Bump version: 0.1.3 → 0.1.4

Speed up the tests with pymatsolver.

.bumpversion.cfg

@@ -1,4 +1,4 @@
 [bumpversion]
-current_version = 0.1.3
+current_version = 0.1.4
 files = setup.py SimPEG/__init__.py docs/conf.py
 

.gitignore

@@ -38,5 +38,4 @@ nosetests.xml
 *.sublime-project
 *.sublime-workspace
 docs/_build/
-*_cython.c
 Makefile

.travis.yml

@@ -2,6 +2,27 @@ language: python
 python:
   - 2.7
 
+sudo: false
+
+addons:
+  apt:
+    packages:
+    - gcc
+    - gfortran
+    - libopenmpi-dev
+    - libmumps-seq-dev
+    - libblas-dev
+    - liblapack-dev
+
+env:
+    - TEST_DIR="tests/mesh tests/base tests/utils"
+    - TEST_DIR=tests/examples
+    - TEST_DIR=tests/em/fdem/forward
+    - TEST_DIR=tests/em/fdem/inverse/derivs
+    - TEST_DIR=tests/em/fdem/inverse/adjoint
+    - TEST_DIR=tests/em/tdem
+    - TEST_DIR=tests/flow
+
 # Setup anaconda
 before_install:
   - if [ ${TRAVIS_PYTHON_VERSION:0:1} == "2" ]; then wget http://repo.continuum.io/miniconda/Miniconda-3.8.3-Linux-x86_64.sh -O miniconda.sh; else wget http://repo.continuum.io/miniconda/Miniconda3-3.8.3-Linux-x86_64.sh -O miniconda.sh; fi
@@ -9,20 +30,21 @@ before_install:
   - ./miniconda.sh -b
   - export PATH=/home/travis/anaconda/bin:/home/travis/miniconda/bin:$PATH
   - conda update --yes conda
-  # The next couple lines fix a crash with multiprocessing on Travis and are not specific to using Miniconda
-  - sudo rm -rf /dev/shm
-  - sudo ln -s /run/shm /dev/shm
 
 # Install packages
 install:
-  - conda install --yes pip python=$TRAVIS_PYTHON_VERSION numpy scipy matplotlib cython
+  - conda install --yes pip python=$TRAVIS_PYTHON_VERSION numpy scipy matplotlib cython ipython nose
   - pip install nose-cov python-coveralls
-  # - pip install -r requirements.txt
+
+  - git clone https://github.com/rowanc1/pymatsolver.git
+  - cd pymatsolver; python setup.py install; cd ..
+
   - python setup.py install
+  - python setup.py build_ext --inplace
 
 # Run test
 script:
-  - nosetests --with-cov --cov SimPEG --cov-config .coveragerc -v -s
+  - nosetests $TEST_DIR --with-cov --cov SimPEG --cov-config .coveragerc -v -s
 
 # Calculate coverage
 after_success:

CITATION.rst

@@ -0,0 +1,22 @@
+Citing SimPEG
+=============
+
+There is a paper about SimPEG!
+
+
+    Cockett, R., Kang, S., Heagy, L. J., Pidlisecky, A., & Oldenburg, D. W. (2015). SimPEG: An open source framework for simulation and gradient based parameter estimation in geophysical applications. Computers & Geosciences.
+
+
+BibTex:
+-------
+
+.. code::
+
+    @article{cockett2015simpeg,
+      title={SimPEG: An open source framework for simulation and gradient based parameter estimation in geophysical applications},
+      author={Cockett, Rowan and Kang, Seogi and Heagy, Lindsey J and Pidlisecky, Adam and Oldenburg, Douglas W},
+      journal={Computers \& Geosciences},
+      year={2015},
+      publisher={Elsevier}
+    }
+

README.rst

@@ -36,6 +36,28 @@ The vision is to create a package for finite volume simulation with applications
 * designed for large-scale inversions
 
 
+Citing SimPEG:
+--------------
+
+There is a paper about SimPEG!
+
+
+    Cockett, R., Kang, S., Heagy, L. J., Pidlisecky, A., & Oldenburg, D. W. (2015). SimPEG: An open source framework for simulation and gradient based parameter estimation in geophysical applications. Computers & Geosciences.
+
+
+**BibTex:**
+
+.. code::
+
+    @article{cockett2015simpeg,
+      title={SimPEG: An open source framework for simulation and gradient based parameter estimation in geophysical applications},
+      author={Cockett, Rowan and Kang, Seogi and Heagy, Lindsey J and Pidlisecky, Adam and Oldenburg, Douglas W},
+      journal={Computers \& Geosciences},
+      year={2015},
+      publisher={Elsevier}
+    }
+
+
 Website:
 http://simpeg.xyz
 
@@ -57,4 +79,4 @@ https://github.com/simpeg/simpeg/issues
 
 
 Code Snippets & Tutorials:
-http://www.row1.ca/simpeg
+http://simpeg.xyz/Journal

SimPEG/Directives.py

@@ -149,7 +149,7 @@ class TargetMisfit(InversionDirective):
     @property
     def target(self):
         if getattr(self, '_target', None) is None:
-            self._target = self.survey.nD
+            self._target = self.survey.nD*0.5
         return self._target
     @target.setter
     def target(self, val):

SimPEG/EM/Analytics/FDEM.py

@@ -0,0 +1,153 @@
+from __future__ import division
+import numpy as np
+from scipy.constants import mu_0, pi
+from scipy.special import erf
+import matplotlib.pyplot as plt
+from SimPEG import Utils
+
+
+def hzAnalyticDipoleF(r, freq, sigma, secondary=True, mu=mu_0):
+    """
+    4.56 in Ward and Hohmann
+
+    .. plot::
+
+        import matplotlib.pyplot as plt
+        from SimPEG import EM
+        freq = np.logspace(-1, 6, 61)
+        test = EM.Analytics.FDEM.hzAnalyticDipoleF(100, freq, 0.001, secondary=False)
+        plt.loglog(freq, abs(test.real))
+        plt.loglog(freq, abs(test.imag))
+        plt.title('Response at $r$=100m')
+        plt.xlabel('Frequency')
+        plt.ylabel('Response')
+        plt.legend(('real','imag'))
+        plt.show()
+
+    """
+    r = np.abs(r)
+    k = np.sqrt(-1j*2.*np.pi*freq*mu*sigma)
+
+    m = 1
+    front = m / (2. * np.pi * (k**2) * (r**5) )
+    back = 9 - ( 9 + 9j * k * r - 4 * (k**2) * (r**2) - 1j * (k**3) * (r**3)) * np.exp(-1j*k*r)
+    hz = front*back
+
+    if secondary:
+        hp =-1/(4*np.pi*r**3)
+        hz = hz-hp
+
+    if hz.ndim == 1:
+        hz = Utils.mkvc(hz,2)
+
+    return hz
+
+def MagneticDipoleWholeSpace(XYZ, srcLoc, sig, f, moment=1., orientation='X', mu = mu_0):
+    """
+    Analytical solution for a dipole in a whole-space.
+
+    Equation 2.57 of Ward and Hohmann
+
+    TODOs:
+        - set it up to instead take a mesh & survey
+        - add E-fields
+        - handle multiple frequencies
+        - add divide by zero safety
+
+
+    .. plot::
+
+        from SimPEG import EM
+        import matplotlib.pyplot as plt
+        freqs = np.logspace(-2,5,100)
+        Bx, By, Bz = EM.Analytics.FDEM.AnalyticMagDipoleWholeSpace([0,100,0], [0,0,0], 1e-2, freqs, m=1, orientation='Z')
+        plt.loglog(freqs, np.abs(Bz.real)/mu_0, 'b')
+        plt.loglog(freqs, np.abs(Bz.imag)/mu_0, 'r')
+        plt.legend(('real','imag'))
+        plt.show()
+
+
+    """
+
+    XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
+
+    dx = XYZ[:,0]-srcLoc[0]
+    dy = XYZ[:,1]-srcLoc[1]
+    dz = XYZ[:,2]-srcLoc[2]
+
+    r  = np.sqrt( dx**2. + dy**2. + dz**2.)
+    k  = np.sqrt( -1j*2.*np.pi*f*mu*sig )
+    kr = k*r
+
+    front = moment / (4.*pi * r**3.) * np.exp(-1j*kr)
+    mid   = -kr**2. + 3.*1j*kr + 3.
+
+    if orientation.upper() == 'X':
+        Hx = front*( (dx/r)**2. * mid + (kr**2. - 1j*kr - 1.) )
+        Hy = front*( (dx*dy/r**2.) * mid )
+        Hz = front*( (dx*dz/r**2.) * mid )
+
+    elif orientation.upper() == 'Y':
+        Hx = front*( (dy*dx/r**2.) * mid )
+        Hy = front*( (dy/r)**2. * mid + (kr**2. - 1j*kr - 1.) )
+        Hz = front*( (dy*dz/r**2.) * mid )
+
+    elif orientation.upper() == 'Z':
+        Hx = front*( (dx*dz/r**2.) * mid )
+        Hy = front*( (dy*dz/r**2.) * mid )
+        Hz = front*( (dz/r)**2. * mid + (kr**2. - 1j*kr - 1.) )
+
+    Bx = mu*Hx
+    By = mu*Hy
+    Bz = mu*Hz
+
+    if Bx.ndim is 1:
+        Bx = Utils.mkvc(Bx,2)
+
+    if By.ndim is 1:
+        By = Utils.mkvc(By,2)
+
+    if Bz.ndim is 1:
+        Bz = Utils.mkvc(Bz,2)
+
+    return Bx, By, Bz
+
+
+def ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', mu=mu_0):
+    XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
+
+    dx = XYZ[:,0]-srcLoc[0]
+    dy = XYZ[:,1]-srcLoc[1]
+    dz = XYZ[:,2]-srcLoc[2]
+
+    r  = np.sqrt( dx**2. + dy**2. + dz**2.)
+    k  = np.sqrt( -1j*2.*np.pi*f*mu*sig )
+    kr = k*r
+
+    front = current * length / (4. * np.pi * sig * r**3) * np.exp(-1j*k*r)
+    mid   = -k**2 * r**2 + 3*1j*k*r + 3
+
+    # Ex = front*((dx**2 / r**2)*mid + (k**2 * r**2 -1j*k*r))
+    # Ey = front*(dx*dy  / r**2)*mid
+    # Ez = front*(dx*dz  / r**2)*mid
+
+    if orientation.upper() == 'X':
+        Ex = front*((dx**2 / r**2)*mid + (k**2 * r**2 -1j*k*r-1.))
+        Ey = front*(dx*dy  / r**2)*mid
+        Ez = front*(dx*dz  / r**2)*mid
+        return Ex, Ey, Ez
+
+    elif orientation.upper() == 'Y':
+        #  x--> y, y--> z, z-->x
+        Ey = front*((dy**2 / r**2)*mid + (k**2 * r**2 -1j*k*r-1.))
+        Ez = front*(dy*dz  / r**2)*mid
+        Ex = front*(dy*dx  / r**2)*mid
+        return Ex, Ey, Ez
+
+    elif orientation.upper() == 'Z':
+        # x --> z, y --> x, z --> y
+        Ez = front*((dz**2 / r**2)*mid + (k**2 * r**2 -1j*k*r-1.))
+        Ex = front*(dz*dx  / r**2)*mid
+        Ey = front*(dz*dy  / r**2)*mid
+        return Ex, Ey, Ez
+        # return Ey, Ez, Ex

SimPEG/EM/Analytics/FDEMcasing.py

@@ -0,0 +1,98 @@
+from SimPEG import Utils, np
+from scipy.constants import mu_0, epsilon_0
+from SimPEG.EM.Utils.EMUtils import k
+
+def getKc(freq,sigma,a,b,mu=mu_0,eps=epsilon_0):
+    a = float(a)
+    b = float(b)
+    # return 1./(2*np.pi) * np.sqrt(b / a) * np.exp(-1j*k(freq,sigma,mu,eps)*(b-a))
+    return np.sqrt(b / a) * np.exp(-1j*k(freq,sigma,mu,eps)*(b-a))
+
+def _r2(xyz):
+    return np.sum(xyz**2,1)
+
+def _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    Kc1 = getKc(freq,sigma[1],a,b,mu[1],eps)
+
+    nobs = obsloc.shape[0]
+    dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
+
+    r2 = _r2(dxyz[:,:2])
+    sqrtr2z2 = np.sqrt(r2 + dxyz[:,2]**2)
+    k2 = k(freq,sigma[2],mu[2],eps)
+
+    return Kc1 * moment / (4.*np.pi) *np.exp(-1j*k2*sqrtr2z2) / sqrtr2z2
+
+
+def _getCasingHertzMagDipoleDeriv_r(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+
+    nobs = obsloc.shape[0]
+    dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
+
+    r2 = _r2(dxyz[:,:2])
+    sqrtr2z2 = np.sqrt(r2 + dxyz[:,2]**2)
+    k2 = k(freq,sigma[2],mu[2],eps)
+
+    return -HertzZ * np.sqrt(r2) / sqrtr2z2 * (1j*k2 + 1./ sqrtr2z2)
+
+
+def _getCasingHertzMagDipoleDeriv_z(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+
+    nobs = obsloc.shape[0]
+    dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
+
+    r2z2 = _r2(dxyz)
+    sqrtr2z2 = np.sqrt(r2z2)
+    k2 = k(freq,sigma[2],mu[2],eps)
+
+    return -HertzZ*dxyz[:,2] /sqrtr2z2 * (1j*k2 + 1./sqrtr2z2)
+
+def _getCasingHertzMagDipole2Deriv_z_r(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+    dHertzZdr = _getCasingHertzMagDipoleDeriv_r(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+
+    nobs = obsloc.shape[0]
+    dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
+
+    r2 = _r2(dxyz[:,:2])
+    r = np.sqrt(r2)
+    z = dxyz[:,2]
+    sqrtr2z2 = np.sqrt(r2 + z**2)
+    k2 = k(freq,sigma[2],mu[2],eps)
+
+    return dHertzZdr*(-z/sqrtr2z2)*(1j*k2+1./sqrtr2z2) + HertzZ*(z*r/sqrtr2z2**3)*(1j*k2 + 2./sqrtr2z2)
+
+def _getCasingHertzMagDipole2Deriv_z_z(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+    dHertzZdz = _getCasingHertzMagDipoleDeriv_z(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+
+    nobs = obsloc.shape[0]
+    dxyz = obsloc - np.c_[np.ones(nobs)]*np.r_[srcloc]
+
+    r2 = _r2(dxyz[:,:2])
+    r = np.sqrt(r2)
+    z = dxyz[:,2]
+    sqrtr2z2 = np.sqrt(r2 + z**2)
+    k2 = k(freq,sigma[2],mu[2],eps)
+
+    return (dHertzZdz*z + HertzZ)/sqrtr2z2*(-1j*k2 - 1./sqrtr2z2) + HertzZ*z/sqrtr2z2**3*(1j*k2*z + 2.*z/sqrtr2z2)
+
+def getCasingEphiMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    return 1j * omega(freq) * mu * _getCasingHertzMagDipoleDeriv_r(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+
+def getCasingHrMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    return _getCasingHertzMagDipole2Deriv_z_r(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+
+def getCasingHzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    d2HertzZdz2 = _getCasingHertzMagDipole2Deriv_z_z(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+    k2 = k(freq,sigma[2],mu[2],eps)
+    HertzZ = _getCasingHertzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+    return d2HertzZdz2 + k2**2 * HertzZ
+
+def getCasingBrMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    return mu_0 * getCasingHrMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)
+
+def getCasingBzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu=mu_0*np.ones(3),eps=epsilon_0,moment=1.):
+    return mu_0 * getCasingHzMagDipole(srcloc,obsloc,freq,sigma,a,b,mu,eps,moment)

