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keep track of _v with notation

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This commit is contained in:
Lindsey Heagy
2016-02-19 17:31:43 -08:00
parent ea6ec4cb55
commit 649525fa88
2 changed files with 70 additions and 70 deletions
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SimPEG/EM/FDEM/FDEM.py
+23 -23
View File
@@ -84,15 +84,15 @@ class BaseFDEMProblem(BaseEMProblem):
for src in self.survey.getSrcByFreq(freq):
ftype = self._fieldType + 'Solution'
u_src = u[src, ftype]
dA_dm = self.getADeriv_m(freq, u_src, v)
dRHS_dm = self.getRHSDeriv_m(freq, src, v)
du_dm = Ainv * ( - dA_dm + dRHS_dm )
dA_dm_v = self.getADeriv(freq, u_src, v)
dRHS_dm_v = self.getRHSDeriv(freq, src, v)
du_dm_v = Ainv * ( - dA_dm_v + dRHS_dm_v )
for rx in src.rxList:
df_dmFun = getattr(u, '_%sDeriv'%rx.projField, None)
df_dm = df_dmFun(src, du_dm, v, adjoint=False)
Df_Dm = np.array(df_dm,dtype=complex)
Jv[src, rx] = rx.projectFieldsDeriv(src, self.mesh, u, Df_Dm)
df_dm_v = df_dmFun(src, du_dm_v, v, adjoint=False)
df_dm_v = np.array(df_dm_v,dtype=complex)
Jv[src, rx] = rx.projectFieldsDeriv(src, self.mesh, u, df_dm_v)
Ainv.clean()
return Utils.mkvc(Jv)
@@ -135,8 +135,8 @@ class BaseFDEMProblem(BaseEMProblem):
ATinvdf_duT = ATinv * df_duT
dA_dmT = self.getADeriv_m(freq, u_src, ATinvdf_duT, adjoint=True)
dRHS_dmT = self.getRHSDeriv_m(freq, src, ATinvdf_duT, adjoint=True)
dA_dmT = self.getADeriv(freq, u_src, ATinvdf_duT, adjoint=True)
dRHS_dmT = self.getRHSDeriv(freq, src, ATinvdf_duT, adjoint=True)
du_dmT = -dA_dmT + dRHS_dmT
df_dmT += du_dmT
@@ -228,7 +228,7 @@ class Problem_e(BaseFDEMProblem):
return C.T*MfMui*C + 1j*omega(freq)*MeSigma
def getADeriv_m(self, freq, u, v, adjoint=False):
def getADeriv(self, freq, u, v, adjoint=False):
"""
Product of the derivative of our system matrix with respect to the model and a vector
@@ -269,7 +269,7 @@ class Problem_e(BaseFDEMProblem):
return C.T * (MfMui * S_m) -1j * omega(freq) * S_e
def getRHSDeriv_m(self, freq, src, v, adjoint=False):
def getRHSDeriv(self, freq, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
@@ -343,7 +343,7 @@ class Problem_b(BaseFDEMProblem):
return MfMui.T*A
return A
def getADeriv_m(self, freq, u, v, adjoint=False):
def getADeriv(self, freq, u, v, adjoint=False):
"""
Product of the derivative of our system matrix with respect to the model and a vector
@@ -400,7 +400,7 @@ class Problem_b(BaseFDEMProblem):
return RHS
def getRHSDeriv_m(self, freq, src, v, adjoint=False):
def getRHSDeriv(self, freq, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
@@ -492,7 +492,7 @@ class Problem_j(BaseFDEMProblem):
return A
def getADeriv_m(self, freq, u, v, adjoint=False):
def getADeriv(self, freq, u, v, adjoint=False):
"""
Product of the derivative of our system matrix with respect to the model and a vector
@@ -513,16 +513,16 @@ class Problem_j(BaseFDEMProblem):
MeMuI = self.MeMuI
MfRho = self.MfRho
C = self.mesh.edgeCurl
MfRhoDeriv_m = self.MfRhoDeriv(u)
MfRhoDeriv = self.MfRhoDeriv(u)
if adjoint:
if self._makeASymmetric is True:
v = MfRho * v
return MfRhoDeriv_m.T * (C * (MeMuI.T * (C.T * v)))
return MfRhoDeriv.T * (C * (MeMuI.T * (C.T * v)))
if self._makeASymmetric is True:
return MfRho.T * (C * ( MeMuI * (C.T * (MfRhoDeriv_m * v) )))
return C * (MeMuI * (C.T * (MfRhoDeriv_m * v)))
return MfRho.T * (C * ( MeMuI * (C.T * (MfRhoDeriv * v) )))
return C * (MeMuI * (C.T * (MfRhoDeriv * v)))
def getRHS(self, freq):
@@ -549,7 +549,7 @@ class Problem_j(BaseFDEMProblem):
return RHS
def getRHSDeriv_m(self, freq, src, v, adjoint=False):
def getRHSDeriv(self, freq, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
@@ -624,7 +624,7 @@ class Problem_h(BaseFDEMProblem):
return C.T * (MfRho * C) + 1j*omega(freq)*MeMu
def getADeriv_m(self, freq, u, v, adjoint=False):
def getADeriv(self, freq, u, v, adjoint=False):
"""
Product of the derivative of our system matrix with respect to the model and a vector
@@ -641,11 +641,11 @@ class Problem_h(BaseFDEMProblem):
MeMu = self.MeMu
C = self.mesh.edgeCurl
MfRhoDeriv_m = self.MfRhoDeriv(C*u)
