Merge branch 'dcip/dev' of https://github.com/simpeg/simpeg into dcip/dev

.travis.yml

@@ -20,6 +20,7 @@ env:
     - TEST_DIR=tests/em/tdem
     - TEST_DIR=tests/dcip
     - TEST_DIR=tests/flow
+    - TEST_DIR=tests/mt
     - TEST_DIR=tests/examples
     - TEST_DIR=tests/em/fdem/inverse/adjoint
     - TEST_DIR=tests/em/fdem/forward
@@ -55,3 +56,5 @@ notifications:
   email:
     - rowanc1@gmail.com
     - lindseyheagy@gmail.com
+    - gkrosen@gmail.com
+    - sgkang09@gmail.com

SimPEG/Directives.py

@@ -237,53 +237,49 @@ class SaveOutputDictEveryIteration(_SaveEveryIteration):
         # Save the file as a npz
         np.savez('{:03d}-{:s}'.format(self.opt.iter,self.fileName), iter=self.opt.iter, beta=self.invProb.beta, phi_d=self.invProb.phi_d, phi_m=self.invProb.phi_m, phi_ms=phi_ms, phi_mx=phi_mx, phi_my=phi_my, phi_mz=phi_mz,f=self.opt.f, m=self.invProb.curModel,dpred=self.invProb.dpred)
 
+class SaveOutputDictEveryIteration(_SaveEveryIteration):
+    """SaveOutputDictEveryIteration
+    A directive that saves some relevant information from the inversion run to a numpy .npz dictionary file (see numpy.savez function for further info).
+    """
+
+    def initialize(self):
+        print "SimPEG.SaveOutputDictEveryIteration will save your inversion progress as dictionary: '%s-###.npz'"%self.fileName
+
+    def endIter(self):
+        # Save the data.
+        ms = self.reg.Ws * ( self.reg.mapping * (self.invProb.curModel - self.reg.mref) )
+        phi_ms = 0.5*ms.dot(ms)
+        if self.reg.smoothModel == True:
+            mref = self.reg.mref
+        else:
+            mref = 0
+        mx = self.reg.Wx * ( self.reg.mapping * (self.invProb.curModel - mref) )
+        phi_mx = 0.5 * mx.dot(mx)
+        if self.prob.mesh.dim==2:
+            my = self.reg.Wy * ( self.reg.mapping * (self.invProb.curModel - mref) )
+            phi_my = 0.5 * my.dot(my)
+        else:
+            phi_my = 'NaN'
+        if self.prob.mesh.dim==3 and 'CYL' not in self.prob.mesh._meshType:
+            mz = self.reg.Wz * ( self.reg.mapping * (self.invProb.curModel - mref) )
+            phi_mz = 0.5 * mz.dot(mz)
+        else:
+            phi_mz = 'NaN'
 
 
-class update_IRLS(InversionDirective):
+        # Save the file as a npz
-
+        np.savez('{:s}-{:03d}'.format(self.fileName,self.opt.iter), iter=self.opt.iter, beta=self.invProb.beta, phi_d=self.invProb.phi_d, phi_m=self.invProb.phi_m, phi_ms=phi_ms, phi_mx=phi_mx, phi_my=phi_my, phi_mz=phi_mz,f=self.opt.f, m=self.invProb.curModel,dpred=self.invProb.dpred)
-     m = None
-     eps_min = None
-     factor = None
-     gamma = None
-     phi_m_last = None
-     
-     def initialize(self):
-        
-         # Scale the regularization for changes in norm
-         if getattr(self, 'phi_m_last', None) is not None:
-             self.reg.gamma = 1.
-             phim_new = self.reg.eval(self.invProb.curModel)
-             self.gamma = self.phi_m_last / phim_new
-         
-         self.reg.gamma = self.gamma
-         
-     def endIter(self):
-         # Cool the threshold parameter 
-         if getattr(self, 'factor', None) is not None:
-             eps = self.reg.eps / self.factor
-             
-             if getattr(self, 'eps_min', None) is not None:
-                 self.reg.eps = np.max([self.eps_min,eps])
-             else:
-                 self.reg.eps = eps
 
 
-         # Update the model used for the IRLS weights
-         if getattr(self, 'm', None) is None:
-             self.reg.m = self.invProb.curModel
 
-         # Update the pre-conditioner
+# class UpdateReferenceModel(Parameter):
-         diagA = np.sum(self.prob.G**2.,axis=0) + self.invProb.beta*(self.reg.W.T*self.reg.W).diagonal() * (self.reg.mapping * np.ones(self.prob.mesh.nC))**2.
-         PC     = Utils.sdiag(diagA**-1.)
 
-         self.opt.approxHinv = PC
+#     mref0 = None
 
-         phim_new = self.reg.eval(self.invProb.curModel)
+#     def nextIter(self):
-         self.reg.gamma = self.reg.gamma * self.invProb.phi_m_last / phim_new
+#         mref = getattr(self, 'm_prev', None)
-
+#         if mref is None:
-#==============================================================================
+#             if self.debug: print 'UpdateReferenceModel is using mref0'
-#          import pylab as plt
+#             mref = self.mref0
-#          plt.figure()
+#         self.m_prev = self.invProb.m_current
-#          ax = plt.subplot(221)
+#         return mref
-#          self.prob.mesh.plotSlice(self.invProb.curModel, ax = ax, normal = 'Z', ind=-5, clim = (0, 0.005))
-#==============================================================================

SimPEG/EM/FDEM/FDEM.py

@@ -15,18 +15,20 @@ class BaseFDEMProblem(BaseEMProblem):
         .. math ::
 
             \mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} \\\\
-            {\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{M_{\sigma}^e} \mathbf{e} = \mathbf{M^e} \mathbf{s_e}}
+            {\mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{M_{\sigma}^e} \mathbf{e} = \mathbf{s_e}}
 
         if using the E-B formulation (:code:`Problem_e`
-        or :code:`Problem_b`) or the magnetic field
+        or :code:`Problem_b`). Note that in this case, :math:`\mathbf{s_e}` is an integrated quantity. 
+
+        If we write Maxwell's equations in terms of 
         \\\(\\\mathbf{h}\\\) and current density \\\(\\\mathbf{j}\\\)
 
         .. math ::
 
-            \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{j} + i \omega \mathbf{M_{\mu}^e} \mathbf{h} = \mathbf{M^e} \mathbf{s_m} \\\\
+            \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{j} + i \omega \mathbf{M_{\mu}^e} \mathbf{h} = \mathbf{s_m} \\\\
             \mathbf{C} \mathbf{h} - \mathbf{j} = \mathbf{s_e}
 
-        if using the H-J formulation (:code:`Problem_j` or :code:`Problem_h`).
+        if using the H-J formulation (:code:`Problem_j` or :code:`Problem_h`). Note that here, :math:`\mathbf{s_m}` is an integrated quantity. 
 
         The problem performs the elimination so that we are solving the system for \\\(\\\mathbf{e},\\\mathbf{b},\\\mathbf{j} \\\) or \\\(\\\mathbf{h}\\\)
     """
@@ -36,7 +38,11 @@ class BaseFDEMProblem(BaseEMProblem):
 
     def fields(self, m=None):
         """
-            Solve the forward problem for the fields.
+        Solve the forward problem for the fields.
+        
+        :param numpy.array m: inversion model (nP,)
+        :rtype numpy.array:
+        :return F: forward solution
         """
 
         self.curModel = m
@@ -55,7 +61,13 @@ class BaseFDEMProblem(BaseEMProblem):
 
     def Jvec(self, m, v, u=None):
         """
-            Sensitivity times a vector
+        Sensitivity times a vector.
+
+        :param numpy.array m: inversion model (nP,)
+        :param numpy.array v: vector which we take sensitivity product with (nP,)
+        :param SimPEG.EM.FDEM.Fields u: fields object 
+        :rtype numpy.array:
+        :return: Jv (ndata,) 
         """
 
         if u is None:
@@ -83,6 +95,7 @@ class BaseFDEMProblem(BaseEMProblem):
                     df_dmFun = getattr(u, '_%sDeriv_m'%rx.projField, None)
                     df_dm = df_dmFun(src, v, adjoint=False)
 
+
                     Df_Dm = np.array(df_dudu_dm + df_dm,dtype=complex)
 
                     P = lambda v: rx.projectFieldsDeriv(src, self.mesh, u, v) # wrt u, also have wrt m
@@ -94,7 +107,13 @@ class BaseFDEMProblem(BaseEMProblem):
 
     def Jtvec(self, m, v, u=None):
         """
-            Sensitivity transpose times a vector
+        Sensitivity transpose times a vector
+
+        :param numpy.array m: inversion model (nP,)
+        :param numpy.array v: vector which we take adjoint product with (nP,)
+        :param SimPEG.EM.FDEM.Fields u: fields object 
+        :rtype numpy.array:
+        :return: Jv (ndata,) 
         """
 
         if u is None:
@@ -133,6 +152,7 @@ class BaseFDEMProblem(BaseEMProblem):
 
                     du_dmT += dfT_dm
 
+                    # TODO: this should be taken care of by the reciever
                     real_or_imag = rx.projComp
                     if real_or_imag is 'real':
                         Jtv +=   np.array(du_dmT,dtype=complex).real
@@ -147,11 +167,11 @@ class BaseFDEMProblem(BaseEMProblem):
 
     def getSourceTerm(self, freq):
         """
-            Evaluates the sources for a given frequency and puts them in matrix form
+        Evaluates the sources for a given frequency and puts them in matrix form
 
-            :param float freq: Frequency
+        :param float freq: Frequency
-            :rtype: numpy.ndarray (nE or nF, nSrc)
+        :rtype: (numpy.ndarray, numpy.ndarray)  
-            :return: S_m, S_e
+        :return: S_m, S_e (nE or nF, nSrc)
         """
         Srcs = self.survey.getSrcByFreq(freq)
         if self._eqLocs is 'FE':
@@ -175,20 +195,22 @@ class BaseFDEMProblem(BaseEMProblem):
 
 class Problem_e(BaseFDEMProblem):
     """
-        By eliminating the magnetic flux density using
+    By eliminating the magnetic flux density using
-
-            .. math ::
-
-                \mathbf{b} = \\frac{1}{i \omega}\\left(-\mathbf{C} \mathbf{e} + \mathbf{s_m}\\right)
-
-
-        we can write Maxwell's equations as a second order system in \\\(\\\mathbf{e}\\\) only:
 
         .. math ::
 
-            \\left(\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{C}+ i \omega \mathbf{M^e_{\sigma}} \\right)\mathbf{e} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M^e}\mathbf{s_e}
+            \mathbf{b} = \\frac{1}{i \omega}\\left(-\mathbf{C} \mathbf{e} + \mathbf{s_m}\\right)
 
-        which we solve for \\\(\\\mathbf{e}\\\).
+
+    we can write Maxwell's equations as a second order system in \\\(\\\mathbf{e}\\\) only:
+
+    .. math ::
+
+        \\left(\mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{C}+ i \omega \mathbf{M^e_{\sigma}} \\right)\mathbf{e} = \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M^e}\mathbf{s_e}
+
+    which we solve for :math:`\mathbf{e}`.
+
+    :param SimPEG.Mesh mesh: mesh
     """
 
     _fieldType = 'e'
@@ -200,13 +222,16 @@ class Problem_e(BaseFDEMProblem):
 
     def getA(self, freq):
         """
-            .. math ::
+        System matrix
-                \mathbf{A} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{C} + i \omega \mathbf{M^e_{\sigma}}
         
-            :param float freq: Frequency
+        .. math ::
-            :rtype: scipy.sparse.csr_matrix
+            \mathbf{A} = \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{C} + i \omega \mathbf{M^e_{\sigma}}
-            :return: A
+
+        :param float freq: Frequency
+        :rtype: scipy.sparse.csr_matrix
+        :return: A
         """
+
         MfMui = self.MfMui
         MeSigma = self.MeSigma
         C = self.mesh.edgeCurl
@@ -215,6 +240,20 @@ class Problem_e(BaseFDEMProblem):
 
 
     def getADeriv_m(self, freq, u, v, adjoint=False):
+        """
+        Product of the derivative of our system matrix with respect to the model and a vector
+
+        .. math ::
+            \\frac{\mathbf{A}(\mathbf{m}) \mathbf{v}}{d \mathbf{m}} = i \omega \\frac{d \mathbf{M^e_{\sigma}}\mathbf{v} }{d\mathbf{m}}
+
+        :param float freq: frequency 
+        :param numpy.ndarray u: solution vector (nE,) 
+        :param numpy.ndarray v: vector to take prodct with (nP,) or (nD,) for adjoint
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: derivative of the system matrix times a vector (nP,) or adjoint (nD,) 
+        """
+
         dsig_dm = self.curModel.sigmaDeriv
         dMe_dsig = self.MeSigmaDeriv(u)
 
@@ -225,26 +264,37 @@ class Problem_e(BaseFDEMProblem):
 
     def getRHS(self, freq):
         """
-            .. math ::
+        Right hand side for the system 
-                \mathbf{RHS} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M_e}\mathbf{s_e}
 
-            :param float freq: Frequency
+        .. math ::
-            :rtype: numpy.ndarray (nE, nSrc)
+            \mathbf{RHS} = \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M_e}\mathbf{s_e}
-            :return: RHS
+
+        :param float freq: Frequency
+        :rtype: numpy.ndarray 
+        :return: RHS (nE, nSrc)
         """
 
         S_m, S_e = self.getSourceTerm(freq)
         C = self.mesh.edgeCurl
         MfMui = self.MfMui
 
-        RHS = C.T * (MfMui * S_m) -1j * omega(freq) * S_e
+        return C.T * (MfMui * S_m) -1j * omega(freq) * S_e
-
-        return RHS
 
     def getRHSDeriv_m(self, freq, src, v, adjoint=False):
+        """
+        Derivative of the right hand side with respect to the model 
+
+        :param float freq: frequency
+        :param SimPEG.EM.FDEM.Src src: FDEM source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: product of rhs deriv with a vector
+        """
+
         C = self.mesh.edgeCurl
         MfMui = self.MfMui
-        S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint)
+        S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint=adjoint)
 
         if adjoint:
             dRHS = MfMui * (C * v)
@@ -256,20 +306,22 @@ class Problem_e(BaseFDEMProblem):
 
 class Problem_b(BaseFDEMProblem):
     """
-        We eliminate \\\(\\\mathbf{e}\\\) using
+    We eliminate :math:`\mathbf{e}` using
 
-        .. math ::
+    .. math ::
 
-             \mathbf{e} = \mathbf{M^e_{\sigma}}^{-1} \\left(\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{s_e}\\right)
+         \mathbf{e} = \mathbf{M^e_{\sigma}}^{-1} \\left(\mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{s_e}\\right)
 
-        and solve for \\\(\\\mathbf{b}\\\) using:
+    and solve for :math:`\mathbf{b}` using:
 
-        .. math ::
+    .. math ::
 
-            \\left(\mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}  + i \omega \\right)\mathbf{b} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{M^e}\mathbf{s_e}
+        \\left(\mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f}  + i \omega \\right)\mathbf{b} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{M^e}\mathbf{s_e}
 
-        .. note ::
+    .. note ::
-            The inverse problem will not work with full anisotropy
+        The inverse problem will not work with full anisotropy
+
+    :param SimPEG.Mesh mesh: mesh
     """
 
     _fieldType = 'b'
@@ -281,12 +333,14 @@ class Problem_b(BaseFDEMProblem):
 
     def getA(self, freq):
         """
-            .. math ::
+        System matrix
-                \mathbf{A} = \mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}  + i \omega
 
-            :param float freq: Frequency
+        .. math ::
-            :rtype: scipy.sparse.csr_matrix
+            \mathbf{A} = \mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f}  + i \omega
-            :return: A
+
+        :param float freq: Frequency
+        :rtype: scipy.sparse.csr_matrix
+        :return: A
         """
 
         MfMui = self.MfMui
@@ -302,6 +356,20 @@ class Problem_b(BaseFDEMProblem):
 
     def getADeriv_m(self, freq, u, v, adjoint=False):
 
+        """
+        Product of the derivative of our system matrix with respect to the model and a vector
+
+        .. math ::
+            \\frac{\mathbf{A}(\mathbf{m}) \mathbf{v}}{d \mathbf{m}} = \mathbf{C} \\frac{\mathbf{M^e_{\sigma}} \mathbf{v}}{d\mathbf{m}}
+
+        :param float freq: frequency 
+        :param numpy.ndarray u: solution vector (nF,) 
+        :param numpy.ndarray v: vector to take prodct with (nP,) or (nD,) for adjoint
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: derivative of the system matrix times a vector (nP,) or adjoint (nD,)  
+        """
+
         MfMui = self.MfMui
         C = self.mesh.edgeCurl
         MeSigmaIDeriv = self.MeSigmaIDeriv
@@ -321,12 +389,14 @@ class Problem_b(BaseFDEMProblem):
 
     def getRHS(self, freq):
         """
-            .. math ::
+        Right hand side for the system 
-                \mathbf{RHS} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{s_e}
 
-            :param float freq: Frequency
+        .. math ::
-            :rtype: numpy.ndarray (nE, nSrc)
+            \mathbf{RHS} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{s_e}
-            :return: RHS
+
+        :param float freq: Frequency
+        :rtype: numpy.ndarray 
+        :return: RHS (nE, nSrc)
         """
 
         S_m, S_e = self.getSourceTerm(freq)
@@ -342,6 +412,17 @@ class Problem_b(BaseFDEMProblem):
         return RHS
 
     def getRHSDeriv_m(self, freq, src, v, adjoint=False):
+        """
+        Derivative of the right hand side with respect to the model
+
+        :param float freq: frequency
+        :param SimPEG.EM.FDEM.Src src: FDEM source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: product of rhs deriv with a vector
+        """
+
         C = self.mesh.edgeCurl
         S_m, S_e = src.eval(self)
         MfMui = self.MfMui
@@ -350,7 +431,7 @@ class Problem_b(BaseFDEMProblem):
             v = self.MfMui * v
 
         MeSigmaIDeriv = self.MeSigmaIDeriv(S_e)
-        S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint)
+        S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint=adjoint)
 
         if not adjoint:
             RHSderiv = C * (MeSigmaIDeriv * v)
@@ -373,21 +454,22 @@ class Problem_b(BaseFDEMProblem):
 
 class Problem_j(BaseFDEMProblem):
     """
-        We eliminate \\\(\\\mathbf{h}\\\) using
+    We eliminate \\\(\\\mathbf{h}\\\) using
 
-        .. math ::
+    .. math ::
 
-            \mathbf{h} = \\frac{1}{i \omega} \mathbf{M_{\mu}^e}^{-1} \\left(-\mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{j}  + \mathbf{M^e} \mathbf{s_m} \\right)
+        \mathbf{h} = \\frac{1}{i \omega} \mathbf{M_{\mu}^e}^{-1} \\left(-\mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{j}  + \mathbf{M^e} \mathbf{s_m} \\right)
 
-        and solve for \\\(\\\mathbf{j}\\\) using
+    and solve for \\\(\\\mathbf{j}\\\) using
 
-        .. math ::
+    .. math ::
 
-            \\left(\mathbf{C} \mathbf{M_{\mu}^e}^{-1} \mathbf{C}^T \mathbf{M_{\\rho}^f} + i \omega\\right)\mathbf{j} = \mathbf{C} \mathbf{M_{\mu}^e}^{-1} \mathbf{M^e} \mathbf{s_m} -i\omega\mathbf{s_e}
+        \\left(\mathbf{C} \mathbf{M_{\mu}^e}^{-1} \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} + i \omega\\right)\mathbf{j} = \mathbf{C} \mathbf{M_{\mu}^e}^{-1} \mathbf{M^e} \mathbf{s_m} -i\omega\mathbf{s_e}
 
-        .. note::
+    .. note::
-            This implementation does not yet work with full anisotropy!!
+        This implementation does not yet work with full anisotropy!!
 
+    :param SimPEG.Mesh mesh: mesh
     """
 
     _fieldType = 'j'
@@ -399,12 +481,14 @@ class Problem_j(BaseFDEMProblem):
 
     def getA(self, freq):
         """
-            .. math ::
+        System matrix
-                    \\mathbf{A} = \\mathbf{C}  \\mathbf{M^e_{mu^{-1}}} \\mathbf{C}^T \\mathbf{M^f_{\\sigma^{-1}}}  + i\\omega
 
-            :param float freq: Frequency
+        .. math ::
-            :rtype: scipy.sparse.csr_matrix
+                \\mathbf{A} = \\mathbf{C}  \\mathbf{M^e_{\\mu^{-1}}} \\mathbf{C}^{\\top} \\mathbf{M^f_{\\sigma^{-1}}}  + i\\omega
-            :return: A
+
+        :param float freq: Frequency
+        :rtype: scipy.sparse.csr_matrix
+        :return: A
         """
 
         MeMuI = self.MeMuI
@@ -421,12 +505,20 @@ class Problem_j(BaseFDEMProblem):
 
     def getADeriv_m(self, freq, u, v, adjoint=False):
         """
-            In this case, we assume that electrical conductivity, \\\(\\\sigma\\\) is the physical property of interest (i.e. \\\(\\\sigma\\\) = model.transform). Then we want
+        Product of the derivative of our system matrix with respect to the model and a vector
 
-            .. math ::
+        In this case, we assume that electrical conductivity, :math:`\sigma` is the physical property of interest (i.e. :math:`\sigma` = model.transform). Then we want
 
-                \\frac{\mathbf{A(\sigma)} \mathbf{v}}{d \\mathbf{m}} &= \\mathbf{C}  \\mathbf{M^e_{mu^{-1}}} \\mathbf{C^T} \\frac{d \\mathbf{M^f_{\\sigma^{-1}}}}{d \\mathbf{m}}
+        .. math ::
-                &= \\mathbf{C}  \\mathbf{M^e_{mu}^{-1}} \\mathbf{C^T} \\frac{d \\mathbf{M^f_{\\sigma^{-1}}}}{d \\mathbf{\\sigma^{-1}}} \\frac{d \\mathbf{\\sigma^{-1}}}{d \\mathbf{\\sigma}} \\frac{d \\mathbf{\\sigma}}{d \\mathbf{m}}
+
+            \\frac{\mathbf{A(\sigma)} \mathbf{v}}{d \mathbf{m}} = \mathbf{C}  \mathbf{M^e_{mu^{-1}}} \mathbf{C^{\\top}} \\frac{d \mathbf{M^f_{\sigma^{-1}}}\mathbf{v} }{d \mathbf{m}}
+
+        :param float freq: frequency 
+        :param numpy.ndarray u: solution vector (nF,) 
+        :param numpy.ndarray v: vector to take prodct with (nP,) or (nD,) for adjoint
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: derivative of the system matrix times a vector (nP,) or adjoint (nD,)  
         """
 
         MeMuI = self.MeMuI
@@ -446,12 +538,15 @@ class Problem_j(BaseFDEMProblem):
 
     def getRHS(self, freq):
         """
-            .. math ::
+        Right hand side for the system 
 
-                \mathbf{RHS} = \mathbf{C} \mathbf{M_{\mu}^e}^{-1}\mathbf{s_m} -i\omega \mathbf{s_e}
+        .. math ::
-            :param float freq: Frequency
+
-            :rtype: numpy.ndarray (nE, nSrc)
+            \mathbf{RHS} = \mathbf{C} \mathbf{M_{\mu}^e}^{-1}\mathbf{s_m} -i\omega \mathbf{s_e}
-            :return: RHS
+
+        :param float freq: Frequency
+        :rtype: numpy.ndarray (nE, nSrc)
+        :return: RHS
         """
 
         S_m, S_e = self.getSourceTerm(freq)
@@ -466,9 +561,20 @@ class Problem_j(BaseFDEMProblem):
         return RHS
 
     def getRHSDeriv_m(self, freq, src, v, adjoint=False):
+        """
+        Derivative of the right hand side with respect to the model 
+
+        :param float freq: frequency
+        :param SimPEG.EM.FDEM.Src src: FDEM source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: product of rhs deriv with a vector
+        """
+
         C = self.mesh.edgeCurl
         MeMuI = self.MeMuI
-        S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint)
+        S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint=adjoint)
 
         if adjoint:
             if self._makeASymmetric:
@@ -489,18 +595,19 @@ class Problem_j(BaseFDEMProblem):
 
 class Problem_h(BaseFDEMProblem):
     """
-        We eliminate \\\(\\\mathbf{j}\\\) using
+    We eliminate \\\(\\\mathbf{j}\\\) using
 
-        .. math ::
+    .. math ::
 
-            \mathbf{j} = \mathbf{C} \mathbf{h} - \mathbf{s_e}
+        \mathbf{j} = \mathbf{C} \mathbf{h} - \mathbf{s_e}
 
-        and solve for \\\(\\\mathbf{h}\\\) using
+    and solve for \\\(\\\mathbf{h}\\\) using
 
-        .. math ::
+    .. math ::
 
-            \\left(\mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}\\right) \mathbf{h} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{s_e}
+        \\left(\mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}\\right) \mathbf{h} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{s_e}
 
+    :param SimPEG.Mesh mesh: mesh
     """
 
     _fieldType = 'h'
@@ -512,13 +619,14 @@ class Problem_h(BaseFDEMProblem):
 
     def getA(self, freq):
         """
-            .. math ::
+        System matrix
 
-                \mathbf{A} = \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}
+        .. math::
+            \mathbf{A} = \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}
 
-            :param float freq: Frequency
+        :param float freq: Frequency
-            :rtype: scipy.sparse.csr_matrix
+        :rtype: scipy.sparse.csr_matrix
-            :return: A
+        :return: A
         """
 
         MeMu = self.MeMu
@@ -528,6 +636,19 @@ class Problem_h(BaseFDEMProblem):
         return C.T * (MfRho * C) + 1j*omega(freq)*MeMu
 
     def getADeriv_m(self, freq, u, v, adjoint=False):
+        """
+        Product of the derivative of our system matrix with respect to the model and a vector
+
+        .. math::
+            \\frac{\mathbf{A}(\mathbf{m}) \mathbf{v}}{d \mathbf{m}} = \mathbf{C}^{\\top}\\frac{d \mathbf{M^f_{\\rho}}\mathbf{v} }{d\mathbf{m}}
+
+        :param float freq: frequency 
+        :param numpy.ndarray u: solution vector (nE,) 
+        :param numpy.ndarray v: vector to take prodct with (nP,) or (nD,) for adjoint
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: derivative of the system matrix times a vector (nP,) or adjoint (nD,)  
+        """
 
         MeMu = self.MeMu
         C = self.mesh.edgeCurl
@@ -539,24 +660,35 @@ class Problem_h(BaseFDEMProblem):
 
     def getRHS(self, freq):
         """
-            .. math ::
+        Right hand side for the system 
 
-                \mathbf{RHS} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{s_e}
+        .. math ::
 
-            :param float freq: Frequency
+            \mathbf{RHS} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{s_e}
-            :rtype: numpy.ndarray (nE, nSrc)
+
-            :return: RHS
+        :param float freq: Frequency
+        :rtype: numpy.ndarray 
+        :return: RHS (nE, nSrc)
         """
 
         S_m, S_e = self.getSourceTerm(freq)
         C = self.mesh.edgeCurl
         MfRho  = self.MfRho
 
-        RHS = S_m + C.T * ( MfRho * S_e )
+        return S_m + C.T * ( MfRho * S_e )
-
-        return RHS
 
     def getRHSDeriv_m(self, freq, src, v, adjoint=False):
+        """
+        Derivative of the right hand side with respect to the model 
+
+        :param float freq: frequency
+        :param SimPEG.EM.FDEM.Src src: FDEM source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: product of rhs deriv with a vector
+        """
+
         _, S_e = src.eval(self)
         C = self.mesh.edgeCurl
         MfRho  = self.MfRho
@@ -567,7 +699,7 @@ class Problem_h(BaseFDEMProblem):
         elif adjoint:
             RHSDeriv = MfRhoDeriv.T * (C * v)
 
-        S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint)
+        S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint=adjoint)
 
         return RHSDeriv + S_mDeriv(v) + C.T * (MfRho * S_eDeriv(v))
 

SimPEG/EM/FDEM/FieldsFDEM.py

@@ -7,11 +7,39 @@ from SimPEG.Utils import Zero, Identity
 
 
 class Fields(SimPEG.Problem.Fields):
-    """Fancy Field Storage for a FDEM survey."""
+    """
+    
+    Fancy Field Storage for a FDEM survey. Only one field type is stored for
+    each problem, the rest are computed. The fields obejct acts like an array and is indexed by
+
+    .. code-block:: python
+
+        f = problem.fields(m)
+        e = f[srcList,'e']
+        b = f[srcList,'b']
+
+    If accessing all sources for a given field, use the :code:`:`
+
+    .. code-block:: python
+
+        f = problem.fields(m)
+        e = f[:,'e']
+        b = f[:,'b']
+
+    The array returned will be size (nE or nF, nSrcs :math:`\\times` nFrequencies)
+    """
+
     knownFields = {}
     dtype = complex
 
 class Fields_e(Fields):
+    """
+    Fields object for Problem_e. 
+
+    :param Mesh mesh: mesh
+    :param Survey survey: survey 
+    """
+
     knownFields = {'eSolution':'E'}
     aliasFields = {
                     'e' : ['eSolution','E','_e'],
@@ -30,6 +58,15 @@ class Fields_e(Fields):
         self._edgeCurl = self.survey.prob.mesh.edgeCurl
 
     def _ePrimary(self, eSolution, srcList):
+        """
+        Primary electric field from source
+
+        :param numpy.ndarray eSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: primary electric field as defined by the sources
+        """
+
         ePrimary = np.zeros_like(eSolution)
         for i, src in enumerate(srcList):
             ep = src.ePrimary(self.prob)
@@ -37,19 +74,67 @@ class Fields_e(Fields):
         return ePrimary
 
     def _eSecondary(self, eSolution, srcList):
+        """
+        Secondary electric field is the thing we solved for
+
+        :param numpy.ndarray eSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: secondary electric field
+        """
+
         return eSolution
 
     def _e(self, eSolution, srcList):
+        """
+        Total electric field is sum of primary and secondary 
+        
+        :param numpy.ndarray eSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: total electric field
+        """
+
         return self._ePrimary(eSolution,srcList) + self._eSecondary(eSolution,srcList)
 
     def _eDeriv_u(self, src, v, adjoint = False):
+        """
+        Derivative of the total electric field with respect to the thing we 
+        solved for
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray 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 Identity()*v
 
     def _eDeriv_m(self, src, v, adjoint = False):
+        """
+        Derivative of the total electric field with respect to the inversion model. Here, we assume that the primary does not depend on the model. 
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: SimPEG.Utils.Zero
+        :return: product of the electric field derivative with respect to the inversion model with a vector
+        """
+
         # assuming primary does not depend on the model
         return Zero()
 
     def _bPrimary(self, eSolution, srcList):
+        """
+        Primary magnetic flux density from source
+
+        :param numpy.ndarray eSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: primary magnetic flux density as defined by the sources
+        """
+
         bPrimary = np.zeros([self._edgeCurl.shape[0],eSolution.shape[1]],dtype = complex)
         for i, src in enumerate(srcList):
             bp = src.bPrimary(self.prob)
@@ -57,6 +142,15 @@ class Fields_e(Fields):
         return bPrimary
 
     def _bSecondary(self, eSolution, srcList):
+        """
+        Secondary magnetic flux density from eSolution
+
+        :param numpy.ndarray eSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: secondary magnetic flux density
+        """
+
         C = self._edgeCurl
         b = (C * eSolution)
         for i, src in enumerate(srcList):
@@ -66,29 +160,84 @@ class Fields_e(Fields):
         return b
 
     def _bSecondaryDeriv_u(self, src, 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 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
+        """
+
         C = self._edgeCurl
         if adjoint:
             return - 1./(1j*omega(src.freq)) * (C.T * v)
         return - 1./(1j*omega(src.freq)) * (C * v)
 
     def _bSecondaryDeriv_m(self, src, v, adjoint = False):
-        S_mDeriv, _ = src.evalDeriv(self.prob, adjoint)
+        """
-        S_mDeriv = S_mDeriv(v)
+        Derivative of the secondary magnetic flux density with respect to the inversion model. 
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: product of the secondary magnetic flux density derivative with respect to the inversion model with a vector
+        """
+
+        S_mDeriv, _ = src.evalDeriv(self.prob, v, adjoint)
         return 1./(1j * omega(src.freq)) * S_mDeriv
 
     def _b(self, eSolution, srcList):
+        """
+        Total magnetic flux density is sum of primary and secondary 
+        
+        :param numpy.ndarray eSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: total magnetic flux density 
+        """
+
         return self._bPrimary(eSolution, srcList) + self._bSecondary(eSolution, srcList)
 
     def _bDeriv_u(self, src, v, adjoint=False):
+        """
+        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 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
+        """
+
         # Primary does not depend on u
         return self._bSecondaryDeriv_u(src, v, adjoint)
 
     def _bDeriv_m(self, src, v, adjoint=False):
+        """
+        Derivative of the total magnetic flux density with respect to the inversion model. 
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: SimPEG.Utils.Zero
+        :return: product of the magnetic flux density derivative with respect to the inversion model with a vector
+        """
+
         # Assuming the primary does not depend on the model
         return self._bSecondaryDeriv_m(src, v, adjoint)
 
 
 class Fields_b(Fields):
+    """
+    Fields object for Problem_b. 
+
+    :param Mesh mesh: mesh
+    :param Survey survey: survey 
+    """
+
     knownFields = {'bSolution':'F'}
     aliasFields = {
                     'b' : ['bSolution','F','_b'],
@@ -111,6 +260,15 @@ class Fields_b(Fields):
         self._Me = self.survey.prob.Me
 
     def _bPrimary(self, bSolution, srcList):
+        """
+        Primary magnetic flux density from source
+
+        :param numpy.ndarray bSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: primary electric field as defined by the sources
+        """
+
         bPrimary = np.zeros_like(bSolution)
         for i, src in enumerate(srcList):
             bp = src.bPrimary(self.prob)
@@ -118,19 +276,66 @@ class Fields_b(Fields):
         return bPrimary
 
     def _bSecondary(self, bSolution, srcList):
+        """
+        Secondary magnetic flux density is the thing we solved for
+
+        :param numpy.ndarray bSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: secondary magnetic flux density
+        """
+
         return bSolution
 
     def _b(self, bSolution, srcList):
+        """
+        Total magnetic flux density is sum of primary and secondary 
+        
+        :param numpy.ndarray bSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: total magnetic flux density 
+        """
+
         return self._bPrimary(bSolution, srcList) + self._bSecondary(bSolution, srcList)
 
     def _bDeriv_u(self, src, v, adjoint=False):
+        """
+        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 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()*v
 
     def _bDeriv_m(self, src, v, adjoint=False):
+        """
+        Derivative of the total magnetic flux density with respect to the inversion model. Here, we assume that the primary does not depend on the model. 
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: SimPEG.Utils.Zero
+        :return: product of the magnetic flux density derivative with respect to the inversion model with a vector
+        """
+
         # assuming primary does not depend on the model
         return Zero()
 
     def _ePrimary(self, bSolution, srcList):
+        """
+        Primary electric field from source
+
+        :param numpy.ndarray bSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: primary electric field as defined by the sources
+        """
+
         ePrimary = np.zeros([self._edgeCurl.shape[1],bSolution.shape[1]],dtype = complex)
         for i,src in enumerate(srcList):
             ep = src.ePrimary(self.prob)
@@ -138,6 +343,15 @@ class Fields_b(Fields):
         return ePrimary
 
     def _eSecondary(self, bSolution, srcList):
+        """
+        Secondary electric field from bSolution
+
+        :param numpy.ndarray bSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: secondary electric field
+        """
+
         e = self._MeSigmaI * ( self._edgeCurl.T * ( self._MfMui * bSolution))
         for i,src in enumerate(srcList):
             _,S_e = src.eval(self.prob)
@@ -145,12 +359,32 @@ class Fields_b(Fields):
         return e
 
     def _eSecondaryDeriv_u(self, src, v, adjoint=False):
+        """
+        Derivative of the secondary electric field with respect to the thing we solved for
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: product of the derivative of the secondary electric field with respect to the field we solved for with a vector
+        """
+
         if not adjoint:
             return self._MeSigmaI * ( self._edgeCurl.T * ( self._MfMui * v) )
         else:
             return self._MfMui.T * (self._edgeCurl * (self._MeSigmaI.T * v))
 
     def _eSecondaryDeriv_m(self, src, v, adjoint=False):
+        """
+        Derivative of the secondary electric field with respect to the inversion model 
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: product of the derivative of the secondary electric field with respect to the model with a vector
+        """
+
         bSolution = self[[src],'bSolution']
         _,S_e = src.eval(self.prob)
         Me = self._Me
@@ -166,25 +400,60 @@ class Fields_b(Fields):
         elif adjoint:
             de_dm = self._MeSigmaIDeriv(w).T * v
 