SimPEG/EM/Analytics/TDEM.py

@@ -0,0 +1,12 @@
+import numpy as np
+from scipy.constants import mu_0, pi
+from scipy.special import erf
+
+def hzAnalyticDipoleT(r, t, sigma):
+    theta = np.sqrt((sigma*mu_0)/(4*t))
+    tr = theta*r
+    etr = erf(tr)
+    t1 = (9/(2*tr**2) - 1)*etr
+    t2 = (1/np.sqrt(pi))*(9/tr + 4*tr)*np.exp(-tr**2)
+    hz = (t1 - t2)/(4*pi*r**3)
+    return hz

SimPEG/EM/Analytics/__init__.py

@@ -0,0 +1,3 @@
+from TDEM import hzAnalyticDipoleT
+from FDEM import hzAnalyticDipoleF
+from FDEMcasing import *

SimPEG/EM/Base.py

@@ -0,0 +1,186 @@
+from SimPEG import Survey, Problem, Utils, Models, Maps, PropMaps, np, sp, Solver as SimpegSolver
+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)) 
+    mui = Maps.Property("Inverse Magnetic Permeability", defaultVal = 1./mu_0, propertyLink=('mu', Maps.ReciprocalMap))
+
+
+class BaseEMProblem(Problem.BaseProblem):
+
+    def __init__(self, mesh, **kwargs):
+        Problem.BaseProblem.__init__(self, mesh, **kwargs)
+
+
+    surveyPair = Survey.BaseSurvey
+    dataPair = Survey.Data
+    
+    PropMap = EMPropMap
+
+    Solver = SimpegSolver
+    solverOpts = {}
+
+    verbose = False
+
+    ####################################################
+    # Make A Symmetric
+    ####################################################
+    @property
+    def _makeASymmetric(self):
+        if getattr(self, '__makeASymmetric', None) is None:
+            self.__makeASymmetric = True
+        return self.__makeASymmetric
+
+
+    ####################################################
+    # Mass Matrices
+    ####################################################
+
+    @property
+    def deleteTheseOnModelUpdate(self):
+        toDelete = []
+        if self.mapping.sigmaMap is not None or self.mapping.rhoMap is not None:
+            toDelete += ['_MeSigma', '_MeSigmaI','_MfRho','_MfRhoI']
+        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):
+        """
+            Edge inner product matrix
+        """
+        if getattr(self, '_Me', None) is None:
+            self._Me = self.mesh.getEdgeInnerProduct()
+        return self._Me
+
+    @property
+    def Mf(self):
+        """
+            Face inner product matrix
+        """
+        if getattr(self, '_Mf', None) is None:
+            self._Mf = self.mesh.getFaceInnerProduct()
+        return self._Mf
+
+
+    # ----- Magnetic Permeability ----- # 
+    @property
+    def MfMui(self):
+        """
+            Face inner product matrix for \\(\\mu^{-1}\\). Used in the E-B formulation
+        """
+        if getattr(self, '_MfMui', None) is None:
+            self._MfMui = self.mesh.getFaceInnerProduct(self.curModel.mui)
+        return self._MfMui
+
+    @property
+    def MfMuiI(self):
+        """
+            Inverse of :code:`MfMui`.
+        """
+        if getattr(self, '_MfMuiI', None) is None:
+            self._MfMuiI = self.mesh.getFaceInnerProduct(self.curModel.mui, invMat=True)
+        return self._MfMuiI
+
+    @property
+    def MeMu(self):
+        """
+            Edge inner product matrix for \\(\\mu\\). Used in the H-J formulation
+        """
+        if getattr(self, '_MeMu', None) is None:
+            self._MeMu = self.mesh.getEdgeInnerProduct(self.curModel.mu)
+        return self._MeMu
+
+    @property
+    def MeMuI(self):
+        """
+            Inverse of :code:`MeMu`
+        """
+        if getattr(self, '_MeMuI', None) is None:
+            self._MeMuI = self.mesh.getEdgeInnerProduct(self.curModel.mu, invMat=True)
+        return self._MeMuI
+
+
+    # ----- Electrical Conductivity ----- # 
+    #TODO: hardcoded to sigma as the model
+    @property
+    def MeSigma(self):
+        """
+            Edge inner product matrix for \\(\\sigma\\). Used in the E-B formulation
+        """
+        if getattr(self, '_MeSigma', None) is None:
+            self._MeSigma = self.mesh.getEdgeInnerProduct(self.curModel.sigma)
+        return self._MeSigma
+
+    # 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\\). 
+        """
+        if getattr(self, '_MeSigmaI', None) is None:
+            self._MeSigmaI = self.mesh.getEdgeInnerProduct(self.curModel.sigma, invMat=True)
+        return self._MeSigmaI
+
+    # TODO: This should take a vector
+    def MeSigmaIDeriv(self, u):
+        """
+            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
+        dMe_dsig = self.mesh.getEdgeInnerProductDeriv(self.curModel.sigma)(u)
+        dsig_dm = self.curModel.sigmaDeriv
+        return dMeSigmaI_dI * ( dMe_dsig * ( dsig_dm))
+        # return self.mesh.getEdgeInnerProductDeriv(self.curModel.sigma, invMat=True)(u)
+
+
+    @property
+    def MfRho(self):
+        """
+            Face inner product matrix for \\(\\rho\\). Used in the H-J formulation
+        """
+        if getattr(self, '_MfRho', None) is None:
+            self._MfRho = self.mesh.getFaceInnerProduct(self.curModel.rho)
+        return self._MfRho
+
+    # TODO: This should take a vector
+    def MfRhoDeriv(self,u):
+        """
+            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
+
+    @property
+    def MfRhoI(self):
+        """
+            Inverse of :code:`MfRho`
+        """
+        if getattr(self, '_MfRhoI', None) is None:
+            self._MfRhoI = self.mesh.getFaceInnerProduct(self.curModel.rho, invMat=True)
+        return self._MfRhoI
+
+    # TODO: This isn't going to work yet
+    # TODO: This should take a vector
+    def MfRhoIDeriv(self,u):
+        """
+            Derivative of :code:`MfRhoI` with respect to the model. 
+        """
+        return self.mesh.getFaceInnerProductDeriv(self.curModel.rho, invMat=True)(u) * self.curModel.rhoDeriv

