Minor changes...test runs fine from here

remove mutable arguments.

.bumpversion.cfg

@@ -1,4 +1,4 @@
 [bumpversion]
-current_version = 0.1.9
+current_version = 0.1.10
 files = setup.py SimPEG/__init__.py docs/conf.py
 

.travis.yml

@@ -18,7 +18,9 @@ env:
     - TEST_DIR="tests/mesh tests/base tests/utils"
     - TEST_DIR=tests/em/fdem/inverse/derivs
     - 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
@@ -54,3 +56,5 @@ notifications:
   email:
     - rowanc1@gmail.com
     - lindseyheagy@gmail.com
+    - gkrosen@gmail.com
+    - sgkang09@gmail.com

README.rst

@@ -25,6 +25,10 @@ SimPEG
     :target: https://coveralls.io/r/simpeg/simpeg?branch=master
     :alt: Coverage status
 
+.. image:: http://img.shields.io/badge/GITTER-JOIN_CHAT-brightgreen.svg?style=flat-square
+    :alt: gitter chat room at https://gitter.im/simpeg/simpeg
+    :target: https://gitter.im/simpeg/simpeg
+    
 Simulation and Parameter Estimation in Geophysics  -  A python package for simulation and gradient based parameter estimation in the context of geophysical applications.
 
 The vision is to create a package for finite volume simulation with applications to geophysical imaging and subsurface flow. To enable the understanding of the many different components, this package has the following features:

SimPEG/DCIP/BaseDC.py

@@ -0,0 +1,292 @@
+from SimPEG import *
+
+class FieldsDC_CC(Problem.Fields):
+    knownFields = {'phi_sol':'CC'}
+    aliasFields = {
+                    'phi' : ['phi_sol','CC','_phi'],
+                    'e' : ['phi_sol','F','_e'],
+                    'j' : ['phi_sol','F','_j']
+                  }
+
+    def __init__(self,mesh,survey,**kwargs):
+        super(FieldsDC_CC, self).__init__(mesh, survey, **kwargs)
+
+    def startup(self):
+        self._cellGrad = self.survey.prob.mesh.cellGrad
+        self._Mfinv = self.survey.prob.mesh.getFaceInnerProduct(invMat=True)
+
+    def _phi(self, phi_sol, srcList):
+        phi = phi_sol
+        # for i, src in enumerate(srcList):
+        #     phi_p = src.phi_p(self.survey.prob)
+        #     if phi_p is not None:
+        #         phi[:,i] += phi_p
+        return phi
+
+    def _e(self, phi_sol, srcList):
+        e = -self._cellGrad*phi_sol
+        # for i, src in enumerate(srcList):
+        #     e_p = src.e_p(self.survey.prob)
+        #     if e_p is not None:
+        #         e[:,i] += e_p
+        return e
+
+    def _j(self, phi_sol, srcList):
+
+        j = -self._Mfinv*self.survey.prob.Msig*self._cellGrad*phi_sol
+        # for i, src in enumerate(srcList):
+        #     j_p = src.j_p(self.survey.prob)
+        #     if j_p is not None:
+        #         j[:,i] += j_p
+        return j
+
+
+
+class SrcDipole(Survey.BaseSrc):
+    """A dipole source, locA and locB are moved to the closest cell-centers"""
+
+    current = 1
+    loc  = None
+    # _rhsDict = None
+
+    def __init__(self, rxList, locA, locB, **kwargs):
+        self.loc = (locA, locB)
+        super(SrcDipole, self).__init__(rxList, **kwargs)
+
+    def eval(self, prob):
+        # Recompute rhs
+        # if getattr(self, '_rhsDict', None) is None:
+        #     self._rhsDict = {}
+        # if mesh not in self._rhsDict:
+        pts = [self.loc[0], self.loc[1]]
+        inds = Utils.closestPoints(prob.mesh, pts)
+        q = np.zeros(prob.mesh.nC)
+        q[inds] = - self.current * ( np.r_[1., -1.] / prob.mesh.vol[inds] )
+        # self._rhsDict[mesh] = q
+        # return self._rhsDict[mesh]
+        return q
+
+
+class RxDipole(Survey.BaseRx):
+    """A dipole source, locA and locB are moved to the closest cell-centers"""
+    def __init__(self, locsM, locsN, **kwargs):
+        locs = (locsM, locsN)
+        assert locsM.shape == locsN.shape, 'locs must be the same shape.'
+        super(RxDipole, self).__init__(locs, 'dipole', storeProjections=False, **kwargs)
+
+    @property
+    def nD(self):
+        """Number of data in the receiver."""
+        return self.locs[0].shape[0]
+
+    def getP(self, mesh):
+        P0 = mesh.getInterpolationMat(self.locs[0], self.projGLoc)
+        P1 = mesh.getInterpolationMat(self.locs[1], self.projGLoc)
+        return P0 - P1
+
+
+class SurveyDC(Survey.BaseSurvey):
+    """
+        **SurveyDC**
+
+        Geophysical DC resistivity data.
+
+    """
+    uncert = None
+    def __init__(self, srcList, **kwargs):
+        self.srcList = srcList
+        Survey.BaseSurvey.__init__(self, **kwargs)
+        # self._rhsDict = {}
+        self._Ps = {}
+
+    def eval(self, u):
+        """
+            Predicted data.
+
+            .. math::
+                d_\\text{pred} = Pu(m)
+        """
+        P = self.getP(self.prob.mesh)
+        return P*mkvc(u[self.srcList, 'phi_sol'])
+
+    def getP(self, mesh):
+        if mesh in self._Ps:
+            return self._Ps[mesh]
+
+        P_src = [sp.vstack([rx.getP(mesh) for rx in src.rxList]) for src in self.srcList]
+
+        self._Ps[mesh] = sp.block_diag(P_src)
+        return self._Ps[mesh]
+
+
+class ProblemDC_CC(Problem.BaseProblem):
+    """
+        **ProblemDC**
+
+        Geophysical DC resistivity problem.
+
+    """
+
+    surveyPair = SurveyDC
+    Solver     = Solver
+    fieldsPair = FieldsDC_CC
+    Ainv = None
+
+    def __init__(self, mesh, **kwargs):
+        Problem.BaseProblem.__init__(self, mesh)
+        self.mesh.setCellGradBC('neumann')
+        Utils.setKwargs(self, **kwargs)
+
+
+    deleteTheseOnModelUpdate = ['_A', '_Msig', '_dMdsig']
+
+    @property
+    def Msig(self):
+        if getattr(self, '_Msig', None) is None:
+            sigma = self.curModel.transform
+            Av = self.mesh.aveF2CC
+            self._Msig = Utils.sdiag(1/(self.mesh.dim * Av.T * (1/sigma)))
+        return self._Msig
+
+    @property
+    def dMdsig(self):
+        if getattr(self, '_dMdsig', None) is None:
+            sigma = self.curModel.transform
+            Av = self.mesh.aveF2CC
+            dMdprop = self.mesh.dim * Utils.sdiag(self.Msig.diagonal()**2) * Av.T * Utils.sdiag(1./sigma**2)
+            self._dMdsig = lambda Gu: Utils.sdiag(Gu) * dMdprop
+        return self._dMdsig
+
+    @property
+    def A(self):
+        """
+            Makes the matrix A(m) for the DC resistivity problem.
+
+            :param numpy.array m: model
+            :rtype: scipy.csc_matrix
+            :return: A(m)
+
+            .. math::
+                c(m,u) = A(m)u - q = G\\text{sdiag}(M(mT(m)))Du - q = 0
+
+            Where M() is the mass matrix and mT is the model transform.
+        """
+        if getattr(self, '_A', None) is None:
+            D = self.mesh.faceDiv
+            G = self.mesh.cellGrad
+            self._A = D*self.Msig*G
+            # Remove the null space from the matrix.
+            self._A[0,0] /= self.mesh.vol[0]
+            self._A = self._A.tocsc()
+        return self._A
+
+    def getRHS(self):
+        # if self.mesh not in self._rhsDict:
+        RHS = np.array([src.eval(self) for src in self.survey.srcList]).T
+        # self._rhsDict[mesh] = RHS
+        # return self._rhsDict[mesh]
+        return RHS
+
+    def fields(self, m):
+
+        F = self.fieldsPair(self.mesh, self.survey)
+        self.curModel = m
+        A    = self.A
+        self.Ainv = self.Solver(A, **self.solverOpts)
+        RHS    = self.getRHS()
+        Phi  = self.Ainv * RHS
+        Srcs = self.survey.srcList
+        F[Srcs, 'phi_sol'] = Phi
+
+        return F
+
+    def Jvec(self, m, v, f=None):
+        """
+            :param numpy.array m: model
+            :param numpy.array v: vector to multiply
+            :param Fields f: fields
+            :rtype: numpy.array
+            :return: Jv
+
+            .. math::
+                c(m,u) = A(m)u - q = G\\text{sdiag}(M(mT(m)))Du - q = 0
+
+                \\nabla_u (A(m)u - q) = A(m)
+
+                \\nabla_m (A(m)u - q) = G\\text{sdiag}(Du)\\nabla_m(M(mT(m)))
+
+            Where M() is the mass matrix and mT is the model transform.
+
+            .. math::
+                J = - P \left( \\nabla_u c(m, u) \\right)^{-1} \\nabla_m c(m, u)
+
+                J(v) = - P ( A(m)^{-1} ( G\\text{sdiag}(Du)\\nabla_m(M(mT(m))) v ) )
+        """
+        # Set current model; clear dependent property $\mathbf{A(m)}$
+        self.curModel = m
+        sigma = self.curModel.transform # $\sigma = \mathcal{M}(\m)$
+        if f is None:
+            # Run forward simulation if $u$ not provided
+            f = self.fields(self.curModel)
+        u = f[self.survey.srcList, 'phi_sol']
+
+        D = self.mesh.faceDiv
+        G = self.mesh.cellGrad
+        # Derivative of model transform, $\deriv{\sigma}{\m}$
+        dsigdm_x_v = self.curModel.transformDeriv * v
+
+        # Take derivative of $C(m,u)$ w.r.t. $m$
+        dCdm_x_v = np.empty_like(u)
+        # loop over fields for each source
+        for i in range(self.survey.nSrc):
+            # Derivative of inner product, $\left(\mathbf{M}_{1/\sigma}^f\right)^{-1}$
+            dAdsig         = D * self.dMdsig( G * u[:,i] )
+            dCdm_x_v[:, i] = dAdsig *  dsigdm_x_v
+
+        # Take derivative of $C(m,u)$ w.r.t. $u$
+        dA_du = self.A
+        # Solve for $\deriv{u}{m}$
+        # dCdu_inv = self.Solver(dCdu, **self.solverOpts)
+        if self.Ainv is None:
+            self.Ainv = self.Solver(dA_du, **self.solverOpts)
+
+        P     = self.survey.getP(self.mesh)
+        Jv    = - P * mkvc( self.Ainv * dCdm_x_v )
+        return Jv
+
+    def Jtvec(self, m, v, f=None):
+
+        self.curModel = m
+        sigma = self.curModel.transform # $\sigma = \mathcal{M}(\m)$
+        if f is None:
+            # Run forward simulation if $f$ not provided
+            f = self.fields(self.curModel)
+        u = f[self.survey.srcList, 'phi_sol']
+
+        shp = u.shape
+        P = self.survey.getP(self.mesh)
+        PT_x_v = (P.T*v).reshape(shp, order='F')
+
+        D = self.mesh.faceDiv
+        G = self.mesh.cellGrad
+        dA_du = self.A
+        mT_dm = self.mapping.deriv(m)
+
+        # We probably always need this due to the linesearch .. (?)
+        self.Ainv = self.Solver(dA_du.T, **self.solverOpts)
+        # if self.Ainv is None:
+        #     self.Ainv = self.Solver(dCdu, **self.solverOpts)
+
+        w = self.Ainv * PT_x_v
+
+        Jtv = 0
+        for i, ui in enumerate(u.T):  # loop over each column
+            Jtv += self.dMdsig( G * ui ).T * ( D.T * w[:,i] )
+
+        Jtv = - mT_dm.T * ( Jtv )
+        return Jtv
+
+
+
+
+

SimPEG/DCIP/BaseIP.py

@@ -0,0 +1,182 @@
+from SimPEG import *
+from BaseDC import SurveyDC, FieldsDC_CC
+
+class SurveyIP(SurveyDC):
+    """
+        **SurveyDC**
+
+        Geophysical DC resistivity data.
+
+    """
+
+    def __init__(self, srcList, **kwargs):
+        self.srcList = srcList
+        Survey.BaseSurvey.__init__(self, **kwargs)
+        self._Ps = {}
+
+    def dpred(self, m, f=None):
+        """
+            Predicted data.
+
+            .. math::
+                d_\\text{pred} = Pf(m)
+        """
+
+        return self.prob.forward(m)
+
+
+class ProblemIP(Problem.BaseProblem):
+    """
+        **ProblemIP**
+
+        Geophysical IP resistivity problem.
+
+    """
+
+    surveyPair = SurveyDC
+    Solver     = Solver
+    sigma = None
+    Ainv = None
+    u = None
+
+    def __init__(self, mesh, **kwargs):
+        Problem.BaseProblem.__init__(self, mesh)
+        self.mesh.setCellGradBC('neumann')
+        Utils.setKwargs(self, **kwargs)
+
+    # deleteTheseOnModelUpdate = ['_A', '_Msig', '_dMdsig']
+
+    @property
+    def Msig(self):
+        if getattr(self, '_Msig', None) is None:
+            # sigma = self.curModel.transform
+            sigma = self.sigma
+            Av = self.mesh.aveF2CC
+            self._Msig = Utils.sdiag(1/(self.mesh.dim * Av.T * (1/sigma)))
+        return self._Msig
+
+    @property
+    def dMdsig(self):
+        if getattr(self, '_dMdsig', None) is None:
+            # sigma = self.curModel.transform
+            sigma = self.sigma
+            Av = self.mesh.aveF2CC
+            dMdprop = self.mesh.dim * Utils.sdiag(self.Msig.diagonal()**2) * Av.T * Utils.sdiag(1./sigma**2)
+            self._dMdsig = lambda Gu: Utils.sdiag(Gu) * dMdprop
+        return self._dMdsig
+
+    @property
+    def A(self):
+        """
+            Makes the matrix A(m) for the DC resistivity problem.
+
+            :param numpy.array m: model
+            :rtype: scipy.csc_matrix
+            :return: A(m)
+
+            .. math::
+                c(m,u) = A(m)u - q = G\\text{sdiag}(M(mT(m)))Du - q = 0
+
+            Where M() is the mass matrix and mT is the model transform.
+        """
+        if getattr(self, '_A', None) is None:
+            D = self.mesh.faceDiv
+            G = self.mesh.cellGrad
+            self._A = D*self.Msig*G
+            # Remove the null space from the matrix.
+            self._A[-1,-1] /= self.mesh.vol[-1]
+            self._A = self._A.tocsc()
+        return self._A
+
+    def getRHS(self):
+        # if self.mesh not in self._rhsDict:
+        RHS = np.array([src.eval(self) for src in self.survey.srcList]).T
+        # self._rhsDict[mesh] = RHS
+        # return self._rhsDict[mesh]
+        return RHS
+
+    def fields(self, m):
+        if self.u is None:
+	        A    = self.A
+	        if self.Ainv == None:
+	        	self.Ainv = self.Solver(A, **self.solverOpts)
+	        Q    = self.getRHS()
+	        self.u  = self.Ainv * Q
+        return self.u
+
+    def forward(self, m, u=None):
+        # Set current model; clear dependent property $\mathbf{A(m)}$
+        self.curModel = m
+        # sigma = self.curModel.transform # $\sigma = \mathcal{M}(\m)$
+        sigma = self.sigma
+        if self.u is None:
+            # Run forward simulation if $u$ not provided
+            u = self.fields(sigma)
+
+        shp = (self.mesh.nC, self.survey.nSrc)
+        u = self.u.reshape(shp, order='F')
+
+        D = self.mesh.faceDiv
+        G = self.mesh.cellGrad
+        # Derivative of model transform, $\deriv{\sigma}{\m}$
+        # dsigdm_x_v = self.curModel.transformDeriv * v
+
+        dsigdm_x_v = Utils.sdiag(sigma) * self.curModel.transformDeriv *  m
+
+        # Take derivative of $C(m,u)$ w.r.t. $m$
+        dCdm_x_v = np.empty_like(u)
+        # loop over fields for each source
+        for i in range(self.survey.nSrc):
+            # Derivative of inner product, $\left(\mathbf{M}_{1/\sigma}^f\right)^{-1}$
+            dAdsig         = D * self.dMdsig( G * u[:,i] )
+            dCdm_x_v[:, i] = dAdsig *  dsigdm_x_v
+
+        # Take derivative of $C(m,u)$ w.r.t. $u$
+
+        if self.Ainv == None:
+        	self.Ainv = self.Solver(A, **self.solverOpts)
+
+        # dCdu = self.A
+        # Solve for $\deriv{u}{m}$
+        # dCdu_inv = self.Solver(dCdu, **self.solverOpts)
+        P        = self.survey.getP(self.mesh)
+        J_x_v    = - P * mkvc( self.Ainv * dCdm_x_v )
+        return -J_x_v
+
+    def Jvec(self, m, v, f=None):
+        return self.forward(v)
+
+    def Jtvec(self, m, v, f=None):
+
+        self.curModel = m
+        # sigma = self.curModel.transform # $\sigma = \mathcal{M}(\m)$
+        sigma = self.sigma
+        if self.u is None:
+            u = self.fields(sigma)
+        else:
+        	u = self.u
+        shp = (self.mesh.nC, self.survey.nSrc)
+        u = u.reshape(shp, order='F')
+        P = self.survey.getP(self.mesh)
+        PT_x_v = (P.T*v).reshape(shp, order='F')
+
+        D = self.mesh.faceDiv
+        G = self.mesh.cellGrad
+        A = self.A
+        mT_dm = Utils.sdiag(sigma)*self.mapping.deriv(m)
+        # mT_dm = self.mapping.deriv(m)
+
+        # dCdu = A.T
+        # Ainv = self.Solver(dCdu, **self.solverOpts)
+        # if self.Ainv == None:
+    	self.Ainv = self.Solver(A.T, **self.solverOpts)
+
+        w = self.Ainv * PT_x_v
+
+        Jtv = 0
+        for i, ui in enumerate(u.T):  # loop over each column
+            Jtv += self.dMdsig( G * ui ).T * ( D.T * w[:,i] )
+
+        Jtv = - mT_dm.T * ( Jtv )
+        return -Jtv
+

SimPEG/DCIP/Utils.py

@@ -0,0 +1,38 @@
+import numpy as np
+
+def WennerSrcList(nElecs, aSpacing, in2D=False, plotIt=False):
+
+    import SimPEG.DCIP as DC
+
+    elocs = np.arange(0,aSpacing*nElecs,aSpacing)
+    elocs -= (nElecs*aSpacing - aSpacing)/2
+    space = 1
+    WENNER = np.zeros((0,),dtype=int)
+    for ii in range(nElecs):
+        for jj in range(nElecs):
+            test = np.r_[jj,jj+space,jj+space*2,jj+space*3]
+            if np.any(test >= nElecs):
+                break
+            WENNER = np.r_[WENNER, test]
+        space += 1
+    WENNER = WENNER.reshape((-1,4))
+
+
+    if plotIt:
+        for i, s in enumerate('rbkg'):
+            plt.plot(elocs[WENNER[:,i]],s+'.')
+        plt.show()
+
+    # Create sources and receivers
+    i = 0
+    if in2D:
+        getLoc = lambda ii, abmn: np.r_[elocs[WENNER[ii,abmn]],0]
+    else:
+        getLoc = lambda ii, abmn: np.r_[elocs[WENNER[ii,abmn]],0, 0]
+    srcList = []
+    for i in range(WENNER.shape[0]):
+        rx = DC.RxDipole(getLoc(i,1),getLoc(i,2))
+        src = DC.SrcDipole([rx], getLoc(i,0),getLoc(i,3))
+        srcList += [src]
+
+    return srcList

SimPEG/DCIP/__init__.py

@@ -0,0 +1,4 @@
+from BaseDC import *
+from BaseIP import *
+from DCIPUtils import *
+import Utils

SimPEG/DataMisfit.py

@@ -22,11 +22,11 @@ class BaseDataMisfit(object):
         Utils.setKwargs(self,**kwargs)
 
     @Utils.timeIt
-    def eval(self, m, u=None):
-        """eval(m, u=None)
+    def eval(self, m, f=None):
+        """eval(m, f=None)
 
             :param numpy.array m: geophysical model
-            :param numpy.array u: fields
+            :param Fields f: fields
             :rtype: float
             :return: data misfit
 
@@ -34,11 +34,11 @@ class BaseDataMisfit(object):
         raise NotImplementedError('This method should be overwritten.')
 
     @Utils.timeIt
-    def evalDeriv(self, m, u=None):
-        """evalDeriv(m, u=None)
+    def evalDeriv(self, m, f=None):
+        """evalDeriv(m, f=None)
 
             :param numpy.array m: geophysical model
-            :param numpy.array u: fields
+            :param Fields f: fields
             :rtype: numpy.array
             :return: data misfit derivative
 
@@ -47,12 +47,12 @@ class BaseDataMisfit(object):
 
 
     @Utils.timeIt
-    def eval2Deriv(self, m, v, u=None):
-        """eval2Deriv(m, v, u=None)
+    def eval2Deriv(self, m, v, f=None):
+        """eval2Deriv(m, v, f=None)
 
             :param numpy.array m: geophysical model
             :param numpy.array v: vector to multiply
-            :param numpy.array u: fields
+            :param Fields f: fields
             :rtype: numpy.array
             :return: data misfit derivative
 
@@ -89,7 +89,7 @@ class l2_DataMisfit(BaseDataMisfit):
         """
 
         if getattr(self, '_Wd', None) is None:
-            
+
             survey = self.survey
 
             if getattr(survey,'std', None) is None:
@@ -108,24 +108,20 @@ class l2_DataMisfit(BaseDataMisfit):
         self._Wd = value
 
     @Utils.timeIt
-    def eval(self, m, u=None):
-        "eval(m, u=None)"
-        prob   = self.prob
-        survey = self.survey
-        R = self.Wd * survey.residual(m, u=u)
+    def eval(self, m, f=None):
+        "eval(m, f=None)"
+        if f is None: f = self.prob.fields(m)
+        R = self.Wd * self.survey.residual(m, f)
         return 0.5*np.vdot(R, R)
 
     @Utils.timeIt
-    def evalDeriv(self, m, u=None):
-        "evalDeriv(m, u=None)"
-        prob   = self.prob
-        survey = self.survey
-        if u is None: u = prob.fields(m)
-        return prob.Jtvec(m, self.Wd * (self.Wd * survey.residual(m, u=u)), u=u)
+    def evalDeriv(self, m, f=None):
+        "evalDeriv(m, f=None)"
+        if f is None: f = self.prob.fields(m)
+        return self.prob.Jtvec(m, self.Wd * (self.Wd * self.survey.residual(m, f=f)), f=f)
 
     @Utils.timeIt
-    def eval2Deriv(self, m, v, u=None):
-        "eval2Deriv(m, v, u=None)"
-        prob   = self.prob
-        if u is None: u = prob.fields(m)
-        return prob.Jtvec_approx(m, self.Wd * (self.Wd * prob.Jvec_approx(m, v, u=u)), u=u)
+    def eval2Deriv(self, m, v, f=None):
+        "eval2Deriv(m, v, f=None)"
+        if f is None: f = self.prob.fields(m)
+        return self.prob.Jtvec_approx(m, self.Wd * (self.Wd * self.prob.Jvec_approx(m, v, f=f)), f=f)

SimPEG/Directives.py

@@ -123,10 +123,10 @@ class BetaEstimate_ByEig(InversionDirective):
         if self.debug: print 'Calculating the beta0 parameter.'
 
         m = self.invProb.curModel
-        u = self.invProb.getFields(m, store=True, deleteWarmstart=False)
+        f = self.invProb.getFields(m, store=True, deleteWarmstart=False)
 
         x0 = np.random.rand(*m.shape)
-        t = x0.dot(self.dmisfit.eval2Deriv(m,x0,u=u))
+        t = x0.dot(self.dmisfit.eval2Deriv(m,x0,f=f))
         b = x0.dot(self.reg.eval2Deriv(m, v=x0))
         self.beta0 = self.beta0_ratio*(t/b)
 
@@ -216,13 +216,13 @@ class SaveOutputDictEveryIteration(_SaveEveryIteration):
         # 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:
+        if self.reg.mrefInSmooth == 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:
+        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:
@@ -238,7 +238,6 @@ class SaveOutputDictEveryIteration(_SaveEveryIteration):
         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 UpdateReferenceModel(Parameter):
 
 #     mref0 = None
@@ -250,3 +249,127 @@ class SaveOutputDictEveryIteration(_SaveEveryIteration):
 #             mref = self.mref0
 #         self.m_prev = self.invProb.m_current
 #         return mref
+
+class Update_IRLS(InversionDirective):
+
+    eps_min = None
+    factor = None
+    gamma = None
+    phi_m_last = None
+    phi_d_last = None
+
+
+    def initialize(self):
+
+        # Scale the regularization for changes in norm
+        if getattr(self, 'phi_m_last', None) is not None:
+
+            self.reg.curModel = self.invProb.curModel
+            self.reg.gamma = 1.
+            phim_new = self.reg.eval(self.invProb.curModel)
+            self.gamma = self.phi_m_last / phim_new
+
+        self.reg.curModel = self.invProb.curModel
+        self.reg.gamma = self.gamma
+        
+        self.reg._W = None
+        if getattr(self, 'phi_d_last', None) is None:
+            self.phi_d_last = self.invProb.phi_d
+
+    def endIter(self):
+        # Cool the threshold parameter if required
+        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
+
+        # Get phi_m at the end of current iteration
+        self.phi_m_last = self.invProb.phi_m_last
+        
+        self.reg._W = None
+         # Update the model used for the IRLS weights
+        self.reg.curModel = self.invProb.curModel
+
+        # Temporarely set gamma to 1. to get raw phi_m
+        self.reg.gamma = 1.
+
+        # Compute new model objective function value
+        phim_new = self.reg.eval(self.invProb.curModel)
+        
+        # Update gamma to scale the regularization between IRLS iterations
+        self.reg.gamma = self.phi_m_last / phim_new
+        
+        # Set the weighting matrix to None so that it is recomputed next time
+        # it is called in the inversion
+        self.reg._W = None
+
+class Update_lin_PreCond(InversionDirective):
+    """
+    Create a Jacobi preconditioner for the linear problem
+    """
+    onlyOnStart=False
+    
+    def initialize(self):
+    
+        if getattr(self.opt, 'approxHinv', None) is None:
+            # Update the pre-conditioner
+            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.reg.curModel.size))**2.
+            PC     = Utils.sdiag((self.prob.mapping.deriv(None).T *diagA)**-1.)
+            self.opt.approxHinv = PC
+            
+    def endIter(self):
+        # Cool the threshold parameter
+        if self.onlyOnStart==True:
+            return
+            
+        if getattr(self.opt, 'approxHinv', None) is not None:
+            # Update the pre-conditioner
+            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.reg.curModel.size))**2.
+            PC     = Utils.sdiag((self.prob.mapping.deriv(None).T *diagA)**-1.)
+            self.opt.approxHinv = PC
+
+
+class Update_Wj(InversionDirective):
+    """
+        Create approx-sensitivity base weighting using the probing method
+    """
+    k = None # Number of probing cycles
+    itr = None # Iteration number to update Wj, or always update if None
+
+    def endIter(self):
+
+        if self.itr is None or self.itr == self.opt.iter:
+
+            m = self.invProb.curModel
+            if self.k is None:
+                self.k = int(self.survey.nD/10)
+
+            def JtJv(v):
+
+                Jv = self.prob.Jvec(m, v)
+
+                return self.prob.Jtvec(m,Jv)
+
+            JtJdiag = Utils.diagEst(JtJv,len(m),k=self.k)
+            JtJdiag = JtJdiag / max(JtJdiag)
+
+            self.reg.wght = JtJdiag
+
+class Scale_Beta(InversionDirective):
+    """
+        Instead of a linear cooling schedule, beta is allowed to change based
+        on the ratio between the target misfit and the current data misfit. The
+        update is done only if the misfit is outside some threshold bounds.
+    """
+    tol = 0.05
+
+    def endIter(self):
+
+        # Check if misfit is within the tolerance, otherwise adjust beta
+        val = self.invProb.phi_d / (self.survey.nD*0.5)
+
+        if np.abs(1.-val) > self.tol:
+            self.invProb.beta = self.invProb.beta * self.survey.nD*0.5 / self.invProb.phi_d

SimPEG/EM/Base.py

@@ -2,14 +2,14 @@ from SimPEG import Survey, Problem, Utils, Models, Maps, PropMaps, np, sp, Solve
 from scipy.constants import mu_0
 
 class EMPropMap(Maps.PropMap):
-    """ 
+    """
         Property Map for EM Problems. The electrical conductivity (\\(\\sigma\\)) is the default inversion property, and the default value of the magnetic permeability is that of free space (\\(\\mu = 4\\pi\\times 10^{-7} \\) H/m)
     """
 
     sigma = Maps.Property("Electrical Conductivity", defaultInvProp = True, propertyLink=('rho',Maps.ReciprocalMap))
     mu = Maps.Property("Inverse Magnetic Permeability", defaultVal = mu_0, propertyLink=('mui',Maps.ReciprocalMap))
 
-    rho = Maps.Property("Electrical Resistivity", propertyLink=('sigma', Maps.ReciprocalMap)) 
+    rho = Maps.Property("Electrical Resistivity", propertyLink=('sigma', Maps.ReciprocalMap))
     mui = Maps.Property("Inverse Magnetic Permeability", defaultVal = 1./mu_0, propertyLink=('mu', Maps.ReciprocalMap))
 
 
@@ -21,7 +21,7 @@ class BaseEMProblem(Problem.BaseProblem):
 
     surveyPair = Survey.BaseSurvey
     dataPair = Survey.Data
-    
+
     PropMap = EMPropMap
 
     Solver = SimpegSolver
@@ -51,7 +51,7 @@ class BaseEMProblem(Problem.BaseProblem):
         if self.mapping.muMap is not None or self.mapping.muiMap is not None:
             toDelete += ['_MeMu', '_MeMuI','_MfMui','_MfMuiI']
         return toDelete
-    
+
     @property
     def Me(self):
         """
@@ -71,7 +71,7 @@ class BaseEMProblem(Problem.BaseProblem):
         return self._Mf
 
 
-    # ----- Magnetic Permeability ----- # 
+    # ----- Magnetic Permeability ----- #
     @property
     def MfMui(self):
         """
@@ -109,7 +109,7 @@ class BaseEMProblem(Problem.BaseProblem):
         return self._MeMuI
 
 
-    # ----- Electrical Conductivity ----- # 
+    # ----- Electrical Conductivity ----- #
     #TODO: hardcoded to sigma as the model
     @property
     def MeSigma(self):
@@ -120,18 +120,18 @@ class BaseEMProblem(Problem.BaseProblem):
             self._MeSigma = self.mesh.getEdgeInnerProduct(self.curModel.sigma)
         return self._MeSigma
 
-    # TODO: This should take a vector 
+    # TODO: This should take a vector
     def MeSigmaDeriv(self, u):
         """
             Derivative of MeSigma with respect to the model
-        """ 
+        """
         return self.mesh.getEdgeInnerProductDeriv(self.curModel.sigma)(u) * self.curModel.sigmaDeriv
-    
+
 
     @property
     def MeSigmaI(self):
         """
-            Inverse of the edge inner product matrix for \\(\\sigma\\). 
+            Inverse of the edge inner product matrix for \\(\\sigma\\).
         """
         if getattr(self, '_MeSigmaI', None) is None:
             self._MeSigmaI = self.mesh.getEdgeInnerProduct(self.curModel.sigma, invMat=True)
@@ -140,8 +140,8 @@ class BaseEMProblem(Problem.BaseProblem):
     # TODO: This should take a vector
     def MeSigmaIDeriv(self, u):
         """
-            Derivative of :code:`MeSigma` with respect to the model 
-        """ 
+            Derivative of :code:`MeSigma` with respect to the model
+        """
         # TODO: only works for diagonal tensors. getEdgeInnerProductDeriv, invMat=True should be implemented in SimPEG
 
         dMeSigmaI_dI = -self.MeSigmaI**2
@@ -163,7 +163,7 @@ class BaseEMProblem(Problem.BaseProblem):
     # TODO: This should take a vector
     def MfRhoDeriv(self,u):
         """
-            Derivative of :code:`MfRho` with respect to the model. 
+            Derivative of :code:`MfRho` with respect to the model.
         """
         return self.mesh.getFaceInnerProductDeriv(self.curModel.rho)(u) * (-Utils.sdiag(self.curModel.rho**2) * self.curModel.sigmaDeriv)
         # self.curModel.rhoDeriv
@@ -181,6 +181,29 @@ class BaseEMProblem(Problem.BaseProblem):
     # TODO: This should take a vector
     def MfRhoIDeriv(self,u):
         """
-            Derivative of :code:`MfRhoI` with respect to the model. 
+            Derivative of :code:`MfRhoI` with respect to the model.
         """
         return self.mesh.getFaceInnerProductDeriv(self.curModel.rho, invMat=True)(u) * self.curModel.rhoDeriv
+
+class BaseEMSurvey(Survey.BaseSurvey):
+
+    def __init__(self, srcList, **kwargs):
+        # Sort these by frequency
+        self.srcList = srcList
+        Survey.BaseSurvey.__init__(self, **kwargs)
+
+    def eval(self, u):
+        """
+        Project fields to receiver locations
+        :param Fields u: fields object
+        :rtype: numpy.ndarray
+        :return: data
+        """
+        data = Survey.Data(self)
+        for src in self.srcList:
+            for rx in src.rxList:
+                data[src, rx] = rx.eval(src, self.mesh, u)
+        return data
+
+    def evalDeriv(self, u):
+        raise Exception('Use Receivers to project fields deriv.')

