart, float):
self._m0 = np.ones(self.nC) * self.mstart
else:
self._m0 = Mesh.TensorMesh.readModelUBC(self.mesh, self.basePath + self.mstart)
return self._m0
def activeModel(self):
if getattr(self, '_activeModel', None) is None:
if self._staticInput == 'FILE':
# Read from file active cells with 0:air, 1:dynamic, -1 static
self._activeModel = Mesh.TensorMesh.readModelUBC(self.mesh, self.basePath + self._staticInput)
else:
self._activeModel = np.ones(self._mesh.nC)
return self._activeModel
def activeModel(self):
if getattr(self, '_activeModel', None) is None:
if isinstance(self._staticInput, str):
# Read from file active cells with 0:air, 1:dynamic, -1 static
self._activeModel = Mesh.TensorMesh.readModelUBC(self.mesh, self.basePath + self._staticInput)
else:
self._activeModel = np.ones(self._mesh.nC)
return self._activeModel
def _getCasingHertzMagDipole(srcloc,
obsloc,
freq,
sigma,
a,
b,
mu=mu_0 * np.ones(3),
eps=epsilon_0,
moment=1.):
Kc1 = getKc(freq, sigma[1], a, b, mu[1], eps)
nobs = obsloc.shape[0]
dxyz = obsloc - np.c_[np.ones(nobs)] * np.r_[srcloc]
r2 = _r2(dxyz[:, :2])
sqrtr2z2 = np.sqrt(r2 + dxyz[:, 2]**2)
k2 = k(freq, sigma[2], mu[2], eps)
return Kc1 * moment / (4. * np.pi) * np.exp(-1j * k2 * sqrtr2z2) / sqrtr2z2
def DCfun(mesh, pts):
D = mesh.faceDiv
sigma = 1e-2 * np.ones(mesh.nC)
MsigI = mesh.getFaceInnerProduct(sigma, invProp=True, invMat=True)
A = -D * MsigI * D.T
A[-1, -1] /= mesh.vol[-1] # Remove null space
rhs = np.zeros(mesh.nC)
txind = Utils.meshutils.closestPoints(mesh, pts)
rhs[txind] = np.r_[1, -1]
return A, rhs
def DCfun(mesh, pts):
D = mesh.faceDiv
sigma = 1e-2*np.ones(mesh.nC)
MsigI = mesh.getFaceInnerProduct(sigma, invProp=True, invMat=True)
A = -D*MsigI*D.T
A[-1,-1] /= mesh.vol[-1] # Remove null space
rhs = np.zeros(mesh.nC)
txind = Utils.meshutils.closestPoints(mesh, pts)
rhs[txind] = np.r_[1,-1]
return A, rhs
def getCasingHrMagDipole(srcloc,
obsloc,
freq,
sigma,
a,
b,
mu=mu_0 * np.ones(3),
eps=epsilon_0,
moment=1.):
return _getCasingHertzMagDipole2Deriv_z_r(srcloc, obsloc, freq, sigma, a,
b, mu, eps, moment)
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 setUp(self):
cs = 25.
hx = [(cs,0, -1.3),(cs,21),(cs,0, 1.3)]
hy = [(cs,0, -1.3),(cs,21),(cs,0, 1.3)]
hz = [(cs,0, -1.3),(cs,20),(cs,0, 1.3)]
mesh = Mesh.TensorMesh([hx, hy, hz],x0="CCC")
blkind0 = Utils.ModelBuilder.getIndicesSphere(np.r_[-100., -100., -200.], 75., mesh.gridCC)
blkind1 = Utils.ModelBuilder.getIndicesSphere(np.r_[100., 100., -200.], 75., mesh.gridCC)
sigma = np.ones(mesh.nC)*1e-2
airind = mesh.gridCC[:,2]>0.
sigma[airind] = 1e-8
eta = np.zeros(mesh.nC)
tau = np.ones_like(sigma)*1.
eta[blkind0] = 0.1
eta[blkind1] = 0.1
tau[blkind0] = 0.1
tau[blkind1] = 0.01
actmapeta = Maps.InjectActiveCells(mesh, ~airind, 0.)
actmaptau = Maps.InjectActiveCells(mesh, ~airind, 1.)
x = mesh.vectorCCx[(mesh.vectorCCx>-155.)&(mesh.vectorCCx<155.)]
y = mesh.vectorCCx[(mesh.vectorCCy>-155.)&(mesh.vectorCCy<155.)]