SimPEG/EM/FDEM/FDEM.py

@@ -0,0 +1,570 @@
+from SimPEG import Problem, Utils, np, sp, Solver as SimpegSolver
+from scipy.constants import mu_0
+from SurveyFDEM import Survey as SurveyFDEM
+from FieldsFDEM import Fields, Fields_e, Fields_b, Fields_h, Fields_j
+from SimPEG.EM.Base import BaseEMProblem
+from SimPEG.EM.Utils import omega
+
+
+class BaseFDEMProblem(BaseEMProblem):
+    """
+        We start by looking at Maxwell's equations in the electric
+        field \\\(\\\mathbf{e}\\\) and the magnetic flux
+        density \\\(\\\mathbf{b}\\\)
+
+        .. math ::
+
+            \mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} \\\\
+            {\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{M_{\sigma}^e} \mathbf{e} = \mathbf{M^e} \mathbf{s_e}}
+
+        if using the E-B formulation (:code:`Problem_e`
+        or :code:`Problem_b`) or the magnetic field
+        \\\(\\\mathbf{h}\\\) and current density \\\(\\\mathbf{j}\\\)
+
+        .. math ::
+
+            \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{j} + i \omega \mathbf{M_{\mu}^e} \mathbf{h} = \mathbf{M^e} \mathbf{s_m} \\\\
+            \mathbf{C} \mathbf{h} - \mathbf{j} = \mathbf{s_e}
+
+        if using the H-J formulation (:code:`Problem_j` or :code:`Problem_h`).
+
+        The problem performs the elimination so that we are solving the system for \\\(\\\mathbf{e},\\\mathbf{b},\\\mathbf{j} \\\) or \\\(\\\mathbf{h}\\\)
+    """
+
+    surveyPair = SurveyFDEM
+    fieldsPair = Fields
+
+    def fields(self, m=None):
+        """
+            Solve the forward problem for the fields.
+        """
+
+        self.curModel = m
+        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
+            Srcs = self.survey.getSrcByFreq(freq)
+            ftype = self._fieldType + 'Solution'
+            F[Srcs, ftype] = sol
+
+        return F
+
+    def Jvec(self, m, v, f=None):
+        """
+            Sensitivity times a vector
+        """
+
+        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)
+
+            for src in self.survey.getSrcByFreq(freq):
+                ftype = self._fieldType + 'Solution'
+                u_src = f[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 )
+                
+                for rx in src.rxList:
+                    df_duFun = getattr(f, '_%sDeriv_u'%rx.projField, None)
+                    df_dudu_dm = df_duFun(src, du_dm, adjoint=False)
+
+                    df_dmFun = getattr(f, '_%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, f, v) # wrt u, also have wrt m
+
+                    Jv[src, rx] = P(Df_Dm)
+
+        return Utils.mkvc(Jv)
+
+    def Jtvec(self, m, v, f=None):
+        """
+            Sensitivity transpose times a vector
+        """
+
+        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'
+                u_src = f[src, ftype]
+
+                for rx in src.rxList:
+                    PTv = rx.projectFieldsDeriv(src, self.mesh, f, v[src, rx], adjoint=True) # wrt u, need possibility wrt m
+
+                    df_duTFun = getattr(f, '_%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)
+                    du_dmT = -dA_dmT + dRHS_dmT
+
+                    df_dmFun = getattr(f, '_%sDeriv_m'%rx.projField, None)
+                    dfT_dm = df_dmFun(src, PTv, adjoint=True)
+
+                    du_dmT += dfT_dm
+
+                    real_or_imag = rx.projComp
+                    if real_or_imag is 'real':
+                        Jtv +=   np.array(du_dmT,dtype=complex).real
+                    elif real_or_imag is 'imag':
+                        Jtv += - np.array(du_dmT,dtype=complex).real
+                    else:
+                        raise Exception('Must be real or imag')
+
+        return Jtv
+
+    def getSourceTerm(self, freq):
+        """
+            Evaluates the sources for a given frequency and puts them in matrix form
+
+            :param float freq: Frequency
+            :rtype: numpy.ndarray (nE or nF, nSrc)
+            :return: S_m, S_e
+        """
+        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)
+
+        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
+
+        return S_m, S_e
+
+
+##########################################################################################
+################################ E-B Formulation #########################################
+##########################################################################################
+
+class Problem_e(BaseFDEMProblem):
+    """
+        By eliminating the magnetic flux density using
+
+            .. math ::
+
+                \mathbf{b} = \\frac{1}{i \omega}\\left(-\mathbf{C} \mathbf{e} + \mathbf{s_m}\\right)
+
+
+        we can write Maxwell's equations as a second order system in \\\(\\\mathbf{e}\\\) only:
+
+        .. math ::
+
+            \\left(\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{C}+ i \omega \mathbf{M^e_{\sigma}} \\right)\mathbf{e} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M^e}\mathbf{s_e}
+
+        which we solve for \\\(\\\mathbf{e}\\\).
+    """
+
+    _fieldType = 'e'
+    _eqLocs    = 'FE'
+    fieldsPair = Fields_e
+
+    def __init__(self, mesh, **kwargs):
+        BaseFDEMProblem.__init__(self, mesh, **kwargs)
+
+    def getA(self, freq):
+        """
+            .. math ::
+                \mathbf{A} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{C} + i \omega \mathbf{M^e_{\sigma}}
+
+            :param float freq: Frequency
+            :rtype: scipy.sparse.csr_matrix
+            :return: A
+        """
+        MfMui = self.MfMui
+        MeSigma = self.MeSigma
+        C = self.mesh.edgeCurl
+
+        return C.T*MfMui*C + 1j*omega(freq)*MeSigma
+
+
+    def getADeriv_m(self, freq, u, v, adjoint=False):
+        dsig_dm = self.curModel.sigmaDeriv
+        dMe_dsig = self.MeSigmaDeriv(u)
+
+        if adjoint:
+            return 1j * omega(freq) * ( dMe_dsig.T * v )
+
+        return 1j * omega(freq) * ( dMe_dsig * v )
+
+    def getRHS(self, freq):
+        """
+            .. math ::
+                \mathbf{RHS} = \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}\mathbf{s_m} -i\omega\mathbf{M_e}\mathbf{s_e}
+
+            :param float freq: Frequency
+            :rtype: numpy.ndarray (nE, nSrc)
+            :return: RHS
+        """
+
+        S_m, S_e = self.getSourceTerm(freq)
+        C = self.mesh.edgeCurl
+        MfMui = self.MfMui
+
+        RHS = C.T * (MfMui * S_m) -1j * omega(freq) * S_e
+
+        return RHS
+
+    def getRHSDeriv_m(self, freq, src, v, adjoint=False):
+        C = self.mesh.edgeCurl
+        MfMui = self.MfMui
+        S_mDeriv, S_eDeriv = src.evalDeriv(self, adjoint)
+
+        if adjoint:
+            dRHS = MfMui * (C * 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)
+
+
+class Problem_b(BaseFDEMProblem):
+    """
+        We eliminate \\\(\\\mathbf{e}\\\) using
+
+        .. math ::
+
+             \mathbf{e} = \mathbf{M^e_{\sigma}}^{-1} \\left(\mathbf{C}^T \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{s_e}\\right)
+
+        and solve for \\\(\\\mathbf{b}\\\) using:
+
+        .. math ::
+
+            \\left(\mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}  + i \omega \\right)\mathbf{b} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{M^e}\mathbf{s_e}
+
+        .. note ::
+            The inverse problem will not work with full anisotropy
+    """
+
+    _fieldType = 'b'
+    _eqLocs    = 'FE'
+    fieldsPair = Fields_b
+
+    def __init__(self, mesh, **kwargs):
+        BaseFDEMProblem.__init__(self, mesh, **kwargs)
+
+    def getA(self, freq):
+        """
+            .. math ::
+                \mathbf{A} = \mathbf{C} \mathbf{M^e_{\sigma}}^{-1} \mathbf{C}^T \mathbf{M_{\mu^{-1}}^f}  + i \omega
+
+            :param float freq: Frequency
+            :rtype: scipy.sparse.csr_matrix
+            :return: A
+        """
+
+        MfMui = self.MfMui
+        MeSigmaI = self.MeSigmaI
+        C = self.mesh.edgeCurl
+        iomega = 1j * omega(freq) * sp.eye(self.mesh.nF)
+
+        A = C * (MeSigmaI * (C.T * MfMui)) + iomega
+
+        if self._makeASymmetric is True:
+            return MfMui.T*A
+        return A
+
+    def getADeriv_m(self, freq, u, v, adjoint=False):
+
+        MfMui = self.MfMui
+        C = self.mesh.edgeCurl
+        MeSigmaIDeriv = self.MeSigmaIDeriv
+        vec = C.T * (MfMui * u)
+
+        MeSigmaIDeriv = MeSigmaIDeriv(vec)
+
+        if adjoint:
+            if self._makeASymmetric is True:
+                v = MfMui * v
+            return MeSigmaIDeriv.T * (C.T * v)
+
+        if self._makeASymmetric is True:
+            return MfMui.T * ( C * ( MeSigmaIDeriv * v ) )
+        return C * ( MeSigmaIDeriv * v )
+
+
+    def getRHS(self, freq):
+        """
+            .. math ::
+                \mathbf{RHS} = \mathbf{s_m} + \mathbf{M^e_{\sigma}}^{-1}\mathbf{s_e}
+
+            :param float freq: Frequency
+            :rtype: numpy.ndarray (nE, nSrc)
+            :return: RHS
+        """
+
+        S_m, S_e = self.getSourceTerm(freq)
+        C = self.mesh.edgeCurl
+        MeSigmaI = self.MeSigmaI
+
+        RHS = S_m + C * ( MeSigmaI * S_e )
+
+        if self._makeASymmetric is True:
+            MfMui = self.MfMui
+            return MfMui.T * RHS
+
+        return RHS
+
+    def getRHSDeriv_m(self, freq, src, v, adjoint=False):
+        C = self.mesh.edgeCurl
+        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)
+
+        if not adjoint:
+            RHSderiv = C * (MeSigmaIDeriv * 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))
+
+        if self._makeASymmetric is True and not adjoint:
+            return MfMui.T * (SrcDeriv + RHSderiv)
+
+        return RHSderiv + SrcDeriv
+
+
+
+##########################################################################################
+################################ H-J Formulation #########################################
+##########################################################################################
+
+
+class Problem_j(BaseFDEMProblem):
+    """
+        We eliminate \\\(\\\mathbf{h}\\\) using
+
+        .. math ::
+
+            \mathbf{h} = \\frac{1}{i \omega} \mathbf{M_{\mu}^e}^{-1} \\left(-\mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{j}  + \mathbf{M^e} \mathbf{s_m} \\right)
+
+        and solve for \\\(\\\mathbf{j}\\\) using
+
+        .. math ::
+
+            \\left(\mathbf{C} \mathbf{M_{\mu}^e}^{-1} \mathbf{C}^T \mathbf{M_{\\rho}^f} + i \omega\\right)\mathbf{j} = \mathbf{C} \mathbf{M_{\mu}^e}^{-1} \mathbf{M^e} \mathbf{s_m} -i\omega\mathbf{s_e}
+
+        .. note::
+            This implementation does not yet work with full anisotropy!!
+
+    """
+
+    _fieldType = 'j'
+    _eqLocs    = 'EF'
+    fieldsPair = Fields_j
+
+    def __init__(self, mesh, **kwargs):
+        BaseFDEMProblem.__init__(self, mesh, **kwargs)
+
+    def getA(self, freq):
+        """
+            .. math ::
+                    \\mathbf{A} = \\mathbf{C}  \\mathbf{M^e_{mu^{-1}}} \\mathbf{C}^T \\mathbf{M^f_{\\sigma^{-1}}}  + i\\omega
+
+            :param float freq: Frequency
+            :rtype: scipy.sparse.csr_matrix
+            :return: A
+        """
+
+        MeMuI = self.MeMuI
+        MfRho = self.MfRho
+        C = self.mesh.edgeCurl
+        iomega = 1j * omega(freq) * sp.eye(self.mesh.nF)
+
+        A = C * MeMuI * C.T * MfRho + iomega
+
+        if self._makeASymmetric is True:
+            return MfRho.T*A
+        return A
+
+
+    def getADeriv_m(self, freq, u, v, adjoint=False):
+        """
+            In this case, we assume that electrical conductivity, \\\(\\\sigma\\\) is the physical property of interest (i.e. \\\(\\\sigma\\\) = model.transform). Then we want
+
+            .. math ::
+
+                \\frac{\mathbf{A(\sigma)} \mathbf{v}}{d \\mathbf{m}} &= \\mathbf{C}  \\mathbf{M^e_{mu^{-1}}} \\mathbf{C^T} \\frac{d \\mathbf{M^f_{\\sigma^{-1}}}}{d \\mathbf{m}}
+                &= \\mathbf{C}  \\mathbf{M^e_{mu}^{-1}} \\mathbf{C^T} \\frac{d \\mathbf{M^f_{\\sigma^{-1}}}}{d \\mathbf{\\sigma^{-1}}} \\frac{d \\mathbf{\\sigma^{-1}}}{d \\mathbf{\\sigma}} \\frac{d \\mathbf{\\sigma}}{d \\mathbf{m}}
+        """
+
+        MeMuI = self.MeMuI
+        MfRho = self.MfRho
+        C = self.mesh.edgeCurl
+        MfRhoDeriv_m = self.MfRhoDeriv(u)
+
+        if adjoint:
+            if self._makeASymmetric is True:
+                v = MfRho * v
+            return MfRhoDeriv_m.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)))
+
+
+    def getRHS(self, freq):
+        """
+            .. math ::
+
+                \mathbf{RHS} = \mathbf{C} \mathbf{M_{\mu}^e}^{-1}\mathbf{s_m} -i\omega \mathbf{s_e}
+            :param float freq: Frequency
+            :rtype: numpy.ndarray (nE, nSrc)
+            :return: RHS
+        """
+
+        S_m, S_e = self.getSourceTerm(freq)
+        C = self.mesh.edgeCurl
+        MeMuI = self.MeMuI
+
+        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):
+        C = self.mesh.edgeCurl
+        MeMuI = self.MeMuI
+        S_mDeriv, S_eDeriv = src.evalDeriv(self, 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)
+
+        else:
+            RHSDeriv = C * (MeMuI * S_mDeriv(v)) - 1j * omega(freq) * S_eDeriv(v)
+
+            if self._makeASymmetric:
+                MfRho = self.MfRho
+                return MfRho.T * RHSDeriv
+            return RHSDeriv
+
+
+
+
+class Problem_h(BaseFDEMProblem):
+    """
+        We eliminate \\\(\\\mathbf{j}\\\) using
+
+        .. math ::
+
+            \mathbf{j} = \mathbf{C} \mathbf{h} - \mathbf{s_e}
+
+        and solve for \\\(\\\mathbf{h}\\\) using
+
+        .. math ::
+
+            \\left(\mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}\\right) \mathbf{h} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{s_e}
+
+    """
+
+    _fieldType = 'h'
+    _eqLocs    = 'EF'
+    fieldsPair = Fields_h
+
+    def __init__(self, mesh, **kwargs):
+        BaseFDEMProblem.__init__(self, mesh, **kwargs)
+
+    def getA(self, freq):
+        """
+            .. math ::
+
+                \mathbf{A} = \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}
+
+            :param float freq: Frequency
+            :rtype: scipy.sparse.csr_matrix
+            :return: A
+        """
+
+        MeMu = self.MeMu
+        MfRho = self.MfRho
+        C = self.mesh.edgeCurl
+
+        return C.T * (MfRho * C) + 1j*omega(freq)*MeMu
+
+    def getADeriv_m(self, freq, u, v, adjoint=False):
+
+        MeMu = self.MeMu
+        C = self.mesh.edgeCurl
+        MfRhoDeriv_m = self.MfRhoDeriv(C*u)
+
+        if adjoint:
+            return MfRhoDeriv_m.T * (C * v)
+        return C.T * (MfRhoDeriv_m * v)
+
+    def getRHS(self, freq):
+        """
+            .. math ::
+
+                \mathbf{RHS} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^T \mathbf{M_{\\rho}^f} \mathbf{s_e}
+
+            :param float freq: Frequency
+            :rtype: numpy.ndarray (nE, nSrc)
+            :return: RHS
+        """
+
+        S_m, S_e = self.getSourceTerm(freq)
+        C = self.mesh.edgeCurl
+        MfRho  = self.MfRho
+
+        RHS = S_m + C.T * ( MfRho * S_e )
+
+        return RHS
+
+    def getRHSDeriv_m(self, freq, src, v, adjoint=False):
+        _, S_e = src.eval(self)
+        C = self.mesh.edgeCurl
+        MfRho  = self.MfRho
+
+        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)
+
+        return RHSDeriv + S_mDeriv(v) + C.T * (MfRho * S_eDeriv(v))
+