SimPEG/EM/FDEM/FDEM.py

@@ -18,9 +18,9 @@ class BaseFDEMProblem(BaseEMProblem):
             {\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`). Note that in this case, :math:`\mathbf{s_e}` is an integrated quantity. 
+        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 
+        If we write Maxwell's equations in terms of
         \\\(\\\mathbf{h}\\\) and current density \\\(\\\mathbf{j}\\\)
 
         .. math ::
@@ -28,7 +28,7 @@ class BaseFDEMProblem(BaseEMProblem):
             \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`). Note that here, :math:`\mathbf{s_m}` is an integrated quantity. 
+        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}\\\)
     """
@@ -36,88 +36,76 @@ class BaseFDEMProblem(BaseEMProblem):
     surveyPair = SurveyFDEM
     fieldsPair = Fields
 
-    def fields(self, m=None):
+    def fields(self, m):
         """
         Solve the forward problem for the fields.
-        
+
         :param numpy.array m: inversion model (nP,)
         :rtype numpy.array:
-        :return F: forward solution
+        :return f: forward solution
         """
 
         self.curModel = m
-        F = self.fieldsPair(self.mesh, self.survey)
+        f = self.fieldsPair(self.mesh, self.survey)
 
         for freq in self.survey.freqs:
             A = self.getA(freq)
             rhs = self.getRHS(freq)
             Ainv = self.Solver(A, **self.solverOpts)
-            sol = Ainv * rhs
+            u = Ainv * rhs
             Srcs = self.survey.getSrcByFreq(freq)
-            ftype = self._fieldType + 'Solution'
-            F[Srcs, ftype] = sol
+            f[Srcs, self._solutionType] = u
             Ainv.clean()
-        return F
+        return f
 
-    def Jvec(self, m, v, u=None):
+    def Jvec(self, m, v, f=None):
         """
         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 
+        :param SimPEG.EM.FDEM.Fields u: fields object
         :rtype numpy.array:
-        :return: Jv (ndata,) 
+        :return: Jv (ndata,)
         """
 
-        if u is None:
-           u = self.fields(m)
+        if f is None:
+           f = self.fields(m)
 
         self.curModel = m
 
         Jv = self.dataPair(self.survey)
 
         for freq in self.survey.freqs:
-            A = self.getA(freq) #
-            Ainv = self.Solver(A, **self.solverOpts)
+            A = self.getA(freq)
+            Ainv = self.Solver(A, **self.solverOpts) # create the concept of Ainv (actually a solve)
 
             for src in self.survey.getSrcByFreq(freq):
-                ftype = self._fieldType + 'Solution'
-                u_src = u[src, ftype]
-                dA_dm = self.getADeriv_m(freq, u_src, v)
-                dRHS_dm = self.getRHSDeriv_m(freq, src, v) 
-                du_dm = Ainv * ( - dA_dm + dRHS_dm )
-                
+                u_src = f[src, self._solutionType]
+                dA_dm_v = self.getADeriv(freq, u_src, v)
+                dRHS_dm_v = self.getRHSDeriv(freq, src, v)
+                du_dm_v = Ainv * ( - dA_dm_v + dRHS_dm_v )
+
                 for rx in src.rxList:
-                    df_duFun = getattr(u, '_%sDeriv_u'%rx.projField, None)
-                    df_dudu_dm = df_duFun(src, du_dm, adjoint=False)
-
-                    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
-
-                    Jv[src, rx] = P(Df_Dm)
-
+                    df_dmFun = getattr(f, '_%sDeriv'%rx.projField, None)
+                    df_dm_v = df_dmFun(src, du_dm_v, v, adjoint=False)
+                    Jv[src, rx] = rx.evalDeriv(src, self.mesh, f, df_dm_v)
             Ainv.clean()
         return Utils.mkvc(Jv)
 
-    def Jtvec(self, m, v, u=None):
+    def Jtvec(self, m, v, f=None):
         """
         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 
+        :param SimPEG.EM.FDEM.Fields u: fields object
         :rtype numpy.array:
-        :return: Jv (ndata,) 
+        :return: Jv (ndata,)
         """
 
-        if u is None:
-            u = self.fields(m)
+        if f is None:
+            f = self.fields(m)
 
         self.curModel = m
 
@@ -132,35 +120,31 @@ class BaseFDEMProblem(BaseEMProblem):
             ATinv = self.Solver(AT, **self.solverOpts)
 
             for src in self.survey.getSrcByFreq(freq):
-                ftype = self._fieldType + 'Solution'
-                u_src = u[src, ftype]
+                u_src = f[src, self._solutionType]
 
                 for rx in src.rxList:
-                    PTv = rx.projectFieldsDeriv(src, self.mesh, u, v[src, rx], adjoint=True) # wrt u, need possibility wrt m
+                    PTv = rx.evalDeriv(src, self.mesh, f, v[src, rx], adjoint=True) # wrt f, need possibility wrt m
+
+                    df_duTFun = getattr(f, '_%sDeriv'%rx.projField, None)
+                    df_duT, df_dmT = df_duTFun(src, None, PTv, adjoint=True)
 
-                    df_duTFun = getattr(u, '_%sDeriv_u'%rx.projField, None)
-                    df_duT = df_duTFun(src, PTv, adjoint=True)
-                    
                     ATinvdf_duT = ATinv * df_duT
 
-                    dA_dmT = self.getADeriv_m(freq, u_src, ATinvdf_duT, adjoint=True)
-                    dRHS_dmT = self.getRHSDeriv_m(freq,src, ATinvdf_duT, adjoint=True)
+                    dA_dmT = self.getADeriv(freq, u_src, ATinvdf_duT, adjoint=True)
+                    dRHS_dmT = self.getRHSDeriv(freq, src, ATinvdf_duT, adjoint=True)
                     du_dmT = -dA_dmT + dRHS_dmT
 
-                    df_dmFun = getattr(u, '_%sDeriv_m'%rx.projField, None)
-                    dfT_dm = df_dmFun(src, PTv, adjoint=True)
+                    df_dmT = df_dmT + du_dmT
 
-                    du_dmT += dfT_dm
-
-                    # TODO: this should be taken care of by the reciever
+                    # 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
+                        Jtv +=   np.array(df_dmT, dtype=complex).real
                     elif real_or_imag is 'imag':
-                        Jtv += - np.array(du_dmT,dtype=complex).real
+                        Jtv += - np.array(df_dmT, dtype=complex).real
                     else:
                         raise Exception('Must be real or imag')
-            
+
             ATinv.clean()
 
         return Utils.mkvc(Jtv)
@@ -170,23 +154,23 @@ class BaseFDEMProblem(BaseEMProblem):
         Evaluates the sources for a given frequency and puts them in matrix form
 
         :param float freq: Frequency
-        :rtype: (numpy.ndarray, numpy.ndarray)  
-        :return: S_m, S_e (nE or nF, nSrc)
+        :rtype: (numpy.ndarray, numpy.ndarray)
+        :return: s_m, s_e (nE or nF, nSrc)
         """
         Srcs = self.survey.getSrcByFreq(freq)
-        if self._eqLocs is 'FE':
-            S_m = np.zeros((self.mesh.nF,len(Srcs)), dtype=complex)
-            S_e = np.zeros((self.mesh.nE,len(Srcs)), dtype=complex)
-        elif self._eqLocs is 'EF':
-            S_m = np.zeros((self.mesh.nE,len(Srcs)), dtype=complex)
-            S_e = np.zeros((self.mesh.nF,len(Srcs)), dtype=complex)
+        if self._formulation is 'EB':
+            s_m = np.zeros((self.mesh.nF,len(Srcs)), dtype=complex)
+            s_e = np.zeros((self.mesh.nE,len(Srcs)), dtype=complex)
+        elif self._formulation is 'HJ':
+            s_m = np.zeros((self.mesh.nE,len(Srcs)), dtype=complex)
+            s_e = np.zeros((self.mesh.nF,len(Srcs)), dtype=complex)
 
         for i, src in enumerate(Srcs):
             smi, sei = src.eval(self)
-            S_m[:,i] = S_m[:,i] + smi
-            S_e[:,i] = S_e[:,i] + sei
+            s_m[:,i] = s_m[:,i] + smi
+            s_e[:,i] = s_e[:,i] + sei
 
-        return S_m, S_e
+        return s_m, s_e
 
 
 ##########################################################################################
@@ -213,9 +197,9 @@ class Problem_e(BaseFDEMProblem):
     :param SimPEG.Mesh mesh: mesh
     """
 
-    _fieldType = 'e'
-    _eqLocs    = 'FE'
-    fieldsPair = Fields_e
+    _solutionType = 'eSolution'
+    _formulation  = 'EB'
+    fieldsPair    = Fields_e
 
     def __init__(self, mesh, **kwargs):
         BaseFDEMProblem.__init__(self, mesh, **kwargs)
@@ -223,7 +207,7 @@ class Problem_e(BaseFDEMProblem):
     def getA(self, freq):
         """
         System matrix
-        
+
         .. math ::
             \mathbf{A} = \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{C} + i \omega \mathbf{M^e_{\sigma}}
 
@@ -239,19 +223,19 @@ class Problem_e(BaseFDEMProblem):
         return C.T*MfMui*C + 1j*omega(freq)*MeSigma
 
 
-    def getADeriv_m(self, freq, u, v, adjoint=False):
+    def getADeriv(self, freq, u, v, adjoint=False):
         """
         Product of the derivative of our system matrix with respect to the model and a vector
 
         .. 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 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,) 
+        :return: derivative of the system matrix times a vector (nP,) or adjoint (nD,)
         """
 
         dsig_dm = self.curModel.sigmaDeriv
@@ -264,25 +248,25 @@ class Problem_e(BaseFDEMProblem):
 
     def getRHS(self, freq):
         """
-        Right hand side for the system 
+        Right hand side for the system
 
         .. math ::
             \mathbf{RHS} = \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M_e}\mathbf{s_e}
 
         :param float freq: Frequency
-        :rtype: numpy.ndarray 
+        :rtype: numpy.ndarray
         :return: RHS (nE, nSrc)
         """
 
-        S_m, S_e = self.getSourceTerm(freq)
+        s_m, s_e = self.getSourceTerm(freq)
         C = self.mesh.edgeCurl
         MfMui = self.MfMui
 
-        return C.T * (MfMui * S_m) -1j * omega(freq) * S_e
+        return C.T * (MfMui * s_m) -1j * omega(freq) * s_e
 
-    def getRHSDeriv_m(self, freq, src, v, adjoint=False):
+    def getRHSDeriv(self, freq, src, v, adjoint=False):
         """
-        Derivative of the right hand side with respect to the model 
+        Derivative of the right hand side with respect to the model
 
         :param float freq: frequency
         :param SimPEG.EM.FDEM.Src src: FDEM source
@@ -294,14 +278,14 @@ class Problem_e(BaseFDEMProblem):
 
         C = self.mesh.edgeCurl
         MfMui = self.MfMui
-        S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint=adjoint)
+        s_mDeriv, s_eDeriv = src.evalDeriv(self, adjoint=adjoint)
 
         if adjoint:
             dRHS = MfMui * (C * v)
-            return S_mDeriv(dRHS) - 1j * omega(freq) * S_eDeriv(v)
+            return s_mDeriv(dRHS) - 1j * omega(freq) * s_eDeriv(v)
 
         else:
-            return C.T * (MfMui * S_mDeriv(v)) -1j * omega(freq) * S_eDeriv(v)
+            return C.T * (MfMui * s_mDeriv(v)) -1j * omega(freq) * s_eDeriv(v)
 
 
 class Problem_b(BaseFDEMProblem):
@@ -324,9 +308,9 @@ class Problem_b(BaseFDEMProblem):
     :param SimPEG.Mesh mesh: mesh
     """
 
-    _fieldType = 'b'
-    _eqLocs    = 'FE'
-    fieldsPair = Fields_b
+    _solutionType = 'bSolution'
+    _formulation  = 'EB'
+    fieldsPair    = Fields_b
 
     def __init__(self, mesh, **kwargs):
         BaseFDEMProblem.__init__(self, mesh, **kwargs)
@@ -354,7 +338,7 @@ class Problem_b(BaseFDEMProblem):
             return MfMui.T*A
         return A
 
-    def getADeriv_m(self, freq, u, v, adjoint=False):
+    def getADeriv(self, freq, u, v, adjoint=False):
 
         """
         Product of the derivative of our system matrix with respect to the model and a vector
@@ -362,12 +346,12 @@ class Problem_b(BaseFDEMProblem):
         .. 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 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,)  
+        :return: derivative of the system matrix times a vector (nP,) or adjoint (nD,)
         """
 
         MfMui = self.MfMui
@@ -389,21 +373,21 @@ class Problem_b(BaseFDEMProblem):
 
     def getRHS(self, freq):
         """
-        Right hand side for the system 
+        Right hand side for the system
 
         .. math ::
             \mathbf{RHS} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{s_e}
 
         :param float freq: Frequency
-        :rtype: numpy.ndarray 
+        :rtype: numpy.ndarray
         :return: RHS (nE, nSrc)
         """
 
-        S_m, S_e = self.getSourceTerm(freq)
+        s_m, s_e = self.getSourceTerm(freq)
         C = self.mesh.edgeCurl
         MeSigmaI = self.MeSigmaI
 
-        RHS = S_m + C * ( MeSigmaI * S_e )
+        RHS = s_m + C * ( MeSigmaI * s_e )
 
         if self._makeASymmetric is True:
             MfMui = self.MfMui
@@ -411,7 +395,7 @@ class Problem_b(BaseFDEMProblem):
 
         return RHS
 
-    def getRHSDeriv_m(self, freq, src, v, adjoint=False):
+    def getRHSDeriv(self, freq, src, v, adjoint=False):
         """
         Derivative of the right hand side with respect to the model
 
@@ -424,21 +408,21 @@ class Problem_b(BaseFDEMProblem):
         """
 
         C = self.mesh.edgeCurl
-        S_m, S_e = src.eval(self)
+        s_m, s_e = src.eval(self)
         MfMui = self.MfMui
 
         if self._makeASymmetric and adjoint:
             v = self.MfMui * v
 
-        MeSigmaIDeriv = self.MeSigmaIDeriv(S_e)
-        S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint=adjoint)
+        MeSigmaIDeriv = self.MeSigmaIDeriv(s_e)
+        s_mDeriv, s_eDeriv = src.evalDeriv(self, adjoint=adjoint)
 
         if not adjoint:
             RHSderiv = C * (MeSigmaIDeriv * v)
-            SrcDeriv = S_mDeriv(v) + C * (self.MeSigmaI * S_eDeriv(v))
+            SrcDeriv = s_mDeriv(v) + C * (self.MeSigmaI * s_eDeriv(v))
         elif adjoint:
             RHSderiv = MeSigmaIDeriv.T * (C.T * v)
-            SrcDeriv = S_mDeriv(v) + self.MeSigmaI.T * (C.T * S_eDeriv(v))
+            SrcDeriv = s_mDeriv(v) + self.MeSigmaI.T * (C.T * s_eDeriv(v))
 
         if self._makeASymmetric is True and not adjoint:
             return MfMui.T * (SrcDeriv + RHSderiv)
@@ -472,9 +456,9 @@ class Problem_j(BaseFDEMProblem):
     :param SimPEG.Mesh mesh: mesh
     """
 
-    _fieldType = 'j'
-    _eqLocs    = 'EF'
-    fieldsPair = Fields_j
+    _solutionType = 'jSolution'
+    _formulation  = 'HJ'
+    fieldsPair    = Fields_j
 
     def __init__(self, mesh, **kwargs):
         BaseFDEMProblem.__init__(self, mesh, **kwargs)
@@ -503,7 +487,7 @@ class Problem_j(BaseFDEMProblem):
         return A
 
 
-    def getADeriv_m(self, freq, u, v, adjoint=False):
+    def getADeriv(self, freq, u, v, adjoint=False):
         """
         Product of the derivative of our system matrix with respect to the model and a vector
 
@@ -513,32 +497,32 @@ class Problem_j(BaseFDEMProblem):
 
             \\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 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,)  
+        :return: derivative of the system matrix times a vector (nP,) or adjoint (nD,)
         """
 
         MeMuI = self.MeMuI
         MfRho = self.MfRho
         C = self.mesh.edgeCurl
-        MfRhoDeriv_m = self.MfRhoDeriv(u)
+        MfRhoDeriv = self.MfRhoDeriv(u)
 
         if adjoint:
             if self._makeASymmetric is True:
                 v = MfRho * v
-            return MfRhoDeriv_m.T * (C * (MeMuI.T * (C.T * v)))
+            return MfRhoDeriv.T * (C * (MeMuI.T * (C.T * v)))
 
         if self._makeASymmetric is True:
-            return MfRho.T * (C * ( MeMuI * (C.T * (MfRhoDeriv_m * v) )))
-        return C * (MeMuI * (C.T * (MfRhoDeriv_m * v)))
+            return MfRho.T * (C * ( MeMuI * (C.T * (MfRhoDeriv * v) )))
+        return C * (MeMuI * (C.T * (MfRhoDeriv * v)))
 
 
     def getRHS(self, freq):
         """
-        Right hand side for the system 
+        Right hand side for the system
 
         .. math ::
 
@@ -549,20 +533,20 @@ class Problem_j(BaseFDEMProblem):
         :return: RHS
         """
 
-        S_m, S_e = self.getSourceTerm(freq)
+        s_m, s_e = self.getSourceTerm(freq)
         C = self.mesh.edgeCurl
         MeMuI = self.MeMuI
 
-        RHS = C * (MeMuI * S_m) - 1j * omega(freq) * S_e
+        RHS = C * (MeMuI * s_m) - 1j * omega(freq) * s_e
         if self._makeASymmetric is True:
             MfRho = self.MfRho
             return MfRho.T*RHS
 
         return RHS
 
-    def getRHSDeriv_m(self, freq, src, v, adjoint=False):
+    def getRHSDeriv(self, freq, src, v, adjoint=False):
         """
-        Derivative of the right hand side with respect to the model 
+        Derivative of the right hand side with respect to the model
 
         :param float freq: frequency
         :param SimPEG.EM.FDEM.Src src: FDEM source
@@ -574,16 +558,16 @@ class Problem_j(BaseFDEMProblem):
 
         C = self.mesh.edgeCurl
         MeMuI = self.MeMuI
-        S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint=adjoint)
+        s_mDeriv, s_eDeriv = src.evalDeriv(self, adjoint=adjoint)
 
         if adjoint:
             if self._makeASymmetric:
                 MfRho = self.MfRho
                 v = MfRho*v
-            return S_mDeriv(MeMuI.T * (C.T * v)) - 1j * omega(freq) * S_eDeriv(v)
+            return s_mDeriv(MeMuI.T * (C.T * v)) - 1j * omega(freq) * s_eDeriv(v)
 
         else:
-            RHSDeriv = C * (MeMuI * S_mDeriv(v)) - 1j * omega(freq) * S_eDeriv(v)
+            RHSDeriv = C * (MeMuI * s_mDeriv(v)) - 1j * omega(freq) * s_eDeriv(v)
 
             if self._makeASymmetric:
                 MfRho = self.MfRho
@@ -610,9 +594,9 @@ class Problem_h(BaseFDEMProblem):
     :param SimPEG.Mesh mesh: mesh
     """
 
-    _fieldType = 'h'
-    _eqLocs    = 'EF'
-    fieldsPair = Fields_h
+    _solutionType = 'hSolution'
+    _formulation  = 'HJ'
+    fieldsPair    = Fields_h
 
     def __init__(self, mesh, **kwargs):
         BaseFDEMProblem.__init__(self, mesh, **kwargs)
@@ -635,51 +619,51 @@ class Problem_h(BaseFDEMProblem):
 
         return C.T * (MfRho * C) + 1j*omega(freq)*MeMu
 
-    def getADeriv_m(self, freq, u, v, adjoint=False):
+    def getADeriv(self, freq, u, v, adjoint=False):
         """
         Product of the derivative of our system matrix with respect to the model and a vector
 
         .. 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 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,)  
+        :return: derivative of the system matrix times a vector (nP,) or adjoint (nD,)
         """
 
         MeMu = self.MeMu
         C = self.mesh.edgeCurl
-        MfRhoDeriv_m = self.MfRhoDeriv(C*u)
+        MfRhoDeriv = self.MfRhoDeriv(C*u)
 
         if adjoint:
-            return MfRhoDeriv_m.T * (C * v)
-        return C.T * (MfRhoDeriv_m * v)
+            return MfRhoDeriv.T * (C * v)
+        return C.T * (MfRhoDeriv * v)
 
     def getRHS(self, freq):
         """
-        Right hand side for the system 
+        Right hand side for the system
 
         .. math ::
 
             \mathbf{RHS} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{s_e}
 
         :param float freq: Frequency
-        :rtype: numpy.ndarray 
+        :rtype: numpy.ndarray
         :return: RHS (nE, nSrc)
         """
 
-        S_m, S_e = self.getSourceTerm(freq)
+        s_m, s_e = self.getSourceTerm(freq)
         C = self.mesh.edgeCurl
         MfRho  = self.MfRho
 
-        return S_m + C.T * ( MfRho * S_e )
+        return s_m + C.T * ( MfRho * s_e )
 
-    def getRHSDeriv_m(self, freq, src, v, adjoint=False):
+    def getRHSDeriv(self, freq, src, v, adjoint=False):
         """
-        Derivative of the right hand side with respect to the model 
+        Derivative of the right hand side with respect to the model
 
         :param float freq: frequency
         :param SimPEG.EM.FDEM.Src src: FDEM source
@@ -689,17 +673,17 @@ class Problem_h(BaseFDEMProblem):
         :return: product of rhs deriv with a vector
         """
 
-        _, S_e = src.eval(self)
+        _, s_e = src.eval(self)
         C = self.mesh.edgeCurl
         MfRho  = self.MfRho
 
-        MfRhoDeriv = self.MfRhoDeriv(S_e)
+        MfRhoDeriv = self.MfRhoDeriv(s_e)
         if not adjoint:
             RHSDeriv = C.T * (MfRhoDeriv * v)
         elif adjoint:
             RHSDeriv = MfRhoDeriv.T * (C * v)
 
-        S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint=adjoint)
+        s_mDeriv, s_eDeriv = src.evalDeriv(self, adjoint=adjoint)
 
-        return RHSDeriv + S_mDeriv(v) + C.T * (MfRho * S_eDeriv(v))
+        return RHSDeriv + s_mDeriv(v) + C.T * (MfRho * s_eDeriv(v))
 

SimPEG/EM/FDEM/SrcFDEM.py

@@ -1,7 +1,7 @@
 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 SimPEG.Utils import Zero
 
 class BaseSrc(Survey.BaseSrc):
     """
@@ -14,34 +14,34 @@ class BaseSrc(Survey.BaseSrc):
 
     def eval(self, prob):
         """
-        Evaluate the source terms. 
-        - :math:`S_m` : magnetic source term
-        - :math:`S_e` : electric source term
+        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
+        s_m = self.s_m(prob)
+        s_e = self.s_e(prob)
+        return s_m, s_e
 
     def evalDeriv(self, prob, v=None, adjoint=False):
         """
         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
+        - :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 
+        :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)
+        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)
+            return lambda v: self.s_mDeriv(prob, v, adjoint), lambda v: self.s_eDeriv(prob, v, adjoint)
 
     def bPrimary(self, prob):
         """
@@ -49,7 +49,7 @@ class BaseSrc(Survey.BaseSrc):
 
         :param Problem prob: FDEM Problem
         :rtype: numpy.ndarray
-        :return: primary magnetic flux density 
+        :return: primary magnetic flux density
         """
         return Zero()
 
@@ -59,7 +59,7 @@ class BaseSrc(Survey.BaseSrc):
 
         :param Problem prob: FDEM Problem
         :rtype: numpy.ndarray
-        :return: primary magnetic field 
+        :return: primary magnetic field
         """
         return Zero()
 
@@ -69,7 +69,7 @@ class BaseSrc(Survey.BaseSrc):
 
         :param Problem prob: FDEM Problem
         :rtype: numpy.ndarray
-        :return: primary electric field 
+        :return: primary electric field
         """
         return Zero()
 
@@ -79,13 +79,13 @@ class BaseSrc(Survey.BaseSrc):
 
         :param Problem prob: FDEM Problem
         :rtype: numpy.ndarray
-        :return: primary current density 
+        :return: primary current density
         """
         return Zero()
 
-    def S_m(self, prob):
+    def s_m(self, prob):
         """
-        Magnetic source term 
+        Magnetic source term
 
         :param Problem prob: FDEM Problem
         :rtype: numpy.ndarray
@@ -93,9 +93,9 @@ class BaseSrc(Survey.BaseSrc):
         """
         return Zero()
 
-    def S_e(self, prob):
+    def s_e(self, prob):
         """
-        Electric source term 
+        Electric source term
 
         :param Problem prob: FDEM Problem
         :rtype: numpy.ndarray
@@ -103,7 +103,7 @@ class BaseSrc(Survey.BaseSrc):
         """
         return Zero()
 
-    def S_mDeriv(self, prob, v, adjoint = False):
+    def s_mDeriv(self, prob, v, adjoint = False):
         """
         Derivative of magnetic source term with respect to the inversion model
 
@@ -116,7 +116,7 @@ class BaseSrc(Survey.BaseSrc):
 
         return Zero()
 
-    def S_eDeriv(self, prob, v, adjoint = False):
+    def s_eDeriv(self, prob, v, adjoint = False):
         """
         Derivative of electric source term with respect to the inversion model
 
@@ -131,88 +131,117 @@ class BaseSrc(Survey.BaseSrc):
 
 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 list rxList: receiver list
     :param float freq: frequency
-    :param numpy.array S_e: electric source term
+    :param numpy.array s_e: electric source term
+    :param bool integrate: Integrate the source term (multiply by Me) [True]
     """
 
-    def __init__(self, rxList, freq, S_e): #, ePrimary=None, bPrimary=None, hPrimary=None, jPrimary=None):
-        self._S_e = np.array(S_e,dtype=complex)
-        self.freq = float(freq)
-        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
-
-    :param float freq: frequency
-    :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()):
-        self._S_m = np.array(S_m,dtype=complex)
+    def __init__(self, rxList, freq, s_e, integrate=True): #, ePrimary=None, bPrimary=None, hPrimary=None, jPrimary=None):
+        self._s_e = np.array(s_e, dtype=complex)
         self.freq = float(freq)
         self.integrate = integrate
 
         BaseSrc.__init__(self, rxList)
 
-    def S_m(self, prob):
+    def s_e(self, prob):
         """
-        Magnetic source term 
+        Electric source term
+
+        :param Problem prob: FDEM Problem
+        :rtype: numpy.ndarray
+        :return: electric source term on mesh
+        """
+        if prob._formulation is 'EB' and self.integrate is True:
+            return prob.Me * self._s_e
+        return self._s_e
+
+
+class RawVec_m(BaseSrc):
+    """
+    RawVec magnetic source. It is defined by the user provided vector s_m
+
+    :param float freq: frequency
+    :param rxList: receiver list
+    :param numpy.array s_m: magnetic source term
+    :param bool integrate: Integrate the source term (multiply by Me) [True]
+    """
+
+    def __init__(self, rxList, freq, s_m, integrate=True):  #ePrimary=Zero(), bPrimary=Zero(), hPrimary=Zero(), jPrimary=Zero()):
+        self._s_m = np.array(s_m, dtype=complex)
+        self.freq = float(freq)
+        self.integrate = integrate
+
+        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
+        if prob._formulation is 'HJ' and self.integrate is True:
+            return prob.Me * self._s_m
+        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 rxList: receiver list
     :param float freq: frequency
-    :param numpy.array S_m: magnetic source term
-    :param numpy.array S_e: electric source term
+    :param numpy.array s_m: magnetic source term
+    :param numpy.array s_e: electric source term
+    :param bool integrate: Integrate the source term (multiply by Me) [True]
     """
-    def __init__(self, rxList, freq, S_m, S_e, integrate = True):
-        self._S_m = np.array(S_m,dtype=complex)
-        self._S_e = np.array(S_e,dtype=complex)
+    def __init__(self, rxList, freq, s_m, s_e, integrate=True):
+        self._s_m = np.array(s_m, dtype=complex)
+        self._s_e = np.array(s_e, dtype=complex)
         self.freq = float(freq)
         self.integrate = integrate
         BaseSrc.__init__(self, rxList)
 
-    def S_m(self, prob):
-        if prob._eqLocs is 'EF' and self.integrate is True:
-            return prob.Me * self._S_m
-        return self._S_m
+    def s_m(self, prob):
+        """
+        Magnetic source term
 
-    def S_e(self, prob):
-        if prob._eqLocs is 'FE' and self.integrate is True:
-            return prob.Me * self._S_e
-        return self._S_e
+        :param Problem prob: FDEM Problem
+        :rtype: numpy.ndarray
+        :return: magnetic source term on mesh
+        """
+        if prob._formulation is 'HJ' and self.integrate is True:
+            return prob.Me * self._s_m
+        return self._s_m
+
+    def s_e(self, prob):
+        """
+        Electric source term
+
+        :param Problem prob: FDEM Problem
+        :rtype: numpy.ndarray
+        :return: electric source term on mesh
+        """
+        if prob._formulation is 'EB' and self.integrate is True:
+            return prob.Me * self._s_e
+        return self._s_e
 
 
 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!). 
+    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:: 
+    .. 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}}
 
@@ -225,17 +254,17 @@ class MagDipole(BaseSrc):
     and define a zero-frequency primary problem, noting that the source is
     generated by a divergence free electric current
 
-    .. math:: 
+    .. 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 
+    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:: 
+    .. 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 
+    Our secondary problem is then
 
     .. math::
         \mathbf{C} \mathbf{e^S} + i \omega \mathbf{b^S} = - i \omega \mathbf{b^P} \\\\
@@ -245,15 +274,15 @@ class MagDipole(BaseSrc):
     :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 
+    :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):
+    def __init__(self, rxList, freq, loc, orientation='Z', moment=1., mu=mu_0):
         self.freq = float(freq)
         self.loc = loc
         self.orientation = orientation
+        assert orientation in ['X','Y','Z'], "Orientation (right now) doesn't actually do anything! The methods in SrcUtils should take care of this..."
         self.moment = moment
         self.mu = mu
         self.integrate = False
@@ -265,17 +294,17 @@ class MagDipole(BaseSrc):
 
         :param Problem prob: FDEM problem
         :rtype: numpy.ndarray
-        :return: primary magnetic field 
+        :return: primary magnetic field
         """
-        eqLocs = prob._eqLocs
+        formulation = prob._formulation
 
-        if eqLocs is 'FE':
+        if formulation is 'EB':
             gridX = prob.mesh.gridEx
             gridY = prob.mesh.gridEy
             gridZ = prob.mesh.gridEz
             C = prob.mesh.edgeCurl
 
-        elif eqLocs is 'EF':
+        elif formulation is 'HJ':
             gridX = prob.mesh.gridFx
             gridY = prob.mesh.gridFy
             gridZ = prob.mesh.gridFz
@@ -303,44 +332,46 @@ class MagDipole(BaseSrc):
 
         :param Problem prob: FDEM problem
         :rtype: numpy.ndarray
-        :return: primary magnetic field 
+        :return: primary magnetic field
         """
         b = self.bPrimary(prob)
-        return h_from_b(prob,b)
+        return 1./self.mu * b
 
-    def S_m(self, prob):
+    def s_m(self, prob):
         """
         The magnetic source term
 
         :param Problem prob: FDEM problem
         :rtype: numpy.ndarray
-        :return: primary magnetic field 
+        :return: primary magnetic field
         """
 
         b_p = self.bPrimary(prob)
+        if prob._formulation is 'HJ':
+            b_p = prob.Me * b_p
         return -1j*omega(self.freq)*b_p
 
-    def S_e(self, prob):
+    def s_e(self, prob):
         """
         The electric source term
 
         :param Problem prob: FDEM problem
         :rtype: numpy.ndarray
-        :return: primary magnetic field 
+        :return: primary magnetic field
         """
 
         if all(np.r_[self.mu] == np.r_[prob.curModel.mu]):
             return Zero()
         else:
-            eqLocs = prob._eqLocs
+            formulation = prob._formulation
 
-            if eqLocs is 'FE':
+            if formulation is 'EB':
                 mui_s = prob.curModel.mui - 1./self.mu
                 MMui_s = prob.mesh.getFaceInnerProduct(mui_s)
                 C = prob.mesh.edgeCurl
-            elif eqLocs is 'EF':
+            elif formulation is 'HJ':
                 mu_s = prob.curModel.mu - self.mu
-                MMui_s = prob.mesh.getEdgeInnerProduct(mu_s,invMat=True)
+                MMui_s = prob.mesh.getEdgeInnerProduct(mu_s, invMat=True)
                 C = prob.mesh.edgeCurl.T
 
             return -C.T * (MMui_s * self.bPrimary(prob))
@@ -353,21 +384,20 @@ class MagDipole_Bfield(BaseSrc):
     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. 
+    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 
+    :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):
         self.freq = float(freq)
         self.loc = loc
+        assert orientation in ['X','Y','Z'], "Orientation (right now) doesn't actually do anything! The methods in SrcUtils should take care of this..."
         self.orientation = orientation
         self.moment = moment
         self.mu = mu
@@ -379,18 +409,18 @@ class MagDipole_Bfield(BaseSrc):
 
         :param Problem prob: FDEM problem
         :rtype: numpy.ndarray
-        :return: primary magnetic field 
+        :return: primary magnetic field
         """
 
-        eqLocs = prob._eqLocs
+        formulation = prob._formulation
 
-        if eqLocs is 'FE':
+        if formulation is 'EB':
             gridX = prob.mesh.gridFx
             gridY = prob.mesh.gridFy
             gridZ = prob.mesh.gridFz
             C = prob.mesh.edgeCurl
 
-        elif eqLocs is 'EF':
+        elif formulation is 'HJ':
             gridX = prob.mesh.gridEx
             gridY = prob.mesh.gridEy
             gridZ = prob.mesh.gridEz
@@ -418,42 +448,44 @@ class MagDipole_Bfield(BaseSrc):
 
         :param Problem prob: FDEM problem
         :rtype: numpy.ndarray
-        :return: primary magnetic field 
+        :return: primary magnetic field
         """
         b = self.bPrimary(prob)
-        return h_from_b(prob, b)
+        return 1/self.mu * b
 
-    def S_m(self, prob):
+    def s_m(self, prob):
         """
         The magnetic source term
 
         :param Problem prob: FDEM problem
         :rtype: numpy.ndarray
-        :return: primary magnetic field 
+        :return: primary magnetic field
         """
         b = self.bPrimary(prob)
+        if prob._formulation is 'HJ':
+            b = prob.Me * b
         return -1j*omega(self.freq)*b
 
-    def S_e(self, prob):
+    def s_e(self, prob):
         """
         The electric source term
 
         :param Problem prob: FDEM problem
         :rtype: numpy.ndarray
-        :return: primary magnetic field 
+        :return: primary magnetic field
         """
         if all(np.r_[self.mu] == np.r_[prob.curModel.mu]):
             return Zero()
         else:
-            eqLocs = prob._eqLocs
+            formulation = prob._formulation
 
-            if eqLocs is 'FE':
+            if formulation is 'EB':
                 mui_s = prob.curModel.mui - 1./self.mu
                 MMui_s = prob.mesh.getFaceInnerProduct(mui_s)
                 C = prob.mesh.edgeCurl
-            elif eqLocs is 'EF':
+            elif formulation is 'HJ':
                 mu_s = prob.curModel.mu - self.mu
-                MMui_s = prob.mesh.getEdgeInnerProduct(mu_s,invMat=True)
+                MMui_s = prob.mesh.getEdgeInnerProduct(mu_s, invMat=True)
                 C = prob.mesh.edgeCurl.T
 
             return -C.T * (MMui_s * self.bPrimary(prob))
@@ -463,22 +495,22 @@ 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!). 
+    flux density is divergence free (no magnetic monopoles!).
 
