def CasingMagDipole2Deriv_z_z(z):
obsloc = np.vstack([xobs, yobs, z]).T
f = Casing._getCasingHertzMagDipoleDeriv_z(srcloc,obsloc,freq,sigma,a,b,mu)
g = Utils.sdiag(Casing._getCasingHertzMagDipole2Deriv_z_z(srcloc,obsloc,freq,sigma,a,b,mu))
return f, g
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 CasingMagDipoleDeriv_r(x):
obsloc = np.vstack([x, yobs, zobs]).T
f = Casing._getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu)
g = Utils.sdiag(Casing._getCasingHertzMagDipoleDeriv_r(srcloc,obsloc,freq,sigma,a,b,mu))
return f, g
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 _e_pxDeriv_u(self, src, v, adjoint = False):
'''
Takes the derivative of e_px wrt u
'''
if adjoint:
# adjoint: returns a 2*nE long vector with zero's for py
return np.vstack((v,np.zeros_like(v)))
# Not adjoint: return only the px part of the vector
return v[:len(v)/2]
def CasingMagDipoleDeriv_z(z):
obsloc = np.vstack([xobs, yobs, z]).T
f = Casing._getCasingHertzMagDipole(srcloc, obsloc, freq, sigma, a, b, mu)
g = Utils.sdiag(
Casing._getCasingHertzMagDipoleDeriv_z(srcloc, obsloc, freq, sigma, a,
b, mu))
return f, g
def _e_pyDeriv_u(self, src, v, adjoint=False):
"""
Takes the derivative of e_py wrt u
"""
if adjoint:
# adjoint: returns a 2*nE long vector with zero's for px
return np.vstack((np.zeros_like(v), v))
# Not adjoint: return only the px part of the vector
return v[len(v) / 2 : :]
def _e_pyDeriv_u(self, src, v, adjoint = False):
'''
Takes the derivative of e_py wrt u
'''
if adjoint:
# adjoint: returns a 2*nE long vector with zero's for px
return np.vstack((np.zeros_like(v),v))
# Not adjoint: return only the px part of the vector
return v[len(v)/2::]
def run(plotIt=True):
"""
Mesh: Basic Forward 2D DC Resistivity
=====================================
2D DC forward modeling example with Tensor and Curvilinear Meshes
"""
# Step1: Generate Tensor and Curvilinear Mesh
sz = [40, 40]
tM = Mesh.TensorMesh(sz)
rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz, 'rotate'))
# Step2: Direct Current (DC) operator
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
pts = np.vstack((np.r_[0.25, 0.5], np.r_[0.75, 0.5]))
#Step3: Solve DC problem (LU solver)
AtM, rhstM = DCfun(tM, pts)
AinvtM = SolverLU(AtM)
phitM = AinvtM * rhstM
ArM, rhsrM = DCfun(rM, pts)
AinvrM = SolverLU(ArM)
phirM = AinvrM * rhsrM
if not plotIt: return
import matplotlib.pyplot as plt
#Step4: Making Figure
fig, axes = plt.subplots(1, 2, figsize=(12 * 1.2, 4 * 1.2))
vmin, vmax = phitM.min(), phitM.max()
dat = tM.plotImage(phitM, ax=axes[0], clim=(vmin, vmax), grid=True)
dat = rM.plotImage(phirM, ax=axes[1], clim=(vmin, vmax), grid=True)
cb = plt.colorbar(dat[0], ax=axes[0])
cb.set_label("Voltage (V)")
cb = plt.colorbar(dat[0], ax=axes[1])
cb.set_label("Voltage (V)")
axes[0].set_title('TensorMesh')
axes[1].set_title('CurvilinearMesh')
plt.show()
def run(plotIt=True):
"""
Mesh: Basic Forward 2D DC Resistivity
=====================================
2D DC forward modeling example with Tensor and Curvilinear Meshes
"""
# Step1: Generate Tensor and Curvilinear Mesh
sz = [40,40]
tM = Mesh.TensorMesh(sz)
rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz,'rotate'))
# Step2: Direct Current (DC) operator
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
pts = np.vstack((np.r_[0.25, 0.5], np.r_[0.75, 0.5]))
#Step3: Solve DC problem (LU solver)
AtM, rhstM = DCfun(tM, pts)
AinvtM = SolverLU(AtM)
phitM = AinvtM*rhstM
ArM, rhsrM = DCfun(rM, pts)
AinvrM = SolverLU(ArM)
phirM = AinvrM*rhsrM
if not plotIt: return
import matplotlib.pyplot as plt
#Step4: Making Figure
fig, axes = plt.subplots(1,2,figsize=(12*1.2,4*1.2))
vmin, vmax = phitM.min(), phitM.max()
dat = tM.plotImage(phitM, ax=axes[0], clim=(vmin, vmax), grid=True)
dat = rM.plotImage(phirM, ax=axes[1], clim=(vmin, vmax), grid=True)
cb = plt.colorbar(dat[0], ax=axes[0]); cb.set_label("Voltage (V)")
cb = plt.colorbar(dat[0], ax=axes[1]); cb.set_label("Voltage (V)")
axes[0].set_title('TensorMesh')
axes[1].set_title('CurvilinearMesh')
plt.show()
def _fDeriv_u(self, src, v, adjoint=False):
"""
Derivative of the fields object wrt u.