-        _, S_eDeriv = src.evalDeriv(self.prob, adjoint)
+        _, S_eDeriv = src.evalDeriv(self.prob, v, adjoint)
-        Se_Deriv = S_eDeriv(v)
 
-        de_dm = de_dm - self._MeSigmaI * Se_Deriv
+        de_dm = de_dm - self._MeSigmaI * S_eDeriv
 
         return de_dm
 
     def _e(self, bSolution, srcList):
+        """
+        Total electric field is sum of primary and secondary 
+        
+        :param numpy.ndarray eSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: total electric field
+        """
+
         return self._ePrimary(bSolution, srcList) + self._eSecondary(bSolution, srcList)
 
     def _eDeriv_u(self, src, v, adjoint=False):
+        """
+        Derivative of the total electric field with respect to the thing we solved for 
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray 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, v, adjoint)
 
     def _eDeriv_m(self, src, v, adjoint=False):
+        """
+        Derivative of the total electric field density with respect to the inversion model. 
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: product of the electric field derivative with respect to the inversion model with a vector
+        """
+
         # assuming primary doesn't depend on model
         return self._eSecondaryDeriv_m(src, v, adjoint)
 
 
 class Fields_j(Fields):
+    """
+    Fields object for Problem_j. 
+
+    :param Mesh mesh: mesh
+    :param Survey survey: survey 
+    """
+
     knownFields = {'jSolution':'F'}
     aliasFields = {
                     'j' : ['jSolution','F','_j'],
@@ -207,6 +476,15 @@ class Fields_j(Fields):
         self._Me = self.survey.prob.Me
 
     def _jPrimary(self, jSolution, srcList):
+        """
+        Primary current density from source
+
+        :param numpy.ndarray jSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: primary current density as defined by the sources
+        """
+
         jPrimary = np.zeros_like(jSolution,dtype = complex)
         for i, src in enumerate(srcList):
             jp = src.jPrimary(self.prob)
@@ -214,19 +492,66 @@ class Fields_j(Fields):
         return jPrimary
 
     def _jSecondary(self, jSolution, srcList):
+        """
+        Secondary current density is the thing we solved for
+
+        :param numpy.ndarray jSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: secondary current density
+        """
+
         return jSolution
 
     def _j(self, jSolution, srcList):
+        """
+        Total current density is sum of primary and secondary 
+        
+        :param numpy.ndarray jSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: total current density 
+        """
+
         return self._jPrimary(jSolution, srcList) + self._jSecondary(jSolution, srcList)
 
     def _jDeriv_u(self, src, v, adjoint=False):
+        """
+        Derivative of the total current density with respect to the thing we 
+        solved for
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray 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 Identity()*v
 
     def _jDeriv_m(self, src, v, adjoint=False):
+        """
+        Derivative of the total current density with respect to the inversion model. Here, we assume that the primary does not depend on the model. 
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: SimPEG.Utils.Zero
+        :return: product of the current density derivative with respect to the inversion model with a vector
+        """
         # assuming primary does not depend on the model
         return Zero()
 
     def _hPrimary(self, jSolution, srcList):
+        """
+        Primary magnetic field from source
+
+        :param numpy.ndarray hSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: primary magnetic field as defined by the sources
+        """
+
         hPrimary = np.zeros([self._edgeCurl.shape[1],jSolution.shape[1]],dtype = complex)
         for i, src in enumerate(srcList):
             hp = src.hPrimary(self.prob)
@@ -234,6 +559,15 @@ class Fields_j(Fields):
         return hPrimary
 
     def _hSecondary(self, jSolution, srcList):
+        """
+        Secondary magnetic field from bSolution
+
+        :param numpy.ndarray jSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: secondary magnetic field
+        """
+
         h =  self._MeMuI * (self._edgeCurl.T * (self._MfRho * jSolution) )
         for i, src in enumerate(srcList):
             h[:,i] *= -1./(1j*omega(src.freq))
@@ -242,12 +576,32 @@ class Fields_j(Fields):
         return h
 
     def _hSecondaryDeriv_u(self, src, 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 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 * v) )
         elif adjoint:
             return  -1./(1j*omega(src.freq)) * self._MfRho.T * (self._edgeCurl * ( self._MeMuI.T * v))
 
     def _hSecondaryDeriv_m(self, src, v, adjoint=False):
+        """
+        Derivative of the secondary magnetic field with respect to the inversion model 
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray 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 model with a vector
+        """
+
         jSolution = self[[src],'jSolution']
         MeMuI = self._MeMuI
         C = self._edgeCurl
@@ -260,7 +614,7 @@ class Fields_j(Fields):
         elif adjoint:
             hDeriv_m =  -1./(1j*omega(src.freq)) * MfRhoDeriv(jSolution).T * ( C * (MeMuI.T * v ) )
 
-        S_mDeriv,_ = src.evalDeriv(self.prob, adjoint)
+        S_mDeriv,_ = src.evalDeriv(self.prob, adjoint = adjoint)
 
         if not adjoint:
             S_mDeriv = S_mDeriv(v)
@@ -272,17 +626,53 @@ class Fields_j(Fields):
 
 
     def _h(self, jSolution, srcList):
+        """
+        Total magnetic field is sum of primary and secondary 
+        
+        :param numpy.ndarray eSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: total magnetic field
+        """
+
         return self._hPrimary(jSolution, srcList) + self._hSecondary(jSolution, srcList)
 
     def _hDeriv_u(self, src, v, adjoint=False):
+        """
+        Derivative of the total magnetic field with respect to the thing we solved for 
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray 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, v, adjoint)
 
     def _hDeriv_m(self, src, v, adjoint=False):
+        """
+        Derivative of the total magnetic field density with respect to the inversion model. 
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: product of the magnetic field derivative with respect to the inversion model with a vector
+        """
+
         # assuming the primary doesn't depend on the model
         return self._hSecondaryDeriv_m(src, v, adjoint)
 
 
 class Fields_h(Fields):
+    """
+    Fields object for Problem_h. 
+
+    :param Mesh mesh: mesh
+    :param Survey survey: survey 
+    """
+
     knownFields = {'hSolution':'E'}
     aliasFields = {
                     'h' : ['hSolution','E','_h'],
@@ -303,6 +693,15 @@ class Fields_h(Fields):
         self._MfRho = self.survey.prob.MfRho
 
     def _hPrimary(self, hSolution, srcList):
+        """
+        Primary magnetic field from source
+
+        :param numpy.ndarray eSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: primary magnetic field as defined by the sources
+        """
+
         hPrimary = np.zeros_like(hSolution,dtype = complex)
         for i, src in enumerate(srcList):
             hp = src.hPrimary(self.prob)
@@ -310,19 +709,67 @@ class Fields_h(Fields):
         return hPrimary
 
     def _hSecondary(self, hSolution, srcList):
+        """
+        Secondary magnetic field is the thing we solved for
+
+        :param numpy.ndarray hSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: secondary magnetic field
+        """
+
         return hSolution
 
     def _h(self, hSolution, srcList):
+        """
+        Total magnetic field is sum of primary and secondary 
+        
+        :param numpy.ndarray hSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: total magnetic field
+        """
+
         return self._hPrimary(hSolution, srcList) + self._hSecondary(hSolution, srcList)
 
     def _hDeriv_u(self, src, v, adjoint=False):
+        """
+        Derivative of the total magnetic field with respect to the thing we 
+        solved for
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray 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()*v
 
     def _hDeriv_m(self, src, v, adjoint=False):
+        """
+        Derivative of the total magnetic field with respect to the inversion model. Here, we assume that the primary does not depend on the model. 
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: SimPEG.Utils.Zero
+        :return: product of the magnetic field derivative with respect to the inversion model with a vector
+        """
+
         # assuming primary does not depend on the model
         return Zero()
 
     def _jPrimary(self, hSolution, srcList):
+        """
+        Primary current density from source
+
+        :param numpy.ndarray hSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: primary current density as defined by the sources
+        """
+
         jPrimary = np.zeros([self._edgeCurl.shape[0], hSolution.shape[1]], dtype = complex)
         for i, src in enumerate(srcList):
             jp = src.jPrimary(self.prob)
@@ -330,6 +777,15 @@ class Fields_h(Fields):
         return jPrimary
 
     def _jSecondary(self, hSolution, srcList):
+        """
+        Secondary current density from eSolution
+
+        :param numpy.ndarray hSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: secondary current density
+        """
+
         j = self._edgeCurl*hSolution
         for i, src in enumerate(srcList):
             _,S_e = src.eval(self.prob)
@@ -337,22 +793,69 @@ class Fields_h(Fields):
         return j
 
     def _jSecondaryDeriv_u(self, src, 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 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*v
         elif adjoint:
             return self._edgeCurl.T*v
 
     def _jSecondaryDeriv_m(self, src, v, adjoint=False):
-        _,S_eDeriv = src.evalDeriv(self.prob, adjoint)
+        """
-        S_eDeriv = S_eDeriv(v)
+        Derivative of the secondary current density with respect to the inversion model. 
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: product of the secondary current density derivative with respect to the inversion model with a vector
+        """
+
+        _,S_eDeriv = src.evalDeriv(self.prob, v, adjoint)
         return -S_eDeriv
 
     def _j(self, hSolution, srcList):
+        """
+        Total current density is sum of primary and secondary 
+        
+        :param numpy.ndarray eSolution: field we solved for
+        :param list srcList: list of sources
+        :rtype: numpy.ndarray
+        :return: total current density 
+        """
+
         return self._jPrimary(hSolution, srcList) + self._jSecondary(hSolution, srcList)
 
     def _jDeriv_u(self, src, v, adjoint=False):
+        """
+        Derivative of the total current density with respect to the thing we solved for
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray 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,v,adjoint)
 
     def _jDeriv_m(self, src, v, adjoint=False):
+        """
+        Derivative of the total current density with respect to the inversion model. 
+        
+        :param SimPEG.EM.FDEM.Src src: source
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: SimPEG.Utils.Zero
+        :return: product of the current density with respect to the inversion model with a vector
+        """
+
         # assuming the primary does not depend on the model
         return self._jSecondaryDeriv_m(src,v,adjoint)

SimPEG/EM/FDEM/SrcFDEM.py

@@ -2,54 +2,140 @@ from SimPEG import Survey, Problem, Utils, np, sp
 from scipy.constants import mu_0
 from SimPEG.EM.Utils import *
 from SimPEG.Utils import Zero 
-# from SurveyFDEM import Rx
- 
 
 class BaseSrc(Survey.BaseSrc):
+    """
+    Base source class for FDEM Survey
+    """
+
     freq = None
-    # rxPair = Rx
+    # rxPair = RxFDEM
     integrate = True
 
     def eval(self, prob):
+        """
+        Evaluate the source terms. 
+        - :math:`S_m` : magnetic source term
+        - :math:`S_e` : electric source term
+
+        :param Problem prob: FDEM Problem
+        :rtype: (numpy.ndarray, numpy.ndarray)
+        :return: tuple with magnetic source term and electric source term
+        """
         S_m = self.S_m(prob)
         S_e = self.S_e(prob)
         return S_m, S_e
 
-    def evalDeriv(self, prob, v, adjoint=False):
+    def evalDeriv(self, prob, v=None, adjoint=False):
-        return lambda v: self.S_mDeriv(prob,v,adjoint), lambda v: self.S_eDeriv(prob,v,adjoint)
+        """
+        Derivatives of the source terms with respect to the inversion model
+        - :code:`S_mDeriv` : derivative of the magnetic source term
+        - :code:`S_eDeriv` : derivative of the electric source term
+
+        :param Problem prob: FDEM Problem
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: (numpy.ndarray, numpy.ndarray)
+        :return: tuple with magnetic source term and electric source term derivatives times a vector 
+        """
+        if v is not None: 
+            return self.S_mDeriv(prob,v,adjoint), self.S_eDeriv(prob,v,adjoint)
+        else:
+            return lambda v: self.S_mDeriv(prob,v,adjoint), lambda v: self.S_eDeriv(prob,v,adjoint)
 
     def bPrimary(self, prob):
+        """
+        Primary magnetic flux density
+
+        :param Problem prob: FDEM Problem
+        :rtype: numpy.ndarray
+        :return: primary magnetic flux density 
+        """
         return Zero()
 
     def hPrimary(self, prob):
+        """
+        Primary magnetic field
+
+        :param Problem prob: FDEM Problem
+        :rtype: numpy.ndarray
+        :return: primary magnetic field 
+        """
         return Zero()
 
     def ePrimary(self, prob):
+        """
+        Primary electric field
+
+        :param Problem prob: FDEM Problem
+        :rtype: numpy.ndarray
+        :return: primary electric field 
+        """
         return Zero()
 
     def jPrimary(self, prob):
+        """
+        Primary current density
+
+        :param Problem prob: FDEM Problem
+        :rtype: numpy.ndarray
+        :return: primary current density 
+        """
         return Zero()
 
     def S_m(self, prob):
+        """
+        Magnetic source term 
+
+        :param Problem prob: FDEM Problem
+        :rtype: numpy.ndarray
+        :return: magnetic source term on mesh
+        """
         return Zero()
 
     def S_e(self, prob):
+        """
+        Electric source term 
+
+        :param Problem prob: FDEM Problem
+        :rtype: numpy.ndarray
+        :return: electric source term on mesh
+        """
         return Zero()
 
     def S_mDeriv(self, prob, v, adjoint = False):
+        """
+        Derivative of magnetic source term with respect to the inversion model
+
+        :param Problem prob: FDEM Problem
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: product of magnetic source term derivative with a vector
+        """
+
         return Zero()
 
     def S_eDeriv(self, prob, v, adjoint = False):
+        """
+        Derivative of electric source term with respect to the inversion model
+
+        :param Problem prob: FDEM Problem
+        :param numpy.ndarray v: vector to take product with
+        :param bool adjoint: adjoint?
+        :rtype: numpy.ndarray
+        :return: product of electric source term derivative with a vector
+        """
         return Zero()
 
 
 class RawVec_e(BaseSrc):
     """
-        RawVec electric source. It is defined by the user provided vector S_e
+    RawVec electric source. It is defined by the user provided vector S_e
 
-        :param numpy.array S_e: electric source term
+    :param list rxList: receiver list
-        :param float freq: frequency
+    :param float freq: frequency
-        :param rxList: receiver list
+    :param numpy.array S_e: electric source term
     """
 
     def __init__(self, rxList, freq, S_e): #, ePrimary=None, bPrimary=None, hPrimary=None, jPrimary=None):
@@ -58,16 +144,17 @@ class RawVec_e(BaseSrc):
         BaseSrc.__init__(self, rxList)
 
     def S_e(self, prob):
+
         return self._S_e
 
 
 class RawVec_m(BaseSrc):
     """
-        RawVec magnetic source. It is defined by the user provided vector S_m
+    RawVec magnetic source. It is defined by the user provided vector S_m
 
-        :param numpy.array S_m: magnetic source term
+    :param float freq: frequency
-        :param float freq: frequency
+    :param rxList: receiver list
-        :param rxList: receiver list
+    :param numpy.array S_m: magnetic source term
     """
 
     def __init__(self, rxList, freq, S_m, integrate = True):  #ePrimary=Zero(), bPrimary=Zero(), hPrimary=Zero(), jPrimary=Zero()):
@@ -78,17 +165,24 @@ class RawVec_m(BaseSrc):
         BaseSrc.__init__(self, rxList)
 
     def S_m(self, prob):
+        """
+        Magnetic source term 
+
+        :param Problem prob: FDEM Problem
+        :rtype: numpy.ndarray
+        :return: magnetic source term on mesh
+        """
         return self._S_m
 
 
 class RawVec(BaseSrc):
     """
-        RawVec source. It is defined by the user provided vectors S_m, S_e
+    RawVec source. It is defined by the user provided vectors S_m, S_e
 
-        :param numpy.array S_m: magnetic source term
+    :param rxList: receiver list
-        :param numpy.array S_e: electric source term
+    :param float freq: frequency
-        :param float freq: frequency
+    :param numpy.array S_m: magnetic source term
-        :param rxList: receiver list
+    :param numpy.array S_e: electric source term
     """
     def __init__(self, rxList, freq, S_m, S_e, integrate = True):
         self._S_m = np.array(S_m,dtype=complex)
@@ -109,6 +203,51 @@ class RawVec(BaseSrc):
 
 
 class MagDipole(BaseSrc):
+    """  
+    Point magnetic dipole source calculated by taking the curl of a magnetic
+    vector potential. By taking the discrete curl, we ensure that the magnetic
+    flux density is divergence free (no magnetic monopoles!). 
+
+    This approach uses a primary-secondary in frequency. Here we show the
+    derivation for E-B formulation noting that similar steps are followed for
+    the H-J formulation.
+
+    .. math:: 
+        \mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} \\\\
+            {\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{M_{\sigma}^e} \mathbf{e} = \mathbf{s_e}}
+
+    We split up the fields and :math:`\mu^{-1}` into primary (:math:`\mathbf{P}`) and secondary (:math:`\mathbf{S}`) components
+
+    - :math:`\mathbf{e} = \mathbf{e^P} + \mathbf{e^S}`
+    - :math:`\mathbf{b} = \mathbf{b^P} + \mathbf{b^S}`
+    - :math:`\\boldsymbol{\mu}^{\mathbf{-1}} = \\boldsymbol{\mu}^{\mathbf{-1}^\mathbf{P}} + \\boldsymbol{\mu}^{\mathbf{-1}^\mathbf{S}}`
+
+    and define a zero-frequency primary problem, noting that the source is
+    generated by a divergence free electric current
+
+    .. math:: 
+        \mathbf{C} \mathbf{e^P} = \mathbf{s_m^P} = 0 \\\\
+            {\mathbf{C}^T \mathbf{{M_{\mu^{-1}}^f}^P} \mathbf{b^P} - \mathbf{M_{\sigma}^e} \mathbf{e^P} = \mathbf{M^e} \mathbf{s_e^P}}
+
+    Since :math:`\mathbf{e^P}` is curl-free, divergence-free, we assume that there is no constant field background, the :math:`\mathbf{e^P} = 0`, so our primary problem is 
+
+    .. math:: 
+        \mathbf{e^P} =  0 \\\\
+            {\mathbf{C}^T \mathbf{{M_{\mu^{-1}}^f}^P} \mathbf{b^P} = \mathbf{s_e^P}}
+
+    Our secondary problem is then 
+
+    .. math::
+        \mathbf{C} \mathbf{e^S} + i \omega \mathbf{b^S} = - i \omega \mathbf{b^P} \\\\
+            {\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b^S} - \mathbf{M_{\sigma}^e} \mathbf{e^S} = -\mathbf{C}^T \mathbf{{M_{\mu^{-1}}^f}^S} \mathbf{b^P}}
+
+    :param list rxList: receiver list
+    :param float freq: frequency
+    :param numpy.ndarray loc: source location (ie: :code:`np.r_[xloc,yloc,zloc]`)
+    :param string orientation: 'X', 'Y', 'Z'
+    :param float moment: magnetic dipole moment 
+    :param float mu: background magnetic permeability 
+    """
 
     #TODO: right now, orientation doesn't actually do anything! The methods in SrcUtils should take care of that
     def __init__(self, rxList, freq, loc, orientation='Z', moment=1., mu = mu_0):
@@ -121,6 +260,13 @@ class MagDipole(BaseSrc):
         BaseSrc.__init__(self, rxList)
 
     def bPrimary(self, prob):
+        """
+        The primary magnetic flux density from a magnetic vector potential
+
+        :param Problem prob: FDEM problem
+        :rtype: numpy.ndarray
+        :return: primary magnetic field 
+        """
         eqLocs = prob._eqLocs
 
         if eqLocs is 'FE':
@@ -152,14 +298,37 @@ class MagDipole(BaseSrc):
         return C*a
 
     def hPrimary(self, prob):
+        """
+        The primary magnetic field from a magnetic vector potential
+
+        :param Problem prob: FDEM problem
+        :rtype: numpy.ndarray
+        :return: primary magnetic field 
+        """
         b = self.bPrimary(prob)
         return h_from_b(prob,b)
 
     def S_m(self, prob):
+        """
+        The magnetic source term
+
+        :param Problem prob: FDEM problem
+        :rtype: numpy.ndarray
+        :return: primary magnetic field 
+        """
+
         b_p = self.bPrimary(prob)
         return -1j*omega(self.freq)*b_p
 
     def S_e(self, prob):
+        """
+        The electric source term
+
+        :param Problem prob: FDEM problem
+        :rtype: numpy.ndarray
+        :return: primary magnetic field 
+        """
+
         if all(np.r_[self.mu] == np.r_[prob.curModel.mu]):
             return Zero()
         else:
@@ -179,6 +348,21 @@ class MagDipole(BaseSrc):
 
 class MagDipole_Bfield(BaseSrc):
 
+    """
+    Point magnetic dipole source calculated with the analytic solution for the
+    fields from a magnetic dipole. No discrete curl is taken, so the magnetic
+    flux density may not be strictly divergence free.
+
+    This approach uses a primary-secondary in frequency in the same fashion as the MagDipole. 
+
+    :param list rxList: receiver list
+    :param float freq: frequency
+    :param numpy.ndarray loc: source location (ie: :code:`np.r_[xloc,yloc,zloc]`)
+    :param string orientation: 'X', 'Y', 'Z'
+    :param float moment: magnetic dipole moment 
+    :param float mu: background magnetic permeability 
+    """
+
     #TODO: right now, orientation doesn't actually do anything! The methods in SrcUtils should take care of that
     #TODO: neither does moment
     def __init__(self, rxList, freq, loc, orientation='Z', moment=1., mu = mu_0):
@@ -190,6 +374,14 @@ class MagDipole_Bfield(BaseSrc):
         BaseSrc.__init__(self, rxList)
 
     def bPrimary(self, prob):
+        """
+        The primary magnetic flux density from the analytic solution for magnetic fields from a dipole
+
+        :param Problem prob: FDEM problem
+        :rtype: numpy.ndarray
+        :return: primary magnetic field 
+        """
+
         eqLocs = prob._eqLocs
 
         if eqLocs is 'FE':
@@ -221,14 +413,35 @@ class MagDipole_Bfield(BaseSrc):
         return b
 
     def hPrimary(self, prob):
+        """
+        The primary magnetic field from a magnetic vector potential
+
+        :param Problem prob: FDEM problem
+        :rtype: numpy.ndarray
+        :return: primary magnetic field 
+        """
         b = self.bPrimary(prob)
         return h_from_b(prob, b)
 
     def S_m(self, prob):
+        """
+        The magnetic source term
+
+        :param Problem prob: FDEM problem
+        :rtype: numpy.ndarray
+        :return: primary magnetic field 
+        """
         b = self.bPrimary(prob)
         return -1j*omega(self.freq)*b
 
     def S_e(self, prob):
+        """
+        The electric source term
+
+        :param Problem prob: FDEM problem
+        :rtype: numpy.ndarray
+        :return: primary magnetic field 
+        """
         if all(np.r_[self.mu] == np.r_[prob.curModel.mu]):
             return Zero()
         else:
@@ -247,6 +460,20 @@ class MagDipole_Bfield(BaseSrc):
 
 
 class CircularLoop(BaseSrc):
+    """
+    Circular loop magnetic source calculated by taking the curl of a magnetic
+    vector potential. By taking the discrete curl, we ensure that the magnetic
+    flux density is divergence free (no magnetic monopoles!). 
+
+    This approach uses a primary-secondary in frequency in the same fashion as the MagDipole. 
+
+    :param list rxList: receiver list
+    :param float freq: frequency
+    :param numpy.ndarray loc: source location (ie: :code:`np.r_[xloc,yloc,zloc]`)
+    :param string orientation: 'X', 'Y', 'Z'
+    :param float moment: magnetic dipole moment 
+    :param float mu: background magnetic permeability 
+    """
 
     #TODO: right now, orientation doesn't actually do anything! The methods in SrcUtils should take care of that
     def __init__(self, rxList, freq, loc, orientation='Z', radius = 1., mu=mu_0):
@@ -259,6 +486,13 @@ class CircularLoop(BaseSrc):
         BaseSrc.__init__(self, rxList)
 
     def bPrimary(self, prob):
+        """
+        The primary magnetic flux density from a magnetic vector potential
+
+        :param Problem prob: FDEM problem
+        :rtype: numpy.ndarray
+        :return: primary magnetic field 
+        """
         eqLocs = prob._eqLocs
 
         if eqLocs is 'FE':
@@ -289,14 +523,35 @@ class CircularLoop(BaseSrc):
         return C*a
 
     def hPrimary(self, prob):
+        """
+        The primary magnetic field from a magnetic vector potential
+
+        :param Problem prob: FDEM problem
+        :rtype: numpy.ndarray
+        :return: primary magnetic field 
+        """
         b = self.bPrimary(prob)
         return 1./self.mu*b
 
     def S_m(self, prob):
+        """
+        The magnetic source term
+
+        :param Problem prob: FDEM problem
+        :rtype: numpy.ndarray
+        :return: primary magnetic field 
+        """
         b = self.bPrimary(prob)
         return -1j*omega(self.freq)*b
 
     def S_e(self, prob):
+        """
+        The electric source term
+
+        :param Problem prob: FDEM problem
+        :rtype: numpy.ndarray
+        :return: primary magnetic field 
+        """
         if all(np.r_[self.mu] == np.r_[prob.curModel.mu]):
             return Zero()
         else:

SimPEG/EM/FDEM/SurveyFDEM.py

@@ -10,6 +10,12 @@ import SrcFDEM as Src
 ####################################################
 
 class Rx(SimPEG.Survey.BaseRx):
+    """
+    Frequency domain receivers
+
+    :param numpy.ndarray locs: receiver locations (ie. :code:`np.r_[x,y,z]`)
+    :param string rxType: reciever type from knownRxTypes
+    """
 
     knownRxTypes = {
                     'exr':['e', 'Ex', 'real'],
@@ -60,15 +66,33 @@ class Rx(SimPEG.Survey.BaseRx):
         """Component projection (real/imag)"""
         return self.knownRxTypes[self.rxType][2]
 
-    def projectFields(self, src, mesh, u):
+    def projectFields(self, src, mesh, f):
-        P = self.getP(mesh)
+        """
-        u_part_complex = u[src, self.projField]
+        Project fields to recievers to get data.
-        # get the real or imag component
+
-        real_or_imag = self.projComp
+        :param Source src: FDEM source
+        :param Mesh mesh: mesh used
+        :param Fields f: fields object
+        :rtype: numpy.ndarray
+        :return: fields projected to recievers
+        """
+        P = self.getP(mesh) # get interpolation to recievers 
+        u_part_complex = f[src, self.projField]
+        real_or_imag = self.projComp # get the real or imag component
         u_part = getattr(u_part_complex, real_or_imag)
         return P*u_part
 
-    def projectFieldsDeriv(self, src, mesh, u, v, adjoint=False):
+    def projectFieldsDeriv(self, src, mesh, f, v, adjoint=False):
+        """
+        Derivative of projected fields with respect to the inversion model times a vector.
+
+        :param Source src: FDEM source
+        :param Mesh mesh: mesh used
+        :param Fields f: fields object
+        :param numpy.ndarray v: vector to multiply
+        :rtype: numpy.ndarray
+        :return: fields projected to recievers
+        """
         P = self.getP(mesh)
 
         if not adjoint:
@@ -95,10 +119,13 @@ class Rx(SimPEG.Survey.BaseRx):
 
 class Survey(SimPEG.Survey.BaseSurvey):
     """
-        docstring for SurveyFDEM
+    Frequency domain electromagnetic survey
+
+    :param list srcList: list of FDEM sources used in the survey
     """
 
     srcPair = Src.BaseSrc
+    rxPaair = Rx 
 
     def __init__(self, srcList, **kwargs):
         # Sort these by frequency
@@ -126,6 +153,7 @@ class Survey(SimPEG.Survey.BaseSurvey):
 
     @property
     def nSrcByFreq(self):
+        """Number of sources at each frequency"""
         if getattr(self, '_nSrcByFreq', None) is None:
             self._nSrcByFreq = {}
             for freq in self.freqs:
@@ -133,11 +161,22 @@ class Survey(SimPEG.Survey.BaseSurvey):
         return self._nSrcByFreq
 
     def getSrcByFreq(self, freq):
-        """Returns the sources associated with a specific frequency."""
+        """
+        Returns the sources associated with a specific frequency.
+        :param float freq: frequency for which we look up sources
+        :rtype: dictionary
+        :return: sources at the sepcified frequency 
+        """
         assert freq in self._freqDict, "The requested frequency is not in this survey."
         return self._freqDict[freq]
 
     def projectFields(self, u):
+        """
+        Project fields to receiver locations
+        :param Fields u: fields object
+        :rtype: numpy.ndarray
+        :return: data
+        """
         data = SimPEG.Survey.Data(self)
         for src in self.srcList:
             for rx in src.rxList:
@@ -145,4 +184,4 @@ class Survey(SimPEG.Survey.BaseSurvey):
         return data
 
     def projectFieldsDeriv(self, u):
-        raise Exception('Use Sources to project fields deriv.')
+        raise Exception('Use Receivers to project fields deriv.')

SimPEG/EM/TDEM/SurveyTDEM.py

@@ -79,12 +79,32 @@ class SrcTDEM(Survey.BaseSrc):
 
 class SrcTDEM_VMD_MVP(SrcTDEM):
 
-    def __init__(self,rxList,loc):
+    def __init__(self,rxList,loc,waveformType="STEPOFF"):
         self.loc = loc
+        self.waveformType = waveformType
         SrcTDEM.__init__(self,rxList)
 
     def getInitialFields(self, mesh):
         """Vertical magnetic dipole, magnetic vector potential"""
+        if self.waveformType == "STEPOFF":
+            print ">> Step waveform: Non-zero initial condition"        
+            if mesh._meshType is 'CYL':
+                if mesh.isSymmetric:
+                    MVP = MagneticDipoleVectorPotential(self.loc, mesh, 'Ey')
+                else:
+                    raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
+            elif mesh._meshType is 'TENSOR':
+                MVP = MagneticDipoleVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'])
+            else:
+                raise Exception('Unknown mesh for VMD') 
+            return {"b": mesh.edgeCurl*MVP}               
+        elif self.waveformType == "GENERAL":
+            print ">> General waveform: Zero initial condition"
+            return {"b": np.zeros(mesh.nF)}
+        else:
+            raise NotImplementedError("Only use STEPOFF or GENERAL")
+
+    def getMeS(self, mesh, MfMui):
         if mesh._meshType is 'CYL':
             if mesh.isSymmetric:
                 MVP = MagneticDipoleVectorPotential(self.loc, mesh, 'Ey')
@@ -94,12 +114,11 @@ class SrcTDEM_VMD_MVP(SrcTDEM):
             MVP = MagneticDipoleVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'])
         else:
             raise Exception('Unknown mesh for VMD')            
-
+        return mesh.edgeCurl.T*MfMui*mesh.edgeCurl*MVP
-        return {"b": mesh.edgeCurl*MVP}
 
 
 class SrcTDEM_CircularLoop_MVP(SrcTDEM):
-    def __init__(self,rxList,loc,radius,waveformType):
+    def __init__(self,rxList,loc,radius,waveformType="STEPOFF"):
         self.loc = loc
         self.radius = radius
         self.waveformType = waveformType

SimPEG/Examples/MT_1D_ForwardAndInversion.py

@@ -0,0 +1,129 @@
+import SimPEG as simpeg
+import numpy as np
+import SimPEG.MT as MT
+from scipy.constants import mu_0
+import matplotlib.pyplot as plt
+
+def run(plotIt=True):
+    """
+        MT: 1D: Inversion
+        =======================
+
+        Forward model 1D MT data.
+        Setup and run a MT 1D inversion.
+
+    """
+
+    ## Setup the forward modeling
+    # Setting up 1D mesh and conductivity models to forward model data.
+    # Frequency
+    nFreq = 31
+    freqs = np.logspace(3,-3,nFreq)
+    # Set mesh parameters
+    ct = 20
+    air = simpeg.Utils.meshTensor([(ct,16,1.4)])
+    core = np.concatenate( (  np.kron(simpeg.Utils.meshTensor([(ct,10,-1.3)]),np.ones((5,))) , simpeg.Utils.meshTensor([(ct,5)]) ) )
+    bot = simpeg.Utils.meshTensor([(core[0],10,-1.4)])
+    x0 = -np.array([np.sum(np.concatenate((core,bot)))])
+    # Make the model
+    m1d = simpeg.Mesh.TensorMesh([np.concatenate((bot,core,air))], x0=x0)
+
+    # Setup model varibles
+    active = m1d.vectorCCx<0.
+    layer1 = (m1d.vectorCCx<-500.) & (m1d.vectorCCx>=-800.)
+    layer2 = (m1d.vectorCCx<-3500.) & (m1d.vectorCCx>=-5000.)
+    # Set the conductivity values
+    sig_half = 2e-3
+    sig_air = 1e-8
+    sig_layer1 = .2
+    sig_layer2 = .2
+    # Make the true model
+    sigma_true = np.ones(m1d.nCx)*sig_air
+    sigma_true[active] = sig_half
+    sigma_true[layer1] = sig_layer1
+    sigma_true[layer2] = sig_layer2
+    # Extract the model
+    m_true = np.log(sigma_true[active])
+    # Make the background model
+    sigma_0 = np.ones(m1d.nCx)*sig_air
+    sigma_0[active] = sig_half
+    m_0 = np.log(sigma_0[active])
+
+    # Set the mapping
+    actMap = simpeg.Maps.ActiveCells(m1d, active, np.log(1e-8), nC=m1d.nCx)
+    mappingExpAct = simpeg.Maps.ExpMap(m1d) * actMap
+
+    ## Setup the layout of the survey, set the sources and the connected receivers
+    # Receivers
+    rxList = []
+    for rxType in ['z1dr','z1di']:
+        rxList.append(MT.Rx(simpeg.mkvc(np.array([0.0]),2).T,rxType))
+    # Source list
+    srcList =[]
+    for freq in freqs:
+            srcList.append(MT.SrcMT.polxy_1Dprimary(rxList,freq))
+    # Make the survey
+    survey = MT.Survey(srcList)
+    survey.mtrue = m_true
+
+    ## Set the problem
+    problem = MT.Problem1D.eForm_psField(m1d,sigmaPrimary=sigma_0,mapping=mappingExpAct)
+    problem.pair(survey)
+
+    ## Forward model data
+    # Project the data
+    survey.dtrue = survey.dpred(m_true)
+    survey.dobs = survey.dtrue + 0.025*abs(survey.dtrue)*np.random.randn(*survey.dtrue.shape)
+
+    if plotIt:
+        fig = MT.Utils.dataUtils.plotMT1DModelData(problem)
+        fig.suptitle('Target - smooth true')
+
+
+    # Assign uncertainties
+    std = 0.05 # 5% std
+    survey.std = np.abs(survey.dobs*std)
+    # Assign the data weight
+    Wd = 1./survey.std
+
+    ## Setup the inversion proceedure
+    # Define a counter
+    C =  simpeg.Utils.Counter()
+    # Set the optimization
+    opt = simpeg.Optimization.InexactGaussNewton(maxIter = 30)
+    opt.counter = C
+    opt.LSshorten = 0.5
+    opt.remember('xc')
+    # Data misfit
+    dmis = simpeg.DataMisfit.l2_DataMisfit(survey)
+    dmis.Wd = Wd
+    # Regularization - with a regularization mesh
+    regMesh = simpeg.Mesh.TensorMesh([m1d.hx[problem.mapping.sigmaMap.maps[-1].indActive]],m1d.x0)
+    reg = simpeg.Regularization.Tikhonov(regMesh)
+    reg.smoothModel = True
+    reg.alpha_s = 1e-7
+    reg.alpha_x = 1.
+    # Inversion problem
+    invProb = simpeg.InvProblem.BaseInvProblem(dmis, reg, opt)
+    invProb.counter = C
+    # Beta cooling
+    beta = simpeg.Directives.BetaSchedule()
+    beta.coolingRate = 4
+    betaest = simpeg.Directives.BetaEstimate_ByEig(beta0_ratio=0.75)
+    targmis = simpeg.Directives.TargetMisfit()
+    targmis.target = survey.nD
+    saveModel = simpeg.Directives.SaveModelEveryIteration()
+    saveModel.fileName = 'Inversion_TargMisEqnD_smoothTrue'
+    # Create an inversion object
+    inv = simpeg.Inversion.BaseInversion(invProb, directiveList=[beta,betaest,targmis])
+
+    ## Run the inversion
+    mopt = inv.run(m_0)
+
+    if plotIt:
+        fig = MT.Utils.dataUtils.plotMT1DModelData(problem,[mopt])
+        fig.suptitle('Target - smooth true')
+        plt.show()
+
+if __name__ == '__main__':
+    run()