-    This approach uses a primary-secondary in frequency in the same fashion as the MagDipole. 
+    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 
+    :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):
+    def __init__(self, rxList, freq, loc, orientation='Z', radius=1., mu=mu_0):
         self.freq = float(freq)
         self.orientation = orientation
+        assert orientation in ['X','Y','Z'], "Orientation (right now) doesn't actually do anything! The methods in SrcUtils should take care of this..."
         self.radius = radius
         self.mu = mu
         self.loc = loc
@@ -491,17 +523,17 @@ class CircularLoop(BaseSrc):
 
         :param Problem prob: FDEM problem
         :rtype: numpy.ndarray
-        :return: primary magnetic field 
+        :return: primary magnetic field
         """
-        eqLocs = prob._eqLocs
+        formulation = prob._formulation
 
-        if eqLocs is 'FE':
+        if formulation is 'EB':
             gridX = prob.mesh.gridEx
             gridY = prob.mesh.gridEy
             gridZ = prob.mesh.gridEz
             C = prob.mesh.edgeCurl
 
-        elif eqLocs is 'EF':
+        elif formulation is 'HJ':
             gridX = prob.mesh.gridFx
             gridY = prob.mesh.gridFy
             gridZ = prob.mesh.gridFz
@@ -528,44 +560,50 @@ class CircularLoop(BaseSrc):
 
         :param Problem prob: FDEM problem
         :rtype: numpy.ndarray
-        :return: primary magnetic field 
+        :return: primary magnetic field
         """
         b = self.bPrimary(prob)
         return 1./self.mu*b
 
-    def S_m(self, prob):
+    def s_m(self, prob):
         """
         The magnetic source term
 
         :param Problem prob: FDEM problem
         :rtype: numpy.ndarray
-        :return: primary magnetic field 
+        :return: primary magnetic field
         """
         b = self.bPrimary(prob)
+        if prob._formulation is 'HJ':
+            b =  prob.Me *  b
         return -1j*omega(self.freq)*b
 
-    def S_e(self, prob):
+    def s_e(self, prob):
         """
         The electric source term
 
         :param Problem prob: FDEM problem
         :rtype: numpy.ndarray
-        :return: primary magnetic field 
+        :return: primary magnetic field
         """
         if all(np.r_[self.mu] == np.r_[prob.curModel.mu]):
             return Zero()
         else:
-            eqLocs = prob._eqLocs
+            formulation = prob._formulation
 
-            if eqLocs is 'FE':
+            if formulation is 'EB':
                 mui_s = prob.curModel.mui - 1./self.mu
                 MMui_s = prob.mesh.getFaceInnerProduct(mui_s)
                 C = prob.mesh.edgeCurl
-            elif eqLocs is 'EF':
+
+
+            elif formulation is 'HJ':
                 mu_s = prob.curModel.mu - self.mu
-                MMui_s = prob.mesh.getEdgeInnerProduct(mu_s,invMat=True)
+                MMui_s = prob.mesh.getEdgeInnerProduct(mu_s, invMat=True)
                 C = prob.mesh.edgeCurl.T
 
             return -C.T * (MMui_s * self.bPrimary(prob))
 
 
+
+

SimPEG/EM/FDEM/SurveyFDEM.py

@@ -1,8 +1,10 @@
 import SimPEG
 from SimPEG.EM.Utils import *
+from SimPEG.EM.Base import BaseEMSurvey
 from scipy.constants import mu_0
 from SimPEG.Utils import Zero, Identity
 import SrcFDEM as Src
+from SimPEG import sp
 
 
 ####################################################
@@ -18,33 +20,33 @@ class Rx(SimPEG.Survey.BaseRx):
     """
 
     knownRxTypes = {
-                    'exr':['e', 'Ex', 'real'],
-                    'eyr':['e', 'Ey', 'real'],
-                    'ezr':['e', 'Ez', 'real'],
-                    'exi':['e', 'Ex', 'imag'],
-                    'eyi':['e', 'Ey', 'imag'],
-                    'ezi':['e', 'Ez', 'imag'],
+                    'exr':['e', 'x', 'real'],
+                    'eyr':['e', 'y', 'real'],
+                    'ezr':['e', 'z', 'real'],
+                    'exi':['e', 'x', 'imag'],
+                    'eyi':['e', 'y', 'imag'],
+                    'ezi':['e', 'z', 'imag'],
 
-                    'bxr':['b', 'Fx', 'real'],
-                    'byr':['b', 'Fy', 'real'],
-                    'bzr':['b', 'Fz', 'real'],
-                    'bxi':['b', 'Fx', 'imag'],
-                    'byi':['b', 'Fy', 'imag'],
-                    'bzi':['b', 'Fz', 'imag'],
+                    'bxr':['b', 'x', 'real'],
+                    'byr':['b', 'y', 'real'],
+                    'bzr':['b', 'z', 'real'],
+                    'bxi':['b', 'x', 'imag'],
+                    'byi':['b', 'y', 'imag'],
+                    'bzi':['b', 'z', 'imag'],
 
-                    'jxr':['j', 'Fx', 'real'],
-                    'jyr':['j', 'Fy', 'real'],
-                    'jzr':['j', 'Fz', 'real'],
-                    'jxi':['j', 'Fx', 'imag'],
-                    'jyi':['j', 'Fy', 'imag'],
-                    'jzi':['j', 'Fz', 'imag'],
+                    'jxr':['j', 'x', 'real'],
+                    'jyr':['j', 'y', 'real'],
+                    'jzr':['j', 'z', 'real'],
+                    'jxi':['j', 'x', 'imag'],
+                    'jyi':['j', 'y', 'imag'],
+                    'jzi':['j', 'z', 'imag'],
 
-                    'hxr':['h', 'Ex', 'real'],
-                    'hyr':['h', 'Ey', 'real'],
-                    'hzr':['h', 'Ez', 'real'],
-                    'hxi':['h', 'Ex', 'imag'],
-                    'hyi':['h', 'Ey', 'imag'],
-                    'hzi':['h', 'Ez', 'imag'],
+                    'hxr':['h', 'x', 'real'],
+                    'hyr':['h', 'y', 'real'],
+                    'hzr':['h', 'z', 'real'],
+                    'hxi':['h', 'x', 'imag'],
+                    'hyi':['h', 'y', 'imag'],
+                    'hzi':['h', 'z', 'imag'],
                    }
     radius = None
 
@@ -56,45 +58,49 @@ class Rx(SimPEG.Survey.BaseRx):
         """Field Type projection (e.g. e b ...)"""
         return self.knownRxTypes[self.rxType][0]
 
-    @property
-    def projGLoc(self):
-        """Grid Location projection (e.g. Ex Fy ...)"""
-        return self.knownRxTypes[self.rxType][1]
-
     @property
     def projComp(self):
         """Component projection (real/imag)"""
         return self.knownRxTypes[self.rxType][2]
 
-    def projectFields(self, src, mesh, u):
+    def projGLoc(self, u):
+        """Grid Location projection (e.g. Ex Fy ...)"""
+        return u._GLoc(self.rxType[0]) + self.knownRxTypes[self.rxType][1]
+
+    def eval(self, src, mesh, f):
         """
         Project fields to recievers to get data.
 
         :param Source src: FDEM source
         :param Mesh mesh: mesh used
-        :param Fields u: fields object
+        :param Fields f: fields object
         :rtype: numpy.ndarray
         :return: fields projected to recievers
         """
-        P = self.getP(mesh)
-        u_part_complex = u[src, self.projField]
+        # projGLoc = u._GLoc(self.knownRxTypes[self.rxType][0])
+        # projGLoc += self.knownRxTypes[self.rxType][1]
+
+        P = self.getP(mesh, self.projGLoc(f))
+        f_part_complex = f[src, self.projField]
         # get the real or imag component
         real_or_imag = self.projComp
-        u_part = getattr(u_part_complex, real_or_imag)
-        return P*u_part
+        f_part = getattr(f_part_complex, real_or_imag)
 
-    def projectFieldsDeriv(self, src, mesh, u, v, adjoint=False):
+        return P*f_part
+
+    def evalDeriv(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 u: fields object
+        :param Fields f: fields object
         :param numpy.ndarray v: vector to multiply
         :rtype: numpy.ndarray
         :return: fields projected to recievers
         """
-        P = self.getP(mesh)
+
+        P = self.getP(mesh, self.projGLoc(f))
 
         if not adjoint:
             Pv_complex = P * v
@@ -118,7 +124,7 @@ class Rx(SimPEG.Survey.BaseRx):
 # Survey
 ####################################################
 
-class Survey(SimPEG.Survey.BaseSurvey):
+class Survey(BaseEMSurvey):
     """
     Frequency domain electromagnetic survey
 
@@ -126,12 +132,12 @@ class Survey(SimPEG.Survey.BaseSurvey):
     """
 
     srcPair = Src.BaseSrc
-    rxPaair = Rx 
+    rxPair = Rx
 
     def __init__(self, srcList, **kwargs):
         # Sort these by frequency
         self.srcList = srcList
-        SimPEG.Survey.BaseSurvey.__init__(self, **kwargs)
+        BaseEMSurvey.__init__(self, srcList, **kwargs)
 
         _freqDict = {}
         for src in srcList:
@@ -166,23 +172,8 @@ class Survey(SimPEG.Survey.BaseSurvey):
         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 
+        :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:
-                data[src, rx] = rx.projectFields(src, self.mesh, u)
-        return data
-
-    def projectFieldsDeriv(self, u):
-        raise Exception('Use Sources to project fields deriv.')

SimPEG/EM/TDEM/BaseTDEM.py

@@ -27,6 +27,7 @@ class FieldsTDEM(Problem.TimeFields):
             else:
                 e = np.zeros((nE,nSrc)) # if nSrc == 1 else (nE, nSrc))
             u = np.concatenate((u, b, e))
+
         return Utils.mkvc(u,nSrc)
 
 
@@ -107,11 +108,11 @@ class BaseTDEMProblem(BaseTimeProblem, BaseEMProblem):
         Ainv.clean()
         return F
 
-    def Jvec(self, m, v, u=None):
+    def Jvec(self, m, v, f=None):
         """
             :param numpy.array m: Conductivity model
             :param numpy.ndarray v: vector (model object)
-            :param simpegEM.TDEM.FieldsTDEM u: Fields resulting from m
+            :param simpegEM.TDEM.FieldsTDEM f: Fields resulting from m
             :rtype: numpy.ndarray
             :return: w (data object)
 
@@ -124,15 +125,15 @@ class BaseTDEMProblem(BaseTimeProblem, BaseEMProblem):
         """
         if self.verbose: print '%s\nCalculating J(v)\n%s'%('*'*50,'*'*50)
         self.curModel = m
-        if u is None:
-            u = self.fields(m)
-        p = self.Gvec(m, v, u)
+        if f is None:
+            f = self.fields(m)
+        p = self.Gvec(m, v, f)
         y = self.solveAh(m, p)
-        Jv = self.survey.projectFieldsDeriv(u, v=y)
+        Jv = self.survey.evalDeriv(f, v=y)
         if self.verbose: print '%s\nDone calculating J(v)\n%s'%('*'*50,'*'*50)
         return - mkvc(Jv)
 
-    def Jtvec(self, m, v, u=None):
+    def Jtvec(self, m, v, f=None):
         """
             :param numpy.array m: Conductivity model
             :param numpy.ndarray,SimPEG.Survey.Data v: vector (data object)
@@ -149,15 +150,15 @@ class BaseTDEMProblem(BaseTimeProblem, BaseEMProblem):
         """
         if self.verbose: print '%s\nCalculating J^T(v)\n%s'%('*'*50,'*'*50)
         self.curModel = m
-        if u is None:
-            u = self.fields(m)
+        if f is None:
+            f = self.fields(m)
 
         if not isinstance(v, self.dataPair):
             v = self.dataPair(self.survey, v)
 
-        p = self.survey.projectFieldsDeriv(u, v=v, adjoint=True)
+        p = self.survey.evalDeriv(f, v=v, adjoint=True)
         y = self.solveAht(m, p)
-        w = self.Gtvec(m, y, u)
+        w = self.Gtvec(m, y, f)
         if self.verbose: print '%s\nDone calculating J^T(v)\n%s'%('*'*50,'*'*50)
         return - mkvc(w)
 

SimPEG/EM/TDEM/SurveyTDEM.py

@@ -51,12 +51,12 @@ class RxTDEM(Survey.BaseTimeRx):
         else:
             return timeMesh.getInterpolationMat(self.times, self.projTLoc)
 
-    def projectFields(self, src, mesh, timeMesh, u):
+    def eval(self, src, mesh, timeMesh, u):
         P = self.getP(mesh, timeMesh)
         u_part = Utils.mkvc(u[src, self.projField, :])
         return P*u_part
 
-    def projectFieldsDeriv(self, src, mesh, timeMesh, u, v, adjoint=False):
+    def evalDeriv(self, src, mesh, timeMesh, u, v, adjoint=False):
         P = self.getP(mesh, timeMesh)
 
         if not adjoint:
@@ -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')
@@ -93,13 +113,12 @@ class SrcTDEM_VMD_MVP(SrcTDEM):
         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}
+            raise Exception('Unknown mesh for VMD')            
+        return mesh.edgeCurl.T*MfMui*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
@@ -149,27 +168,27 @@ class SurveyTDEM(Survey.BaseSurvey):
         self.srcList = srcList
         Survey.BaseSurvey.__init__(self, **kwargs)
 
-    def projectFields(self, u):
+    def eval(self, u):
         data = Survey.Data(self)
         for src in self.srcList:
             for rx in src.rxList:
-                data[src, rx] = rx.projectFields(src, self.mesh, self.prob.timeMesh, u)
+                data[src, rx] = rx.eval(src, self.mesh, self.prob.timeMesh, u)
         return data
 
-    def projectFieldsDeriv(self, u, v=None, adjoint=False):
+    def evalDeriv(self, u, v=None, adjoint=False):
         assert v is not None, 'v to multiply must be provided.'
 
         if not adjoint:
             data = Survey.Data(self)
             for src in self.srcList:
                 for rx in src.rxList:
-                    data[src, rx] = rx.projectFieldsDeriv(src, self.mesh, self.prob.timeMesh, u, v)
+                    data[src, rx] = rx.evalDeriv(src, self.mesh, self.prob.timeMesh, u, v)
             return data
         else:
             f = FieldsTDEM(self.mesh, self)
             for src in self.srcList:
                 for rx in src.rxList:
-                    Ptv = rx.projectFieldsDeriv(src, self.mesh, self.prob.timeMesh, u, v, adjoint=True)
+                    Ptv = rx.evalDeriv(src, self.mesh, self.prob.timeMesh, u, v, adjoint=True)
                     Ptv = Ptv.reshape((-1, self.prob.timeMesh.nN), order='F')
                     if rx.projField not in f: # first time we are projecting
                         f[src, rx.projField, :] = Ptv

SimPEG/EM/Utils/EMUtils.py

@@ -13,37 +13,4 @@ def k(freq, sigma, mu=mu_0, eps=epsilon_0):
     beta = w * np.sqrt( mu*eps/2 * ( np.sqrt(1. + (sigma / (eps*w))**2 ) - 1) ) 
     return alp - 1j*beta
 
-# Constitutive relations
-def e_from_j(prob,j):
-    eqLocs = prob._eqLocs
-    if eqLocs is 'FE':
-        MSigmaI = prob.MeSigmaI
-    elif eqLocs is 'EF':
-        MSigmaI = prob.MfRho
-    return MSigmaI*j
-
-def j_from_e(prob,e):
-    eqLocs = prob._eqLocs
-    if eqLocs is 'FE':
-        MSigma = prob.MeSigma
-    elif eqLocs is 'EF':
-        MSigma = prob.MfRhoI
-    return MSigma*e
-
-def b_from_h(prob,h):
-    eqLocs = prob._eqLocs
-    if eqLocs is 'FE':
-        MMu = prob.MfMuiI
-    elif eqLocs is 'EF':
-        MMu = prob.MeMu
-    return MMu*h
-
-def h_from_b(prob,b):
-    eqLocs = prob._eqLocs
-    if eqLocs is 'FE':
-        MMuI = prob.MfMui
-    elif eqLocs is 'EF':
-        MMuI = prob.MeMuI
-    return MMuI*b 
-
 

SimPEG/EM/Utils/__init__.py

@@ -1,5 +1,2 @@
-# import Sources
-# import Ana
-# import Solver
-from EMUtils import omega, e_from_j, j_from_e, b_from_h, h_from_b
+from EMUtils import omega, k
 from AnalyticUtils import MagneticDipoleFields, MagneticDipoleVectorPotential, MagneticLoopVectorPotential

SimPEG/EM/Utils/testingUtils.py

@@ -4,19 +4,28 @@ from SimPEG import EM
 import sys
 from scipy.constants import mu_0
 
-def getFDEMProblem(fdemType, comp, SrcList, freq, verbose=False):
-    cs = 5.
-    ncx, ncy, ncz = 6, 6, 6
-    npad = 3
+FLR = 1e-20 # "zero", so if residual below this --> pass regardless of order
+CONDUCTIVITY = 1e1
+MU = mu_0
+freq = 5e-1
+
+
+def getFDEMProblem(fdemType, comp, SrcList, freq, useMu=False, verbose=False):
+    cs = 10.
+    ncx, ncy, ncz = 0, 0, 0
+    npad = 8
     hx = [(cs,npad,-1.3), (cs,ncx), (cs,npad,1.3)]
     hy = [(cs,npad,-1.3), (cs,ncy), (cs,npad,1.3)]
     hz = [(cs,npad,-1.3), (cs,ncz), (cs,npad,1.3)]
     mesh = Mesh.TensorMesh([hx,hy,hz],['C','C','C'])
 
-    mapping = Maps.ExpMap(mesh)
+    if useMu is True:
+        mapping = [('sigma', Maps.ExpMap(mesh)), ('mu', Maps.IdentityMap(mesh))] 
+    else:
+        mapping = Maps.ExpMap(mesh)
 
-    x = np.array([np.linspace(-30,-15,3),np.linspace(15,30,3)]) #don't sample right by the source
-    XYZ = Utils.ndgrid(x,x,np.r_[0.])
+    x = np.array([np.linspace(-5.*cs,-2.*cs,3),np.linspace(5.*cs,2.*cs,3)]) + cs/4. #don't sample right by the source, slightly off alignment from either staggered grid
+    XYZ = Utils.ndgrid(x,x,np.linspace(-2.*cs,2.*cs,5))
     Rx0 = EM.FDEM.Rx(XYZ, comp)
 
     Src = []
@@ -32,15 +41,15 @@ def getFDEMProblem(fdemType, comp, SrcList, freq, verbose=False):
             if fdemType is 'e' or fdemType is 'b':
                 S_m = np.zeros(mesh.nF)
                 S_e = np.zeros(mesh.nE)
-                S_m[Utils.closestPoints(mesh,[0.,0.,0.],'Fz') + np.sum(mesh.vnF[:1])] = 1.
-                S_e[Utils.closestPoints(mesh,[0.,0.,0.],'Ez') + np.sum(mesh.vnE[:1])] = 1.
+                S_m[Utils.closestPoints(mesh,[0.,0.,0.],'Fz') + np.sum(mesh.vnF[:1])] = 1e-3
+                S_e[Utils.closestPoints(mesh,[0.,0.,0.],'Ez') + np.sum(mesh.vnE[:1])] = 1e-3
                 Src.append(EM.FDEM.Src.RawVec([Rx0], freq, S_m, S_e))
 
             elif fdemType is 'h' or fdemType is 'j':
                 S_m = np.zeros(mesh.nE)
                 S_e = np.zeros(mesh.nF)
-                S_m[Utils.closestPoints(mesh,[0.,0.,0.],'Ez') + np.sum(mesh.vnE[:1])] = 1.
-                S_e[Utils.closestPoints(mesh,[0.,0.,0.],'Fz') + np.sum(mesh.vnF[:1])] = 1.
+                S_m[Utils.closestPoints(mesh,[0.,0.,0.],'Ez') + np.sum(mesh.vnE[:1])] = 1e-3
+                S_e[Utils.closestPoints(mesh,[0.,0.,0.],'Fz') + np.sum(mesh.vnF[:1])] = 1e-3
                 Src.append(EM.FDEM.Src.RawVec([Rx0], freq, S_m, S_e))
 
     if verbose:
@@ -70,6 +79,48 @@ def getFDEMProblem(fdemType, comp, SrcList, freq, verbose=False):
         from pymatsolver import MumpsSolver
         prb.Solver = MumpsSolver
     except ImportError, e:
-        pass
+        prb.Solver = SolverLU
 
-    return prb
+    return prb
+
+def crossCheckTest(SrcList, fdemType1, fdemType2, comp, addrandoms = False, useMu=False, TOL=1e-5, verbose=False):
+
+    l2norm = lambda r: np.sqrt(r.dot(r))
+
+    prb1 = getFDEMProblem(fdemType1, comp, SrcList, freq, useMu, verbose)
+    mesh = prb1.mesh
+    print 'Cross Checking Forward: %s, %s formulations - %s' % (fdemType1, fdemType2, comp)
+    
+    logsig = np.log(np.ones(mesh.nC)*CONDUCTIVITY)
+    mu = np.ones(mesh.nC)*MU
+
+    if addrandoms is True:
+        logsig  += np.random.randn(mesh.nC)*np.log(CONDUCTIVITY)*1e-1
+        mu += np.random.randn(mesh.nC)*MU*1e-1
+
+    if useMu is True:
+        m = np.r_[logsig, mu]
+    else:
+        m = logsig
+
+    survey1 = prb1.survey
+    d1 = survey1.dpred(m)
+
+    if verbose:
+        print '  Problem 1 solved'
+
+
+    prb2 = getFDEMProblem(fdemType2, comp, SrcList, freq, useMu, verbose)
+
+    survey2 = prb2.survey
+    d2 = survey2.dpred(m)
+
+    if verbose:
+        print '  Problem 2 solved'
+
+    r = d2-d1
+    l2r = l2norm(r)
+
+    tol = np.max([TOL*(10**int(np.log10(0.5* (l2norm(d1) + l2norm(d2)) ))),FLR])
+    print l2norm(d1), l2norm(d2),  l2r , tol, l2r < tol
+    return l2r < tol

SimPEG/Examples/DC_Analytic_Dipole.py

@@ -0,0 +1,68 @@
+from SimPEG import *
+import SimPEG.DCIP as DC
+
+def run(plotIt=False):
+    cs = 25.
+    hx = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
+    hy = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
+    hz = [(cs,7, -1.3),(cs,20)]
+    mesh = Mesh.TensorMesh([hx, hy, hz], 'CCN')
+    sighalf = 1e-2
+    sigma = np.ones(mesh.nC)*sighalf
+    xtemp = np.linspace(-150, 150, 21)
+    ytemp = np.linspace(-150, 150, 21)
+    xyz_rxP = Utils.ndgrid(xtemp-10., ytemp, np.r_[0.])
+    xyz_rxN = Utils.ndgrid(xtemp+10., ytemp, np.r_[0.])
+    xyz_rxM = Utils.ndgrid(xtemp, ytemp, np.r_[0.])
+
+    # if plotIt:
+    #     fig, ax = plt.subplots(1,1, figsize = (5,5))
+    #     mesh.plotSlice(sigma, grid=True, ax = ax)
+    #     ax.plot(xyz_rxP[:,0],xyz_rxP[:,1], 'w.')
+    #     ax.plot(xyz_rxN[:,0],xyz_rxN[:,1], 'r.', ms = 3)
+
+    rx = DC.RxDipole(xyz_rxP, xyz_rxN)
+    src = DC.SrcDipole([rx], [-200, 0, -12.5], [+200, 0, -12.5])
+    survey = DC.SurveyDC([src])
+    problem = DC.ProblemDC_CC(mesh)
+    problem.pair(survey)
+    try:
+        from pymatsolver import MumpsSolver
+        problem.Solver = MumpsSolver
+    except Exception, e:
+        pass
+    data = survey.dpred(sigma)
+
+    def DChalf(srclocP, srclocN, rxloc, sigma, I=1.):
+        rp = (srclocP.reshape([1,-1])).repeat(rxloc.shape[0], axis = 0)
+        rn = (srclocN.reshape([1,-1])).repeat(rxloc.shape[0], axis = 0)
+        rP = np.sqrt(((rxloc-rp)**2).sum(axis=1))
+        rN = np.sqrt(((rxloc-rn)**2).sum(axis=1))
+        return I/(sigma*2.*np.pi)*(1/rP-1/rN)
+
+    data_anaP = DChalf(np.r_[-200, 0, 0.],np.r_[+200, 0, 0.], xyz_rxP, sighalf)
+    data_anaN = DChalf(np.r_[-200, 0, 0.],np.r_[+200, 0, 0.], xyz_rxN, sighalf)
+    data_ana = data_anaP-data_anaN
+    Data_ana = data_ana.reshape((21, 21), order = 'F')
+    Data = data.reshape((21, 21), order = 'F')
+    X = xyz_rxM[:,0].reshape((21, 21), order = 'F')
+    Y = xyz_rxM[:,1].reshape((21, 21), order = 'F')
+
+    if plotIt:
+        import matplotlib.pyplot as plt
+        fig, ax = plt.subplots(1,2, figsize = (12, 5))
+        vmin = np.r_[data, data_ana].min()
+        vmax = np.r_[data, data_ana].max()
+        dat1 = ax[1].contourf(X, Y, Data, 60, vmin = vmin, vmax = vmax)
+        dat0 = ax[0].contourf(X, Y, Data_ana, 60, vmin = vmin, vmax = vmax)
+        cb0 = plt.colorbar(dat1, orientation = 'horizontal', ax = ax[0])
+        cb1 = plt.colorbar(dat1, orientation = 'horizontal', ax = ax[1])
+        ax[1].set_title('Analytic')
+        ax[0].set_title('Computed')
+        plt.show()
+
+    return np.linalg.norm(data-data_ana)/np.linalg.norm(data_ana)
+
+
+if __name__ == '__main__':
+    print run(plotIt=True)

SimPEG/Examples/DC_Forward_PseudoSection.py

@@ -0,0 +1,210 @@
+from SimPEG import Mesh, Utils, np, sp
+import SimPEG.DCIP as DC
+import time
+
+def run(loc=None, sig=None, radi=None, param=None, stype='dpdp', dtype='appc', plotIt=True):
+    """
+        DC Forward Simulation
+        =====================
+
+        Forward model two conductive spheres in a half-space and plot a
+        pseudo-section. Assumes an infinite line source and measures along the
+        center of the spheres.
+
+        INPUT:
+        loc     = Location of spheres [[x1,y1,z1],[x2,y2,z2]]
+        radi    = Radius of spheres [r1,r2]
+        param   = Conductivity of background and two spheres [m0,m1,m2]
+        stype   = survey type "pdp" (pole dipole) or "dpdp" (dipole dipole)
+        dtype   = Data type "appr" (app res) | "appc" (app cond) | "volt" (potential)
+        Created by @fourndo
+
+    """
+
+    assert stype in ['pdp', 'dpdp'], "Source type (stype) must be pdp or dpdp (pole dipole or dipole dipole)"
+    assert dtype in ['appr', 'appc', 'volt'], "Data type (dtype) must be appr (app res) or appc (app cond) or volt (potential)"
+
+    if loc is None:
+        loc = np.c_[[-50.,0.,-50.],[50.,0.,-50.]]
+    if sig is None:
+        sig = np.r_[1e-2,1e-1,1e-3]
+    if radi is None:
+        radi = np.r_[25.,25.]
+    if param is None:
+        param = np.r_[30.,30.,5]
+
+
+    # First we need to create a mesh and a model.
+    # This is our mesh
+    dx    = 5.
+
+    hxind = [(dx,15,-1.3), (dx, 75), (dx,15,1.3)]
+    hyind = [(dx,15,-1.3), (dx, 10), (dx,15,1.3)]
+    hzind = [(dx,15,-1.3),(dx, 15)]
+
+    mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCN')
+
+
+    # Set background conductivity
+    model = np.ones(mesh.nC) * sig[0]
+
+    # First anomaly
+    ind = Utils.ModelBuilder.getIndicesSphere(loc[:,0],radi[0],mesh.gridCC)
+    model[ind] = sig[1]
+
+    # Second anomaly
+    ind = Utils.ModelBuilder.getIndicesSphere(loc[:,1],radi[1],mesh.gridCC)
+    model[ind] = sig[2]
+
+    # Get index of the center
+    indy = int(mesh.nCy/2)
+
+    # Plot the model for reference
+    # Define core mesh extent
+    xlim = 200
+    zlim = 100
+
+    # Then specify the end points of the survey. Let's keep it simple for now and survey above the anomalies, top of the mesh
+    ends = [(-175,0),(175,0)]
+    ends = np.c_[np.asarray(ends),np.ones(2).T*mesh.vectorNz[-1]]
+
+    # Snap the endpoints to the grid. Easier to create 2D section.
+    indx = Utils.closestPoints(mesh, ends )
+    locs = np.c_[mesh.gridCC[indx,0],mesh.gridCC[indx,1],np.ones(2).T*mesh.vectorNz[-1]]
+
+    # We will handle the geometry of the survey for you and create all the combination of tx-rx along line
+    # [Tx, Rx] = DC.gen_DCIPsurvey(locs, mesh, stype, param[0], param[1], param[2])
+    survey, Tx, Rx = DC.gen_DCIPsurvey(locs, mesh, stype, param[0], param[1], param[2])
+
+    # Define some global geometry
+    dl_len = np.sqrt( np.sum((locs[0,:] - locs[1,:])**2) )
+    dl_x = ( Tx[-1][0,1] - Tx[0][0,0] ) / dl_len
+    dl_y = ( Tx[-1][1,1] - Tx[0][1,0]  ) / dl_len
+    #azm =  np.arctan(dl_y/dl_x)
+
+    #Set boundary conditions
+    mesh.setCellGradBC('neumann')
+
+    # Define the linear system needed for the DC problem. We assume an infitite
+    # line source for simplicity.
+    Div = mesh.faceDiv
+    Grad = mesh.cellGrad
+    Msig = Utils.sdiag(1./(mesh.aveF2CC.T*(1./model)))
+
+    A = Div*Msig*Grad
+
+    # Change one corner to deal with nullspace
+    A[0,0] = 1
+    A = sp.csc_matrix(A)
+
+    # We will solve the system iteratively, so a pre-conditioner is helpful
+    # This is simply a Jacobi preconditioner (inverse of the main diagonal)
+    dA = A.diagonal()
+    P = sp.spdiags(1/dA,0,A.shape[0],A.shape[0])
+
+    # Now we can solve the system for all the transmitters
+    # We want to store the data
+    data = []
+
+    # There is probably a more elegant way to do this, but we can just for-loop through the transmitters
+    for ii in range(len(Tx)):
+
+        start_time = time.time() # Let's time the calculations
+
+        #print("Transmitter %i / %i\r" % (ii+1,len(Tx)))
+
+        # Select dipole locations for receiver
+        rxloc_M = np.asarray(Rx[ii][:,0:3])
+        rxloc_N = np.asarray(Rx[ii][:,3:])
+
+
+        # For usual cases "dpdp" or "gradient"
+        if stype == 'pdp':
+            # Create an "inifinity" pole
+            tx =  np.squeeze(Tx[ii][:,0:1])
+            tinf = tx + np.array([dl_x,dl_y,0])*dl_len*2
+            inds = Utils.closestPoints(mesh, np.c_[tx,tinf].T)
+            RHS = mesh.getInterpolationMat(np.asarray(Tx[ii]).T, 'CC').T*( [-1] / mesh.vol[inds] )
+        else:
+            inds = Utils.closestPoints(mesh, np.asarray(Tx[ii]).T )
+            RHS = mesh.getInterpolationMat(np.asarray(Tx[ii]).T, 'CC').T*( [-1,1] / mesh.vol[inds] )
+
+        # Iterative Solve
+        Ainvb = sp.linalg.bicgstab(P*A,P*RHS, tol=1e-5)
+
+        # We now have the potential everywhere
+        phi = Utils.mkvc(Ainvb[0])
+
+        # Solve for phi on pole locations
+        P1 = mesh.getInterpolationMat(rxloc_M, 'CC')
+        P2 = mesh.getInterpolationMat(rxloc_N, 'CC')
+
+        # Compute the potential difference
+        dtemp = (P1*phi - P2*phi)*np.pi
+
+        data.append( dtemp )
+        print '\rTransmitter {0} of {1} -> Time:{2} sec'.format(ii,len(Tx),time.time()- start_time),
+
+    print 'Transmitter {0} of {1}'.format(ii,len(Tx))
+    print 'Forward completed'
+
+    # Let's just convert the 3D format into 2D (distance along line) and plot
+    survey2D = DC.convertObs_DC3D_to_2D(survey, np.ones(survey.nSrc) , 'Xloc')
+    survey2D.dobs =np.hstack(data)
+
+    if plotIt:
+        import matplotlib.pyplot as plt
+        fig = plt.figure(figsize=(7,7))
+        ax = plt.subplot(2,1,1, aspect='equal')
+        # Plot the location of the spheres for reference
+        circle1=plt.Circle((loc[0,0],loc[2,0]),radi[0],color='w',fill=False, lw=3)
+        circle2=plt.Circle((loc[0,1],loc[2,1]),radi[1],color='k',fill=False, lw=3)
+        ax.add_artist(circle1)
+        ax.add_artist(circle2)
+
+        dat = mesh.plotSlice(np.log10(model), ax =ax, normal = 'Y',
+                             ind = indy,grid=True, clim = np.log10([sig.min(),sig.max()]))
+
+        ax.set_title('3-D model')
+        plt.gca().set_aspect('equal', adjustable='box')
+
+        plt.scatter(Tx[0][0,:],Tx[0][2,:],s=40,c='g', marker='v')
+        plt.scatter(Rx[0][:,0::3],Rx[0][:,2::3],s=40,c='y')
+        plt.xlim([-xlim,xlim])
+        plt.ylim([-zlim,mesh.vectorNz[-1]+dx])
+
+
+        pos =  ax.get_position()
+        ax.set_position([pos.x0 , pos.y0 + 0.025 ,  pos.width, pos.height])
+        pos =  ax.get_position()
+        cbarax = fig.add_axes([pos.x0 , pos.y0 + 0.025 ,  pos.width, pos.height * 0.04])  ## the parameters are the specified position you set
+        cb = fig.colorbar(dat[0],cax=cbarax, orientation="horizontal",
+                          ax = ax, ticks=np.linspace(np.log10(sig.min()),
+                         np.log10(sig.max()), 3), format="$10^{%.1f}$")
+        cb.set_label("Conductivity (S/m)",size=12)
+        cb.ax.tick_params(labelsize=12)
+
+        # Second plot for the predicted apparent resistivity data
+        ax2 = plt.subplot(2,1,2, aspect='equal')
+
+        # Plot the location of the spheres for reference
+        circle1=plt.Circle((loc[0,0],loc[2,0]),radi[0],color='w',fill=False, lw=3)
+        circle2=plt.Circle((loc[0,1],loc[2,1]),radi[1],color='k',fill=False, lw=3)
+        ax2.add_artist(circle1)
+        ax2.add_artist(circle2)
+
+        # Add the speudo section
+        dat = DC.plot_pseudoSection(survey2D,ax2,stype=stype, dtype = dtype)
+
+        # plt.scatter(Tx2d[0][:],Tx[0][2,:],s=40,c='g', marker='v')
+        # plt.scatter(Rx2d[0][:],Rx[0][:,2::3],s=40,c='y')
+        # plt.plot(np.r_[Tx2d[0][0],Rx2d[-1][-1,-1]],np.ones(2)*mesh.vectorNz[-1], color='k')
+        ax2.set_title('Apparent Conductivity data')
+
+        plt.ylim([-zlim,mesh.vectorNz[-1]+dx])
+        plt.show()
+
+        return fig, ax
+
+if __name__ == '__main__':
+    run()

SimPEG/Examples/EM_FDEM_1D_Inversion.py

@@ -21,8 +21,8 @@ def run(plotIt=True):
 
     active = mesh.vectorCCz<0.
     layer = (mesh.vectorCCz<0.) & (mesh.vectorCCz>=layerz)
-    actMap = Maps.ActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
-    mapping = Maps.ExpMap(mesh) * Maps.Vertical1DMap(mesh) * actMap
+    actMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
+    mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * actMap
     sig_half = 2e-2
     sig_air = 1e-8
     sig_layer = 1e-2
@@ -48,8 +48,7 @@ def run(plotIt=True):
     freqs = np.logspace(1,3,10)
     srcLoc = np.array([0., 0., 10.])
 