MfRhoDeriv = self.MfRhoDeriv(C*u)
if adjoint:
return MfRhoDeriv_m.T * (C * v)
return C.T * (MfRhoDeriv_m * v)
return MfRhoDeriv.T * (C * v)
return C.T * (MfRhoDeriv * v)
def getRHS(self, freq):
"""
@@ -666,7 +666,7 @@ class Problem_h(BaseFDEMProblem):
return S_m + C.T * ( MfRho * S_e )
def getRHSDeriv_m(self, freq, src, v, adjoint=False):
def getRHSDeriv(self, freq, src, v, adjoint=False):
"""
Derivative of the right hand side with respect to the model
SimPEG/EM/FDEM/FieldsFDEM.py
+47 -47
View File
@@ -88,12 +88,12 @@ class Fields(SimPEG.Problem.Fields):
return self._jPrimary(solution, srcList) + self._jSecondary(solution, srcList)
def _eDeriv(self, src, du_dm, v, adjoint = False):
def _eDeriv(self, src, du_dm_v, v, adjoint = False):
"""
Total derivative of e with respect to the inversion model. Returns :math:`d\mathbf{e}/d\mathbf{m}` for forward and (:math:`d\mathbf{e}/d\mathbf{u}`, :math:`d\mathb{u}/d\mathbf{m}`) for the adjoint
:param Src src: sorce
:param numpy.ndarray du_dm: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
:param numpy.ndarray du_dm_v: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
:param numpy.ndarray v: vector to take sensitivity product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
@@ -104,14 +104,14 @@ class Fields(SimPEG.Problem.Fields):
if adjoint:
return self._eDeriv_u(src, v, adjoint), self._eDeriv_m(src, v, adjoint)
return self._eDeriv_u(src, du_dm, adjoint) + self._eDeriv_m(src, v, adjoint)
return self._eDeriv_u(src, du_dm_v, adjoint) + self._eDeriv_m(src, v, adjoint)
def _bDeriv(self, src, du_dm, v, adjoint = False):
def _bDeriv(self, src, du_dm_v, v, adjoint = False):
"""
Total derivative of b with respect to the inversion model. Returns :math:`d\mathbf{b}/d\mathbf{m}` for forward and (:math:`d\mathbf{b}/d\mathbf{u}`, :math:`d\mathb{u}/d\mathbf{m}`) for the adjoint
:param Src src: sorce
:param numpy.ndarray du_dm: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
:param numpy.ndarray du_dm_v: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
:param numpy.ndarray v: vector to take sensitivity product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
@@ -122,14 +122,14 @@ class Fields(SimPEG.Problem.Fields):
if adjoint:
return self._bDeriv_u(src, v, adjoint), self._bDeriv_m(src, v, adjoint)
return self._bDeriv_u(src, du_dm, adjoint) + self._bDeriv_m(src, v, adjoint)
return self._bDeriv_u(src, du_dm_v, adjoint) + self._bDeriv_m(src, v, adjoint)
def _hDeriv(self, src, du_dm, v, adjoint = False):
def _hDeriv(self, src, du_dm_v, v, adjoint = False):
"""
Total derivative of h with respect to the inversion model. Returns :math:`d\mathbf{h}/d\mathbf{m}` for forward and (:math:`d\mathbf{h}/d\mathbf{u}`, :math:`d\mathb{u}/d\mathbf{m}`) for the adjoint
:param Src src: sorce
:param numpy.ndarray du_dm: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
:param numpy.ndarray du_dm_v: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
:param numpy.ndarray v: vector to take sensitivity product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
@@ -140,14 +140,14 @@ class Fields(SimPEG.Problem.Fields):
if adjoint:
return self._hDeriv_u(src, v, adjoint), self._hDeriv_m(src, v, adjoint)
return self._hDeriv_u(src, du_dm, adjoint) + self._hDeriv_m(src, v, adjoint)
return self._hDeriv_u(src, du_dm_v, adjoint) + self._hDeriv_m(src, v, adjoint)
def _jDeriv(self, src, du_dm, v, adjoint = False):
def _jDeriv(self, src, du_dm_v, v, adjoint = False):
"""
Total derivative of j with respect to the inversion model. Returns :math:`d\mathbf{j}/d\mathbf{m}` for forward and (:math:`d\mathbf{j}/d\mathbf{u}`, :math:`d\mathb{u}/d\mathbf{m}`) for the adjoint
:param Src src: sorce
:param numpy.ndarray du_dm: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
:param numpy.ndarray du_dm_v: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
:param numpy.ndarray v: vector to take sensitivity product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
@@ -158,7 +158,7 @@ class Fields(SimPEG.Problem.Fields):
if adjoint:
return self._jDeriv_u(src, v, adjoint), self._jDeriv_m(src, v, adjoint)