SimPEG/Examples/MT_3D_Foward.py

@@ -0,0 +1,64 @@
+# Test script to use SimPEG.MT platform to forward model synthetic data.
+
+# Import
+import SimPEG as simpeg
+from SimPEG import MT
+import numpy as np
+try:
+    from pymatsolver import MumpsSolver as Solver
+except:
+    from SimPEG import Solver
+
+def run(plotIt=True, nFreq=1):
+    """
+        MT: 3D: Forward
+        =======================
+
+        Forward model 3D MT data.
+
+    """
+
+    # Make a mesh
+    M = simpeg.Mesh.TensorMesh([[(100,5,-1.5),(100.,10),(100,5,1.5)],[(100,5,-1.5),(100.,10),(100,5,1.5)],[(100,5,1.6),(100.,10),(100,3,2)]], x0=['C','C',-3529.5360])
+    # Setup the model
+    conds = [1e-2,1]
+    sig = simpeg.Utils.ModelBuilder.defineBlock(M.gridCC,[-1000,-1000,-400],[1000,1000,-200],conds)
+    sig[M.gridCC[:,2]>0] = 1e-8
+    sig[M.gridCC[:,2]<-600] = 1e-1
+    sigBG = np.zeros(M.nC) + conds[0]
+    sigBG[M.gridCC[:,2]>0] = 1e-8
+
+    ## Setup the the survey object
+    # Receiver locations
+    rx_x, rx_y = np.meshgrid(np.arange(-500,501,50),np.arange(-500,501,50))
+    rx_loc = np.hstack((simpeg.Utils.mkvc(rx_x,2),simpeg.Utils.mkvc(rx_y,2),np.zeros((np.prod(rx_x.shape),1))))
+    # Make a receiver list
+    rxList = []
+    for loc in rx_loc:
+        # NOTE: loc has to be a (1,3) np.ndarray otherwise errors accure
+        for rxType in ['zxxr','zxxi','zxyr','zxyi','zyxr','zyxi','zyyr','zyyi','tzxr','tzxi','tzyr','tzyi']:
+            rxList.append(MT.Rx(simpeg.mkvc(loc,2).T,rxType))
+    # Source list
+    srcList =[]
+    for freq in np.logspace(3,-3,nFreq):
+        srcList.append(MT.SrcMT.polxy_1Dprimary(rxList,freq))
+    # Survey MT
+    survey = MT.Survey(srcList)
+
+    ## Setup the problem object
+    problem = MT.Problem3D.eForm_ps(M, sigmaPrimary=sigBG)
+    problem.pair(survey)
+    problem.Solver = Solver
+
+    # Calculate the data
+    fields = problem.fields(sig)
+    dataVec = survey.projectFields(fields)
+
+    # Make the data
+    mtData = MT.Data(survey,dataVec)
+    # Add plots
+    if plotIt:
+        pass
+
+if __name__ == '__main__':
+    run()

SimPEG/Examples/__init__.py

@@ -16,8 +16,10 @@ import Mesh_QuadTree_Creation
 import Mesh_QuadTree_FaceDiv
 import Mesh_QuadTree_HangingNodes
 import Mesh_Tensor_Creation
+import MT_1D_ForwardAndInversion
+import MT_3D_Foward
 
-__examples__ = ["DC_Analytic_Dipole", "DC_Forward_PseudoSection", "EM_FDEM_1D_Inversion", "EM_FDEM_Analytic_MagDipoleWholespace", "EM_TDEM_1D_Inversion", "FLOW_Richards_1D_Celia1990", "Forward_BasicDirectCurrent", "Inversion_Linear", "Mesh_Basic_PlotImage", "Mesh_Basic_Types", "Mesh_Operators_CahnHilliard", "Mesh_QuadTree_Creation", "Mesh_QuadTree_FaceDiv", "Mesh_QuadTree_HangingNodes", "Mesh_Tensor_Creation"]
+__examples__ = ["DC_Analytic_Dipole", "DC_Forward_PseudoSection", "EM_FDEM_1D_Inversion", "EM_FDEM_Analytic_MagDipoleWholespace", "EM_TDEM_1D_Inversion", "FLOW_Richards_1D_Celia1990", "Forward_BasicDirectCurrent", "Inversion_Linear", "Mesh_Basic_PlotImage", "Mesh_Basic_Types", "Mesh_Operators_CahnHilliard", "Mesh_QuadTree_Creation", "Mesh_QuadTree_FaceDiv", "Mesh_QuadTree_HangingNodes", "Mesh_Tensor_Creation", "MT_1D_ForwardAndInversion", "MT_3D_Foward"]
 
 ##### AUTOIMPORTS #####
 

SimPEG/MT/BaseMT.py

@@ -0,0 +1,132 @@
+from SimPEG import SolverLU as SimpegSolver, PropMaps, Utils, mkvc, sp, np
+from SimPEG.EM.FDEM.FDEM import BaseFDEMProblem
+from SurveyMT import Survey, Data
+from FieldsMT import BaseMTFields
+
+
+class BaseMTProblem(BaseFDEMProblem):
+    """
+        Base class for all Natural source problems.
+    """
+
+    def __init__(self, mesh, **kwargs):
+        BaseFDEMProblem.__init__(self, mesh, **kwargs)
+        Utils.setKwargs(self, **kwargs)
+    # Set the default pairs of the problem
+    surveyPair = Survey
+    dataPair = Data
+    fieldsPair = BaseMTFields
+
+    # Set the solver
+    Solver = SimpegSolver
+    solverOpts = {}
+
+    verbose = False
+    # Notes:
+    # Use the forward and devs from BaseFDEMProblem
+    # Might need to add more stuff here.
+
+    ## NEED to clean up the Jvec and Jtvec to use Zero and Identities for None components.
+    def Jvec(self, m, v, u=None):
+        """
+        Function to calculate the data sensitivities dD/dm times a vector.
+
+            :param numpy.ndarray m (nC, 1) - conductive model
+            :param numpy.ndarray v (nC, 1) - random vector
+            :param MTfields object (optional) - MT fields object, if not given it is calculated
+            :rtype: MTdata object
+            :return: Data sensitivities wrt m
+        """
+
+        # Calculate the fields
+        if u is None:
+           u = self.fields(m)
+        # Set current model
+        self.curModel = m
+        # Initiate the Jv object
+        Jv = self.dataPair(self.survey)
+
+        # Loop all the frequenies
+        for freq in self.survey.freqs:
+            dA_du = self.getA(freq) #
+
+            dA_duI = self.Solver(dA_du, **self.solverOpts)
+
+            for src in self.survey.getSrcByFreq(freq):
+                # We need fDeriv_m = df/du*du/dm + df/dm
+                # Construct du/dm, it requires a solve
+                # NOTE: need to account for the 2 polarizations in the derivatives.
+                u_src = u[src,:]
+                # dA_dm and dRHS_dm should be of size nE,2, so that we can multiply by dA_duI. The 2 columns are each of the polarizations.
+                dA_dm = self.getADeriv_m(freq, u_src, v) # Size: nE,2 (u_px,u_py) in the columns.
+                dRHS_dm = self.getRHSDeriv_m(freq, v) # Size: nE,2 (u_px,u_py) in the columns.
+                if dRHS_dm is None:
+                    du_dm = dA_duI * ( -dA_dm )
+                else:
+                    du_dm = dA_duI * ( -dA_dm + dRHS_dm )
+                # Calculate the projection derivatives
+                for rx in src.rxList:
+                    # Get the projection derivative
+                    # v should be of size 2*nE (for 2 polarizations)
+                    PDeriv_u = lambda t: rx.projectFieldsDeriv(src, self.mesh, u, t) # wrt u, we don't have have PDeriv wrt m
+                    Jv[src, rx] = PDeriv_u(mkvc(du_dm))
+            dA_duI.clean()
+        # Return the vectorized sensitivities
+        return mkvc(Jv)
+
+    def Jtvec(self, m, v, u=None):
+        """
+        Function to calculate the transpose of the data sensitivities (dD/dm)^T times a vector.
+
+            :param numpy.ndarray m (nC, 1) - conductive model
+            :param numpy.ndarray v (nD, 1) - vector
+            :param MTfields object u (optional) - MT fields object, if not given it is calculated
+            :rtype: MTdata object
+            :return: Data sensitivities wrt m
+        """
+
+        if u is None:
+            u = self.fields(m)
+
+        self.curModel = m
+
+        # Ensure v is a data object.
+        if not isinstance(v, self.dataPair):
+            v = self.dataPair(self.survey, v)
+
+        Jtv = np.zeros(m.size)
+
+        for freq in self.survey.freqs:
+            AT = self.getA(freq).T
+
+            ATinv = self.Solver(AT, **self.solverOpts)
+
+            for src in self.survey.getSrcByFreq(freq):
+                ftype = self._fieldType + 'Solution'
+                u_src = u[src, :]
+
+                for rx in src.rxList:
+                    # Get the adjoint projectFieldsDeriv
+                    # PTv needs to be nE,
+                    PTv = rx.projectFieldsDeriv(src, self.mesh, u, mkvc(v[src, rx],2), adjoint=True) # wrt u, need possibility wrt m
+                    # Get the
+                    dA_duIT = ATinv * PTv
+                    dA_dmT = self.getADeriv_m(freq, u_src, mkvc(dA_duIT), adjoint=True)
+                    dRHS_dmT = self.getRHSDeriv_m(freq, mkvc(dA_duIT), adjoint=True)
+                    # Make du_dmT
+                    if dRHS_dmT is None:
+                        du_dmT = -dA_dmT
+                    else:
+                        du_dmT = -dA_dmT + dRHS_dmT
+                    # Select the correct component
+                    # du_dmT needs to be of size nC,
+                    real_or_imag = rx.projComp
+                    if real_or_imag == 'real':
+                        Jtv +=  du_dmT.real
+                    elif real_or_imag == 'imag':
+                        Jtv +=  -du_dmT.real
+                    else:
+                        raise Exception('Must be real or imag')
+            # Clean the factorization, clear memory.
+            ATinv.clean()
+        return Jtv

SimPEG/MT/FieldsMT.py

@@ -0,0 +1,351 @@
+from SimPEG import Survey, Utils, Problem, np, sp, mkvc
+from scipy.constants import mu_0
+import sys
+from numpy.lib import recfunctions as recFunc
+from SimPEG.EM.Utils import omega
+
+##############
+### Fields ###
+##############
+class BaseMTFields(Problem.Fields):
+    """Field Storage for a MT survey."""
+    knownFields = {}
+    dtype = complex
+
+
+class Fields1D_e(BaseMTFields):
+    """
+    Fields storage for the 1D MT solution.
+    """
+    knownFields = {'e_1dSolution':'F'}
+    aliasFields = {
+                    'e_1d' : ['e_1dSolution','F','_e'],
+                    'e_1dPrimary' : ['e_1dSolution','F','_ePrimary'],
+                    'e_1dSecondary' : ['e_1dSolution','F','_eSecondary'],
+                    'b_1d' : ['e_1dSolution','E','_b'],
+                    'b_1dPrimary' : ['e_1dSolution','E','_bPrimary'],
+                    'b_1dSecondary' : ['e_1dSolution','E','_bSecondary']
+                  }
+
+    def __init__(self,mesh,survey,**kwargs):
+        BaseMTFields.__init__(self,mesh,survey,**kwargs)
+
+    def _ePrimary(self, eSolution, srcList):
+        ePrimary = np.zeros_like(eSolution)
+        for i, src in enumerate(srcList):
+            ep = src.ePrimary(self.survey.prob)
+            if ep is not None:
+                ePrimary[:,i] = ep[:,-1]
+        return ePrimary
+
+    def _eSecondary(self, eSolution, srcList):
+        return eSolution
+
+    def _e(self, eSolution, srcList):
+        return self._ePrimary(eSolution,srcList) + self._eSecondary(eSolution,srcList)
+
+    def _eDeriv_u(self, src, v, adjoint = False):
+        return v
+
+    def _eDeriv_m(self, src, v, adjoint = False):
+        # assuming primary does not depend on the model
+        return None
+
+    def _bPrimary(self, eSolution, srcList):
+        bPrimary = np.zeros([self.survey.mesh.nE,eSolution.shape[1]], dtype = complex)
+        for i, src in enumerate(srcList):
+            bp = src.bPrimary(self.survey.prob)
+            if bp is not None:
+                bPrimary[:,i] += bp[:,-1]
+        return bPrimary
+
+    def _bSecondary(self, eSolution, srcList):
+        C = self.mesh.nodalGrad
+        b = (C * eSolution)
+        for i, src in enumerate(srcList):
+            b[:,i] *= - 1./(1j*omega(src.freq))
+            # There is no magnetic source in the MT problem
+            # S_m, _ = src.eval(self.survey.prob)
+            # if S_m is not None:
+            #     b[:,i] += 1./(1j*omega(src.freq)) * S_m
+        return b
+
+    def _b(self, eSolution, srcList):
+        return self._bPrimary(eSolution, srcList) + self._bSecondary(eSolution, srcList)
+
+    def _bSecondaryDeriv_u(self, src, v, adjoint = False):
+        C = self.mesh.nodalGrad
+        if adjoint:
+            return - 1./(1j*omega(src.freq)) * (C.T * v)
+        return - 1./(1j*omega(src.freq)) * (C * v)
+
+    def _bSecondaryDeriv_m(self, src, v, adjoint = False):
+        # Doesn't depend on m
+        # _, S_eDeriv = src.evalDeriv(self.survey.prob, adjoint)
+        # S_eDeriv = S_eDeriv(v)
+        # if S_eDeriv is not None:
+        #     return 1./(1j * omega(src.freq)) * S_eDeriv
+        return None
+
+    def _bDeriv_u(self, src, v, adjoint=False):
+        # Primary does not depend on u
+        return self._bSecondaryDeriv_u(src, v, adjoint)
+
+    def _bDeriv_m(self, src, v, adjoint=False):
+        # Assuming the primary does not depend on the model
+        return self._bSecondaryDeriv_m(src, v, adjoint)
+
+    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_m(self, src, v, adjoint=False):
+        """
+        Derivative of the fields object wrt m.
+
+        This function stacks the fields derivatives appropriately
+        """
+        return None
+
+class Fields3D_e(BaseMTFields):
+    """
+    Fields storage for the 3D MT solution. Labels polarizations by px and py.
+
+        :param SimPEG object mesh: The solution mesh
+        :param SimPEG object survey: A survey object
+    """
+    # Define the known the alias fields
+    # Assume that the solution of e on the E.
+    ## NOTE: Need to make this more general, to allow for other solutions formats.
+    knownFields = {'e_pxSolution':'E','e_pySolution':'E'}
+    aliasFields = {
+                    'e_px' : ['e_pxSolution','E','_e_px'],
+                    'e_pxPrimary' : ['e_pxSolution','E','_e_pxPrimary'],
+                    'e_pxSecondary' : ['e_pxSolution','E','_e_pxSecondary'],
+                    'e_py' : ['e_pySolution','E','_e_py'],
+                    'e_pyPrimary' : ['e_pySolution','E','_e_pyPrimary'],
+                    'e_pySecondary' : ['e_pySolution','E','_e_pySecondary'],
+                    'b_px' : ['e_pxSolution','F','_b_px'],
+                    'b_pxPrimary' : ['e_pxSolution','F','_b_pxPrimary'],
+                    'b_pxSecondary' : ['e_pxSolution','F','_b_pxSecondary'],
+                    'b_py' : ['e_pySolution','F','_b_py'],
+                    'b_pyPrimary' : ['e_pySolution','F','_b_pyPrimary'],
+                    'b_pySecondary' : ['e_pySolution','F','_b_pySecondary']
+                  }
+
+    def __init__(self,mesh,survey,**kwargs):
+        BaseMTFields.__init__(self,mesh,survey,**kwargs)
+
+    def _e_pxPrimary(self, e_pxSolution, srcList):
+        e_pxPrimary = np.zeros_like(e_pxSolution)
+        for i, src in enumerate(srcList):
+            ep = src.ePrimary(self.survey.prob)
+            if ep is not None:
+                e_pxPrimary[:,i] = ep[:,0]
+        return e_pxPrimary
+
+    def _e_pyPrimary(self, e_pySolution, srcList):
+        e_pyPrimary = np.zeros_like(e_pySolution)
+        for i, src in enumerate(srcList):
+            ep = src.ePrimary(self.survey.prob)
+            if ep is not None:
+                e_pyPrimary[:,i] = ep[:,1]
+        return e_pyPrimary
+
+    def _e_pxSecondary(self, e_pxSolution, srcList):
+        return e_pxSolution
+
+    def _e_pySecondary(self, e_pySolution, srcList):
+        return e_pySolution
+
+    def _e_px(self, e_pxSolution, srcList):
+        return self._e_pxPrimary(e_pxSolution,srcList) + self._e_pxSecondary(e_pxSolution,srcList)
+
+    def _e_py(self, e_pySolution, srcList):
+        return self._e_pyPrimary(e_pySolution,srcList) + self._e_pySecondary(e_pySolution,srcList)
+
+    #NOTE: For e_p?Deriv_u,
+    # v has to be u(2*nE) long for the not adjoint and nE long for adjoint.
+    # Returns nE long for not adjoint and 2*nE long for adjoint
+    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 _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_pxDeriv_m(self, src, v, adjoint = False):
+        # assuming primary does not depend on the model
+        return None
+    def _e_pyDeriv_m(self, src, v, adjoint = False):
+        # assuming primary does not depend on the model
+        return None
+
+    def _b_pxPrimary(self, e_pxSolution, srcList):
+        b_pxPrimary = np.zeros([self.survey.mesh.nF,e_pxSolution.shape[1]], dtype = complex)
+        for i, src in enumerate(srcList):
+            bp = src.bPrimary(self.survey.prob)
+            if bp is not None:
+                b_pxPrimary[:,i] += bp[:,0]
+        return b_pxPrimary
+
+    def _b_pyPrimary(self, e_pySolution, srcList):
+        b_pyPrimary = np.zeros([self.survey.mesh.nF,e_pySolution.shape[1]], dtype = complex)
+        for i, src in enumerate(srcList):
+            bp = src.bPrimary(self.survey.prob)
+            if bp is not None:
+                b_pyPrimary[:,i] += bp[:,1]
+        return b_pyPrimary
+
+    def _b_pxSecondary(self, e_pxSolution, srcList):
+        C = self.mesh.edgeCurl
+        b = (C * e_pxSolution)
+        for i, src in enumerate(srcList):
+            b[:,i] *= - 1./(1j*omega(src.freq))
+            # There is no magnetic source in the MT problem
+            # S_m, _ = src.eval(self.survey.prob)
+            # if S_m is not None:
+            #     b[:,i] += 1./(1j*omega(src.freq)) * S_m
+        return b
+
+    def _b_pySecondary(self, e_pySolution, srcList):
+        C = self.mesh.edgeCurl
+        b = (C * e_pySolution)
+        for i, src in enumerate(srcList):
+            b[:,i] *= - 1./(1j*omega(src.freq))
+            # There is no magnetic source in the MT problem
+            # S_m, _ = src.eval(self.survey.prob)
+            # if S_m is not None:
+            #     b[:,i] += 1./(1j*omega(src.freq)) * S_m
+        return b
+
+    def _b_px(self, eSolution, srcList):
+        return self._b_pxPrimary(eSolution, srcList) + self._b_pxSecondary(eSolution, srcList)
+
+    def _b_py(self, eSolution, srcList):
+        return self._b_pyPrimary(eSolution, srcList) + self._b_pySecondary(eSolution, srcList)
+
+    # NOTE: v needs to be length 2*nE to account for both polarizations
+    def _b_pxSecondaryDeriv_u(self, src, v, adjoint = False):
+        # C = sp.kron(self.mesh.edgeCurl,[[1,0],[0,0]])
+        C = sp.hstack((self.mesh.edgeCurl,Utils.spzeros(self.mesh.nF,self.mesh.nE))) # This works for adjoint = None
+        if adjoint:
+            return - 1./(1j*omega(src.freq)) * (C.T * v)
+        return - 1./(1j*omega(src.freq)) * (C * v)
+
+    def _b_pySecondaryDeriv_u(self, src, v, adjoint = False):
+        # C = sp.kron(self.mesh.edgeCurl,[[0,0],[0,1]])
+        C = sp.hstack((Utils.spzeros(self.mesh.nF,self.mesh.nE),self.mesh.edgeCurl)) # This works for adjoint = None
+        if adjoint:
+            return - 1./(1j*omega(src.freq)) * (C.T * v)
+        return - 1./(1j*omega(src.freq)) * (C * v)
+
+    def _b_pxSecondaryDeriv_m(self, src, v, adjoint = False):
+        # Doesn't depend on m
+        # _, S_eDeriv = src.evalDeriv(self.survey.prob, adjoint)
+        # S_eDeriv = S_eDeriv(v)
+        # if S_eDeriv is not None:
+        #     return 1./(1j * omega(src.freq)) * S_eDeriv
+        return None
+
+    def _b_pySecondaryDeriv_m(self, src, v, adjoint = False):
+        # Doesn't depend on m
+        # _, S_eDeriv = src.evalDeriv(self.survey.prob, adjoint)
+        # S_eDeriv = S_eDeriv(v)
+        # if S_eDeriv is not None:
+        #     return 1./(1j * omega(src.freq)) * S_eDeriv
+        return None
+
+    def _b_pxDeriv_u(self, src, v, adjoint=False):
+        # Primary does not depend on u
+        return self._b_pxSecondaryDeriv_u(src, v, adjoint)
+
+    def _b_pyDeriv_u(self, src, v, adjoint=False):
+        # Primary does not depend on u
+        return self._b_pySecondaryDeriv_u(src, v, adjoint)
+
+    def _b_pxDeriv_m(self, src, v, adjoint=False):
+        # Assuming the primary does not depend on the model
+        return self._b_pxSecondaryDeriv_m(src, v, adjoint)
+
+    def _b_pyDeriv_m(self, src, v, adjoint=False):
+        # Assuming the primary does not depend on the model
+        return self._b_pySecondaryDeriv_m(src, v, adjoint)
+
+    def _f_pxDeriv_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._b_pxDeriv_u(src, v, adjoint)
+        # Return the stack
+        # This doesn't work...
+        return np.vstack((de_du,db_du))
+
+    def _f_pyDeriv_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._b_pyDeriv_u(src, v, adjoint)
+        # Return the stack
+        # This doesn't work...
+        return np.vstack((de_du,db_du))
+
+    def _f_pxDeriv_m(self, src, v, adjoint=False):
+        """
+        Derivative of the fields object wrt m.
+
+        This function stacks the fields derivatives appropriately
+        """
+        # The fields have no dependance to the model.
+        return None
+
+    def _f_pyDeriv_m(self, src, v, adjoint=False):
+        """
+        Derivative of the fields object wrt m.
+
+        This function stacks the fields derivatives appropriately
+        """
+        # The fields have no dependance to the model.
+        return None

SimPEG/MT/Problem1D/Probs.py

@@ -0,0 +1,291 @@
+from SimPEG.EM.Utils import omega
+from SimPEG import mkvc
+from scipy.constants import mu_0
+from SimPEG.MT.BaseMT import BaseMTProblem
+from SimPEG.MT.SurveyMT import Survey, Data
+from SimPEG.MT.FieldsMT import Fields1D_e
+from SimPEG.MT.Utils.MT1Danalytic import getEHfields
+import numpy as np
+import multiprocessing, sys, time
+
+
+class eForm_psField(BaseMTProblem):
+    """
+    A MT problem soving a e formulation and primary/secondary fields decomposion.
+
+    By eliminating the magnetic flux density using
+
+        .. math ::
+
+            \mathbf{b} = \\frac{1}{i \omega}\\left(-\mathbf{C} \mathbf{e} \\right)
+
+
+    we can write Maxwell's equations as a second order system in \\\(\\\mathbf{e}\\\) only:
+
+    .. math ::
+        \\left(\mathbf{C}^T \mathbf{M^e_{\mu^{-1}}} \mathbf{C} + i \omega \mathbf{M^f_\sigma}] \mathbf{e}_{s} =& i \omega \mathbf{M^f_{\delta \sigma}} \mathbf{e}_{p}
+    which we solve for \\\(\\\mathbf{e_s}\\\). The total field \\\mathbf{e}\\ = \\\mathbf{e_p}\\ + \\\mathbf{e_s}\\.
+
+    The primary field is estimated from a background model (commonly half space ).
+
+
+    """
+    # From FDEMproblem: Used to project the fields. Currently not used for MTproblem.
+    _fieldType = 'e_1d'
+    _eqLocs    = 'EF'
+    _sigmaPrimary = None
+
+
+    def __init__(self, mesh, **kwargs):
+        BaseMTProblem.__init__(self, mesh, **kwargs)
+        self.fieldsPair = Fields1D_e
+        # self._sigmaPrimary = sigmaPrimary
+    @property
+    def MeMui(self):
+        """
+            Edge inner product matrix
+        """
+        if getattr(self, '_MeMui', None) is None:
+            self._MeMui = self.mesh.getEdgeInnerProduct(1.0/mu_0)
+        return self._MeMui
+
+    @property
+    def MfSigma(self):
+        """
+            Edge inner product matrix
+        """
+        if getattr(self, '_MfSigma', None) is None:
+            self._MfSigma = self.mesh.getFaceInnerProduct(self.curModel.sigma)
+        return self._MfSigma
+
+    @property
+    def sigmaPrimary(self):
+        """
+        A background model, use for the calculation of the primary fields.
+
+        """
+        return self._sigmaPrimary
+
+    @sigmaPrimary.setter
+    def sigmaPrimary(self, val):
+        # Note: TODO add logic for val, make sure it is the correct size.
+        self._sigmaPrimary = val
+
+    def getA(self, freq):
+        """
+            Function to get the A matrix.
+
+            :param float freq: Frequency
+            :rtype: scipy.sparse.csr_matrix
+            :return: A
+        """
+
+        # Note: need to use the code above since in the 1D problem I want
+        # e to live on Faces(nodes) and h on edges(cells). Might need to rethink this
+        # Possible that _fieldType and _eqLocs can fix this
+        MeMui = self.MeMui
+        MfSigma = self.MfSigma
+        C = self.mesh.nodalGrad
+        # Make A
+        A = C.T*MeMui*C + 1j*omega(freq)*MfSigma
+        # Either return full or only the inner part of A
+        return A
+
+    def getADeriv_m(self, freq, u, v, adjoint=False):
+        """
+        The derivative of A wrt sigma
+        """
+
+        dsig_dm = self.curModel.sigmaDeriv
+        MeMui = self.MeMui
+        #
+        u_src = u['e_1dSolution']
+        dMfSigma_dm = self.mesh.getFaceInnerProductDeriv(self.curModel.sigma)(u_src) * self.curModel.sigmaDeriv
+        if adjoint:
+            return 1j * omega(freq) * (  dMfSigma_dm.T * v )
+        # Note: output has to be nN/nF, not nC/nE.
+        # v should be nC
+        return 1j * omega(freq) * ( dMfSigma_dm * v )
+
+    def getRHS(self, freq):
+        """
+            Function to return the right hand side for the system.
+            :param float freq: Frequency
+            :rtype: numpy.ndarray (nF, 1), numpy.ndarray (nF, 1)
+            :return: RHS for 1 polarizations, primary fields
+        """
+
+        # Get sources for the frequncy(polarizations)
+        Src = self.survey.getSrcByFreq(freq)[0]
+        S_e = Src.S_e(self)
+        return -1j * omega(freq) * S_e
+
+    def getRHSDeriv_m(self, freq, v, adjoint=False):
+        """
+        The derivative of the RHS wrt sigma
+        """
+
+        Src = self.survey.getSrcByFreq(freq)[0]
+        S_eDeriv = Src.S_eDeriv_m(self, v, adjoint)
+        return -1j * omega(freq) * S_eDeriv
+
+    def fields(self, m):
+        '''
+        Function to calculate all the fields for the model m.
+
+        :param np.ndarray (nC,) m: Conductivity model
+        '''
+        # Set the current model
+        self.curModel = m
+
+        F = Fields1D_e(self.mesh, self.survey)
+        for freq in self.survey.freqs:
+            if self.verbose:
+                startTime = time.time()
+                print 'Starting work for {:.3e}'.format(freq)
+                sys.stdout.flush()
+            A = self.getA(freq)
+            rhs  = self.getRHS(freq)
+            Ainv = self.Solver(A, **self.solverOpts)
+            e_s = Ainv * rhs
+
+            # Store the fields
+            Src = self.survey.getSrcByFreq(freq)[0]
+            # NOTE: only store the e_solution(secondary), all other components calculated in the fields object
+            F[Src, 'e_1dSolution'] = e_s[:,-1] # Only storing the yx polarization as 1d
+
+            # Note curl e = -iwb so b = -curl e /iw
+            # b = -( self.mesh.nodalGrad * e )/( 1j*omega(freq) )
+            # F[Src, 'b_1d'] = b[:,1]
+            if self.verbose:
+                print 'Ran for {:f} seconds'.format(time.time()-startTime)
+                sys.stdout.flush()
+        return F
+
+# Note this is not fully functional.
+# Missing:
+# Fields class corresponding to the fields
+# Update Jvec and Jtvec to include all the derivatives components
+# Other things ...
+class eForm_TotalField(BaseMTProblem):
+    """
+    A MT problem solving a e formulation and a Total bondary domain decompostion.
+
+    Solves the equation:
+
+    Math:
+
+
+    """
+
+    # From FDEMproblem: Used to project the fields. Currently not used for MTproblem.
+    _fieldType = 'e'
+    _eqLocs    = 'EF'
+
+
+    def __init__(self, mesh, **kwargs):
+        BaseMTProblem.__init__(self, mesh, **kwargs)
+    @property
+    def MeMui(self):
+        """
+            Edge inner product matrix
+        """
+        if getattr(self, '_MeMui', None) is None:
+            self._MeMui = self.mesh.getEdgeInnerProduct(1.0/mu_0)
+        return self._MeMui
+
+    @property
+    def MfSigma(self):
+        """
+            Edge inner product matrix
+        """
+        if getattr(self, '_MfSigma', None) is None:
+            self._MfSigma = self.mesh.getFaceInnerProduct(self.curModel.sigma)
+        return self._MfSigma
+
+    def getA(self, freq, full=False):
+        """
+            Function to get the A matrix.
+
+            :param float freq: Frequency
+            :param logic full: Return full A or the inner part
+            :rtype: scipy.sparse.csr_matrix
+            :return: A
+        """
+
+        MeMui = self.MeMui
+        MfSigma = self.MfSigma
+        # Note: need to use the code above since in the 1D problem I want
+        # e to live on Faces(nodes) and h on edges(cells). Might need to rethink this
+        # Possible that _fieldType and _eqLocs can fix this
+        # MeMui = self.MfMui
+        # MfSigma = self.MfSigma
+        C = self.mesh.nodalGrad
+        # Make A
+        A = C.T*MeMui*C + 1j*omega(freq)*MfSigma
+        # Either return full or only the inner part of A
+        if full:
+            return A
+        else:
+            return A[1:-1,1:-1]
+
+    def getADeriv_m(self, freq, u, v, adjoint=False):
+        raise NotImplementedError('getADeriv is not implemented')
+
+    def getRHS(self, freq):
+        """
+            Function to return the right hand side for the system.
+            :param float freq: Frequency
+            :rtype: numpy.ndarray (nE, 2), numpy.ndarray (nE, 2)
+            :return: RHS for both polarizations, primary fields
+        """
+        # Get sources for the frequency
+        # NOTE: Need to use the source information, doesn't really apply in 1D
+        src = self.survey.getSrcByFreq(freq)
+        # Get the full A
+        A = self.getA(freq,full=True)
+        # Define the outer part of the solution matrix
+        Aio = A[1:-1,[0,-1]]
+        Ed, Eu, Hd, Hu = getEHfields(self.mesh,self.curModel.sigma,freq,self.mesh.vectorNx)
+        Etot = (Ed + Eu)
+        sourceAmp = 1.0
+        Etot = ((Etot/Etot[-1])*sourceAmp) # Scale the fields to be equal to sourceAmp at the top
+        ## Note: The analytic solution is derived with e^iwt
+        eBC = np.r_[Etot[0],Etot[-1]]
+        # The right hand side
+
+        return -Aio*eBC, eBC
+
+    def getRHSderiv_m(self, freq, backSigma, u, v, adjoint=False):
+        raise NotImplementedError('getRHSDeriv not implemented yet')
+        return None
+
+    def fields(self, m):
+        '''
+        Function to calculate all the fields for the model m.
+
+        :param np.ndarray (nC,) m: Conductivity model
+        :param np.ndarray (nC,) m_back: Background conductivity model
+        '''
+        self.curModel = m
+        # RHS, CalcFields = self.getRHS(freq,m_back), self.calcFields
+
+        F = Fields1D_e(self.mesh, self.survey)
+        for freq in self.survey.freqs:
+            if self.verbose:
+                startTime = time.time()
+                print 'Starting work for {:.3e}'.format(freq)
+                sys.stdout.flush()
+            A = self.getA(freq)
+            rhs, e_o = self.getRHS(freq)
+            Ainv = self.Solver(A, **self.solverOpts)
+            e_i = Ainv * rhs
+            e = mkvc(np.r_[e_o[0], e_i, e_o[1]],2)
+            # Store the fields
+            Src = self.survey.getSrcByFreq(freq)
+            # NOTE: only store e fields
+            F[Src, 'e_1dSolution'] = e[:,0]
+            if self.verbose:
+                print 'Ran for {:f} seconds'.format(time.time()-startTime)
+                sys.stdout.flush()
+        return F

SimPEG/MT/Problem1D/__init__.py

@@ -0,0 +1 @@
+from Probs import eForm_TotalField, eForm_psField

SimPEG/MT/Problem2D/__init__.py

@@ -0,0 +1 @@
+pass

SimPEG/MT/Problem3D/Probs.py

@@ -0,0 +1,138 @@
+from SimPEG import Survey, Problem, Utils, Models, np, sp, mkvc, SolverLU as SimpegSolver
+from SimPEG.EM.Utils import omega
+from scipy.constants import mu_0
+from SimPEG.MT.BaseMT import BaseMTProblem
+from SimPEG.MT.SurveyMT import Survey, Data
+from SimPEG.MT.FieldsMT import Fields3D_e
+import multiprocessing, sys, time
+
+
+
+class eForm_ps(BaseMTProblem):
+    """
+    A MT problem solving a e formulation and a primary/secondary fields decompostion.
+
+    By eliminating the magnetic flux density using
+
+        .. math ::
+
+            \mathbf{b} = \\frac{1}{i \omega}\\left(-\mathbf{C} \mathbf{e} \\right)
+
+
+    we can write Maxwell's equations as a second order system in \\\(\\\mathbf{e}\\\) only:
+
+    .. math ::
+        \\left(\mathbf{C}^T \mathbf{M^f_{\mu^{-1}}} \mathbf{C} + i \omega \mathbf{M^e_\sigma}] \mathbf{e}_{s} =& i \omega \mathbf{M^e_{\delta \sigma}} \mathbf{e}_{p}
+    which we solve for \\\(\\\mathbf{e_s}\\\). The total field \\\mathbf{e}\\ = \\\mathbf{e_p}\\ + \\\mathbf{e_s}\\.
+
+    The primary field is estimated from a background model (commonly as a 1D model).
+
+    """
+
+    # From FDEMproblem: Used to project the fields. Currently not used for MTproblem.
+    _fieldType = 'e'
+    _eqLocs    = 'FE'
+    fieldsPair = Fields3D_e
+    _sigmaPrimary = None
+
+    def __init__(self, mesh, **kwargs):
+        BaseMTProblem.__init__(self, mesh, **kwargs)
+
+    @property
+    def sigmaPrimary(self):
+        """
+        A background model, use for the calculation of the primary fields.
+
+        """
+        return self._sigmaPrimary
+    @sigmaPrimary.setter
+    def sigmaPrimary(self, val):
+        # Note: TODO add logic for val, make sure it is the correct size.
+        self._sigmaPrimary = val
+
+    def getA(self, freq):
+        """
+            Function to get the A system.
+
+            :param float freq: Frequency
+            :rtype: scipy.sparse.csr_matrix
+            :return: A
+        """
+        Mmui = self.MfMui
+        Msig = self.MeSigma
+        C = self.mesh.edgeCurl
+
+        return C.T*Mmui*C + 1j*omega(freq)*Msig
+
+    def getADeriv_m(self, freq, u, v, adjoint=False):
+        """
+        Calculate the derivative of A wrt m.
+
+        """
+
+        # This considers both polarizations and returns a nE,2 matrix for each polarization
+        if adjoint:
+            dMe_dsigV = sp.hstack(( self.MeSigmaDeriv( u['e_pxSolution'] ).T, self.MeSigmaDeriv(u['e_pySolution'] ).T ))*v
+        else:
+            # Need a nE,2 matrix to be returned
+            dMe_dsigV = np.hstack(( mkvc(self.MeSigmaDeriv( u['e_pxSolution'] )*v,2), mkvc( self.MeSigmaDeriv(u['e_pySolution'] )*v,2) ))
+        return 1j * omega(freq) * dMe_dsigV
+
+
+    def getRHS(self, freq):
+        """
+        Function to return the right hand side for the system.
+
+            :param float freq: Frequency
+            :rtype: numpy.ndarray (nE, 2), numpy.ndarray (nE, 2)
+            :return: RHS for both polarizations, primary fields
+        """
+
+        # Get sources for the frequncy(polarizations)
+        Src = self.survey.getSrcByFreq(freq)[0]
+        S_e = Src.S_e(self)
+        return -1j * omega(freq) * S_e
+
+    def getRHSDeriv_m(self, freq, v, adjoint=False):
+        """
+        The derivative of the RHS with respect to sigma
+        """
+
+        Src = self.survey.getSrcByFreq(freq)[0]
+        S_eDeriv = Src.S_eDeriv_m(self, v, adjoint)
+        return -1j * omega(freq) * S_eDeriv
+
+    def fields(self, m):
+        '''
+        Function to calculate all the fields for the model m.
+
+        :param np.ndarray (nC,) m: Conductivity model
+        '''
+        # Set the current model
+        self.curModel = m
+
+        F = Fields3D_e(self.mesh, self.survey)
+        for freq in self.survey.freqs:
+            if self.verbose:
+                startTime = time.time()
+                print 'Starting work for {:.3e}'.format(freq)
+                sys.stdout.flush()
+            A = self.getA(freq)
+            rhs  = self.getRHS(freq)
+            # Solve the system
+            Ainv = self.Solver(A, **self.solverOpts)
+            e_s = Ainv * rhs
+
+            # Store the fields
+            Src = self.survey.getSrcByFreq(freq)[0]
+            # Store the fieldss
+            F[Src, 'e_pxSolution'] = e_s[:,0]
+            F[Src, 'e_pySolution'] = e_s[:,1]
+            # Note curl e = -iwb so b = -curl/iw
+
+            if self.verbose:
+                print 'Ran for {:f} seconds'.format(time.time()-startTime)
+                sys.stdout.flush()
+            Ainv.clean()
+        return F
+