-    srcList = []
-    [srcList.append(EM.FDEM.Src.MagDipole([bzi],freq, srcLoc,orientation='Z')) for freq in freqs]
+    srcList = [EM.FDEM.Src.MagDipole([bzi],freq, srcLoc,orientation='Z') for freq in freqs]
 
     survey = EM.FDEM.Survey(srcList)
     prb = EM.FDEM.Problem_b(mesh, mapping=mapping)

SimPEG/Examples/EM_Schenkel_Morrison_Casing.py

@@ -0,0 +1,275 @@
+from SimPEG import *
+from SimPEG.EM import FDEM, Analytics, mu_0
+import time
+
+try:
+    from pymatsolver import MumpsSolver
+    solver = MumpsSolver
+except Exception:
+    solver = SolverLU
+    pass
+
+def run(plotIt=True):
+    """
+        EM: Schenkel and Morrison Casing Model
+        ======================================
+
+        Here we create and run a FDEM forward simulation to calculate the vertical
+        current inside a steel-cased. The model is based on the Schenkel and
+        Morrison Casing Model, and the results are used in a 2016 SEG abstract by
+        Yang et al.
+
+        - Schenkel, C.J., and H.F. Morrison, 1990, Effects of well casing on potential field measurements using downhole current sources: Geophysical prospecting, 38, 663-686.
+
+
+        The model consists of:
+        - Air: Conductivity 1e-8 S/m, above z = 0
+        - Background: conductivity 1e-2 S/m, below z = 0
+        - Casing: conductivity 1e6 S/m
+            - 300m long
+            - radius of 0.1m
+            - thickness of 6e-3m
+
+        Inside the casing, we take the same conductivity as the background.
+
+        We are using an EM code to simulate DC, so we use frequency low enough
+        that the skin depth inside the casing is longer than the casing length (f
+        = 1e-6 Hz). The plot produced is of the current inside the casing.
+
+        These results are shown in the SEG abstract by Yang et al., 2016: 3D DC
+        resistivity modeling of steel casing for reservoir monitoring using
+        equivalent resistor network. The solver used to produce these results and
+        achieve the CPU time of ~30s is Mumps, which was installed using pymatsolver_
+
+        .. _pymatsolver: https://github.com/rowanc1/pymatsolver
+
+        This example is on figshare: https://dx.doi.org/10.6084/m9.figshare.3126961.v1
+
+        If you would use this example for a code comparison, or build upon it, a
+        citation would be much appreciated!
+
+    """
+
+    if plotIt:
+        import matplotlib.pylab as plt
+
+    # ------------------ MODEL ------------------
+    sigmaair = 1e-8 # air
+    sigmaback = 1e-2 # background
+    sigmacasing = 1e6 # casing
+    sigmainside = sigmaback # inside the casing
+
+
+    casing_t = 0.006  # 1cm thickness
+    casing_l = 300   # length of the casing
+
+    casing_r = 0.1
+    casing_a = casing_r - casing_t/2. # inner radius
+    casing_b = casing_r + casing_t/2. # outer radius
+    casing_z = np.r_[-casing_l,0.]
+
+
+    # ------------------ SURVEY PARAMETERS ------------------
+    freqs = np.r_[1e-6] #[1e-1, 1, 5] # frequencies
+    dsz = -300 # down-hole z source location
+    src_loc = np.r_[0.,0.,dsz]
+    inf_loc = np.r_[0.,0.,1e4]
+
+    print 'Skin Depth: ', [(500./np.sqrt(sigmaback*_)) for _ in freqs]
+
+
+    # ------------------ MESH ------------------
+    # fine cells near well bore
+    csx1, csx2 = 2e-3, 60.
+    pfx1, pfx2 = 1.3, 1.3
+    ncx1 = np.ceil(casing_b/csx1+2)
+
+    # pad nicely to second cell size
+    npadx1 = np.floor(np.log(csx2/csx1) / np.log(pfx1))
+    hx1a,hx1b = Utils.meshTensor([(csx1,ncx1)]),Utils.meshTensor([(csx1,npadx1,pfx1)])
+    dx1 = sum(hx1a)+sum(hx1b)
+    dx1 = np.floor(dx1/csx2)
+    hx1b *= (dx1*csx2 - sum(hx1a))/sum(hx1b)
+
+    # second chunk of mesh
+    dx2 = 300. # uniform mesh out to here
+    ncx2 = np.ceil((dx2 - dx1)/csx2)
+    npadx2 = 45
+    hx2a, hx2b = Utils.meshTensor([(csx2,ncx2)]), Utils.meshTensor([(csx2,npadx2,pfx2)])
+    hx = np.hstack([hx1a,hx1b,hx2a,hx2b])
+
+    # z-direction
+    csz = 0.05
+    nza = 10
+    ncz, npadzu, npadzd = np.int(np.ceil(np.diff(casing_z)[0]/csz))+10, 68, 68 # cell size, number of core cells, number of padding cells in the x- direction
+    hz = Utils.meshTensor([(csz,npadzd,-1.3), (csz,ncz), (csz,npadzu,1.3)]) # vector of cell widths in the z-direction
+
+    # Mesh
+    mesh = Mesh.CylMesh([hx,1.,hz], [0.,0.,-np.sum(hz[:npadzu+ncz-nza])])
+
+    print 'Mesh Extent xmax: %f,: zmin: %f, zmax: %f'%(mesh.vectorCCx.max(), mesh.vectorCCz.min(), mesh.vectorCCz.max())
+    print 'Number of cells', mesh.nC
+
+    if plotIt is True:
+        fig, ax = plt.subplots(1, 1, figsize=(6, 4))
+        ax.set_title('Simulation Mesh')
+        mesh.plotGrid(ax=ax)
+        plt.show()
+
+    # Put the model on the mesh
+    sigWholespace = sigmaback*np.ones((mesh.nC))
+
+    sigBack = sigWholespace.copy()
+    sigBack[mesh.gridCC[:,2] > 0.] = sigmaair
+
+    sigCasing = sigBack.copy()
+    iCasingZ = (mesh.gridCC[:,2] <= casing_z[1]) & (mesh.gridCC[:,2] >= casing_z[0])
+    iCasingX = (mesh.gridCC[:,0] >= casing_a) & (mesh.gridCC[:,0] <= casing_b)
+    iCasing = iCasingX & iCasingZ
+    sigCasing[iCasing] = sigmacasing
+
+
+    if plotIt is True:
+
+        # plotting parameters
+        xlim = np.r_[0., 0.2]
+        zlim = np.r_[-350., 10.]
+        clim_sig = np.r_[-8,6]
+
+        # plot models
+        fig, ax = plt.subplots(1,1,figsize=(4,4))
+
+        f = plt.colorbar(mesh.plotImage(np.log10(sigCasing),ax=ax)[0], ax=ax)
+        ax.grid(which='both')
+        ax.set_title('Log_10 (Sigma)')
+        ax.set_xlim(xlim)
+        ax.set_ylim(zlim)
+        f.set_clim(clim_sig)
+
+        plt.show()
+
+
+    # -------------- Sources --------------------
+    # Define Custom Current Sources
+
+    # surface source
+    sg_x = np.zeros(mesh.vnF[0],dtype=complex)
+    sg_y = np.zeros(mesh.vnF[1],dtype=complex)
+    sg_z = np.zeros(mesh.vnF[2],dtype=complex)
+
+    nza = 2 # put the wire two cells above the surface
+    ncin = 2
+
+    # vertically directed wire
+    sgv_indx = (mesh.gridFz[:,0] > casing_a) & (mesh.gridFz[:,0] < casing_a + csx1)  # hook it up to casing at the surface
+    sgv_indz = (mesh.gridFz[:,2] <= +csz*nza) & (mesh.gridFz[:,2] >= -csz*2)
+    sgv_ind = sgv_indx & sgv_indz
+    sg_z[sgv_ind] = -1.
+
+    # horizontally directed wire
+    sgh_indx = (mesh.gridFx[:,0] > casing_a)    & (mesh.gridFx[:,0] <= inf_loc[2])
+    sgh_indz = (mesh.gridFx[:,2] > csz*(nza-0.5)) & (mesh.gridFx[:,2] < csz*(nza+0.5))
+    sgh_ind = sgh_indx & sgh_indz
+    sg_x[sgh_ind] = -1.
+
+    sgv2_indx = (mesh.gridFz[:,0] >= mesh.gridFx[sgh_ind,0].max()) & (mesh.gridFz[:,0] <= inf_loc[2]*1.2)  # hook it up to casing at the surface
+    sgv2_indz = (mesh.gridFz[:,2] <= +csz*nza) & (mesh.gridFz[:,2] >= -csz*2)
+    sgv2_ind = sgv2_indx & sgv2_indz
+    sg_z[sgv2_ind] = 1.
+
+    # assemble the source
+    sg = np.hstack([sg_x,sg_y,sg_z])
+    sg_p = [FDEM.Src.RawVec_e([],_,sg/mesh.area) for _ in freqs]
+
+    # downhole source
+    dg_x = np.zeros(mesh.vnF[0],dtype=complex)
+    dg_y = np.zeros(mesh.vnF[1],dtype=complex)
+    dg_z = np.zeros(mesh.vnF[2],dtype=complex)
+
+    # vertically directed wire
+    dgv_indx = (mesh.gridFz[:,0] < csx1)  # go through the center of the well
+    dgv_indz = (mesh.gridFz[:,2] <= +csz*nza) & (mesh.gridFz[:,2] > dsz + csz/2.)
+    dgv_ind = dgv_indx & dgv_indz
+    dg_z[dgv_ind] = -1.
+
+    # couple to the casing downhole
+    dgh_indx = mesh.gridFx[:,0] < casing_a + csx1
+    dgh_indz = (mesh.gridFx[:,2] < dsz + csz)  & (mesh.gridFx[:,2] >= dsz)
+    dgh_ind = dgh_indx & dgh_indz
+    dg_x[dgh_ind] = 1.
+
+    # horizontal part at surface
+    dgh2_indx = mesh.gridFx[:,0] <= inf_loc[2]*1.2
+    dgh2_indz = sgh_indz.copy()
+    dgh2_ind = dgh2_indx & dgh2_indz
+    dg_x[dgh2_ind] = -1.
+
+    # vertical part at surface
+    dgv2_ind = sgv2_ind.copy()
+    dg_z[dgv2_ind] = 1.
+
+    # assemble the source
+    dg = np.hstack([dg_x,dg_y,dg_z])
+    dg_p = [FDEM.Src.RawVec_e([],_,dg/mesh.area) for _ in freqs]
+
+    # ------------ Problem and Survey ---------------
+    survey = FDEM.Survey(sg_p + dg_p)
+    mapping = [('sigma', Maps.IdentityMap(mesh))]
+    problem = FDEM.Problem_h(mesh, mapping=mapping)
+    problem.pair(survey)
+
+    # ------------- Solve ---------------------------
+    t0 = time.time()
+    fieldsCasing = problem.fields(sigCasing)
+    print 'Time to solve 2 sources', time.time() - t0
+
+    # Plot current
+
+    # current density
+    jn0 = fieldsCasing[dg_p,'j']
+    jn1 = fieldsCasing[sg_p,'j']
+
+    # current
+    in0 = [mesh.area*fieldsCasing[dg_p,'j'][:,i] for i in range(len(freqs))]
+    in1 = [mesh.area*fieldsCasing[sg_p,'j'][:,i] for i in range(len(freqs))]
+
+    in0 = np.vstack(in0).T
+    in1 = np.vstack(in1).T
+
+    # integrate to get z-current inside casing
+    inds_inx = (mesh.gridFz[:,0] >= casing_a) & (mesh.gridFz[:,0] <= casing_b)
+    inds_inz = (mesh.gridFz[:,2] >= dsz )     & (mesh.gridFz[:,2] <= 0)
+    inds_fz = inds_inx & inds_inz
+
+    indsx = [False]*mesh.nFx
+    inds = list(indsx) + list(inds_fz)
+
+    in0_in = in0[np.r_[inds]]
+    in1_in = in1[np.r_[inds]]
+    z_in = mesh.gridFz[inds_fz,2]
+
+    in0_in = in0_in.reshape([in0_in.shape[0]/3,3])
+    in1_in = in1_in.reshape([in1_in.shape[0]/3,3])
+    z_in = z_in.reshape([z_in.shape[0]/3,3])
+
+    I0 = in0_in.sum(1).real
+    I1 = in1_in.sum(1).real
+    z_in = z_in[:,0]
+
+    if plotIt is True:
+        fig, ax = plt.subplots(1,2,figsize=(12,4))
+
+        ax[0].plot(z_in,np.absolute(I0), z_in,np.absolute(I1))
+        ax[0].legend(['top casing', 'bottom casing'],loc='best')
+        ax[0].set_title('Magnitude of Vertical Current in Casing')
+
+        ax[1].semilogy(z_in,np.absolute(I0), z_in,np.absolute(I1))
+        ax[1].legend(['top casing', 'bottom casing'],loc='best')
+        ax[1].set_title('Magnitude of Vertical Current in Casing')
+        ax[1].set_ylim([1e-2, 1.])
+
+        plt.show()
+
+if __name__ == '__main__':
+    run()
+

SimPEG/Examples/EM_TDEM_1D_Inversion.py

@@ -19,8 +19,8 @@ def run(plotIt=True):
 
     active = mesh.vectorCCz<0.
     layer = (mesh.vectorCCz<0.) & (mesh.vectorCCz>=-100.)
-    actMap = Maps.ActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
-    mapping = Maps.ExpMap(mesh) * Maps.Vertical1DMap(mesh) * actMap
+    actMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
+    mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * actMap
     sig_half = 2e-3
     sig_air = 1e-8
     sig_layer = 1e-3

SimPEG/Examples/Inversion_IRLS.py

@@ -0,0 +1,132 @@
+from SimPEG import *
+
+
+def run(N=200, plotIt=True):
+    """
+        Inversion: Linear Problem
+        =========================
+
+        Here we go over the basics of creating a linear problem and inversion.
+
+    """
+
+
+    np.random.seed(1)
+
+    std_noise = 1e-2
+
+    mesh = Mesh.TensorMesh([N])
+
+    m0 = np.ones(mesh.nC) * 1e-4
+    nk = 10
+    jk = np.linspace(1.,nk,nk)
+    p = -2.
+    q = 1.
+
+    g = lambda k: np.exp(p*jk[k]*mesh.vectorCCx)*np.cos(np.pi*q*jk[k]*mesh.vectorCCx)
+
+    G = np.empty((nk, mesh.nC))
+
+    for i in range(nk):
+        G[i,:] = g(i)
+
+    mtrue = np.zeros(mesh.nC)
+    mtrue[mesh.vectorCCx > 0.3] = 1.
+    mtrue[mesh.vectorCCx > 0.45] = -0.5
+    mtrue[mesh.vectorCCx > 0.6] = 0
+
+
+    prob = Problem.LinearProblem(mesh, G)
+    survey = Survey.LinearSurvey()
+    survey.pair(prob)
+    survey.dobs = prob.fields(mtrue) + std_noise * np.random.randn(nk)
+    #survey.makeSyntheticData(mtrue, std=std_noise)
+
+    wd = np.ones(nk) * std_noise
+
+    #print survey.std[0]
+    #M = prob.mesh
+    # Distance weighting
+    wr = np.sum(prob.G**2.,axis=0)**0.5
+    wr = ( wr/np.max(wr) )
+
+    reg = Regularization.Simple(mesh)
+    reg.wght = wr
+
+    dmis = DataMisfit.l2_DataMisfit(survey)
+    dmis.Wd = 1./wd
+
+    opt = Optimization.ProjectedGNCG(maxIter=30,lower=-2.,upper=2., maxIterCG= 20, tolCG = 1e-4)
+    invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
+    invProb.curModel = m0
+
+    beta = Directives.BetaSchedule(coolingFactor=2, coolingRate=1)
+    target = Directives.TargetMisfit()
+
+    betaest = Directives.BetaEstimate_ByEig()
+    inv = Inversion.BaseInversion(invProb, directiveList=[beta, betaest, target])
+
+
+    mrec = inv.run(m0)
+    ml2 = mrec
+    print "Final misfit:" + str(invProb.dmisfit.eval(mrec))
+
+    # Switch regularization to sparse
+    phim = invProb.phi_m_last
+    phid =  invProb.phi_d
+
+    reg = Regularization.Sparse(mesh)
+
+#==============================================================================
+#     fig, axes = plt.subplots(1,2,figsize=(12*1.2,4*1.2))
+#     dmdx = reg.mesh.cellDiffxStencil * mrec
+#     plt.plot(np.sort(dmdx))
+#==============================================================================
+
+    #reg.recModel = mrec
+    reg.wght = np.ones(mesh.nC)
+    reg.mref = np.zeros(mesh.nC)
+    reg.eps_p = 5e-2
+    reg.eps_q = 1e-2
+    reg.norms   = [0., 0., 2., 2.]
+    reg.wght = wr
+
+    opt = Optimization.ProjectedGNCG(maxIter=10 ,lower=-2.,upper=2., maxIterLS = 20, maxIterCG= 20, tolCG = 1e-3)
+    invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta = invProb.beta*2.)
+    beta = Directives.BetaSchedule(coolingFactor=1, coolingRate=1)
+    #betaest = Directives.BetaEstimate_ByEig()
+    target = Directives.TargetMisfit()
+    IRLS =Directives.Update_IRLS( phi_m_last = phim, phi_d_last = phid )
+
+    inv = Inversion.BaseInversion(invProb, directiveList=[beta,IRLS])
+
+    m0 = mrec
+
+    # Run inversion
+    mrec = inv.run(m0)
+
+    print "Final misfit:" + str(invProb.dmisfit.eval(mrec))
+
+
+    if plotIt:
+        import matplotlib.pyplot as plt
+
+        fig, axes = plt.subplots(1,2,figsize=(12*1.2,4*1.2))
+        for i in range(prob.G.shape[0]):
+            axes[0].plot(prob.G[i,:])
+        axes[0].set_title('Columns of matrix G')
+
+        axes[1].plot(mesh.vectorCCx, mtrue, 'b-')
+        axes[1].plot(mesh.vectorCCx, ml2, 'r-')
+        #axes[1].legend(('True Model', 'Recovered Model'))
+        axes[1].set_ylim(-1.0,1.25)
+
+        axes[1].plot(mesh.vectorCCx, mrec, 'k-',lw = 2)
+        axes[1].legend(('True Model', 'Smooth l2-l2',
+        'Sparse lp:' + str(reg.norms[0]) + ', lqx:' + str(reg.norms[1]) ), fontsize = 12)
+        plt.show()
+
+    return prob, survey, mesh, mrec
+
+if __name__ == '__main__':
+    run()

SimPEG/Examples/Inversion_Linear.py

@@ -10,28 +10,6 @@ def run(N=100, plotIt=True):
 
     """
 
-    class LinearSurvey(Survey.BaseSurvey):
-        def projectFields(self, u):
-            return u
-
-    class LinearProblem(Problem.BaseProblem):
-
-        surveyPair = LinearSurvey
-
-        def __init__(self, mesh, G, **kwargs):
-            Problem.BaseProblem.__init__(self, mesh, **kwargs)
-            self.G = G
-
-        def fields(self, m, u=None):
-            return self.G.dot(m)
-
-        def Jvec(self, m, v, u=None):
-            return self.G.dot(v)
-
-        def Jtvec(self, m, v, u=None):
-            return self.G.T.dot(v)
-
-
     np.random.seed(1)
 
     mesh = Mesh.TensorMesh([N])
@@ -53,8 +31,8 @@ def run(N=100, plotIt=True):
     mtrue[mesh.vectorCCx > 0.45] = -0.5
     mtrue[mesh.vectorCCx > 0.6] = 0
 
-    prob = LinearProblem(mesh, G)
-    survey = LinearSurvey()
+    prob = Problem.LinearProblem(mesh, G)
+    survey = Survey.LinearSurvey()
     survey.pair(prob)
     survey.makeSyntheticData(mtrue, std=0.01)
 

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.mrefInSmooth = 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.eval(fields)
+
+    # Make the data
+    mtData = MT.Data(survey,dataVec)
+    # Add plots
+    if plotIt:
+        pass
+
+if __name__ == '__main__':
+    run()

SimPEG/Examples/__init__.py

@@ -1,11 +1,15 @@
 # Run this file to add imports.
 
 ##### AUTOIMPORTS #####
+import DC_Analytic_Dipole
+import DC_Forward_PseudoSection
 import EM_FDEM_1D_Inversion
 import EM_FDEM_Analytic_MagDipoleWholespace
+import EM_Schenkel_Morrison_Casing
 import EM_TDEM_1D_Inversion
 import FLOW_Richards_1D_Celia1990
 import Forward_BasicDirectCurrent
+import Inversion_IRLS
 import Inversion_Linear
 import Mesh_Basic_PlotImage
 import Mesh_Basic_Types
@@ -14,8 +18,10 @@ 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__ = ["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_Schenkel_Morrison_Casing", "EM_TDEM_1D_Inversion", "FLOW_Richards_1D_Celia1990", "Forward_BasicDirectCurrent", "Inversion_IRLS", "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/FLOW/Richards/RichardsProblem.py

@@ -8,7 +8,7 @@ class RichardsRx(Survey.BaseTimeRx):
 
     knownRxTypes = ['saturation','pressureHead']
 
-    def projectFields(self, U, m, mapping, mesh, timeMesh):
+    def eval(self, U, m, mapping, mesh, timeMesh):
 
         if self.rxType == 'pressureHead':
             u = np.concatenate(U)
@@ -17,7 +17,7 @@ class RichardsRx(Survey.BaseTimeRx):
 
         return self.getP(mesh, timeMesh) * u
 
-    def projectFieldsDeriv(self, U, m, mapping, mesh, timeMesh):
+    def evalDeriv(self, U, m, mapping, mesh, timeMesh):
 
         P = self.getP(mesh, timeMesh)
         if self.rxType == 'pressureHead':
@@ -45,25 +45,25 @@ class RichardsSurvey(Survey.BaseSurvey):
 
     @Utils.count
     @Utils.requires('prob')
-    def dpred(self, m, u=None):
+    def dpred(self, m, f=None):
         """
             Create the projected data from a model.
-            The field, u, (if provided) will be used for the predicted data
+            The field, f, (if provided) will be used for the predicted data
             instead of recalculating the fields (which may be expensive!).
 
             .. math::
-                d_\\text{pred} = P(u(m), m)
+                d_\\text{pred} = P(f(m), m)
 
             Where P is a projection of the fields onto the data space.
         """
-        if u is None: u = self.prob.fields(m)
-        return Utils.mkvc(self.projectFields(u, m))
+        if f is None: f = self.prob.fields(m)
+        return Utils.mkvc(self.eval(f, m))
 
     @Utils.requires('prob')
-    def projectFields(self, U, m):
+    def eval(self, U, m):
         Ds = range(len(self.rxList))
         for ii, rx in enumerate(self.rxList):
-            Ds[ii] = rx.projectFields(U, m,
+            Ds[ii] = rx.eval(U, m,
                                 self.prob.mapping,
                                 self.prob.mesh,
                                 self.prob.timeMesh)
@@ -71,11 +71,11 @@ class RichardsSurvey(Survey.BaseSurvey):
         return np.concatenate(Ds)
 
     @Utils.requires('prob')
-    def projectFieldsDeriv(self, U, m):
+    def evalDeriv(self, U, m):
         """The Derivative with respect to the fields."""
         Ds = range(len(self.rxList))
         for ii, rx in enumerate(self.rxList):
-            Ds[ii] = rx.projectFieldsDeriv(U, m,
+            Ds[ii] = rx.evalDeriv(U, m,
                                 self.prob.mapping,
                                 self.prob.mesh,
                                 self.prob.timeMesh)
@@ -233,16 +233,16 @@ class RichardsProblem(Problem.BaseTimeProblem):
         return r, J
 
     @Utils.timeIt
-    def Jfull(self, m, u=None):
-        if u is None:
-            u = self.fields(m)
+    def Jfull(self, m, f=None):
+        if f is None:
+            f = self.fields(m)
 
-        nn = len(u)-1
+        nn = len(f)-1
         Asubs, Adiags, Bs = range(nn), range(nn), range(nn)
         for ii in range(nn):
             dt = self.timeSteps[ii]
-            bc = self.getBoundaryConditions(ii, u[ii])
-            Asubs[ii], Adiags[ii], Bs[ii] = self.diagsJacobian(m, u[ii], u[ii+1], dt, bc)
+            bc = self.getBoundaryConditions(ii, f[ii])
+            Asubs[ii], Adiags[ii], Bs[ii] = self.diagsJacobian(m, f[ii], f[ii+1], dt, bc)
         Ad = sp.block_diag(Adiags)
         zRight = Utils.spzeros((len(Asubs)-1)*Asubs[0].shape[0],Adiags[0].shape[1])
         zTop = Utils.spzeros(Adiags[0].shape[0], len(Adiags)*Adiags[0].shape[1])
@@ -251,7 +251,7 @@ class RichardsProblem(Problem.BaseTimeProblem):
         B = np.array(sp.vstack(Bs).todense())
 
         Ainv = self.Solver(A, **self.solverOpts)
-        P = self.survey.projectFieldsDeriv(u, m)
+        P = self.survey.evalDeriv(f, m)
         AinvB = Ainv * B
         z = np.zeros((self.mesh.nC, B.shape[1]))
         zAinvB = np.vstack((z, AinvB))
@@ -259,41 +259,41 @@ class RichardsProblem(Problem.BaseTimeProblem):
         return J
 
     @Utils.timeIt
-    def Jvec(self, m, v, u=None):
-        if u is None:
-            u = self.fields(m)
+    def Jvec(self, m, v, f=None):
+        if f is None:
+            f = self.fields(m)
 
-        JvC = range(len(u)-1) # Cell to hold each row of the long vector.
+        JvC = range(len(f)-1) # Cell to hold each row of the long vector.
 
         # This is done via forward substitution.
-        bc = self.getBoundaryConditions(0, u[0])
-        temp, Adiag, B = self.diagsJacobian(m, u[0], u[1], self.timeSteps[0], bc)
+        bc = self.getBoundaryConditions(0, f[0])
+        temp, Adiag, B = self.diagsJacobian(m, f[0], f[1], self.timeSteps[0], bc)
         Adiaginv = self.Solver(Adiag, **self.solverOpts)
         JvC[0] = Adiaginv * (B*v)
 
-        for ii in range(1,len(u)-1):
-            bc = self.getBoundaryConditions(ii, u[ii])
-            Asub, Adiag, B = self.diagsJacobian(m, u[ii], u[ii+1], self.timeSteps[ii], bc)
+        for ii in range(1,len(f)-1):
+            bc = self.getBoundaryConditions(ii, f[ii])
+            Asub, Adiag, B = self.diagsJacobian(m, f[ii], f[ii+1], self.timeSteps[ii], bc)
             Adiaginv = self.Solver(Adiag, **self.solverOpts)
             JvC[ii] = Adiaginv * (B*v - Asub*JvC[ii-1])
 
-        P = self.survey.projectFieldsDeriv(u, m)
+        P = self.survey.evalDeriv(f, m)
         return P * np.concatenate([np.zeros(self.mesh.nC)] + JvC)
 
     @Utils.timeIt
-    def Jtvec(self, m, v, u=None):
-        if u is None:
-            u = self.field(m)
+    def Jtvec(self, m, v, f=None):
+        if f is None:
+            f = self.field(m)
 
-        P = self.survey.projectFieldsDeriv(u, m)
+        P = self.survey.evalDeriv(f, m)
         PTv = P.T*v
 
         # This is done via backward substitution.
         minus = 0
         BJtv = 0
-        for ii in range(len(u)-1,0,-1):
-            bc = self.getBoundaryConditions(ii-1, u[ii-1])
-            Asub, Adiag, B = self.diagsJacobian(m, u[ii-1], u[ii], self.timeSteps[ii-1], bc)
+        for ii in range(len(f)-1,0,-1):
+            bc = self.getBoundaryConditions(ii-1, f[ii-1])
+            Asub, Adiag, B = self.diagsJacobian(m, f[ii-1], f[ii], self.timeSteps[ii-1], bc)
             #select the correct part of v
             vpart = range((ii)*Adiag.shape[0], (ii+1)*Adiag.shape[0])
             AdiaginvT = self.Solver(Adiag.T, **self.solverOpts)

SimPEG/InvProblem.py

@@ -82,23 +82,23 @@ class BaseInvProblem(object):
         self._warmstart = value
 
     def getFields(self, m, store=False, deleteWarmstart=True):
-        u = None
+        f = None
 
         for mtest, u_ofmtest in self.warmstart:
             if m is mtest:
-                u = u_ofmtest
+                f = u_ofmtest
                 if self.debug: print 'InvProb is Warm Starting!'
                 break
 
-        if u is None:
-            u = self.prob.fields(m)
+        if f is None:
+            f = self.prob.fields(m)
 
         if deleteWarmstart:
             self.warmstart = []
         if store:
-            self.warmstart += [(m,u)]
+            self.warmstart += [(m,f)]
 
-        return u
+        return f
 
     @Utils.timeIt
     def evalFunction(self, m, return_g=True, return_H=True):
@@ -109,21 +109,21 @@ class BaseInvProblem(object):
         gc.collect()
 
         # Store fields if doing a line-search
-        u = self.getFields(m, store=(return_g==False and return_H==False))
+        f = self.getFields(m, store=(return_g==False and return_H==False))
 
-        phi_d = self.dmisfit.eval(m, u=u)
+        phi_d = self.dmisfit.eval(m, f=f)
         phi_m = self.reg.eval(m)
 
-        self.dpred = self.survey.dpred(m, u=u)  # This is a cheap matrix vector calculation.
+        self.dpred = self.survey.dpred(m, f=f)  # This is a cheap matrix vector calculation.
 
         self.phi_d, self.phi_d_last  = phi_d, self.phi_d
         self.phi_m, self.phi_m_last  = phi_m, self.phi_m
 
-        f = phi_d + self.beta * phi_m
+        phi = phi_d + self.beta * phi_m
 
-        out = (f,)
+        out = (phi,)
         if return_g:
-            phi_dDeriv = self.dmisfit.evalDeriv(m, u=u)
+            phi_dDeriv = self.dmisfit.evalDeriv(m, f=f)
             phi_mDeriv = self.reg.evalDeriv(m)
 
             g = phi_dDeriv + self.beta * phi_mDeriv
@@ -131,7 +131,7 @@ class BaseInvProblem(object):
 
         if return_H:
             def H_fun(v):
-                phi_d2Deriv = self.dmisfit.eval2Deriv(m, v, u=u)
+                phi_d2Deriv = self.dmisfit.eval2Deriv(m, v, f=f)
                 phi_m2Deriv = self.reg.eval2Deriv(m, v=v)
 
                 return phi_d2Deriv + self.beta * phi_m2Deriv

SimPEG/Inversion.py

@@ -33,7 +33,9 @@ class BaseInversion(object):
         self._directiveList = value
         self._directiveList.inversion = self
 
-    def __init__(self, invProb, directiveList=[], **kwargs):
+    def __init__(self, invProb, directiveList=None, **kwargs):
+        if directiveList is None:
+            directiveList = []
         self.directiveList = directiveList
         Utils.setKwargs(self, **kwargs)
 

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, f=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 f is None:
+           f= 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.
+                f_src = f[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, f_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.evalDeriv(src, self.mesh, f, 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, f=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 f is None:
+            f = 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'
+                f_src = f[src, :]
+
+                for rx in src.rxList:
+                    # Get the adjoint evalDeriv
+                    # PTv needs to be nE,
+                    PTv = rx.evalDeriv(src, self.mesh, f, 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, f_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 eval(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 evalDeriv(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 eval(self, f):
+        data = Data(self)
+        for src in self.srcList:
+            sys.stdout.flush()
+            for rx in src.rxList:
+                data[src, rx] = rx.eval(src, self.mesh, f)
+        return data
+
+    def evalDeriv(self, f):
+        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 +1,180 @@
+# 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
+
+
+class EDIimporter:
+    """
+    A class to import EDIfiles.
+
+    """
+
+
+    # Define data converters
+    _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 # Project info
+    _2out = None    # The projection operator
+
+
+    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):
+        # Import the coordinate projections
+        try:
+            import osr
+        except ImportError as e:
+            print 'Could not import osr, missing the gdal package\nCan not project coordinates'
+            raise e
+        # 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/Maps.py

@@ -4,6 +4,7 @@ from Tests import checkDerivative
 from PropMaps import PropMap, Property
 from numpy.polynomial import polynomial
 from scipy.interpolate import UnivariateSpline
+import warnings
 
 class IdentityMap(object):
     """
@@ -296,11 +297,11 @@ class LogMap(IdentityMap):
     def inverse(self, m):
         return np.exp(Utils.mkvc(m))
 
-class FullMap(IdentityMap):
+class SurjectFull(IdentityMap):
     """
-    FullMap
+    SurjectFull
 
-    Given a scalar, the FullMap maps the value to the
+    Given a scalar, the SurjectFull maps the value to the
     full model space.
     """
 
@@ -327,9 +328,15 @@ class FullMap(IdentityMap):
         """
         return np.ones([self.mesh.nC,1])
 
+class FullMap(SurjectFull):
+    def __init__(self,mesh,**kwargs):
+        warnings.warn(
+            "`FullMap` is deprecated and will be removed in future versions. Use `SurjectFull` instead",
+            FutureWarning)
+        SurjectFull.__init__(self,mesh,**kwargs)
 
-class Vertical1DMap(IdentityMap):
-    """Vertical1DMap
+class SurjectVertical1D(IdentityMap):
+    """SurjectVertical1DMap
 
         Given a 1D vector through the last dimension
         of the mesh, this will extend to the full
@@ -369,8 +376,14 @@ class Vertical1DMap(IdentityMap):
                     ), shape=(repNum, 1))
         return sp.kron(sp.identity(self.nP), repVec)
 
+class Vertical1DMap(SurjectVertical1D):
+    def __init__(self,mesh,**kwargs):
+        warnings.warn(
+            "`Vertical1DMap` is deprecated and will be removed in future versions. Use `SurjectVertical1D` instead",
+            FutureWarning)
+        SurjectVertical1D.__init__(self,mesh,**kwargs)
 
-class Map2Dto3D(IdentityMap):
+class Surject2Dto3D(IdentityMap):
     """Map2Dto3D
 
         Given a 2D vector, this will extend to the full
@@ -425,6 +438,13 @@ class Map2Dto3D(IdentityMap):
                 ), shape=(nC, nP))
         return P
 
+class Map2Dto3D(Surject2Dto3D):
+    def __init__(self,mesh,**kwargs):
+        warnings.warn(
+            "`Map2Dto3D` is deprecated and will be removed in future versions. Use `Surject2Dto3D` instead",
+            FutureWarning)
+        Surject2Dto3D.__init__(self,mesh,**kwargs)
+
 class Mesh2Mesh(IdentityMap):
     """
         Takes a model on one mesh are translates it to another mesh.
@@ -458,7 +478,7 @@ class Mesh2Mesh(IdentityMap):
         return self.P
 
 
-class ActiveCells(IdentityMap):
+class InjectActiveCells(IdentityMap):
     """
         Active model parameters.
 