SimPEG/EM/FDEM/FieldsFDEM.py

@@ -0,0 +1,358 @@
+import numpy as np
+import scipy.sparse as sp
+import SimPEG
+from SimPEG import Utils
+from SimPEG.EM.Utils import omega
+from SimPEG.Utils import Zero, Identity
+
+
+class Fields(SimPEG.Problem.Fields):
+    """Fancy Field Storage for a FDEM survey."""
+    knownFields = {}
+    dtype = complex
+
+class Fields_e(Fields):
+    knownFields = {'eSolution':'E'}
+    aliasFields = {
+                    'e' : ['eSolution','E','_e'],
+                    'ePrimary' : ['eSolution','E','_ePrimary'],
+                    'eSecondary' : ['eSolution','E','_eSecondary'],
+                    'b' : ['eSolution','F','_b'],
+                    'bPrimary' : ['eSolution','F','_bPrimary'],
+                    'bSecondary' : ['eSolution','F','_bSecondary']
+                  }
+
+    def __init__(self,mesh,survey,**kwargs):
+        Fields.__init__(self,mesh,survey,**kwargs)
+
+    def startup(self):
+        self.prob = self.survey.prob
+        self._edgeCurl = self.survey.prob.mesh.edgeCurl
+
+    def _ePrimary(self, eSolution, srcList):
+        ePrimary = np.zeros_like(eSolution)
+        for i, src in enumerate(srcList):
+            ep = src.ePrimary(self.prob)
+            ePrimary[:,i] = ePrimary[:,i] + ep
+        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 Identity()*v
+
+    def _eDeriv_m(self, src, v, adjoint = False):
+        # assuming primary does not depend on the model
+        return Zero()
+
+    def _bPrimary(self, eSolution, srcList):
+        bPrimary = np.zeros([self._edgeCurl.shape[0],eSolution.shape[1]],dtype = complex)
+        for i, src in enumerate(srcList):
+            bp = src.bPrimary(self.prob)
+            bPrimary[:,i] = bPrimary[:,i] + bp
+        return bPrimary
+
+    def _bSecondary(self, eSolution, srcList):
+        C = self._edgeCurl
+        b = (C * eSolution)
+        for i, src in enumerate(srcList):
+            b[:,i] *= - 1./(1j*omega(src.freq))
+            S_m, _ = src.eval(self.prob)
+            b[:,i] = b[:,i]+ 1./(1j*omega(src.freq)) * S_m
+        return b
+
+    def _bSecondaryDeriv_u(self, src, v, adjoint = False):
+        C = self._edgeCurl
+        if adjoint:
+            return - 1./(1j*omega(src.freq)) * (C.T * v)
+        return - 1./(1j*omega(src.freq)) * (C * v)
+
+    def _bSecondaryDeriv_m(self, src, v, adjoint = False):
+        S_mDeriv, _ = src.evalDeriv(self.prob, adjoint)
+        S_mDeriv = S_mDeriv(v)
+        return 1./(1j * omega(src.freq)) * S_mDeriv
+
+    def _b(self, eSolution, srcList):
+        return self._bPrimary(eSolution, srcList) + self._bSecondary(eSolution, srcList)
+
+    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)
+
+
+class Fields_b(Fields):
+    knownFields = {'bSolution':'F'}
+    aliasFields = {
+                    'b' : ['bSolution','F','_b'],
+                    'bPrimary' : ['bSolution','F','_bPrimary'],
+                    'bSecondary' : ['bSolution','F','_bSecondary'],
+                    'e' : ['bSolution','E','_e'],
+                    'ePrimary' : ['bSolution','E','_ePrimary'],
+                    'eSecondary' : ['bSolution','E','_eSecondary'],
+                  }
+
+    def __init__(self,mesh,survey,**kwargs):
+        Fields.__init__(self,mesh,survey,**kwargs)
+
+    def startup(self):
+        self.prob = self.survey.prob
+        self._edgeCurl = self.survey.prob.mesh.edgeCurl
+        self._MeSigmaI = self.survey.prob.MeSigmaI
+        self._MfMui = self.survey.prob.MfMui
+        self._MeSigmaIDeriv = self.survey.prob.MeSigmaIDeriv
+        self._Me = self.survey.prob.Me
+
+    def _bPrimary(self, bSolution, srcList):
+        bPrimary = np.zeros_like(bSolution)
+        for i, src in enumerate(srcList):
+            bp = src.bPrimary(self.prob)
+            bPrimary[:,i] = bPrimary[:,i] + bp
+        return bPrimary
+
+    def _bSecondary(self, bSolution, srcList):
+        return bSolution
+
+    def _b(self, bSolution, srcList):
+        return self._bPrimary(bSolution, srcList) + self._bSecondary(bSolution, srcList)
+
+    def _bDeriv_u(self, src, v, adjoint=False):
+        return Identity()*v
+
+    def _bDeriv_m(self, src, v, adjoint=False):
+        # assuming primary does not depend on the model
+        return Zero()
+
+    def _ePrimary(self, bSolution, srcList):
+        ePrimary = np.zeros([self._edgeCurl.shape[1],bSolution.shape[1]],dtype = complex)
+        for i,src in enumerate(srcList):
+            ep = src.ePrimary(self.prob)
+            ePrimary[:,i] = ePrimary[:,i] + ep
+        return ePrimary
+
+    def _eSecondary(self, bSolution, srcList):
+        e = self._MeSigmaI * ( self._edgeCurl.T * ( self._MfMui * bSolution))
+        for i,src in enumerate(srcList):
+            _,S_e = src.eval(self.prob)
+            e[:,i] = e[:,i]+ -self._MeSigmaI * S_e
+        return e
+
+    def _eSecondaryDeriv_u(self, src, v, adjoint=False):
+        if not adjoint:
+            return self._MeSigmaI * ( self._edgeCurl.T * ( self._MfMui * v) )
+        else:
+            return self._MfMui.T * (self._edgeCurl * (self._MeSigmaI.T * v))
+
+    def _eSecondaryDeriv_m(self, src, v, adjoint=False):
+        bSolution = self[[src],'bSolution']
+        _,S_e = src.eval(self.prob)
+        Me = self._Me
+
+        if adjoint:
+            Me = Me.T
+
+        w = self._edgeCurl.T * (self._MfMui * bSolution)
+        w = w - Utils.mkvc(Me * S_e,2)
+
+        if not adjoint:
+            de_dm = self._MeSigmaIDeriv(w) * v
+        elif adjoint:
+            de_dm = self._MeSigmaIDeriv(w).T * v
+
+        _, S_eDeriv = src.evalDeriv(self.prob, adjoint)
+        Se_Deriv = S_eDeriv(v)
+
+        de_dm = de_dm - self._MeSigmaI * Se_Deriv
+
+        return de_dm
+
+    def _e(self, bSolution, srcList):
+        return self._ePrimary(bSolution, srcList) + self._eSecondary(bSolution, srcList)
+
+    def _eDeriv_u(self, src, v, adjoint=False):
+        return self._eSecondaryDeriv_u(src, v, adjoint)
+
+    def _eDeriv_m(self, src, v, adjoint=False):
+        # assuming primary doesn't depend on model
+        return self._eSecondaryDeriv_m(src, v, adjoint)
+
+
+class Fields_j(Fields):
+    knownFields = {'jSolution':'F'}
+    aliasFields = {
+                    'j' : ['jSolution','F','_j'],
+                    'jPrimary' : ['jSolution','F','_jPrimary'],
+                    'jSecondary' : ['jSolution','F','_jSecondary'],
+                    'h' : ['jSolution','E','_h'],
+                    'hPrimary' : ['jSolution','E','_hPrimary'],
+                    'hSecondary' : ['jSolution','E','_hSecondary'],
+                  }
+
+    def __init__(self,mesh,survey,**kwargs):
+        Fields.__init__(self,mesh,survey,**kwargs)
+
+    def startup(self):
+        self.prob = self.survey.prob
+        self._edgeCurl = self.survey.prob.mesh.edgeCurl
+        self._MeMuI = self.survey.prob.MeMuI
+        self._MfRho = self.survey.prob.MfRho
+        self._MfRhoDeriv = self.survey.prob.MfRhoDeriv
+        self._Me = self.survey.prob.Me
+
+    def _jPrimary(self, jSolution, srcList):
+        jPrimary = np.zeros_like(jSolution,dtype = complex)
+        for i, src in enumerate(srcList):
+            jp = src.jPrimary(self.prob)
+            jPrimary[:,i] = jPrimary[:,i] + jp
+        return jPrimary
+
+    def _jSecondary(self, jSolution, srcList):
+        return jSolution
+
+    def _j(self, jSolution, srcList):
+        return self._jPrimary(jSolution, srcList) + self._jSecondary(jSolution, srcList)
+
+    def _jDeriv_u(self, src, v, adjoint=False):
+        return Identity()*v
+
+    def _jDeriv_m(self, src, v, adjoint=False):
+        # assuming primary does not depend on the model
+        return Zero()
+
+    def _hPrimary(self, jSolution, srcList):
+        hPrimary = np.zeros([self._edgeCurl.shape[1],jSolution.shape[1]],dtype = complex)
+        for i, src in enumerate(srcList):
+            hp = src.hPrimary(self.prob)
+            hPrimary[:,i] = hPrimary[:,i] + hp
+        return hPrimary
+
+    def _hSecondary(self, jSolution, srcList):
+        h =  self._MeMuI * (self._edgeCurl.T * (self._MfRho * jSolution) )
+        for i, src in enumerate(srcList):
+            h[:,i] *= -1./(1j*omega(src.freq))
+            S_m,_ = src.eval(self.prob)
+            h[:,i] = h[:,i]+ 1./(1j*omega(src.freq)) * self._MeMuI * (S_m)
+        return h
+
+    def _hSecondaryDeriv_u(self, src, v, adjoint=False):
+        if not adjoint:
+            return  -1./(1j*omega(src.freq)) * self._MeMuI * (self._edgeCurl.T * (self._MfRho * v) )
+        elif adjoint:
+            return  -1./(1j*omega(src.freq)) * self._MfRho.T * (self._edgeCurl * ( self._MeMuI.T * v))
+
+    def _hSecondaryDeriv_m(self, src, v, adjoint=False):
+        jSolution = self[[src],'jSolution']
+        MeMuI = self._MeMuI
+        C = self._edgeCurl
+        MfRho = self._MfRho
+        MfRhoDeriv = self._MfRhoDeriv
+        Me = self._Me
+
+        if not adjoint:
+            hDeriv_m =  -1./(1j*omega(src.freq)) * MeMuI * (C.T * (MfRhoDeriv(jSolution)*v ) )
+        elif adjoint:
+            hDeriv_m =  -1./(1j*omega(src.freq)) * MfRhoDeriv(jSolution).T * ( C * (MeMuI.T * v ) )
+
+        S_mDeriv,_ = src.evalDeriv(self.prob, adjoint)
+
+        if not adjoint:
+            S_mDeriv = S_mDeriv(v)
+            hDeriv_m = hDeriv_m + 1./(1j*omega(src.freq)) * MeMuI * (Me * S_mDeriv)
+        elif adjoint:
+            S_mDeriv = S_mDeriv(Me.T * (MeMuI.T * v))
+            hDeriv_m = hDeriv_m + 1./(1j*omega(src.freq)) * S_mDeriv
+        return hDeriv_m
+
+
+    def _h(self, jSolution, srcList):
+        return self._hPrimary(jSolution, srcList) + self._hSecondary(jSolution, srcList)
+
+    def _hDeriv_u(self, src, v, adjoint=False):
+        return self._hSecondaryDeriv_u(src, v, adjoint)
+
+    def _hDeriv_m(self, src, v, adjoint=False):
+        # assuming the primary doesn't depend on the model
+        return self._hSecondaryDeriv_m(src, v, adjoint)
+
+
+class Fields_h(Fields):
+    knownFields = {'hSolution':'E'}
+    aliasFields = {
+                    'h' : ['hSolution','E','_h'],
+                    'hPrimary' : ['hSolution','E','_hPrimary'],
+                    'hSecondary' : ['hSolution','E','_hSecondary'],
+                    'j' : ['hSolution','F','_j'],
+                    'jPrimary' : ['hSolution','F','_jPrimary'],
+                    'jSecondary' : ['hSolution','F','_jSecondary']
+                  }
+
+    def __init__(self,mesh,survey,**kwargs):
+        Fields.__init__(self,mesh,survey,**kwargs)
+
+    def startup(self):
+        self.prob = self.survey.prob
+        self._edgeCurl = self.survey.prob.mesh.edgeCurl
+        self._MeMuI = self.survey.prob.MeMuI
+        self._MfRho = self.survey.prob.MfRho
+
+    def _hPrimary(self, hSolution, srcList):
+        hPrimary = np.zeros_like(hSolution,dtype = complex)
+        for i, src in enumerate(srcList):
+            hp = src.hPrimary(self.prob)
+            hPrimary[:,i] = hPrimary[:,i] + hp
+        return hPrimary
+
+    def _hSecondary(self, hSolution, srcList):
+        return hSolution
+
+    def _h(self, hSolution, srcList):
+        return self._hPrimary(hSolution, srcList) + self._hSecondary(hSolution, srcList)
+
+    def _hDeriv_u(self, src, v, adjoint=False):
+        return Identity()*v
+
+    def _hDeriv_m(self, src, v, adjoint=False):
+        # assuming primary does not depend on the model
+        return Zero()
+
+    def _jPrimary(self, hSolution, srcList):
+        jPrimary = np.zeros([self._edgeCurl.shape[0], hSolution.shape[1]], dtype = complex)
+        for i, src in enumerate(srcList):
+            jp = src.jPrimary(self.prob)
+            jPrimary[:,i] = jPrimary[:,i] + jp
+        return jPrimary
+
+    def _jSecondary(self, hSolution, srcList):
+        j = self._edgeCurl*hSolution
+        for i, src in enumerate(srcList):
+            _,S_e = src.eval(self.prob)
+            j[:,i] = j[:,i]+ -S_e
+        return j
+
+    def _jSecondaryDeriv_u(self, src, v, adjoint=False):
+        if not adjoint:
+            return self._edgeCurl*v
+        elif adjoint:
+            return self._edgeCurl.T*v
+
+    def _jSecondaryDeriv_m(self, src, v, adjoint=False):
+        _,S_eDeriv = src.evalDeriv(self.prob, adjoint)
+        S_eDeriv = S_eDeriv(v)
+        return -S_eDeriv
+
+    def _j(self, hSolution, srcList):
+        return self._jPrimary(hSolution, srcList) + self._jSecondary(hSolution, srcList)
+
+    def _jDeriv_u(self, src, v, adjoint=False):
+        return self._jSecondaryDeriv_u(src,v,adjoint)
+
+    def _jDeriv_m(self, src, v, adjoint=False):
+        # assuming the primary does not depend on the model
+        return self._jSecondaryDeriv_m(src,v,adjoint)

SimPEG/EM/FDEM/SrcFDEM.py

@@ -0,0 +1,316 @@
+from SimPEG import Survey, Problem, Utils, np, sp
+from scipy.constants import mu_0
+from SimPEG.EM.Utils import *
+from SimPEG.Utils import Zero
+# from SurveyFDEM import Rx
+ 
+
+class BaseSrc(Survey.BaseSrc):
+    freq = None
+    # rxPair = Rx
+    integrate = True
+
+    def eval(self, prob):
+        S_m = self.S_m(prob)
+        S_e = self.S_e(prob)
+        return S_m, S_e
+
+    def evalDeriv(self, prob, v, adjoint=False):
+        return lambda v: self.S_mDeriv(prob,v,adjoint), lambda v: self.S_eDeriv(prob,v,adjoint)
+
+    def bPrimary(self, prob):
+        return Zero()
+
+    def hPrimary(self, prob):
+        return Zero()
+
+    def ePrimary(self, prob):
+        return Zero()
+
+    def jPrimary(self, prob):
+        return Zero()
+
+    def S_m(self, prob):
+        return Zero()
+
+    def S_e(self, prob):
+        return Zero()
+
+    def S_mDeriv(self, prob, v, adjoint = False):
+        return Zero()
+
+    def S_eDeriv(self, prob, v, adjoint = False):
+        return Zero()
+
+
+class RawVec_e(BaseSrc):
+    """
+        RawVec electric source. It is defined by the user provided vector S_e
+
+        :param numpy.array S_e: electric source term
+        :param float freq: frequency
+        :param rxList: receiver list
+    """
+
+    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 numpy.array S_m: magnetic source term
+        :param float freq: frequency
+        :param rxList: receiver list
+    """
+
+    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):
+        return self._S_m
+
+
+class RawVec(BaseSrc):
+    """
+        RawVec source. It is defined by the user provided vectors S_m, S_e
+
+        :param numpy.array S_m: magnetic source term
+        :param numpy.array S_e: electric source term
+        :param float freq: frequency
+        :param rxList: receiver list
+    """
+    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_e(self, prob):
+        if prob._eqLocs is 'FE' and self.integrate is True:
+            return prob.Me * self._S_e
+        return self._S_e
+
+
+class MagDipole(BaseSrc):
+
+    #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):
+        self.freq = float(freq)
+        self.loc = loc
+        self.orientation = orientation
+        self.moment = moment
+        self.mu = mu
+        self.integrate = False
+        BaseSrc.__init__(self, rxList)
+
+    def bPrimary(self, prob):
+        eqLocs = prob._eqLocs
+
+        if eqLocs is 'FE':
+            gridX = prob.mesh.gridEx
+            gridY = prob.mesh.gridEy
+            gridZ = prob.mesh.gridEz
+            C = prob.mesh.edgeCurl
+
+        elif eqLocs is 'EF':
+            gridX = prob.mesh.gridFx
+            gridY = prob.mesh.gridFy
+            gridZ = prob.mesh.gridFz
+            C = prob.mesh.edgeCurl.T
+
+
+        if prob.mesh._meshType is 'CYL':
+            if not prob.mesh.isSymmetric:
+                # TODO ?
+                raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
+            a = MagneticDipoleVectorPotential(self.loc, gridY, 'y', mu=self.mu, moment=self.moment)
+
+        else:
+            srcfct = MagneticDipoleVectorPotential
+            ax = srcfct(self.loc, gridX, 'x', mu=self.mu, moment=self.moment)
+            ay = srcfct(self.loc, gridY, 'y', mu=self.mu, moment=self.moment)
+            az = srcfct(self.loc, gridZ, 'z', mu=self.mu, moment=self.moment)
+            a = np.concatenate((ax, ay, az))
+
+        return C*a
+
+    def hPrimary(self, prob):
+        b = self.bPrimary(prob)
+        return h_from_b(prob,b)
+
+    def S_m(self, prob):
+        b_p = self.bPrimary(prob)
+        return -1j*omega(self.freq)*b_p
+
+    def S_e(self, prob):
+        if all(np.r_[self.mu] == np.r_[prob.curModel.mu]):
+            return Zero()
+        else:
+            eqLocs = prob._eqLocs
+
+            if eqLocs is 'FE':
+                mui_s = prob.curModel.mui - 1./self.mu
+                MMui_s = prob.mesh.getFaceInnerProduct(mui_s)
+                C = prob.mesh.edgeCurl
+            elif eqLocs is 'EF':
+                mu_s = prob.curModel.mu - self.mu
+                MMui_s = prob.mesh.getEdgeInnerProduct(mu_s,invMat=True)
+                C = prob.mesh.edgeCurl.T
+
+            return -C.T * (MMui_s * self.bPrimary(prob))
+
+
+class MagDipole_Bfield(BaseSrc):
+
+    #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
+        self.orientation = orientation
+        self.moment = moment
+        self.mu = mu
+        BaseSrc.__init__(self, rxList)
+
+    def bPrimary(self, prob):
+        eqLocs = prob._eqLocs
+
+        if eqLocs is 'FE':
+            gridX = prob.mesh.gridFx
+            gridY = prob.mesh.gridFy
+            gridZ = prob.mesh.gridFz
+            C = prob.mesh.edgeCurl
+
+        elif eqLocs is 'EF':
+            gridX = prob.mesh.gridEx
+            gridY = prob.mesh.gridEy
+            gridZ = prob.mesh.gridEz
+            C = prob.mesh.edgeCurl.T
+
+        srcfct = MagneticDipoleFields
+        if prob.mesh._meshType is 'CYL':
+            if not prob.mesh.isSymmetric:
+                # TODO ?
+                raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
+            bx = srcfct(self.loc, gridX, 'x', mu=self.mu, moment=self.moment)
+            bz = srcfct(self.loc, gridZ, 'z', mu=self.mu, moment=self.moment)
+            b = np.concatenate((bx,bz))
+        else:
+            bx = srcfct(self.loc, gridX, 'x', mu=self.mu, moment=self.moment)
+            by = srcfct(self.loc, gridY, 'y', mu=self.mu, moment=self.moment)
+            bz = srcfct(self.loc, gridZ, 'z', mu=self.mu, moment=self.moment)
+            b = np.concatenate((bx,by,bz))
+
+        return b
+
+    def hPrimary(self, prob):
+        b = self.bPrimary(prob)
+        return h_from_b(prob, b)
+
+    def S_m(self, prob):
+        b = self.bPrimary(prob)
+        return -1j*omega(self.freq)*b
+
+    def S_e(self, prob):
+        if all(np.r_[self.mu] == np.r_[prob.curModel.mu]):
+            return Zero()
+        else:
+            eqLocs = prob._eqLocs
+
+            if eqLocs is 'FE':
+                mui_s = prob.curModel.mui - 1./self.mu
+                MMui_s = prob.mesh.getFaceInnerProduct(mui_s)
+                C = prob.mesh.edgeCurl
+            elif eqLocs is 'EF':
+                mu_s = prob.curModel.mu - self.mu
+                MMui_s = prob.mesh.getEdgeInnerProduct(mu_s,invMat=True)
+                C = prob.mesh.edgeCurl.T
+
+            return -C.T * (MMui_s * self.bPrimary(prob))
+
+
+class CircularLoop(BaseSrc):
+
+    #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):
+        self.freq = float(freq)
+        self.orientation = orientation
+        self.radius = radius
+        self.mu = mu
+        self.loc = loc
+        self.integrate = False
+        BaseSrc.__init__(self, rxList)
+
+    def bPrimary(self, prob):
+        eqLocs = prob._eqLocs
+
+        if eqLocs is 'FE':
+            gridX = prob.mesh.gridEx
+            gridY = prob.mesh.gridEy
+            gridZ = prob.mesh.gridEz
+            C = prob.mesh.edgeCurl
+
+        elif eqLocs is 'EF':
+            gridX = prob.mesh.gridFx
+            gridY = prob.mesh.gridFy
+            gridZ = prob.mesh.gridFz
+            C = prob.mesh.edgeCurl.T
+
+        if prob.mesh._meshType is 'CYL':
+            if not prob.mesh.isSymmetric:
+                # TODO ?
+                raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
+            a = MagneticDipoleVectorPotential(self.loc, gridY, 'y', moment=self.radius, mu=self.mu)
+
+        else:
+            srcfct = MagneticDipoleVectorPotential
+            ax = srcfct(self.loc, gridX, 'x', self.radius, mu=self.mu)
+            ay = srcfct(self.loc, gridY, 'y', self.radius, mu=self.mu)
+            az = srcfct(self.loc, gridZ, 'z', self.radius, mu=self.mu)
+            a = np.concatenate((ax, ay, az))
+
+        return C*a
+
+    def hPrimary(self, prob):
+        b = self.bPrimary(prob)
+        return 1./self.mu*b
+
+    def S_m(self, prob):
+        b = self.bPrimary(prob)
+        return -1j*omega(self.freq)*b
+
+    def S_e(self, prob):
+        if all(np.r_[self.mu] == np.r_[prob.curModel.mu]):
+            return Zero()
+        else:
+            eqLocs = prob._eqLocs
+
+            if eqLocs is 'FE':
+                mui_s = prob.curModel.mui - 1./self.mu
+                MMui_s = prob.mesh.getFaceInnerProduct(mui_s)
+                C = prob.mesh.edgeCurl
+            elif eqLocs is 'EF':
+                mu_s = prob.curModel.mu - self.mu
+                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