SimPEG/MT/Problem3D/__init__.py

@@ -0,0 +1 @@
+from Probs import eForm_ps

SimPEG/MT/SrcMT.py

@@ -0,0 +1,206 @@
+from SimPEG import Utils, Problem, Maps, np, sp, mkvc
+from SimPEG.EM.FDEM.SrcFDEM import BaseSrc as FDEMBaseSrc
+from SimPEG.EM.Utils import omega
+from scipy.constants import mu_0
+from numpy.lib import recfunctions as recFunc
+from Utils.sourceUtils import homo1DModelSource
+from Utils import rec2ndarr
+import sys
+
+#################
+###   Sources ###
+#################
+
+class BaseMTSrc(FDEMBaseSrc):
+    '''
+    Sources for the MT problem.
+    Use the SimPEG BaseSrc, since the source fields share properties with the transmitters.
+
+    :param float freq: The frequency of the source
+    :param list rxList: A list of receivers associated with the source
+    '''
+
+    freq = None #: Frequency (float)
+
+
+    def __init__(self, rxList, freq):
+
+        self.freq = float(freq)
+        FDEMBaseSrc.__init__(self, rxList)
+
+# 1D sources
+class polxy_1DhomotD(BaseMTSrc):
+    """
+    MT source for both polarizations (x and y) for the total Domain.
+
+    It calculates fields calculated based on conditions on the boundary of the domain.
+    """
+    def __init__(self, rxList, freq):
+        BaseMTSrc.__init__(self, rxList, freq)
+
+
+    # TODO: need to add the  primary fields calc and source terms into the problem.
+
+# Need to implement such that it works for all dims.
+class polxy_1Dprimary(BaseMTSrc):
+    """
+    MT source for both polarizations (x and y) given a 1D primary models.
+    It assigns fields calculated from the 1D model as fields in the full space of the problem.
+    """
+    def __init__(self, rxList, freq):
+        # assert mkvc(self.mesh.hz.shape,1) == mkvc(sigma1d.shape,1),'The number of values in the 1D background model does not match the number of vertical cells (hz).'
+        self.sigma1d = None
+        BaseMTSrc.__init__(self, rxList, freq)
+        # Hidden property of the ePrimary
+        self._ePrimary = None
+
+    def ePrimary(self,problem):
+        # Get primary fields for both polarizations
+        if self.sigma1d is None:
+            # Set the sigma1d as the 1st column in the background model
+            if len(problem._sigmaPrimary) == problem.mesh.nC:
+                if problem.mesh.dim == 1:
+                    self.sigma1d = problem.mesh.r(problem._sigmaPrimary,'CC','CC','M')[:]
+                elif problem.mesh.dim == 3:
+                    self.sigma1d = problem.mesh.r(problem._sigmaPrimary,'CC','CC','M')[0,0,:]
+            # Or as the 1D model that matches the vertical cell number
+            elif len(problem._sigmaPrimary) == problem.mesh.nCz:
+                self.sigma1d = problem._sigmaPrimary
+
+        if self._ePrimary is None:
+            self._ePrimary = homo1DModelSource(problem.mesh,self.freq,self.sigma1d)
+        return self._ePrimary
+
+    def bPrimary(self,problem):
+        # Project ePrimary to bPrimary
+        # Satisfies the primary(background) field conditions
+        if problem.mesh.dim == 1:
+            C = problem.mesh.nodalGrad
+        elif problem.mesh.dim == 3:
+            C = problem.mesh.edgeCurl
+        bBG_bp = (- C * self.ePrimary(problem) )*(1/( 1j*omega(self.freq) ))
+        return bBG_bp
+
+    def S_e(self,problem):
+        """
+        Get the electrical field source
+        """
+        e_p = self.ePrimary(problem)
+        Map_sigma_p = Maps.Vertical1DMap(problem.mesh)
+        sigma_p = Map_sigma_p._transform(self.sigma1d)
+        # Make mass matrix
+        # Note: M(sig) - M(sig_p) = M(sig - sig_p)
+        # Need to deal with the edge/face discrepencies between 1d/2d/3d
+        if problem.mesh.dim == 1:
+            Mesigma = problem.mesh.getFaceInnerProduct(problem.curModel.sigma)
+            Mesigma_p = problem.mesh.getFaceInnerProduct(sigma_p)
+        if problem.mesh.dim == 2:
+            pass
+        if problem.mesh.dim == 3:
+            Mesigma = problem.MeSigma
+            Mesigma_p = problem.mesh.getEdgeInnerProduct(sigma_p)
+        return (Mesigma - Mesigma_p) * e_p
+
+    def S_eDeriv_m(self, problem, v, adjoint = False):
+        '''
+        Get the derivative of S_e wrt to sigma (m)
+        '''
+        # Need to deal with
+        if problem.mesh.dim == 1:
+            # Need to use the faceInnerProduct
+            MsigmaDeriv = problem.mesh.getFaceInnerProductDeriv(problem.curModel.sigma)(self.ePrimary(problem)[:,1]) * problem.curModel.sigmaDeriv
+            # MsigmaDeriv = ( MsigmaDeriv * MsigmaDeriv.T)**2
+        if problem.mesh.dim == 2:
+            pass
+        if problem.mesh.dim == 3:
+            # Need to take the derivative of both u_px and u_py
+            ePri = self.ePrimary(problem)
+            # MsigmaDeriv = problem.MeSigmaDeriv(ePri[:,0]) + problem.MeSigmaDeriv(ePri[:,1])
+            # MsigmaDeriv = problem.MeSigmaDeriv(np.sum(ePri,axis=1))
+            if adjoint:
+                return sp.hstack(( problem.MeSigmaDeriv(ePri[:,0]).T, problem.MeSigmaDeriv(ePri[:,1]).T ))*v
+            else:
+                return np.hstack(( mkvc(problem.MeSigmaDeriv(ePri[:,0]) * v,2), mkvc(problem.MeSigmaDeriv(ePri[:,1])*v,2) ))
+        if adjoint:
+            #
+            return MsigmaDeriv.T * v
+        else:
+            # v should be nC size
+            return MsigmaDeriv * v
+
+class polxy_3Dprimary(BaseMTSrc):
+    """
+    MT source for both polarizations (x and y) given a 3D primary model. It assigns fields calculated from the 1D model
+    as fields in the full space of the problem.
+    """
+    def __init__(self, rxList, freq):
+        # assert mkvc(self.mesh.hz.shape,1) == mkvc(sigma1d.shape,1),'The number of values in the 1D background model does not match the number of vertical cells (hz).'
+        self.sigmaPrimary = None
+        BaseMTSrc.__init__(self, rxList, freq)
+        # Hidden property of the ePrimary
+        self._ePrimary = None
+
+    def ePrimary(self,problem):
+        # Get primary fields for both polarizations
+        self.sigmaPrimary = problem._sigmaPrimary
+
+        if self._ePrimary is None:
+            self._ePrimary = homo3DModelSource(problem.mesh,self.sigmaPrimary,self.freq)
+        return self._ePrimary
+
+    def bPrimary(self,problem):
+        # Project ePrimary to bPrimary
+        # Satisfies the primary(background) field conditions
+        if problem.mesh.dim == 1:
+            C = problem.mesh.nodalGrad
+        elif problem.mesh.dim == 3:
+            C = problem.mesh.edgeCurl
+        bBG_bp = (- C * self.ePrimary(problem) )*(1/( 1j*omega(self.freq) ))
+        return bBG_bp
+
+    def S_e(self,problem):
+        """
+        Get the electrical field source
+        """
+        e_p = self.ePrimary(problem)
+        Map_sigma_p = Maps.Vertical1DMap(problem.mesh)
+        sigma_p = Map_sigma_p._transform(self.sigma1d)
+        # Make mass matrix
+        # Note: M(sig) - M(sig_p) = M(sig - sig_p)
+        # Need to deal with the edge/face discrepencies between 1d/2d/3d
+        if problem.mesh.dim == 1:
+            Mesigma = problem.mesh.getFaceInnerProduct(problem.curModel.sigma)
+            Mesigma_p = problem.mesh.getFaceInnerProduct(sigma_p)
+        if problem.mesh.dim == 2:
+            pass
+        if problem.mesh.dim == 3:
+            Mesigma = problem.MeSigma
+            Mesigma_p = problem.mesh.getEdgeInnerProduct(sigma_p)
+        return (Mesigma - Mesigma_p) * e_p
+
+    def S_eDeriv_m(self, problem, v, adjoint = False):
+        '''
+        Get the derivative of S_e wrt to sigma (m)
+        '''
+        # Need to deal with
+        if problem.mesh.dim == 1:
+            # Need to use the faceInnerProduct
+            MsigmaDeriv = problem.mesh.getFaceInnerProductDeriv(problem.curModel.sigma)(self.ePrimary(problem)[:,1]) * problem.curModel.sigmaDeriv
+            # MsigmaDeriv = ( MsigmaDeriv * MsigmaDeriv.T)**2
+        if problem.mesh.dim == 2:
+            pass
+        if problem.mesh.dim == 3:
+            # Need to take the derivative of both u_px and u_py
+            ePri = self.ePrimary(problem)
+            # MsigmaDeriv = problem.MeSigmaDeriv(ePri[:,0]) + problem.MeSigmaDeriv(ePri[:,1])
+            # MsigmaDeriv = problem.MeSigmaDeriv(np.sum(ePri,axis=1))
+            if adjoint:
+                return sp.hstack(( problem.MeSigmaDeriv(ePri[:,0]).T, problem.MeSigmaDeriv(ePri[:,1]).T ))*v
+            else:
+                return np.hstack(( mkvc(problem.MeSigmaDeriv(ePri[:,0]) * v,2), mkvc(problem.MeSigmaDeriv(ePri[:,1])*v,2) ))
+        if adjoint:
+            #
+            return MsigmaDeriv.T * v
+        else:
+            # v should be nC size
+            return MsigmaDeriv * v

SimPEG/MT/SurveyMT.py

@@ -0,0 +1,562 @@
+from SimPEG import Survey as SimPEGsurvey, Utils, Problem, Maps, np, sp, mkvc
+from SimPEG.EM.FDEM.SrcFDEM import BaseSrc as FDEMBaseSrc
+from SimPEG.EM.Utils import omega
+from scipy.constants import mu_0
+from numpy.lib import recfunctions as recFunc
+from Utils import rec2ndarr
+import SrcMT
+import sys
+
+#################
+### Receivers ###
+#################
+class Rx(SimPEGsurvey.BaseRx):
+    """
+        Class that defines natural source receivers.
+
+        See knownRxTypes for types of allowed receivers.
+
+        :param ndArray locs: Locations of the receivers
+        :param str rxType: The type of receiver
+
+    """
+
+    knownRxTypes = {
+                    # 3D impedance
+                    'zxxr':['Z3D', 'real'],
+                    'zxyr':['Z3D', 'real'],
+                    'zyxr':['Z3D', 'real'],
+                    'zyyr':['Z3D', 'real'],
+                    'zxxi':['Z3D', 'imag'],
+                    'zxyi':['Z3D', 'imag'],
+                    'zyxi':['Z3D', 'imag'],
+                    'zyyi':['Z3D', 'imag'],
+                    # 2D impedance
+                    # TODO:
+                    # 1D impedance
+                    'z1dr':['Z1D', 'real'],
+                    'z1di':['Z1D', 'imag'],
+                    # Tipper
+                    'tzxr':['T3D','real'],
+                    'tzxi':['T3D','imag'],
+                    'tzyr':['T3D','real'],
+                    'tzyi':['T3D','imag']
+                   }
+    # TODO: Have locs as single or double coordinates for both or numerator and denominator separately, respectively.
+    def __init__(self, locs, rxType):
+        SimPEGsurvey.BaseRx.__init__(self, locs, rxType)
+
+    @property
+    def projType(self):
+        """
+        Receiver type for projection.
+
+        """
+        return self.knownRxTypes[self.rxType][0]
+
+    @property
+    def projComp(self):
+        """Component projection (real/imag)"""
+        return self.knownRxTypes[self.rxType][1]
+
+    def projectFields(self, src, mesh, f):
+        '''
+        Project the fields to natural source data.
+
+            :param SrcMT src: The source of the fields to project
+            :param SimPEG.Mesh mesh:
+            :param FieldsMT f: Natural source fields object to project
+        '''
+
+        ## NOTE: Assumes that e is on t
+        if self.projType is 'Z1D':
+            Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
+            Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
+            ex = Pex*mkvc(f[src,'e_1d'],2)
+            bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
+            # Note: Has a minus sign in front, to comply with quadrant calculations.
+            # Can be derived from zyx case for the 3D case.
+            f_part_complex = -ex/bx
+        # elif self.projType is 'Z2D':
+        elif self.projType is 'Z3D':
+            ## NOTE: Assumes that e is on edges and b on the faces. Need to generalize that or use a prop of fields to determine that.
+            if self.locs.ndim == 3:
+                eFLocs = self.locs[:,:,0]
+                bFLocs = self.locs[:,:,1]
+            else:
+                eFLocs = self.locs
+                bFLocs = self.locs
+            # Get the projection
+            Pex = mesh.getInterpolationMat(eFLocs,'Ex')
+            Pey = mesh.getInterpolationMat(eFLocs,'Ey')
+            Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
+            Pby = mesh.getInterpolationMat(bFLocs,'Fy')
+            # Get the fields at location
+            # px: x-polaration and py: y-polaration.
+            ex_px = Pex*f[src,'e_px']
+            ey_px = Pey*f[src,'e_px']
+            ex_py = Pex*f[src,'e_py']
+            ey_py = Pey*f[src,'e_py']
+            hx_px = Pbx*f[src,'b_px']/mu_0
+            hy_px = Pby*f[src,'b_px']/mu_0
+            hx_py = Pbx*f[src,'b_py']/mu_0
+            hy_py = Pby*f[src,'b_py']/mu_0
+            # Make the complex data
+            if 'zxx' in self.rxType:
+                f_part_complex = ( ex_px*hy_py - ex_py*hy_px)/(hx_px*hy_py - hx_py*hy_px)
+            elif 'zxy' in self.rxType:
+                f_part_complex = (-ex_px*hx_py + ex_py*hx_px)/(hx_px*hy_py - hx_py*hy_px)
+            elif 'zyx' in self.rxType:
+                f_part_complex = ( ey_px*hy_py - ey_py*hy_px)/(hx_px*hy_py - hx_py*hy_px)
+            elif 'zyy' in self.rxType:
+                f_part_complex = (-ey_px*hx_py + ey_py*hx_px)/(hx_px*hy_py - hx_py*hy_px)
+        elif self.projType is 'T3D':
+            if self.locs.ndim == 3:
+                horLoc = self.locs[:,:,0]
+                vertLoc = self.locs[:,:,1]
+            else:
+                horLoc = self.locs
+                vertLoc = self.locs
+            Pbx = mesh.getInterpolationMat(horLoc,'Fx')
+            Pby = mesh.getInterpolationMat(horLoc,'Fy')
+            Pbz = mesh.getInterpolationMat(vertLoc,'Fz')
+            bx_px = Pbx*f[src,'b_px']
+            by_px = Pby*f[src,'b_px']
+            bz_px = Pbz*f[src,'b_px']
+            bx_py = Pbx*f[src,'b_py']
+            by_py = Pby*f[src,'b_py']
+            bz_py = Pbz*f[src,'b_py']
+            if 'tzx' in self.rxType:
+                f_part_complex = (- by_px*bz_py + by_py*bz_px)/(bx_px*by_py - bx_py*by_px)
+            if 'tzy' in self.rxType:
+                f_part_complex = (  bx_px*bz_py - bx_py*bz_px)/(bx_px*by_py - bx_py*by_px)
+
+        else:
+            NotImplementedError('Projection of {:s} receiver type is not implemented.'.format(self.rxType))
+        # Get the real or imag component
+        real_or_imag = self.projComp
+        f_part = getattr(f_part_complex, real_or_imag)
+        # print f_part
+        return f_part
+
+    def projectFieldsDeriv(self, src, mesh, f, v, adjoint=False):
+        """
+        The derivative of the projection wrt u
+
+        :param MTsrc src: MT source
+        :param TensorMesh mesh: Mesh defining the topology of the problem
+        :param MTfields f: MT fields object of the source
+        :param numpy.ndarray v: Random vector of size
+        """
+
+        real_or_imag = self.projComp
+
+        if not adjoint:
+            if self.projType is 'Z1D':
+                Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
+                Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
+                # ex = Pex*mkvc(f[src,'e_1d'],2)
+                # bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
+                dP_de = -mkvc(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))*(Pex*v),2)
+                dP_db = mkvc( Utils.sdiag(Pex*mkvc(f[src,'e_1d'],2))*(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)).T*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)))*(Pbx*f._bDeriv_u(src,v)/mu_0),2)
+                PDeriv_complex = np.sum(np.hstack((dP_de,dP_db)),1)
+            elif self.projType is 'Z2D':
+                raise NotImplementedError('Has not been implement for 2D impedance tensor')
+            elif self.projType is 'Z3D':
+                if self.locs.ndim == 3:
+                    eFLocs = self.locs[:,:,0]
+                    bFLocs = self.locs[:,:,1]
+                else:
+                    eFLocs = self.locs
+                    bFLocs = self.locs
+                # Get the projection
+                Pex = mesh.getInterpolationMat(eFLocs,'Ex')
+                Pey = mesh.getInterpolationMat(eFLocs,'Ey')
+                Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
+                Pby = mesh.getInterpolationMat(bFLocs,'Fy')
+                # Get the fields at location
+                # px: x-polaration and py: y-polaration.
+                ex_px = Pex*f[src,'e_px']
+                ey_px = Pey*f[src,'e_px']
+                ex_py = Pex*f[src,'e_py']
+                ey_py = Pey*f[src,'e_py']
+                hx_px = Pbx*f[src,'b_px']/mu_0
+                hy_px = Pby*f[src,'b_px']/mu_0
+                hx_py = Pbx*f[src,'b_py']/mu_0
+                hy_py = Pby*f[src,'b_py']/mu_0
+                # Derivatives as lambda functions
+                # The size of the diratives should be nD,nU
+                ex_px_u = lambda vec: Pex*f._e_pxDeriv_u(src,vec)
+                ey_px_u = lambda vec: Pey*f._e_pxDeriv_u(src,vec)
+                ex_py_u = lambda vec: Pex*f._e_pyDeriv_u(src,vec)
+                ey_py_u = lambda vec: Pey*f._e_pyDeriv_u(src,vec)
+                # NOTE: Think b_p?Deriv_u should return a 2*nF size matrix
+                hx_px_u = lambda vec: Pbx*f._b_pxDeriv_u(src,vec)/mu_0
+                hy_px_u = lambda vec: Pby*f._b_pxDeriv_u(src,vec)/mu_0
+                hx_py_u = lambda vec: Pbx*f._b_pyDeriv_u(src,vec)/mu_0
+                hy_py_u = lambda vec: Pby*f._b_pyDeriv_u(src,vec)/mu_0
+                # Update the input vector
+                sDiag = lambda t: Utils.sdiag(mkvc(t,2))
+                # Define the components of the derivative
+                Hd = sDiag(1./(sDiag(hx_px)*hy_py - sDiag(hx_py)*hy_px))
+                Hd_uV = sDiag(hy_py)*hx_px_u(v) + sDiag(hx_px)*hy_py_u(v) - sDiag(hx_py)*hy_px_u(v) - sDiag(hy_px)*hx_py_u(v)
+                # Calculate components
+                if 'zxx' in self.rxType:
+                    Zij = sDiag(Hd*( sDiag(ex_px)*hy_py - sDiag(ex_py)*hy_px ))
+                    ZijN_uV =  sDiag(hy_py)*ex_px_u(v) + sDiag(ex_px)*hy_py_u(v) - sDiag(ex_py)*hy_px_u(v) - sDiag(hy_px)*ex_py_u(v)
+                elif 'zxy' in self.rxType:
+                    Zij = sDiag(Hd*(-sDiag(ex_px)*hx_py + sDiag(ex_py)*hx_px ))
+                    ZijN_uV = -sDiag(hx_py)*ex_px_u(v) - sDiag(ex_px)*hx_py_u(v) + sDiag(ex_py)*hx_px_u(v) + sDiag(hx_px)*ex_py_u(v)
+                elif 'zyx' in self.rxType:
+                    Zij = sDiag(Hd*( sDiag(ey_px)*hy_py - sDiag(ey_py)*hy_px ))
+                    ZijN_uV =  sDiag(hy_py)*ey_px_u(v) + sDiag(ey_px)*hy_py_u(v) - sDiag(ey_py)*hy_px_u(v) - sDiag(hy_px)*ey_py_u(v)
+                elif 'zyy' in self.rxType:
+                    Zij = sDiag(Hd*(-sDiag(ey_px)*hx_py + sDiag(ey_py)*hx_px ))
+                    ZijN_uV = -sDiag(hx_py)*ey_px_u(v) - sDiag(ey_px)*hx_py_u(v) + sDiag(ey_py)*hx_px_u(v) + sDiag(hx_px)*ey_py_u(v)
+
+                # Calculate the complex derivative
+                PDeriv_complex = Hd * (ZijN_uV - Zij * Hd_uV )
+            elif self.projType is 'T3D':
+                if self.locs.ndim == 3:
+                    eFLocs = self.locs[:,:,0]
+                    bFLocs = self.locs[:,:,1]
+                else:
+                    eFLocs = self.locs
+                    bFLocs = self.locs
+                # Get the projection
+                Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
+                Pby = mesh.getInterpolationMat(bFLocs,'Fy')
+                Pbz = mesh.getInterpolationMat(bFLocs,'Fz')
+
+                # Get the fields at location
+                # px: x-polaration and py: y-polaration.
+                bx_px = Pbx*f[src,'b_px']
+                by_px = Pby*f[src,'b_px']
+                bz_px = Pbz*f[src,'b_px']
+                bx_py = Pbx*f[src,'b_py']
+                by_py = Pby*f[src,'b_py']
+                bz_py = Pbz*f[src,'b_py']
+                # Derivatives as lambda functions
+                # NOTE: Think b_p?Deriv_u should return a 2*nF size matrix
+                bx_px_u = lambda vec: Pbx*f._b_pxDeriv_u(src,vec)
+                by_px_u = lambda vec: Pby*f._b_pxDeriv_u(src,vec)
+                bz_px_u = lambda vec: Pbz*f._b_pxDeriv_u(src,vec)
+                bx_py_u = lambda vec: Pbx*f._b_pyDeriv_u(src,vec)
+                by_py_u = lambda vec: Pby*f._b_pyDeriv_u(src,vec)
+                bz_py_u = lambda vec: Pbz*f._b_pyDeriv_u(src,vec)
+                # Update the input vector
+                sDiag = lambda t: Utils.sdiag(mkvc(t,2))
+                # Define the components of the derivative
+                Hd = sDiag(1./(sDiag(bx_px)*by_py - sDiag(bx_py)*by_px))
+                Hd_uV = sDiag(by_py)*bx_px_u(v) + sDiag(bx_px)*by_py_u(v) - sDiag(bx_py)*by_px_u(v) - sDiag(by_px)*bx_py_u(v)
+                if 'tzx' in self.rxType:
+                    Tij = sDiag(Hd*( - sDiag(by_px)*bz_py + sDiag(by_py)*bz_px ))
+                    TijN_uV = -sDiag(by_px)*bz_py_u(v) - sDiag(bz_py)*by_px_u(v) + sDiag(by_py)*bz_px_u(v) + sDiag(bz_px)*by_py_u(v)
+                elif 'tzy' in self.rxType:
+                    Tij = sDiag(Hd*( sDiag(bx_px)*bz_py - sDiag(bx_py)*bz_px ))
+                    TijN_uV =  sDiag(bz_py)*bx_px_u(v) + sDiag(bx_px)*bz_py_u(v) - sDiag(bx_py)*bz_px_u(v) - sDiag(bz_px)*bx_py_u(v)
+                # Calculate the complex derivative
+                PDeriv_complex = Hd * (TijN_uV - Tij * Hd_uV )
+
+            # Extract the real number for the real/imag components.
+            Pv = np.array(getattr(PDeriv_complex, real_or_imag))
+        elif adjoint:
+            # Note: The v vector is real and the return should be complex
+            if self.projType is 'Z1D':
+                Pex = mesh.getInterpolationMat(self.locs[:,-1],'Fx')
+                Pbx = mesh.getInterpolationMat(self.locs[:,-1],'Ex')
+                # ex = Pex*mkvc(f[src,'e_1d'],2)
+                # bx = Pbx*mkvc(f[src,'b_1d'],2)/mu_0
+                dP_deTv = -mkvc(Pex.T*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0)).T*v,2)
+                db_duv = Pbx.T/mu_0*Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))*(Utils.sdiag(1./(Pbx*mkvc(f[src,'b_1d'],2)/mu_0))).T*Utils.sdiag(Pex*mkvc(f[src,'e_1d'],2)).T*v
+                dP_dbTv = mkvc(f._bDeriv_u(src,db_duv,adjoint=True),2)
+                PDeriv_real = np.sum(np.hstack((dP_deTv,dP_dbTv)),1)
+            elif self.projType is 'Z2D':
+                raise NotImplementedError('Has not be implement for 2D impedance tensor')
+            elif self.projType is 'Z3D':
+                if self.locs.ndim == 3:
+                    eFLocs = self.locs[:,:,0]
+                    bFLocs = self.locs[:,:,1]
+                else:
+                    eFLocs = self.locs
+                    bFLocs = self.locs
+                # Get the projection
+                Pex = mesh.getInterpolationMat(eFLocs,'Ex')
+                Pey = mesh.getInterpolationMat(eFLocs,'Ey')
+                Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
+                Pby = mesh.getInterpolationMat(bFLocs,'Fy')
+                # Get the fields at location
+                # px: x-polaration and py: y-polaration.
+                aex_px = mkvc(mkvc(f[src,'e_px'],2).T*Pex.T)
+                aey_px = mkvc(mkvc(f[src,'e_px'],2).T*Pey.T)
+                aex_py = mkvc(mkvc(f[src,'e_py'],2).T*Pex.T)
+                aey_py = mkvc(mkvc(f[src,'e_py'],2).T*Pey.T)
+                ahx_px = mkvc(mkvc(f[src,'b_px'],2).T/mu_0*Pbx.T)
+                ahy_px = mkvc(mkvc(f[src,'b_px'],2).T/mu_0*Pby.T)
+                ahx_py = mkvc(mkvc(f[src,'b_py'],2).T/mu_0*Pbx.T)
+                ahy_py = mkvc(mkvc(f[src,'b_py'],2).T/mu_0*Pby.T)
+                # Derivatives as lambda functions
+                aex_px_u = lambda vec: f._e_pxDeriv_u(src,Pex.T*vec,adjoint=True)
+                aey_px_u = lambda vec: f._e_pxDeriv_u(src,Pey.T*vec,adjoint=True)
+                aex_py_u = lambda vec: f._e_pyDeriv_u(src,Pex.T*vec,adjoint=True)
+                aey_py_u = lambda vec: f._e_pyDeriv_u(src,Pey.T*vec,adjoint=True)
+                ahx_px_u = lambda vec: f._b_pxDeriv_u(src,Pbx.T*vec,adjoint=True)/mu_0
+                ahy_px_u = lambda vec: f._b_pxDeriv_u(src,Pby.T*vec,adjoint=True)/mu_0
+                ahx_py_u = lambda vec: f._b_pyDeriv_u(src,Pbx.T*vec,adjoint=True)/mu_0
+                ahy_py_u = lambda vec: f._b_pyDeriv_u(src,Pby.T*vec,adjoint=True)/mu_0
+
+                # Update the input vector
+                # Define shortcuts
+                sDiag = lambda t: Utils.sdiag(mkvc(t,2))
+                sVec = lambda t: Utils.sp.csr_matrix(mkvc(t,2))
+                # Define the components of the derivative
+                aHd = sDiag(1./(sDiag(ahx_px)*ahy_py - sDiag(ahx_py)*ahy_px))
+                aHd_uV = lambda x: ahx_px_u(sDiag(ahy_py)*x) + ahx_px_u(sDiag(ahy_py)*x) - ahy_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(ahy_px)*x)
+                # Need to fix this to reflect the adjoint
+                if 'zxx' in self.rxType:
+                    Zij = sDiag(aHd*( sDiag(ahy_py)*aex_px - sDiag(ahy_px)*aex_py))
+                    ZijN_uV = lambda x: aex_px_u(sDiag(ahy_py)*x) + ahy_py_u(sDiag(aex_px)*x) - ahy_px_u(sDiag(aex_py)*x) - aex_py_u(sDiag(ahy_px)*x)
+                elif 'zxy' in self.rxType:
+                    Zij = sDiag(aHd*(-sDiag(ahx_py)*aex_px + sDiag(ahx_px)*aex_py))
+                    ZijN_uV = lambda x:-aex_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(aex_px)*x) + ahx_px_u(sDiag(aex_py)*x) + aex_py_u(sDiag(ahx_px)*x)
+                elif 'zyx' in self.rxType:
+                    Zij = sDiag(aHd*( sDiag(ahy_py)*aey_px - sDiag(ahy_px)*aey_py))
+                    ZijN_uV = lambda x: aey_px_u(sDiag(ahy_py)*x) + ahy_py_u(sDiag(aey_px)*x) - ahy_px_u(sDiag(aey_py)*x) - aey_py_u(sDiag(ahy_px)*x)
+                elif 'zyy' in self.rxType:
+                    Zij = sDiag(aHd*(-sDiag(ahx_py)*aey_px + sDiag(ahx_px)*aey_py))
+                    ZijN_uV = lambda x:-aey_px_u(sDiag(ahx_py)*x) - ahx_py_u(sDiag(aey_px)*x) + ahx_px_u(sDiag(aey_py)*x) + aey_py_u(sDiag(ahx_px)*x)
+
+                # Calculate the complex derivative
+                PDeriv_real = ZijN_uV(aHd*v) - aHd_uV(Zij.T*aHd*v)#
+                # NOTE: Need to reshape the output to go from 2*nU array to a (nU,2) matrix for each polarization
+                # PDeriv_real = np.hstack((mkvc(PDeriv_real[:len(PDeriv_real)/2],2),mkvc(PDeriv_real[len(PDeriv_real)/2::],2)))
+                PDeriv_real = PDeriv_real.reshape((2,mesh.nE)).T
+
+            elif self.projType is 'T3D':
+                if self.locs.ndim == 3:
+                    bFLocs = self.locs[:,:,1]
+                else:
+                    bFLocs = self.locs
+                # Get the projection
+                Pbx = mesh.getInterpolationMat(bFLocs,'Fx')
+                Pby = mesh.getInterpolationMat(bFLocs,'Fy')
+                Pbz = mesh.getInterpolationMat(bFLocs,'Fz')
+                # Get the fields at location
+                # px: x-polaration and py: y-polaration.
+                abx_px = mkvc(mkvc(f[src,'b_px'],2).T*Pbx.T)
+                aby_px = mkvc(mkvc(f[src,'b_px'],2).T*Pby.T)
+                abz_px = mkvc(mkvc(f[src,'b_px'],2).T*Pbz.T)
+                abx_py = mkvc(mkvc(f[src,'b_py'],2).T*Pbx.T)
+                aby_py = mkvc(mkvc(f[src,'b_py'],2).T*Pby.T)
+                abz_py = mkvc(mkvc(f[src,'b_py'],2).T*Pbz.T)
+                # Derivatives as lambda functions
+                abx_px_u = lambda vec: f._b_pxDeriv_u(src,Pbx.T*vec,adjoint=True)
+                aby_px_u = lambda vec: f._b_pxDeriv_u(src,Pby.T*vec,adjoint=True)
+                abz_px_u = lambda vec: f._b_pxDeriv_u(src,Pbz.T*vec,adjoint=True)
+                abx_py_u = lambda vec: f._b_pyDeriv_u(src,Pbx.T*vec,adjoint=True)
+                aby_py_u = lambda vec: f._b_pyDeriv_u(src,Pby.T*vec,adjoint=True)
+                abz_py_u = lambda vec: f._b_pyDeriv_u(src,Pbz.T*vec,adjoint=True)
+
+                # Update the input vector
+                # Define shortcuts
+                sDiag = lambda t: Utils.sdiag(mkvc(t,2))
+                sVec = lambda t: Utils.sp.csr_matrix(mkvc(t,2))
+                # Define the components of the derivative
+                aHd = sDiag(1./(sDiag(abx_px)*aby_py - sDiag(abx_py)*aby_px))
+                aHd_uV = lambda x: abx_px_u(sDiag(aby_py)*x) + abx_px_u(sDiag(aby_py)*x) - aby_px_u(sDiag(abx_py)*x) - abx_py_u(sDiag(aby_px)*x)
+                # Need to fix this to reflect the adjoint
+                if 'tzx' in self.rxType:
+                    Tij = sDiag(aHd*( -sDiag(abz_py)*aby_px + sDiag(abz_px)*aby_py))
+                    TijN_uV = lambda x: -abz_py_u(sDiag(aby_px)*x) - aby_px_u(sDiag(abz_py)*x) + aby_py_u(sDiag(abz_px)*x) + abz_px_u(sDiag(aby_py)*x)
+                elif 'tzy' in self.rxType:
+                    Tij = sDiag(aHd*( sDiag(abz_py)*abx_px - sDiag(abz_px)*abx_py))
+                    TijN_uV = lambda x: abx_px_u(sDiag(abz_py)*x) + abz_py_u(sDiag(abx_px)*x) - abx_py_u(sDiag(abz_px)*x) - abz_px_u(sDiag(abx_py)*x)
+                # Calculate the complex derivative
+                PDeriv_real = TijN_uV(aHd*v) - aHd_uV(Tij.T*aHd*v)#
+                # NOTE: Need to reshape the output to go from 2*nU array to a (nU,2) matrix for each polarization
+                # PDeriv_real = np.hstack((mkvc(PDeriv_real[:len(PDeriv_real)/2],2),mkvc(PDeriv_real[len(PDeriv_real)/2::],2)))
+                PDeriv_real = PDeriv_real.reshape((2,mesh.nE)).T
+            # Extract the data
+            if real_or_imag == 'imag':
+                Pv = 1j*PDeriv_real
+            elif real_or_imag == 'real':
+                Pv = PDeriv_real.astype(complex)
+
+
+        return Pv
+
+#################
+###  Survey   ###
+#################
+class Survey(SimPEGsurvey.BaseSurvey):
+    """
+        Survey class for MT. Contains all the sources associated with the survey.
+
+        :param list srcList: List of sources associated with the survey
+
+    """
+    srcPair = SrcMT.BaseMTSrc
+
+    def __init__(self, srcList, **kwargs):
+        # Sort these by frequency
+        self.srcList = srcList
+        SimPEGsurvey.BaseSurvey.__init__(self, **kwargs)
+
+        _freqDict = {}
+        for src in srcList:
+            if src.freq not in _freqDict:
+                _freqDict[src.freq] = []
+            _freqDict[src.freq] += [src]
+
+        self._freqDict = _freqDict
+        self._freqs = sorted([f for f in self._freqDict])
+
+    @property
+    def freqs(self):
+        """Frequencies"""
+        return self._freqs
+
+    @property
+    def nFreq(self):
+        """Number of frequencies"""
+        return len(self._freqDict)
+
+    # TODO: Rename to getSources
+    def getSrcByFreq(self, freq):
+        """Returns the sources associated with a specific frequency."""
+        assert freq in self._freqDict, "The requested frequency is not in this survey."
+        return self._freqDict[freq]
+
+    def projectFields(self, u):
+        data = Data(self)
+        for src in self.srcList:
+            sys.stdout.flush()
+            for rx in src.rxList:
+                data[src, rx] = rx.projectFields(src, self.mesh, u)
+        return data
+
+    def projectFieldsDeriv(self, u):
+        raise Exception('Use Transmitters to project fields deriv.')
+
+#################
+###   Data    ###
+#################
+class Data(SimPEGsurvey.Data):
+    '''
+    Data class for MTdata. Stores the data vector indexed by the survey.
+
+    :param SimPEG survey object survey:
+    :param v vector of the data in order matching of the survey
+
+
+    '''
+    def __init__(self, survey, v=None):
+        # Pass the variables to the "parent" method
+        SimPEGsurvey.Data.__init__(self, survey, v)
+
+    # # Import data
+    # @classmethod
+    # def fromEDIFiles():
+    #     pass
+
+    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
+
+    @classmethod
+    def fromRecArray(cls, recArray, srcType='primary'):
+        """
+        Class method that reads in a numpy record array to MTdata object.
+
+        Only imports the impedance data.
+
+        """
+        if srcType=='primary':
+            src = SrcMT.polxy_1Dprimary
+        elif srcType=='total':
+            src = SrcMT.polxy_1DhomotD
+        else:
+            raise NotImplementedError('{:s} is not a valid source type for MTdata')
+
+        # Find all the frequencies in recArray
+        uniFreq = np.unique(recArray['freq'])
+        srcList = []
+        dataList = []
+        for freq in uniFreq:
+            # Initiate rxList
+            rxList = []
+            # Find that data for freq
+            dFreq = recArray[recArray['freq'] == freq].copy()
+            # Find the impedance rxTypes in the recArray.
+            rxTypes = [ comp for comp in recArray.dtype.names if (len(comp)==4 or len(comp)==3) and 'z' in comp]
+            for rxType in rxTypes:
+                # Find index of not nan values in rxType
+                notNaNind = ~np.isnan(dFreq[rxType])
+                if np.any(notNaNind): # Make sure that there is any data to add.
+                    locs = rec2ndarr(dFreq[['x','y','z']][notNaNind].copy())
+                    if dFreq[rxType].dtype.name in 'complex128':
+                        rxList.append(Rx(locs,rxType+'r'))
+                        dataList.append(dFreq[rxType][notNaNind].real.copy())
+                        rxList.append(Rx(locs,rxType+'i'))
+                        dataList.append(dFreq[rxType][notNaNind].imag.copy())
+                    else:
+                        rxList.append(Rx(locs,rxType))
+                        dataList.append(dFreq[rxType][notNaNind].copy())
+            srcList.append(src(rxList,freq))
+
+        # Make a survey
+        survey = Survey(srcList)
+        dataVec = np.hstack(dataList)
+        return cls(survey,dataVec)
+