@@ -506,7 +526,14 @@ class ActiveCells(IdentityMap):
     def deriv(self, m):
         return self.P
 
-class ActiveCellsTopo(IdentityMap):
+class ActiveCells(InjectActiveCells):
+    def __init__(self, mesh, indActive, valInactive, nC=None):
+        warnings.warn(
+            "`ActiveCells` is deprecated and will be removed in future versions. Use `InjectActiveCells` instead",
+            FutureWarning)
+        InjectActiveCells.__init__(self, mesh, indActive, valInactive, nC)
+
+class InjectActiveCellsTopo(IdentityMap):
     """
         Active model parameters. Extend for cells on topography to air cell (only works for tensor mesh)
 
@@ -577,6 +604,12 @@ class ActiveCellsTopo(IdentityMap):
     def deriv(self, m):
         return self.P
 
+class ActiveCellsTopo(InjectActiveCellsTopo):
+    def __init__(self, mesh, indActive, valInactive, nC=None):
+        warnings.warn(
+            "`ActiveCellsTopo` is deprecated and will be removed in future versions. Use `InjectActiveCellsTopo` instead",
+            FutureWarning)
+        InjectActiveCellsTopo.__init__(self, mesh, indActive, valInactive, nC)
 
 class Weighting(IdentityMap):
     """
@@ -726,15 +759,29 @@ class PolyMap(IdentityMap):
 
             m = [\sigma_1, \sigma_2, c]
 
+        Can take in an actInd vector to account for topography.
+
     """
-    def __init__(self, mesh, order, logSigma=True, normal='X'):
+    def __init__(self, mesh, order, logSigma=True, normal='X', actInd = None):
         IdentityMap.__init__(self, mesh)
         self.logSigma = logSigma
         self.order = order
         self.normal = normal
+        self.actInd = actInd
+
+        if getattr(self, 'actInd', None) is None:
+            self.actInd = range(self.mesh.nC)
+            self.nC = self.mesh.nC
+
+        else:
+            self.nC = len(self.actInd)
 
     slope = 1e4
 
+    @property
+    def shape(self):
+        return (self.nC, self.nP)
+
     @property
     def nP(self):
         if np.isscalar(self.order):
@@ -752,8 +799,8 @@ class PolyMap(IdentityMap):
             sig1, sig2 = np.exp(sig1), np.exp(sig2)
         #2D
         if self.mesh.dim == 2:
-            X = self.mesh.gridCC[:,0]
-            Y = self.mesh.gridCC[:,1]
+            X = self.mesh.gridCC[self.actInd,0]
+            Y = self.mesh.gridCC[self.actInd,1]
             if self.normal =='X':
                 f = polynomial.polyval(Y, c) - X
             elif self.normal =='Y':
@@ -762,9 +809,9 @@ class PolyMap(IdentityMap):
                 raise(Exception("Input for normal = X or Y or Z"))
         #3D
         elif self.mesh.dim == 3:
-            X = self.mesh.gridCC[:,0]
-            Y = self.mesh.gridCC[:,1]
-            Z = self.mesh.gridCC[:,2]
+            X = self.mesh.gridCC[self.actInd,0]
+            Y = self.mesh.gridCC[self.actInd,1]
+            Z = self.mesh.gridCC[self.actInd,2]
             if self.normal =='X':
                 f = polynomial.polyval2d(Y, Z, c.reshape((self.order[0]+1,self.order[1]+1))) - X
             elif self.normal =='Y':
@@ -773,6 +820,7 @@ class PolyMap(IdentityMap):
                 f = polynomial.polyval2d(X, Y, c.reshape((self.order[0]+1,self.order[1]+1))) - Z
             else:
                 raise(Exception("Input for normal = X or Y or Z"))
+
         else:
             raise(Exception("Only supports 2D"))
 
@@ -786,8 +834,8 @@ class PolyMap(IdentityMap):
             sig1, sig2 = np.exp(sig1), np.exp(sig2)
         #2D
         if self.mesh.dim == 2:
-            X = self.mesh.gridCC[:,0]
-            Y = self.mesh.gridCC[:,1]
+            X = self.mesh.gridCC[self.actInd,0]
+            Y = self.mesh.gridCC[self.actInd,1]
 
             if self.normal =='X':
                 f = polynomial.polyval(Y, c) - X
@@ -799,9 +847,9 @@ class PolyMap(IdentityMap):
                 raise(Exception("Input for normal = X or Y or Z"))
         #3D
         elif self.mesh.dim == 3:
-            X = self.mesh.gridCC[:,0]
-            Y = self.mesh.gridCC[:,1]
-            Z = self.mesh.gridCC[:,2]
+            X = self.mesh.gridCC[self.actInd,0]
+            Y = self.mesh.gridCC[self.actInd,1]
+            Z = self.mesh.gridCC[self.actInd,2]
 
             if self.normal =='X':
                 f = polynomial.polyval2d(Y, Z, c.reshape((self.order[0]+1,self.order[1]+1))) - X

SimPEG/Mesh/DiffOperators.py

@@ -307,24 +307,28 @@ class DiffOperators(object):
         return BC
     _cellGradBC_list = 'neumann'
 
+    def _cellGradStencil(self):
+        BC = self.setCellGradBC(self._cellGradBC_list)
+        n = self.vnC
+        if(self.dim == 1):
+            G = ddxCellGrad(n[0], BC[0])
+        elif(self.dim == 2):
+            G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC[0]))
+            G2 = sp.kron(ddxCellGrad(n[1], BC[1]), speye(n[0]))
+            G = sp.vstack((G1, G2), format="csr")
+        elif(self.dim == 3):
+            G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC[0]))
+            G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC[1]), speye(n[0]))
+            G3 = kron3(ddxCellGrad(n[2], BC[2]), speye(n[1]), speye(n[0]))
+            G = sp.vstack((G1, G2, G3), format="csr")
+        return G
+
     def cellGrad():
         doc = "The cell centered Gradient, takes you to cell faces."
 
         def fget(self):
             if(self._cellGrad is None):
-                BC = self.setCellGradBC(self._cellGradBC_list)
-                n = self.vnC
-                if(self.dim == 1):
-                    G = ddxCellGrad(n[0], BC[0])
-                elif(self.dim == 2):
-                    G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC[0]))
-                    G2 = sp.kron(ddxCellGrad(n[1], BC[1]), speye(n[0]))
-                    G = sp.vstack((G1, G2), format="csr")
-                elif(self.dim == 3):
-                    G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC[0]))
-                    G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC[1]), speye(n[0]))
-                    G3 = kron3(ddxCellGrad(n[2], BC[2]), speye(n[1]), speye(n[0]))
-                    G = sp.vstack((G1, G2, G3), format="csr")
+                G = self._cellGradStencil()
                 # Compute areas of cell faces & volumes
                 S = self.area
                 V = self.aveCC2F*self.vol  # Average volume between adjacent cells
@@ -361,19 +365,24 @@ class DiffOperators(object):
     _cellGradBC = None
     cellGradBC = property(**cellGradBC())
 
+    def _cellGradxStencil(self):
+        BC = ['neumann', 'neumann']
+        n = self.vnC
+        if(self.dim == 1):
+            G1 = ddxCellGrad(n[0], BC)
+        elif(self.dim == 2):
+            G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC))
+        elif(self.dim == 3):
+            G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC))
+        return G1
+
+
     def cellGradx():
         doc = "Cell centered Gradient in the x dimension. Has neumann boundary conditions."
 
         def fget(self):
             if getattr(self, '_cellGradx', None) is None:
-                BC = ['neumann', 'neumann']
-                n = self.vnC
-                if(self.dim == 1):
-                    G1 = ddxCellGrad(n[0], BC)
-                elif(self.dim == 2):
-                    G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC))
-                elif(self.dim == 3):
-                    G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC))
+                G1 = self._cellGradxStencil()
                 # Compute areas of cell faces & volumes
                 V = self.aveCC2F*self.vol
                 L = self.r(self.area/V, 'F','Fx', 'V')
@@ -382,17 +391,22 @@ class DiffOperators(object):
         return locals()
     cellGradx = property(**cellGradx())
 
+    def _cellGradyStencil(self):
+        if self.dim < 2: return None
+        BC = ['neumann', 'neumann']
+        n = self.vnC
+        if(self.dim == 2):
+            G2 = sp.kron(ddxCellGrad(n[1], BC), speye(n[0]))
+        elif(self.dim == 3):
+            G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC), speye(n[0]))
+        return G2
+
     def cellGrady():
         doc = "Cell centered Gradient in the x dimension. Has neumann boundary conditions."
         def fget(self):
             if self.dim < 2: return None
             if getattr(self, '_cellGrady', None) is None:
-                BC = ['neumann', 'neumann']
-                n = self.vnC
-                if(self.dim == 2):
-                    G2 = sp.kron(ddxCellGrad(n[1], BC), speye(n[0]))
-                elif(self.dim == 3):
-                    G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC), speye(n[0]))
+                G2 = self._cellGradyStencil()
                 # Compute areas of cell faces & volumes
                 V = self.aveCC2F*self.vol
                 L = self.r(self.area/V, 'F','Fy', 'V')
@@ -401,14 +415,19 @@ class DiffOperators(object):
         return locals()
     cellGrady = property(**cellGrady())
 
+    def _cellGradzStencil(self):
+        if self.dim < 3: return None
+        BC = ['neumann', 'neumann']
+        n = self.vnC
+        G3 = kron3(ddxCellGrad(n[2], BC), speye(n[1]), speye(n[0]))
+        return G3
+
     def cellGradz():
         doc = "Cell centered Gradient in the x dimension. Has neumann boundary conditions."
         def fget(self):
             if self.dim < 3: return None
             if getattr(self, '_cellGradz', None) is None:
-                BC = ['neumann', 'neumann']
-                n = self.vnC
-                G3 = kron3(ddxCellGrad(n[2], BC), speye(n[1]), speye(n[0]))
+                G3 = self._cellGradzStencil()
                 # Compute areas of cell faces & volumes
                 V = self.aveCC2F*self.vol
                 L = self.r(self.area/V, 'F','Fz', 'V')
@@ -746,4 +765,3 @@ 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/Mesh/MeshIO.py

@@ -21,10 +21,9 @@ class TensorMeshIO(object):
                 if '*' in seg:
                     st = seg
                     sp = seg.split('*')
-                    re = np.array(sp[0],dtype=int)*(' ' + sp[1])
+                    re = int(sp[0])*(' ' + sp[1])
                     line = line.replace(st,re.strip())
             return np.array(line.split(),dtype=float)
-
         # Read the file as line strings, remove lines with comment = !
         msh = np.genfromtxt(fileName,delimiter='\n',dtype=np.str,comments='!')
 

SimPEG/Mesh/TensorMesh.py

@@ -234,6 +234,9 @@ class BaseTensorMesh(BaseMesh):
             'Fz'    -> z-component of field defined on faces
             'N'     -> scalar field defined on nodes
             'CC'    -> scalar field defined on cell centers
+            'CCVx'  -> x-component of vector field defined on cell centers
+            'CCVy'  -> y-component of vector field defined on cell centers
+            'CCVz'  -> z-component of vector field defined on cell centers
         """
         if self._meshType == 'CYL' and self.isSymmetric and locType in ['Ex','Ez','Fy']:
             raise Exception('Symmetric CylMesh does not support %s interpolation, as this variable does not exist.' % locType)
@@ -257,6 +260,16 @@ class BaseTensorMesh(BaseMesh):
             Q = sp.hstack(components)
         elif locType in ['CC', 'N']:
             Q = Utils.interpmat(loc, *self.getTensor(locType))
+        elif locType in ['CCVx', 'CCVy', 'CCVz']:
+            Q = Utils.interpmat(loc, *self.getTensor('CC'))
+            Z = Utils.spzeros(loc.shape[0],self.nC)
+            if locType == 'CCVx':
+                Q = sp.hstack([Q,Z,Z])
+            elif locType == 'CCVy':
+                Q = sp.hstack([Z,Q,Z])
+            elif locType == 'CCVz':
+                Q = sp.hstack([Z,Z,Q])
+
         else:
             raise NotImplementedError('getInterpolationMat: locType=='+locType+' and mesh.dim=='+str(self.dim))
 

SimPEG/Mesh/TreeMesh.py

@@ -2131,10 +2131,16 @@ class TreeMesh(BaseTensorMesh, InnerProducts, TreeMeshIO):
     def plotSlice(self, v, vType='CC',
         normal='Z', ind=None, grid=True, view='real',
         ax=None, clim=None, showIt=False,
-        pcolorOpts={},
-        streamOpts={'color':'k'},
-        gridOpts={'color':'k', 'alpha':0.5}):
+        pcolorOpts=None,
+        streamOpts=None,
+        gridOpts=None):
 
+        if pcolorOpts is None:
+            pcolorOpts = {}
+        if streamOpts is None:
+            streamOpts = {'color':'k'}
+        if gridOpts is None:
+            gridOpts = {'color':'k', 'alpha':0.5}
         assert vType in ['CC','F','E']
         assert self.dim == 3
 

SimPEG/Mesh/View.py

@@ -42,9 +42,9 @@ class TensorView(object):
 
     def plotImage(self, v, vType='CC', grid=False, view='real',
               ax=None, clim=None, showIt=False,
-              pcolorOpts={},
-              streamOpts={'color':'k'},
-              gridOpts={'color':'k'},
+              pcolorOpts=None,
+              streamOpts=None,
+              gridOpts=None,
               numbering=True, annotationColor='w'
               ):
         """
@@ -84,6 +84,12 @@ class TensorView(object):
             M.plotImage(v, annotationColor='k', showIt=True)
 
         """
+        if pcolorOpts is None:
+            pcolorOpts = {}
+        if streamOpts is None:
+            streamOpts = {'color':'k'}
+        if gridOpts is None:
+            gridOpts = {'color':'k'}
 
         if ax is None:
             fig = plt.figure()
@@ -174,9 +180,9 @@ class TensorView(object):
     def plotSlice(self, v, vType='CC',
                   normal='Z', ind=None, grid=False, view='real',
                   ax=None, clim=None, showIt=False,
-                  pcolorOpts={},
-                  streamOpts={'color':'k'},
-                  gridOpts={'color':'k', 'alpha':0.5}
+                  pcolorOpts=None,
+                  streamOpts=None,
+                  gridOpts=None
                   ):
 
         """
@@ -197,6 +203,12 @@ class TensorView(object):
             M.plotSlice(M.cellGrad*b, 'F', view='vec', grid=True, showIt=True, pcolorOpts={'alpha':0.8})
 
         """
+        if pcolorOpts is None:
+            pcolorOpts = {}
+        if streamOpts is None:
+            streamOpts = {'color':'k'}
+        if gridOpts is None:
+            gridOpts = {'color':'k', 'alpha':0.5}
         if type(vType) in [list, tuple]:
             assert ax is None, "cannot specify an axis to plot on with this function."
             fig, axs = plt.subplots(1,len(vType))
@@ -289,11 +301,17 @@ class TensorView(object):
 
     def _plotImage2D(self, v, vType='CC', grid=False, view='real',
               ax=None, clim=None, showIt=False,
-              pcolorOpts={},
-              streamOpts={'color':'k'},
-              gridOpts={'color':'k'}
+              pcolorOpts=None,
+              streamOpts=None,
+              gridOpts=None
               ):
 
+        if pcolorOpts is None:
+            pcolorOpts = {}
+        if streamOpts is None:
+            streamOpts = {'color':'k'}
+        if gridOpts is None:
+            gridOpts = {'color':'k'}
         vTypeOptsCC = ['N','CC','Fx','Fy','Ex','Ey']
         vTypeOptsV = ['CCv','F','E']
         vTypeOpts = vTypeOptsCC + vTypeOptsV

SimPEG/Optimization.py

@@ -888,6 +888,8 @@ class ProjectedGNCG(BFGS, Minimize, Remember):
     maxIterCG = 5
     tolCG = 1e-1
 
+    stepOffBoundsFact = 0.1 # perturbation of the inactive set off the bounds
+
     lower = -np.inf
     upper = np.inf
 
@@ -990,4 +992,20 @@ 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) )
+
+                # perturb inactive set off of bounds so that they are included in the step
+                delx = delx + self.stepOffBoundsFact * (rhs_a * dm_i / dm_a)
+
+
+            # 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/Problem.py

@@ -88,28 +88,28 @@ class BaseProblem(object):
         return self.survey is not None
 
     @Utils.timeIt
-    def Jvec(self, m, v, u=None):
-        """Jvec(m, v, u=None)
+    def Jvec(self, m, v, f=None):
+        """Jvec(m, v, f=None)
 
             Effect of J(m) on a vector v.
 
             :param numpy.array m: model
             :param numpy.array v: vector to multiply
-            :param numpy.array u: fields
+            :param Fields f: fields
             :rtype: numpy.array
             :return: Jv
         """
         raise NotImplementedError('J is not yet implemented.')
 
     @Utils.timeIt
-    def Jtvec(self, m, v, u=None):
-        """Jtvec(m, v, u=None)
+    def Jtvec(self, m, v, f=None):
+        """Jtvec(m, v, f=None)
 
             Effect of transpose of J(m) on a vector v.
 
             :param numpy.array m: model
             :param numpy.array v: vector to multiply
-            :param numpy.array u: fields
+            :param Fields f: fields
             :rtype: numpy.array
             :return: JTv
         """
@@ -117,32 +117,32 @@ class BaseProblem(object):
 
 
     @Utils.timeIt
-    def Jvec_approx(self, m, v, u=None):
-        """Jvec_approx(m, v, u=None)
+    def Jvec_approx(self, m, v, f=None):
+        """Jvec_approx(m, v, f=None)
 
             Approximate effect of J(m) on a vector v
 
             :param numpy.array m: model
             :param numpy.array v: vector to multiply
-            :param numpy.array u: fields
+            :param Fields f: fields
             :rtype: numpy.array
             :return: approxJv
         """
-        return self.Jvec(m, v, u)
+        return self.Jvec(m, v, f)
 
     @Utils.timeIt
-    def Jtvec_approx(self, m, v, u=None):
-        """Jtvec_approx(m, v, u=None)
+    def Jtvec_approx(self, m, v, f=None):
+        """Jtvec_approx(m, v, f=None)
 
             Approximate effect of transpose of J(m) on a vector v.
 
             :param numpy.array m: model
             :param numpy.array v: vector to multiply
-            :param numpy.array u: fields
+            :param Fields f: fields
             :rtype: numpy.array
             :return: JTv
         """
-        return self.Jtvec(m, v, u)
+        return self.Jtvec(m, v, f)
 
     def fields(self, m):
         """
@@ -213,5 +213,20 @@ class BaseTimeProblem(BaseProblem):
         if hasattr(self, '_timeMesh'):
             del self._timeMesh
 
+class LinearProblem(BaseProblem):
 
+    surveyPair = Survey.LinearSurvey
+
+    def __init__(self, mesh, G, **kwargs):
+        BaseProblem.__init__(self, mesh, **kwargs)
+        self.G = G
+
+    def fields(self, m):
+        return self.G.dot(m)
+
+    def Jvec(self, m, v, f=None):
+        return self.G.dot(v)
+
+    def Jtvec(self, m, v, f=None):
+        return self.G.T.dot(v)
 

SimPEG/PropMaps.py

@@ -12,7 +12,6 @@ class Property(object):
         # Set the default after all other params are set
         self.doc = doc
         Utils.setKwargs(self, **kwargs)
-        self._kwargs = kwargs
 
     @property
     def propertyLink(self):
@@ -111,11 +110,6 @@ class Property(object):
             return getattr(self.propMap, '_%sMap'%prop.name, None)
         return property(fget=fget)
 
-    def toJSON(self):
-        out = dict(doc=self.doc)
-        for k in self._kwargs:
-            out[k] = self._kwargs[k]
-        return out
 
 
 class PropModel(object):
@@ -195,12 +189,6 @@ class _PropMapMetaClass(type):
 
         return type(name.replace('PropMap', 'PropModel'), (PropModel, ), attrs)
 
-def fromPickle(name, properties, maps, slices):
-    attrs = dict()
-    for p in properties:
-        attrs[p] = Property(**properties[p])
-    PM = type(name, (PropMap,), attrs)
-    return PM(dict(maps=maps, slices=slices))
 
 class PropMap(object):
     __metaclass__ = _PropMapMetaClass
@@ -209,7 +197,6 @@ class PropMap(object):
         """
             PropMap takes a multi parameter model and maps it to the equivalent PropModel
         """
-
         if type(mappings) is dict:
             assert np.all([k in ['maps', 'slices'] for k in mappings]), 'Dict must only have properties "maps" and "slices"'
             self.setup(mappings['maps'], slices=mappings['slices'])
@@ -252,11 +239,7 @@ class PropMap(object):
             setattr(self, '%sMap'%name, mapping)
             setattr(self, '%sIndex'%name, slices.get(name, slice(nP, nP + mapping.nP)))
             nP += mapping.nP
-
-        self._maps   = maps
-        self._slices = slices
-
-        self.nP = nP
+        self.nP = nP 
 
     @property
     def defaultInvProp(self):
@@ -270,27 +253,9 @@ class PropMap(object):
             setattr(self, '%sMap'%name, None)
             setattr(self, '%sIndex'%name, None)
 
-        self._maps   = None
-        self._slices = None
-
     def __call__(self, vec):
         return self.PropModel(self, vec)
 
     def __contains__(self, val):
         activeMaps = [name for name in self._properties if getattr(self, '%sMap'%name) is not None]
         return val in activeMaps
-
-    def __reduce__(self):
-
-        import cPickle
-        props = dict()
-        for p in self._properties:
-            props[p] = self._properties[p].toJSON()
-        className = self.__class__.__name__
-
-
-        pickledMaps = []
-        for name, mapping in self._maps:
-            pickledMaps += [name, cPickle.dumps(mapping)]
-
-        return (fromPickle, (className, props, self._maps, self._slices))

SimPEG/Regularization.py

@@ -1,5 +1,289 @@
 import Utils, Maps, Mesh, numpy as np, scipy.sparse as sp
 
+class RegularizationMesh(object):
+    """
+    **Regularization Mesh**
+
+    This contains the operators used in the regularization. Note that these
+    are not necessarily true differential operators, but are constructed from
+    a SimPEG Mesh.
+
+    :param Mesh mesh: problem mesh
+    :param numpy.array indActive: bool array, size nC, that is True where we have active cells. Used to reduce the operators so we regularize only on active cells
+    """
+
+    def __init__(self, mesh, indActive=None):
+        self.mesh = mesh
+        assert indActive is None or indActive.dtype == 'bool', 'indActive needs to be None or a bool'
+        self.indActive = indActive
+
+    @property
+    def vol(self):
+        """
+        reduced volume vector
+        :rtype: numpy.array
+        :return: reduced cell volume
+        """
+        if getattr(self, '_vol', None) is None:
+            self._vol = self._Pac.T * self.mesh.vol
+        return self._vol
+
+    @property
+    def nC(self):
+        """
+        reduced number of cells
+        :rtype: int
+        :return: number of cells being regularized
+        """
+        if getattr(self, '_nC', None) is None:
+            if self.indActive is None:
+                self._nC = self.mesh.nC
+            else:
+                self._nC = sum(self.indActive)
+        return self._nC
+
+    @property
+    def dim(self):
+        """
+        dimension of regularization mesh (1D, 2D, 3D)
+        :rtype: int
+        :return: dimension
+        """
+        if getattr(self, '_dim', None) is None:
+            self._dim = self.mesh.dim
+        return self._dim
+
+
+    @property
+    def _Pac(self):
+        """
+        projection matrix that takes from the reduced space of active cells to full modelling space (ie. nC x nindActive)
+        :rtype: scipy.sparse.csr_matrix
+        :return: active cell projection matrix
+        """
+        if getattr(self, '__Pac', None) is None:
+            if self.indActive is None:
+                self.__Pac = Utils.speye(self.mesh.nC)
+            else:
+                self.__Pac = Utils.speye(self.mesh.nC)[:,self.indActive]
+        return self.__Pac
+
+    @property
+    def _Pafx(self):
+        """
+        projection matrix that takes from the reduced space of active x-faces to full modelling space (ie. nFx x nindActive_Fx )
+        :rtype: scipy.sparse.csr_matrix
+        :return: active face-x projection matrix
+        """
+        if getattr(self, '__Pafx', None) is None:
+            if self.indActive is None:
+                self.__Pafx = Utils.speye(self.mesh.nFx)
+            else:
+                indActive_Fx = (self.mesh.aveFx2CC.T * self.indActive) == 1
+                self.__Pafx = Utils.speye(self.mesh.nFx)[:,indActive_Fx]
+        return self.__Pafx
+
+    @property
+    def _Pafy(self):
+        """
+        projection matrix that takes from the reduced space of active y-faces to full modelling space (ie. nFy x nindActive_Fy )
+        :rtype: scipy.sparse.csr_matrix
+        :return: active face-y projection matrix
+        """
+        if getattr(self, '__Pafy', None) is None:
+            if self.indActive is None:
+                self.__Pafy = Utils.speye(self.mesh.nFy)
+            else:
+                indActive_Fy = (self.mesh.aveFy2CC.T * self.indActive) == 1
+                self.__Pafy = Utils.speye(self.mesh.nFy)[:,indActive_Fy]
+        return self.__Pafy
+
+    @property
+    def _Pafz(self):
+        """
+        projection matrix that takes from the reduced space of active z-faces to full modelling space (ie. nFz x nindActive_Fz )
+        :rtype: scipy.sparse.csr_matrix
+        :return: active face-z projection matrix
+        """
+        if getattr(self, '__Pafz', None) is None:
+            if self.indActive is None:
+                self.__Pafz = Utils.speye(self.mesh.nFz)
+            else:
+                indActive_Fz = (self.mesh.aveFz2CC.T * self.indActive) == 1
+                self.__Pafz = Utils.speye(self.mesh.nFz)[:,indActive_Fz]
+        return self.__Pafz
+
+    @property
+    def aveFx2CC(self):
+        """
+        averaging from active cell centers to active x-faces
+        :rtype: scipy.sparse.csr_matrix
+        :return: averaging from active cell centers to active x-faces
+        """
+        if getattr(self, '_aveFx2CC', None) is None:
+            self._aveFx2CC =  self._Pac.T * self.mesh.aveFx2CC * self._Pafx
+        return self._aveFx2CC
+
+    @property
+    def aveCC2Fx(self):
+        """
+        averaging from active x-faces to active cell centers
+        :rtype: scipy.sparse.csr_matrix
+        :return: averaging matrix from active x-faces to active cell centers
+        """
+        if getattr(self, '_aveCC2Fx', None) is None:
+            self._aveCC2Fx =  Utils.sdiag(1./(self.aveFx2CC.T).sum(1)) * self.aveFx2CC.T
+        return self._aveCC2Fx
+
+    @property
+    def aveFy2CC(self):
+        """
+        averaging from active cell centers to active y-faces
+        :rtype: scipy.sparse.csr_matrix
+        :return: averaging from active cell centers to active y-faces
+        """
+        if getattr(self, '_aveFy2CC', None) is None:
+            self._aveFy2CC = self._Pac.T * self.mesh.aveFy2CC * self._Pafy
+        return self._aveFy2CC
+
+    @property
+    def aveCC2Fy(self):
+        """
+        averaging from active y-faces to active cell centers
+        :rtype: scipy.sparse.csr_matrix
+        :return: averaging matrix from active y-faces to active cell centers
+        """
+        if getattr(self, '_aveCC2Fy', None) is None:
+            self._aveCC2Fy =  Utils.sdiag(1./(self.aveFy2CC.T).sum(1)) * self.aveFy2CC.T
+        return self._aveCC2Fy
+
+    @property
+    def aveFz2CC(self):
+        """
+        averaging from active cell centers to active z-faces
+        :rtype: scipy.sparse.csr_matrix
+        :return: averaging from active cell centers to active z-faces
+        """
+        if getattr(self, '_aveFz2CC', None) is None:
+            self._aveFz2CC = self._Pac.T * self.mesh.aveFz2CC * self._Pafz
+        return self._aveFz2CC
+
+    @property
+    def aveCC2Fz(self):
+        """
+        averaging from active z-faces to active cell centers
+        :rtype: scipy.sparse.csr_matrix
+        :return: averaging matrix from active z-faces to active cell centers
+        """
+        if getattr(self, '_aveCC2Fz', None) is None:
+            self._aveCC2Fz =  Utils.sdiag(1./(self.aveFz2CC.T).sum(1)) * self.aveFz2CC.T
+        return self._aveCC2Fz
+
+    @property
+    def cellDiffx(self):
+        """
+        cell centered difference in the x-direction
+        :rtype: scipy.sparse.csr_matrix
+        :return: differencing matrix for active cells in the x-direction
+        """
+        if getattr(self, '_cellDiffx', None) is None:
+            self._cellDiffx = self._Pafx.T * self.mesh.cellGradx * self._Pac
+        return self._cellDiffx
+
+    @property
+    def cellDiffy(self):
+        """
+        cell centered difference in the y-direction
+        :rtype: scipy.sparse.csr_matrix
+        :return: differencing matrix for active cells in the y-direction
+        """
+        if getattr(self, '_cellDiffy', None) is None:
+            self._cellDiffy = self._Pafy.T * self.mesh.cellGrady * self._Pac
+        return self._cellDiffy
+
+    @property
+    def cellDiffz(self):
+        """
+        cell centered difference in the z-direction
+        :rtype: scipy.sparse.csr_matrix
+        :return: differencing matrix for active cells in the z-direction
+        """
+        if getattr(self, '_cellDiffz', None) is None:
+            self._cellDiffz = self._Pafz.T * self.mesh.cellGradz * self._Pac
+        return self._cellDiffz
+
+    @property
+    def faceDiffx(self):
+        """
+        x-face differences
+        :rtype: scipy.sparse.csr_matrix
+        :return: differencing matrix for active faces in the x-direction
+        """
+        if getattr(self, '_faceDiffx', None) is None:
+            self._faceDiffx = self._Pac.T * self.mesh.faceDivx * self._Pafx
+        return self._faceDiffx
+
+    @property
+    def faceDiffy(self):
+        """
+        y-face differences
+        :rtype: scipy.sparse.csr_matrix
+        :return: differencing matrix for active faces in the y-direction
+        """
+        if getattr(self, '_faceDiffy', None) is None:
+            self._faceDiffy = self._Pac.T * self.mesh.faceDivy * self._Pafy
+        return self._faceDiffy
+
+    @property
+    def faceDiffz(self):
+        """
+        z-face differences
+        :rtype: scipy.sparse.csr_matrix
+        :return: differencing matrix for active faces in the z-direction
+        """
+        if getattr(self, '_faceDiffz', None) is None:
+            self._faceDiffz = self._Pac.T * self.mesh.faceDivz * self._Pafz
+        return self._faceDiffz
+
+    @property
+    def cellDiffxStencil(self):
+        """
+        cell centered difference stencil (no cell lengths include) in the x-direction
+        :rtype: scipy.sparse.csr_matrix
+        :return: differencing matrix for active cells in the x-direction
+        """
+        if getattr(self, '_cellDiffxStencil', None) is None:
+
+            self._cellDiffxStencil = self._Pafx.T * self.mesh._cellGradxStencil() * self._Pac
+        return self._cellDiffxStencil
+
+    @property
+    def cellDiffyStencil(self):
+        """
+        cell centered difference stencil (no cell lengths include) in the y-direction
+        :rtype: scipy.sparse.csr_matrix
+        :return: differencing matrix for active cells in the y-direction
+        """
+        if self.dim < 2: return None
+        if getattr(self, '_cellDiffyStencil', None) is None:
+
+            self._cellDiffyStencil = self._Pafy.T * self.mesh._cellGradyStencil() * self._Pac
+        return self._cellDiffyStencil
+
+    @property
+    def cellDiffzStencil(self):
+        """
+        cell centered difference stencil (no cell lengths include) in the y-direction
+        :rtype: scipy.sparse.csr_matrix
+        :return: differencing matrix for active cells in the y-direction
+        """
+        if self.dim < 3: return None
+        if getattr(self, '_cellDiffzStencil', None) is None:
+
+            self._cellDiffzStencil = self._Pafz.T * self.mesh._cellGradzStencil() * self._Pac
+        return self._cellDiffzStencil
+
+
 class BaseRegularization(object):
     """
     **Base Regularization Class**
@@ -18,12 +302,16 @@ class BaseRegularization(object):
 
     mapping = None    #: A SimPEG.Map instance.
     mesh    = None    #: A SimPEG.Mesh instance.
-    mref = None       #: Reference model.
+    mref    = None    #: Reference model.
 
     def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
         Utils.setKwargs(self, **kwargs)
-        self.mesh = mesh
         assert isinstance(mesh, Mesh.BaseMesh), "mesh must be a SimPEG.Mesh object."
+        if indActive is not None and indActive.dtype != 'bool':
+            tmp = indActive
+            indActive = np.zeros(mesh.nC, dtype=bool)
+            indActive[tmp] = True
+        self.regmesh = RegularizationMesh(mesh,indActive)
         self.mapping = mapping or self.mapPair(mesh)
         self.mapping._assertMatchesPair(self.mapPair)
         self.indActive = indActive
@@ -55,8 +343,7 @@ class BaseRegularization(object):
     @property
     def W(self):
         """Full regularization weighting matrix W."""
-        return sp.identity(self.mapping.nP)
-
+        return sp.identity(self.regmesh.nC)
 
     @Utils.timeIt
     def eval(self, m):
@@ -87,11 +374,12 @@ class BaseRegularization(object):
     @Utils.timeIt
     def eval2Deriv(self, m, v=None):
         """
+        Second derivative
 
-            :param numpy.array m: geophysical model
-            :param numpy.array v: vector to multiply
-            :rtype: scipy.sparse.csr_matrix or numpy.ndarray
-            :return: WtW or WtW*v
+        :param numpy.array m: geophysical model
+        :param numpy.array v: vector to multiply
+        :rtype: scipy.sparse.csr_matrix or numpy.ndarray
+        :return: WtW or WtW*v
 
         The regularization is:
 
@@ -112,112 +400,94 @@ class BaseRegularization(object):
 
         return mD.T * ( self.W.T * ( self.W * ( mD * v) ) )
 
-
 class Tikhonov(BaseRegularization):
     """
+    L2 Tikhonov regularization with both smallness and smoothness (first order
+    derivative) contributions.
+
+    .. math::
+        \phi_m(\mathbf{m}) = \\alpha_s \| W_s (\mathbf{m} - \mathbf{m_{ref}} ) \|^2
+        + \\alpha_x \| W_x \\frac{\partial}{\partial x} (\mathbf{m} - \mathbf{m_{ref}} ) \|^2
+        + \\alpha_y \| W_y \\frac{\partial}{\partial y} (\mathbf{m} - \mathbf{m_{ref}} ) \|^2
+        + \\alpha_z \| W_z \\frac{\partial}{\partial z} (\mathbf{m} - \mathbf{m_{ref}} ) \|^2
+
+    Note if the key word argument `mrefInSmooth` is False, then mref is not
+    included in the smoothness contribution.
+
+    :param Mesh mesh: SimPEG mesh
+    :param Maps mapping: regularization mapping, takes the model from model space to the thing you want to regularize
+    :param numpy.ndarray indActive: active cell indices for reducing the size of differential operators in the definition of a regularization mesh
+    :param bool mrefInSmooth: (default = False) put mref in the smoothness component?
+    :param float alpha_s: (default 1e-6) smallness weight
+    :param float alpha_x: (default 1) smoothness weight for first derivative in the x-direction
+    :param float alpha_y: (default 1) smoothness weight for first derivative in the y-direction
+    :param float alpha_z: (default 1) smoothness weight for first derivative in the z-direction
+    :param float alpha_xx: (default 1) smoothness weight for second derivative in the x-direction
+    :param float alpha_yy: (default 1) smoothness weight for second derivative in the y-direction
+    :param float alpha_zz: (default 1) smoothness weight for second derivative in the z-direction
     """
-    smoothModel = True  #: SMOOTH and SMOOTH_MOD_DIF options
-    alpha_s  = Utils.dependentProperty('_alpha_s', 1e-6, ['_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")
-    alpha_xx = Utils.dependentProperty('_alpha_xx', 0.0, ['_W', '_Wxx'], "Weight for the second derivative in the x direction")
-    alpha_yy = Utils.dependentProperty('_alpha_yy', 0.0, ['_W', '_Wyy'], "Weight for the second derivative in the y direction")
-    alpha_zz = Utils.dependentProperty('_alpha_zz', 0.0, ['_W', '_Wzz'], "Weight for the second derivative in the z direction")
+    mrefInSmooth = False  # put mref in the smoothness contribution
+    alpha_s      = Utils.dependentProperty('_alpha_s', 1e-6, ['_W', '_Wsmall'], "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")
+    alpha_xx     = Utils.dependentProperty('_alpha_xx', 0.0, ['_W', '_Wxx'],    "Weight for the second derivative in the x direction")
+    alpha_yy     = Utils.dependentProperty('_alpha_yy', 0.0, ['_W', '_Wyy'],    "Weight for the second derivative in the y direction")
+    alpha_zz     = Utils.dependentProperty('_alpha_zz', 0.0, ['_W', '_Wzz'],    "Weight for the second derivative in the z direction")
 
     def __init__(self, mesh, mapping=None, indActive = None, **kwargs):
-        BaseRegularization.__init__(self, mesh, mapping=mapping, **kwargs)
-        self.indActive = indActive
+        BaseRegularization.__init__(self, mesh, mapping=mapping, indActive=indActive, **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)
-            if self.indActive is not None:
-                Pac = Utils.speye(self.mesh.nC)[:,self.indActive]
-                self._Ws = Pac.T * self._Ws * Pac
-        return self._Ws
+    def Wsmall(self):
+        """Regularization matrix Wsmall"""
+        if getattr(self,'_Wsmall', None) is None:
+            self._Wsmall = Utils.sdiag((self.regmesh.vol*self.alpha_s)**0.5)
+        return self._Wsmall
 
     @property
     def Wx(self):
         """Regularization matrix Wx"""
         if getattr(self, '_Wx', None) is None:
-            Ave_x_vol = self.mesh.aveF2CC[:,:self.mesh.nFx].T*self.mesh.vol
-            self._Wx = Utils.sdiag((Ave_x_vol*self.alpha_x)**0.5)*self.mesh.cellGradx
-
-            if self.indActive is not None:
-                indActive_Fx = (self.mesh.aveFx2CC.T * self.indActive) == 1
-                Pac = Utils.speye(self.mesh.nC)[:,self.indActive]
-                Pafx = Utils.speye(self.mesh.nFx)[:,indActive_Fx]
-                self._Wx = Pafx.T*self._Wx*Pac
-
+            Ave_x_vol = self.regmesh.aveCC2Fx * self.regmesh.vol
+            self._Wx = Utils.sdiag((Ave_x_vol*self.alpha_x)**0.5)*self.regmesh.cellDiffx
         return self._Wx
 