return self._jDeriv_u(src, du_dm, adjoint) + self._jDeriv_m(src, v, adjoint)
return self._jDeriv_u(src, du_dm_v, adjoint) + self._jDeriv_m(src, v, adjoint)
class Fields_e(Fields):
@@ -277,12 +277,12 @@ class Fields_e(Fields):
b[:,i] = b[:,i]+ 1./(1j*omega(src.freq)) * S_m
return b
def _bSecondaryDeriv_u(self, src, du_dm, adjoint = False):
def _bSecondaryDeriv_u(self, src, du_dm_v, adjoint = False):
"""
Derivative of the secondary magnetic flux density with respect to the thing we solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray du_dm: vector to take product with
:param numpy.ndarray du_dm_v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the secondary magnetic flux density with respect to the field we solved for with a vector
@@ -290,8 +290,8 @@ class Fields_e(Fields):
C = self._edgeCurl
if adjoint:
return - 1./(1j*omega(src.freq)) * (C.T * du_dm)
return - 1./(1j*omega(src.freq)) * (C * du_dm)
return - 1./(1j*omega(src.freq)) * (C.T * du_dm_v)
return - 1./(1j*omega(src.freq)) * (C * du_dm_v)
def _bSecondaryDeriv_m(self, src, v, adjoint = False):
"""
@@ -308,18 +308,18 @@ class Fields_e(Fields):
return 1./(1j * omega(src.freq)) * S_mDeriv
def _bDeriv_u(self, src, du_dm, adjoint=False):
def _bDeriv_u(self, src, du_dm_v, adjoint=False):
"""
Partial derivative of the total magnetic flux density with respect to the thing we solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray du_dm: vector to take product with
:param numpy.ndarray du_dm_v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the magnetic flux density with respect to the field we solved for with a vector
"""
return self._bSecondaryDeriv_u(src, du_dm, adjoint)
return self._bSecondaryDeriv_u(src, du_dm_v, adjoint)
def _bDeriv_m(self, src, v, adjoint=False):
"""
@@ -393,19 +393,19 @@ class Fields_b(Fields):
return bSolution
def _bDeriv_u(self, src, du_dm, adjoint=False):
def _bDeriv_u(self, src, du_dm_v, adjoint=False):
"""
Partial derivative of the total magnetic flux density with respect to the thing we
solved for.
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray du_dm: vector to take product with
:param numpy.ndarray du_dm_v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the magnetic flux density with respect to the field we solved for with a vector
"""
return Identity()*du_dm
return Identity()*du_dm_v
def _bDeriv_m(self, src, v, adjoint=False):
"""
@@ -453,7 +453,7 @@ class Fields_b(Fields):
e[:,i] = e[:,i]+ -self._MeSigmaI * S_e
return e
def _eSecondaryDeriv_u(self, src, du_dm, adjoint=False):
def _eSecondaryDeriv_u(self, src, du_dm_v, adjoint=False):
"""
Derivative of the secondary electric field with respect to the thing we solved for
@@ -465,9 +465,9 @@ class Fields_b(Fields):
"""
if not adjoint:
return self._MeSigmaI * ( self._edgeCurl.T * ( self._MfMui * du_dm) )
return self._MeSigmaI * ( self._edgeCurl.T * ( self._MfMui * du_dm_v) )
else:
return self._MfMui.T * (self._edgeCurl * (self._MeSigmaI.T * du_dm))
return self._MfMui.T * (self._edgeCurl * (self._MeSigmaI.T * du_dm_v))
def _eSecondaryDeriv_m(self, src, v, adjoint=False):
"""
@@ -501,18 +501,18 @@ class Fields_b(Fields):
return de_dm
def _eDeriv_u(self, src, du_dm, adjoint=False):
def _eDeriv_u(self, src, du_dm_v, adjoint=False):
"""
Partial derivative of the total electric field with respect to the thing we solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray du_dm: vector to take product with
:param numpy.ndarray du_dm_v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the electric field with respect to the field we solved for with a vector
"""
return self._eSecondaryDeriv_u(src, du_dm, adjoint)
return self._eSecondaryDeriv_u(src, du_dm_v, adjoint)
def _eDeriv_m(self, src, v, adjoint=False):
"""
@@ -599,7 +599,7 @@ class Fields_j(Fields):
return self._jPrimary(jSolution, srcList) + self._jSecondary(jSolution, srcList)
def _jDeriv_u(self, src, du_dm, adjoint=False):
def _jDeriv_u(self, src, du_dm_v, adjoint=False):
"""
Partial derivative of the total current density with respect to the thing we
solved for.