Aloc = np.r_[-200., 0., 0.]
Bloc = np.r_[200., 0., 0.]
M = Utils.ndgrid(x-25.,y, np.r_[0.])
N = Utils.ndgrid(x+25.,y, np.r_[0.])
times = np.arange(10)*1e-3 + 1e-3
rx = SIP.Rx.Dipole(M, N, times)
src = SIP.Src.Dipole([rx], Aloc, Bloc)
survey = SIP.Survey([src])
colemap = [("eta", Maps.IdentityMap(mesh)*actmapeta), ("taui", Maps.IdentityMap(mesh)*actmaptau)]
problem = SIP.Problem3D_N(mesh, sigma=sigma, mapping=colemap)
problem.Solver = Solver
problem.pair(survey)
mSynth = np.r_[eta[~airind], 1./tau[~airind]]
survey.makeSyntheticData(mSynth)
# Now set up the problem to do some minimization
dmis = DataMisfit.l2_DataMisfit(survey)
regmap = Maps.IdentityMap(nP=int(mSynth[~airind].size*2))
reg = SIP.MultiRegularization(mesh, mapping=regmap, nModels=2, indActive=~airind)
opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e4)
inv = Inversion.BaseInversion(invProb)
self.inv = inv
self.reg = reg
self.p = problem
self.mesh = mesh
self.m0 = mSynth
self.survey = survey
self.dmis = dmis
def _getCasingHertzMagDipoleDeriv_z(srcloc,
obsloc,
freq,
sigma,
a,
b,
mu=mu_0 * np.ones(3),
eps=epsilon_0,
moment=1.):
HertzZ = _getCasingHertzMagDipole(srcloc, obsloc, freq, sigma, a, b, mu,
eps, moment)
nobs = obsloc.shape[0]
dxyz = obsloc - np.c_[np.ones(nobs)] * np.r_[srcloc]
r2z2 = _r2(dxyz)
sqrtr2z2 = np.sqrt(r2z2)
k2 = k(freq, sigma[2], mu[2], eps)
return -HertzZ * dxyz[:, 2] / sqrtr2z2 * (1j * k2 + 1. / sqrtr2z2)
def test_sub2ind(self):
x = np.ones((5, 2))
self.assertTrue(np.all(sub2ind(x.shape, [0, 0]) == [0]))
self.assertTrue(np.all(sub2ind(x.shape, [4, 0]) == [4]))
self.assertTrue(np.all(sub2ind(x.shape, [0, 1]) == [5]))
self.assertTrue(np.all(sub2ind(x.shape, [4, 1]) == [9]))
self.assertTrue(np.all(sub2ind(x.shape, [[4, 1]]) == [9]))
self.assertTrue(
np.all(
sub2ind(x.shape, [[0, 0], [4, 0], [0, 1], [4, 1]]) ==
[0, 4, 5, 9]))
def getCasingEphiMagDipole(srcloc,
obsloc,
freq,
sigma,
a,
b,
mu=mu_0 * np.ones(3),
eps=epsilon_0,
moment=1.):
return 1j * omega(freq) * mu * _getCasingHertzMagDipoleDeriv_r(
srcloc, obsloc, freq, sigma, a, b, mu, eps, moment)
def getCasingBzMagDipole(srcloc,
obsloc,
freq,
sigma,
a,
b,
mu=mu_0 * np.ones(3),
eps=epsilon_0,
moment=1.):
return mu_0 * getCasingHzMagDipole(srcloc, obsloc, freq, sigma, a, b, mu,
eps, moment)
def setFrequency(self, time=np.logspace(-7, -1, 256)):
self.Nch = self.time.size
wt = np.array([7.214369775966785e-20, 5.997984537445829e-20, 1.383536819510307e-20, 6.127201193993877e-20, 2.735622069700930e-20, 6.567948836420383e-20, 4.144963335850363e-20, 7.316414067200350e-20, 5.682375914662966e-20, 8.391977074915078e-20, 7.418756524583309e-20, 9.829637687190485e-20, 9.430643800653847e-20, 1.168146262188112e-19, 1.180370735968097e-19, 1.401723019040171e-19, 1.463726071463266e-19, 1.692722072070252e-19, 1.804796158499069e-19, 