     @property
     def Wy(self):
         """Regularization matrix Wy"""
         if getattr(self, '_Wy', None) is None:
-            Ave_y_vol = self.mesh.aveF2CC[:,self.mesh.nFx:np.sum(self.mesh.vnF[:2])].T*self.mesh.vol
-            self._Wy = Utils.sdiag((Ave_y_vol*self.alpha_y)**0.5)*self.mesh.cellGrady
-
-            if self.indActive is not None:
-                indActive_Fy = (self.mesh.aveFy2CC.T * self.indActive) == 1
-                Pac = Utils.speye(self.mesh.nC)[:,self.indActive]
-                Pafy = Utils.speye(self.mesh.nFy)[:,indActive_Fy]
-                self._Wy = Pafy.T*self._Wy*Pac
-
+            Ave_y_vol = self.regmesh.aveCC2Fy * self.regmesh.vol
+            self._Wy = Utils.sdiag((Ave_y_vol*self.alpha_y)**0.5)*self.regmesh.cellDiffy
         return self._Wy
 
     @property
     def Wz(self):
         """Regularization matrix Wz"""
         if getattr(self, '_Wz', None) is None:
-            Ave_z_vol = self.mesh.aveF2CC[:,np.sum(self.mesh.vnF[:2]):].T*self.mesh.vol
-            self._Wz = Utils.sdiag((Ave_z_vol*self.alpha_z)**0.5)*self.mesh.cellGradz
-
-            if self.indActive is not None:
-                indActive_Fz = (self.mesh.aveFz2CC.T * self.indActive) == 1
-                Pac = Utils.speye(self.mesh.nC)[:,self.indActive]
-                Pafz = Utils.speye(self.mesh.nFz)[:,indActive_Fz]
-                self._Wz = Pafz.T*self._Wz*Pac
-
+            Ave_z_vol = self.regmesh.aveCC2Fz * self.regmesh.vol
+            self._Wz = Utils.sdiag((Ave_z_vol*self.alpha_z)**0.5)*self.regmesh.cellDiffz
         return self._Wz
 
     @property
     def Wxx(self):
         """Regularization matrix Wxx"""
         if getattr(self, '_Wxx', None) is None:
-            self._Wxx = Utils.sdiag((self.mesh.vol*self.alpha_xx)**0.5)*self.mesh.faceDivx*self.mesh.cellGradx
-
-            if self.indActive is not None:
-                Pac = Utils.speye(self.mesh.nC)[:,self.indActive]
-                self._Wxx = Pac.T*self._Wxx*Pac
-
+            self._Wxx = Utils.sdiag((self.regmesh.vol*self.alpha_xx)**0.5)*self.regmesh.faceDiffx*self.regmesh.cellDiffx
         return self._Wxx
 
     @property
     def Wyy(self):
         """Regularization matrix Wyy"""
         if getattr(self, '_Wyy', None) is None:
-            self._Wyy = Utils.sdiag((self.mesh.vol*self.alpha_yy)**0.5)*self.mesh.faceDivy*self.mesh.cellGrady
-
-            if self.indActive is not None:
-                Pac = Utils.speye(self.mesh.nC)[:,self.indActive]
-                self._Wyy = Pac.T*self._Wyy*Pac
-
+            self._Wyy = Utils.sdiag((self.regmesh.vol*self.alpha_yy)**0.5)*self.regmesh.faceDiffy*self.regmesh.cellDiffy
         return self._Wyy
 
     @property
     def Wzz(self):
         """Regularization matrix Wzz"""
         if getattr(self, '_Wzz', None) is None:
-            self._Wzz = Utils.sdiag((self.mesh.vol*self.alpha_zz)**0.5)*self.mesh.faceDivz*self.mesh.cellGradz
-
-            if self.indActive is not None:
-                Pac = Utils.speye(self.mesh.nC)[:,self.indActive]
-                self._Wzz = Pac.T*self._Wzz*Pac
-
+            self._Wzz = Utils.sdiag((self.regmesh.vol*self.alpha_zz)**0.5)*self.regmesh.faceDiffz*self.regmesh.cellDiffz
         return self._Wzz
 
     @property
@@ -225,9 +495,9 @@ class Tikhonov(BaseRegularization):
         """Full smoothness regularization matrix W"""
         if getattr(self, '_Wsmooth', None) is None:
             wlist = (self.Wx, self.Wxx)
-            if self.mesh.dim > 1:
+            if self.regmesh.dim > 1:
                 wlist += (self.Wy, self.Wyy)
-            if self.mesh.dim > 2:
+            if self.regmesh.dim > 2:
                 wlist += (self.Wz, self.Wzz)
             self._Wsmooth = sp.vstack(wlist)
         return self._Wsmooth
@@ -236,25 +506,44 @@ class Tikhonov(BaseRegularization):
     def W(self):
         """Full regularization matrix W"""
         if getattr(self, '_W', None) is None:
-            wlist = (self.Ws, self.Wsmooth)
+            wlist = (self.Wsmall, 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)
+    def _evalSmall(self, m):
+        r = self.Wsmall * ( self.mapping * (m - self.mref) )
+        return 0.5 * r.dot(r)
 
+    @Utils.timeIt
+    def _evalSmooth(self, m):
+        if self.mrefInSmooth == True:
+            r = self.Wsmooth * ( self.mapping * (m - self.mref) )
+        elif self.mrefInSmooth == False:
+            r = self.Wsmooth * ( self.mapping * (m) )
+        return 0.5 * r.dot(r)
+
+    @Utils.timeIt
+    def eval(self, m):
+        return self._evalSmall(m) + self._evalSmooth(m)
+
+    @Utils.timeIt
+    def _evalSmallDeriv(self,m):
+        r = self.Wsmall * ( self.mapping * (m - self.mref) )
+        return r.T * ( self.Wsmall * self.mapping.deriv(m - self.mref) )
+
+    @Utils.timeIt
+    def _evalSmoothDeriv(self,m):
+        if self.mrefInSmooth == True:
+            r = self.Wsmooth * ( self.mapping * ( m - self.mref ) )
+            return r.T * ( self.Wsmooth * self.mapping.deriv(m - self.mref) )
+        elif self.mrefInSmooth == False:
+            r = self.Wsmooth * ( self.mapping * m )
+            return r.T * ( self.Wsmooth * self.mapping.deriv(m) )
 
     @Utils.timeIt
     def evalDeriv(self, m):
         """
-
         The regularization is:
 
         .. math::
@@ -268,17 +557,185 @@ class Tikhonov(BaseRegularization):
             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
+        return self._evalSmallDeriv(m) + self._evalSmoothDeriv(m)
 
+
+class Simple(Tikhonov):
+    """
+    Simple regularization that does not include length scales in the derivatives.
+    """
+
+    mrefInSmooth = False  #: SMOOTH and SMOOTH_MOD_DIF options
+    alpha_s     = Utils.dependentProperty('_alpha_s', 1.0, ['_W', '_Wsmall'], "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")
+    wght        = 1.
+
+    def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
+        BaseRegularization.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
+
+        if isinstance(self.wght,float):
+            self.wght = np.ones(self.regmesh.nC) * self.wght
+
+    @property
+    def Wsmall(self):
+        """Regularization matrix Wsmall"""
+        if getattr(self,'_Wsmall', None) is None:
+            self._Wsmall = Utils.sdiag((self.regmesh.vol*self.alpha_s*self.wght)**0.5)
+        return self._Wsmall
+
+    @property
+    def Wx(self):
+        """Regularization matrix Wx"""
+        if getattr(self, '_Wx', None) is None:
+            self._Wx = Utils.sdiag((self.regmesh.aveCC2Fx * self.regmesh.vol*self.alpha_x*(self.regmesh.aveCC2Fx*self.wght))**0.5)*self.regmesh.cellDiffxStencil
+        return self._Wx
+
+    @property
+    def Wy(self):
+        """Regularization matrix Wy"""
+        if getattr(self, '_Wy', None) is None:
+            self._Wy = Utils.sdiag((self.regmesh.aveCC2Fy * self.regmesh.vol * self.alpha_y*(self.regmesh.aveCC2Fy*self.wght))**0.5)*self.regmesh.cellDiffyStencil
+        return self._Wy
+
+    @property
+    def Wz(self):
+        """Regularization matrix Wz"""
+        if getattr(self, '_Wz', None) is None:
+            self._Wz = Utils.sdiag((self.regmesh.aveCC2Fz * self.regmesh.vol*self.alpha_z*(self.regmesh.aveCC2Fz*self.wght))**0.5)*self.regmesh.cellDiffzStencil
+        return self._Wz
+
+    @property
+    def Wsmooth(self):
+        """Full smoothness regularization matrix W"""
+        if getattr(self, '_Wsmooth', None) is None:
+            wlist = (self.Wx,)
+            if self.regmesh.dim > 1:
+                wlist += (self.Wy,)
+            if self.regmesh.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.Wsmall, self.Wsmooth)
+            self._W = sp.vstack(wlist)
+        return self._W
+
+    @Utils.timeIt
+    def _evalSmall(self, m):
+        r = self.Wsmall * ( self.mapping * (m - self.mref) )
+        return 0.5 * r.dot(r)
+
+    @Utils.timeIt
+    def _evalSmooth(self, m):
+        if self.mrefInSmooth == True:
+            r = self.Wsmooth * ( self.mapping * (m - self.mref) )
+        elif self.mrefInSmooth == False:
+            r = self.Wsmooth * ( self.mapping * m)
+        return 0.5 * r.dot(r)
+
+
+class Sparse(Simple):
+
+    # set default values
+    eps_p      = 1e-1
+    eps_q      = 1e-1
+    curModel = None # use a model to compute the weights
+    gamma    = 1.
+    norms    = [0., 2., 2., 2.]
+    wght     = 1.
+
+    def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
+        Simple.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
+
+        if isinstance(self.wght,float):
+            self.wght = np.ones(self.regmesh.nC) * self.wght
+
+    @property
+    def Wsmall(self):
+        """Regularization matrix Wsmall"""
+        if getattr(self, 'curModel', None) is None:
+            self.Rs = Utils.speye(self.regmesh.nC)
+
+        else:
+            f_m = self.mapping * (self.curModel - self.reg.mref)
+            self.rs = self.R(f_m , self.eps_p, self.norms[0])
+            self.Rs = Utils.sdiag( self.rs )
+
+        return Utils.sdiag((self.regmesh.vol*self.alpha_s*self.gamma*self.wght)**0.5)*self.Rs
+
+
+    @property
+    def Wx(self):
+        """Regularization matrix Wx"""
+
+        if getattr(self, 'curModel', None) is None:
+            self.Rx = Utils.speye(self.regmesh.cellDiffxStencil.shape[0])
+
+        else:
+            f_m = self.regmesh.cellDiffxStencil * (self.mapping * self.curModel)
+            self.rx = self.R( f_m , self.eps_q, self.norms[1])
+            self.Rx = Utils.sdiag( self.rx )
+
+        return Utils.sdiag(( (self.regmesh.aveCC2Fx * self.regmesh.vol) *self.alpha_x*self.gamma*(self.regmesh.aveCC2Fx*self.wght))**0.5)*self.Rx*self.regmesh.cellDiffxStencil
+
+    @property
+    def Wy(self):
+        """Regularization matrix Wy"""
+
+        if getattr(self, 'curModel', None) is None:
+            self.Ry = Utils.speye(self.regmesh.cellDiffyStencil.shape[0])
+
+        else:
+            f_m = self.regmesh.cellDiffyStencil * (self.mapping * self.curModel)
+            self.ry = self.R( f_m , self.eps_q, self.norms[2])
+            self.Ry = Utils.sdiag( self.ry )
+
+        return Utils.sdiag(((self.regmesh.aveCC2Fy * self.regmesh.vol)*self.alpha_y*self.gamma*(self.regmesh.aveCC2Fy*self.wght))**0.5)*self.Ry*self.regmesh.cellDiffyStencil
+
+    @property
+    def Wz(self):
+        """Regularization matrix Wz"""
+
+        if getattr(self, 'curModel', None) is None:
+            self.Rz = Utils.speye(self.regmesh.cellDiffzStencil.shape[0])
+
+        else:
+            f_m = self.regmesh.cellDiffzStencil * (self.mapping * self.curModel)
+            self.rz = self.R( f_m , self.eps_q, self.norms[3])
+            self.Rz = Utils.sdiag( self.rz )
+
+        return Utils.sdiag(((self.regmesh.aveCC2Fz * self.regmesh.vol)*self.alpha_z*self.gamma*(self.regmesh.aveCC2Fz*self.wght))**0.5)*self.Rz*self.regmesh.cellDiffzStencil
+
+    @property
+    def Wsmooth(self):
+        """Full smoothness regularization matrix W"""
+        #if getattr(self, '_Wsmooth', None) is None:
+        wlist = (self.Wx,)
+        if self.regmesh.dim > 1:
+            wlist += (self.Wy,)
+        if self.regmesh.dim > 2:
+            wlist += (self.Wz,)
+        #self._Wsmooth = sp.vstack(wlist)
+        return sp.vstack(wlist)
+
+    @property
+    def W(self):
+        """Full regularization matrix W"""
+        if getattr(self, '_W', None) is None:
+    
+            wlist = (self.Wsmall, self.Wsmooth)
+            self._W = sp.vstack(wlist)
+        return self._W
+
+    def R(self, f_m , eps, exponent):
+
+        eta = (eps**(1.-exponent/2.))**0.5
+        r = eta / (f_m**2.+ eps**2.)**((1.-exponent/2.)/2.)
+
+        return r

SimPEG/Survey.py

@@ -1,6 +1,5 @@
 import Utils, numpy as np, scipy.sparse as sp, uuid
 
-
 class BaseRx(object):
     """SimPEG Receiver Object"""
 
@@ -35,7 +34,7 @@ class BaseRx(object):
         """Number of data in the receiver."""
         return self.locs.shape[0]
 
-    def getP(self, mesh):
+    def getP(self, mesh, projGLoc=None):
         """
             Returns the projection matrices as a
             list for all components collected by
@@ -48,7 +47,10 @@ class BaseRx(object):
         if mesh in self._Ps:
             return self._Ps[mesh]
 
-        P = mesh.getInterpolationMat(self.locs, self.projGLoc)
+        if projGLoc is None:
+            projGLoc = self.projGLoc
+
+        P = mesh.getInterpolationMat(self.locs, projGLoc)
         if self.storeProjections:
             self._Ps[mesh] = P
         return P
@@ -293,38 +295,38 @@ class BaseSurvey(object):
 
     @Utils.count
     @Utils.requires('prob')
-    def dpred(self, m, u=None):
-        """dpred(m, u=None)
+    def dpred(self, m, f=None):
+        """dpred(m, f=None)
 
             Create the projected data from a model.
-            The field, u, (if provided) will be used for the predicted data
+            The fields, f, (if provided) will be used for the predicted data
             instead of recalculating the fields (which may be expensive!).
 
             .. math::
 
-                d_\\text{pred} = P(u(m))
+                d_\\text{pred} = P(f(m))
 
             Where P is a projection of the fields onto the data space.
         """
-        if u is None: u = self.prob.fields(m)
-        return Utils.mkvc(self.projectFields(u))
+        if f is None: f = self.prob.fields(m)
+        return Utils.mkvc(self.eval(f))
 
 
     @Utils.count
-    def projectFields(self, u):
-        """projectFields(u)
+    def eval(self, f):
+        """eval(f)
 
             This function projects the fields onto the data space.
 
             .. math::
 
-                d_\\text{pred} = \mathbf{P} u(m)
+                d_\\text{pred} = \mathbf{P} f(m)
         """
-        raise NotImplemented('projectFields is not yet implemented.')
+        raise NotImplemented('eval is not yet implemented.')
 
     @Utils.count
-    def projectFieldsDeriv(self, u):
-        """projectFieldsDeriv(u)
+    def evalDeriv(self, f):
+        """evalDeriv(f)
 
             This function s the derivative of projects the fields onto the data space.
 
@@ -332,14 +334,14 @@ class BaseSurvey(object):
 
                 \\frac{\partial d_\\text{pred}}{\partial u} = \mathbf{P}
         """
-        raise NotImplemented('projectFields is not yet implemented.')
+        raise NotImplemented('eval is not yet implemented.')
 
     @Utils.count
-    def residual(self, m, u=None):
-        """residual(m, u=None)
+    def residual(self, m, f=None):
+        """residual(m, f=None)
 
             :param numpy.array m: geophysical model
-            :param numpy.array u: fields
+            :param numpy.array f: fields
             :rtype: numpy.array
             :return: data residual
 
@@ -350,14 +352,14 @@ class BaseSurvey(object):
                 \mu_\\text{data} = \mathbf{d}_\\text{pred} - \mathbf{d}_\\text{obs}
 
         """
-        return Utils.mkvc(self.dpred(m, u=u) - self.dobs)
+        return Utils.mkvc(self.dpred(m, f=f) - self.dobs)
 
     @property
     def isSynthetic(self):
         "Check if the data is synthetic."
         return self.mtrue is not None
 
-    def makeSyntheticData(self, m, std=0.05, u=None, force=False):
+    def makeSyntheticData(self, m, std=0.05, f=None, force=False):
         """
             Make synthetic data given a model, and a standard deviation.
 
@@ -370,8 +372,16 @@ class BaseSurvey(object):
         if getattr(self, 'dobs', None) is not None and not force:
             raise Exception('Survey already has dobs. You can use force=True to override this exception.')
         self.mtrue = m
-        self.dtrue = self.dpred(m, u=u)
+        self.dtrue = self.dpred(m, f=f)
         noise = std*abs(self.dtrue)*np.random.randn(*self.dtrue.shape)
         self.dobs = self.dtrue+noise
         self.std = self.dobs*0 + std
         return self.dobs
+
+class LinearSurvey(BaseSurvey):
+    def eval(self, f):
+        return f
+
+    @property
+    def nD(self):
+        return self.prob.G.shape[0]

SimPEG/Utils/ModelBuilder.py

@@ -88,12 +88,14 @@ def getIndicesBlock(p0,p1,ccMesh):
     # Return a tuple
     return ind
 
-def defineBlock(ccMesh,p0,p1,vals=[0,1]):
+def defineBlock(ccMesh,p0,p1,vals=None):
     """
         Build a block with the conductivity specified by condVal.  Returns an array.
         vals[0]  conductivity of the block
         vals[1]  conductivity of the ground
     """
+    if vals is None:
+        vals = [0,1]
     sigma = np.zeros(ccMesh.shape[0]) + vals[1]
     ind   = getIndicesBlock(p0,p1,ccMesh)
 
@@ -101,7 +103,11 @@ def defineBlock(ccMesh,p0,p1,vals=[0,1]):
 
     return mkvc(sigma)
 
-def defineElipse(ccMesh, center=[0,0,0], anisotropy=[1,1,1], slope=10., theta=0.):
+def defineElipse(ccMesh, center=None, anisotropy=None, slope=10., theta=0.):
+    if center is None:
+        center = [0,0,0]
+    if anisotropy is None:
+        anisotropy = [1,1,1]
     G = ccMesh.copy()
     dim = ccMesh.shape[1]
     for i in range(dim):
@@ -118,7 +124,45 @@ def defineElipse(ccMesh, center=[0,0,0], anisotropy=[1,1,1], slope=10., theta=0.
     D = np.sqrt(np.sum(G**2,axis=1))
     return -np.arctan((D-1)*slope)*(2./np.pi)/2.+0.5
 
-def defineTwoLayers(ccMesh,depth,vals=[0,1]):
+def getIndicesSphere(center,radius,ccMesh):
+    """
+        Creates a vector containing the sphere indices in the cell centers mesh.
+        Returns a tuple
+
+        The sphere is defined by the points
+
+        p0, describe the position of the center of the cell
+
+        r, describe the radius of the sphere.
+
+        ccMesh represents the cell-centered mesh
+
+        The points p0 must live in the the same dimensional space as the mesh.
+
+    """
+
+    # Validation: mesh and point (p0) live in the same dimensional space
+    dimMesh = np.size(ccMesh[0,:])
+    assert len(center) == dimMesh, "Dimension mismatch. len(p0) != dimMesh"
+
+    if dimMesh == 1:
+       # Define the reference points
+        
+        ind  = np.abs(center[0] - ccMesh[:,0]) < radius
+
+    elif dimMesh == 2:
+       # Define the reference points
+
+        ind = np.sqrt( ( center[0] - ccMesh[:,0] )**2 + ( center[1] - ccMesh[:,1] )**2 ) < radius
+
+    elif dimMesh == 3:
+        # Define the points
+        ind = np.sqrt( ( center[0] - ccMesh[:,0] )**2 + ( center[1] - ccMesh[:,1] )**2 + ( center[2] - ccMesh[:,2] )**2 ) < radius
+
+    # Return a tuple
+    return ind
+
+def defineTwoLayers(ccMesh,depth,vals=None):
     """
     Define a two layered model.  Depth of the first layer must be specified.
     CondVals vector with the conductivity values of the layers.  Eg:
@@ -129,6 +173,8 @@ def defineTwoLayers(ccMesh,depth,vals=[0,1]):
         0                          depth                                 zf
              1st layer                       2nd layer
     """
+    if vals is None:
+        vals = [0,1]
     sigma = np.zeros(ccMesh.shape[0]) + vals[1]
 
     dim = np.size(ccMesh[0,:])
@@ -214,7 +260,7 @@ def layeredModel(ccMesh, layerTops, layerValues):
 
 
 
-def randomModel(shape, seed=None, anisotropy=None, its=100, bounds=[0,1]):
+def randomModel(shape, seed=None, anisotropy=None, its=100, bounds=None):
     """
         Create a random model by convolving a kernel with a
         uniformly distributed model.
@@ -238,6 +284,8 @@ def randomModel(shape, seed=None, anisotropy=None, its=100, bounds=[0,1]):
 
 
     """
+    if bounds is None:
+        bounds = [0,1]
 
     if seed is None:
         seed = np.random.randint(1e3)

SimPEG/Utils/codeutils.py

@@ -55,8 +55,10 @@ def hook(obj, method, name=None, overwrite=False, silent=False):
         print 'Method '+name+' was not overwritten.'
 
 
-def setKwargs(obj, ignore=[],  **kwargs):
+def setKwargs(obj, ignore=None,  **kwargs):
     """Sets key word arguments (kwargs) that are present in the object, throw an error if they don't exist."""
+    if ignore is None:
+        ignore = []
     for attr in kwargs:
         if attr in ignore:
             continue
@@ -65,8 +67,8 @@ def setKwargs(obj, ignore=[],  **kwargs):
         else:
             raise Exception('%s attr is not recognized' % attr)
 
-    # hook(obj,hook, silent=True)
-    # hook(obj,setKwargs, silent=True)
+    hook(obj,hook, silent=True)
+    hook(obj,setKwargs, silent=True)
 
 def printTitles(obj, printers, name='Print Titles', pad=''):
     titles = ''

SimPEG/Utils/io_utils.py

@@ -0,0 +1,137 @@
+from SimPEG import np, Mesh
+import time as tm
+import vtk, vtk.util.numpy_support as npsup
+import re
+
+def read_GOCAD_ts(tsfile):
+    """
+
+    Read GOCAD triangulated surface (*.ts) file
+    INPUT:
+    tsfile: Triangulated surface
+
+    OUTPUT:
+    vrts : Array of vertices in XYZ coordinates [n x 3]
+    trgl : Array of index for triangles [m x 3]. The order of the vertices
+            is important and describes the normal
+            n = cross( (P2 - P1 ) , (P3 - P1) )
+
+    Author: @fourndo
+
+
+    .. note::
+
+        Remove all attributes from the GoCAD surface before exporting it!
+
+    """
+
+
+    fid = open(tsfile,'r')
+    line = fid.readline()
+
+    # Skip all the lines until the vertices
+    while re.match('TFACE',line)==None:
+        line = fid.readline()
+
+    line = fid.readline()
+    vrtx = []
+
+    # Run down all the vertices and save in array
+    while re.match('VRTX',line):
+        l_input  = re.split('[\s*]',line)
+        temp = np.array(l_input[2:5])
+        vrtx.append(temp.astype(np.float))
+
+        # Read next line
+        line = fid.readline()
+
+    vrtx = np.asarray(vrtx)
+
+    # Skip lines to the triangles
+    while re.match('TRGL',line)==None:
+        line = fid.readline()
+
+    # Run down the list of triangles
+    trgl = []
+
+    # Run down all the vertices and save in array
+    while re.match('TRGL',line):
+        l_input  = re.split('[\s*]',line)
+        temp = np.array(l_input[1:4])
+        trgl.append(temp.astype(np.int))
+
+        # Read next line
+        line = fid.readline()
+
+    trgl = np.asarray(trgl)
+
+    return vrtx, trgl
+
+def surface2inds(vrtx, trgl, mesh, boundaries=True, internal=True):
+    """"
+    Function to read gocad polystructure file and output indexes of mesh with in the structure.
+
+    """
+    # Adjust the index
+    trgl = trgl - 1
+
+    # Make vtk pts
+    ptsvtk = vtk.vtkPoints()
+    ptsvtk.SetData(npsup.numpy_to_vtk(vrtx,deep=1))
+
+    # Make the polygon connection
+    polys = vtk.vtkCellArray()
+    for face in trgl:
+        poly = vtk.vtkPolygon()
+        poly.GetPointIds().SetNumberOfIds(len(face))
+        for nrv, vert in enumerate(face):
+            poly.GetPointIds().SetId(nrv,vert)
+        polys.InsertNextCell(poly)
+
+    # Make the polydata, structure of connections and vrtx
+    polyData = vtk.vtkPolyData()
+    polyData.SetPoints(ptsvtk)
+    polyData.SetPolys(polys)
+
+    # Make implicit func
+    ImpDistFunc = vtk.vtkImplicitPolyDataDistance()
+    ImpDistFunc.SetInput(polyData)
+
+    # Convert the mesh
+    vtkMesh = vtk.vtkRectilinearGrid()
+    vtkMesh.SetDimensions(mesh.nNx,mesh.nNy,mesh.nNz)
+    vtkMesh.SetXCoordinates(npsup.numpy_to_vtk(mesh.vectorNx, deep=1))
+    vtkMesh.SetYCoordinates(npsup.numpy_to_vtk(mesh.vectorNy, deep=1))
+    vtkMesh.SetZCoordinates(npsup.numpy_to_vtk(mesh.vectorNz, deep=1))
+    # Add indexes
+    vtkInd = npsup.numpy_to_vtk(np.arange(mesh.nC), deep=1)
+    vtkInd.SetName('Index')
+    vtkMesh.GetCellData().AddArray(vtkInd)
+
+    extractImpDistRectGridFilt = vtk.vtkExtractGeometry() # Object constructor
+    extractImpDistRectGridFilt.SetImplicitFunction(ImpDistFunc) #
+    extractImpDistRectGridFilt.SetInputData(vtkMesh)
+
+    if boundaries is True:
+        extractImpDistRectGridFilt.ExtractBoundaryCellsOn()
+
+    else:
+        extractImpDistRectGridFilt.ExtractBoundaryCellsOff()
+
+    if internal is True:
+        extractImpDistRectGridFilt.ExtractInsideOn()
+
+    else:
+        extractImpDistRectGridFilt.ExtractInsideOff()
+
+    print "Extracting indices from grid..."
+    # Executing the pipe
+    extractImpDistRectGridFilt.Update()
+
+    # Get index inside
+    insideGrid = extractImpDistRectGridFilt.GetOutput()
+    insideGrid = npsup.vtk_to_numpy(insideGrid.GetCellData().GetArray('Index'))
+
+
+    # Return the indexes inside
+    return insideGrid

SimPEG/__init__.py

@@ -15,7 +15,7 @@ import Directives
 import Inversion
 import Tests
 
-__version__   = '0.1.9'
+__version__   = '0.1.10'
 __author__    = 'Rowan Cockett'
 __license__   = 'MIT'
 __copyright__ = 'Copyright 2014 Rowan Cockett'

docs/api_DC.rst

@@ -0,0 +1,150 @@
+.. _api_DC:
+
+.. math::
+
+    \renewcommand{\div}{\nabla\cdot\,}
+    \newcommand{\grad}{\vec \nabla}
+    \newcommand{\curl}{{\vec \nabla}\times\,}
+    \newcommand{\dcurl}{{\mathbf C}}
+    \newcommand{\dgrad}{{\mathbf G}}
+    \newcommand{\Acf}{{\mathbf A_c^f}}
+    \newcommand{\Ace}{{\mathbf A_c^e}}
+    \renewcommand{\S}{{\mathbf \Sigma}}
+    \renewcommand{\Div}{{\mathbf {Div}}}
+    \renewcommand{\Grad}{{\mathbf {Grad}}}
+    \newcommand{\St}{{\mathbf \Sigma_\tau}}
+    \newcommand{\diag}{\mathbf{diag}}
+    \newcommand{\M}{{\mathbf M}}
+    \newcommand{\Me}{{\M^e}}
+    \newcommand{\Mes}[1]{{\M^e_{#1}}}
+    \newcommand{\be}{\mathbf{e}}
+    \newcommand{\bj}{\mathbf{j}}
+    \newcommand{\bphi}{\mathbf{\phi}}
+    \newcommand{\bq}{\mathbf{q}}
+    \newcommand{\bJ}{\mathbf{J}}
+    \newcommand{\bG}{\mathbf{G}}
+    \newcommand{\bP}{\mathbf{P}}
+    \newcommand{\bA}{\mathbf{A}}
+    \newcommand{\bm}{\mathbf{m}}
+    \newcommand{\B}{\vec{B}}
+    \newcommand{\D}{\vec{D}}
+    \renewcommand{\H}{\vec{H}}
+    \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}}
+
+DC resistivity survey
+*********************
+
+Electrical resistivity of subsurface materials is measured by causing an electrical current to flow in the earth between one pair of electrodes while the voltage across a second pair of electrodes is measured. The result is an "apparent" resistivity which is a value representing the weighted average resistivity over a volume of the earth. Variations in this measurement are caused by variations in the soil, rock, and pore fluid electrical resistivity. Surveys require contact with the ground, so they can be labour intensive. Results are sometimes interpreted directly, but more commonly, 1D, 2D or 3D models are estimated using inversion procedures (`GPG <http://www.eos.ubc.ca/courses/eosc350/content/>`_).
+
+
+Background
+==========
+
+As direct current (DC) implies, in DC resistivity survey, we assume steady-state. We consider Maxwell's equations in steady state as
+
+.. math::
+
+    \curl \frac{1}{\mu} \vec{b} - \j = \j_s \\
+
+    \curl \e = 0
+
+Then by taking \\(\\curl\\) for the first equation, we have
+
+.. math::
+
+     - \div\j = q \\
+
+
+where
+
+.. math::
+
+    \div \j_s = q = I(\delta(\vec{r}-\vec{r}_{s+})-\delta(\vec{r}-\vec{r}_{s-}))
+
+Since \\(\\curl \\e = 0\\), we have
+
+.. math::
+
+    \e = \grad \phi
+
+And by Ohm's law, we have
+
+.. math::
+
+    \j = \sigma \grad \phi
+
+Finally, we can compute the solution of the system:
+
+.. math::
+
+    - \div\j = q
+
+    \j = \sigma \grad \phi
+
+    \frac{\partial \phi}{\partial r}\Big|_{\partial \Omega_{BC}} = 0
+
+
+Discretization
+==============
+
+By using finite volume method (FVM), we discretize our system as
+
+.. math::
+
+    -\Div \bj = \bq
+
+    \diag(\Acf^{T}\sigma^{-1}) \bj = \Grad \bphi
+
+Here boundary condtions are embedded in the discrete differential operators. With some linear algebra we have
+
+.. math::
+
+    \bA\bphi  = -\bq
+
+where
+
+.. math::
+
+    \bA = \Div (\diag(\Acf^{T}\sigma^{-1}))^{-1} \Grad
+
+By solving this linear equation, we can compute the solution of \\(\\phi\\). Based on this discretization, we derive sensitivity in discretized space. Sensitivity matrix can be in general can be written as
+
+.. math ::
+
+    \bJ = -\bP\bA^{-1}\bG
+
+where
+
+.. math ::
+
+    \bP: \text{Projection}
+
+    \bJ = \bP\frac{\partial \phi}{\partial \bm}
+
+Here \\(\\bm\\) indicates model parameters in discretized space.
+
+Verification
+============
+
+Comparing to the analytic function:
+
+.. plot::
+
+    import simpegDC as DC
+    DC.Examples.Verification.run(plotIt=True)
+
+API
+===
+
+.. automodule:: simpegDC.BaseDC
+    :show-inheritance:
+    :members:
+    :undoc-members:
+    :inherited-members:

docs/conf.py

@@ -51,9 +51,9 @@ copyright = u'2013, SimPEG Developers'
 # built documents.
 #
 # The short X.Y version.
-version = '0.1.9'
+version = '0.1.10'
 # The full version, including alpha/beta/rc tags.
-release = '0.1.9'
+release = '0.1.10'
 
 # The language for content autogenerated by Sphinx. Refer to documentation
 # for a list of supported languages.

docs/examples/DC_Analytic_Dipole.rst

@@ -0,0 +1,21 @@
+.. _examples_DC_Analytic_Dipole:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+DC Analytic Dipole
+==================
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.DC_Analytic_Dipole.run()
+
+.. literalinclude:: ../../SimPEG/Examples/DC_Analytic_Dipole.py
+    :language: python
+    :linenos:

docs/examples/DC_Forward_PseudoSection.rst

@@ -0,0 +1,36 @@
+.. _examples_DC_Forward_PseudoSection:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+
+DC Forward Simulation
+=====================
+
+Forward model two conductive spheres in a half-space and plot a
+pseudo-section. Assumes an infinite line source and measures along the
+center of the spheres.
+
+INPUT:
+loc     = Location of spheres [[x1,y1,z1],[x2,y2,z2]]
+radi    = Radius of spheres [r1,r2]
+param   = Conductivity of background and two spheres [m0,m1,m2]
+stype   = survey type "pdp" (pole dipole) or "dpdp" (dipole dipole)
+dtype   = Data type "appr" (app res) | "appc" (app cond) | "volt" (potential)
+Created by @fourndo on Mon Feb 01 19:28:06 2016
+
+
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.DC_Forward_PseudoSection.run()
+
+.. literalinclude:: ../../SimPEG/Examples/DC_Forward_PseudoSection.py
+    :language: python
+    :linenos:

docs/examples/EM_Schenkel_Morrison_Casing.rst

@@ -0,0 +1,58 @@
+.. _examples_EM_Schenkel_Morrison_Casing:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+
+EM: Schenkel and Morrison Casing Model
+======================================
+
+Here we create and run a FDEM forward simulation to calculate the vertical
+current inside a steel-cased. The model is based on the Schenkel and
+Morrison Casing Model, and the results are used in a 2016 SEG abstract by
+Yang et al.
+
+- Schenkel, C.J., and H.F. Morrison, 1990, Effects of well casing on potential field measurements using downhole current sources: Geophysical prospecting, 38, 663-686.
+
+
+The model consists of:
+- Air: Conductivity 1e-8 S/m, above z = 0
+- Background: conductivity 1e-2 S/m, below z = 0
+- Casing: conductivity 1e6 S/m
+    - 300m long
+    - radius of 0.1m
+    - thickness of 6e-3m
+
+Inside the casing, we take the same conductivity as the background.
+
+We are using an EM code to simulate DC, so we use frequency low enough
+that the skin depth inside the casing is longer than the casing length (f
+= 1e-6 Hz). The plot produced is of the current inside the casing.
+
+These results are shown in the SEG abstract by Yang et al., 2016: 3D DC
+resistivity modeling of steel casing for reservoir monitoring using
+equivalent resistor network. The solver used to produce these results and
+achieve the CPU time of ~30s is Mumps, which was installed using pymatsolver_
+
+.. _pymatsolver: https://github.com/rowanc1/pymatsolver
+
+This example is on figshare: https://dx.doi.org/10.6084/m9.figshare.3126961.v1
+
+If you would use this example for a code comparison, or build upon it, a
+citation would be much appreciated!
+
+
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.EM_Schenkel_Morrison_Casing.run()
+
+.. literalinclude:: ../../SimPEG/Examples/EM_Schenkel_Morrison_Casing.py
+    :language: python
+    :linenos:

docs/examples/Inversion_IRLS.rst

@@ -0,0 +1,26 @@
+.. _examples_Inversion_IRLS:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+
+Inversion: Linear Problem
+=========================
+
+Here we go over the basics of creating a linear problem and inversion.
+
+
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.Inversion_IRLS.run()
+
+.. literalinclude:: ../../SimPEG/Examples/Inversion_IRLS.py
+    :language: python
+    :linenos:

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

@@ -49,9 +49,7 @@ 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:

setup.py

@@ -77,7 +77,7 @@ with open("README.rst") as f:
 
 setup(
     name = "SimPEG",
-    version = "0.1.9",
+    version = "0.1.10",
     packages = find_packages(),
     install_requires = ['numpy>=1.7',
                         'scipy>=0.13',

tests/base/test_PropMaps.py

@@ -1,7 +1,6 @@
 import unittest
 from SimPEG import *
 from scipy.constants import mu_0
-import cPickle
 
 
 class MyPropMap(Maps.PropMap):
@@ -29,10 +28,9 @@ class TestPropMaps(unittest.TestCase):
         PM3 = MyPropMap({'maps':[('sigma', expMap)], 'slices':{'sigma':slice(0,3)}})
 
         for PM in [PM1,PM2,PM3]:
-            PM = cPickle.loads( cPickle.dumps(PM) )
             assert PM.defaultInvProp == 'sigma'
             assert PM.sigmaMap is not None
-            assert PM.sigmaMap.__class__ is expMap.__class__
+            assert PM.sigmaMap is expMap
             assert PM.sigmaIndex == slice(0,3)
             assert getattr(PM, 'sigma', None) is None
             assert PM.muMap is None
@@ -54,7 +52,7 @@ class TestPropMaps(unittest.TestCase):
             assert m.muDeriv is None
 
             assert np.all(m.sigmaModel == np.r_[1.,2,3])
-            assert m.sigmaMap.__class__ is expMap.__class__
+            assert m.sigmaMap is expMap
             assert np.all(m.sigma == np.exp(np.r_[1.,2,3]))
             assert m.sigmaDeriv is not None
 

tests/base/test_maps.py

@@ -5,8 +5,8 @@ from scipy.sparse.linalg import dsolve
 
 TOL = 1e-14
 
-MAPS_TO_TEST_2D = ["CircleMap", "ComplexMap", "ExpMap", "IdentityMap", "Vertical1DMap", "Weighting", "FullMap"]
-MAPS_TO_TEST_3D = [             "ComplexMap", "ExpMap", "IdentityMap", "Vertical1DMap", "Weighting", "FullMap"]
+MAPS_TO_TEST_2D = ["CircleMap", "ComplexMap", "ExpMap", "IdentityMap", "SurjectVertical1D", "Weighting", "SurjectFull","FullMap","Vertical1DMap"]
+MAPS_TO_TEST_3D = [             "ComplexMap", "ExpMap", "IdentityMap", "SurjectVertical1D", "Weighting", "SurjectFull","FullMap","Vertical1DMap"]
 
 class MapTests(unittest.TestCase):
 
@@ -52,7 +52,7 @@ class MapTests(unittest.TestCase):
     def test_mapMultiplication(self):
         M = Mesh.TensorMesh([2,3])
         expMap = Maps.ExpMap(M)
-        vertMap = Maps.Vertical1DMap(M)
+        vertMap = Maps.SurjectVertical1D(M)
         combo = expMap*vertMap
         m = np.arange(3.0)
         t_true = np.exp(np.r_[0,0,1,1,2,2.])
@@ -83,22 +83,23 @@ class MapTests(unittest.TestCase):
     def test_activeCells(self):
         M = Mesh.TensorMesh([2,4],'0C')
         expMap = Maps.ExpMap(M)
-        actMap = Maps.ActiveCells(M, M.vectorCCy <=0, 10, nC=M.nCy)
-        vertMap = Maps.Vertical1DMap(M)
-        combo = vertMap * actMap
-        m = np.r_[1,2.]
-        mod = Models.Model(m,combo)
-        # import matplotlib.pyplot as plt
-        # plt.colorbar(M.plotImage(mod.transform)[0])
-        # plt.show()
-        self.assertLess(np.linalg.norm(mod.transform - np.r_[1,1,2,2,10,10,10,10.]), TOL)
-        self.assertLess((mod.transformDeriv - combo.deriv(m)).toarray().sum(), TOL)
+        for actMap in [Maps.InjectActiveCells(M, M.vectorCCy <=0, 10, nC=M.nCy), Maps.ActiveCells(M, M.vectorCCy <=0, 10, nC=M.nCy)]:
+        # actMap = Maps.InjectActiveCells(M, M.vectorCCy <=0, 10, nC=M.nCy)
+            vertMap = Maps.SurjectVertical1D(M)
+            combo = vertMap * actMap
+            m = np.r_[1,2.]
+            mod = Models.Model(m,combo)
+            # import matplotlib.pyplot as plt
+            # plt.colorbar(M.plotImage(mod.transform)[0])
+            # plt.show()
+            self.assertLess(np.linalg.norm(mod.transform - np.r_[1,1,2,2,10,10,10,10.]), TOL)
+            self.assertLess((mod.transformDeriv - combo.deriv(m)).toarray().sum(), TOL)
 
     def test_tripleMultiply(self):
         M = Mesh.TensorMesh([2,4],'0C')
         expMap = Maps.ExpMap(M)
-        vertMap = Maps.Vertical1DMap(M)
-        actMap = Maps.ActiveCells(M, M.vectorCCy <=0, 10, nC=M.nCy)
+        vertMap = Maps.SurjectVertical1D(M)
+        actMap = Maps.InjectActiveCells(M, M.vectorCCy <=0, 10, nC=M.nCy)
         m = np.r_[1,2.]
         t_true = np.exp(np.r_[1,1,2,2,10,10,10,10.])
         self.assertLess(np.linalg.norm((expMap * vertMap * actMap * m)-t_true,np.inf),TOL)
@@ -115,29 +116,33 @@ class MapTests(unittest.TestCase):
         M2 = Mesh.TensorMesh([2,4])
         M3 = Mesh.TensorMesh([3,2,4])
         m = np.random.rand(M2.nC)
-        m2to3 = Maps.Map2Dto3D(M3, normal='X')
-        m = np.arange(m2to3.nP)
-        self.assertTrue(m2to3.test())
-        self.assertTrue(np.all(Utils.mkvc( (m2to3 * m).reshape(M3.vnC,order='F')[0,:,:] ) == m))
+
+        for m2to3 in [Maps.Surject2Dto3D(M3, normal='X'), Maps.Map2Dto3D(M3, normal='X')]:
+        # m2to3 = Maps.Surject2Dto3D(M3, normal='X')
+            m = np.arange(m2to3.nP)
+            self.assertTrue(m2to3.test())
+            self.assertTrue(np.all(Utils.mkvc( (m2to3 * m).reshape(M3.vnC,order='F')[0,:,:] ) == m))
 
 
     def test_map2Dto3D_y(self):
         M2 = Mesh.TensorMesh([3,4])
         M3 = Mesh.TensorMesh([3,2,4])
         m = np.random.rand(M2.nC)
-        m2to3 = Maps.Map2Dto3D(M3, normal='Y')
-        m = np.arange(m2to3.nP)
-        self.assertTrue(m2to3.test())
-        self.assertTrue(np.all(Utils.mkvc( (m2to3 * m).reshape(M3.vnC,order='F')[:,0,:] ) == m))
+        for m2to3 in [Maps.Surject2Dto3D(M3, normal='Y'),Maps.Map2Dto3D(M3, normal='Y')]:
+        # m2to3 = Maps.Surject2Dto3D(M3, normal='Y')
+            m = np.arange(m2to3.nP)
+            self.assertTrue(m2to3.test())
+            self.assertTrue(np.all(Utils.mkvc( (m2to3 * m).reshape(M3.vnC,order='F')[:,0,:] ) == m))
 
     def test_map2Dto3D_z(self):
         M2 = Mesh.TensorMesh([3,2])
         M3 = Mesh.TensorMesh([3,2,4])
         m = np.random.rand(M2.nC)
-        m2to3 = Maps.Map2Dto3D(M3, normal='Z')
-        m = np.arange(m2to3.nP)
-        self.assertTrue(m2to3.test())
-        self.assertTrue(np.all(Utils.mkvc( (m2to3 * m).reshape(M3.vnC,order='F')[:,:,0] ) == m))
+        for m2to3 in [Maps.Surject2Dto3D(M3, normal='Z'),Maps.Map2Dto3D(M3, normal='Z')]:
+        # m2to3 = Maps.Surject2Dto3D(M3, normal='Z')
+            m = np.arange(m2to3.nP)
+            self.assertTrue(m2to3.test())
+            self.assertTrue(np.all(Utils.mkvc( (m2to3 * m).reshape(M3.vnC,order='F')[:,:,0] ) == m))
 
 
 if __name__ == '__main__':

tests/base/test_regularization.py

@@ -5,6 +5,8 @@ from scipy.sparse.linalg import dsolve
 import inspect
 
 TOL = 1e-20
+testReg = True
+testRegMesh = True
 
 class RegularizationTests(unittest.TestCase):
 
@@ -16,44 +18,82 @@ class RegularizationTests(unittest.TestCase):
         mesh3 = Mesh.TensorMesh([hx, hy, hz])
         self.meshlist = [mesh1,mesh2, mesh3]
 
-    def test_regularization(self):
-        for R in dir(Regularization):
-            r = getattr(Regularization, R)
-            if not inspect.isclass(r): continue
-            if not issubclass(r, Regularization.BaseRegularization):
-                continue
+    if testReg:
+        def test_regularization(self):
+            for R in dir(Regularization):
+                r = getattr(Regularization, R)
+                if not inspect.isclass(r): continue
+                if not issubclass(r, Regularization.BaseRegularization):
+                    continue
+
+                for i, mesh in enumerate(self.meshlist):
+
+                    print 'Testing %iD'%mesh.dim
+
+                    mapping = r.mapPair(mesh)
+                    reg = r(mesh, mapping=mapping)
+                    m = np.random.rand(mapping.nP)
+                    reg.mref = np.ones_like(m)*np.mean(m)
+
+                    print 'Check: phi_m (mref) = %f' %reg.eval(reg.mref)
+                    passed = reg.eval(reg.mref) < TOL
+                    self.assertTrue(passed)
+
+                    print 'Check:', R
+                    passed = Tests.checkDerivative(lambda m : [reg.eval(m), reg.evalDeriv(m)], m, plotIt=False)
+                    self.assertTrue(passed)
+
+                    print 'Check 2 Deriv:', R
+                    passed = Tests.checkDerivative(lambda m : [reg.evalDeriv(m), reg.eval2Deriv(m)], m, plotIt=False)
+                    self.assertTrue(passed)
+
+        def test_regularization_ActiveCells(self):
+            for R in dir(Regularization):
+                r = getattr(Regularization, R)
+                if not inspect.isclass(r): continue
+                if not issubclass(r, Regularization.BaseRegularization):
+                    continue
+
+                for i, mesh in enumerate(self.meshlist):
+
+                    print 'Testing Active Cells %iD'%(mesh.dim)
+
+                    if mesh.dim == 1:
+                        indActive = Utils.mkvc(mesh.gridCC <= 0.8)
+                    elif mesh.dim == 2:
+                        indActive = Utils.mkvc(mesh.gridCC[:,-1] <= 2*np.sin(2*np.pi*mesh.gridCC[:,0])+0.5)
+                    elif mesh.dim == 3:
+                        indActive = Utils.mkvc(mesh.gridCC[:,-1] <= 2*np.sin(2*np.pi*mesh.gridCC[:,0])+0.5 * 2*np.sin(2*np.pi*mesh.gridCC[:,1])+0.5)
+
+                    mapping = Maps.IdentityMap(nP=indActive.nonzero()[0].size)
+
+                    for indAct in [indActive, indActive.nonzero()[0]]: # test both bool and integers
+                        reg = r(mesh, mapping=mapping, indActive=indAct)
+                        m = np.random.rand(mesh.nC)[indAct]
+                        reg.mref = np.ones_like(m)*np.mean(m)
+
+                    print 'Check: phi_m (mref) = %f' %reg.eval(reg.mref)
+                    passed = reg.eval(reg.mref) < TOL
+                    self.assertTrue(passed)
+
+                    print 'Check:', R
+                    passed = Tests.checkDerivative(lambda m : [reg.eval(m), reg.evalDeriv(m)], m, plotIt=False)
+                    self.assertTrue(passed)
+
+                    print 'Check 2 Deriv:', R
+                    passed = Tests.checkDerivative(lambda m : [reg.evalDeriv(m), reg.eval2Deriv(m)], m, plotIt=False)
+                    self.assertTrue(passed)
+
+    if testRegMesh:
+        def test_regularizationMesh(self):
 
             for i, mesh in enumerate(self.meshlist):
 
                 print 'Testing %iD'%mesh.dim
 
-                mapping = r.mapPair(mesh)
-                reg = r(mesh, mapping=mapping)
-                m = np.random.rand(mapping.nP)
-                reg.mref = np.ones_like(m)*np.mean(m)
-
-                print 'Check: phi_m (mref) = %f' %reg.eval(reg.mref)
-                passed = reg.eval(reg.mref) < TOL
-                self.assertTrue(passed)
-
-                print 'Check:', R
-                passed = Tests.checkDerivative(lambda m : [reg.eval(m), reg.evalDeriv(m)], m, plotIt=False)
-                self.assertTrue(passed)
-
-                print 'Check 2 Deriv:', R
-                passed = Tests.checkDerivative(lambda m : [reg.evalDeriv(m), reg.eval2Deriv(m)], m, plotIt=False)
-                self.assertTrue(passed)
-
-    def test_regularization_ActiveCells(self):
-        for R in dir(Regularization):
-            r = getattr(Regularization, R)
-            if not inspect.isclass(r): continue
-            if not issubclass(r, Regularization.BaseRegularization):
-                continue
-
-            for i, mesh in enumerate(self.meshlist):
-
-                print 'Testing Active Cells %iD'%(mesh.dim)
+                # mapping = r.mapPair(mesh)
+                # reg = r(mesh, mapping=mapping)
+                # m = np.random.rand(mapping.nP)
 
                 if mesh.dim == 1:
                     indAct = Utils.mkvc(mesh.gridCC <= 0.8)
@@ -62,23 +102,9 @@ class RegularizationTests(unittest.TestCase):
                 elif mesh.dim == 3:
                     indAct = Utils.mkvc(mesh.gridCC[:,-1] <= 2*np.sin(2*np.pi*mesh.gridCC[:,0])+0.5 * 2*np.sin(2*np.pi*mesh.gridCC[:,1])+0.5)
 
-                mapping = Maps.IdentityMap(nP=indAct.nonzero()[0].size)
+                regmesh = Regularization.RegularizationMesh(mesh, indActive=indAct)
 
-                reg = r(mesh, mapping=mapping, indActive=indAct)
-                m = np.random.rand(mesh.nC)[indAct]
-                reg.mref = np.ones_like(m)*np.mean(m)
-
-                print 'Check: phi_m (mref) = %f' %reg.eval(reg.mref)
-                passed = reg.eval(reg.mref) < TOL
-                self.assertTrue(passed)
-
-                print 'Check:', R
-                passed = Tests.checkDerivative(lambda m : [reg.eval(m), reg.evalDeriv(m)], m, plotIt=False)
-                self.assertTrue(passed)
-
-                print 'Check 2 Deriv:', R
-                passed = Tests.checkDerivative(lambda m : [reg.evalDeriv(m), reg.eval2Deriv(m)], m, plotIt=False)
-                self.assertTrue(passed)
+                assert (regmesh.vol == mesh.vol[indAct]).all()
 
 
 if __name__ == '__main__':

tests/dcip/__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/dcip/test_forward_DCproblem.py

@@ -0,0 +1,77 @@
+import unittest
+from SimPEG import *
+import SimPEG.DCIP as DC
+
+
+class DCProblemTests(unittest.TestCase):
+
+    def setUp(self):
+
+        aSpacing=2.5
+        nElecs=10
+
+        surveySize = nElecs*aSpacing - aSpacing
+        cs = surveySize/nElecs/4
+
+        mesh = Mesh.TensorMesh([
+                [(cs,10, -1.3),(cs,surveySize/cs),(cs,10, 1.3)],
+                [(cs,3, -1.3),(cs,3,1.3)],
+        #         [(cs,5, -1.3),(cs,10)]
+            ],'CN')
+
+        srcList = DC.Utils.WennerSrcList(nElecs, aSpacing, in2D=True)
+        survey = DC.SurveyDC(srcList)
+        problem = DC.ProblemDC_CC(mesh)
+        problem.pair(survey)
+
+        mSynth = np.ones(mesh.nC)
+        survey.makeSyntheticData(mSynth)
+
+        # Now set up the problem to do some minimization
+        dmis = DataMisfit.l2_DataMisfit(survey)
+        reg = Regularization.Tikhonov(mesh)
+        opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6)
+        invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e4)
+        inv = Inversion.BaseInversion(invProb)
+
+        self.inv = inv
+        self.reg = reg
+        self.p = problem
+        self.mesh = mesh
+        self.m0 = mSynth
+        self.survey = survey
+        self.dmis = dmis
+
+    def test_misfit(self):
+        derChk = lambda m: [self.survey.dpred(m), lambda mx: self.p.Jvec(self.m0, mx)]
+        passed = Tests.checkDerivative(derChk, self.m0, plotIt=False)
+        self.assertTrue(passed)
+
+    def test_adjoint(self):
+        # Adjoint Test
+        u = np.random.rand(self.mesh.nC*self.survey.nSrc)
+        v = np.random.rand(self.mesh.nC)
+        w = np.random.rand(self.survey.dobs.shape[0])
+        wtJv = w.dot(self.p.Jvec(self.m0, v))
+        vtJtw = v.dot(self.p.Jtvec(self.m0, w))
+        passed = np.abs(wtJv - vtJtw) < 1e-10
+        print 'Adjoint Test', np.abs(wtJv - vtJtw), passed
+        self.assertTrue(passed)
+
+    def test_dataObj(self):
+        derChk = lambda m: [self.dmis.eval(m), self.dmis.evalDeriv(m)]
+        passed = Tests.checkDerivative(derChk, self.m0, plotIt=False)
+        self.assertTrue(passed)
+
+
+    def test_massMatrices(self):
+        Gu = np.random.rand(self.mesh.nF)
+        def derChk(m):
+            self.p.curModel = m
+            return [self.p.Msig * Gu, self.p.dMdsig(Gu)]
+        passed = Tests.checkDerivative(derChk, self.m0, plotIt=False)
+        self.assertTrue(passed)
+
+
+if __name__ == '__main__':
+    unittest.main()

tests/dcip/test_forward_IPproblem.py

@@ -0,0 +1,65 @@
+import unittest
+import SimPEG.DCIP as DC
+from SimPEG import *
+
+class IPforwardTests(unittest.TestCase):
+
+    def test_IPforward(self):
+
+        cs = 12.5
+        nc = 200/cs+1
+        hx = [(cs,7, -1.3),(cs,nc),(cs,7, 1.3)]
+        hy = [(cs,7, -1.3),(cs,int(nc/2+1)),(cs,7, 1.3)]
+        hz = [(cs,7, -1.3),(cs,int(nc/2+1))]
+        mesh = Mesh.TensorMesh([hx, hy, hz], 'CCN')
+        sighalf = 1e-2
+        sigma = np.ones(mesh.nC)*sighalf
+        p0 = np.r_[-50., 50., -50.]
+        p1 = np.r_[ 50.,-50., -150.]
+        blk_ind = Utils.ModelBuilder.getIndicesBlock(p0, p1, mesh.gridCC)
+        sigma[blk_ind] = 1e-3
+        eta = np.zeros_like(sigma)
+        eta[blk_ind] = 0.1
+        sigmaInf = sigma.copy()
+        sigma0 = sigma*(1-eta)
+
+        nElecs = 11
+        x_temp = np.linspace(-100, 100, nElecs)
+        aSpacing = x_temp[1]-x_temp[0]
+        y_temp = 0.
+        xyz = Utils.ndgrid(x_temp, np.r_[y_temp], np.r_[0.])
+        srcList = DC.Utils.WennerSrcList(nElecs,aSpacing)
+        survey = DC.SurveyDC(srcList)
+
+        imap   = Maps.IdentityMap(mesh)
+        problem = DC.ProblemDC_CC(mesh, mapping=imap)
+
+        try:
+            from pymatsolver import MumpsSolver
+            solver = MumpsSolver
+        except ImportError, e:
+            solver = SolverLU
+
+        problem.Solver = solver
+        problem.pair(survey)
+
+        phi0 = survey.dpred(sigma0)
+        phiInf = survey.dpred(sigmaInf)
+
+        phiIP_true = phi0-phiInf
+
+        surveyIP = DC.SurveyIP(srcList)
+        problemIP = DC.ProblemIP(mesh, sigma=sigma)
+        problemIP.pair(surveyIP)
+
+        problemIP.Solver = solver
+
+        phiIP_approx = surveyIP.dpred(eta)
+
+        err =  np.linalg.norm(phiIP_true-phiIP_approx) / np.linalg.norm(phiIP_true)
+
+        self.assertTrue(err < 0.02)
+
+
+if __name__ == '__main__':
+    unittest.main()

tests/dcip/test_sens_IPproblem.py

@@ -0,0 +1,82 @@
+import unittest
+from SimPEG import *
+import SimPEG.DCIP as DC
+
+class IPProblemTests(unittest.TestCase):
+
+    def setUp(self):
+
+        cs = 12.5
+        nc = 500/cs+1
+        hx = [(cs,0, -1.3),(cs,nc),(cs,0, 1.3)]
+        hy = [(cs,0, -1.3),(cs,int(nc/2+1)),(cs,0, 1.3)]
+        hz = [(cs,0, -1.3),(cs,int(nc/2+1))]
+        mesh = Mesh.TensorMesh([hx, hy, hz], 'CCN')
+        sighalf = 1e-2
+        sigma = np.ones(mesh.nC)*sighalf
+        p0 = np.r_[-50., 50., -50.]
+        p1 = np.r_[ 50.,-50., -150.]
+        blk_ind = Utils.ModelBuilder.getIndicesBlock(p0, p1, mesh.gridCC)
+        sigma[blk_ind] = 1e-3
+        eta = np.zeros_like(sigma)
+        eta[blk_ind] = 0.1
+
+        nElecs = 5
+        x_temp = np.linspace(-250, 250, nElecs)
+        aSpacing = x_temp[1]-x_temp[0]
+        y_temp = 0.
+        xyz = Utils.ndgrid(x_temp, np.r_[y_temp], np.r_[0.])
+        srcList = DC.Utils.WennerSrcList(nElecs,aSpacing)
+        survey = DC.SurveyIP(srcList)
+        imap   = Maps.IdentityMap(mesh)
+        problem = DC.ProblemIP(mesh, sigma=sigma, mapping= imap)
+        problem.pair(survey)
+
+        try:
+            from pymatsolver import MumpsSolver
+            problem.Solver = MumpsSolver
+        except ImportError, e:
+            problem.Solver = SolverLU
+
+        mSynth = eta
+        survey.makeSyntheticData(mSynth)
+
+        # Now set up the problem to do some minimization
+        dmis = DataMisfit.l2_DataMisfit(survey)
+        reg = Regularization.Tikhonov(mesh)
+        opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6)
+        invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e4)
+        inv = Inversion.BaseInversion(invProb)
+
+        self.inv = inv
+        self.reg = reg
+        self.p = problem
+        self.mesh = mesh
+        self.m0 = mSynth
+        self.survey = survey
+        self.dmis = dmis
+
+    def test_misfit(self):
+        derChk = lambda m: [self.survey.dpred(m), lambda mx: self.p.Jvec(self.m0, mx)]
+        passed = Tests.checkDerivative(derChk, self.m0*0, plotIt=False)
+        self.assertTrue(passed)
+
+    def test_adjoint(self):
+        # Adjoint Test
+        u = np.random.rand(self.mesh.nC*self.survey.nSrc)
+        v = np.random.rand(self.mesh.nC)
+        w = np.random.rand(self.survey.dobs.shape[0])
+        wtJv = w.dot(self.p.Jvec(self.m0, v))
+        vtJtw = v.dot(self.p.Jtvec(self.m0, w))
+        passed = np.abs(wtJv - vtJtw) < 1e-10
+        print 'Adjoint Test', np.abs(wtJv - vtJtw), passed
+        self.assertTrue(passed)
+
+    def test_dataObj(self):
+        derChk = lambda m: [self.dmis.eval(m), self.dmis.evalDeriv(m)]
+        passed = Tests.checkDerivative(derChk, self.m0, plotIt=False)
+        self.assertTrue(passed)
+
+
+if __name__ == '__main__':
+    unittest.main()

tests/em/fdem/forward/test_FDEM_forward.py

@@ -3,125 +3,75 @@ from SimPEG import *
 from SimPEG import EM
 import sys
 from scipy.constants import mu_0
-from SimPEG.EM.Utils.testingUtils import getFDEMProblem
+from SimPEG.EM.Utils.testingUtils import getFDEMProblem, crossCheckTest
 
 testEB = True
 testHJ = True
-
+testEJ = True
+testBH = True
 verbose = False
 
-TOL = 1e-5
-FLR = 1e-20 # "zero", so if residual below this --> pass regardless of order
-CONDUCTIVITY = 1e1
-MU = mu_0
-freq = 1e-1
-addrandoms = True
+TOLEBHJ = 1e-5
+TOLEJHB = 1 # averaging and more sensitive to boundary condition violations (ie. the impact of violating the boundary conditions in each case is different.)
+#TODO: choose better testing parameters to lower this 
 
 SrcList = ['RawVec', 'MagDipole_Bfield', 'MagDipole', 'CircularLoop']
 
 
-def crossCheckTest(fdemType, comp):
-
-    l2norm = lambda r: np.sqrt(r.dot(r))
-
-    prb1 = getFDEMProblem(fdemType, comp, SrcList, freq, verbose)
-    mesh = prb1.mesh
-    print 'Cross Checking Forward: %s formulation - %s' % (fdemType, comp)
-    m = np.log(np.ones(mesh.nC)*CONDUCTIVITY)
-    mu = np.log(np.ones(mesh.nC)*MU)
-
-    if addrandoms is True:
-        m  = m + np.random.randn(mesh.nC)*np.log(CONDUCTIVITY)*1e-1
-        mu = mu + np.random.randn(mesh.nC)*MU*1e-1
-
-    # prb1.PropMap.PropModel.mu = mu
-    # prb1.PropMap.PropModel.mui = 1./mu
-    survey1 = prb1.survey
-    d1 = survey1.dpred(m)
-
-    if verbose:
-        print '  Problem 1 solved'
-
-    if fdemType == 'e':
-        prb2 = getFDEMProblem('b', comp, SrcList, freq, verbose)
-    elif fdemType == 'b':
-        prb2 = getFDEMProblem('e', comp, SrcList, freq, verbose)
-    elif fdemType == 'j':
-        prb2 = getFDEMProblem('h', comp, SrcList, freq, verbose)
-    elif fdemType == 'h':
-        prb2 = getFDEMProblem('j', comp, SrcList, freq, verbose)
-    else:
-        raise NotImplementedError()
-
-    # prb2.mu = mu
-    survey2 = prb2.survey
-    d2 = survey2.dpred(m)
-
-    if verbose:
-        print '  Problem 2 solved'
-
-    r = d2-d1
-    l2r = l2norm(r)
-
-    tol = np.max([TOL*(10**int(np.log10(l2norm(d1)))),FLR])
-    print l2norm(d1), l2norm(d2),  l2r , tol, l2r < tol
-    return l2r < tol
-
-
 class FDEM_CrossCheck(unittest.TestCase):
     if testEB:
         def test_EB_CrossCheck_exr_Eform(self):
-            self.assertTrue(crossCheckTest('e', 'exr'))
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'b', 'exr', verbose=verbose))
         def test_EB_CrossCheck_eyr_Eform(self):
-            self.assertTrue(crossCheckTest('e', 'eyr'))
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'b', 'eyr', verbose=verbose))
         def test_EB_CrossCheck_ezr_Eform(self):
-            self.assertTrue(crossCheckTest('e', 'ezr'))
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'b', 'ezr', verbose=verbose))
         def test_EB_CrossCheck_exi_Eform(self):
-            self.assertTrue(crossCheckTest('e', 'exi'))
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'b', 'exi', verbose=verbose))
         def test_EB_CrossCheck_eyi_Eform(self):
-            self.assertTrue(crossCheckTest('e', 'eyi'))
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'b', 'eyi', verbose=verbose))
         def test_EB_CrossCheck_ezi_Eform(self):
-            self.assertTrue(crossCheckTest('e', 'ezi'))
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'b', 'ezi', verbose=verbose))
 
         def test_EB_CrossCheck_bxr_Eform(self):
-            self.assertTrue(crossCheckTest('e', 'bxr'))
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'b', 'bxr', verbose=verbose))
         def test_EB_CrossCheck_byr_Eform(self):
-            self.assertTrue(crossCheckTest('e', 'byr'))
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'b', 'byr', verbose=verbose))
         def test_EB_CrossCheck_bzr_Eform(self):
-            self.assertTrue(crossCheckTest('e', 'bzr'))
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'b', 'bzr', verbose=verbose))
         def test_EB_CrossCheck_bxi_Eform(self):
-            self.assertTrue(crossCheckTest('e', 'bxi'))
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'b', 'bxi', verbose=verbose))
         def test_EB_CrossCheck_byi_Eform(self):
-            self.assertTrue(crossCheckTest('e', 'byi'))
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'b', 'byi', verbose=verbose))
         def test_EB_CrossCheck_bzi_Eform(self):
-            self.assertTrue(crossCheckTest('e', 'bzi'))
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'b', 'bzi', verbose=verbose))
 
     if testHJ:
         def test_HJ_CrossCheck_jxr_Jform(self):
-            self.assertTrue(crossCheckTest('j', 'jxr'))
+            self.assertTrue(crossCheckTest(SrcList, 'j', 'h', 'jxr', verbose=verbose))
         def test_HJ_CrossCheck_jyr_Jform(self):
-            self.assertTrue(crossCheckTest('j', 'jyr'))
+            self.assertTrue(crossCheckTest(SrcList, 'j', 'h', 'jyr', verbose=verbose))
         def test_HJ_CrossCheck_jzr_Jform(self):
-            self.assertTrue(crossCheckTest('j', 'jzr'))
+            self.assertTrue(crossCheckTest(SrcList, 'j', 'h', 'jzr', verbose=verbose))
         def test_HJ_CrossCheck_jxi_Jform(self):
-            self.assertTrue(crossCheckTest('j', 'jxi'))
+            self.assertTrue(crossCheckTest(SrcList, 'j', 'h', 'jxi', verbose=verbose))
         def test_HJ_CrossCheck_jyi_Jform(self):
-            self.assertTrue(crossCheckTest('j', 'jyi'))
+            self.assertTrue(crossCheckTest(SrcList, 'j', 'h', 'jyi', verbose=verbose))
         def test_HJ_CrossCheck_jzi_Jform(self):
-            self.assertTrue(crossCheckTest('j', 'jzi'))
+            self.assertTrue(crossCheckTest(SrcList, 'j', 'h', 'jzi', verbose=verbose))
 
         def test_HJ_CrossCheck_hxr_Jform(self):
-            self.assertTrue(crossCheckTest('j', 'hxr'))
+            self.assertTrue(crossCheckTest(SrcList, 'j', 'h', 'hxr', verbose=verbose))
         def test_HJ_CrossCheck_hyr_Jform(self):
-            self.assertTrue(crossCheckTest('j', 'hyr'))
+            self.assertTrue(crossCheckTest(SrcList, 'j', 'h', 'hyr', verbose=verbose))
         def test_HJ_CrossCheck_hzr_Jform(self):
-            self.assertTrue(crossCheckTest('j', 'hzr'))
+            self.assertTrue(crossCheckTest(SrcList, 'j', 'h', 'hzr', verbose=verbose))
         def test_HJ_CrossCheck_hxi_Jform(self):
-            self.assertTrue(crossCheckTest('j', 'hxi'))
+            self.assertTrue(crossCheckTest(SrcList, 'j', 'h', 'hxi', verbose=verbose))
         def test_HJ_CrossCheck_hyi_Jform(self):
-            self.assertTrue(crossCheckTest('j', 'hyi'))
+            self.assertTrue(crossCheckTest(SrcList, 'j', 'h', 'hyi', verbose=verbose))
         def test_HJ_CrossCheck_hzi_Jform(self):
-            self.assertTrue(crossCheckTest('j', 'hzi'))
+            self.assertTrue(crossCheckTest(SrcList, 'j', 'h', 'hzi', verbose=verbose))
 
 if __name__ == '__main__':
     unittest.main()

tests/em/fdem/forward/test_FDEM_forwardEJHB.py

@@ -0,0 +1,125 @@
+import unittest
+from SimPEG import *
+from SimPEG import EM
+import sys
+from scipy.constants import mu_0
+from SimPEG.EM.Utils.testingUtils import getFDEMProblem, crossCheckTest
+
+testEJ = True
+testBH = True
+
+TOLEJHB = 1 # averaging and more sensitive to boundary condition violations (ie. the impact of violating the boundary conditions in each case is different.)
+#TODO: choose better testing parameters to lower this 
+
+SrcList = ['RawVec', 'MagDipole', 'MagDipole_Bfield', 'MagDipole', 'CircularLoop']
+
+
+class FDEM_CrossCheck(unittest.TestCase):
+    if testEJ:
+        def test_EJ_CrossCheck_jxr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'jxr', TOL=TOLEJHB))
+        def test_EJ_CrossCheck_jyr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'jyr',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_jzr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'jzr',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_jxi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'jxi',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_jyi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'jyi',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_jzi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'jzi',  TOL=TOLEJHB))
+
+        def test_EJ_CrossCheck_exr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'exr',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_eyr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'eyr',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_ezr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'ezr',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_exi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'exi',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_eyi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'eyi',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_ezi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'ezi',  TOL=TOLEJHB))
+
+        def test_EJ_CrossCheck_bxr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'bxr',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_byr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'byr',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_bzr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'bzr',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_bxi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'bxi',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_byi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'byi',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_bzi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'bzi',  TOL=TOLEJHB))
+
+        def test_EJ_CrossCheck_hxr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'hxr',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_hyr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'hyr',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_hzr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'hzr',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_hxi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'hxi',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_hyi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'hyi',  TOL=TOLEJHB))
+        def test_EJ_CrossCheck_hzi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'e', 'j', 'hzi',  TOL=TOLEJHB))
+
+    if testBH:
+        def test_HB_CrossCheck_jxr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'jxr', TOL=TOLEJHB))
+        def test_HB_CrossCheck_jyr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'jyr',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_jzr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'jzr',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_jxi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'jxi',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_jyi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'jyi',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_jzi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'jzi',  TOL=TOLEJHB))
+
+        def test_HB_CrossCheck_exr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'exr',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_eyr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'eyr',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_ezr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'ezr',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_exi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'exi',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_eyi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'eyi',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_ezi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'ezi',  TOL=TOLEJHB))
+
+        def test_HB_CrossCheck_bxr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'bxr',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_byr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'byr',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_bzr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'bzr',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_bxi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'bxi',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_byi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'byi',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_bzi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'bzi',  TOL=TOLEJHB))
+
+        def test_HB_CrossCheck_hxr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'hxr',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_hyr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'hyr',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_hzr_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'hzr',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_hxi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'hxi',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_hyi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'hyi',  TOL=TOLEJHB))
+        def test_HB_CrossCheck_hzi_Jform(self):
+            self.assertTrue(crossCheckTest(SrcList, 'h', 'b', 'hzi',  TOL=TOLEJHB))
+
+if __name__ == '__main__':
+    unittest.main()

tests/em/fdem/forward/test_FDEM_forwardHB.py

@@ -0,0 +1,128 @@
+import unittest
+from SimPEG import *
+from SimPEG import EM
+import sys
+from scipy.constants import mu_0
+from SimPEG.EM.Utils.testingUtils import getFDEMProblem, crossCheckTest
+
+testEB = True
+testHJ = True
+testEJ = True
+testBH = True
+verbose = False
+
+TOLEJHB = 1 # averaging and more sensitive to boundary condition violations (ie. the impact of violating the boundary conditions in each case is different.)
+#TODO: choose better testing parameters to lower this 
+
+SrcList = ['RawVec', 'MagDipole_Bfield', 'MagDipole', 'CircularLoop']
+
+
+class FDEM_CrossCheck(unittest.TestCase):
+    if testBH:
+        def test_BH_CrossCheck_jxr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'jxr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_jyr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'jyr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_jzr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'jzr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_jxi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'jxi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_jyi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'jyi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_jzi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'jzi', verbose=verbose, TOL=TOLEJHB))
+
+        def test_BH_CrossCheck_exr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'exr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_eyr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'eyr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_ezr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'ezr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_exi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'exi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_eyi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'eyi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_ezi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'ezi', verbose=verbose, TOL=TOLEJHB))
+
+        def test_BH_CrossCheck_bxr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'bxr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_byr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'byr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_bzr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'bzr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_bxi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'bxi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_byi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'byi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_bzi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'bzi', verbose=verbose, TOL=TOLEJHB))
+
+        def test_BH_CrossCheck_hxr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'hxr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_hyr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'hyr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_hzr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'hzr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_hxi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'hxi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_hyi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'hyi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_hzi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'hzi', verbose=verbose, TOL=TOLEJHB))
+
+    if testBH:
+        def test_BH_CrossCheck_jxr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'jxr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_jyr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'jyr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_jzr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'jzr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_jxi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'jxi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_jyi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'jyi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_jzi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'jzi', verbose=verbose, TOL=TOLEJHB))
+
+        def test_BH_CrossCheck_exr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'exr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_eyr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'eyr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_ezr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'ezr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_exi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'exi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_eyi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'eyi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_ezi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'ezi', verbose=verbose, TOL=TOLEJHB))
+
+        def test_BH_CrossCheck_bxr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'bxr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_byr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'byr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_bzr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'bzr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_bxi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'bxi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_byi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'byi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_bzi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'bzi', verbose=verbose, TOL=TOLEJHB))
+
+        def test_BH_CrossCheck_hxr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'hxr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_hyr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'hyr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_hzr(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'hzr', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_hxi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'hxi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_hyi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'hyi', verbose=verbose, TOL=TOLEJHB))
+        def test_BH_CrossCheck_hzi(self):
+            self.assertTrue(crossCheckTest(SrcList, 'b', 'h', 'hzi', verbose=verbose, TOL=TOLEJHB))
+
+if __name__ == '__main__':
+    unittest.main()

tests/em/fdem/inverse/adjoint/test_FDEM_adjointEB.py

@@ -5,8 +5,8 @@ import sys
 from scipy.constants import mu_0
 from SimPEG.EM.Utils.testingUtils import getFDEMProblem
 