:param MTsrc src: MT source
:param numpy.ndarray v: random vector of f_sol.size
This function stacks the fields derivatives appropriately
return a vector of size (nreEle+nrbEle)
"""
de_du = v # Utils.spdiag(np.ones((self.nF,)))
db_du = self._bDeriv_u(src, v, adjoint)
# Return the stack
# This doesn't work...
return np.vstack((de_du, db_du))
def _fDeriv_u(self, src, v, adjoint=False):
"""
Derivative of the fields object wrt u.
:param MTsrc src: MT source
:param numpy.ndarray v: random vector of f_sol.size
This function stacks the fields derivatives appropriately
return a vector of size (nreEle+nrbEle)
"""
de_du = v #Utils.spdiag(np.ones((self.nF,)))
db_du = self._bDeriv_u(src, v, adjoint)
# Return the stack
# This doesn't work...
return np.vstack((de_du,db_du))
def getActiveindfromTopo(mesh, topo):
# def genActiveindfromTopo(mesh, topo):
"""
Get active indices from topography
"""
from scipy.interpolate import NearestNDInterpolator
if mesh.dim==3:
nCxy = mesh.nCx*mesh.nCy
Zcc = mesh.gridCC[:,2].reshape((nCxy, mesh.nCz), order='F')
Ftopo = NearestNDInterpolator(topo[:,:2], topo[:,2])
XY = Utils.ndgrid(mesh.vectorCCx, mesh.vectorCCy)
XY.shape
topo = Ftopo(XY)
actind = []
for ixy in range(nCxy):
actind.append(topo[ixy] <= Zcc[ixy,:])
else:
raise NotImplementedError("Only 3D is working")
return Utils.mkvc(np.vstack(actind))
def projectFields(self, u):
"""
Decompose frequency domain EM responses as real and imaginary
components
"""
ureal = (u.real).copy()
uimag = (u.imag).copy()
if self.rxType == 'Hz':
if self.switchRI == 'all':
ureal = (u.real).copy()
uimag = (u.imag).copy()
if ureal.ndim == 1 or 0:
resp = np.r_[ureal, uimag]
elif ureal.ndim ==2:
resp = np.vstack((ureal, uimag))
else:
raise Exception('Not implemented!!')
elif self.switchRI == 'Real':
resp = (u.real).copy()
elif self.switchRI == 'Imag':
resp = (u.imag).copy()
else:
raise Exception('Not implemented')
else:
raise Exception('Not implemnted!!')
return mu_0*resp
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
# Step2: Direct Current (DC) operator
def DCfun(mesh, pts):
D = mesh.faceDiv
G = D.T
sigma = 1e-2 * np.ones(mesh.nC)
Msigi = mesh.getFaceInnerProduct(1.0 / 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
pts = np.vstack((np.r_[0.25, 0.5], np.r_[0.75, 0.5]))
# Step3: Solve DC problem (LU solver)
AtM, rhstM = DCfun(tM, pts)
AinvtM = SolverLU(AtM)
phitM = AinvtM * rhstM
ArM, rhsrM = DCfun(rM, pts)
AinvrM = SolverLU(ArM)
phirM = AinvrM * rhsrM
# Step4: Making Figure
fig, axes = plt.subplots(1, 2, figsize=(12 * 1.2, 4 * 1.2))
label = ["(a)", "(b)"]
opts = {}
vmin, vmax = phitM.min(), phitM.max()
def readUBC_DC3Dobstopo(filename,mesh,topo,probType="CC"):
"""
Seogi's personal readObs function.