SimPEG/MT/Utils/MT1Danalytic.py

@@ -0,0 +1,108 @@
+# Analytic solution of EM fields due to a plane wave
+
+import numpy as np, SimPEG as simpeg
+from scipy.constants import mu_0, epsilon_0 as eps_0
+
+def getEHfields(m1d,sigma,freq,zd,scaleUD=True):
+    '''Analytic solution for MT 1D layered earth. Returns E and H fields.
+
+    :param SimPEG.mesh, object m1d: Mesh object with the 1D spatial information.
+    :param numpy.array, vector sigma: Physical property of conductivity corresponding with the mesh.
+    :param float, freq: Frequency to calculate data at.
+    :param numpy array, vector zd: location to calculate EH fields at
+    :param bollean, scaleUD: scales the output to be 1 at the top, increases numeracal stability.
+
+    Assumes a halfspace with the same conductive as the last cell below.
+
+    '''
+    # Note add an error check for the mesh and sigma are the same size.
+
+    # Constants: Assume constant
+    mu = mu_0*np.ones((m1d.nC+1))
+    eps = eps_0*np.ones((m1d.nC+1))
+    # Angular freq
+    w = 2*np.pi*freq
+    # Add the halfspace value to the property
+    sig = np.concatenate((np.array([sigma[0]]),sigma))
+    # Calculate the wave number
+    k = np.sqrt(eps*mu*w**2-1j*mu*sig*w)
+
+    # Initiate the propagation matrix, in the order down up.
+    UDp = np.zeros((2,m1d.nC+1),dtype=complex)
+    UDp[1,0] = 1. # Set the wave amplitude as 1 into the half-space at the bottom of the mesh
+    # Loop over all the layers, starting at the bottom layer
+    for lnr, h in enumerate(m1d.hx): # lnr-number of layer, h-thickness of the layer
+        # Calculate
+        yp1 = k[lnr]/(w*mu[lnr]) # Admittance of the layer below the current layer
+        zp = (w*mu[lnr+1])/k[lnr+1] # Impedance in the current layer
+        # Build the propagation matrix
+
+        # Convert fields to down/up going components in layer below current layer
+        Pj1 = np.array([[1,1],[yp1,-yp1]])
+        # Convert fields to down/up going components in current layer
+        Pjinv = 1./2*np.array([[1,zp],[1,-zp]])
+        # Propagate down and up components through the current layer
+        elamh = np.array([[np.exp(-1j*k[lnr+1]*h),0],[0,np.exp(1j*k[lnr+1]*h)]])
+
+        # The down and up component in current layer.
+        UDp[:,lnr+1] = elamh.dot(Pjinv.dot(Pj1)).dot(UDp[:,lnr])
+
+        if scaleUD:
+             UDp[:,lnr+1::-1] = UDp[:,lnr+1::-1]/UDp[1,lnr+1]
+
+    # Calculate the fields
+    Ed = np.empty((zd.size,),dtype=complex)
+    Eu = np.empty((zd.size,),dtype=complex)
+    Hd = np.empty((zd.size,),dtype=complex)
+    Hu = np.empty((zd.size,),dtype=complex)
+
+    # Loop over the layers and calculate the fields
+    # In the halfspace below the mesh
+    dup = m1d.vectorNx[0]
+    dind = dup >= zd
+    Ed[dind] = UDp[1,0]*np.exp(-1j*k[0]*(dup-zd[dind]))
+    Eu[dind] = UDp[0,0]*np.exp(1j*k[0]*(dup-zd[dind]))
+    Hd[dind] = (k[0]/(w*mu[0]))*UDp[1,0]*np.exp(-1j*k[0]*(dup-zd[dind]))
+    Hu[dind] = -(k[0]/(w*mu[0]))*UDp[0,0]*np.exp(1j*k[0]*(dup-zd[dind]))
+    for ki,mui,epsi,dlow,dup,Up,Dp in zip(k[1::],mu[1::],eps[1::],m1d.vectorNx[:-1],m1d.vectorNx[1::],UDp[0,1::],UDp[1,1::]):
+        dind = np.logical_and(dup >= zd, zd > dlow)
+        Ed[dind] = Dp*np.exp(-1j*ki*(dup-zd[dind]))
+        Eu[dind] = Up*np.exp(1j*ki*(dup-zd[dind]))
+        Hd[dind] = (ki/(w*mui))*Dp*np.exp(-1j*ki*(dup-zd[dind]))
+        Hu[dind] = -(ki/(w*mui))*Up*np.exp(1j*ki*(dup-zd[dind]))
+
+    # Return return the fields
+    return Ed, Eu, Hd, Hu
+
+def getImpedance(m1d,sigma,freq):
+    """Analytic solution for MT 1D layered earth. Returns the impedance at the surface.
+
+    :param SimPEG.mesh, object m1d: Mesh object with the 1D spatial information.
+    :param numpy.array, vector sigma: Physical property corresponding with the mesh.
+    :param numpy.array, vector freq: Frequencies to calculate data at.
+
+
+    """
+
+    # Initiate the impedances
+    Z1d = np.empty(len(freq) , dtype='complex')
+    h = m1d.hx   #vectorNx[:-1]
+    # Start the process
+    for nrFr, fr in enumerate(freq):
+        om = 2*np.pi*fr
+        Zall = np.empty(len(h)+1,dtype='complex')
+        # Calculate the impedance for the bottom layer
+        Zall[0] = (mu_0*om)/np.sqrt(mu_0*eps_0*(om)**2 - 1j*mu_0*sigma[0]*om)
+
+        for nr,hi in enumerate(h):
+            # Calculate the wave number
+            # print nr,sigma[nr]
+            k = np.sqrt(mu_0*eps_0*om**2 - 1j*mu_0*sigma[nr]*om)
+            Z = (mu_0*om)/k
+
+            Zall[nr+1] = Z *((Zall[nr] + Z*np.tanh(1j*k*hi))/(Z + Zall[nr]*np.tanh(1j*k*hi)))
+
+        #pdb.set_trace()
+        Z1d[nrFr] = Zall[-1]
+
+    return Z1d

SimPEG/MT/Utils/MT1Dsolutions.py

@@ -0,0 +1,45 @@
+import numpy as np, SimPEG as simpeg
+from MT1Danalytic import getEHfields
+from scipy.constants import mu_0
+
+def get1DEfields(m1d,sigma,freq,sourceAmp=1.0):
+    """Function to get 1D electrical fields"""
+
+    # Get the gradient
+    G = m1d.nodalGrad
+    # Mass matrices
+    # Magnetic permeability
+    Mmu = simpeg.Utils.sdiag(m1d.vol*(1.0/mu_0))
+    # Conductivity
+    Msig = m1d.getFaceInnerProduct(sigma)
+    # Set up the solution matrix
+    A = G.T*Mmu*G + 1j*2.*np.pi*freq*Msig
+    # Define the inner part of the solution matrix
+    Aii = A[1:-1,1:-1]
+    # Define the outer part of the solution matrix
+    Aio = A[1:-1,[0,-1]]
+
+    # Set the boundary conditions
+    Ed, Eu, Hd, Hu = getEHfields(m1d,sigma,freq,m1d.vectorNx)
+    Etot = (Ed + Eu)
+    if sourceAmp is not None:
+        Etot = ((Etot/Etot[-1])*sourceAmp) # Scale the fields to be equal to sourceAmp at the top
+    ## Note: The analytic solution is derived with e^iwt
+    bc = np.r_[Etot[0],Etot[-1]]
+    # The right hand side
+    rhs = Aio*bc
+    # Solve the system
+    Aii_inv = simpeg.Solver(Aii)
+    eii = Aii_inv*rhs
+    # Assign the boundary conditions
+    e = np.r_[bc[0],eii,bc[1]]
+    # Return the electrical fields
+    return e
+
+
+if __name__ == '__main__':
+
+    hz = [(100.,18)]
+    M = simpeg.Mesh.TensorMesh([hz],'C')
+    sig = np.zeros(M.nC) + 1e-8
+    sig[M.vectorCCx<=0] = sigHalf

SimPEG/MT/Utils/__init__.py

@@ -0,0 +1,4 @@
+from MT1Dsolutions import *  # Add the names of the functions
+from MT1Danalytic import *
+from dataUtils import *
+from ediFilesUtils import *

SimPEG/MT/Utils/dataUtils.py

@@ -0,0 +1,245 @@
+# Utils used for the data,
+import numpy as np, matplotlib.pyplot as plt, sys
+import SimPEG as simpeg
+import numpy.lib.recfunctions as recFunc
+from scipy.constants import mu_0
+from scipy import interpolate as sciint
+
+def getAppRes(MTdata):
+    # Make impedance
+    zList = []
+    for src in MTdata.survey.srcList:
+        zc = [src.freq]
+        for rx in src.rxList:
+            if 'i' in rx.rxType:
+                m=1j
+            else:
+                m = 1
+            zc.append(m*MTdata[src,rx])
+        zList.append(zc)
+    return [appResPhs(zList[i][0],np.sum(zList[i][1:3])) for i in np.arange(len(zList))]
+
+def rotateData(MTdata,rotAngle):
+    '''
+    Function that rotates clockwist by rotAngle (- negative for a counter-clockwise rotation)
+    '''
+    recData = MTdata.toRecArray('Complex')
+    impData = rec2ndarr(recData[['zxx','zxy','zyx','zyy']],complex)
+    # Make the rotation matrix
+    # c,s,zxx,zxy,zyx,zyy = sympy.symbols('c,s,zxx,zxy,zyx,zyy')
+    # rotM = sympy.Matrix([[c,-s],[s, c]])
+    # zM = sympy.Matrix([[zxx,zxy],[zyx,zyy]])
+    # rotM*zM*rotM.T
+    # [c*(c*zxx - s*zyx) - s*(c*zxy - s*zyy), c*(c*zxy - s*zyy) + s*(c*zxx - s*zyx)],
+    # [c*(c*zyx + s*zxx) - s*(c*zyy + s*zxy), c*(c*zyy + s*zxy) + s*(c*zyx + s*zxx)]])
+    s = np.sin(-np.deg2rad(rotAngle))
+    c = np.cos(-np.deg2rad(rotAngle))
+    rotMat = np.array([[c,-s],[s,c]])
+    rotData = (rotMat.dot(impData.reshape(-1,2,2).dot(rotMat.T))).transpose(1,0,2).reshape(-1,4)
+    outRec = recData.copy()
+    for nr,comp in enumerate(['zxx','zxy','zyx','zyy']):
+        outRec[comp] = rotData[:,nr]
+
+    from SimPEG import MT
+    return MT.Data.fromRecArray(outRec)
+
+
+def appResPhs(freq,z):
+    app_res = ((1./(8e-7*np.pi**2))/freq)*np.abs(z)**2
+    app_phs = np.arctan2(z.imag,z.real)*(180/np.pi)
+    return app_res, app_phs
+
+def skindepth(rho,freq):
+    ''' Function to calculate the skindepth of EM waves'''
+    return np.sqrt( (rho*((1/(freq * mu_0 * np.pi )))))
+
+def rec2ndarr(x,dt=float):
+    return x.view((dt, len(x.dtype.names)))
+
+def makeAnalyticSolution(mesh,model,elev,freqs):
+    from SimPEG import MT
+    data1D = []
+    for freq in freqs:
+        anaEd, anaEu, anaHd, anaHu = MT.Utils.MT1Danalytic.getEHfields(mesh,model,freq,elev)
+        anaE = anaEd+anaEu
+        anaH = anaHd+anaHu
+
+        anaZ = anaE/anaH
+        # Add to the list
+        data1D.append((freq,0,0,elev,anaZ[0]))
+    dataRec = np.array(data1D,dtype=[('freq',float),('x',float),('y',float),('z',float),('zyx',complex)])
+    return dataRec
+
+def plotMT1DModelData(problem,models,symList=None):
+    from SimPEG import MT
+    # Setup the figure
+    fontSize = 15
+
+    fig = plt.figure(figsize=[9,7])
+    axM = fig.add_axes([0.075,.1,.25,.875])
+    axM.set_xlabel('Resistivity [Ohm*m]',fontsize=fontSize)
+    axM.set_xlim(1e-1,1e5)
+    axM.set_ylim(-10000,5000)
+    axM.set_ylabel('Depth [km]',fontsize=fontSize)
+    axR = fig.add_axes([0.42,.575,.5,.4])
+    axR.set_xscale('log')
+    axR.set_yscale('log')
+    axR.invert_xaxis()
+    # axR.set_xlabel('Frequency [Hz]')
+    axR.set_ylabel('Apparent resistivity [Ohm m]',fontsize=fontSize)
+
+    axP = fig.add_axes([0.42,.1,.5,.4])
+    axP.set_xscale('log')
+    axP.invert_xaxis()
+    axP.set_ylim(0,90)
+    axP.set_xlabel('Frequency [Hz]',fontsize=fontSize)
+    axP.set_ylabel('Apparent phase [deg]',fontsize=fontSize)
+
+    # if not symList:
+    #   symList = ['x']*len(models)
+    import plotDataTypes as pDt
+    # Loop through the models.
+    modelList = [problem.survey.mtrue]
+    modelList.extend(models)
+    if False:
+        modelList = [problem.mapping.sigmaMap*mod for mod in modelList]
+    for nr, model in enumerate(modelList):
+        # Calculate the data
+        if nr==0:
+            data1D = problem.dataPair(problem.survey,problem.survey.dobs).toRecArray('Complex')
+        else:
+            data1D = problem.dataPair(problem.survey,problem.survey.dpred(model)).toRecArray('Complex')
+        # Plot the data and the model
+        colRat = nr/((len(modelList)-1.999)*1.)
+        if colRat > 1.:
+            col = 'k'
+        else:
+            col = plt.cm.seismic(1-colRat)
+        # The model - make the pts to plot
+        meshPts = np.concatenate((problem.mesh.gridN[0:1],np.kron(problem.mesh.gridN[1::],np.ones(2))[:-1]))
+        modelPts = np.kron(1./(problem.mapping.sigmaMap*model),np.ones(2,))
+        axM.semilogx(modelPts,meshPts,color=col)
+
+        ## Data
+        # Appres
+        pDt.plotIsoStaImpedance(axR,np.array([0,0]),data1D,'zyx','res',pColor=col)
+        # Appphs
+        pDt.plotIsoStaImpedance(axP,np.array([0,0]),data1D,'zyx','phs',pColor=col)
+        try:
+            allData = np.concatenate((allData,simpeg.mkvc(data1D['zyx'],2)),1)
+        except:
+            allData = simpeg.mkvc(data1D['zyx'],2)
+    freq = simpeg.mkvc(data1D['freq'],2)
+    res, phs = appResPhs(freq,allData)
+
+    stdCol = 'gray'
+    axRtw = axR.twinx()
+    axRtw.set_ylabel('Std of log10',color=stdCol)
+    [(t.set_color(stdCol), t.set_rotation(-45)) for t in axRtw.get_yticklabels()]
+    axPtw = axP.twinx()
+    axPtw.set_ylabel('Std ',color=stdCol)
+    [t.set_color(stdCol) for t in axPtw.get_yticklabels()]
+    axRtw.plot(freq, np.std(np.log10(res),1),'--',color=stdCol)
+    axPtw.plot(freq, np.std(phs,1),'--',color=stdCol)
+
+    # Fix labels and ticks
+
+    yMtick = [l/1000 for l in axM.get_yticks().tolist()]
+    axM.set_yticklabels(yMtick)
+    [ l.set_rotation(90) for l in axM.get_yticklabels()]
+    [ l.set_rotation(90) for l in axR.get_yticklabels()]
+    [(t.set_color(stdCol), t.set_rotation(-45)) for t in axRtw.get_yticklabels()]
+    [t.set_color(stdCol) for t in axPtw.get_yticklabels()]
+    for ax in [axM,axR,axP]:
+        ax.xaxis.set_tick_params(labelsize=fontSize)
+        ax.yaxis.set_tick_params(labelsize=fontSize)
+    return fig
+
+def printTime():
+    import time
+    print time.strftime("%a, %d %b %Y %H:%M:%S +0000", time.localtime())
+
+def convert3Dto1Dobject(MTdata,rxType3D='zyx'):
+    from SimPEG import MT
+    # Find the unique locations
+    # Need to find the locations
+    recDataTemp = MTdata.toRecArray()
+    # Check if survey.std has been assigned.
+    ## NEED TO: write this...
+    # Calculte and add the DET of the tensor to the recArray
+    if 'det' in rxType3D:
+        Zon = (recDataTemp['zxxr']+1j*recDataTemp['zxxi'])*(recDataTemp['zyyr']+1j*recDataTemp['zyyi'])
+        Zoff = (recDataTemp['zxyr']+1j*recDataTemp['zxyi'])*(recDataTemp['zyxr']+1j*recDataTemp['zyxi'])
+        det = np.sqrt(Zon.data - Zoff.data)
+        recData = recFunc.append_fields(recDataTemp,['zdetr','zdeti'],[det.real,det.imag] )
+    else:
+        recData = recDataTemp
+
+    uniLocs = rec2ndarr(np.unique(recData[['x','y','z']])).data
+    mtData1DList = []
+    if 'zxy' in rxType3D:
+        corr = -1 # Shift the data to comply with the quadtrature of the 1d problem
+    else:
+        corr = 1
+    for loc in uniLocs:
+        # Make the receiver list
+        rx1DList = []
+        for rxType in ['z1dr','z1di']:
+            rx1DList.append(MT.Rx(simpeg.mkvc(loc,2).T,rxType))
+        # Source list
+        locrecData = recData[np.sqrt(np.sum( (rec2ndarr(recData[['x','y','z']]).data - loc )**2,axis=1)) < 1e-5]
+        dat1DList = []
+        src1DList = []
+        for freq in locrecData['freq']:
+            src1DList.append(MT.SrcMT.src_polxy_1Dprimary(rx1DList,freq))
+            for comp  in ['r','i']:
+                dat1DList.append( corr * locrecData[rxType3D+comp][locrecData['freq']== freq].data )
+
+        # Make the survey
+        sur1D = MT.Survey(src1DList)
+
+        # Make the data
+        dataVec = np.hstack(dat1DList)
+        dat1D = MT.Data(sur1D,dataVec)
+        sur1D.dobs = dataVec
+        # Need to take MTdata.survey.std and split it as well.
+        std=0.05
+        sur1D.std =  np.abs(sur1D.dobs*std) #+ 0.01*np.linalg.norm(sur1D.dobs)
+        mtData1DList.append(dat1D)
+
+    # Return the the list of data.
+    return mtData1DList
+
+def resampleMTdataAtFreq(MTdata,freqs):
+    """
+    Function to resample MTdata at set of frequencies
+
+    """
+    from SimPEG import MT
+    # Make a rec array
+    MTrec = MTdata.toRecArray().data
+
+    # Find unique locations
+    uniLoc = np.unique(MTrec[['x','y','z']])
+    uniFreq = MTdata.survey.freqs
+    # Get the comps
+    dNames = MTrec.dtype
+
+    # Loop over all the locations and interpolate
+    for loc in uniLoc:
+        # Find the index of the station
+        ind = np.sqrt(np.sum((rec2ndarr(MTrec[['x','y','z']]) - rec2ndarr(loc))**2,axis=1)) < 1. # Find dist of 1 m accuracy
+        # Make a temporary recArray and interpolate all the components
+        tArrRec = np.concatenate((simpeg.mkvc(freqs,2),np.ones((len(freqs),1))*rec2ndarr(loc),np.nan*np.ones((len(freqs),12))),axis=1).view(dNames)
+        for comp in ['zxxr','zxxi','zxyr','zxyi','zyxr','zyxi','zyyr','zyyi','tzxr','tzxi','tzyr','tzyi']:
+            int1d = sciint.interp1d(MTrec[ind]['freq'],MTrec[ind][comp],bounds_error=False)
+            tArrRec[comp] = simpeg.mkvc(int1d(freqs),2)
+
+        # Join together
+        try:
+            outRecArr = recFunc.stack_arrays((outRecArr,tArrRec))
+        except NameError as e:
+            outRecArr = tArrRec
+
+    # Make the MTdata and return
+    return MT.Data.fromRecArray(outRecArr)

SimPEG/MT/Utils/ediFilesUtils.py

@@ -0,0 +1,175 @@
+# Functions to import and export MT EDI files.
+from SimPEG import mkvc
+from scipy.constants import mu_0
+from numpy.lib import recfunctions as recFunc
+from SimPEG.MT.Utils.dataUtils import rec2ndarr
+
+# Import modules
+import numpy as np
+import os, sys, re
+try:
+    import osr
+except ImportError as e:
+    print 'Could not import osr, missing the gdal package'
+    pass
+
+class EDIimporter:
+    """
+    A class to import EDIfiles.
+
+    """
+    _impUnitEDI2SI = 4*np.pi*1e-4 # Convert Z[mV/km/nT] (as in EDI)to Z[V/A] SI unit
+    _impUnitSI2EDI = 1./_impUnitEDI2SI # ConvertZ[V/A] SI unit to Z[mV/km/nT] (as in EDI)
+
+    # Properties
+    filesList = None
+    comps = None
+
+    # Hidden properties
+    _outEPSG = None
+    _2out = None
+
+
+    def __init__(self, EDIfilesList, compList=None, outEPSG=None):
+
+        # Set the fileList
+        self.filesList = EDIfilesList
+        # Set the components to import
+        if compList is None:
+            self.comps = ['ZXXR','ZXYR','ZYXR','ZYYR','ZXXI','ZXYI','ZYXI','ZYYI','ZXX.VAR','ZXY.VAR','ZYX.VAR','ZYY.VAR']
+        else:
+            self.comps = compList
+        if outEPSG is not None:
+            self._outEPSG = outEPSG
+
+    def __call__(self,comps=None):
+
+        if comps is None:
+            return self._data
+
+        return self._data[comps]
+
+    def importFiles(self):
+        """
+        Function to import EDI files into a object.
+
+
+        """
+
+        # Constants that are needed for convertion of units
+
+        # Temp lists
+        tmpStaList = []
+
+        tmpCompList = ['freq','x','y','z']
+        tmpCompList.extend(self.comps)
+        # Make the outarray
+        dtRI = [(compS.lower().replace('.',''),float) for compS in tmpCompList]
+        # Loop through all the files
+        for nrEDI, EDIfile in enumerate(self.filesList):
+            # Read the file into a list of the lines
+            with open(EDIfile,'r') as fid:
+                EDIlines = fid.readlines()
+            # Find the location
+            latD, longD, elevM = _findLatLong(EDIlines)
+            # Transfrom coordinates
+            transCoord = self._transfromPoints(longD,latD)
+            # Extract the name of the file (station)
+            EDIname = EDIfile.split(os.sep)[-1].split('.')[0]
+            # Arrange the data
+            staList = [EDIname, EDIfile, transCoord[0], transCoord[1], elevM[0]]
+            # Add to the station list
+            tmpStaList.extend(staList)
+
+            # Read the frequency data
+            freq = _findEDIcomp('>FREQ',EDIlines)
+            # Make the temporary rec array.
+            tArrRec = ( np.nan*np.ones( (len(freq),len(dtRI)) ) ).view(dtRI)     #np.concatenate((freq*np.ones((locs.shape[0],1)),locs,np.nan*np.ones((locs.shape[0],8))),axis=1).view(dtRI)
+            # Add data to the array
+            tArrRec['freq'] = mkvc(freq,2)
+            tArrRec['x'] = mkvc(np.ones((len(freq),1))*transCoord[0],2)
+            tArrRec['y'] = mkvc(np.ones((len(freq),1))*transCoord[1],2)
+            tArrRec['z'] = mkvc(np.ones((len(freq),1))*elevM[0],2)
+            for comp in self.comps:
+                # Deal with converting units of the impedance tensor
+                if 'Z' in comp:
+                    unitConvert = self._impUnitEDI2SI
+                else:
+                    unitConvert = 1
+                # Rotate the data since EDI x is *north, y *east but Simpeg uses x *east, y *north (* means internal reference frame)
+                key = [comp.lower().replace('.','').replace(s,t) for s,t in [['xx','yy'],['xy','yx'],['yx','xy'],['yy','xx']] if s in comp.lower()][0]
+                tArrRec[key] = mkvc(unitConvert*_findEDIcomp('>'+comp,EDIlines),2)
+            # Make a masked array
+            mArrRec = np.ma.MaskedArray(rec2ndarr(tArrRec),mask=np.isnan(rec2ndarr(tArrRec))).view(dtype=tArrRec.dtype)
+            try:
+                outTemp = recFunc.stack_arrays((outTemp,mArrRec))
+            except NameError as e:
+                outTemp = mArrRec
+
+        # Assign the data
+        self._data = outTemp
+
+    # % Assign the data to the obj
+    # nOutData=length(obj.data);
+    # obj.data(nOutData+1:nOutData+length(TEMP.data),:) = TEMP.data;
+    def _transfromPoints(self,longD,latD):
+        # Coordinates convertor
+        if self._2out is None:
+            src = osr.SpatialReference()
+            src.ImportFromEPSG(4326)
+            out = osr.SpatialReference()
+            if self._outEPSG is None:
+                # Find the UTM EPSG number
+                Nnr =  700 if latD < 0.0 else 600
+                utmZ = int(1+(longD+180.0)/6.0)
+                self._outEPSG = 32000 + Nnr + utmZ
+            out.ImportFromEPSG(self._outEPSG)
+            self._2out = osr.CoordinateTransformation(src,out)
+        # Return the transfrom
+        return self._2out.TransformPoint(longD,latD)
+
+# Hidden functions
+def _findLatLong(fileLines):
+    latDMS = np.array(fileLines[_findLine('LAT=',fileLines)[0]].split('=')[1].split()[0].split(':'),float)
+    longDMS = np.array(fileLines[_findLine('LONG=',fileLines)[0]].split('=')[1].split()[0].split(':'),float)
+    elevM = np.array([fileLines[_findLine('ELEV=',fileLines)[0]].split('=')[1].split()[0]],float)
+    # Convert to D.ddddd values
+    latS = np.sign(latDMS[0])
+    longS = np.sign(longDMS[0])
+    latD = latDMS[0] + latS*latDMS[1]/60 + latS*latDMS[2]/3600
+    longD = longDMS[0] + longS*longDMS[1]/60 + longS*longDMS[2]/3600
+    return latD, longD, elevM
+
+def _findLine(comp,fileLines):
+    """ Find a line number in the file"""
+    # Line counter
+    c = 0
+    # List of indices for found lines
+    found = []
+    # Loop through all the lines
+    for line in fileLines:
+        if comp in line:
+            # Append if found
+            found.append(c)
+        # Increse the counter
+        c += 1
+    # Return the found indices
+    return found
+
+def _findEDIcomp(comp,fileLines,dt=float):
+    """
+    Extract the data vector.
+
+    Returns a list of the data.
+    """
+    # Find the data
+    headLine, indHead = [(st,nr) for nr,st in enumerate(fileLines) if re.search(comp,st)][0]
+    # Extract the data
+    nrVec = int(headLine.split()[-1])
+    c = 0
+    dataList = []
+    while c < nrVec:
+        indHead += 1
+        dataList.extend(fileLines[indHead].split())
+        c = len(dataList)
+    return np.array(dataList,dt)