@@ -0,0 +1,148 @@
+import SimPEG
+from SimPEG.EM.Utils import *
+from scipy.constants import mu_0
+from SimPEG.Utils import Zero, Identity
+import SrcFDEM as Src
+
+
+####################################################
+# Receivers
+####################################################
+
+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'],
+
+                    'bxr':['b', 'Fx', 'real'],
+                    'byr':['b', 'Fy', 'real'],
+                    'bzr':['b', 'Fz', 'real'],
+                    'bxi':['b', 'Fx', 'imag'],
+                    'byi':['b', 'Fy', 'imag'],
+                    'bzi':['b', 'Fz', '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'],
+
+                    'hxr':['h', 'Ex', 'real'],
+                    'hyr':['h', 'Ey', 'real'],
+                    'hzr':['h', 'Ez', 'real'],
+                    'hxi':['h', 'Ex', 'imag'],
+                    'hyi':['h', 'Ey', 'imag'],
+                    'hzi':['h', 'Ez', 'imag'],
+                   }
+    radius = None
+
+    def __init__(self, locs, rxType):
+        SimPEG.Survey.BaseRx.__init__(self, locs, rxType)
+
+    @property
+    def projField(self):
+        """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):
+        P = self.getP(mesh)
+        u_part_complex = u[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
+
+    def projectFieldsDeriv(self, src, mesh, u, v, adjoint=False):
+        P = self.getP(mesh)
+
+        if not adjoint:
+            Pv_complex = P * v
+            real_or_imag = self.projComp
+            Pv = getattr(Pv_complex, real_or_imag)
+        elif adjoint:
+            Pv_real = P.T * v
+
+            real_or_imag = self.projComp
+            if real_or_imag == 'imag':
+                Pv = 1j*Pv_real
+            elif real_or_imag == 'real':
+                Pv = Pv_real.astype(complex)
+            else:
+                raise NotImplementedError('must be real or imag')
+
+        return Pv
+
+
+####################################################
+# Survey
+####################################################
+
+class Survey(SimPEG.Survey.BaseSurvey):
+    """
+        docstring for SurveyFDEM
+    """
+
+    srcPair = Src.BaseSrc
+
+    def __init__(self, srcList, **kwargs):
+        # Sort these by frequency
+        self.srcList = srcList
+        SimPEG.Survey.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)
+
+    @property
+    def nSrcByFreq(self):
+        if getattr(self, '_nSrcByFreq', None) is None:
+            self._nSrcByFreq = {}
+            for freq in self.freqs:
+                self._nSrcByFreq[freq] = len(self.getSrcByFreq(freq))
+        return self._nSrcByFreq
+
+    def getSrcByFreq(self, freq):
+        """Returns the sources associated with a specific frequency."""
+        assert freq in self._freqDict, "The requested frequency is not in this survey."
+        return self._freqDict[freq]
+
+    def projectFields(self, u):
+        data = 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/FDEM/__init__.py

@@ -0,0 +1,3 @@
+from SurveyFDEM import Rx, Src, Survey
+from FDEM import BaseFDEMProblem, Problem_e, Problem_b, Problem_j, Problem_h
+from FieldsFDEM import *

SimPEG/EM/TDEM/BaseTDEM.py

@@ -0,0 +1,155 @@
+from SimPEG import Solver, Problem
+from SimPEG.Problem import BaseTimeProblem
+from SimPEG.EM.Utils import *
+from scipy.constants import mu_0
+from SimPEG.Utils import sdiag, mkvc
+from SimPEG import Utils, Mesh
+from SimPEG.EM.Base import BaseEMProblem
+import numpy as np
+
+
+class FieldsTDEM(Problem.TimeFields):
+    """Fancy Field Storage for a TDEM survey."""
+    knownFields = {'b': 'F', 'e': 'E'}
+
+    def tovec(self):
+        nSrc, nF, nE = self.survey.nSrc, self.mesh.nF, self.mesh.nE
+        u = np.empty((0,nSrc)) #((0,1) if nSrc == 1 else (0, nSrc))
+
+        for i in range(self.survey.prob.nT):
+            if 'b' in self:
+                b = self[:,'b',i+1]
+            else:
+                b = np.zeros((nF,nSrc)) # if nSrc == 1 else (nF, nSrc))
+
+            if 'e' in self:
+                e = self[:,'e',i+1]
+            else:
+                e = np.zeros((nE,nSrc)) # if nSrc == 1 else (nE, nSrc))
+            u = np.concatenate((u, b, e))
+        return Utils.mkvc(u,nSrc)
+
+
+class BaseTDEMProblem(BaseTimeProblem, BaseEMProblem):
+    """docstring for ProblemTDEM1D"""
+    def __init__(self, mesh, mapping=None, **kwargs):
+        BaseTimeProblem.__init__(self, mesh, mapping=mapping, **kwargs)
+
+    _FieldsForward_pair = FieldsTDEM  #: used for the forward calculation only
+
+    def fields(self, m):
+        if self.verbose: print '%s\nCalculating fields(m)\n%s'%('*'*50,'*'*50)
+        self.curModel = m
+        # Create a fields storage object
+        F = self._FieldsForward_pair(self.mesh, self.survey)
+        for src in self.survey.srcList:
+            # Set the initial conditions
+            F[src,:,0] = src.getInitialFields(self.mesh)
+        F = self.forward(m, self.getRHS, F=F)
+        if self.verbose: print '%s\nDone calculating fields(m)\n%s'%('*'*50,'*'*50)
+        return F
+
+    def forward(self, m, RHS, F=None):
+        self.curModel = m
+        F = F or FieldsTDEM(self.mesh, self.survey)
+
+        dtFact = None
+        Ainv   = None
+        for tInd, dt in enumerate(self.timeSteps):
+            if dt != dtFact:
+                dtFact = dt
+                if Ainv is not None:
+                    Ainv.clean()
+                A = self.getA(tInd)
+                if self.verbose: print 'Factoring...   (dt = %e)'%dt
+                Ainv = self.Solver(A, **self.solverOpts)
+                if self.verbose: print 'Done'
+            rhs = RHS(tInd, F)
+            if self.verbose: print '    Solving...   (tInd = %d)'%tInd
+            sol = Ainv * rhs
+            if self.verbose: print '    Done...'
+            if sol.ndim == 1:
+                sol.shape = (sol.size,1)
+            F[:,self.solType,tInd+1] = sol
+        Ainv.clean()
+        return F
+
+    def adjoint(self, m, RHS, F=None):
+        self.curModel = m
+        F = F or FieldsTDEM(self.mesh, self.survey)
+
+        dtFact = None
+        Ainv   = None
+        for tInd, dt in reversed(list(enumerate(self.timeSteps))):
+            if dt != dtFact:
+                dtFact = dt
+                if Ainv is not None:
+                    Ainv.clean()
+                A = self.getA(tInd)
+                if self.verbose: print 'Factoring (Adjoint)...   (dt = %e)'%dt
+                Ainv = self.Solver(A, **self.solverOpts)
+                if self.verbose: print 'Done'
+            rhs = RHS(tInd, F)
+            if self.verbose: print '    Solving (Adjoint)...   (tInd = %d)'%tInd
+            sol = Ainv * rhs
+            if self.verbose: print '    Done...'
+            if sol.ndim == 1:
+                sol.shape = (sol.size,1)
+            F[:,self.solType,tInd+1] = sol
+        Ainv.clean()
+        return F
+
+    def Jvec(self, m, v, u=None):
+        """
+            :param numpy.array m: Conductivity model
+            :param numpy.ndarray v: vector (model object)
+            :param simpegEM.TDEM.FieldsTDEM u: Fields resulting from m
+            :rtype: numpy.ndarray
+            :return: w (data object)
+
+            Multiplying \\\(\\\mathbf{J}\\\) onto a vector can be broken into three steps
+
+            * Compute \\\(\\\\vec{p} = \\\mathbf{G}v\\\)
+            * Solve \\\(\\\hat{\\\mathbf{A}} \\\\vec{y} = \\\\vec{p}\\\)
+            * Compute \\\(\\\\vec{w} = -\\\mathbf{Q} \\\\vec{y}\\\)
+
+        """
+        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)
+        y = self.solveAh(m, p)
+        Jv = self.survey.projectFieldsDeriv(u, 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):
+        """
+            :param numpy.array m: Conductivity model
+            :param numpy.ndarray,SimPEG.Survey.Data v: vector (data object)
+            :param simpegEM.TDEM.FieldsTDEM u: Fields resulting from m
+            :rtype: numpy.ndarray
+            :return: w (model object)
+
+            Multiplying \\\(\\\mathbf{J}^\\\\top\\\) onto a vector can be broken into three steps
+
+            * Compute \\\(\\\\vec{p} = \\\mathbf{Q}^\\\\top \\\\vec{v}\\\)
+            * Solve \\\(\\\hat{\\\mathbf{A}}^\\\\top \\\\vec{y} = \\\\vec{p}\\\)
+            * Compute \\\(\\\\vec{w} = -\\\mathbf{G}^\\\\top y\\\)
+
+        """
+        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 not isinstance(v, self.dataPair):
+            v = self.dataPair(self.survey, v)
+
+        p = self.survey.projectFieldsDeriv(u, v=v, adjoint=True)
+        y = self.solveAht(m, p)
+        w = self.Gtvec(m, y, u)
+        if self.verbose: print '%s\nDone calculating J^T(v)\n%s'%('*'*50,'*'*50)
+        return - mkvc(w)
+

SimPEG/EM/TDEM/SurveyTDEM.py

@@ -0,0 +1,162 @@
+from SimPEG import Utils, Survey, np
+from SimPEG.Survey import BaseSurvey
+from SimPEG.EM.Utils import *
+from BaseTDEM import FieldsTDEM
+
+
+class RxTDEM(Survey.BaseTimeRx):
+
+    knownRxTypes = {
+                    'ex':['e', 'Ex', 'N'],
+                    'ey':['e', 'Ey', 'N'],
+                    'ez':['e', 'Ez', 'N'],
+
+                    'bx':['b', 'Fx', 'N'],
+                    'by':['b', 'Fy', 'N'],
+                    'bz':['b', 'Fz', 'N'],
+
+                    'dbxdt':['b', 'Fx', 'CC'],
+                    'dbydt':['b', 'Fy', 'CC'],
+                    'dbzdt':['b', 'Fz', 'CC'],
+                   }
+
+    def __init__(self, locs, times, rxType):
+        Survey.BaseTimeRx.__init__(self, locs, times, rxType)
+
+    @property
+    def projField(self):
+        """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 projTLoc(self):
+        """Time Location projection (e.g. CC N)"""
+        return self.knownRxTypes[self.rxType][2]
+
+    def getTimeP(self, timeMesh):
+        """
+            Returns the time projection matrix.
+
+            .. note::
+
+                This is not stored in memory, but is created on demand.
+        """
+        if self.rxType in ['dbxdt','dbydt','dbzdt']:
+            return timeMesh.getInterpolationMat(self.times, self.projTLoc)*timeMesh.faceDiv
+        else:
+            return timeMesh.getInterpolationMat(self.times, self.projTLoc)
+
+    def projectFields(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):
+        P = self.getP(mesh, timeMesh)
+
+        if not adjoint:
+            return P * Utils.mkvc(v[src, self.projField, :])
+        elif adjoint:
+            return P.T * v[src, self]
+
+
+class SrcTDEM(Survey.BaseSrc):
+    rxPair = RxTDEM
+    radius = None
+
+    def getInitialFields(self, mesh):
+        F0 = getattr(self, '_getInitialFields_' + self.srcType)(mesh)
+        return F0
+
+    def getJs(self, mesh, time):
+        return None
+
+
+class SrcTDEM_VMD_MVP(SrcTDEM):
+
+    def __init__(self,rxList,loc):
+        self.loc = loc
+        SrcTDEM.__init__(self,rxList)
+
+    def getInitialFields(self, mesh):
+        """Vertical magnetic dipole, magnetic vector potential"""
+        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}
+
+
+class SrcTDEM_CircularLoop_MVP(SrcTDEM):
+
+    def __init__(self,rxList,loc,radius):
+        self.loc = loc
+        self.radius = radius
+        SrcTDEM.__init__(self,rxList)
+
+    def getInitialFields(self, mesh):
+        """Circular Loop, magnetic vector potential"""
+        if mesh._meshType is 'CYL':
+            if mesh.isSymmetric:
+                MVP = MagneticLoopVectorPotential(self.loc, mesh, 'Ey', self.radius)
+            else:
+                raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
+        elif mesh._meshType is 'TENSOR':
+            MVP = MagneticLoopVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'], self.radius)
+        else:
+            raise Exception('Unknown mesh for CircularLoop')
+
+        return {"b": mesh.edgeCurl*MVP}
+
+
+class SurveyTDEM(Survey.BaseSurvey):
+    """
+        docstring for SurveyTDEM
+    """
+    srcPair = SrcTDEM
+
+    def __init__(self, srcList, **kwargs):
+        # Sort these by frequency
+        self.srcList = srcList
+        Survey.BaseSurvey.__init__(self, **kwargs)
+
+    def projectFields(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)
+        return data
+
+    def projectFieldsDeriv(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)
+            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 = Ptv.reshape((-1, self.prob.timeMesh.nN), order='F')
+                    if rx.projField not in f: # first time we are projecting
+                        f[src, rx.projField, :] = Ptv
+                    else: # there are already fields, so let's add to them!
+                        f[src, rx.projField, :] += Ptv
+            return f
+
+