"""
text_file = open(filename, "r")
lines = text_file.readlines()
text_file.close()
SRC = []
DATA = []
srcLists = []
isrc = 0
# airind = getActiveindfromTopo(mesh, topo)
# mesh2D, topoCC = gettopoCC(mesh, airind)
for line in lines:
if "!" in line.split(): continue
elif line == '\n': continue
elif line == ' \n': continue
temp = map(float, line.split())
# Read a line for the current electrode
if len(temp) == 5: # SRC: Only X and Y are provided (assume no topography)
#TODO consider topography and assign the closest cell center in the earth
if isrc == 0:
DATA_temp = []
else:
DATA.append(np.asarray(DATA_temp))
DATA_temp = []
indM = Utils.closestPoints(mesh2D, DATA[isrc-1][:,1:3])
indN = Utils.closestPoints(mesh2D, DATA[isrc-1][:,3:5])
rx = DCIP.RxDipole(np.c_[DATA[isrc-1][:,1:3], topoCC[indM]], np.c_[DATA[isrc-1][:,3:5], topoCC[indN]])
temp = np.asarray(temp)
if [SRC[isrc-1][0], SRC[isrc-1][1]] == [SRC[isrc-1][2], SRC[isrc-1][3]]:
indA = Utils.closestPoints(mesh2D, [SRC[isrc-1][0], SRC[isrc-1][1]])
tx = DCIP.SrcDipole([rx], [SRC[isrc-1][0], SRC[isrc-1][1], topoCC[indA]],[mesh.vectorCCx.max(), mesh.vectorCCy.max(), topoCC[-1]])
else:
indA = Utils.closestPoints(mesh2D, [SRC[isrc-1][0], SRC[isrc-1][1]])
indB = Utils.closestPoints(mesh2D, [SRC[isrc-1][2], SRC[isrc-1][3]])
tx = DCIP.SrcDipole([rx], [SRC[isrc-1][0], SRC[isrc-1][1], topoCC[indA]],[SRC[isrc-1][2], SRC[isrc-1][3], topoCC[indB]])
srcLists.append(tx)
SRC.append(temp)
isrc += 1
elif len(temp) == 7: # SRC: X, Y and Z are provided
SRC.append(temp)
isrc += 1
elif len(temp) == 6: #
DATA_temp.append(np.r_[isrc, np.asarray(temp)])
elif len(temp) > 7:
DATA_temp.append(np.r_[isrc, np.asarray(temp)])
DATA.append(np.asarray(DATA_temp))
DATA_temp = []
indM = Utils.closestPoints(mesh2D, DATA[isrc-1][:,1:3])
indN = Utils.closestPoints(mesh2D, DATA[isrc-1][:,3:5])
rx = DCIP.RxDipole(np.c_[DATA[isrc-1][:,1:3], topoCC[indM]], np.c_[DATA[isrc-1][:,3:5], topoCC[indN]])
temp = np.asarray(temp)
if [SRC[isrc-1][0], SRC[isrc-1][1]] == [SRC[isrc-1][2], SRC[isrc-1][3]]:
indA = Utils.closestPoints(mesh2D, [SRC[isrc-1][0], SRC[isrc-1][1]])
tx = DCIP.SrcDipole([rx], [SRC[isrc-1][0], SRC[isrc-1][1], topoCC[indA]],[mesh.vectorCCx.max(), mesh.vectorCCy.max(), topoCC[-1]])
else:
indA = Utils.closestPoints(mesh2D, [SRC[isrc-1][0], SRC[isrc-1][1]])
indB = Utils.closestPoints(mesh2D, [SRC[isrc-1][2], SRC[isrc-1][3]])
tx = DCIP.SrcDipole([rx], [SRC[isrc-1][0], SRC[isrc-1][1], topoCC[indA]],[SRC[isrc-1][2], SRC[isrc-1][3], topoCC[indB]])
srcLists.append(tx)
text_file.close()
survey = DCIP.SurveyDC(srcLists)