2.052560499147526e-19, 2.217507732438609e-19, 2.495469564846162e-19, 2.718603842873614e-19, 3.039069705922034e-19, 3.328334008394297e-19, 3.705052796297763e-19, 4.071277819975917e-19, 4.520053409594589e-19, 4.977334107366132e-19, 5.516707191291291e-19, 6.082931168675559e-19, 6.734956703766505e-19, 7.432489554623685e-19, 8.223651399147256e-19, 9.080210233648037e-19, 1.004250388267800e-18, 1.109225156214032e-18, 1.226448534750949e-18, 1.354938655056596e-18, 1.497875155579711e-18, 1.655024636692164e-18, 1.829422009902478e-18, 2.021527957180686e-18, 2.234394042862191e-18, 2.469158736824458e-18, 2.729043278909879e-18, 3.015882778812807e-18, 3.333221019045560e-18, 3.683642665131121e-18, 4.071174485366807e-18, 4.499238428427072e-18, 4.972519918024098e-18, 5.495403162992602e-18, 6.073431145514256e-18, 6.712116746365455e-18, 7.418091347704607e-18, 8.198210388921290e-18, 9.060466264497684e-18, 1.001332641867938e-17, 1.106647001686341e-17, 1.223031194783507e-17, 1.351661046246575e-17, 1.493814249254853e-17, 1.650922025025269e-17, 1.824549287949245e-17, 2.016440324953847e-17, 2.228509875325462e-17, 2.462885473506622e-17, 2.721908372832262e-17, 3.008174877960754e-17, 3.324546598231868e-17, 3.674192913569353e-17, 4.060610542324258e-17, 4.487669220181069e-17, 4.959641037849226e-17, 5.481251456381401e-17, 6.057719336989671e-17, 6.694815564512041e-17, 7.398915178848498e-17, 8.177066132132114e-17, 9.037055462918574e-17, 9.987491078055815e-17, 1.103788451159722e-16, 1.219874911140742e-16, 1.348170262066998e-16, 1.489958578076007e-16, 1.646658879212839e-16, 1.819839514458913e-16, 2.011233698894207e-16, 2.222757000537238e-16, 2.456526388749016e-16, 2.714881529754608e-16, 3.000408107960083e-16, 3.315963787425073e-16, 3.664706739627943e-16, 4.050127315080793e-16, 4.476082920363670e-16, 4.946836672898304e-16, 5.467100025245505e-16, 6.042079955957903e-16, 6.677531050397348e-16, 7.379813122861424e-16, 8.155954842977402e-16, 9.013724102689123e-16, 9.961705740887021e-16, 1.100938748010566e-15, 1.216725486808607e-15, 1.344689623369201e-15, 1.486111865526057e-15, 1.642407614840039e-15, 1.815141131499014e-15, 2.006041190779248e-15, 2.217018384471440e-15, 2.450184243392977e-15, 2.707872369692257e-15, 2.992661792874233e-15, 3.307402781094011e-15, 3.655245368051253e-15, 4.039670879180488e-15, 4.464526774284602e-15, 4.934065153895433e-15, 5.452985315986473e-15, 6.026480787914038e-15, 6.660291305149181e-15, 7.360760256360466e-15, 8.134898170257041e-15, 8.990452879276204e-15, 9.935987062502841e-15, 1.098096394385775e-14, 1.213584200318437e-14, 1.341217964828528e-14, 1.482275089528562e-14, 1.638167321535499e-14, 1.810454882702344e-14, 2.000862084851265e-14, 2.211294587257239e-14, 2.443858469135401e-14, 2.700881307980678e-14, 2.984935474755050e-14, 3.298863879030854e-14, 3.645808421795958e-14, 