SimPEG/MT/Utils/plotDataTypes.py

@@ -0,0 +1,416 @@
+from matplotlib import pyplot as plt, colors, numpy as np
+
+
+def rec2nd(structArray):
+	""" Converts a structured/record array to ndarray to do operations on."""
+	return structArray.view((np.float,len(structArray.dtype.names)))
+
+def plotIsoFreqNSimpedance(ax,freq,array,flag,par='abs',colorbar=True,colorNorm='SymLog',cLevel=True,contour=True):
+
+	indUniFreq = np.where(freq==array['freq'])
+
+
+	x, y = array['x'][indUniFreq],array['y'][indUniFreq]
+	if par == 'abs':
+		zPlot = np.abs(array[flag][indUniFreq])
+		cmap = plt.get_cmap('OrRd_r')#seismic')
+		level = np.logspace(0,-5,31)
+		clevel = np.logspace(0,-4,5)
+		plotNorm = colors.LogNorm()
+	elif par == 'real':
+		zPlot = np.real(array[flag][indUniFreq])
+		cmap = plt.get_cmap('RdYlBu')
+		if cLevel:
+			level = np.concatenate((-np.logspace(0,-10,31),np.logspace(-10,0,31)))
+			clevel = np.concatenate((-np.logspace(0,-8,5),np.logspace(-8,0,5)))
+		else:
+			level = np.linspace(zPlot.min(),zPlot.max(),100)
+			clevel = np.linspace(zPlot.min(),zPlot.max(),10)
+		if colorNorm=='SymLog':
+			plotNorm = colors.SymLogNorm(1e-10,linscale=2)
+		else:
+			plotNorm = colors.Normalize()
+	elif par == 'imag':
+		zPlot = np.imag(array[flag][indUniFreq])
+		cmap = plt.get_cmap('RdYlBu')
+		level = np.concatenate((-np.logspace(0,-10,31),np.logspace(-10,0,31)))
+		clevel = np.concatenate((-np.logspace(0,-8,5),np.logspace(-8,0,5)))
+		plotNorm = colors.SymLogNorm(1e-10,linscale=2)		
+		if cLevel:
+			level = np.concatenate((-np.logspace(0,-10,31),np.logspace(-10,0,31)))
+			clevel = np.concatenate((-np.logspace(0,-8,5),np.logspace(-8,0,5)))
+		else:
+			level = np.linspace(zPlot.min(),zPlot.max(),100)
+			clevel = np.linspace(zPlot.min(),zPlot.max(),10)
+		if colorNorm=='SymLog':
+			plotNorm = colors.SymLogNorm(1e-10,linscale=2)
+		elif colorNorm=='Lin':
+			plotNorm = colors.Normalize()
+	if contour:
+		cs = ax.tricontourf(x,y,zPlot,levels=level,cmap=cmap,norm=plotNorm)#,extend='both')
+	else:
+		uniX,uniY = np.unique(x),np.unique(y)
+		X,Y = np.meshgrid(np.append(uniX-25,uniX[-1]+25),np.append(uniY-25,uniY[-1]+25))
+		cs = ax.pcolor(X,Y,np.reshape(zPlot,(len(uniY),len(uniX))),cmap=cmap,norm=plotNorm)
+	if colorbar:
+		plt.colorbar(cs,cax=ax.cax,ticks=clevel,format='%1.2e')
+		ax.set_title(flag+' '+par,fontsize=8)
+	return cs
+
+def plotIsoFreqNSDiff(ax,freq,arrayList,flag,par='abs',colorbar=True,cLevel=True,mask=None,contourLine=True,useLog=False):
+
+	indUniFreq0 = np.where(freq==arrayList[0]['freq'])
+	indUniFreq1 = np.where(freq==arrayList[1]['freq'])
+	seicmap = plt.get_cmap('RdYlBu')#seismic')
+	x, y = arrayList[0]['x'][indUniFreq0],arrayList[0]['y'][indUniFreq0]
+	if par == 'abs':
+		if useLog:
+			zPlot = (np.log10(np.abs(arrayList[0][flag][indUniFreq0])) - np.log10(np.abs(arrayList[1][flag][indUniFreq1])))/np.log10(np.abs(arrayList[1][flag][indUniFreq1]))
+		else:
+			zPlot = (np.abs(arrayList[0][flag][indUniFreq0]) - np.abs(arrayList[1][flag][indUniFreq1]))/np.abs(arrayList[1][flag][indUniFreq1])
+		if mask:
+			maskInd = np.logical_or(np.abs(arrayList[0][flag][indUniFreq0])< 1e-3,np.abs(arrayList[1][flag][indUniFreq1]) < 1e-3)
+			zPlot = np.ma.array(zPlot)
+			zPlot[maskInd] = mask
+		if cLevel:
+			level = np.arange(-200,201,10) 
+			clevel = np.arange(-200,201,25)
+		else:
+			level = np.linspace(zPlot.min(),zPlot.max(),100)
+			clevel = np.linspace(zPlot.min(),zPlot.max(),10)
+	elif par == 'real':
+		if useLog:
+			zPlot = (np.log10(np.real(arrayList[0][flag][indUniFreq0])) -np.log10(np.real(arrayList[1][flag][indUniFreq1])))/np.log10(np.abs((np.real(arrayList[1][flag][indUniFreq1]))))
+		else:
+			zPlot = (np.real(arrayList[0][flag][indUniFreq0]) -np.real(arrayList[1][flag][indUniFreq1]))/np.abs((np.real(arrayList[1][flag][indUniFreq1])))
+		if mask:
+			maskInd = np.logical_or(np.abs(np.real(arrayList[0][flag][indUniFreq0])) < 1e-3,np.abs(np.real(arrayList[1][flag][indUniFreq1])) < 1e-3)
+			zPlot = np.ma.array(zPlot)
+			zPlot[maskInd] = mask
+		if cLevel:
+			level = np.arange(-200,201,10) 
+			clevel = np.arange(-200,201,25)
+		else:
+			level = np.linspace(zPlot.min(),zPlot.max(),100)
+			clevel = np.linspace(zPlot.min(),zPlot.max(),10)
+	elif par == 'imag':
+		if useLog:
+			zPlot = (np.log10(np.imag(arrayList[0][flag][indUniFreq0])) -np.log10(np.imag(arrayList[1][flag][indUniFreq1])))/np.log10(np.abs((np.imag(arrayList[1][flag][indUniFreq1]))))
+		else:
+			zPlot = (np.imag(arrayList[0][flag][indUniFreq0]) -np.imag(arrayList[1][flag][indUniFreq1]))/np.abs((np.imag(arrayList[1][flag][indUniFreq1])))
+		if mask:
+			maskInd = np.logical_or(np.abs(np.imag(arrayList[0][flag][indUniFreq0])) < 1e-3,np.abs(np.imag(arrayList[1][flag][indUniFreq1])) < 1e-3)
+			zPlot = np.ma.array(zPlot)
+			zPlot[maskInd] = mask
+		if cLevel:
+			level = np.arange(-200,201,10) 
+			clevel = np.arange(-200,201,25)
+		else:
+			level = np.linspace(zPlot.min(),zPlot.max(),100)
+			clevel = np.linspace(zPlot.min(),zPlot.max(),10)
+	cs = ax.tricontourf(x,y,zPlot*100,levels=level*100,cmap=seicmap,extend='both') #,norm=colors.SymLogNorm(1e-2,linscale=2))
+	if contourLine:
+		csl = ax.tricontour(x,y,zPlot*100,levels=clevel*100,colors='k')
+		plt.clabel(csl, fontsize=7, inline=1,fmt='%1.1e',inline_spacing=10)
+	if colorbar:
+		cb = plt.colorbar(cs,cax=ax.cax,ticks=clevel*100,format='%1.1e')
+		for t in cb.ax.get_yticklabels():
+			t.set_rotation(60)
+			t.set_fontsize(8)
+
+	ax.set_title(flag+' '+par,fontsize=8)
+
+def plotIsoFreqNStipper(ax,freq,array,flag,par='abs',colorbar=True,colorNorm='SymLog',cLevel=True,contour=True):
+
+	indUniFreq = np.where(freq==array['freq'])
+
+	x, y = array['x'][indUniFreq],array['y'][indUniFreq]
+	if par == 'abs':
+		cmap = plt.get_cmap('OrRd_r')#seismic')
+		zPlot = np.abs(array[flag][indUniFreq])
+		if cLevel:
+			level = np.logspace(-4,0,33)
+			clevel = np.logspace(-4,0,5)
+		else:
+			level = np.linspace(zPlot.min(),zPlot.max(),100)
+			clevel = np.linspace(zPlot.min(),zPlot.max(),10)
+		if colorNorm=='SymLog':
+			plotNorm = colors.LogNorm()
+		else:
+			plotNorm = colors.Normalize()
+	elif par == 'real':
+		cmap = plt.get_cmap('RdYlBu')
+		zPlot = np.real(array[flag][indUniFreq])
+		if cLevel:
+			level = np.concatenate((-np.logspace(0,-4,33),np.logspace(-4,0,33)))
+			clevel = np.concatenate((-np.logspace(0,-4,5),np.logspace(-4,0,5)))
+		else:
+			level = np.linspace(zPlot.min(),zPlot.max(),100)
+			clevel = np.linspace(zPlot.min(),zPlot.max(),10)
+		if colorNorm=='SymLog':
+			plotNorm = colors.SymLogNorm(1e-4,linscale=2)
+		else:
+			plotNorm = colors.Normalize()
+	elif par == 'imag':
+		cmap = plt.get_cmap('RdYlBu')
+		zPlot = np.imag(array[flag][indUniFreq])
+		if cLevel:
+			level = np.concatenate((-np.logspace(0,-4,33),np.logspace(-4,0,33)))
+			clevel = np.concatenate((-np.logspace(0,-4,5),np.logspace(-4,0,5)))
+		else:
+			level = np.linspace(zPlot.min(),zPlot.max(),100)
+			clevel = np.linspace(zPlot.min(),zPlot.max(),10)
+		if colorNorm=='SymLog':
+			plotNorm = colors.SymLogNorm(1e-4,linscale=2)
+		else:
+			plotNorm = colors.Normalize()
+	if contour:
+		cs = ax.tricontourf(x,y,zPlot,levels=level,cmap=cmap,norm=plotNorm)#,extend='both')
+	else:
+		uniX,uniY = np.unique(x),np.unique(y)
+		X,Y = np.meshgrid(np.append(uniX-25,uniX[-1]+25),np.append(uniY-25,uniY[-1]+25))
+		cs = ax.pcolor(X,Y,np.reshape(zPlot,(len(uniY),len(uniX))),levels=level,cmap=cmap,norm=plotNorm,edgecolors='k', linewidths=0.5)
+	if colorbar:
+		plt.colorbar(cs,cax=ax.cax,ticks=clevel,format='%1.2e')
+	ax.set_title(flag+' '+par,fontsize=8)
+
+def plotIsoStaImpedance(ax,loc,array,flag,par='abs',pSym='s',pColor=None):	
+	
+	appResFact = 1/(8*np.pi**2*10**(-7))
+	treshold = 1.0 # 1 meter
+	indUniSta = np.sqrt(np.sum((rec2nd(array[['x','y']])-loc)**2,axis=1)) < treshold
+	freq = array['freq'][indUniSta]
+	
+	if par == 'abs':
+		zPlot = np.abs(array[flag][indUniSta])
+	elif par == 'real':
+		zPlot = np.real(array[flag][indUniSta])
+	elif par == 'imag':
+		zPlot = np.imag(array[flag][indUniSta])
+	elif par == 'res':
+		zPlot = (appResFact/freq)*np.abs(array[flag][indUniSta])**2
+	elif par == 'phs':
+		zPlot = np.arctan2(array[flag][indUniSta].imag,array[flag][indUniSta].real)*(180/np.pi)
+
+	if not pColor:
+		if 'xx' in flag:
+			lab = 'XX'
+			pColor = 'g'
+		elif 'xy' in flag:
+			lab = 'XY'
+			pColor = 'r'	
+		elif 'yx' in flag:
+			lab = 'YX'
+			pColor = 'b'
+		elif 'yy' in flag:
+			lab = 'YY'
+			pColor = 'y'
+
+	ax.plot(freq,zPlot,color=pColor,marker=pSym,label=flag)
+	
+
+def plotPsudoSectNSimpedance(ax,sectDict,array,flag,par='abs',colorbar=True,colorNorm='None',cLevel=None,contour=True):
+
+	indSect = np.where(sectDict.values()[0]==array[sectDict.keys()[0]])
+
+	# Define the plot axes
+	if 'x' in sectDict.keys()[0]:
+		x = array['y'][indSect]
+	else:
+		x = array['x'][indSect]
+	y = array['freq'][indSect]
+
+	if par == 'abs':
+		zPlot = np.abs(array[flag][indSect])
+		cmap = plt.get_cmap('OrRd_r')#seismic')
+		if cLevel:
+			level = np.logspace(0,-5,31,endpoint=True)
+			clevel = np.logspace(0,-4,5,endpoint=True)
+		else:
+			level = np.linspace(zPlot.min(),zPlot.max(),100,endpoint=True)
+			clevel = np.linspace(zPlot.min(),zPlot.max(),10,endpoint=True)
+		
+	elif par == 'ares':	
+		zPlot = np.abs(array[flag][indSect])**2/(8*np.pi**2*10**(-7)*array['freq'][indSect])
+		cmap = plt.get_cmap('RdYlBu')#seismic)
+		if cLevel:
+			zMax = np.log10(cLevel[1])
+			zMin = np.log10(cLevel[0])
+		else:
+			zMax = (np.ceil(np.log10(np.abs(zPlot).max())))
+			zMin = (np.floor(np.log10(np.abs(zPlot).min())))
+		level = np.logspace(zMin,zMax,(zMax-zMin)*8+1,endpoint=True)
+		clevel = np.logspace(zMin,zMax,(zMax-zMin)*2+1,endpoint=True)
+		plotNorm = colors.LogNorm()
+
+	elif par == 'aphs':
+		zPlot = np.arctan2(array[flag][indSect].imag,array[flag][indSect].real)*(180/np.pi)
+		cmap = plt.get_cmap('RdYlBu')#seismic)
+		if cLevel:
+			zMax = cLevel[1]
+			zMin = cLevel[0]
+		else:
+			zMax = (np.ceil(zPlot).max())
+			zMin = (np.floor(zPlot).min())
+		level = np.arange(zMin,zMax+.1,1)
+		clevel = np.arange(zMin,zMax+.1,10)
+		plotNorm = colors.Normalize()
+
+	elif par == 'real':
+		zPlot = np.real(array[flag][indSect])
+		cmap = plt.get_cmap('Spectral') #('RdYlBu')
+		if cLevel:
+			zMax = np.log10(cLevel[1])
+			zMin = np.log10(cLevel[0])
+		else:
+			zMax = (np.ceil(np.log10(np.abs(zPlot).max())))
+			zMin = (np.floor(np.log10(np.abs(zPlot).min())))
+		level = np.concatenate((-np.logspace(zMax,zMin-.125,(zMax-zMin)*8+1,endpoint=True),np.logspace(zMin-.125,zMax,(zMax-zMin)*8+1,endpoint=True)))
+		clevel = np.concatenate((-np.logspace(zMax,zMin,(zMax-zMin)*1+1,endpoint=True),np.logspace(zMin,zMax,(zMax-zMin)*1+1,endpoint=True)))
+		plotNorm = colors.SymLogNorm(np.abs(level).min(),linscale=0.1)
+	elif par == 'imag':
+		zPlot = np.imag(array[flag][indSect])
+		cmap = plt.get_cmap('Spectral') #('RdYlBu')
+		
+		if cLevel:
+			zMax = np.log10(cLevel[1])
+			zMin = np.log10(cLevel[0])
+		else:
+			zMax = (np.ceil(np.log10(np.abs(zPlot).max())))
+			zMin = (np.floor(np.log10(np.abs(zPlot).min())))
+		level = np.concatenate((-np.logspace(zMax,zMin-.125,(zMax-zMin)*8+1,endpoint=True),np.logspace(zMin-.125,zMax,(zMax-zMin)*8+1,endpoint=True)))
+		clevel = np.concatenate((-np.logspace(zMax,zMin,(zMax-zMin)*1+1,endpoint=True),np.logspace(zMin,zMax,(zMax-zMin)*1+1,endpoint=True)))
+		plotNorm = colors.SymLogNorm(np.abs(level).min(),linscale=0.1)
+	
+	if colorNorm=='SymLog':
+		plotNorm = colors.SymLogNorm(np.abs(level).min(),linscale=0.1)
+	elif colorNorm=='Lin':
+		plotNorm = colors.Normalize()
+	elif colorNorm=='Log':
+		plotNorm = colors.LogNorm()
+	if contour:
+		cs = ax.tricontourf(x,y,zPlot,levels=level,cmap=cmap,norm=plotNorm)#,extend='both')
+	else:
+		uniX,uniY = np.unique(x),np.unique(y)
+		X,Y = np.meshgrid(np.append(uniX-25,uniX[-1]+25),np.append(uniY-25,uniY[-1]+25))
+		cs = ax.pcolor(X,Y,np.reshape(zPlot,(len(uniY),len(uniX))),cmap=cmap,norm=plotNorm)
+	if colorbar:
+		csB = plt.colorbar(cs,cax=ax.cax,ticks=clevel,format='%1.2e')
+		# csB.on_mappable_changed(cs)
+		ax.set_title(flag+' '+par,fontsize=8)
+		return cs, csB
+	return cs,None
+
+
+def plotPsudoSectNSDiff(ax,sectDict,arrayList,flag,par='abs',colorbar=True,colorNorm='SymLog',cLevel=None,contour=True,mask=None,useLog=False):
+
+	def sortInArr(arr):
+		return np.sort(arr,order=['freq','x','y','z'])
+	# Find the index for the slice
+	indSect0 = np.where(sectDict.values()[0]==arrayList[0][sectDict.keys()[0]])
+	indSect1 = np.where(sectDict.values()[0]==arrayList[1][sectDict.keys()[0]])
+	# Extract and sort the mats
+	arr0 = sortInArr(arrayList[0][indSect0])
+	arr1 = sortInArr(arrayList[1][indSect1])
+
+	# Define the plot axes
+	if 'x' in sectDict.keys()[0]:
+		x0 = arr0['y']
+		x1 = arr1['y']
+	else:
+		x0 = arr0['x']
+		x1 = arr1['x']
+	y0 = arr0['freq']
+	y1 = arr1['freq']
+	
+
+	if par == 'abs':
+		if useLog:
+			zPlot = (np.log10(np.abs(arr0[flag])) - np.log10(np.abs(arr1[flag])))/np.log10(np.abs(arr1[flag]))
+		else:
+			zPlot = (np.abs(arr0[flag]) - np.abs(arr1[flag]))/np.abs(arr1[flag])
+		if mask:
+			maskInd = np.logical_or(np.abs(arr0[flag])< 1e-3,np.abs(arr1[flag]) < 1e-3)
+			zPlot = np.ma.array(zPlot)
+			zPlot[maskInd] = mask
+		cmap = plt.get_cmap('RdYlBu')#seismic)
+	elif par == 'ares':
+		arF = 1/(8*np.pi**2*10**(-7))		
+		if useLog:
+			zPlot = (np.log10((arF/arr0['freq'])*np.abs(arr0[flag])**2) - np.log10((arF/arr1['freq'])*np.abs(arr1[flag])**2))/np.log10((arF/arr1['freq'])*np.abs(arr1[flag])**2)
+		else:
+			zPlot = ((arF/arr0['freq'])*np.abs(arr0[flag])**2 - (arF/arr1['freq'])*np.abs(arr1[flag])**2)/((arF/arr1['freq'])*np.abs(arr1[flag])**2)
+		if mask:
+			maskInd = np.logical_or(np.abs(arr0[flag])< 1e-3,np.abs(arr1[flag]) < 1e-3)
+			zPlot = np.ma.array(zPlot)
+			zPlot[maskInd] = mask
+		cmap = plt.get_cmap('Spectral')#seismic)
+	
+	elif par == 'aphs':
+		if useLog:
+			zPlot = (np.log10(np.arctan2(arr0[flag].imag,arr0[flag].real)*(180/np.pi)) - np.log10(np.arctan2(arr1[flag].imag,arr1[flag].real)*(180/np.pi)) )/np.log10(np.arctan2(arr1[flag].imag,arr1[flag].real)*(180/np.pi))
+		else:
+			zPlot = ( np.arctan2(arr0[flag].imag,arr0[flag].real)*(180/np.pi) - np.arctan2(arr1[flag].imag,arr1[flag].real)*(180/np.pi) )/(np.arctan2(arr1[flag].imag,arr1[flag].real)*(180/np.pi))
+		if mask:
+			maskInd = np.logical_or(np.abs(arr0[flag])< 1e-3,np.abs(arr1[flag]) < 1e-3)
+			zPlot = np.ma.array(zPlot)
+			zPlot[maskInd] = mask
+		cmap = plt.get_cmap('Spectral')#seismic)
+	elif par == 'real':
+		if useLog:
+			zPlot = (np.log10(arr0[flag].real) - np.log10(arr1[flag].real))/np.log10(arr1[flag].real)
+		else:
+			zPlot = (arr0[flag].real - arr1[flag].real)/arr1[flag].real
+		if mask:
+			maskInd = np.logical_or(arr0[flag].real< 1e-3,arr1[flag].real < 1e-3)
+			zPlot = np.ma.array(zPlot)
+			zPlot[maskInd] = mask
+		cmap = plt.get_cmap('Spectral') #('Spectral')
+		
+	elif par == 'imag':
+		if useLog:
+			zPlot = (np.log10(arr0[flag].imag) - np.log10(arr1[flag].imag))/np.log10(arr1[flag].imag)
+		else:
+			zPlot = (arr0[flag].imag - arr1[flag].imag)/arr1[flag].imag
+		if mask:
+			maskInd = np.logical_or(arr0[flag].imag< 1e-3,arr1[flag].imag < 1e-3)
+			zPlot = np.ma.array(zPlot)
+			zPlot[maskInd] = mask
+		cmap = plt.get_cmap('Spectral') #('RdYlBu')
+		
+	if cLevel:
+		zMax = np.log10(cLevel[1])
+		zMin = np.log10(cLevel[0])
+	else:
+		zMax = (np.ceil(np.log10(np.abs(zPlot).max())))
+		zMin = (np.floor(np.log10(np.abs(zPlot).min())))
+
+	
+	if colorNorm=='SymLog':
+		level = np.concatenate((-np.logspace(zMax,zMin-.125,(zMax-zMin)*8+1,endpoint=True),np.logspace(zMin-.125,zMax,(zMax-zMin)*8+1,endpoint=True)))
+		clevel = np.concatenate((-np.logspace(zMax,zMin,(zMax-zMin)*1+1,endpoint=True),np.logspace(zMin,zMax,(zMax-zMin)*1+1,endpoint=True)))
+		plotNorm = colors.SymLogNorm(np.abs(level).min(),linscale=0.1)
+	elif colorNorm=='Lin':
+		if cLevel:
+			level = np.arange(cLevel[0],cLevel[1]+.1,(cLevel[1] - cLevel[0])/50.) 
+			clevel = np.arange(cLevel[0],cLevel[1]+.1,(cLevel[1] - cLevel[0])/10.)
+		else:
+			level = np.arange(zPlot.min(),zPlot.max(),(zPlot.max() - zPlot.min())/50.)
+			clevel = np.arange(zPlot.min(),zPlot.max(),(zPlot.max() - zPlot.min())/10.)
+		plotNorm = colors.Normalize()
+	elif colorNorm=='Log':
+		level = np.logspace(zMin-.125,zMax,(zMax-zMin)*8+1,endpoint=True)
+		clevel = np.logspace(zMin,zMax,(zMax-zMin)*2+1,endpoint=True)
+		plotNorm = colors.LogNorm()
+	if contour:
+		cs = ax.tricontourf(x0,y0,zPlot*100,levels=level*100,cmap=cmap,norm=plotNorm,extend='both')#,extend='both')
+	else:
+		uniX,uniY = np.unique(x0),np.unique(y0)
+		X,Y = np.meshgrid(np.append(uniX-25,uniX[-1]+25),np.append(uniY-25,uniY[-1]+25))
+		cs = ax.pcolor(X,Y,np.reshape(zPlot,(len(uniY),len(uniX))),cmap=cmap,norm=plotNorm)
+	if colorbar:
+		csB = plt.colorbar(cs,cax=ax.cax,ticks=clevel*100,format='%1.2e')
+		# csB.on_mappable_changed(cs)
+		ax.set_title(flag+' '+par + ' diff',fontsize=8)
+		return cs, csB
+	return cs,None

SimPEG/MT/Utils/sourceUtils.py

@@ -0,0 +1,178 @@
+import SimPEG as simpeg, numpy as np
+
+def homo1DModelSource(mesh,freq,sigma_1d):
+    '''
+        Function that calculates and return background fields
+
+        :param Simpeg mesh object mesh: Holds information on the discretization
+        :param float freq: The frequency to solve at
+        :param np.array sigma_1d: Background model of conductivity to base the calculations on, 1d model.
+        :rtype: numpy.ndarray (mesh.nE,2)
+        :return: eBG_bp, E fields for the background model at both polarizations.
+
+    '''
+    # import
+    from SimPEG.MT.Utils import get1DEfields
+    # Get a 1d solution for a halfspace background
+    if mesh.dim == 1:
+        mesh1d = mesh
+    elif mesh.dim == 2:
+        mesh1d = simpeg.Mesh.TensorMesh([mesh.hy],np.array([mesh.x0[1]]))
+    elif mesh.dim == 3:
+        mesh1d = simpeg.Mesh.TensorMesh([mesh.hz],np.array([mesh.x0[2]]))
+
+    # # Note: Everything is using e^iwt
+    e0_1d = get1DEfields(mesh1d,sigma_1d,freq)
+    if mesh.dim == 1:
+        eBG_px = simpeg.mkvc(e0_1d,2)
+        eBG_py = -simpeg.mkvc(e0_1d,2) # added a minus to make the results in the correct quadrents.
+    elif mesh.dim == 2:
+        ex_px = np.zeros(mesh.vnEx,dtype=complex)
+        ey_px = np.zeros((mesh.nEy,1),dtype=complex)
+        for i in np.arange(mesh.vnEx[0]):
+            ex_px[i,:] = -e0_1d
+        eBG_px = np.vstack((simpeg.Utils.mkvc(ex_px,2),ey_px))
+        # Setup y (north) polarization (_py)
+        ex_py = np.zeros((mesh.nEx,1), dtype='complex128')
+        ey_py = np.zeros(mesh.vnEy, dtype='complex128')
+        # Assign the source to ey_py
+        for i in np.arange(mesh.vnEy[0]):
+            ey_py[i,:] = e0_1d
+        # ey_py[1:-1,1:-1,1:-1] = 0
+        eBG_py = np.vstack((ex_py,simpeg.Utils.mkvc(ey_py,2),ez_py))
+    elif mesh.dim == 3:
+        # Setup x (east) polarization (_x)
+        ex_px = np.zeros(mesh.vnEx,dtype=complex)
+        ey_px = np.zeros((mesh.nEy,1),dtype=complex)
+        ez_px = np.zeros((mesh.nEz,1),dtype=complex)
+        # Assign the source to ex_x
+        for i in np.arange(mesh.vnEx[0]):
+            for j in np.arange(mesh.vnEx[1]):
+                ex_px[i,j,:] = -e0_1d
+        eBG_px = np.vstack((simpeg.Utils.mkvc(ex_px,2),ey_px,ez_px))
+        # Setup y (north) polarization (_py)
+        ex_py = np.zeros((mesh.nEx,1), dtype='complex128')
+        ey_py = np.zeros(mesh.vnEy, dtype='complex128')
+        ez_py = np.zeros((mesh.nEz,1), dtype='complex128')
+        # Assign the source to ey_py
+        for i in np.arange(mesh.vnEy[0]):
+            for j in np.arange(mesh.vnEy[1]):
+                ey_py[i,j,:] = e0_1d
+        # ey_py[1:-1,1:-1,1:-1] = 0
+        eBG_py = np.vstack((ex_py,simpeg.Utils.mkvc(ey_py,2),ez_py))
+
+    # Return the electric fields
+    eBG_bp = np.hstack((eBG_px,eBG_py))
+    return eBG_bp
+
+def analytic1DModelSource(mesh,freq,sigma_1d):
+    '''
+        Function that calculates and return background fields
+
+        :param Simpeg mesh object mesh: Holds information on the discretization
+        :param float freq: The frequency to solve at
+        :param np.array sigma_1d: Background model of conductivity to base the calculations on, 1d model.
+        :rtype: numpy.ndarray (mesh.nE,2)
+        :return: eBG_bp, E fields for the background model at both polarizations.
+
+    '''
+    # import
+    from SimPEG.MT.Utils import getEHfields
+    # Get a 1d solution for a halfspace background
+    if mesh.dim == 1:
+        mesh1d = mesh
+    elif mesh.dim == 2:
+        mesh1d = simpeg.Mesh.TensorMesh([mesh.hy],np.array([mesh.x0[1]]))
+    elif mesh.dim == 3:
+        mesh1d = simpeg.Mesh.TensorMesh([mesh.hz],np.array([mesh.x0[2]]))
+
+    # # Note: Everything is using e^iwt
+    Eu, Ed, _, _ = getEHfields(mesh1d,sigma_1d,freq,mesh.vectorNz)
+    # Make the fields into a dictionary of location and the fields
+    e0_1d = Eu+Ed
+    E1dFieldDict = dict(zip(mesh.vectorNz,e0_1d))
+    if mesh.dim == 1:
+        eBG_px = simpeg.mkvc(e0_1d,2)
+        eBG_py = -simpeg.mkvc(e0_1d,2) # added a minus to make the results in the correct quadrents.
+    elif mesh.dim == 2:
+        ex_px = np.zeros(mesh.vnEx,dtype=complex)
+        ey_px = np.zeros((mesh.nEy,1),dtype=complex)
+        for i in np.arange(mesh.vnEx[0]):
+            ex_px[i,:] = -e0_1d
+        eBG_px = np.vstack((simpeg.Utils.mkvc(ex_px,2),ey_px))
+        # Setup y (north) polarization (_py)
+        ex_py = np.zeros((mesh.nEx,1), dtype='complex128')
+        ey_py = np.zeros(mesh.vnEy, dtype='complex128')
+        # Assign the source to ey_py
+        for i in np.arange(mesh.vnEy[0]):
+            ey_py[i,:] = e0_1d
+        # ey_py[1:-1,1:-1,1:-1] = 0
+        eBG_py = np.vstack((ex_py,simpeg.Utils.mkvc(ey_py,2),ez_py))
+    elif mesh.dim == 3:
+        # Setup x (east) polarization (_x)
+        ex_px = -np.array([E1dFieldDict[i] for i in mesh.gridEx[:,2]]).reshape(-1,1)
+        ey_px = np.zeros((mesh.nEy,1),dtype=complex)
+        ez_px = np.zeros((mesh.nEz,1),dtype=complex)
+        # Construct the full fields
+        eBG_px = np.vstack((ex_px,ey_px,ez_px))
+        # Setup y (north) polarization (_py)
+        ex_py = np.zeros((mesh.nEx,1), dtype='complex128')
+        ey_py = np.array([E1dFieldDict[i] for i in mesh.gridEy[:,2]]).reshape(-1,1)
+        ez_py = np.zeros((mesh.nEz,1), dtype='complex128')
+        # Construct the full fields
+        eBG_py = np.vstack((ex_py,simpeg.Utils.mkvc(ey_py,2),ez_py))
+
+    # Return the electric fields
+    eBG_bp = np.hstack((eBG_px,eBG_py))
+    return eBG_bp
+
+# def homo3DModelSource(mesh,model,freq):
+#     '''
+#         Function that estimates 1D analytic background fields from a 3D model.
+
+#         :param Simpeg mesh object mesh: Holds information on the discretization
+#         :param float freq: The frequency to solve at
+#         :param np.array sigma_1d: Background model of conductivity to base the calculations on, 1d model.
+#         :rtype: numpy.ndarray (mesh.nE,2)
+#         :return: eBG_bp, E fields for the background model at both polarizations.
+
+#     '''
+
+#     if mesh.dim < 3:
+#         raise IOError('Input mesh has to have 3 dimensions.')
+
+
+#     # Get the locations
+#     a = mesh.gridCC[:,0:2].copy()
+#     unixy = np.unique(a.view(a.dtype.descr * a.shape[1])).view(float).reshape(-1,2)
+#     uniz = np.unique(mesh.gridCC[:,2])
+#     # # Note: Everything is using e^iwt
+#     # Need to loop thourgh the xy locations, assess the model and calculate the fields at the phusdo cell centers.
+#     # Then interpolate the cc fields to the edges.
+
+#     e0_1d = get1DEfields(mesh1d,sigma_1d,freq)
+
+#     elif mesh.dim == 3:
+#         # Setup x (east) polarization (_x)
+#         ex_px = np.zeros(mesh.vnEx,dtype=complex)
+#         ey_px = np.zeros((mesh.nEy,1),dtype=complex)
+#         ez_px = np.zeros((mesh.nEz,1),dtype=complex)
+#         # Assign the source to ex_x
+#         for i in np.arange(mesh.vnEx[0]):
+#             for j in np.arange(mesh.vnEx[1]):
+#                 ex_px[i,j,:] = -e0_1d
+#         eBG_px = np.vstack((simpeg.Utils.mkvc(ex_px,2),ey_px,ez_px))
+#         # Setup y (north) polarization (_py)
+#         ex_py = np.zeros((mesh.nEx,1), dtype='complex128')
+#         ey_py = np.zeros(mesh.vnEy, dtype='complex128')
+#         ez_py = np.zeros((mesh.nEz,1), dtype='complex128')
+#         # Assign the source to ey_py
+#         for i in np.arange(mesh.vnEy[0]):
+#             for j in np.arange(mesh.vnEy[1]):
+#                 ey_py[i,j,:] = e0_1d
+#         # ey_py[1:-1,1:-1,1:-1] = 0
+#         eBG_py = np.vstack((ex_py,simpeg.Utils.mkvc(ey_py,2),ez_py))
+
+#     # Return the electric fields
+#     eBG_bp = np.hstack((eBG_px,eBG_py))
+#     return eBG_bp

SimPEG/MT/Utils/srcUtils.py

@@ -0,0 +1,46 @@
+import SimPEG as simpeg, numpy as np
+
+def homo1DModelSource(mesh,freq,m_back):
+    '''
+        Function that calculates and return background fields for a 3D mesh and model.
+        The calculuations use 1D field solution for a vertical slice throught model (south-western most column),
+        which is assigned at the fields everywhere for the respective polarizations.2
+
+        :param Simpeg mesh object mesh: Holds information on the discretization
+        :param float freq: The frequency to solve at
+        :param np.array m_back: Background model of conductivity to base the calculations on.
+        :rtype: numpy.ndarray (mesh.nE,2)
+        :return: eBG_bp, E fields for the background model at both polarizations.
+
+    '''
+
+    # import
+    from SimPEG.MT.Utils import get1DEfields
+    # Get a 1d solution for a halfspace background
+    mesh1d = simpeg.Mesh.TensorMesh([mesh.hz],np.array([mesh.x0[2]]))
+    # Note: Everything is using e^iwt
+    e0_1d = get1DEfields(mesh1d,mesh.r(m_back,'CC','CC','M')[0,0,:],freq)
+    # Setup x (east) polarization (_x)
+    ex_px = np.zeros(mesh.vnEx,dtype=complex)
+    ey_px = np.zeros((mesh.nEy,1),dtype=complex)
+    ez_px = np.zeros((mesh.nEz,1),dtype=complex)
+    # Assign the source to ex_x
+    for i in np.arange(mesh.vnEx[0]):
+        for j in np.arange(mesh.vnEx[1]):
+            ex_px[i,j,:] = -e0_1d
+    eBG_px = np.vstack((simpeg.Utils.mkvc(ex_px,2),ey_px,ez_px))
+    # Setup y (north) polarization (_py)
+    ex_py = np.zeros((mesh.nEx,1), dtype='complex128')
+    ey_py = np.zeros(mesh.vnEy, dtype='complex128')
+    ez_py = np.zeros((mesh.nEz,1), dtype='complex128')
+    # Assign the source to ey_py
+
+    for i in np.arange(mesh.vnEy[0]):
+        for j in np.arange(mesh.vnEy[1]):
+            ey_py[i,j,:] = e0_1d
+    # ey_py[1:-1,1:-1,1:-1] = 0
+    eBG_py = np.vstack((ex_py,simpeg.Utils.mkvc(ey_py,2),ez_py))
+
+    # Return the electric fields
+    eBG_bp = np.hstack((eBG_px,eBG_py))
+    return eBG_bp

SimPEG/MT/__init__.py

@@ -0,0 +1,5 @@
+import Utils
+from SurveyMT import Rx, Survey, Data
+from FieldsMT import Fields1D_e, Fields3D_e
+import Problem1D, Problem2D, Problem3D
+import SrcMT

SimPEG/Mesh/DiffOperators.py

@@ -566,57 +566,6 @@ class DiffOperators(object):
         return Pbc, Pin, Pout
 
 
-    def unitCellGradx():
-        doc = """Cell centered Gradient in the x dimension used for 
-                regularization. The gradient operator is square (nC-by-nC)"""
-        def fget(self):
-            if self.dim < 3: return None
-            if getattr(self, '_unitCellGradx', None) is None:
-                
-                n = self.vnC
-                gx = ddx(n[0]-1)
-                gx_square = sp.vstack((gx,gx[-1,:]*-1), format="csr")
-                
-                self._unitCellGradx = kron3(speye(n[2]), speye(n[1]), gx_square)
-        
-            return self._unitCellGradx
-        return locals()
-    unitCellGradx = property(**unitCellGradx())
-    
-    def unitCellGrady():
-        doc = """Cell centered Gradient in they dimension used for 
-                regularization. The gradient operator is square (nC-by-nC)"""
-        def fget(self):
-            if self.dim < 3: return None
-            if getattr(self, '_unitCellGrady', None) is None:
-        
-                n = self.vnC
-                gy = ddx(n[1]-1)
-                gy_square = sp.vstack((gy,gy[-1,:]*-1), format="csr")
-                
-                self._unitCellGrady = kron3(speye(n[2]), gy_square, speye(n[0]))
-            
-            return self._unitCellGrady
-        return locals()
-    unitCellGrady = property(**unitCellGrady())
-        
-    def unitCellGradz():
-        doc = """Cell centered Gradient in they dimension used for 
-                regularization. The gradient operator is square (nC-by-nC)"""
-        def fget(self):
-            if self.dim < 3: return None
-            if getattr(self, '_unitCellGradz', None) is None:
-        
-                n = self.vnC
-                gz = ddx(n[2]-1)
-                gz_square = sp.vstack((gz,gz[-1,:]*-1), format="csr")
-                
-                self._unitCellGradz = kron3( gz_square , speye(n[1]), speye(n[0]))
-            
-            return self._unitCellGradz
-        return locals()
-    unitCellGradz = property(**unitCellGradz())        
-        
     # --------------- Averaging ---------------------
 
     @property
@@ -797,4 +746,3 @@ class DiffOperators(object):
                                           kron3(av(n[2]), speye(n[1]+1), av(n[0])),
                                           kron3(speye(n[2]+1), av(n[1]), av(n[0]))), format="csr")
         return self._aveN2F
-

SimPEG/Optimization.py

@@ -990,19 +990,4 @@ class ProjectedGNCG(BFGS, Minimize, Remember):
                     cgFlag = 1
                 # End CG Iterations
 
-            # Take a gradient step on the active cells if exist
-            if temp != self.xc.size:
-
-                rhs_a = (Active) * -self.g
-
-                dm_i = max( abs( delx ) )
-                dm_a = max( abs(rhs_a) )
-
-                delx = delx + rhs_a * dm_i / dm_a /10.
-
-            # Only keep gradients going in the right direction on the active set
-            indx = ((self.xc<=self.lower) & (delx < 0)) | ((self.xc>=self.upper) & (delx > 0))
-            delx[indx] = 0.
-
             return delx
-