# Do we need this?
SRC = np.asarray(SRC)
DATA = np.vstack(DATA)
survey.dobs = np.vstack(DATA)[:,-2]
return {'DCsurvey':survey, 'airind':airind, 'topoCC':topoCC, 'SRC':SRC}
def interpFFT(x, y, m):
"""
Load in a 2D grid and resample
OUTPUT:
m_out
"""
from SimPEG import np, sp
import scipy.signal as sn
# Add padding values by reflection (2**n)
lenx = np.round(np.log2(2 * len(x)))
npadx = int(np.floor((2**lenx - len(x)) / 2.))
#Create hemming taper
if np.mod(npadx * 2 + len(x), 2) != 0:
oddx = 1
else:
oddx = 0
tap0 = sn.hamming(npadx * 2)
tapl = sp.spdiags(tap0[0:npadx], 0, npadx, npadx)
tapr = sp.spdiags(tap0[npadx:], 0, npadx, npadx + oddx)
# Mirror the 2d data over the half lenght and apply 0-taper
mpad = np.hstack(
[np.fliplr(m[:, 0:npadx]) * tapl, m,
np.fliplr(m[:, -npadx:]) * tapr])
# Repeat along the second dimension
leny = np.round(np.log2(2 * len(y)))
npady = int(np.floor((2**leny - len(y)) / 2.))
#Create hemming taper
if np.mod(npady * 2 + len(y), 2) != 0:
oddy = 1
else:
oddy = 0
tap0 = sn.hamming(npady * 2)
tapu = sp.spdiags(tap0[0:npady], 0, npady, npady)
tapd = sp.spdiags(tap0[npady:], 0, npady + oddy, npady)
mpad = np.vstack([
tapu * np.flipud(mpad[0:npady, :]), mpad,
tapd * np.flipud(mpad[-npady:, :])
])
# Compute FFT
FFTm = np.fft.fft2(mpad)
# Do an FFT shift
FFTshift = np.fft.fftshift(FFTm)
# Pad high frequencies with zeros to increase the sampling rate
py = int(FFTm.shape[0] / 2)
px = int(FFTm.shape[1] / 2)
FFTshift = np.hstack([
np.zeros((FFTshift.shape[0], px)), FFTshift,
np.zeros((FFTshift.shape[0], px))
])
FFTshift = np.vstack([
np.zeros((py, FFTshift.shape[1])), FFTshift,
np.zeros((py, FFTshift.shape[1]))
])
# Inverse shift
FFTm = np.fft.ifftshift(FFTshift)
# Compute inverse FFT
IFFTm = np.fft.ifft2(FFTm) * FFTm.size / mpad.size
m_out = np.real(IFFTm)
# Extract core
#m_out = np.real(IFFTm[npady*2:-(npady*2+oddy+1),npadx*2:-(npadx*2+oddx+1)])
m_out = m_out[npady * 2:-(npady + oddy) * 2, npadx * 2:-(npadx + oddx) * 2]
if np.mod(m.shape[0], 2) != 0:
m_out = m_out[:-1, :]
if np.mod(m.shape[1], 2) != 0:
m_out = m_out[:, :-1]
return m_out
def run(plotIt=True):
# Step1: Generate Tensor and Curvilinear Mesh
sz = [40,40]
# Tensor Mesh
tM = Mesh.TensorMesh(sz)
# Curvilinear Mesh
rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz,'rotate'))
# Step2: Direct Current (DC) operator
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
pts = np.vstack((np.r_[0.25, 0.5], np.r_[0.75, 0.5]))
#Step3: Solve DC problem (LU solver)
AtM, rhstM = DCfun(tM, pts)
AinvtM = SolverLU(AtM)
phitM = AinvtM*rhstM
ArM, rhsrM = DCfun(rM, pts)
AinvrM = SolverLU(ArM)
phirM = AinvrM*rhsrM
if not plotIt: return
import matplotlib.pyplot as plt
import matplotlib
from matplotlib.mlab import griddata
#Step4: Making Figure
fig, axes = plt.subplots(1,2,figsize=(12*1.2,4*1.2))
label = ["(a)", "(b)"]
opts = {}
vmin, vmax = phitM.min(), phitM.max()
dat = tM.plotImage(phitM, ax=axes[0], clim=(vmin, vmax), grid=True)