4.029241440643229e-14, 4.453000462105175e-14, 4.921326608894885e-14, 5.438907046503769e-14, 6.010921893911273e-14, 6.643096067976429e-14, 7.341756580308676e-14, 8.113895860149252e-14, 8.967241736929777e-14, 9.910334783010448e-14, 1.095261379057530e-13, 1.210451023825933e-13, 1.337755269287210e-13, 1.478448219118764e-13, 1.633937975650728e-13, 1.805780732628623e-13, 1.995696350122467e-13, 2.205585567465074e-13, 2.437549026489779e-13, 2.693908295460095e-13, 2.977229104105259e-13, 3.290347022305518e-13, 3.636395839428896e-13, 4.018838928348062e-13, 4.441503908040617e-13, 4.908620951685787e-13, 5.424865123659980e-13, 5.995403169151822e-13, 6.625945224685207e-13, 7.322801967084261e-13, 8.092947772848716e-13, 8.944090520057436e-13, 9.884748731403624e-13, 1.092433683043238e-12, 1.207325936425662e-12, 1.334301513576084e-12, 1.474631228748613e-12, 1.629719548899119e-12, 1.801118650062676e-12, 1.990543952052933e-12, 2.199891286960273e-12, 2.431255873276498e-12, 2.686953285545802e-12, 2.969542629413028e-12, 3.281852154013172e-12, 3.627007558039277e-12, 4.008463272785582e-12, 4.430037035256956e-12, 4.895948097364050e-12, 5.410859453614547e-12, 5.979924509929487e-12, 6.608838660661838e-12, 7.303896290017477e-12, 8.072053768367932e-12, 8.920999073943177e-12, 9.859228736701785e-12, 1.089613287445852e-11, 1.204208917233957e-11, 1.330856674614333e-11, 1.470824092910627e-11, 1.625512013089818e-11, 1.796468603849469e-11, 1.985404856210394e-11, 2.194211707689892e-11, 2.424978967439970e-11, 2.680016231759770e-11, 2.961875999311579e-11, 3.273379217385409e-11, 3.617643514887572e-11, 3.998114404618718e-11, 4.418599767123930e-11, 4.883307961241208e-11, 5.396889942771051e-11, 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4.395813739277522e-09, 4.858125505931142e-09, 5.369059025511281e-09, 5.933727892433384e-09, 6.557783502483194e-09, 7.247471613991360e-09, 8.009694857348590e-09, 8.852081819018630e-09, 9.783063390784292e-09, 1.081195714921208e-08, 1.194906060875559e-08, 1.320575428316232e-08, 1.459461558495058e-08, 1.612954470504804e-08, 1.782590372973567e-08, 1.970067039062624e-08, 2.177260798218037e-08, 2.406245315273551e-08, 2.659312344174916e-08, 2.938994664888302e-08, 3.248091431980495e-08, 3.589696189917651e-08, 3.967227833770833e-08, 4.384464827330457e-08, 4.845583018407081e-08, 5.355197433170284e-08, 5.918408463559961e-08, 6.540852915386353e-08, 7.228760421284378e-08, 7.989015791604288e-08, 8.829227916594097e-08, 9.757805922900159e-08, 1.078404332968648e-07, 1.191821106789995e-07, 1.317166026689236e-07, 1.455693587079098e-07, 1.608790217936311e-07, 1.777988162313823e-07, 1.964980809461758e-07, 2.171639645456637e-07, 2.400032980365736e-07, 2.652446652738443e-07, 2.931406901825997e-07, 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ab = 0.7866057737580476e0