SimPEG/Regularization.py

@@ -281,212 +281,3 @@ class Tikhonov(BaseRegularization):
             r = self.W * ( self.mapping * (m - self.mref) )
             out = mD.T * ( self.W.T * r )
         return out
-
-class Simple(BaseRegularization):
-    """
-        Only for tensor mesh
-    """
-
-    smoothModel = True  #: SMOOTH and SMOOTH_MOD_DIF options
-    alpha_s     = Utils.dependentProperty('_alpha_s', 1.0, ['_W', '_Ws'], "Smallness weight")
-    alpha_x     = Utils.dependentProperty('_alpha_x', 1.0, ['_W', '_Wx'], "Weight for the first derivative in the x direction")
-    alpha_y     = Utils.dependentProperty('_alpha_y', 1.0, ['_W', '_Wy'], "Weight for the first derivative in the y direction")
-    alpha_z     = Utils.dependentProperty('_alpha_z', 1.0, ['_W', '_Wz'], "Weight for the first derivative in the z direction")
-
-    def __init__(self, mesh, mapping=None, **kwargs):
-        BaseRegularization.__init__(self, mesh, mapping=mapping, **kwargs)
-
-    @property
-    def Ws(self):
-        """Regularization matrix Ws"""
-        if getattr(self,'_Ws', None) is None:
-                self._Ws = Utils.sdiag((self.mesh.vol*self.alpha_s)**0.5)
-        return self._Ws
-
-    @property
-    def Wx(self):
-        """Regularization matrix Wx"""
-        if getattr(self, '_Wx', None) is None:
-            self._Wx = Utils.sdiag((self.mesh.vol*self.alpha_x)**0.5)*self.mesh.unitCellGradx
-        return self._Wx
-
-    @property
-    def Wy(self):
-        """Regularization matrix Wy"""
-        if getattr(self, '_Wy', None) is None:
-            self._Wy = Utils.sdiag((self.mesh.vol*self.alpha_y)**0.5)*self.mesh.unitCellGrady
-        return self._Wy
-
-    @property
-    def Wz(self):
-        """Regularization matrix Wz"""
-        if getattr(self, '_Wz', None) is None:
-            self._Wz = Utils.sdiag((self.mesh.vol*self.alpha_z)**0.5)*self.mesh.unitCellGradz
-        return self._Wz
-
-    @property
-    def Wsmooth(self):
-        """Full smoothness regularization matrix W"""
-        if getattr(self, '_Wsmooth', None) is None:
-            wlist = (self.Wx,)
-            if self.mesh.dim > 1:
-                wlist += (self.Wy,)
-            if self.mesh.dim > 2:
-                wlist += (self.Wz,)
-            self._Wsmooth = sp.vstack(wlist)
-        return self._Wsmooth
-
-    @property
-    def W(self):
-        """Full regularization matrix W"""
-        if getattr(self, '_W', None) is None:
-            wlist = (self.Ws, self.Wsmooth)
-            self._W = sp.vstack(wlist)
-        return self._W
-
-    @Utils.timeIt
-    def eval(self, m):
-        if self.smoothModel == True:
-            r1 = self.Wsmooth * ( self.mapping * (m) )
-            r2 = self.Ws * ( self.mapping * (m - self.mref) )
-            return 0.5*(r1.dot(r1)+r2.dot(r2))
-        elif self.smoothModel == False:
-            r = self.W * ( self.mapping * (m - self.mref) )
-            return 0.5*r.dot(r)
-
-
-    @Utils.timeIt
-    def evalDeriv(self, m):
-        """
-
-        The regularization is:
-
-        .. math::
-
-            R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top W(m-m_\\text{ref})}
-
-        So the derivative is straight forward:
-
-        .. math::
-
-            R(m) = \mathbf{W^\\top W (m-m_\\text{ref})}
-
-        """
-        if self.smoothModel == True:
-            mD1 = self.mapping.deriv(m)
-            mD2 = self.mapping.deriv(m - self.mref)
-            r1 = self.Wsmooth * ( self.mapping * (m))
-            r2 = self.Ws * ( self.mapping * (m - self.mref) )
-            out1 = mD1.T * ( self.Wsmooth.T * r1 )
-            out2 = mD2.T * ( self.Ws.T * r2 )
-            out = out1+out2
-        elif self.smoothModel == False:
-            mD = self.mapping.deriv(m - self.mref)
-            r = self.W * ( self.mapping * (m - self.mref) )
-            out = mD.T * ( self.W.T * r )
-        return out
-
-class SparseRegularization(Simple):
-
-    eps   = 1e-1
-    m     = None
-    gamma = 1.
-    p     = 0.
-    qx    = 2.
-    qy    = 2.
-    qz    = 2.
-
-    def __init__(self, mesh, mapping=None, **kwargs):
-        Simple.__init__(self, mesh, mapping=mapping, **kwargs)
-
-    @property
-    def Wsmooth(self):
-        """Full smoothness regularization matrix W"""
-        if getattr(self, '_Wsmooth', None) is None:
-            wlist = (self.Wx, self.Wxx)
-            if self.mesh.dim > 1:
-                wlist += (self.Wy, self.Wyy)
-            if self.mesh.dim > 2:
-                wlist += (self.Wz, self.Wzz)
-            self._Wsmooth = sp.vstack(wlist)
-        return self._Wsmooth
-
-    @property
-    def W(self):
-        """Full regularization matrix W"""
-        if getattr(self, '_W', None) is None:
-            wlist = (self.Ws, self.Wsmooth)
-            self._W = sp.vstack(wlist)
-        return self._W
-
-    @property
-    def Ws(self):
-        """Regularization matrix Ws"""
-        if getattr(self, 'm', None) is None:
-            self.Rs = Utils.speye(self.mesh.nC)
-
-        else:
-            f_m = self.m
-            self.rs = self.R(f_m , self.p, self.eps)
-            #print "Min rs: " + str(np.max(self.rs)) + "Max rs: " + str(np.min(self.rs))
-            self.Rs = Utils.sdiag( self.rs )
-
-        self._Ws = Utils.sdiag((self.mesh.vol*self.alpha_s*self.gamma)**0.5)*self.Rs
-
-        return self._Ws
-
-    @property
-    def Wx(self):
-        """Regularization matrix Wx"""
-
-        if getattr(self, 'm', None) is None:
-            self.Rx = Utils.speye(self.mesh.unitCellGradx.shape[0])
-
-        else:
-            f_m = self.mesh.unitCellGradx * self.m
-            self.rx = self.R( f_m , self.qx, self.eps)
-            self.Rx = Utils.sdiag( self.rx )
-
-        if getattr(self, '_Wx', None) is None:
-            self._Wx = Utils.sdiag((self.mesh.vol*self.alpha_x*self.gamma)**0.5)*self.Rx*self.mesh.unitCellGradx
-        return self._Wx
-
-    @property
-    def Wy(self):
-        """Regularization matrix Wy"""
-
-        if getattr(self, 'm', None) is None:
-            self.Ry = Utils.speye(self.mesh.unitCellGrady.shape[0])
-
-        else:
-            f_m = self.mesh.unitCellGrady * self.m
-            self.ry = self.R( f_m , self.qy, self.eps)
-            self.Ry = Utils.sdiag( self.ry )
-
-        if getattr(self, '_Wy', None) is None:
-            self._Wy = Utils.sdiag((self.mesh.vol*self.alpha_y*self.gamma)**0.5)*self.Ry*self.mesh.unitCellGrady
-        return self._Wy
-
-    @property
-    def Wz(self):
-        """Regularization matrix Wz"""
-
-        if getattr(self, 'm', None) is None:
-            self.Rz = Utils.speye(self.mesh.unitCellGradz.shape[0])
-
-        else:
-            f_m = self.mesh.unitCellGradz * self.m
-            self.rz = self.R( f_m , self.qz, self.eps)
-            self.Rz = Utils.sdiag( self.rz )
-
-        if getattr(self, '_Wz', None) is None:
-            self._Wz = Utils.sdiag((self.mesh.vol*self.alpha_z*self.gamma)**0.5)*self.Rz*self.mesh.unitCellGradz
-        return self._Wz
-
-
-    def R(self, f_m , p, dec):
-
-        eta = (self.eps**(1-p/2.))**0.5
-        r = eta / (f_m**2.+self.eps**2.)**((1-p/2.)/2.)
-
-        return r

SimPEG/Utils/matutils.py

@@ -2,7 +2,6 @@ import numpy as np
 import scipy.sparse as sp
 from codeutils import isScalar
 
-
 def mkvc(x, numDims=1):
     """Creates a vector with the number of dimension specified
 
@@ -41,7 +40,7 @@ def mkvc(x, numDims=1):
 def sdiag(h):
     """Sparse diagonal matrix"""
     if isinstance(h, Zero):
-        return h
+        return Zero()
 
     return sp.spdiags(mkvc(h), 0, h.size, h.size, format="csr")
 

docs/em/api_FDEM.rst

@@ -19,14 +19,14 @@ Electromagnetic phenomena are governed by Maxwell's equations. They describe the
 
 Fourier Transform Convention
 ----------------------------
-In order to examine Maxwell's equations in the frequency domain, we must first define our choice of harmonic time-dependence by choosing a Fourier transform convention. We use the \\(e^{i \\omega t} \\) convention, so we define our Fourier Transform pair as
+In order to examine Maxwell's equations in the frequency domain, we must first define our choice of harmonic time-dependence by choosing a Fourier transform convention. We use the :math:`e^{i \omega t}` convention, so we define our Fourier Transform pair as
 
 .. math ::
-	F(\omega) = \int_{-\infty}^{\infty} f(t) e^{- i \omega t} dt \\
+    F(\omega) = \int_{-\infty}^{\infty} f(t) e^{- i \omega t} dt \\
 
-	f(t) = \frac{1}{2\pi}\int_{-\infty}^{\infty} F(\omega) e^{i \omega t} d \omega
+    f(t) = \frac{1}{2\pi}\int_{-\infty}^{\infty} F(\omega) e^{i \omega t} d \omega
 
-where \\(\\omega\\) is angular frequency, \\(t\\) is time, \\(F(\\omega)\\) is the function defined in the frequency domain and \\(f(t)\\) is the function defined in the time domain.
+where :math:`\omega` is angular frequency, :math:`t` is time, :math:`F(\omega)` is the function defined in the frequency domain and :math:`f(t)` is the function defined in the time domain.
 
 
 Maxwell's Equations
@@ -34,44 +34,46 @@ Maxwell's Equations
 In the frequency domain, Maxwell's equations are given by
 
 .. math ::
-	\curl \vec{E} = - i \omega \vec{B} \\
+    \curl \vec{E} + i \omega \vec{B} = \vec{S_m}\\
 
-	\curl \vec{H} = \vec{J} + i \omega \vec{D} + \vec{S} \\
+    \curl \vec{H} - \vec{J} - i \omega \vec{D} = \vec{S_e} \\
 
-	\div \vec{B} = 0 \\
+    \div \vec{B} = 0 \\
 
-	\div \vec{D} = \rho_f
+    \div \vec{D} = \rho_f
 
 where:
 
-	- \\(\\vec{E}\\) : electric field (\\(V/m\\))
+    - :math:`\vec{E}`   : electric field (:math:`V/m` )
-	- \\(\\vec{H}\\) : magnetic field (\\(A/m\\))
+    - :math:`\vec{H}`   : magnetic field (:math:`A/m` )
-	- \\(\\vec{B}\\) : magnetic flux density (\\(Wb/m^2\\))
+    - :math:`\vec{B}`   : magnetic flux density (:math:`Wb/m^2` )
-	- \\(\\vec{D}\\) : electric displacement / electric flux density (\\(C/m^2\\))
+    - :math:`\vec{D}`   : electric displacement / electric flux density (:math:`C/m^2` )
-	- \\(\\vec{J}\\) : electric current density (\\(A/m^2\\))
+    - :math:`\vec{J}`   : electric current density (:math:`A/m^2` )
-	- \\(\\rho_f\\) : free charge density
+    - :math:`\vec{S_m}` : magnetic source term (:math:`V/m^2` )
+    - :math:`\vec{S_e}` : electric source term (:math:`A/m^2` )
+    - :math:`\rho_f`   : free charge density (:math:`\Omega m` )
 
-The source term is \\(\\vec{S}\\)
 
 
 Constitutive Relations
 ----------------------
+
 The fields and fluxes are related through the constitutive relations. At each frequency, they are given by
 
 .. math ::
-	\vec{J} = \sigma \vec{E} \\
+    \vec{J} = \sigma \vec{E} \\
 
-	\vec{B} = \mu \vec{H} \\
+    \vec{B} = \mu \vec{H} \\
 
-	\vec{D} = \varepsilon \vec{E}
+    \vec{D} = \varepsilon \vec{E}
 
 where:
 
-- \\(\\sigma\\) : electrical conductivity \\(S/m\\)
+- :math:`\sigma` : electrical conductivity (:math:`S/m`)
-- \\(\\mu\\) : magnetic permeability \\(H/m\\)
+- :math:`\mu` : magnetic permeability (:math:`H/m`)
-- \\(\\varepsilon\\) : dielectric permittivity \\(F/m\\)
+- :math:`\varepsilon` : dielectric permittivity (:math:`F/m`)
 
-\\(\\sigma\\), \\(\\mu\\), \\(\\varepsilon\\) are physical properties which depend on the material. \\(\\sigma\\) describes how easily electric current passes through a material, \\(\\mu\\) describes how easily a material is magnetized, and \\(\\varepsilon\\) describes how easily a material is electrically polarized. In most geophysical applications of EM, \\(\\sigma\\) is the the primary physical property of interest, and \\(\\mu\\), \\(\\varepsilon\\) are assumed to have their free-space values \\(\\mu_0 = 4\\pi \\times 10^{-7} H/m \\), \\(\\varepsilon_0 = 8.85 \\times 10^{-12} F/m\\)
+:math:`\sigma`, :math:`\mu`, :math:`\varepsilon` are physical properties which depend on the material. :math:`\sigma` describes how easily electric current passes through a material, :math:`\mu` describes how easily a material is magnetized, and :math:`\varepsilon` describes how easily a material is electrically polarized. In most geophysical applications of EM, :math:`\sigma` is the the primary physical property of interest, and :math:`\mu`, :math:`\varepsilon` are assumed to have their free-space values :math:`\mu_0 = 4\pi \times 10^{-7} H/m` , :math:`\varepsilon_0 = 8.85 \times 10^{-12} F/m`
 
 
 Quasi-static Approximation
@@ -80,8 +82,8 @@ Quasi-static Approximation
 For the frequency range typical of most geophysical surveys, the contribution of the electric displacement is negligible compared to the electric current density. In this case, we use the Quasi-static approximation and assume that this term can be neglected, giving
 
 .. math ::
-	\nabla \times \vec{E} = -i \omega \vec{B} \\
+    \nabla \times \vec{E} + i \omega \vec{B} = \vec{S_m} \\
-	\nabla \times \vec{H} = \vec{J} + \vec{S}
+    \nabla \times \vec{H} - \vec{J} = \vec{S_e}
 
 
 Implementation in SimPEG.EM
@@ -90,14 +92,14 @@ Implementation in SimPEG.EM
 We consider two formulations in SimPEG.EM, both first-order and both in terms of one field and one flux. We allow for the definition of magnetic and electric sources (see for example: Ward and Hohmann, starting on page 144). The E-B formulation is in terms of the electric field and the magnetic flux:
 
 .. math ::
-	\nabla \times \vec{E} + i \omega \vec{B} = \vec{S}_m \\
+    \nabla \times \vec{E} + i \omega \vec{B} = \vec{S}_m \\
-	\nabla \times \mu^{-1} \vec{B} - \sigma \vec{E} = \vec{S}_e
+    \nabla \times \mu^{-1} \vec{B} - \sigma \vec{E} = \vec{S}_e
 
 The H-J formulation is in terms of the current density and the magnetic field:
 
 .. math ::
-	\nabla \times \sigma^{-1} \vec{J} + i \omega \mu \vec{H} = \vec{S}_m \\
+    \nabla \times \sigma^{-1} \vec{J} + i \omega \mu \vec{H} = \vec{S}_m \\
-	\nabla \times \vec{H} - \vec{J} = \vec{S}_e
+    \nabla \times \vec{H} - \vec{J} = \vec{S}_e
 
 
 Discretizing
@@ -106,34 +108,34 @@ For both formulations, we use a finite volume discretization
 and discretize fields on cell edges, fluxes on cell faces and
 physical properties in cell centers. This is particularly
 important when using symmetry to reduce the dimensionality of a problem
-(for instance on a 2D CylMesh, there are \\(r\\), \\(z\\) faces and \\(\\theta\\) edges)
+(for instance on a 2D CylMesh, there are :math:`r`, :math:`z` faces and :math:`\theta` edges)
 
 .. figure:: ../images/finitevolrealestate.png
-	:align: center
+    :align: center
-	:scale: 60 %
+    :scale: 60 %
 
 For the two formulations, the discretization of the physical properties, fields and fluxes are summarized below.
 
 .. figure:: ../images/ebjhdiscretizations.png
-	:align: center
+    :align: center
-	:scale: 60 %
+    :scale: 60 %
 
-Note that resistivity is the inverse of conductivity, \\(\\rho = \\sigma^{-1}\\).
+Note that resistivity is the inverse of conductivity, :math:`\rho = \sigma^{-1}`.
 
 
-E-B Formulation:
+E-B Formulation
-****************
+---------------
 
 .. math ::
-	\mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} \\
+    \mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} \\
-	\mathbf{C^T} \mathbf{M^f_{\mu^{-1}}} \mathbf{b} - \mathbf{M^e_\sigma} \mathbf{e} = \mathbf{M^e} \mathbf{s_e}
+    \mathbf{C^T} \mathbf{M^f_{\mu^{-1}}} \mathbf{b} - \mathbf{M^e_\sigma} \mathbf{e} = \mathbf{M^e} \mathbf{s_e}
 
-H-J Formulation:
+H-J Formulation
-****************
+---------------
 
 .. math ::
-	\mathbf{C^T} \mathbf{M^f_\rho} \mathbf{j} + i \omega \mathbf{M^e_\mu} \mathbf{h} = \mathbf{M^e} \mathbf{s_m} \\
+    \mathbf{C^T} \mathbf{M^f_\rho} \mathbf{j} + i \omega \mathbf{M^e_\mu} \mathbf{h} = \mathbf{M^e} \mathbf{s_m} \\
-	\mathbf{C} \mathbf{h} - \mathbf{j} = \mathbf{s_e}
+    \mathbf{C} \mathbf{h} - \mathbf{j} = \mathbf{s_e}
 
 
 .. Forward Problem
@@ -144,6 +146,10 @@ H-J Formulation:
 
 API
 ===
+
+FDEM Problem
+------------
+
 .. automodule:: SimPEG.EM.FDEM.FDEM
     :show-inheritance:
     :members:
@@ -157,3 +163,17 @@ FDEM Survey
     :show-inheritance:
     :members:
     :undoc-members:
+
+.. automodule:: SimPEG.EM.FDEM.SrcFDEM
+    :show-inheritance:
+    :members:
+    :undoc-members:
+
+FDEM Fields
+-----------
+
+.. automodule:: SimPEG.EM.FDEM.FieldsFDEM
+    :show-inheritance:
+    :members:
+    :undoc-members:
+

docs/em/api_TDEM.rst

@@ -48,6 +48,305 @@
     \newcommand{\I}{\vec{I}}
 
 
+Time Domain Electromagnetics
+****************************
+
+.. _api_TDEM_derivation:
+
+Time-Domain EM Derivation
+=========================
+
+The following shows the derivation for the TDEM problem. We use the b-formulation below.
+(More to come soon..!)
+
+
+Sensitivity Calculation
+-----------------------
+
+.. math::
+
+    \begin{align}
+        \dcurl \e^{(t+1)} + \frac{\b^{(t+1)} - \b^{(t)}}{\delta t} = 0 \\
+        \dcurl^\top \MfMui \b^{(t+1)} - \MeSig \e^{(t+1)} = \Me \j_s^{(t+1)}
+    \end{align}
+
+Using Gauss-Newton to solve the inverse problem requires the ability to calculate the product of the
+Jacobian and a vector, as well as the transpose of the Jacobian times a vector.
+The above system can be rewritten as:
+
+.. math::
+
+    \begin{align}
+        \mathbf{A} \u^{(t+1)} + \mathbf{B} \u^{(t)}= \s^{(t+1)}
+    \end{align}
+
+where
+
+.. math::
+
+    \begin{align}
+        \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] \\
+        \u^{(k)} = \left[
+        \begin{array}{c}
+            \b^{(k)}\\
+            \e^{(k)}
+        \end{array}
+        \right] \\
+        \s^{(k)} = \left[
+        \begin{array}{c}
+            0\\
+            \Me \j^{(k)}_s
+        \end{array}
+        \right]
+    \end{align}
+
+.. note::
+
+    Here we have multiplied through by \\(\\MfMui\\) to make A and B symmetric!
+
+The entire time dependent system can be written in a single matrix expression
+
+.. math::
+
+    \begin{align}
+        \hat{\mathbf{A}} \hat{u} = \hat{s}
+    \end{align}
+
+where
+
+.. math::
+
+    \begin{align}
+        \mathbf{\hat{A}} = \left[
+        \begin{array}{cccc}
+            A & 0 & & \\
+            B & A & & \\
+              & \ddots & \ddots & \\
+              & & B & A
+        \end{array}
+        \right] \\
+        \hat{u} = \left[
+            \begin{array}{c}
+                \u^{(1)} \\
+                \u^{(2)} \\
+                \vdots \\
+                \u^{(N)}
+            \end{array} \right]\\
+        \hat{s} = \left[
+            \begin{array}{c}
+                \s^{(1)} - \mathbf{B} \u^{(0)} \\
+                \s^{(2)} \\
+                \vdots \\
+                \s^{(N)}
+            \end{array}
+        \right]
+    \end{align}
+
+For the fields \\(\\u\\), the measured data is given by
+
+.. math::
+
+    \begin{align}
+        \vec{d} = \mathbf{Q} \u
+    \end{align}
+
+The sensitivity matrix **J** is then defined as
+
+.. math::
+
+    \begin{align}
+        \mathbf{J} = \mathbf{Q} \frac{\partial \u}{\partial \sigma}
+    \end{align}
+
+
+Defining the function \\(\\c(m,\\u)\\) to be
+
+.. math::
+
+    \begin{align}
+        \vec{c}(m,\u) = \hat{\mathbf{A}} \vec{u} - \vec{q} = \vec{0}
+    \end{align}
+
+then
+
+.. math::
+
+    \begin{align}
+        \frac{\partial \vec{c}}{\partial m} \partial m
+        + \frac{\partial \vec{c}}{\partial \u} \partial \vec{u} = 0
+    \end{align}
+
+or
+
+.. math::
+
+    \begin{align}
+        \frac{\partial \vec{u}}{\partial m} = -\left(\frac{\partial \vec{c}}{\partial \u} \right)^{-1} \frac{\partial \vec{c}}{\partial m}
+    \end{align}
+
+
+Differentiating, we find that
+
+.. math::
+
+    \begin{align}
+        \frac{\partial \vec{c}}{\partial \hat{u}} = \hat{\mathbf{A}}
+    \end{align}
+
+and
+
+.. math::
+
+    \begin{align}
+        \frac{\partial \vec{c}}{\partial \sigma} = \mathbf{G}_\sigma =
+        \left[
+            \begin{array}{c}
+                g_\sigma^{(1)}\\
+                g_\sigma^{(2)}\\
+                \vdots \\
+                g_\sigma^{(N)}
+            \end{array}
+        \right]
+    \end{align}
+
+with
+
+.. math::
+
+    \begin{align}
+        g_\sigma^{(n)} =
+        \left[
+            \begin{array}{c}
+                \mathbf{0} \\
+                - \diag{\e^{(n)}} \Ace \diag{\vec{V}}
+            \end{array}
+        \right]
+    \end{align}
+
+
+Implementing **J** times a vector
+---------------------------------
+
+Multiplying **J** onto a vector can be broken into three steps
+
+
+* Compute \\(\\vec{p} = \\mathbf{G}m\\)
+* Solve \\(\\hat{\\mathbf{A}} \\vec{y} = \\vec{p}\\)
+* Compute \\(\\vec{w} = -\\mathbf{Q} \\vec{y}\\)
+
+.. math::
+
+    \begin{align}
+        \vec{p}^{(n)} = \left[
+            \begin{array}{c}
+                \vec{p}_b^{(n)} \\
+                \vec{p}_e^{(n)}
+            \end{array}
+        \right] \\
+        \vec{p}_b^{(n)} = 0 \\
+        \vec{p}_e^{(n)} = - \diag{\e^{(n)}} \Ace \diag{V} m
+    \end{align}
+
+
+For all time steps:
+
+.. math::
+
+    \begin{align}
+        \frac{1}{\delta t} \MfMui\vec{y}_{b}^{(t+1)} + \MfMui\dcurl \vec{y}_{e}^{(t+1)}
+        - \frac{1}{\delta t} \MfMui \vec{y}_{b}^{(t)}
+        = \vec{p}_b^{(t+1)} \\
+        \dcurl^\top \MfMui \vec{y}_b^{(t+1)} - \MeSig \vec{y}_e^{(t+1)} = \vec{p}_e^{(t+1)}
+    \end{align}
+
+and
+
+.. math::
+
+    \begin{align}
+        \left( \MfMui \dcurl \MeSig^{-1} \dcurl^\top \MfMui + \frac{1}{\delta t} \MfMui \right) \vec{y}_{b}^{(t+1)} =
+        \frac{1}{\delta t} \MfMui \vec{y}_b^{(t)}
+        + \MfMui \dcurl \MeSig^{-1} \vec{p}_e^{(t+1)} + \vec{p}_b^{(t+1)} \\
+        \vec{y}_e^{(t+1)} = \MeSig^{-1} \dcurl^\top \MfMui \vec{y}_b^{(t+1)} - \MeSig^{-1} \vec{p}_e^{(t+1)}
+    \end{align}
+
+.. note::
+
+    For the first time step, \\\(t=0\\\), the term: \\\(\\frac{1}{\\delta t} \\MfMui \\vec{y}_b^{(0)}\\\) is zero.
+
+
+
+
+Implementing **J** transpose times a vector
+-------------------------------------------
+
+Multiplying \\(\\mathbf{J}^\\top\\) onto a vector can be broken into three steps
+
+
+* Compute \\(\\vec{p} = \\mathbf{Q}^\\top \\vec{v}\\)
+* Solve \\(\\hat{\\mathbf{A}}^\\top \\vec{y} = \\vec{p}\\)
+* Compute \\(\\vec{w} = -\\mathbf{G}^\\top y\\)
+
+
+.. math::
+
+    \mathbf{\hat{A}}^\top = \left[
+        \begin{array}{cccc}
+            A & B & & \\
+              & \ddots & \ddots & \\
+              & & A & B \\
+              & & 0 & A
+        \end{array}
+    \right]
+
+For the all time-steps (going backwards in time):
+
+
+.. math::
+
+    A \vec{y}^{(t)} + B \vec{y}^{(t+1)} = \vec{p}^{(t)}
+
+
+.. math::
+
+    \begin{align}
+        \frac{1}{\delta t} \MfMui\vec{y}_{b}^{(t)} + \MfMui\dcurl \vec{y}_{e}^{(t)}
+        - \frac{1}{\delta t} \MfMui \vec{y}_{b}^{(t+1)}
+        = \vec{p}_b^{(t)} \\
+        \dcurl^\top \MfMui \vec{y}_b^{(t)} - \MeSig \vec{y}_e^{(t)} = \vec{p}_e^{(t)}
+    \end{align}
+
+and
+
+.. math::
+
+    \begin{align}
+        \left( \MfMui \dcurl \MeSig^{-1} \dcurl^\top \MfMui + \frac{1}{\delta t} \MfMui \right) \vec{y}_{b}^{(t)} =
+        \frac{1}{\delta t} \MfMui \vec{y}_b^{(t+1)}
+        + \MfMui \dcurl \MeSig^{-1} \vec{p}_e^{(t)} + \vec{p}_b^{(t)} \\
+        \vec{y}_e^{(t)} = \MeSig^{-1} \dcurl^\top \MfMui \vec{y}_b^{(t)} - \MeSig^{-1} \vec{p}_e^{(t)}
+    \end{align}
+
+
+.. note::
+
+    For the last time step, \\\(t=N\\\), the term: \\\(\\frac{1}{\\delta t} \\MfMui \\vec{y}_b^{(N+1)}\\\) is zero.
+
+
+
 TDEM - B formulation
 ====================
 

docs/em/api_TDEM_derivation.rst

@@ -1,341 +0,0 @@
-.. _api_TDEM_derivation:
-
-
-.. math::
-
-    \renewcommand{\div}{\nabla\cdot\,}
-    \newcommand{\grad}{\vec \nabla}
-    \newcommand{\curl}{{\vec \nabla}\times\,}
-    \newcommand {\J}{{\vec J}}
-    \renewcommand{\H}{{\vec H}}
-    \newcommand {\E}{{\vec E}}
-    \newcommand{\dcurl}{{\mathbf C}}
-    \newcommand{\dgrad}{{\mathbf G}}
-    \newcommand{\Acf}{{\mathbf A_c^f}}
-    \newcommand{\Ace}{{\mathbf A_c^e}}
-    \renewcommand{\S}{{\mathbf \Sigma}}
-    \newcommand{\St}{{\mathbf \Sigma_\tau}}
-    \newcommand{\T}{{\mathbf T}}
-    \newcommand{\Tt}{{\mathbf T_\tau}}
-    \newcommand{\diag}[1]{\,{\sf diag}\left( #1 \right)}
-    \newcommand{\M}{{\mathbf M}}
-    \newcommand{\MfMui}{{\M^f_{\mu^{-1}}}}
-    \newcommand{\MeSig}{{\M^e_\sigma}}
-    \newcommand{\MeSigInf}{{\M^e_{\sigma_\infty}}}
-    \newcommand{\MeSigO}{{\M^e_{\sigma_0}}}
-    \newcommand{\Me}{{\M^e}}
-    \newcommand{\Mes}[1]{{\M^e_{#1}}}
-    \newcommand{\Mee}{{\M^e_e}}
-    \newcommand{\Mej}{{\M^e_j}}
-    \newcommand{\BigO}[1]{\mathcal{O}\bigl(#1\bigr)}
-    \newcommand{\bE}{\mathbf{E}}
-    \newcommand{\bH}{\mathbf{H}}
-    \newcommand{\B}{\vec{B}}
-    \newcommand{\D}{\vec{D}}
-    \renewcommand{\H}{\vec{H}}
-    \newcommand{\s}{\vec{s}}
-    \newcommand{\bfJ}{\bf{J}}
-    \newcommand{\vecm}{\vec m}
-    \renewcommand{\Re}{\mathsf{Re}}
-    \renewcommand{\Im}{\mathsf{Im}}
-    \renewcommand {\j}  { {\vec j} }
-    \newcommand {\h}  { {\vec h} }
-    \renewcommand {\b}  { {\vec b} }
-    \newcommand {\e}  { {\vec e} }
-    \newcommand {\c}  { {\vec c} }
-    \renewcommand {\d}  { {\vec d} }
-    \renewcommand {\u}  { {\vec u} }
-    \newcommand{\I}{\vec{I}}
-
-
-Time-Domain EM Derivation
-*************************
-
-The following shows the derivation for the TDEM problem. We use the b-formulation below.
-(More to come soon..!)
-
-
-Sensitivity Calculation
-=======================
-
-.. math::
-
-    \begin{align}
-        \dcurl \e^{(t+1)} + \frac{\b^{(t+1)} - \b^{(t)}}{\delta t} = 0 \\
-        \dcurl^\top \MfMui \b^{(t+1)} - \MeSig \e^{(t+1)} = \Me \j_s^{(t+1)}
-    \end{align}
-
-Using Gauss-Newton to solve the inverse problem requires the ability to calculate the product of the
-Jacobian and a vector, as well as the transpose of the Jacobian times a vector.
-The above system can be rewritten as:
-
-.. math::
-
-    \begin{align}
-        \mathbf{A} \u^{(t+1)} + \mathbf{B} \u^{(t)}= \s^{(t+1)}
-    \end{align}
-
-where
-
-.. math::
-
-    \begin{align}
-        \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] \\
-        \u^{(k)} = \left[
-        \begin{array}{c}
-            \b^{(k)}\\
-            \e^{(k)}
-        \end{array}
-        \right] \\
-        \s^{(k)} = \left[
-        \begin{array}{c}
-            0\\
-            \Me \j^{(k)}_s
-        \end{array}
-        \right]
-    \end{align}
-
-.. note::
-
-    Here we have multiplied through by \\(\\MfMui\\) to make A and B symmetric!
-
-The entire time dependent system can be written in a single matrix expression
-
-.. math::
-
-    \begin{align}
-        \hat{\mathbf{A}} \hat{u} = \hat{s}
-    \end{align}
-
-where
-
-.. math::
-
-    \begin{align}
-        \mathbf{\hat{A}} = \left[
-        \begin{array}{cccc}
-            A & 0 & & \\
-            B & A & & \\
-              & \ddots & \ddots & \\
-              & & B & A
-        \end{array}
-        \right] \\
-        \hat{u} = \left[
-            \begin{array}{c}
-                \u^{(1)} \\
-                \u^{(2)} \\
-                \vdots \\
-                \u^{(N)}
-            \end{array} \right]\\
-        \hat{s} = \left[
-            \begin{array}{c}
-                \s^{(1)} - \mathbf{B} \u^{(0)} \\
-                \s^{(2)} \\
-                \vdots \\
-                \s^{(N)}
-            \end{array}
-        \right]
-    \end{align}
-
-For the fields \\(\\u\\), the measured data is given by
-
-.. math::
-
-    \begin{align}
-        \vec{d} = \mathbf{Q} \u
-    \end{align}
-
-The sensitivity matrix **J** is then defined as
-
-.. math::
-
-    \begin{align}
-        \mathbf{J} = \mathbf{Q} \frac{\partial \u}{\partial \sigma}
-    \end{align}
-
-
-Defining the function \\(\\c(m,\\u)\\) to be
-
-.. math::
-
-    \begin{align}
-        \vec{c}(m,\u) = \hat{\mathbf{A}} \vec{u} - \vec{q} = \vec{0}
-    \end{align}
-
-then
-
-.. math::
-
-    \begin{align}
-        \frac{\partial \vec{c}}{\partial m} \partial m
-        + \frac{\partial \vec{c}}{\partial \u} \partial \vec{u} = 0
-    \end{align}
-
-or
-
-.. math::
-
-    \begin{align}
-        \frac{\partial \vec{u}}{\partial m} = -\left(\frac{\partial \vec{c}}{\partial \u} \right)^{-1} \frac{\partial \vec{c}}{\partial m}
-    \end{align}
-
-
-Differentiating, we find that
-
-.. math::
-
-    \begin{align}
-        \frac{\partial \vec{c}}{\partial \hat{u}} = \hat{\mathbf{A}}
-    \end{align}
-
-and
-
-.. math::
-
-    \begin{align}
-        \frac{\partial \vec{c}}{\partial \sigma} = \mathbf{G}_\sigma =
-        \left[
-            \begin{array}{c}
-                g_\sigma^{(1)}\\
-                g_\sigma^{(2)}\\
-                \vdots \\
-                g_\sigma^{(N)}
-            \end{array}
-        \right]
-    \end{align}
-
-with
-
-.. math::
-
-    \begin{align}
-        g_\sigma^{(n)} =
-        \left[
-            \begin{array}{c}
-                \mathbf{0} \\
-                - \diag{\e^{(n)}} \Ace \diag{\vec{V}}
-            \end{array}
-        \right]
-    \end{align}
-
-
-Implementing **J** times a vector
-=================================
-
-Multiplying **J** onto a vector can be broken into three steps
-
-
-* Compute \\(\\vec{p} = \\mathbf{G}m\\)
-* Solve \\(\\hat{\\mathbf{A}} \\vec{y} = \\vec{p}\\)
-* Compute \\(\\vec{w} = -\\mathbf{Q} \\vec{y}\\)
-
-.. math::
-
-    \begin{align}
-        \vec{p}^{(n)} = \left[
-            \begin{array}{c}
-                \vec{p}_b^{(n)} \\
-                \vec{p}_e^{(n)}
-            \end{array}
-        \right] \\
-        \vec{p}_b^{(n)} = 0 \\
-        \vec{p}_e^{(n)} = - \diag{\e^{(n)}} \Ace \diag{V} m
-    \end{align}
-
-
-For all time steps:
-
-.. math::
-
-    \begin{align}
-        \frac{1}{\delta t} \MfMui\vec{y}_{b}^{(t+1)} + \MfMui\dcurl \vec{y}_{e}^{(t+1)}
-        - \frac{1}{\delta t} \MfMui \vec{y}_{b}^{(t)}
-        = \vec{p}_b^{(t+1)} \\
-        \dcurl^\top \MfMui \vec{y}_b^{(t+1)} - \MeSig \vec{y}_e^{(t+1)} = \vec{p}_e^{(t+1)}
-    \end{align}
-
-and
-
-.. math::
-
-    \begin{align}
-        \left( \MfMui \dcurl \MeSig^{-1} \dcurl^\top \MfMui + \frac{1}{\delta t} \MfMui \right) \vec{y}_{b}^{(t+1)} =
-        \frac{1}{\delta t} \MfMui \vec{y}_b^{(t)}
-        + \MfMui \dcurl \MeSig^{-1} \vec{p}_e^{(t+1)} + \vec{p}_b^{(t+1)} \\
-        \vec{y}_e^{(t+1)} = \MeSig^{-1} \dcurl^\top \MfMui \vec{y}_b^{(t+1)} - \MeSig^{-1} \vec{p}_e^{(t+1)}
-    \end{align}
-
-.. note::
-
-    For the first time step, \\\(t=0\\\), the term: \\\(\\frac{1}{\\delta t} \\MfMui \\vec{y}_b^{(0)}\\\) is zero.
-
-
-
-
-Implementing **J** transpose times a vector
-===========================================
-
-Multiplying \\(\\mathbf{J}^\\top\\) onto a vector can be broken into three steps
-
-
-* Compute \\(\\vec{p} = \\mathbf{Q}^\\top \\vec{v}\\)
-* Solve \\(\\hat{\\mathbf{A}}^\\top \\vec{y} = \\vec{p}\\)
-* Compute \\(\\vec{w} = -\\mathbf{G}^\\top y\\)
-
-
-.. math::
-
-    \mathbf{\hat{A}}^\top = \left[
-        \begin{array}{cccc}
-            A & B & & \\
-              & \ddots & \ddots & \\
-              & & A & B \\
-              & & 0 & A
-        \end{array}
-    \right]
-
-For the all time-steps (going backwards in time):
-
-
-.. math::
-
-    A \vec{y}^{(t)} + B \vec{y}^{(t+1)} = \vec{p}^{(t)}
-
-
-.. math::
-
-    \begin{align}
-        \frac{1}{\delta t} \MfMui\vec{y}_{b}^{(t)} + \MfMui\dcurl \vec{y}_{e}^{(t)}
-        - \frac{1}{\delta t} \MfMui \vec{y}_{b}^{(t+1)}
-        = \vec{p}_b^{(t)} \\
-        \dcurl^\top \MfMui \vec{y}_b^{(t)} - \MeSig \vec{y}_e^{(t)} = \vec{p}_e^{(t)}
-    \end{align}
-
-and
-
-.. math::
-
-    \begin{align}
-        \left( \MfMui \dcurl \MeSig^{-1} \dcurl^\top \MfMui + \frac{1}{\delta t} \MfMui \right) \vec{y}_{b}^{(t)} =
-        \frac{1}{\delta t} \MfMui \vec{y}_b^{(t+1)}
-        + \MfMui \dcurl \MeSig^{-1} \vec{p}_e^{(t)} + \vec{p}_b^{(t)} \\
-        \vec{y}_e^{(t)} = \MeSig^{-1} \dcurl^\top \MfMui \vec{y}_b^{(t)} - \MeSig^{-1} \vec{p}_e^{(t)}
-    \end{align}
-
-
-.. note::
-
-    For the last time step, \\\(t=N\\\), the term: \\\(\\frac{1}{\\delta t} \\MfMui \\vec{y}_b^{(N+1)}\\\) is zero.

docs/em/api_Utils.rst

@@ -4,6 +4,16 @@ simpegEM Utilities
 SimPEG for EM provides a few EM specific utility codes,
 sources, and analytic functions.
 