SimPEG/EM/TDEM/TDEM_b.py

@@ -0,0 +1,356 @@
+from BaseTDEM import BaseTDEMProblem, FieldsTDEM
+from SimPEG.Utils import mkvc, sdiag
+import numpy as np
+from SurveyTDEM import SurveyTDEM
+
+
+class FieldsTDEM_e_from_b(FieldsTDEM):
+    """Fancy Field Storage for a TDEM survey."""
+    knownFields = {'b': 'F'}
+    aliasFields = {'e': ['b','E','e_from_b']}
+
+    def startup(self):
+        self.MeSigmaI  = self.survey.prob.MeSigmaI
+        self.edgeCurlT = self.survey.prob.mesh.edgeCurl.T
+        self.MfMui     = self.survey.prob.MfMui
+
+    def e_from_b(self, b, srcInd, timeInd):
+        # TODO: implement non-zero js
+        return self.MeSigmaI*(self.edgeCurlT*(self.MfMui*b))
+
+class FieldsTDEM_e_from_b_Ah(FieldsTDEM):
+    """Fancy Field Storage for a TDEM survey.
+
+        This is used when solving Ahat and AhatT
+    """
+    knownFields = {'b': 'F'}
+    aliasFields = {'e': ['b','E','e_from_b']}
+    p = None
+
+    def startup(self):
+        self.MeSigmaI  = self.survey.prob.MeSigmaI
+        self.edgeCurlT = self.survey.prob.mesh.edgeCurl.T
+        self.MfMui     = self.survey.prob.MfMui
+
+    def e_from_b(self, y_b, srcInd, tInd):
+        y_e = self.MeSigmaI*(self.edgeCurlT*(self.MfMui*y_b))
+        if 'e' in self.p:
+            y_e = y_e - self.MeSigmaI*self.p[srcInd,'e',tInd]
+        return y_e
+
+class ProblemTDEM_b(BaseTDEMProblem):
+    """
+        Time-Domain EM problem - B-formulation
+
+        TDEM_b treats the following discretization of Maxwell's equations
+
+        .. math::
+            \dcurl \e^{(t+1)} + \\frac{\\b^{(t+1)} - \\b^{(t)}}{\delta t} = 0 \\\\
+            \dcurl^\\top \MfMui \\b^{(t+1)} - \MeSig \e^{(t+1)} = \Me \j_s^{(t+1)}
+
+        with \\\(\\b\\\) defined on cell faces and \\\(\e\\\) defined on edges.
+    """
+    def __init__(self, mesh, mapping=None, **kwargs):
+        BaseTDEMProblem.__init__(self, mesh, mapping=mapping, **kwargs)
+
+    solType = 'b' #: Type of the solution, in this case the 'b' field
+
+    surveyPair = SurveyTDEM
+    _FieldsForward_pair = FieldsTDEM_e_from_b     #: used for the forward calculation only
+
+    ####################################################
+    # Internal Methods
+    ####################################################
+
+    def getA(self, tInd):
+        """
+            :param int tInd: Time index
+            :rtype: scipy.sparse.csr_matrix
+            :return: A
+        """
+        dt = self.timeSteps[tInd]
+        return self.MfMui*self.mesh.edgeCurl*self.MeSigmaI*self.mesh.edgeCurl.T*self.MfMui + (1.0/dt)*self.MfMui
+
+    def getRHS(self, tInd, F):
+        dt = self.timeSteps[tInd]
+        B_n = np.c_[[F[src,'b',tInd] for src in self.survey.srcList]].T
+        if B_n.shape[0] is not 1:
+            raise NotImplementedError('getRHS not implemented for this shape of B_n')
+        RHS = (1.0/dt)*self.MfMui*B_n[0,:,:] #TODO: This is a hack
+        return RHS
+
+    ####################################################
+    # Derivatives
+    ####################################################
+
+    def Gvec(self, m, vec, u=None):
+        """
+            :param numpy.array m: Conductivity model
+            :param numpy.array vec: vector (like a model)
+            :param simpegEM.TDEM.FieldsTDEM u: Fields resulting from m
+            :rtype: simpegEM.TDEM.FieldsTDEM
+            :return: f
+
+            Multiply G by a vector
+        """
+        if u is None:
+            u = self.fields(m)
+        self.curModel = m
+
+        # Note: Fields has shape (nF/E, nSrc, nT+1)
+        #       However, p will only really fill (:,:,1:nT+1)
+        #       meaning the 'initial fields' are zero (:,:,0)
+        p = FieldsTDEM(self.mesh, self.survey)
+        # 'b' at all times is zero.
+        #       However, to save memory we will **not** do:
+        #
+        #               p[:, 'b', :] = 0.0
+
+        # fake initial 'e' fields
+        p[:, 'e', 0] = 0.0
+        dMdsig = self.MeSigmaDeriv
+        # self.mesh.getEdgeInnerProductDeriv(self.curModel.transform)
+        # dsigdm_x_v = self.curModel.sigmaDeriv*vec
+        # dsigdm_x_v = self.curModel.transformDeriv*vec
+        for i in range(1,self.nT+1):
+            # TODO: G[1] may be dependent on the model
+            #       for a galvanic source (deriv of the dc problem)
+            #
+            # Do multiplication for all src in self.survey.srcList
+            for src in self.survey.srcList:
+                p[src, 'e', i] = - dMdsig(u[src,'e',i]) *  vec
+        return p
+
+    def Gtvec(self, m, vec, u=None):
+        """
+            :param numpy.array m: Conductivity model
+            :param numpy.array vec: vector (like a fields)
+            :param simpegEM.TDEM.FieldsTDEM u: Fields resulting from m
+            :rtype: np.ndarray (like a model)
+            :return: p
+
+            Multiply G.T by a vector
+        """
+        if u is None:
+            u = self.fields(m)
+        self.curModel = m
+        # dMdsig = self.mesh.getEdgeInnerProductDeriv(self.curModel.transform)
+        # dsigdm = self.curModel.transformDeriv
+        MeSigmaDeriv = self.MeSigmaDeriv
+
+        nSrc = self.survey.nSrc
+        VUs = None
+        # Here we can do internal multiplications of Gt*v and then multiply by MsigDeriv.T in one go.
+        for i in range(1,self.nT+1):
+            vu = None
+            for src in self.survey.srcList:
+                vusrc = MeSigmaDeriv(u[src,'e',i]).T * vec[src,'e',i]
+                vu = vusrc if vu is None else vu + vusrc
+            VUs = vu if VUs is None else VUs + vu
+        # p = -dsigdm.T*VUs
+        return -VUs
+
+    def solveAh(self, m, p):
+        """
+            :param numpy.array m: Conductivity model
+            :param simpegEM.TDEM.FieldsTDEM p: Fields object
+            :rtype: simpegEM.TDEM.FieldsTDEM
+            :return: y
+
+            Solve the block-matrix system \\\(\\\hat{A} \\\hat{y} = \\\hat{p}\\\):
+
+            .. math::
+                \mathbf{\hat{A}} = \left[
+                    \\begin{array}{cccc}
+                        A & 0 & & \\\\
+                        B & A & & \\\\
+                        & \ddots & \ddots & \\\\
+                        & & B & A
+                    \end{array}
+                \\right] \\\\
+                \mathbf{A} =
+                \left[
+                    \\begin{array}{cc}
+                        \\frac{1}{\delta t} \MfMui & \MfMui\dcurl \\\\
+                        \dcurl^\\top \MfMui & -\MeSig
+                    \end{array}
+                \\right] \\\\
+                \mathbf{B} =
+                \left[
+                    \\begin{array}{cc}
+                        -\\frac{1}{\delta t} \MfMui & 0 \\\\
+                        0 & 0
+                    \end{array}
+                \\right] \\\\
+        """
+
+        def AhRHS(tInd, y):
+            rhs = self.MfMui*(self.mesh.edgeCurl*(self.MeSigmaI*p[:,'e',tInd+1]))
+            if 'b' in p:
+                rhs = rhs + p[:,'b',tInd+1]
+            if tInd == 0:
+                return rhs
+            dt = self.timeSteps[tInd]
+            return rhs + 1.0/dt*self.MfMui*y[:,'b',tInd]
+
+        F = FieldsTDEM_e_from_b_Ah(self.mesh, self.survey, p=p)
+
+        return self.forward(m, AhRHS, F)
+
+    def solveAht(self, m, p):
+        """
+            :param numpy.array m: Conductivity model
+            :param simpegEM.TDEM.FieldsTDEM p: Fields object
+            :rtype: simpegEM.TDEM.FieldsTDEM
+            :return: y
+
+            Solve the block-matrix system \\\(\\\hat{A}^\\\\top \\\hat{y} = \\\hat{p}\\\):
+
+            .. math::
+                \mathbf{\hat{A}}^\\top = \left[
+                    \\begin{array}{cccc}
+                        A & B & & \\\\
+                          & \ddots & \ddots & \\\\
+                          & & A & B \\\\
+                          & & 0 & A
+                    \end{array}
+                \\right] \\\\
+                \mathbf{A} =
+                \left[
+                    \\begin{array}{cc}
+                        \\frac{1}{\delta t} \MfMui & \MfMui\dcurl \\\\
+                        \dcurl^\\top \MfMui & -\MeSig
+                    \end{array}
+                \\right] \\\\
+                \mathbf{B} =
+                \left[
+                    \\begin{array}{cc}
+                        -\\frac{1}{\delta t} \MfMui & 0 \\\\
+                        0 & 0
+                    \end{array}
+                \\right] \\\\
+        """
+
+        #  Mini Example:
+        #
+        #       nT = 3, len(times) == 4, fields stored in F[:,:,1:4]
+        #
+        #       0 is held for initial conditions (this shifts the storage by +1)
+        #       ^
+        #  fLoc 0     1     2     3
+        #       |-----|-----|-----|
+        #  tInd    0     1     2
+        #                        / ___/
+        #                      2          (tInd=2 uses fields 3 and would use 4 but it doesn't exist)
+        #                 / ___/
+        #                1                (tInd=1 uses fields 2 and 3)
+
+        def AhtRHS(tInd, y):
+            nSrc, nF = self.survey.nSrc, self.mesh.nF
+            rhs = np.zeros((nF,1) if nSrc == 1 else (nF, nSrc))
+
+            if 'e' in p:
+                rhs += self.MfMui*(self.mesh.edgeCurl*(self.MeSigmaI*p[:,'e',tInd+1]))
+            if 'b' in p:
+                rhs += p[:,'b',tInd+1]
+
+            if tInd == self.nT-1:
+                return rhs
+            dt = self.timeSteps[tInd+1]
+            return rhs + 1.0/dt*self.MfMui*y[:,'b',tInd+2]
+
+        F = FieldsTDEM_e_from_b_Ah(self.mesh, self.survey, p=p)
+
+        return self.adjoint(m, AhtRHS, F)
+
+    ####################################################
+    # Functions for tests
+    ####################################################
+
+    def _AhVec(self, m, vec):
+        """
+            :param numpy.array m: Conductivity model
+            :param simpegEM.TDEM.FieldsTDEM vec: Fields object
+            :rtype: simpegEM.TDEM.FieldsTDEM
+            :return: f
+
+            Multiply the matrix \\\(\\\hat{A}\\\) by a fields vector where
+
+            .. math::
+                \mathbf{\hat{A}} = \left[
+                    \\begin{array}{cccc}
+                        A & 0 & & \\\\
+                        B & A & & \\\\
+                        & \ddots & \ddots & \\\\
+                        & & B & A
+                    \end{array}
+                \\right] \\\\
+                \mathbf{A} =
+                \left[
+                    \\begin{array}{cc}
+                        \\frac{1}{\delta t} \MfMui & \MfMui\dcurl \\\\
+                        \dcurl^\\top \MfMui & -\MeSig
+                    \end{array}
+                \\right] \\\\
+                \mathbf{B} =
+                \left[
+                    \\begin{array}{cc}
+                        -\\frac{1}{\delta t} \MfMui & 0 \\\\
+                        0 & 0
+                    \end{array}
+                \\right] \\\\
+        """
+
+        self.curModel = m
+        f = FieldsTDEM(self.mesh, self.survey)
+        for i in range(1,self.nT+1):
+            dt = self.timeSteps[i-1]
+            b = 1.0/dt*self.MfMui*vec[:,'b',i] + self.MfMui*(self.mesh.edgeCurl*vec[:,'e',i])
+            if i > 1:
+                b = b - 1.0/dt*self.MfMui*vec[:,'b',i-1]
+            f[:,'b',i] = b
+            f[:,'e',i] = self.mesh.edgeCurl.T*(self.MfMui*vec[:,'b',i]) - self.MeSigma*vec[:,'e',i]
+        return f
+
+    def _AhtVec(self, m, vec):
+        """
+            :param numpy.array m: Conductivity model
+            :param simpegEM.TDEM.FieldsTDEM vec: Fields object
+            :rtype: simpegEM.TDEM.FieldsTDEM
+            :return: f
+
+            Multiply the matrix \\\(\\\hat{A}\\\) by a fields vector where
+
+            .. math::
+                \mathbf{\hat{A}}^\\top = \left[
+                    \\begin{array}{cccc}
+                        A & B & & \\\\
+                          & \ddots & \ddots & \\\\
+                          & & A & B \\\\
+                          & & 0 & A
+                    \end{array}
+                \\right] \\\\
+                \mathbf{A} =
+                \left[
+                    \\begin{array}{cc}
+                        \\frac{1}{\delta t} \MfMui & \MfMui\dcurl \\\\
+                        \dcurl^\\top \MfMui & -\MeSig
+                    \end{array}
+                \\right] \\\\
+                \mathbf{B} =
+                \left[
+                    \\begin{array}{cc}
+                        -\\frac{1}{\delta t} \MfMui & 0 \\\\
+                        0 & 0
+                    \end{array}
+                \\right] \\\\
+        """
+        self.curModel = m
+        f = FieldsTDEM(self.mesh, self.survey)
+        for i in range(self.nT):
+            b = 1.0/self.timeSteps[i]*self.MfMui*vec[:,'b',i+1] + self.MfMui*(self.mesh.edgeCurl*vec[:,'e',i+1])
+            if i < self.nT-1:
+                b = b - 1.0/self.timeSteps[i+1]*self.MfMui*vec[:,'b',i+2]
+            f[:,'b', i+1] = b
+            f[:,'e', i+1] = self.mesh.edgeCurl.T*(self.MfMui*vec[:,'b',i+1]) - self.MeSigma*vec[:,'e',i+1]
+        return f