#------- Compute Frequency components reqired for transform -------#
# This is for Digital filtering and here we evalute frequency domain responses
# ritght at this bases.
# a. Generate time base
n = np.ceil(-10*np.log(time.min()/time.max()))
tbase = time.max()*np.exp(-0.1*np.arange(0, n+1))
self.wt = wt
self.ab = ab
self.n = n
self.tbase = tbase
# b. Determine required frequencies
omega_int = (ab/tbase[0])*np.exp(0.1*(np.r_[1:786+tbase.size:(786+tbase.size)*1j]-425))
# Case1: Compute frequency domain reponses right at filter coefficient values
if self.switchInterp == False:
self.frequency = omega_int/(2*np.pi)
self.Nfreq = self.frequency.size
# Case2: Compute frequency domain reponses in logarithmic then intepolate
elif self.switchInterp == True:
# This is tested decision: works well 1e-4-1e0 S/m
self.frequency = np.logspace(-3, 8, 81)
self.omega_int = omega_int
self.Nfreq = self.frequency.size
else:
raise Exception('Not implemented!!')
if self.offset is not None and np.isscalar(self.offset):
self.offset = self.offset*np.ones(self.Nfreq)
elif self.offset is not None and not np.isscalar(self.offset):
self.offset = self.offset[0]*np.ones(self.Nfreq)
def DCfun(mesh, pts):
D = mesh.faceDiv
G = D.T
sigma = 1e-2*np.ones(mesh.nC)
Msigi = mesh.getFaceInnerProduct(1./sigma)
MsigI = Utils.sdInv(Msigi)
A = D*MsigI*G
A[-1,-1] /= mesh.vol[-1] # Remove null space
rhs = np.zeros(mesh.nC)
txind = Utils.meshutils.closestPoints(mesh, pts)
rhs[txind] = np.r_[1,-1]
return A, rhs
def DCfun(mesh, pts):
D = mesh.faceDiv
G = D.T
sigma = 1e-2 * np.ones(mesh.nC)
Msigi = mesh.getFaceInnerProduct(1. / sigma)
MsigI = Utils.sdInv(Msigi)
A = D * MsigI * G
A[-1, -1] /= mesh.vol[-1] # Remove null space
rhs = np.zeros(mesh.nC)
txind = Utils.meshutils.closestPoints(mesh, pts)
rhs[txind] = np.r_[1, -1]
return A, rhs
def magnetizationModel(self):
"""
magnetization vector
"""
if self.magfile == 'DEFAULT':
return Magnetics.dipazm_2_xyz(np.ones(self.nC) * self.survey.srcField.param[1], np.ones(self.nC) * self.survey.srcField.param[2])
else:
raise NotImplementedError("this will require you to read in a three column vector model")
self._mref = Utils.meshutils.readUBCTensorModel(self.basePath + self._mrefInput, self.mesh)
return np.genfromtxt(self.magfile,delimiter=' \n',dtype=np.str,comments='!')
def area(self):
"""Construct face areas of the 3D model as 1d array."""
if getattr(self, '_area', None) is None:
# Ensure that we are working with column vectors
vh = self.h
# The number of cell centers in each direction
n = self.vnC
# Compute areas of cell faces
if (self.dim == 1):
self._area = np.ones(n[0] + 1)
elif (self.dim == 2):
area1 = np.outer(np.ones(n[0] + 1), vh[1])
area2 = np.outer(vh[0], np.ones(n[1] + 1))
self._area = np.r_[Utils.mkvc(area1), Utils.mkvc(area2)]
elif (self.dim == 3):
area1 = np.outer(np.ones(n[0] + 1),
Utils.mkvc(np.outer(vh[1], vh[2])))
area2 = np.outer(
vh[0], Utils.mkvc(np.outer(np.ones(n[1] + 1), vh[2])))
area3 = np.outer(
vh[0], Utils.mkvc(np.outer(vh[1], np.ones(n[2] + 1))))
self._area = np.r_[Utils.mkvc(area1),
Utils.mkvc(area2),
Utils.mkvc(area3)]
return self._area
def magnetizationModel(self):
"""
magnetization vector
"""
if getattr(self, 'magfile', None) is None:
M = Magnetics.dipazm_2_xyz(np.ones(self.nC) *
self.survey.srcField.param[1],
np.ones(self.nC) *
self.survey.srcField.param[2])
else:
with open(self.basePath + self.magfile) as f:
magmodel = f.read()
magmodel = magmodel.splitlines()
M = []
for line in magmodel:
M.append(map(float, line.split()))
# Convert list to 2d array
M = np.vstack(M)
# Cycle through three components and permute from UBC to SimPEG
for ii in range(3):
m = np.reshape(M[:, ii],
(self.mesh.nCz, self.mesh.nCx, self.mesh.nCy),
order='F')
m = m[::-1, :, :]
m = np.transpose(m, (1, 2, 0))
M[:, ii] = Utils.mkvc(m)
self._M = M
return self._M
def _fastInnerProduct(self, projType, prop=None, invProp=False, invMat=False):
"""
Fast version of getFaceInnerProduct.