+Utilities for Electromagnetics
+==============================
+
+.. automodule:: SimPEG.EM.Utils
+    :show-inheritance:
+    :members:
+    :undoc-members:
+    :inherited-members:
+
+
 Analytic Functions - Time
 =========================
 
@@ -22,12 +32,3 @@ Analytic Functions - Frequency
     :members:
     :undoc-members:
     :inherited-members:
-
-
-Sources
-=======
-
-.. autoclass:: SimPEG.EM.FDEM.SrcFDEM.MagDipole
-    :show-inheritance:
-    :members:
-    :undoc-members:

docs/em/index.rst

@@ -5,40 +5,22 @@ Electromagnetics
 `SimPEG.EM` uses SimPEG as the framework for the forward and inverse
 electromagnetics geophysical problems. 
 
-Time Domian Electromagnetics
+To solve for predicted data, we follow the framework shown below. The model is
-----------------------------
+what we invert for. This is mapped to a physical property on the simulation
-
+mesh. A source which is used to excite the system is specified. Having a model
-.. toctree::
+and a source, we can solve Maxwell's equations for fields. We sample these
-    :maxdepth: 2
+fields with recievers to give us predicted data. 
-
-    api_TDEM_derivation
 
 
-Code for Time Domian Electromagnetics
+.. image:: ../images/simpegEM_noMath.png
--------------------------------------
+    :scale: 50%
 
-.. toctree::
-    :maxdepth: 2
-
-    api_TDEM
-
-Frequency Domian Electromagnetics
----------------------------------
 
 .. toctree::
    :maxdepth: 2
 
    api_FDEM
-
+   api_TDEM
-
-Utility Codes
--------------
-
-.. toctree::
-   :maxdepth: 2
-
    api_Utils
 
 
-
-

docs/examples/MT_1D_ForwardAndInversion.rst

@@ -0,0 +1,27 @@
+.. _examples_MT_1D_ForwardAndInversion:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+
+MT: 1D: Inversion
+=======================
+
+Forward model 1D MT data.
+Setup and run a MT 1D inversion.
+
+
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.MT_1D_ForwardAndInversion.run()
+
+.. literalinclude:: ../../SimPEG/Examples/MT_1D_ForwardAndInversion.py
+    :language: python
+    :linenos:

docs/examples/MT_3D_Foward.rst

@@ -0,0 +1,26 @@
+.. _examples_MT_3D_Foward:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+
+MT: 3D: Forward
+=======================
+
+Forward model 3D MT data.
+
+
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.MT_3D_Foward.run()
+
+.. literalinclude:: ../../SimPEG/Examples/MT_3D_Foward.py
+    :language: python
+    :linenos:

docs/index.rst

@@ -49,10 +49,8 @@ Examples
 
 .. toctree::
    :maxdepth: 2
-
    api_Examples
 
-
 Packages
 ********
 
@@ -60,9 +58,9 @@ Packages
    :maxdepth: 3
 
    em/index
+   mt/index
    flow/index
 
-
 Finite Volume
 *************
 

docs/mt/index.rst

@@ -0,0 +1,19 @@
+Magnetotellurics
+****************
+
+SimPEG (Simulation and Parameter Estimation in Geophysics) is a python
+package for simulation and gradient based parameter estimation in the
+context of geoscience applications.
+
+simpegMT uses SimPEG as the framework for the forward and inverse
+magnetotellurics geophysical problems.
+
+
+
+Problem
+=======
+
+.. autoclass:: SimPEG.MT.BaseMT.BaseMTProblem
+    :show-inheritance:
+    :members:
+    :undoc-members:

tests/examples/test_examples.py

@@ -1,8 +1,28 @@
 import unittest
 import sys
+import os
 from SimPEG import Examples
 import numpy as np
 
+class compareInitFiles(unittest.TestCase):
+    def test_compareInitFiles(self):
+        print 'Checking that __init__.py up-to-date in SimPEG/Examples'
+        fName = os.path.abspath(__file__)
+        ExamplesDir = os.path.sep.join(fName.split(os.path.sep)[:-3] + ['SimPEG', 'Examples'])
+
+        files = os.listdir(ExamplesDir)
+
+        pyfiles = []
+        [pyfiles.append(py.rstrip('.py')) for py in files if py.endswith('.py') and py != '__init__.py']
+
+        setdiff = set(pyfiles) - set(Examples.__examples__)
+
+        print ' Any missing files? ', setdiff 
+
+        didpass = (setdiff == set())
+
+        self.assertTrue(didpass, "Examples not up to date, run 'python __init__.py' from SimPEG/Examples to update")
+
 def get(test):
     def test_func(self):
         print '\nTesting %s.run(plotIt=False)\n'%test
@@ -10,11 +30,11 @@ def get(test):
         self.assertTrue(True)
     return test_func
 attrs = dict()
+
 for test in Examples.__examples__:
     attrs['test_'+test] = get(test)
 
 TestExamples = type('TestExamples', (unittest.TestCase,), attrs)
 
-
 if __name__ == '__main__':
     unittest.main()

tests/mt/__init__.py

@@ -0,0 +1,12 @@
+import os
+import glob
+import unittest
+
+if __name__ == '__main__':
+    test_file_strings = glob.glob('test_*.py')
+    module_strings = [str[0:len(str)-3] for str in test_file_strings]
+    suites = [unittest.defaultTestLoader.loadTestsFromName(str) for str
+              in module_strings]
+    testSuite = unittest.TestSuite(suites)
+
+    unittest.TextTestRunner(verbosity=2).run(testSuite)

tests/mt/test_ApparentResistivityAnalytic.py

@@ -0,0 +1,48 @@
+import unittest
+from SimPEG import *
+from SimPEG import MT
+
+TOL = 1e-6
+
+def appResPhs(freq,z):
+    app_res = ((1./(8e-7*np.pi**2))/freq)*np.abs(z)**2
+    app_phs = np.arctan2(-z.imag,z.real)*(180/np.pi)
+    return app_res, app_phs
+
+def appResNorm(sigmaHalf):
+    nFreq = 26
+
+    m1d = Mesh.TensorMesh([[(100,5,1.5),(100.,10),(100,5,1.5)]], x0=['C'])
+    sigma = np.zeros(m1d.nC) + sigmaHalf
+    sigma[m1d.gridCC[:]>200] = 1e-8
+
+    # Calculate the analytic fields
+    freqs = np.logspace(4,-4,nFreq)
+    Z = []
+    for freq in freqs:
+        Ed, Eu, Hd, Hu = MT.Utils.getEHfields(m1d,sigma,freq,np.array([200]))
+        Z.append((Ed + Eu)/(Hd + Hu))
+
+    Zarr = np.concatenate(Z)
+
+    app_r, app_p = appResPhs(freqs,Zarr)
+
+    return np.linalg.norm(np.abs(app_r - np.ones(nFreq)/sigmaHalf)) / np.log10(sigmaHalf)
+
+
+class TestAnalytics(unittest.TestCase):
+
+    def setUp(self):
+        pass
+    def test_appRes2en1(self):self.assertLess(appResNorm(2e-1), TOL)
+    def test_appRes2en2(self):self.assertLess(appResNorm(2e-2), TOL)
+    def test_appRes2en3(self):self.assertLess(appResNorm(2e-3), TOL)
+    def test_appRes2en4(self):self.assertLess(appResNorm(2e-4), TOL)
+    def test_appRes2en5(self):self.assertLess(appResNorm(2e-5), TOL)
+    def test_appRes2en6(self):self.assertLess(appResNorm(2e-6), TOL)
+
+
+
+
+if __name__ == '__main__':
+    unittest.main()

tests/mt/test_Problem1D_againstAnalyticHalfspace.py

@@ -0,0 +1,162 @@
+import unittest
+import SimPEG as simpeg
+from SimPEG import MT
+from SimPEG.Utils import meshTensor
+import numpy as np
+# Define the tolerances
+TOLr = 5e-2
+TOLp = 5e-2
+
+
+def setupSurvey(sigmaHalf,tD=True):
+
+    # Frequency
+    nFreq = 33
+    freqs = np.logspace(3,-3,nFreq)
+    # Make the mesh
+    ct = 5
+    air = meshTensor([(ct,25,1.3)])
+    # coreT0 = meshTensor([(ct,15,1.2)])
+    # coreT1 = np.kron(meshTensor([(coreT0[-1],15,1.3)]),np.ones((7,)))
+    core = np.concatenate( (  np.kron(meshTensor([(ct,15,-1.2)]),np.ones((10,))) , meshTensor([(ct,20)]) ) )
+    bot = meshTensor([(core[0],10,-1.3)])
+    x0 = -np.array([np.sum(np.concatenate((core,bot)))])
+    m1d = simpeg.Mesh.TensorMesh([np.concatenate((bot,core,air))], x0=x0)
+    # Make the model
+    sigma = np.zeros(m1d.nC) + sigmaHalf
+    sigma[m1d.gridCC > 0 ] = 1e-8
+
+    rxList = []
+    for rxType in ['z1dr','z1di']:
+        rxList.append(MT.Rx(simpeg.mkvc(np.array([0.0]),2).T,rxType))
+    # Source list
+    srcList =[]
+    if tD:
+        for freq in freqs:
+            srcList.append(MT.SrcMT.polxy_1DhomotD(rxList,freq))
+    else:
+        for freq in freqs:
+            srcList.append(MT.SrcMT.polxy_1Dprimary(rxList,freq))
+
+    survey = MT.Survey(srcList)
+    return survey, sigma, m1d
+
+def getAppResPhs(MTdata):
+    # Make impedance
+    def appResPhs(freq,z):
+        app_res = ((1./(8e-7*np.pi**2))/freq)*np.abs(z)**2
+        app_phs = np.arctan2(z.imag,z.real)*(180/np.pi)
+        return app_res, app_phs
+    zList = []
+    for src in MTdata.survey.srcList:
+        zc = [src.freq]
+        for rx in src.rxList:
+            if 'i' in rx.rxType:
+                m=1j
+            else:
+                m = 1
+            zc.append(m*MTdata[src,rx])
+        zList.append(zc)
+    return [appResPhs(zList[i][0],np.sum(zList[i][1:3])) for i in np.arange(len(zList))]
+
+def appRes_TotalFieldNorm(sigmaHalf):
+
+    # Make the survey
+    survey, sigma, mesh = setupSurvey(sigmaHalf)
+    problem = MT.Problem1D.eForm_TotalField(mesh)
+    problem.pair(survey)
+
+    # Get the fields
+    fields = problem.fields(sigma)
+
+    # Project the data
+    data = survey.projectFields(fields)
+
+    # Calculate the app res and phs
+    app_r = np.array(getAppResPhs(data))[:,0]
+
+    return np.linalg.norm(np.abs(app_r - np.ones(survey.nFreq)/sigmaHalf)*sigmaHalf)
+
+def appPhs_TotalFieldNorm(sigmaHalf):
+
+    # Make the survey
+    survey, sigma, mesh = setupSurvey(sigmaHalf)
+    problem = MT.Problem1D.eForm_TotalField(mesh)
+    problem.pair(survey)
+
+    # Get the fields
+    fields = problem.fields(sigma)
+
+    # Project the data
+    data = survey.projectFields(fields)
+
+    # Calculate the app  phs
+    app_p = np.array(getAppResPhs(data))[:,1]
+
+    return np.linalg.norm(np.abs(app_p - np.ones(survey.nFreq)*45)/ 45)
+
+def appRes_psFieldNorm(sigmaHalf):
+
+    # Make the survey
+    survey, sigma, mesh = setupSurvey(sigmaHalf,False)
+    problem = MT.Problem1D.eForm_psField(mesh, sigmaPrimary = sigma)
+    problem.pair(survey)
+
+    # Get the fields
+    fields = problem.fields(sigma)
+
+    # Project the data
+    data = survey.projectFields(fields)
+
+    # Calculate the app res and phs
+    app_r = np.array(getAppResPhs(data))[:,0]
+
+    return np.linalg.norm(np.abs(app_r - np.ones(survey.nFreq)/sigmaHalf)*sigmaHalf)
+
+def appPhs_psFieldNorm(sigmaHalf):
+
+    # Make the survey
+    survey, sigma, mesh = setupSurvey(sigmaHalf,False)
+    problem = MT.Problem1D.eForm_psField(mesh, sigmaPrimary = sigma)
+    problem.pair(survey)
+
+    # Get the fields
+    fields = problem.fields(sigma)
+
+    # Project the data
+    data = survey.projectFields(fields)
+
+    # Calculate the app  phs
+    app_p = np.array(getAppResPhs(data))[:,1]
+
+    return np.linalg.norm(np.abs(app_p - np.ones(survey.nFreq)*45)/ 45)
+
+class TestAnalytics(unittest.TestCase):
+
+    def setUp(self):
+        pass
+    # Total Fields
+    # def test_appRes2en1(self):self.assertLess(appRes_TotalFieldNorm(2e-1), TOLr)
+    # def test_appPhs2en1(self):self.assertLess(appPhs_TotalFieldNorm(2e-1), TOLp)
+
+    # def test_appRes2en2(self):self.assertLess(appRes_TotalFieldNorm(2e-2), TOLr)
+    # def test_appPhs2en2(self):self.assertLess(appPhs_TotalFieldNorm(2e-2), TOLp)
+
+    # def test_appRes2en3(self):self.assertLess(appRes_TotalFieldNorm(2e-3), TOLr)
+    # def test_appPhs2en3(self):self.assertLess(appPhs_TotalFieldNorm(2e-3), TOLp)
+
+    # def test_appRes2en4(self):self.assertLess(appRes_TotalFieldNorm(2e-4), TOLr)
+    # def test_appPhs2en4(self):self.assertLess(appPhs_TotalFieldNorm(2e-4), TOLp)
+
+    # def test_appRes2en5(self):self.assertLess(appRes_TotalFieldNorm(2e-5), TOLr)
+    # def test_appPhs2en5(self):self.assertLess(appPhs_TotalFieldNorm(2e-5), TOLp)
+
+    # def test_appRes2en6(self):self.assertLess(appRes_TotalFieldNorm(2e-6), TOLr)
+    # def test_appPhs2en6(self):self.assertLess(appPhs_TotalFieldNorm(2e-6), TOLp)
+
+    # Primary/secondary
+    def test_appRes2en2_ps(self):self.assertLess(appRes_psFieldNorm(2e-2), TOLr)
+    def test_appPhs2en2_ps(self):self.assertLess(appPhs_psFieldNorm(2e-2), TOLp)
+
+if __name__ == '__main__':
+    unittest.main()

tests/mt/test_Problem1D_totalDvsPSvsAnalytic.py

@@ -0,0 +1,135 @@
+import unittest
+import SimPEG as simpeg
+from SimPEG import MT
+from SimPEG.Utils import meshTensor
+import numpy as np
+# Define the tolerances
+TOLr = 5e-2
+TOLp = 5e-2
+
+
+def setupSurvey(sigmaHalf,tD=True):
+
+    # Frequency
+    nFreq = 33
+    freqs = np.logspace(3,-3,nFreq)
+    # Make the mesh
+    ct = 5
+    air = meshTensor([(ct,25,1.3)])
+    # coreT0 = meshTensor([(ct,15,1.2)])
+    # coreT1 = np.kron(meshTensor([(coreT0[-1],15,1.3)]),np.ones((7,)))
+    core = np.concatenate( (  np.kron(meshTensor([(ct,15,-1.2)]),np.ones((10,))) , meshTensor([(ct,20)]) ) )
+    bot = meshTensor([(core[0],15,-1.3)])
+    x0 = -np.array([np.sum(np.concatenate((core,bot)))])
+    m1d = simpeg.Mesh.TensorMesh([np.concatenate((bot,core,air))], x0=x0)
+    # Make the model
+    sigma = np.zeros(m1d.nC) + sigmaHalf
+    sigma[m1d.gridCC > 0 ] = 1e-8
+    sigmaBack = sigma.copy()
+    # Add structure
+    shallow = (m1d.gridCC < -200) * (m1d.gridCC > -600)
+    deep = (m1d.gridCC < -3000) * (m1d.gridCC > -5000)
+    sigma[shallow] = 1
+    sigma[deep] = 0.1
+
+    rxList = []
+    for rxType in ['z1dr','z1di']:
+        rxList.append(MT.Rx(simpeg.mkvc(np.array([0.0]),2).T,rxType))
+    # Source list
+    srcList =[]
+    if tD:
+        for freq in freqs:
+            srcList.append(MT.SrcMT.polxy_1DhomotD(rxList,freq))
+    else:
+        for freq in freqs:
+            srcList.append(MT.SrcMT.polxy_1Dprimary(rxList,freq))
+
+    survey = MT.Survey(srcList)
+    return survey, sigma, m1d
+
+def getAppResPhs(MTdata):
+    # Make impedance
+    def appResPhs(freq,z):
+        app_res = ((1./(8e-7*np.pi**2))/freq)*np.abs(z)**2
+        app_phs = np.arctan2(z.imag,z.real)*(180/np.pi)
+        return app_res, app_phs
+    zList = []
+    for src in MTdata.survey.srcList:
+        zc = [src.freq]
+        for rx in src.rxList:
+            if 'i' in rx.rxType:
+                m=1j
+            else:
+                m = 1
+            zc.append(m*MTdata[src,rx])
+        zList.append(zc)
+    return [appResPhs(zList[i][0],np.sum(zList[i][1:3])) for i in np.arange(len(zList))]
+
+def calculateAnalyticSolution(srcList,mesh,model):
+    surveyAna = MT.Survey(srcList)
+    data1D = MT.Data(surveyAna)
+    for src in surveyAna.srcList:
+        elev = src.rxList[0].locs[0]
+        anaEd, anaEu, anaHd, anaHu = MT.Utils.MT1Danalytic.getEHfields(mesh,model,src.freq,elev)
+        anaE = anaEd+anaEu
+        anaH = anaHd+anaHu
+        # Scale the solution
+        # anaE = (anaEtemp/anaEtemp[-1])#.conj()
+        # anaH = (anaHtemp/anaEtemp[-1])#.conj()
+        anaZ = anaE/anaH
+        for rx in src.rxList:
+            data1D[src,rx] = getattr(anaZ, rx.projComp)
+    return data1D
+
+def dataMis_AnalyticTotalDomain(sigmaHalf):
+
+    # Make the survey
+
+    # Total domain solution
+    surveyTD, sigma, mesh = setupSurvey(sigmaHalf)
+    problemTD = MT.Problem1D.eForm_TotalField(mesh)
+    problemTD.pair(surveyTD)
+    # Analytic data
+    dataAnaObj = calculateAnalyticSolution(surveyTD.srcList,mesh,sigma)
+    # dataTDObj = MT.DataMT.DataMT(surveyTD, surveyTD.dpred(sigma))
+    dataTD = surveyTD.dpred(sigma)
+    dataAna = simpeg.mkvc(dataAnaObj)
+    return np.all((dataTD - dataAna)/dataAna < 2.)
+    # surveyTD.dtrue = -simpeg.mkvc(dataAna,2)
+    # surveyTD.dobs = -simpeg.mkvc(dataAna,2)
+    # surveyTD.Wd = np.ones(surveyTD.dtrue.shape) #/(np.abs(surveyTD.dtrue)*0.01)
+    # # Setup the data misfit
+    # dmis = simpeg.DataMisfit.l2_DataMisfit(surveyTD)
+    # dmis.Wd = surveyTD.Wd
+    # return dmis.eval(sigma)
+
+
+def dataMis_AnalyticPrimarySecondary(sigmaHalf):
+
+    # Make the survey
+    # Primary secondary
+    surveyPS, sigmaPS, mesh = setupSurvey(sigmaHalf,tD=False)
+    problemPS = MT.Problem1D.eForm_psField(mesh)
+    problemPS.sigmaPrimary = sigmaPS
+    problemPS.pair(surveyPS)
+    # Analytic data
+    dataAnaObj = calculateAnalyticSolution(surveyPS.srcList,mesh,sigmaPS)
+
+    dataPS = surveyPS.dpred(sigmaPS)
+    dataAna = simpeg.mkvc(dataAnaObj)
+    return np.all((dataPS - dataAna)/dataAna < 2.)
+
+
+
+class TestNumericVsAnalytics(unittest.TestCase):
+
+    def setUp(self):
+        pass
+    # Total Fields
+    # def test_appRes2en2(self):self.assertTrue(dataMis_AnalyticTotalDomain(2e-2))
+
+    # Primary/secondary
+    def test_appRes2en2_ps(self):self.assertTrue(dataMis_AnalyticPrimarySecondary(2e-2))
+
+if __name__ == '__main__':
+    unittest.main()

tests/mt/test_Problem3D_againstAnalytic.py

@@ -0,0 +1,271 @@
+# Test functions
+from glob import glob
+import numpy as np, sys, os, time, scipy, subprocess
+import SimPEG as simpeg
+import unittest
+from SimPEG import MT
+from SimPEG.Utils import meshTensor
+from scipy.constants import mu_0
+
+TOLr = 5e-2
+TOL = 1e-4
+FLR = 1e-20 # "zero", so if residual below this --> pass regardless of order
+CONDUCTIVITY = 1e1
+MU = mu_0
+freq = [1e-1, 2e-1]
+addrandoms = True
+
+
+def getInputs():
+    """
+    Function that returns Mesh, freqs, rx_loc, elev.
+    """
+    # Make a mesh
+    # M = simpeg.Mesh.TensorMesh([[(100,5,-1.5),(100.,10),(100,5,1.5)],[(100,5,-1.5),(100.,10),(100,5,1.5)],[(100,5,1.6),(100.,10),(100,3,2)]], x0=['C','C',-3529.5360])
+    # M = simpeg.Mesh.TensorMesh([[(1000,6,-1.5),(1000.,6),(1000,6,1.5)],[(1000,6,-1.5),(1000.,2),(1000,6,1.5)],[(1000,6,-1.3),(1000.,6),(1000,6,1.3)]], x0=['C','C','C'])# Setup the model
+    M = simpeg.Mesh.TensorMesh([[(1000,6,-1.5),(1000.,4),(1000,6,1.5)],[(1000,6,-1.5),(1000.,4),(1000,6,1.5)],[(500,8,-1.3),(500.,8),(500,8,1.3)]], x0=['C','C','C'])# Setup the model
+    # Set the frequencies
+    freqs = np.logspace(1,-3,5)
+    elev = 0
+
+    ## Setup the the survey object
+    # Receiver locations
+    rx_x, rx_y = np.meshgrid(np.arange(-1000,1001,500),np.arange(-1000,1001,500))
+    rx_loc = np.hstack((simpeg.Utils.mkvc(rx_x,2),simpeg.Utils.mkvc(rx_y,2),elev+np.zeros((np.prod(rx_x.shape),1))))
+
+    return M, freqs, rx_loc, elev
+
+def random(conds):
+    ''' Returns a halfspace model based on the inputs'''
+    M, freqs, rx_loc, elev = getInputs()
+
+    # Backround
+    sigBG = np.ones(M.nC)*conds
+    # Add randomness to the model (10% of the value).
+    sig = np.exp( np.log(sigBG) + np.random.randn(M.nC)*(conds)*1e-1 )
+
+    return (M, freqs, sig, sigBG, rx_loc)
+
+def halfSpace(conds):
+    ''' Returns a halfspace model based on the inputs'''
+    M, freqs, rx_loc, elev = getInputs()
+
+    # Model
+    ccM = M.gridCC
+    # conds = [1e-2]
+    groundInd = ccM[:,2] < elev
+    sig = np.zeros(M.nC) + 1e-8
+    sig[groundInd] = conds
+    # Set the background, not the same as the model
+    sigBG = np.zeros(M.nC) + 1e-8
+    sigBG[groundInd] = conds
+
+    return (M, freqs, sig, sigBG, rx_loc)
+
+def blockInhalfSpace(conds):
+    ''' Returns a halfspace model based on the inputs'''
+    M, freqs, rx_loc, elev = getInputs()
+
+    # Model
+    ccM = M.gridCC
+    # conds = [1e-2]
+    groundInd = ccM[:,2] < elev
+    sig = simpeg.Utils.ModelBuilder.defineBlock(M.gridCC,np.array([-1000,-1000,-1500]),np.array([1000,1000,-1000]),conds)
+    sig[~groundInd] = 1e-8
+    # Set the background, not the same as the model
+    sigBG = np.zeros(M.nC) + 1e-8
+    sigBG[groundInd] = conds[1]
+
+    return (M, freqs, sig, sigBG, rx_loc)
+
+def twoLayer(conds):
+    ''' Returns a 2 layer model based on the conductivity values given'''
+    M, freqs, rx_loc, elev = getInputs()
+
+    # Model
+    ccM = M.gridCC
+    groundInd = ccM[:,2] < elev
+    botInd = ccM[:,2] < -3000
+    sig = np.zeros(M.nC) + 1e-8
+    sig[groundInd] = conds[1]
+    sig[botInd] = conds[0]
+    # Set the background, not the same as the model
+    sigBG = np.zeros(M.nC) + 1e-8
+    sigBG[groundInd] = conds[1]
+
+
+    return (M, freqs, sig, sigBG, rx_loc)
+
+
+
+def setupSimpegMTfwd_eForm_ps(inputSetup,comp='Imp',singleFreq=False,expMap=True):
+    M,freqs,sig,sigBG,rx_loc = inputSetup
+    # Make a receiver list
+    rxList = []
+    if comp == 'All':
+        for rxType in ['zxxr','zxxi','zxyr','zxyi','zyxr','zyxi','zyyr','zyyi','tzxr','tzxi','tzyr','tzyi']:
+            rxList.append(MT.Rx(rx_loc,rxType))
+    elif comp == 'Imp':
+        for rxType in ['zxxr','zxxi','zxyr','zxyi','zyxr','zyxi','zyyr','zyyi']:
+            rxList.append(MT.Rx(rx_loc,rxType))
+    elif comp == 'Tip':
+        for rxType in ['tzxr','tzxi','tzyr','tzyi']:
+            rxList.append(MT.Rx(rx_loc,rxType))
+    else:
+        rxList.append(MT.Rx(rx_loc,comp))
+    # Source list
+    srcList =[]
+
+    if singleFreq:
+        srcList.append(MT.SrcMT.polxy_1Dprimary(rxList,singleFreq))
+    else:
+        for freq in freqs:
+            srcList.append(MT.SrcMT.polxy_1Dprimary(rxList,freq))
+    # Survey MT
+    survey = MT.Survey(srcList)
+
+    ## Setup the problem object
+    sigma1d = M.r(sigBG,'CC','CC','M')[0,0,:]
+    if expMap:
+        problem = MT.Problem3D.eForm_ps(M,sigmaPrimary= np.log(sigma1d) )
+        problem.mapping = simpeg.Maps.ExpMap(problem.mesh)
+        problem.curModel = np.log(sig)
+    else:
+        problem = MT.Problem3D.eForm_ps(M,sigmaPrimary= sigma1d)
+        problem.curModel = sig
+    problem.pair(survey)
+    problem.verbose = False
+    try:
+        from pymatsolver import MumpsSolver
+        problem.Solver = MumpsSolver
+    except:
+        pass
+
+    return (survey, problem)
+
+def getAppResPhs(MTdata):
+    # Make impedance
+    def appResPhs(freq,z):
+        app_res = ((1./(8e-7*np.pi**2))/freq)*np.abs(z)**2
+        app_phs = np.arctan2(z.imag,z.real)*(180/np.pi)
+        return app_res, app_phs
+    recData = MTdata.toRecArray('Complex')
+    return appResPhs(recData['freq'],recData['zxy']), appResPhs(recData['freq'],recData['zyx'])
+
+def JvecAdjointTest(inputSetup,comp='All',freq=False):
+    (M, freqs, sig, sigBG, rx_loc) = inputSetup
+    survey, problem = setupSimpegMTfwd_eForm_ps(inputSetup,comp='All',singleFreq=freq)
+    print 'Adjoint test of eForm primary/secondary for {:s} comp at {:s}\n'.format(comp,str(survey.freqs))
+
+    m  = sig
+    u = problem.fields(m)
+
+    v = np.random.rand(survey.nD,)
+    # print problem.PropMap.PropModel.nP
+    w = np.random.rand(problem.mesh.nC,)
+
+    vJw = v.ravel().dot(problem.Jvec(m, w, u))
+    wJtv = w.ravel().dot(problem.Jtvec(m, v, u))
+    tol = np.max([TOL*(10**int(np.log10(np.abs(vJw)))),FLR])
+    print ' vJw   wJtv  vJw - wJtv     tol    abs(vJw - wJtv) < tol'
+    print vJw, wJtv, vJw - wJtv, tol, np.abs(vJw - wJtv) < tol
+    return np.abs(vJw - wJtv) < tol
+
+# Test the Jvec derivative
+def DerivJvecTest(inputSetup,comp='All',freq=False,expMap=True):
+    (M, freqs, sig, sigBG, rx_loc) = inputSetup
+    survey, problem = setupSimpegMTfwd_eForm_ps(inputSetup,comp=comp,singleFreq=freq,expMap=expMap)
+    print 'Derivative test of Jvec for eForm primary/secondary for {:s} comp at {:s}\n'.format(comp,survey.freqs)
+    # problem.mapping = simpeg.Maps.ExpMap(problem.mesh)
+    # problem.sigmaPrimary = np.log(sigBG)
+    x0 = np.log(sigBG)
+    # cond = sig[0]
+    # x0 = np.log(np.ones(problem.mesh.nC)*cond)
+    # problem.sigmaPrimary = x0
+    # if True:
+    #     x0  = x0 + np.random.randn(problem.mesh.nC)*cond*1e-1
+    survey = problem.survey
+    def fun(x):
+        return survey.dpred(x), lambda x: problem.Jvec(x0, x)
+    return simpeg.Tests.checkDerivative(fun, x0, num=3, plotIt=False, eps=FLR)
+
+def DerivProjfieldsTest(inputSetup,comp='All',freq=False):
+
+    survey, problem = setupSimpegMTfwd_eForm_ps(inputSetup,comp,freq)
+    print 'Derivative test of data projection for eFormulation primary/secondary\n\n'
+    # problem.mapping = simpeg.Maps.ExpMap(problem.mesh)
+    # Initate things for the derivs Test
+    src = survey.srcList[0]
+    rx = src.rxList[0]
+
+    u0x = np.random.randn(survey.mesh.nE)+np.random.randn(survey.mesh.nE)*1j
+    u0y = np.random.randn(survey.mesh.nE)+np.random.randn(survey.mesh.nE)*1j
+    u0 = np.vstack((simpeg.mkvc(u0x,2),simpeg.mkvc(u0y,2)))
+    f0 = problem.fieldsPair(survey.mesh,survey)
+    # u0 = np.hstack((simpeg.mkvc(u0_px,2),simpeg.mkvc(u0_py,2)))
+    f0[src,'e_pxSolution'] =  u0[:len(u0)/2]#u0x
+    f0[src,'e_pySolution'] = u0[len(u0)/2::]#u0y
+
+    def fun(u):
+        f = problem.fieldsPair(survey.mesh,survey)
+        f[src,'e_pxSolution'] = u[:len(u)/2]
+        f[src,'e_pySolution'] = u[len(u)/2::]
+        return rx.projectFields(src,survey.mesh,f), lambda t: rx.projectFieldsDeriv(src,survey.mesh,f0,simpeg.mkvc(t,2))
+
+    return simpeg.Tests.checkDerivative(fun, u0, num=3, plotIt=False, eps=FLR)
+
+def appResPhsHalfspace_eFrom_ps_Norm(sigmaHalf,appR=True,expMap=False):
+    if appR:
+        label = 'resistivity'
+    else:
+        label = 'phase'
+    # Make the survey and the problem
+    survey, problem = setupSimpegMTfwd_eForm_ps(halfSpace(sigmaHalf),expMap=expMap)
+    print 'Apperent {:s} test of eFormulation primary/secondary at {:g}\n\n'.format(label,sigmaHalf)
+
+    data = problem.dataPair(survey,survey.dpred(problem.curModel))
+    # Calculate the app  phs
+    app_rpxy, app_rpyx = np.array(getAppResPhs(data))
+    if appR:
+        return np.all(np.abs(app_rpxy[0,:] - 1./sigmaHalf) * sigmaHalf < .4)
+    else:
+        return np.all(np.abs(app_rpxy[1,:] + 135) / 135 < .4)
+
+class TestAnalytics(unittest.TestCase):
+
+    def setUp(self):
+        pass
+    # # Test apparent resistivity and phase
+    def test_appRes1en2(self):self.assertTrue(appResPhsHalfspace_eFrom_ps_Norm(1e-2))
+    def test_appPhs1en2(self):self.assertTrue(appResPhsHalfspace_eFrom_ps_Norm(1e-2,False))
+
+    def test_appRes1en3(self):self.assertTrue(appResPhsHalfspace_eFrom_ps_Norm(1e-3))
+    def test_appPhs1en3(self):self.assertTrue(appResPhsHalfspace_eFrom_ps_Norm(1e-3,False))
+
+    # Do a derivative test
+    def test_derivProj1(self):self.assertTrue(DerivProjfieldsTest(halfSpace(1e-2)))
+
+    # Do a derivative test of Jvec
+    # def test_derivJvec_zxxr(self):self.assertTrue(DerivJvecTest(random(1e-2),'zxxr',.1))
+    # def test_derivJvec_zxxi(self):self.assertTrue(DerivJvecTest(random(1e-2),'zxxi',.1))
+    # def test_derivJvec_zxyr(self):self.assertTrue(DerivJvecTest(random(1e-2),'zxyr',.1))
+    # def test_derivJvec_zxyi(self):self.assertTrue(DerivJvecTest(random(1e-2),'zxyi',.1))
+    # def test_derivJvec_zyxr(self):self.assertTrue(DerivJvecTest(random(1e-2),'zyxr',.1))
+    # def test_derivJvec_zyxi(self):self.assertTrue(DerivJvecTest(random(1e-2),'zyxi',.1))
+    # def test_derivJvec_zyyr(self):self.assertTrue(DerivJvecTest(random(1e-2),'zyyr',.1))
+    # def test_derivJvec_zyyi(self):self.assertTrue(DerivJvecTest(random(1e-2),'zyyi',.1))
+    def test_derivJvec_All(self):self.assertTrue(DerivJvecTest(random(1e-2),'All',.1))
+
+    # Test the adjoint of Jvec and Jtvec
+    # def test_JvecAdjoint_zxxr(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zxxr',.1))
+    # def test_JvecAdjoint_zxxi(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zxxi',.1))
+    # def test_JvecAdjoint_zxyr(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zxyr',.1))
+    # def test_JvecAdjoint_zxyi(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zxyi',.1))
+    # def test_JvecAdjoint_zyxr(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zyxr',.1))
+    # def test_JvecAdjoint_zyxi(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zyxi',.1))
+    # def test_JvecAdjoint_zyyr(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zyyr',.1))
+    # def test_JvecAdjoint_zyyi(self):self.assertTrue(JvecAdjointTest(random(1e-2),'zyyi',.1))
+    def test_JvecAdjoint_All(self):self.assertTrue(JvecAdjointTest(random(1e-2),'All',.1))
+
+if __name__ == '__main__':
+    unittest.main()