#TODO: At the moment Curvilinear Mesh do not have plotimage
Xi = tM.gridCC[:,0].reshape(sz[0], sz[1], order='F')
Yi = tM.gridCC[:,1].reshape(sz[0], sz[1], order='F')
PHIrM = griddata(rM.gridCC[:,0], rM.gridCC[:,1], phirM, Xi, Yi, interp='linear')
axes[1].contourf(Xi, Yi, PHIrM, 100, vmin=vmin, vmax=vmax)
cb = plt.colorbar(dat[0], ax=axes[0]); cb.set_label("Voltage (V)")
cb = plt.colorbar(dat[0], ax=axes[1]); cb.set_label("Voltage (V)")
tM.plotGrid(ax=axes[0], **opts)
axes[0].set_title('TensorMesh')
rM.plotGrid(ax=axes[1], **opts)
axes[1].set_title('CurvilinearMesh')
for i in range(2):
axes[i].set_xlim(0.025, 0.975)
axes[i].set_ylim(0.025, 0.975)
axes[i].text(0., 1.0, label[i], fontsize=20)
if i==0:
axes[i].set_ylabel("y")
else:
axes[i].set_ylabel(" ")
axes[i].set_xlabel("x")
plt.show()
def MagneticDipoleFields(srcLoc, obsLoc, component,
orientation='Z', moment=1., mu=mu_0):
"""
Calculate the vector potential of a set of magnetic dipoles
at given locations 'ref. <http://en.wikipedia.org/wiki/Dipole#Magnetic_vector_potential>'
.. math::
B = \frac{\mu_0}{4 \pi r^3} \left( \frac{3 \vec{r} (\vec{m} \cdot
\vec{r})}{r^2})
- \vec{m}
\right) \cdot{\hat{rx}}
:param numpy.ndarray srcLoc: Location of the source(s) (x, y, z)
:param numpy.ndarray obsLoc: Where the potentials will be calculated
(x, y, z)
:param str component: The component to calculate - 'x', 'y', or 'z'
:param numpy.ndarray moment: The vector dipole moment (vertical)
:rtype: numpy.ndarray
:return: The vector potential each dipole at each observation location
"""
if isinstance(orientation, str):
assert orientation.upper() in ['X', 'Y', 'Z'], ("orientation must be 'x', "
"'y', or 'z' or a vector"
"not {}".format(orientation)
)
elif (not np.allclose(np.r_[1., 0., 0.], orientation) or
not np.allclose(np.r_[0., 1., 0.], orientation) or
not np.allclose(np.r_[0., 0., 1.], orientation)):
warnings.warn('Arbitrary trasnmitter orientations ({}) not thouroughly tested '
'Pull request on a test anyone? bueller?').format(orientation)
if isinstance(component, str):
assert component.upper() in ['X', 'Y', 'Z'], ("component must be 'x', "
"'y', or 'z' or a vector"
"not {}".format(component)
)
elif (not np.allclose(np.r_[1., 0., 0.], component) or
not np.allclose(np.r_[0., 1., 0.], component) or
not np.allclose(np.r_[0., 0., 1.], component)):
warnings.warn('Arbitrary receiver orientations ({}) not thouroughly tested '
'Pull request on a test anyone? bueller?').format(component)
if isinstance(orientation, str):
orientation = orientationDict[orientation.upper()]
if isinstance(component, str):
component = orientationDict[component.upper()]
assert np.linalg.norm(orientation, 2) == 1., ('orientation must be a unit '
'vector. Use "moment=X to '
'scale source fields')
if np.linalg.norm(component, 2) != 1.:
warnings.warn('The magnitude of the receiver component vector is > 1, '
' it is {}. The receiver fields will be scaled.'