SimPEG/EM/TDEM/__init__.py

@@ -0,0 +1,3 @@
+from SurveyTDEM import * #SurveyTDEM, RxTDEM, SrcTDEM
+from BaseTDEM import BaseTDEMProblem, FieldsTDEM
+from TDEM_b import ProblemTDEM_b

SimPEG/EM/Utils/AnalyticUtils.py

@@ -0,0 +1,203 @@
+from SimPEG import *
+from scipy.special import ellipk, ellipe
+from scipy.constants import mu_0, pi
+
+def MagneticDipoleVectorPotential(srcLoc, obsLoc, component, moment=1., dipoleMoment=(0., 0., 1.), mu = mu_0):
+    """
+        Calculate the vector potential of a set of magnetic dipoles
+        at given locations 'ref. <http://en.wikipedia.org/wiki/Dipole#Magnetic_vector_potential>'
+
+        :param numpy.ndarray srcLoc: Location of the source(s) (x, y, z)
+        :param numpy.ndarray,SimPEG.Mesh obsLoc: Where the potentials will be calculated (x, y, z) or a SimPEG Mesh
+        :param str,list component: The component to calculate - 'x', 'y', or 'z' if an array, or grid type if mesh, can be a list
+        :param numpy.ndarray dipoleMoment: The vector dipole moment
+        :rtype: numpy.ndarray
+        :return: The vector potential each dipole at each observation location
+    """
+    #TODO: break this out!
+
+    if type(component) in [list, tuple]:
+        out = range(len(component))
+        for i, comp in enumerate(component):
+            out[i] = MagneticDipoleVectorPotential(srcLoc, obsLoc, comp, dipoleMoment=dipoleMoment)
+        return np.concatenate(out)
+
+    if isinstance(obsLoc, Mesh.BaseMesh):
+        mesh = obsLoc
+        assert component in ['Ex','Ey','Ez','Fx','Fy','Fz'], "Components must be in: ['Ex','Ey','Ez','Fx','Fy','Fz']"
+        return MagneticDipoleVectorPotential(srcLoc, getattr(mesh,'grid'+component), component[1], dipoleMoment=dipoleMoment)
+
+    if component == 'x':
+        dimInd = 0
+    elif component == 'y':
+        dimInd = 1
+    elif component == 'z':
+        dimInd = 2
+    else:
+        raise ValueError('Invalid component')
+
+    srcLoc = np.atleast_2d(srcLoc)
+    obsLoc = np.atleast_2d(obsLoc)
+    dipoleMoment = np.atleast_2d(dipoleMoment)
+
+    nEdges = obsLoc.shape[0]
+    nSrc = srcLoc.shape[0]
+
+    m = np.array(dipoleMoment).repeat(nEdges, axis=0)
+    A = np.empty((nEdges, nSrc))
+    for i in range(nSrc):
+        dR = obsLoc - srcLoc[i, np.newaxis].repeat(nEdges, axis=0)
+        mCr = np.cross(m, dR)
+        r = np.sqrt((dR**2).sum(axis=1))
+        A[:, i] = +(mu/(4*pi)) * mCr[:,dimInd]/(r**3)
+    if nSrc == 1:
+        return A.flatten()
+    return A
+
+
+def MagneticDipoleFields(srcLoc, obsLoc, component, moment=1., mu = mu_0):
+    """
+        Calculate the vector potential of a set of magnetic dipoles
+        at given locations 'ref. <http://en.wikipedia.org/wiki/Dipole#Magnetic_vector_potential>'
+
+        :param numpy.ndarray srcLoc: Location of the source(s) (x, y, z)
+        :param numpy.ndarray obsLoc: Where the potentials will be calculated (x, y, z)
+        :param str component: The component to calculate - 'x', 'y', or 'z'
+        :param numpy.ndarray moment: The vector dipole moment (vertical)
+        :rtype: numpy.ndarray
+        :return: The vector potential each dipole at each observation location
+    """
+
+    if component=='x':
+        dimInd = 0
+    elif component=='y':
+        dimInd = 1
+    elif component=='z':
+        dimInd = 2
+    else:
+        raise ValueError('Invalid component')
+
+    srcLoc = np.atleast_2d(srcLoc)
+    obsLoc = np.atleast_2d(obsLoc)
+    moment = np.atleast_2d(moment)
+
+    nFaces = obsLoc.shape[0]
+    nSrc = srcLoc.shape[0]
+
+    m = np.array(moment).repeat(nFaces, axis=0)
+    B = np.empty((nFaces, nSrc))
+    for i in range(nSrc):
+        dR = obsLoc - srcLoc[i, np.newaxis].repeat(nFaces, axis=0)
+        r = np.sqrt((dR**2).sum(axis=1))
+        if dimInd == 0:
+            B[:, i] = +(mu/(4*pi)) /(r**3) * (3*dR[:,2]*dR[:,0]/r**2)
+        elif dimInd == 1:
+            B[:, i] = +(mu/(4*pi)) /(r**3) * (3*dR[:,2]*dR[:,1]/r**2)
+        elif dimInd == 2:
+            B[:, i] = +(mu/(4*pi)) /(r**3) * (3*dR[:,2]**2/r**2-1)
+        else:
+            raise Exception("Not Implemented")
+    if nSrc == 1:
+        return B.flatten()
+    return B
+
+
+
+def MagneticLoopVectorPotential(srcLoc, obsLoc, component, radius, mu=mu_0):
+    """
+        Calculate the vector potential of horizontal circular loop
+        at given locations
+
+        :param numpy.ndarray srcLoc: Location of the source(s) (x, y, z)
+        :param numpy.ndarray,SimPEG.Mesh obsLoc: Where the potentials will be calculated (x, y, z) or a SimPEG Mesh
+        :param str,list component: The component to calculate - 'x', 'y', or 'z' if an array, or grid type if mesh, can be a list
+        :param numpy.ndarray I: Input current of the loop
+        :param numpy.ndarray radius: radius of the loop
+        :rtype: numpy.ndarray
+        :return: The vector potential each dipole at each observation location
+    """
+
+    if type(component) in [list, tuple]:
+        out = range(len(component))
+        for i, comp in enumerate(component):
+            out[i] = MagneticLoopVectorPotential(srcLoc, obsLoc, comp, radius, mu)
+        return np.concatenate(out)
+
+    if isinstance(obsLoc, Mesh.BaseMesh):
+        mesh = obsLoc
+        assert component in ['Ex','Ey','Ez','Fx','Fy','Fz'], "Components must be in: ['Ex','Ey','Ez','Fx','Fy','Fz']"
+        return MagneticLoopVectorPotential(srcLoc, getattr(mesh,'grid'+component), component[1], radius, mu)
+
+    srcLoc = np.atleast_2d(srcLoc)
+    obsLoc = np.atleast_2d(obsLoc)
+
+    n = obsLoc.shape[0]
+    nSrc = srcLoc.shape[0]
+
+    if component=='z':
+        A = np.zeros((n, nSrc))
+        if nSrc ==1:
+            return A.flatten()
+        return A
+
+    else:
+
+        A = np.zeros((n, nSrc))
+        for i in range (nSrc):
+            x = obsLoc[:, 0] - srcLoc[i, 0]
+            y = obsLoc[:, 1] - srcLoc[i, 1]
+            z = obsLoc[:, 2] - srcLoc[i, 2]
+            r = np.sqrt(x**2 + y**2)
+            m = (4 * radius * r) / ((radius + r)**2 + z**2)
+            m[m > 1.] = 1.
+            # m might be slightly larger than 1 due to rounding errors
+            # but ellipke requires 0 <= m <= 1
+            K = ellipk(m)
+            E = ellipe(m)
+            ind = (r > 0) & (m < 1)
+            # % 1/r singular at r = 0 and K(m) singular at m = 1
+            Aphi = np.zeros(n)
+            # % Common factor is (mu * I) / pi with I = 1 and mu = 4e-7 * pi.
+            Aphi[ind] = 4e-7 / np.sqrt(m[ind])  * np.sqrt(radius / r[ind]) *((1. - m[ind] / 2.) * K[ind] - E[ind])
+            if component == 'x':
+                A[ind, i] = Aphi[ind] * (-y[ind] / r[ind] )
+            elif component == 'y':
+                A[ind, i] = Aphi[ind] * ( x[ind] / r[ind] )
+            else:
+                raise ValueError('Invalid component')
+
+        if nSrc == 1:
+            return A.flatten()
+        return A
+
+if __name__ == '__main__':
+    from SimPEG import Mesh
+    import matplotlib.pyplot as plt
+    cs = 20
+    ncx, ncy, ncz = 41, 41, 40
+    hx = np.ones(ncx)*cs
+    hy = np.ones(ncy)*cs
+    hz = np.ones(ncz)*cs
+    mesh = Mesh.TensorMesh([hx, hy, hz], 'CCC')
+    srcLoc = np.r_[0., 0., 0.]
+    Ax = MagneticLoopVectorPotential(srcLoc, mesh.gridEx, 'x', 200)
+    Ay = MagneticLoopVectorPotential(srcLoc, mesh.gridEy, 'y', 200)
+    Az = MagneticLoopVectorPotential(srcLoc, mesh.gridEz, 'z', 200)
+    A = np.r_[Ax, Ay, Az]
+    B0 = mesh.edgeCurl*A
+    J0 = mesh.edgeCurl.T*B0
+
+    # mesh.plotImage(A, vType = 'Ex')
+    # mesh.plotImage(A, vType = 'Ey')
+
+    mesh.plotImage(B0, vType = 'Fx')
+    mesh.plotImage(B0, vType = 'Fy')
+    mesh.plotImage(B0, vType = 'Fz')
+
+    # # mesh.plotImage(J0, vType = 'Ex')
+    # mesh.plotImage(J0, vType = 'Ey')
+    # mesh.plotImage(J0, vType = 'Ez')
+
+    plt.show()
+
+

SimPEG/EM/Utils/EMUtils.py

@@ -0,0 +1,49 @@
+import numpy as np
+from scipy.constants import mu_0, epsilon_0
+
+# useful params
+def omega(freq):
+    """Angular frequency, omega"""
+    return 2.*np.pi*freq
+
+def k(freq, sigma, mu=mu_0, eps=epsilon_0):
+    """ Eq 1.47 - 1.49 in Ward and Hohmann """
+    w = omega(freq)
+    alp  = w * np.sqrt( mu*eps/2 * ( np.sqrt(1. + (sigma / (eps*w))**2 ) + 1) ) 
+    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

@@ -0,0 +1,5 @@
+# import Sources
+# import Ana
+# import Solver
+from EMUtils import omega, e_from_j, j_from_e, b_from_h, h_from_b
+from AnalyticUtils import MagneticDipoleFields, MagneticDipoleVectorPotential, MagneticLoopVectorPotential

SimPEG/EM/Utils/testingUtils.py

@@ -0,0 +1,75 @@
+import unittest
+from SimPEG import *
+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
+    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)
+
+    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.])
+    Rx0 = EM.FDEM.Rx(XYZ, comp)
+
+    Src = []
+
+    for SrcType in SrcList:
+        if SrcType is 'MagDipole':
+            Src.append(EM.FDEM.Src.MagDipole([Rx0], freq=freq, loc=np.r_[0.,0.,0.]))
+        elif SrcType is 'MagDipole_Bfield':
+            Src.append(EM.FDEM.Src.MagDipole_Bfield([Rx0], freq=freq, loc=np.r_[0.,0.,0.]))
+        elif SrcType is 'CircularLoop':
+            Src.append(EM.FDEM.Src.CircularLoop([Rx0], freq=freq, loc=np.r_[0.,0.,0.]))
+        elif SrcType is 'RawVec':
+            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.
+                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.
+                Src.append(EM.FDEM.Src.RawVec([Rx0], freq, S_m, S_e))
+
+    if verbose:
+        print '  Fetching %s problem' % (fdemType)
+
+    if fdemType == 'e':
+        survey = EM.FDEM.Survey(Src)
+        prb = EM.FDEM.Problem_e(mesh, mapping=mapping)
+
+    elif fdemType == 'b':
+        survey = EM.FDEM.Survey(Src)
+        prb = EM.FDEM.Problem_b(mesh, mapping=mapping)
+
+    elif fdemType == 'j':
+        survey = EM.FDEM.Survey(Src)
+        prb = EM.FDEM.Problem_j(mesh, mapping=mapping)
+
+    elif fdemType == 'h':
+        survey = EM.FDEM.Survey(Src)
+        prb = EM.FDEM.Problem_h(mesh, mapping=mapping)
+
+    else:
+        raise NotImplementedError()
+    prb.pair(survey)
+
+    try:
+        from pymatsolver import MumpsSolver
+        prb.Solver = MumpsSolver
+    except ImportError, e:
+        pass
+
+    return prb

SimPEG/EM/__init__.py

@@ -0,0 +1,6 @@
+# from EM import *
+import TDEM
+import FDEM
+import Base
+import Analytics
+import Utils

