def evalDeriv(self, u, v=None, adjoint=False):
assert v is not None, 'v to multiply must be provided.'
if not adjoint:
data = Survey.Data(self)
for src in self.srcList:
for rx in src.rxList:
data[src, rx] = rx.evalDeriv(src, self.mesh,
self.prob.timeMesh, u, v)
return data
else:
f = FieldsTDEM(self.mesh, self)
for src in self.srcList:
for rx in src.rxList:
Ptv = rx.evalDeriv(src,
self.mesh,
self.prob.timeMesh,
u,
v,
adjoint=True)
Ptv = Ptv.reshape((-1, self.prob.timeMesh.nN), order='F')
if rx.projField not in f: # first time we are projecting
f[src, rx.projField, :] = Ptv
else: # there are already fields, so let's add to them!
f[src, rx.projField, :] += Ptv
return f
def _AhtVec(self, m, vec):
"""
:param numpy.array m: Conductivity model
:param FieldsTDEM vec: Fields object
:rtype: FieldsTDEM
:return: f
Multiply the matrix \\\(\\\hat{A}\\\) by a fields vector where
.. math::
\mathbf{\hat{A}}^\\top = \left[
\\begin{array}{cccc}
A & B & & \\\\
& \ddots & \ddots & \\\\
& & A & B \\\\
& & 0 & A
\end{array}
\\right] \\\\
\mathbf{A} =
\left[
\\begin{array}{cc}
\\frac{1}{\delta t} \MfMui & \MfMui\dcurl \\\\
\dcurl^\\top \MfMui & -\MeSig
\end{array}
\\right] \\\\
\mathbf{B} =
\left[
\\begin{array}{cc}
-\\frac{1}{\delta t} \MfMui & 0 \\\\
0 & 0
\end{array}
\\right] \\\\
"""
self.curModel = m
f = FieldsTDEM(self.mesh, self.survey)
for i in range(self.nT):
b = 1.0 / self.timeSteps[
i] * self.MfMui * vec[:, 'b', i + 1] + self.MfMui * (
self.mesh.edgeCurl * vec[:, 'e', i + 1])
if i < self.nT - 1:
b = b - 1.0 / self.timeSteps[i + 1] * self.MfMui * vec[:, 'b',
i + 2]
f[:, 'b', i + 1] = b
f[:, 'e', i + 1] = self.mesh.edgeCurl.T * (
self.MfMui * vec[:, 'b', i + 1]) - self.MeSigma * vec[:, 'e',
i + 1]
return f
def Gvec(self, m, vec, u=None):
"""
:param numpy.array m: Conductivity model
:param numpy.array vec: vector (like a model)
:param FieldsTDEM u: Fields resulting from m
:rtype: FieldsTDEM
:return: f
Multiply G by a vector
"""
if u is None:
u = self.fields(m)
self.curModel = m
# Note: Fields has shape (nF/E, nSrc, nT+1)
# However, p will only really fill (:,:,1:nT+1)
# meaning the 'initial fields' are zero (:,:,0)
p = FieldsTDEM(self.mesh, self.survey)
# 'b' at all times is zero.
# However, to save memory we will **not** do:
#
# p[:, 'b', :] = 0.0
# fake initial 'e' fields
p[:, 'e', 0] = 0.0
dMdsig = self.MeSigmaDeriv
# self.mesh.getEdgeInnerProductDeriv(self.curModel.transform)
# dsigdm_x_v = self.curModel.sigmaDeriv*vec
# dsigdm_x_v = self.curModel.transformDeriv*vec
for i in range(1, self.nT + 1):
# TODO: G[1] may be dependent on the model
# for a galvanic source (deriv of the dc problem)
#
# Do multiplication for all src in self.survey.srcList
for src in self.survey.srcList:
p[src, 'e', i] = -dMdsig(u[src, 'e', i]) * vec
return p