).format(np.linalg.norm(component, 2))
srcLoc = np.atleast_2d(srcLoc)
component = np.atleast_2d(component)
obsLoc = np.atleast_2d(obsLoc)
orientation = np.atleast_2d(orientation)
nObs = obsLoc.shape[0]
nSrc = int(srcLoc.size / 3.)
# use outer product to construct an array of [x_src, y_src, z_src]
m = moment*orientation.repeat(nObs, axis=0)
B = []
for i in range(nSrc):
srcLoc = srcLoc[i, np.newaxis].repeat(nObs, axis=0)
rx = component.repeat(nObs, axis=0)
dR = obsLoc - srcLoc
r = np.sqrt((dR**2).sum(axis=1))
# mult each element and sum along the axis (vector dot product)
m_dot_dR_div_r2 = (m * dR).sum(axis=1) / (r**2)
# multiply the scalar m_dot_dR by the 3D vector r
rvec_m_dot_dR_div_r2 = np.vstack([m_dot_dR_div_r2 * dR[:, i] for
i in range(3)]).T
inside = (3. * rvec_m_dot_dR_div_r2) - m
# dot product with rx orientation
inside_dot_rx = (inside * rx).sum(axis=1)
front = (mu/(4.* np.pi * r**3))
B.append(Utils.mkvc(front * inside_dot_rx))
return np.vstack(B).T
# Compute tmi mag data
survey.pair(prob_tmi)
dtmi = prob_tmi.fields(m)
# Compute analytical response from a magnetized sphere
bxa, bya, bza = PF.MagAnalytics.MagSphereFreeSpace(locXyz[:, 0],
locXyz[:, 1],
locXyz[:, 2],
rad, 0, 0, 0,
chi, b0)
# Projection matrix
Ptmi = mkvc(b0)/np.sqrt(np.sum(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)
#fig = plt.figure()
#axs = plt.subplot(111)
#mesh.plotSlice(model, normal='Z', ind = mesh.nCz/2, ax= axs)
#axs.set_aspect('equal')
#PF.Magnetics.plot_obs_2D(locXyz,dtmi)
#%% Repeat using PDE solve
m_mu = PF.BaseMag.BaseMagMap(mesh)
def run(plotIt=True):
# Step1: Generate Tensor and Curvilinear Mesh
sz = [40, 40]
# Tensor Mesh
tM = Mesh.TensorMesh(sz)
# Curvilinear Mesh
rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz, 'rotate'))
# Step2: Direct Current (DC) operator
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
pts = np.vstack((np.r_[0.25, 0.5], np.r_[0.75, 0.5]))
#Step3: Solve DC problem (LU solver)
AtM, rhstM = DCfun(tM, pts)
AinvtM = SolverLU(AtM)
phitM = AinvtM * rhstM
ArM, rhsrM = DCfun(rM, pts)
AinvrM = SolverLU(ArM)
phirM = AinvrM * rhsrM
if not plotIt: return
import matplotlib.pyplot as plt
import matplotlib
from matplotlib.mlab import griddata
#Step4: Making Figure
fig, axes = plt.subplots(1, 2, figsize=(12 * 1.2, 4 * 1.2))
label = ["(a)", "(b)"]
opts = {}
vmin, vmax = phitM.min(), phitM.max()
dat = tM.plotImage(phitM, ax=axes[0], clim=(vmin, vmax), grid=True)
#TODO: At the moment Curvilinear Mesh do not have plotimage
Xi = tM.gridCC[:, 0].reshape(sz[0], sz[1], order='F')
Yi = tM.gridCC[:, 1].reshape(sz[0], sz[1], order='F')
PHIrM = griddata(rM.gridCC[:, 0],
rM.gridCC[:, 1],
phirM,
Xi,
Yi,
interp='linear')
axes[1].contourf(Xi, Yi, PHIrM, 100, vmin=vmin, vmax=vmax)
cb = plt.colorbar(dat[0], ax=axes[0])
cb.set_label("Voltage (V)")
cb = plt.colorbar(dat[0], ax=axes[1])
cb.set_label("Voltage (V)")
tM.plotGrid(ax=axes[0], **opts)
axes[0].set_title('TensorMesh')
rM.plotGrid(ax=axes[1], **opts)
axes[1].set_title('CurvilinearMesh')
for i in range(2):
axes[i].set_xlim(0.025, 0.975)
axes[i].set_ylim(0.025, 0.975)
axes[i].text(0., 1.0, label[i], fontsize=20)
if i == 0:
axes[i].set_ylabel("y")