This does not handle the case of a full tensor prop.
:param numpy.array prop: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
:param str projType: 'E' or 'F'
:param bool returnP: returns the projection matrices
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:rtype: scipy.csr_matrix
:return: M, the inner product matrix (nF, nF)
"""
assert projType in ['F', 'E'], "projType must be 'F' for faces or 'E' for edges"
if prop is None:
prop = np.ones(self.nC)
if invProp:
prop = 1./prop
if Utils.isScalar(prop):
prop = prop*np.ones(self.nC)
if prop.size == self.nC:
Av = getattr(self, 'ave'+projType+'2CC')
Vprop = self.vol * Utils.mkvc(prop)
M = self.dim * Utils.sdiag(Av.T * Vprop)
elif prop.size == self.nC*self.dim:
Av = getattr(self, 'ave'+projType+'2CCV')
V = sp.kron(sp.identity(self.dim), Utils.sdiag(self.vol))
M = Utils.sdiag(Av.T * V * Utils.mkvc(prop))
else:
return None
if invMat:
return Utils.sdInv(M)
else:
return M
def _fastInnerProductDeriv(self, projType, prop, invProp=False, invMat=False):
"""
:param str projType: 'E' or 'F'
:param TensorType tensorType: type of the tensor
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:rtype: function
:return: dMdmu, the derivative of the inner product matrix
"""
assert projType in ['F', 'E'], "projType must be 'F' for faces or 'E' for edges"
tensorType = Utils.TensorType(self, prop)
dMdprop = None
if invMat:
MI = self._fastInnerProduct(projType, prop, invProp=invProp, invMat=invMat)
if tensorType == 0:
Av = getattr(self, 'ave'+projType+'2CC')
V = Utils.sdiag(self.vol)
ones = sp.csr_matrix((np.ones(self.nC), (range(self.nC), np.zeros(self.nC))), shape=(self.nC,1))
if not invMat and not invProp:
dMdprop = self.dim * Av.T * V * ones
elif invMat and invProp:
dMdprop = self.dim * Utils.sdiag(MI.diagonal()**2) * Av.T * V * ones * Utils.sdiag(1./prop**2)
if tensorType == 1:
Av = getattr(self, 'ave'+projType+'2CC')
V = Utils.sdiag(self.vol)
if not invMat and not invProp:
dMdprop = self.dim * Av.T * V
elif invMat and invProp:
dMdprop = self.dim * Utils.sdiag(MI.diagonal()**2) * Av.T * V * Utils.sdiag(1./prop**2)
if tensorType == 2: # anisotropic
Av = getattr(self, 'ave'+projType+'2CCV')
V = sp.kron(sp.identity(self.dim), Utils.sdiag(self.vol))
if not invMat and not invProp:
dMdprop = Av.T * V
elif invMat and invProp:
dMdprop = Utils.sdiag(MI.diagonal()**2) * Av.T * V * Utils.sdiag(1./prop**2)
if dMdprop is not None:
def innerProductDeriv(v=None):
if v is None:
print 'Depreciation Warning: TensorMesh.innerProductDeriv. You should be supplying a vector. Use: sdiag(u)*dMdprop'
return dMdprop
return Utils.sdiag(v) * dMdprop
return innerProductDeriv
else:
return None