-testEB = True
-testHJ = True
+testE = True
+testB = True
 
 verbose = False
 
@@ -17,10 +17,10 @@ MU = mu_0
 freq = 1e-1
 addrandoms = True
 
-SrcType = 'RawVec' #or 'MAgDipole_Bfield', 'CircularLoop', 'RawVec'
+SrcList = ['RawVec', 'MagDipole'] #or 'MAgDipole_Bfield', 'CircularLoop', 'RawVec'
 
 def adjointTest(fdemType, comp):
-    prb = getFDEMProblem(fdemType, comp, [SrcType], freq)
+    prb = getFDEMProblem(fdemType, comp, SrcList, freq)
     print 'Adjoint %s formulation - %s' % (fdemType, comp)
 
     m  = np.log(np.ones(prb.mapping.nP)*CONDUCTIVITY)
@@ -45,7 +45,7 @@ def adjointTest(fdemType, comp):
     return np.abs(vJw - wJtv) < tol
 
 class FDEM_AdjointTests(unittest.TestCase):
-    if testEB:
+    if testE:
         def test_Jtvec_adjointTest_exr_Eform(self):
             self.assertTrue(adjointTest('e', 'exr'))
         def test_Jtvec_adjointTest_eyr_Eform(self):
@@ -72,6 +72,33 @@ class FDEM_AdjointTests(unittest.TestCase):
         def test_Jtvec_adjointTest_bzi_Eform(self):
             self.assertTrue(adjointTest('e', 'bzi'))
 
+        def test_Jtvec_adjointTest_jxr_Eform(self):
+            self.assertTrue(adjointTest('e', 'jxr'))
+        def test_Jtvec_adjointTest_jyr_Eform(self):
+            self.assertTrue(adjointTest('e', 'jyr'))
+        def test_Jtvec_adjointTest_jzr_Eform(self):
+            self.assertTrue(adjointTest('e', 'jzr'))
+        def test_Jtvec_adjointTest_jxi_Eform(self):
+            self.assertTrue(adjointTest('e', 'jxi'))
+        def test_Jtvec_adjointTest_jyi_Eform(self):
+            self.assertTrue(adjointTest('e', 'jyi'))
+        def test_Jtvec_adjointTest_jzi_Eform(self):
+            self.assertTrue(adjointTest('e', 'jzi'))
+
+        def test_Jtvec_adjointTest_hxr_Eform(self):
+            self.assertTrue(adjointTest('e', 'hxr'))
+        def test_Jtvec_adjointTest_hyr_Eform(self):
+            self.assertTrue(adjointTest('e', 'hyr'))
+        def test_Jtvec_adjointTest_hzr_Eform(self):
+            self.assertTrue(adjointTest('e', 'hzr'))
+        def test_Jtvec_adjointTest_hxi_Eform(self):
+            self.assertTrue(adjointTest('e', 'hxi'))
+        def test_Jtvec_adjointTest_hyi_Eform(self):
+            self.assertTrue(adjointTest('e', 'hyi'))
+        def test_Jtvec_adjointTest_hzi_Eform(self):
+            self.assertTrue(adjointTest('e', 'hzi'))
+
+    if testB:
         def test_Jtvec_adjointTest_exr_Bform(self):
             self.assertTrue(adjointTest('b', 'exr'))
         def test_Jtvec_adjointTest_eyr_Bform(self):
@@ -84,6 +111,7 @@ class FDEM_AdjointTests(unittest.TestCase):
             self.assertTrue(adjointTest('b', 'eyi'))
         def test_Jtvec_adjointTest_ezi_Bform(self):
             self.assertTrue(adjointTest('b', 'ezi'))
+
         def test_Jtvec_adjointTest_bxr_Bform(self):
             self.assertTrue(adjointTest('b', 'bxr'))
         def test_Jtvec_adjointTest_byr_Bform(self):
@@ -97,59 +125,31 @@ class FDEM_AdjointTests(unittest.TestCase):
         def test_Jtvec_adjointTest_bzi_Bform(self):
             self.assertTrue(adjointTest('b', 'bzi'))
 
+        def test_Jtvec_adjointTest_jxr_Bform(self):
+            self.assertTrue(adjointTest('b', 'jxr'))
+        def test_Jtvec_adjointTest_jyr_Bform(self):
+            self.assertTrue(adjointTest('b', 'jyr'))
+        def test_Jtvec_adjointTest_jzr_Bform(self):
+            self.assertTrue(adjointTest('b', 'jzr'))
+        def test_Jtvec_adjointTest_jxi_Bform(self):
+            self.assertTrue(adjointTest('b', 'jxi'))
+        def test_Jtvec_adjointTest_jyi_Bform(self):
+            self.assertTrue(adjointTest('b', 'jyi'))
+        def test_Jtvec_adjointTest_jzi_Bform(self):
+            self.assertTrue(adjointTest('b', 'jzi'))
 
-    if testHJ:
-        def test_Jtvec_adjointTest_jxr_Jform(self):
-            self.assertTrue(adjointTest('j', 'jxr'))
-        def test_Jtvec_adjointTest_jyr_Jform(self):
-            self.assertTrue(adjointTest('j', 'jyr'))
-        def test_Jtvec_adjointTest_jzr_Jform(self):
-            self.assertTrue(adjointTest('j', 'jzr'))
-        def test_Jtvec_adjointTest_jxi_Jform(self):
-            self.assertTrue(adjointTest('j', 'jxi'))
-        def test_Jtvec_adjointTest_jyi_Jform(self):
-            self.assertTrue(adjointTest('j', 'jyi'))
-        def test_Jtvec_adjointTest_jzi_Jform(self):
-            self.assertTrue(adjointTest('j', 'jzi'))
-
-        def test_Jtvec_adjointTest_hxr_Jform(self):
-            self.assertTrue(adjointTest('j', 'hxr'))
-        def test_Jtvec_adjointTest_hyr_Jform(self):
-            self.assertTrue(adjointTest('j', 'hyr'))
-        def test_Jtvec_adjointTest_hzr_Jform(self):
-            self.assertTrue(adjointTest('j', 'hzr'))
-        def test_Jtvec_adjointTest_hxi_Jform(self):
-            self.assertTrue(adjointTest('j', 'hxi'))
-        def test_Jtvec_adjointTest_hyi_Jform(self):
-            self.assertTrue(adjointTest('j', 'hyi'))
-        def test_Jtvec_adjointTest_hzi_Jform(self):
-             self.assertTrue(adjointTest('j', 'hzi'))
-
-        def test_Jtvec_adjointTest_hxr_Hform(self):
-            self.assertTrue(adjointTest('h', 'hxr'))
-        def test_Jtvec_adjointTest_hyr_Hform(self):
-            self.assertTrue(adjointTest('h', 'hyr'))
-        def test_Jtvec_adjointTest_hzr_Hform(self):
-            self.assertTrue(adjointTest('h', 'hzr'))
-        def test_Jtvec_adjointTest_hxi_Hform(self):
-            self.assertTrue(adjointTest('h', 'hxi'))
-        def test_Jtvec_adjointTest_hyi_Hform(self):
-            self.assertTrue(adjointTest('h', 'hyi'))
-        def test_Jtvec_adjointTest_hzi_Hform(self):
-            self.assertTrue(adjointTest('h', 'hzi'))
-
-        def test_Jtvec_adjointTest_hxr_Hform(self):
-            self.assertTrue(adjointTest('h', 'jxr'))
-        def test_Jtvec_adjointTest_hyr_Hform(self):
-            self.assertTrue(adjointTest('h', 'jyr'))
-        def test_Jtvec_adjointTest_hzr_Hform(self):
-            self.assertTrue(adjointTest('h', 'jzr'))
-        def test_Jtvec_adjointTest_hxi_Hform(self):
-            self.assertTrue(adjointTest('h', 'jxi'))
-        def test_Jtvec_adjointTest_hyi_Hform(self):
-            self.assertTrue(adjointTest('h', 'jyi'))
-        def test_Jtvec_adjointTest_hzi_Hform(self):
-            self.assertTrue(adjointTest('h', 'jzi'))
+        def test_Jtvec_adjointTest_hxr_Bform(self):
+            self.assertTrue(adjointTest('b', 'hxr'))
+        def test_Jtvec_adjointTest_hyr_Bform(self):
+            self.assertTrue(adjointTest('b', 'hyr'))
+        def test_Jtvec_adjointTest_hzr_Bform(self):
+            self.assertTrue(adjointTest('b', 'hzr'))
+        def test_Jtvec_adjointTest_hxi_Bform(self):
+            self.assertTrue(adjointTest('b', 'hxi'))
+        def test_Jtvec_adjointTest_hyi_Bform(self):
+            self.assertTrue(adjointTest('b', 'hyi'))
+        def test_Jtvec_adjointTest_hzi_Bform(self):
+            self.assertTrue(adjointTest('b', 'hzi'))
 
 
 if __name__ == '__main__':

tests/em/fdem/inverse/adjoint/test_FDEM_adjointHJ.py

@@ -0,0 +1,155 @@
+import unittest
+from SimPEG import *
+from SimPEG import EM
+import sys
+from scipy.constants import mu_0
+from SimPEG.EM.Utils.testingUtils import getFDEMProblem
+
+testJ = True
+testH = True
+
+verbose = False
+
+TOL = 1e-5
+FLR = 1e-20 # "zero", so if residual below this --> pass regardless of order
+CONDUCTIVITY = 1e1
+MU = mu_0
+freq = 1e-1
+addrandoms = True
+
+SrcList = ['RawVec', 'MagDipole'] #or 'MAgDipole_Bfield', 'CircularLoop', 'RawVec'
+
+def adjointTest(fdemType, comp):
+    prb = getFDEMProblem(fdemType, comp, SrcList, freq)
+    print 'Adjoint %s formulation - %s' % (fdemType, comp)
+
+    m  = np.log(np.ones(prb.mapping.nP)*CONDUCTIVITY)
+    mu = np.ones(prb.mesh.nC)*MU
+
+    if addrandoms is True:
+        m  = m + np.random.randn(prb.mapping.nP)*np.log(CONDUCTIVITY)*1e-1
+        mu = mu + np.random.randn(prb.mesh.nC)*MU*1e-1
+
+    survey = prb.survey
+    u = prb.fields(m)
+
+    v = np.random.rand(survey.nD)
+    w = np.random.rand(prb.mesh.nC)
+
+    vJw = v.dot(prb.Jvec(m, w, u))
+    wJtv = w.dot(prb.Jtvec(m, v, u))
+    tol = np.max([TOL*(10**int(np.log10(np.abs(vJw)))),FLR])
+    print vJw, wJtv, vJw - wJtv, tol, np.abs(vJw - wJtv) < tol
+    return np.abs(vJw - wJtv) < tol
+
+class FDEM_AdjointTests(unittest.TestCase):
+
+    if testJ:
+        def test_Jtvec_adjointTest_jxr_Jform(self):
+            self.assertTrue(adjointTest('j', 'jxr'))
+        def test_Jtvec_adjointTest_jyr_Jform(self):
+            self.assertTrue(adjointTest('j', 'jyr'))
+        def test_Jtvec_adjointTest_jzr_Jform(self):
+            self.assertTrue(adjointTest('j', 'jzr'))
+        def test_Jtvec_adjointTest_jxi_Jform(self):
+            self.assertTrue(adjointTest('j', 'jxi'))
+        def test_Jtvec_adjointTest_jyi_Jform(self):
+            self.assertTrue(adjointTest('j', 'jyi'))
+        def test_Jtvec_adjointTest_jzi_Jform(self):
+            self.assertTrue(adjointTest('j', 'jzi'))
+
+        def test_Jtvec_adjointTest_hxr_Jform(self):
+            self.assertTrue(adjointTest('j', 'hxr'))
+        def test_Jtvec_adjointTest_hyr_Jform(self):
+            self.assertTrue(adjointTest('j', 'hyr'))
+        def test_Jtvec_adjointTest_hzr_Jform(self):
+            self.assertTrue(adjointTest('j', 'hzr'))
+        def test_Jtvec_adjointTest_hxi_Jform(self):
+            self.assertTrue(adjointTest('j', 'hxi'))
+        def test_Jtvec_adjointTest_hyi_Jform(self):
+            self.assertTrue(adjointTest('j', 'hyi'))
+        def test_Jtvec_adjointTest_hzi_Jform(self):
+            self.assertTrue(adjointTest('j', 'hzi'))
+
+        def test_Jtvec_adjointTest_exr_Jform(self):
+            self.assertTrue(adjointTest('j', 'exr'))
+        def test_Jtvec_adjointTest_eyr_Jform(self):
+            self.assertTrue(adjointTest('j', 'eyr'))
+        def test_Jtvec_adjointTest_ezr_Jform(self):
+            self.assertTrue(adjointTest('j', 'ezr'))
+        def test_Jtvec_adjointTest_exi_Jform(self):
+            self.assertTrue(adjointTest('j', 'exi'))
+        def test_Jtvec_adjointTest_eyi_Jform(self):
+            self.assertTrue(adjointTest('j', 'eyi'))
+        def test_Jtvec_adjointTest_ezi_Jform(self):
+            self.assertTrue(adjointTest('j', 'ezi'))
+
+        def test_Jtvec_adjointTest_bxr_Jform(self):
+            self.assertTrue(adjointTest('j', 'bxr'))
+        def test_Jtvec_adjointTest_byr_Jform(self):
+            self.assertTrue(adjointTest('j', 'byr'))
+        def test_Jtvec_adjointTest_bzr_Jform(self):
+            self.assertTrue(adjointTest('j', 'bzr'))
+        def test_Jtvec_adjointTest_bxi_Jform(self):
+            self.assertTrue(adjointTest('j', 'bxi'))
+        def test_Jtvec_adjointTest_byi_Jform(self):
+            self.assertTrue(adjointTest('j', 'byi'))
+        def test_Jtvec_adjointTest_bzi_Jform(self):
+            self.assertTrue(adjointTest('j', 'bzi'))
+
+    if testH: 
+        def test_Jtvec_adjointTest_hxr_Hform(self):
+            self.assertTrue(adjointTest('h', 'hxr'))
+        def test_Jtvec_adjointTest_hyr_Hform(self):
+            self.assertTrue(adjointTest('h', 'hyr'))
+        def test_Jtvec_adjointTest_hzr_Hform(self):
+            self.assertTrue(adjointTest('h', 'hzr'))
+        def test_Jtvec_adjointTest_hxi_Hform(self):
+            self.assertTrue(adjointTest('h', 'hxi'))
+        def test_Jtvec_adjointTest_hyi_Hform(self):
+            self.assertTrue(adjointTest('h', 'hyi'))
+        def test_Jtvec_adjointTest_hzi_Hform(self):
+            self.assertTrue(adjointTest('h', 'hzi'))
+
+        def test_Jtvec_adjointTest_jxr_Hform(self):
+            self.assertTrue(adjointTest('h', 'jxr'))
+        def test_Jtvec_adjointTest_jyr_Hform(self):
+            self.assertTrue(adjointTest('h', 'jyr'))
+        def test_Jtvec_adjointTest_jzr_Hform(self):
+            self.assertTrue(adjointTest('h', 'jzr'))
+        def test_Jtvec_adjointTest_jxi_Hform(self):
+            self.assertTrue(adjointTest('h', 'jxi'))
+        def test_Jtvec_adjointTest_jyi_Hform(self):
+            self.assertTrue(adjointTest('h', 'jyi'))
+        def test_Jtvec_adjointTest_jzi_Hform(self):
+            self.assertTrue(adjointTest('h', 'jzi'))
+
+        def test_Jtvec_adjointTest_exr_Hform(self):
+            self.assertTrue(adjointTest('h', 'exr'))
+        def test_Jtvec_adjointTest_eyr_Hform(self):
+            self.assertTrue(adjointTest('h', 'eyr'))
+        def test_Jtvec_adjointTest_ezr_Hform(self):
+            self.assertTrue(adjointTest('h', 'ezr'))
+        def test_Jtvec_adjointTest_exi_Hform(self):
+            self.assertTrue(adjointTest('h', 'exi'))
+        def test_Jtvec_adjointTest_eyi_Hform(self):
+            self.assertTrue(adjointTest('h', 'eyi'))
+        def test_Jtvec_adjointTest_ezi_Hform(self):
+            self.assertTrue(adjointTest('h', 'ezi'))
+
+        def test_Jtvec_adjointTest_bxr_Hform(self):
+            self.assertTrue(adjointTest('h', 'bxr'))
+        def test_Jtvec_adjointTest_byr_Hform(self):
+            self.assertTrue(adjointTest('h', 'byr'))
+        def test_Jtvec_adjointTest_bzr_Hform(self):
+            self.assertTrue(adjointTest('h', 'bzr'))
+        def test_Jtvec_adjointTest_bxi_Hform(self):
+            self.assertTrue(adjointTest('h', 'bxi'))
+        def test_Jtvec_adjointTest_byi_Hform(self):
+            self.assertTrue(adjointTest('h', 'byi'))
+        def test_Jtvec_adjointTest_bzi_Hform(self):
+            self.assertTrue(adjointTest('h', 'bzi'))
+
+
+if __name__ == '__main__':
+    unittest.main()

tests/em/fdem/inverse/derivs/test_FDEM_derivs.py

@@ -5,9 +5,11 @@ import sys
 from scipy.constants import mu_0
 from SimPEG.EM.Utils.testingUtils import getFDEMProblem
 
-testDerivs = True
-testEB = True
-testHJ = True
+
+testE = True
+testB = True
+testH = True
+testJ = True
 
 verbose = False
 
@@ -18,12 +20,12 @@ MU = mu_0
 freq = 1e-1
 addrandoms = True
 
-SrcType = 'RawVec' #or 'MAgDipole_Bfield', 'CircularLoop', 'RawVec'
+SrcType = ['MagDipole', 'RawVec'] #or 'MAgDipole_Bfield', 'CircularLoop', 'RawVec'
 
 
 def derivTest(fdemType, comp):
 
-    prb = getFDEMProblem(fdemType, comp, [SrcType], freq)
+    prb = getFDEMProblem(fdemType, comp, SrcType, freq)
     print '%s formulation - %s' % (fdemType, comp)
     x0 = np.log(np.ones(prb.mapping.nP)*CONDUCTIVITY)
     mu = np.log(np.ones(prb.mesh.nC)*MU)
@@ -32,9 +34,6 @@ def derivTest(fdemType, comp):
         x0 = x0 + np.random.randn(prb.mapping.nP)*np.log(CONDUCTIVITY)*1e-1
         mu = mu + np.random.randn(prb.mapping.nP)*MU*1e-1
 
-    # prb.PropMap.PropModel.mu = mu
-    # prb.PropMap.PropModel.mui = 1./mu
-
     survey = prb.survey
     def fun(x):
         return survey.dpred(x), lambda x: prb.Jvec(x0, x)
@@ -43,7 +42,7 @@ def derivTest(fdemType, comp):
 
 class FDEM_DerivTests(unittest.TestCase):
 
-    if testEB:
+    if testE:
         def test_Jvec_exr_Eform(self):
             self.assertTrue(derivTest('e', 'exr'))
         def test_Jvec_eyr_Eform(self):
@@ -70,6 +69,33 @@ class FDEM_DerivTests(unittest.TestCase):
         def test_Jvec_bzi_Eform(self):
             self.assertTrue(derivTest('e', 'bzi'))
 
+        def test_Jvec_exr_Eform(self):
+            self.assertTrue(derivTest('e', 'jxr'))
+        def test_Jvec_eyr_Eform(self):
+            self.assertTrue(derivTest('e', 'jyr'))
+        def test_Jvec_ezr_Eform(self):
+            self.assertTrue(derivTest('e', 'jzr'))
+        def test_Jvec_exi_Eform(self):
+            self.assertTrue(derivTest('e', 'jxi'))
+        def test_Jvec_eyi_Eform(self):
+            self.assertTrue(derivTest('e', 'jyi'))
+        def test_Jvec_ezi_Eform(self):
+            self.assertTrue(derivTest('e', 'jzi'))
+
+        def test_Jvec_bxr_Eform(self):
+            self.assertTrue(derivTest('e', 'hxr'))
+        def test_Jvec_byr_Eform(self):
+            self.assertTrue(derivTest('e', 'hyr'))
+        def test_Jvec_bzr_Eform(self):
+            self.assertTrue(derivTest('e', 'hzr'))
+        def test_Jvec_bxi_Eform(self):
+            self.assertTrue(derivTest('e', 'hxi'))
+        def test_Jvec_byi_Eform(self):
+            self.assertTrue(derivTest('e', 'hyi'))
+        def test_Jvec_bzi_Eform(self):
+            self.assertTrue(derivTest('e', 'hzi'))
+
+    if testB:
         def test_Jvec_exr_Bform(self):
             self.assertTrue(derivTest('b', 'exr'))
         def test_Jvec_eyr_Bform(self):
@@ -96,7 +122,33 @@ class FDEM_DerivTests(unittest.TestCase):
         def test_Jvec_bzi_Bform(self):
             self.assertTrue(derivTest('b', 'bzi'))
 
-    if testHJ:
+        def test_Jvec_jxr_Bform(self):
+            self.assertTrue(derivTest('b', 'jxr'))
+        def test_Jvec_jyr_Bform(self):
+            self.assertTrue(derivTest('b', 'jyr'))
+        def test_Jvec_jzr_Bform(self):
+            self.assertTrue(derivTest('b', 'jzr'))
+        def test_Jvec_jxi_Bform(self):
+            self.assertTrue(derivTest('b', 'jxi'))
+        def test_Jvec_jyi_Bform(self):
+            self.assertTrue(derivTest('b', 'jyi'))
+        def test_Jvec_jzi_Bform(self):
+            self.assertTrue(derivTest('b', 'jzi'))
+
+        def test_Jvec_hxr_Bform(self):
+            self.assertTrue(derivTest('b', 'hxr'))
+        def test_Jvec_hyr_Bform(self):
+            self.assertTrue(derivTest('b', 'hyr'))
+        def test_Jvec_hzr_Bform(self):
+            self.assertTrue(derivTest('b', 'hzr'))
+        def test_Jvec_hxi_Bform(self):
+            self.assertTrue(derivTest('b', 'hxi'))
+        def test_Jvec_hyi_Bform(self):
+            self.assertTrue(derivTest('b', 'hyi'))
+        def test_Jvec_hzi_Bform(self):
+            self.assertTrue(derivTest('b', 'hzi'))
+
+    if testJ:
         def test_Jvec_jxr_Jform(self):
             self.assertTrue(derivTest('j', 'jxr'))
         def test_Jvec_jyr_Jform(self):
@@ -123,6 +175,34 @@ class FDEM_DerivTests(unittest.TestCase):
         def test_Jvec_hzi_Jform(self):
             self.assertTrue(derivTest('j', 'hzi'))
 
+        def test_Jvec_exr_Jform(self):
+            self.assertTrue(derivTest('j', 'exr'))
+        def test_Jvec_eyr_Jform(self):
+            self.assertTrue(derivTest('j', 'eyr'))
+        def test_Jvec_ezr_Jform(self):
+            self.assertTrue(derivTest('j', 'ezr'))
+        def test_Jvec_exi_Jform(self):
+            self.assertTrue(derivTest('j', 'exi'))
+        def test_Jvec_eyi_Jform(self):
+            self.assertTrue(derivTest('j', 'eyi'))
+        def test_Jvec_ezi_Jform(self):
+            self.assertTrue(derivTest('j', 'ezi'))
+
+        def test_Jvec_bxr_Jform(self):
+            self.assertTrue(derivTest('j', 'bxr'))
+        def test_Jvec_byr_Jform(self):
+            self.assertTrue(derivTest('j', 'byr'))
+        def test_Jvec_bzr_Jform(self):
+            self.assertTrue(derivTest('j', 'bzr'))
+        def test_Jvec_bxi_Jform(self):
+            self.assertTrue(derivTest('j', 'bxi'))
+        def test_Jvec_byi_Jform(self):
+            self.assertTrue(derivTest('j', 'byi'))
+        def test_Jvec_bzi_Jform(self):
+            self.assertTrue(derivTest('j', 'bzi'))
+
+
+    if testH:
         def test_Jvec_hxr_Hform(self):
             self.assertTrue(derivTest('h', 'hxr'))
         def test_Jvec_hyr_Hform(self):
@@ -149,6 +229,32 @@ class FDEM_DerivTests(unittest.TestCase):
         def test_Jvec_hzi_Hform(self):
             self.assertTrue(derivTest('h', 'jzi'))
 
+        def test_Jvec_exr_Hform(self):
+            self.assertTrue(derivTest('h', 'exr'))
+        def test_Jvec_eyr_Hform(self):
+            self.assertTrue(derivTest('h', 'eyr'))
+        def test_Jvec_ezr_Hform(self):
+            self.assertTrue(derivTest('h', 'ezr'))
+        def test_Jvec_exi_Hform(self):
+            self.assertTrue(derivTest('h', 'exi'))
+        def test_Jvec_eyi_Hform(self):
+            self.assertTrue(derivTest('h', 'eyi'))
+        def test_Jvec_ezi_Hform(self):
+            self.assertTrue(derivTest('h', 'ezi'))
+
+        def test_Jvec_bxr_Hform(self):
+            self.assertTrue(derivTest('h', 'bxr'))
+        def test_Jvec_byr_Hform(self):
+            self.assertTrue(derivTest('h', 'byr'))
+        def test_Jvec_bzr_Hform(self):
+            self.assertTrue(derivTest('h', 'bzr'))
+        def test_Jvec_bxi_Hform(self):
+            self.assertTrue(derivTest('h', 'bxi'))
+        def test_Jvec_byi_Hform(self):
+            self.assertTrue(derivTest('h', 'byi'))
+        def test_Jvec_bzi_Hform(self):
+            self.assertTrue(derivTest('h', 'bzi'))
+
 
 if __name__ == '__main__':
     unittest.main()

tests/em/tdem/test_TDEM_b_DerivAdjoint.py

@@ -18,8 +18,8 @@ class TDEM_bDerivTests(unittest.TestCase):
         mesh = Mesh.CylMesh([hx,1,hy], '00C')
 
         active = mesh.vectorCCz<0.
-        activeMap = Maps.ActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
-        mapping = Maps.ExpMap(mesh) * Maps.Vertical1DMap(mesh) * activeMap
+        activeMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
+        mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * activeMap
 
         rxOffset = 40.
         rx = EM.TDEM.RxTDEM(np.array([[rxOffset, 0., 0.]]), np.logspace(-4,-3, 20), 'bz')
@@ -204,8 +204,8 @@ class TDEM_bDerivTests(unittest.TestCase):
         d = Survey.Data(survey,v=d_vec)
 
         # Check that d.T*Q*f = f.T*Q.T*d
-        V1 = d_vec.dot(survey.projectFieldsDeriv(None, v=f).tovec())
-        V2 = f.tovec().dot(survey.projectFieldsDeriv(None, v=d, adjoint=True).tovec())
+        V1 = d_vec.dot(survey.evalDeriv(None, v=f).tovec())
+        V2 = f.tovec().dot(survey.evalDeriv(None, v=d, adjoint=True).tovec())
 
         self.assertTrue((V1-V2)/np.abs(V1) < tol)
 

tests/em/tdem/test_TDEM_b_MultiSrc_DerivAdjoint.py

@@ -17,8 +17,8 @@ class TDEM_bDerivTests(unittest.TestCase):
         mesh = Mesh.CylMesh([hx,1,hy], '00C')
 
         active = mesh.vectorCCz<0.
-        activeMap = Maps.ActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
-        mapping = Maps.ExpMap(mesh) * Maps.Vertical1DMap(mesh) * activeMap
+        activeMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
+        mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * activeMap
 
         rxOffset = 40.
         rx = EM.TDEM.RxTDEM(np.array([[rxOffset, 0., 0.]]), np.logspace(-4,-3, 20), 'bz')
@@ -108,8 +108,8 @@ class TDEM_bDerivTests(unittest.TestCase):
         d = Survey.Data(survey,v=d_vec)
 
         # Check that d.T*Q*f = f.T*Q.T*d
-        V1 = d_vec.dot(survey.projectFieldsDeriv(None, v=f).tovec())
-        V2 = np.sum((f.tovec())*(survey.projectFieldsDeriv(None, v=d, adjoint=True).tovec()))
+        V1 = d_vec.dot(survey.evalDeriv(None, v=f).tovec())
+        V2 = np.sum((f.tovec())*(survey.evalDeriv(None, v=d, adjoint=True).tovec()))
 
         self.assertTrue((V1-V2)/np.abs(V1) < 1e-6)
 

tests/em/tdem/test_TDEM_combos.py

@@ -14,8 +14,8 @@ def getProb(meshType='CYL',rxTypes='bx,bz',nSrc=1):
     mesh = Mesh.CylMesh([hx,1,hy], '00C')
 
     active = mesh.vectorCCz<0.
-    activeMap = Maps.ActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
-    mapping = Maps.ExpMap(mesh) * Maps.Vertical1DMap(mesh) * activeMap
+    activeMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
+    mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * activeMap
 
     rxOffset = 40.
 

tests/em/tdem/test_TDEM_forward_Analytic.py

@@ -10,7 +10,9 @@ except ImportError, e:
     MumpsSolver = SolverLU
 
 
-def halfSpaceProblemAnaDiff(meshType, sig_half=1e-2, rxOffset=50., bounds=[1e-5,1e-3], showIt=False):
+def halfSpaceProblemAnaDiff(meshType, sig_half=1e-2, rxOffset=50., bounds=None, showIt=False):
+    if bounds is None:
+        bounds = [1e-5,1e-3]
     if meshType == 'CYL':
         cs, ncx, ncz, npad = 5., 30, 10, 15
         hx = [(cs,ncx), (cs,npad,1.3)]
@@ -24,8 +26,8 @@ def halfSpaceProblemAnaDiff(meshType, sig_half=1e-2, rxOffset=50., bounds=[1e-5,
         mesh = Mesh.TensorMesh([hx,hy,hz], 'CCC')
 
     active = mesh.vectorCCz<0.
-    actMap = Maps.ActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
-    mapping = Maps.ExpMap(mesh) * Maps.Vertical1DMap(mesh) * actMap
+    actMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
+    mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * actMap
 
     rx = EM.TDEM.RxTDEM(np.array([[rxOffset, 0., 0.]]), np.logspace(-5,-4, 21), 'bz')
     src = EM.TDEM.SrcTDEM_VMD_MVP([rx], loc=np.array([0., 0., 0.]))

tests/flow/test_Richards.py

@@ -116,8 +116,8 @@ class RichardsTests1D(unittest.TestCase):
         v = np.random.rand(self.survey.nD)
         z = np.random.rand(self.M.nC)
         Hs = self.prob.fields(self.Ks)
-        vJz = v.dot(self.prob.Jvec(self.Ks,z,u=Hs))
-        zJv = z.dot(self.prob.Jtvec(self.Ks,v,u=Hs))
+        vJz = v.dot(self.prob.Jvec(self.Ks,z,f=Hs))
+        zJv = z.dot(self.prob.Jtvec(self.Ks,v,f=Hs))
         tol = TOL*(10**int(np.log10(np.abs(zJv))))
         passed = np.abs(vJz - zJv) < tol
         print 'Richards Adjoint Test - PressureHead'
@@ -188,8 +188,8 @@ class RichardsTests2D(unittest.TestCase):
         v = np.random.rand(self.survey.nD)
         z = np.random.rand(self.M.nC)
         Hs = self.prob.fields(self.Ks)
-        vJz = v.dot(self.prob.Jvec(self.Ks,z,u=Hs))
-        zJv = z.dot(self.prob.Jtvec(self.Ks,v,u=Hs))
+        vJz = v.dot(self.prob.Jvec(self.Ks,z,f=Hs))
+        zJv = z.dot(self.prob.Jtvec(self.Ks,v,f=Hs))
         tol = TOL*(10**int(np.log10(np.abs(zJv))))
         passed = np.abs(vJz - zJv) < tol
         print '2D: Richards Adjoint Test - PressureHead'
@@ -260,8 +260,8 @@ class RichardsTests3D(unittest.TestCase):
         v = np.random.rand(self.survey.nD)
         z = np.random.rand(self.M.nC)
         Hs = self.prob.fields(self.Ks)
-        vJz = v.dot(self.prob.Jvec(self.Ks,z,u=Hs))
-        zJv = z.dot(self.prob.Jtvec(self.Ks,v,u=Hs))
+        vJz = v.dot(self.prob.Jvec(self.Ks,z,f=Hs))
+        zJv = z.dot(self.prob.Jtvec(self.Ks,v,f=Hs))
         tol = TOL*(10**int(np.log10(np.abs(zJv))))
         passed = np.abs(vJz - zJv) < tol
         print '3D: Richards Adjoint Test - PressureHead'

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.eval(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.eval(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.eval(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.eval(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()