else:
axes[i].set_ylabel(" ")
axes[i].set_xlabel("x")
plt.show()
def MagneticDipoleFields(srcLoc, obsLoc, component,
orientation='Z', moment=1., mu=mu_0):
"""
Calculate the vector potential of a set of magnetic dipoles
at given locations 'ref. <http://en.wikipedia.org/wiki/Dipole#Magnetic_vector_potential>'
.. math::
B = \frac{\mu_0}{4 \pi r^3} \left( \frac{3 \vec{r} (\vec{m} \cdot
\vec{r})}{r^2})
- \vec{m}
\right) \cdot{\hat{rx}}
:param numpy.ndarray srcLoc: Location of the source(s) (x, y, z)
:param numpy.ndarray obsLoc: Where the potentials will be calculated
(x, y, z)
:param str component: The component to calculate - 'x', 'y', or 'z'
:param numpy.ndarray moment: The vector dipole moment (vertical)
:rtype: numpy.ndarray
:return: The vector potential each dipole at each observation location
"""
if isinstance(orientation, str):
assert orientation.upper() in ['X', 'Y', 'Z'], ("orientation must be 'x', "
"'y', or 'z' or a vector"
"not {}".format(orientation)
)
elif (not np.allclose(np.r_[1., 0., 0.], orientation) or
not np.allclose(np.r_[0., 1., 0.], orientation) or
not np.allclose(np.r_[0., 0., 1.], orientation)):
warnings.warn('Arbitrary trasnmitter orientations ({}) not thouroughly tested '
'Pull request on a test anyone? bueller?').format(orientation)
if isinstance(component, str):
assert component.upper() in ['X', 'Y', 'Z'], ("component must be 'x', "
"'y', or 'z' or a vector"
"not {}".format(component)
)
elif (not np.allclose(np.r_[1., 0., 0.], component) or
not np.allclose(np.r_[0., 1., 0.], component) or
not np.allclose(np.r_[0., 0., 1.], component)):
warnings.warn('Arbitrary receiver orientations ({}) not thouroughly tested '
'Pull request on a test anyone? bueller?').format(component)
if isinstance(orientation, str):
orientation = orientationDict[orientation.upper()]
if isinstance(component, str):
component = orientationDict[component.upper()]
assert np.linalg.norm(orientation, 2) == 1., ('orientation must be a unit '
'vector. Use "moment=X to '
'scale source fields')
if np.linalg.norm(component, 2) != 1.:
warnings.warn('The magnitude of the receiver component vector is > 1, '
' it is {}. The receiver fields will be scaled.'
).format(np.linalg.norm(component, 2))
srcLoc = np.atleast_2d(srcLoc)
component = np.atleast_2d(component)
obsLoc = np.atleast_2d(obsLoc)
orientation = np.atleast_2d(orientation)
nObs = obsLoc.shape[0]
nSrc = int(srcLoc.size / 3.)
# use outer product to construct an array of [x_src, y_src, z_src]
m = moment*orientation.repeat(nObs, axis=0)
B = []
for i in range(nSrc):
srcLoc = srcLoc[i, np.newaxis].repeat(nObs, axis=0)
rx = component.repeat(nObs, axis=0)
dR = obsLoc - srcLoc
r = np.sqrt((dR**2).sum(axis=1))
# mult each element and sum along the axis (vector dot product)
m_dot_dR_div_r2 = (m * dR).sum(axis=1) / (r**2)
# multiply the scalar m_dot_dR by the 3D vector r
rvec_m_dot_dR_div_r2 = np.vstack([m_dot_dR_div_r2 * dR[:, i] for
i in range(3)]).T
inside = (3. * rvec_m_dot_dR_div_r2) - m
# dot product with rx orientation
inside_dot_rx = (inside * rx).sum(axis=1)
front = (mu/(4.* np.pi * r**3))
B.append(Utils.mkvc(front * inside_dot_rx))
return np.vstack(B).T