@@ -611,7 +611,7 @@ class Fields_j(Fields):
:return: product of the derivative of the current density with respect to the field we solved for with a vector
"""
return Identity()*du_dm
return Identity()*du_dm_v
def _jDeriv_m(self, src, v, adjoint=False):
@@ -661,21 +661,21 @@ class Fields_j(Fields):
return h
def _hSecondaryDeriv_u(self, src, du_dm, adjoint=False):
def _hSecondaryDeriv_u(self, src, du_dm_v, adjoint=False):
"""
Derivative of the secondary magnetic field with respect to the thing we solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray du_dm: vector to take product with
:param numpy.ndarray du_dm_v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the secondary magnetic field with respect to the field we solved for with a vector
"""
if not adjoint:
return -1./(1j*omega(src.freq)) * self._MeMuI * (self._edgeCurl.T * (self._MfRho * du_dm) )
return -1./(1j*omega(src.freq)) * self._MeMuI * (self._edgeCurl.T * (self._MfRho * du_dm_v) )
elif adjoint:
return -1./(1j*omega(src.freq)) * self._MfRho.T * (self._edgeCurl * ( self._MeMuI.T * du_dm))
return -1./(1j*omega(src.freq)) * self._MfRho.T * (self._edgeCurl * ( self._MeMuI.T * du_dm_v))
def _hSecondaryDeriv_m(self, src, v, adjoint=False):
"""
@@ -711,18 +711,18 @@ class Fields_j(Fields):
return hDeriv_m
def _hDeriv_u(self, src, du_dm, adjoint=False):
def _hDeriv_u(self, src, du_dm_v, adjoint=False):
"""
Partial derivative of the total magnetic field with respect to the thing we solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray du_dm: vector to take product with
:param numpy.ndarray du_dm_v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the magnetic field with respect to the field we solved for with a vector
"""
return self._hSecondaryDeriv_u(src, du_dm, adjoint)
return self._hSecondaryDeriv_u(src, du_dm_v, adjoint)
def _hDeriv_m(self, src, v, adjoint=False):
"""
@@ -795,19 +795,19 @@ class Fields_h(Fields):
return hSolution
def _hDeriv_u(self, src, du_dm, adjoint=False):
def _hDeriv_u(self, src, du_dm_v, adjoint=False):
"""
Partial derivative of the total magnetic field with respect to the thing we
solved for.
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray du_dm: vector to take product with
:param numpy.ndarray du_dm_v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the magnetic field with respect to the field we solved for with a vector
"""
return Identity()*du_dm
return Identity()*du_dm_v
def _hDeriv_m(self, src, v, adjoint=False):
"""
@@ -855,21 +855,21 @@ class Fields_h(Fields):
j[:,i] = j[:,i]+ -S_e
return j
def _jSecondaryDeriv_u(self, src, du_dm, adjoint=False):
def _jSecondaryDeriv_u(self, src, du_dm_v, adjoint=False):
"""
Derivative of the secondary current density with respect to the thing we solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray du_dm: vector to take product with
:param numpy.ndarray du_dm_v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the secondary current density with respect to the field we solved for with a vector
"""
if not adjoint:
return self._edgeCurl*du_dm
return self._edgeCurl*du_dm_v
elif adjoint:
return self._edgeCurl.T*du_dm
return self._edgeCurl.T*du_dm_v
def _jSecondaryDeriv_m(self, src, v, adjoint=False):
"""
@@ -886,18 +886,18 @@ class Fields_h(Fields):
return -S_eDeriv
def _jDeriv_u(self, src, du_dm, adjoint=False):
def _jDeriv_u(self, src, du_dm_v, adjoint=False):
"""
Partial derivative of the total current density with respect to the thing we solved for
:param SimPEG.EM.FDEM.Src src: source
:param numpy.ndarray du_dm: vector to take product with
:param numpy.ndarray du_dm_v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: product of the derivative of the current density with respect to the field we solved for with a vector
"""
return self._jSecondaryDeriv_u(src,du_dm,adjoint)
return self._jSecondaryDeriv_u(src,du_dm_v,adjoint)
def _jDeriv_m(self, src, v, adjoint=False):
"""