SimPEG/Examples/DCfwd.py

@@ -1,71 +0,0 @@
-from SimPEG import Mesh, Utils, np, SolverLU
-import matplotlib.pyplot as plt
-import matplotlib
-from matplotlib.mlab import griddata
-
-## 2D DC forward modeling example with Tensor and Curvilinear Meshes
-
-# Step1: Generate Tensor and Curvilinear Mesh
-sz = [40,40]
-# Tensor Mesh
-tM = Mesh.TensorMesh(sz)
-# Curvilinear Mesh
-rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz,'rotate'))
-
-# Step2: Direct Current (DC) operator
-def DCfun(mesh, pts):
-    D = mesh.faceDiv
-    G = D.T
-    sigma = 1e-2*np.ones(mesh.nC)
-    Msigi = mesh.getFaceInnerProduct(1./sigma)
-    MsigI = Utils.sdInv(Msigi)
-    A = D*MsigI*G
-    A[-1,-1] /= mesh.vol[-1] # Remove null space
-    rhs = np.zeros(mesh.nC)
-    txind = Utils.meshutils.closestPoints(mesh, pts)
-    rhs[txind] = np.r_[1,-1]
-    return A, rhs
-
-pts = np.vstack((np.r_[0.25, 0.5], np.r_[0.75, 0.5]))
-
-#Step3: Solve DC problem (LU solver)
-AtM, rhstM = DCfun(tM, pts)
-AinvtM = SolverLU(AtM)
-phitM = AinvtM*rhstM
-
-ArM, rhsrM = DCfun(rM, pts)
-AinvrM = SolverLU(ArM)
-phirM = AinvrM*rhsrM
-
-#Step4: Making Figure
-fig, axes = plt.subplots(1,2,figsize=(12*1.2,4*1.2))
-label = ["(a)", "(b)"]
-opts = {}
-vmin, vmax = phitM.min(), phitM.max()
-dat = tM.plotImage(phitM, ax=axes[0], clim=(vmin, vmax), grid=True)
-
-#TODO: At the moment Curvilinear Mesh do not have plotimage 
-
-Xi = tM.gridCC[:,0].reshape(sz[0], sz[1], order='F')
-Yi = tM.gridCC[:,1].reshape(sz[0], sz[1], order='F')
-PHIrM = griddata(rM.gridCC[:,0], rM.gridCC[:,1], phirM, Xi, Yi, interp='linear')
-axes[1].contourf(Xi, Yi, PHIrM, 100, vmin=vmin, vmax=vmax)
-
-cb = plt.colorbar(dat[0], ax=axes[0]); cb.set_label("Voltage (V)")
-cb = plt.colorbar(dat[0], ax=axes[1]); cb.set_label("Voltage (V)")
-
-tM.plotGrid(ax=axes[0], **opts)
-axes[0].set_title('TensorMesh')
-rM.plotGrid(ax=axes[1], **opts)
-axes[1].set_title('CurvilinearMesh')
-for i in range(2):
-    axes[i].set_xlim(0.025, 0.975)
-    axes[i].set_ylim(0.025, 0.975)
-    axes[i].text(0., 1.0, label[i], fontsize=20)
-    if i==0:        
-        axes[i].set_ylabel("y")
-    else:
-        axes[i].set_ylabel(" ")
-    axes[i].set_xlabel("x")
-
-plt.show()

SimPEG/Examples/EM_FDEM_1D_Inversion.py

@@ -0,0 +1,104 @@
+from SimPEG import *
+import SimPEG.EM as EM
+from scipy.constants import mu_0
+import matplotlib.pyplot as plt
+
+def run(plotIt=True):
+    """
+        EM: FDEM: 1D: Inversion
+        =======================
+
+        Here we will create and run a FDEM 1D inversion.
+
+    """
+
+    cs, ncx, ncz, npad = 5., 25, 15, 15
+    hx = [(cs,ncx), (cs,npad,1.3)]
+    hz = [(cs,npad,-1.3), (cs,ncz), (cs,npad,1.3)]
+    mesh = Mesh.CylMesh([hx,1,hz], '00C')
+
+    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
+    sig_half = 2e-3
+    sig_air = 1e-8
+    sig_layer = 1e-3
+    sigma = np.ones(mesh.nCz)*sig_air
+    sigma[active] = sig_half
+    sigma[layer] = sig_layer
+    mtrue = np.log(sigma[active])
+
+
+    if plotIt:
+        fig, ax = plt.subplots(1,1, figsize = (3, 6))
+        plt.semilogx(sigma[active], mesh.vectorCCz[active])
+        ax.set_ylim(-600, 0)
+        ax.set_xlim(1e-4, 1e-2)
+        ax.set_xlabel('Conductivity (S/m)', fontsize = 14)
+        ax.set_ylabel('Depth (m)', fontsize = 14)
+        ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5)
+
+
+    rxOffset=1e-3
+    rx = EM.TDEM.RxTDEM(np.array([[rxOffset, 0., 30]]), np.logspace(-5,-3, 31), 'bz')
+    src = EM.TDEM.SrcTDEM_VMD_MVP([rx], np.array([0., 0., 80]))
+    survey = EM.TDEM.SurveyTDEM([src])
+    prb = EM.TDEM.ProblemTDEM_b(mesh, mapping=mapping)
+
+    prb.Solver = SolverLU
+    prb.timeSteps = [(1e-06, 20),(1e-05, 20), (0.0001, 20)]
+    prb.pair(survey)
+    dtrue = survey.dpred(mtrue)
+
+
+    survey.dtrue = dtrue
+    std = 0.05
+    noise = std*abs(survey.dtrue)*np.random.randn(*survey.dtrue.shape)
+    survey.dobs = survey.dtrue+noise
+    survey.std = survey.dobs*0 + std
+    survey.Wd = 1/(abs(survey.dobs)*std)
+
+    if plotIt:
+        fig, ax = plt.subplots(1,1, figsize = (10, 6))
+        ax.loglog(rx.times, dtrue, 'b.-')
+        ax.loglog(rx.times, survey.dobs, 'r.-')
+        ax.legend(('Noisefree', '$d^{obs}$'), fontsize = 16)
+        ax.set_xlabel('Time (s)', fontsize = 14)
+        ax.set_ylabel('$B_z$ (T)', fontsize = 16)
+        ax.set_xlabel('Time (s)', fontsize = 14)
+        ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5)
+
+    dmisfit = DataMisfit.l2_DataMisfit(survey)
+    regMesh = Mesh.TensorMesh([mesh.hz[mapping.maps[-1].indActive]])
+    reg = Regularization.Tikhonov(regMesh)
+    opt = Optimization.InexactGaussNewton(maxIter = 5)
+    invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt)
+    # Create an inversion object
+    beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=2)
+    betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0)
+    inv = Inversion.BaseInversion(invProb, directiveList=[beta,betaest])
+    m0 = np.log(np.ones(mtrue.size)*sig_half)
+    reg.alpha_s = 1e-2
+    reg.alpha_x = 1.
+    prb.counter = opt.counter = Utils.Counter()
+    opt.LSshorten = 0.5
+    opt.remember('xc')
+
+    mopt = inv.run(m0)
+
+    if plotIt:
+        fig, ax = plt.subplots(1,1, figsize = (3, 6))
+        plt.semilogx(sigma[active], mesh.vectorCCz[active])
+        plt.semilogx(np.exp(mopt), mesh.vectorCCz[active])
+        ax.set_ylim(-600, 0)
+        ax.set_xlim(1e-4, 1e-2)
+        ax.set_xlabel('Conductivity (S/m)', fontsize = 14)
+        ax.set_ylabel('Depth (m)', fontsize = 14)
+        ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5)
+        plt.legend(['$\sigma_{true}$', '$\sigma_{pred}$'])
+        plt.show()
+
+
+if __name__ == '__main__':
+    run()

SimPEG/Examples/FLOW_Richards_1D_Celia1990.py

@@ -0,0 +1,86 @@
+from SimPEG import *
+from SimPEG.FLOW import Richards
+import matplotlib.pyplot as plt
+
+def run(plotIt=True):
+    """
+        FLOW: Richards: 1D: Celia1990
+        =============================
+
+        There are two different forms of Richards equation that differ
+        on how they deal with the non-linearity in the time-stepping term.
+
+        The most fundamental form, referred to as the
+        'mixed'-form of Richards Equation Celia1990_
+
+        .. math::
+
+            \\frac{\partial \\theta(\psi)}{\partial t} - \\nabla \cdot k(\psi) \\nabla \psi - \\frac{\partial k(\psi)}{\partial z} = 0
+            \quad \psi \in \Omega
+
+        where \\\\(\\\\theta\\\\) is water content, and \\\\(\\\\psi\\\\) is pressure head.
+        This formulation of Richards equation is called the
+        'mixed'-form because the equation is parameterized in \\\\(\\\\psi\\\\)
+        but the time-stepping is in terms of \\\\(\\\\theta\\\\).
+
+        As noted in Celia1990_ the 'head'-based form of Richards
+        equation can be written in the continuous form as:
+
+        .. math::
+
+            \\frac{\partial \\theta}{\partial \psi}\\frac{\partial \psi}{\partial t} - \\nabla \cdot k(\psi) \\nabla \psi - \\frac{\partial k(\psi)}{\partial z} = 0 \quad \psi \in \Omega
+
+        However, it can be shown that this does not conserve mass in the discrete formulation.
+
+        Here we reproduce the results from Celia1990_ demonstrating the head-based formulation and the mixed-formulation.
+
+        .. _Celia1990: http://www.webpages.uidaho.edu/ch/papers/Celia.pdf
+    """
+    M = Mesh.TensorMesh([np.ones(40)])
+    M.setCellGradBC('dirichlet')
+    params = Richards.Empirical.HaverkampParams().celia1990
+    params['Ks'] = np.log(params['Ks'])
+    E = Richards.Empirical.Haverkamp(M, **params)
+
+    bc = np.array([-61.5,-20.7])
+    h = np.zeros(M.nC) + bc[0]
+
+
+    def getFields(timeStep,method):
+        timeSteps = np.ones(360/timeStep)*timeStep
+        prob = Richards.RichardsProblem(M, mapping=E, timeSteps=timeSteps,
+                                        boundaryConditions=bc, initialConditions=h,
+                                        doNewton=False, method=method)
+        return prob.fields(params['Ks'])
+
+    Hs_M10 = getFields(10., 'mixed')
+    Hs_M30 = getFields(30., 'mixed')
+    Hs_M120= getFields(120.,'mixed')
+    Hs_H10 = getFields(10., 'head')
+    Hs_H30 = getFields(30., 'head')
+    Hs_H120= getFields(120.,'head')
+
+    if not plotIt:return
+    plt.figure(figsize=(13,5))
+    plt.subplot(121)
+    plt.plot(40-M.gridCC, Hs_M10[-1],'b-')
+    plt.plot(40-M.gridCC, Hs_M30[-1],'r-')
+    plt.plot(40-M.gridCC, Hs_M120[-1],'k-')
+    plt.ylim([-70,-10])
+    plt.title('Mixed Method')
+    plt.xlabel('Depth, cm')
+    plt.ylabel('Pressure Head, cm')
+    plt.legend(('$\Delta t$ = 10 sec','$\Delta t$ = 30 sec','$\Delta t$ = 120 sec'))
+    plt.subplot(122)
+    plt.plot(40-M.gridCC, Hs_H10[-1],'b-')
+    plt.plot(40-M.gridCC, Hs_H30[-1],'r-')
+    plt.plot(40-M.gridCC, Hs_H120[-1],'k-')
+    plt.ylim([-70,-10])
+    plt.title('Head-Based Method')
+    plt.xlabel('Depth, cm')
+    plt.ylabel('Pressure Head, cm')
+    plt.legend(('$\Delta t$ = 10 sec','$\Delta t$ = 30 sec','$\Delta t$ = 120 sec'))
+    plt.show()
+
+if __name__ == '__main__':
+    run()

SimPEG/Examples/Forward_BasicDirectCurrent.py

@@ -0,0 +1,76 @@
+from SimPEG import Mesh, Utils, np, SolverLU
+import matplotlib.pyplot as plt
+import matplotlib
+from matplotlib.mlab import griddata
+
+## 2D DC forward modeling example with Tensor and Curvilinear Meshes
+
+def run(plotIt=True):
+    # Step1: Generate Tensor and Curvilinear Mesh
+    sz = [40,40]
+    # Tensor Mesh
+    tM = Mesh.TensorMesh(sz)
+    # Curvilinear Mesh
+    rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz,'rotate'))
+    # Step2: Direct Current (DC) operator
+    def DCfun(mesh, pts):
+        D = mesh.faceDiv
+        G = D.T
+        sigma = 1e-2*np.ones(mesh.nC)
+        Msigi = mesh.getFaceInnerProduct(1./sigma)
+        MsigI = Utils.sdInv(Msigi)
+        A = D*MsigI*G
+        A[-1,-1] /= mesh.vol[-1] # Remove null space
+        rhs = np.zeros(mesh.nC)
+        txind = Utils.meshutils.closestPoints(mesh, pts)
+        rhs[txind] = np.r_[1,-1]
+        return A, rhs
+
+    pts = np.vstack((np.r_[0.25, 0.5], np.r_[0.75, 0.5]))
+
+    #Step3: Solve DC problem (LU solver)
+    AtM, rhstM = DCfun(tM, pts)
+    AinvtM = SolverLU(AtM)
+    phitM = AinvtM*rhstM
+
+    ArM, rhsrM = DCfun(rM, pts)
+    AinvrM = SolverLU(ArM)
+    phirM = AinvrM*rhsrM
+
+    if not plotIt: return
+
+    #Step4: Making Figure
+    fig, axes = plt.subplots(1,2,figsize=(12*1.2,4*1.2))
+    label = ["(a)", "(b)"]
+    opts = {}
+    vmin, vmax = phitM.min(), phitM.max()
+    dat = tM.plotImage(phitM, ax=axes[0], clim=(vmin, vmax), grid=True)
+
+    #TODO: At the moment Curvilinear Mesh do not have plotimage
+
+    Xi = tM.gridCC[:,0].reshape(sz[0], sz[1], order='F')
+    Yi = tM.gridCC[:,1].reshape(sz[0], sz[1], order='F')
+    PHIrM = griddata(rM.gridCC[:,0], rM.gridCC[:,1], phirM, Xi, Yi, interp='linear')
+    axes[1].contourf(Xi, Yi, PHIrM, 100, vmin=vmin, vmax=vmax)
+
+    cb = plt.colorbar(dat[0], ax=axes[0]); cb.set_label("Voltage (V)")
+    cb = plt.colorbar(dat[0], ax=axes[1]); cb.set_label("Voltage (V)")
+
+    tM.plotGrid(ax=axes[0], **opts)
+    axes[0].set_title('TensorMesh')
+    rM.plotGrid(ax=axes[1], **opts)
+    axes[1].set_title('CurvilinearMesh')
+    for i in range(2):
+        axes[i].set_xlim(0.025, 0.975)
+        axes[i].set_ylim(0.025, 0.975)
+        axes[i].text(0., 1.0, label[i], fontsize=20)
+        if i==0:
+            axes[i].set_ylabel("y")
+        else:
+            axes[i].set_ylabel(" ")
+        axes[i].set_xlabel("x")
+    plt.show()
+
+
+if __name__ == '__main__':
+    run()

SimPEG/Examples/Inversion_Linear.py

@@ -1,29 +1,39 @@
 from SimPEG import *
 
-class LinearSurvey(Survey.BaseSurvey):
-    def projectFields(self, u):
-        return u
 
-class LinearProblem(Problem.BaseProblem):
-    """docstring for LinearProblem"""
+def run(N=100, plotIt=True):
+    """
+        Inversion: Linear Problem
+        =========================
 
-    surveyPair = LinearSurvey
+        Here we go over the basics of creating a linear problem and inversion.
 
-    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)
+    class LinearSurvey(Survey.BaseSurvey):
+        def projectFields(self, u):
+            return u
 
-    def Jvec(self, m, v, u=None):
-        return self.G.dot(v)
+    class LinearProblem(Problem.BaseProblem):
 
-    def Jtvec(self, m, v, u=None):
-        return self.G.T.dot(v)
+        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)
 
 
-def run(N, plotIt=True):
+    np.random.seed(1)
+
     mesh = Mesh.TensorMesh([N])
 
     nk = 20
@@ -52,7 +62,7 @@ def run(N, plotIt=True):
 
     reg = Regularization.Tikhonov(mesh)
     dmis = DataMisfit.l2_DataMisfit(survey)
-    opt = Optimization.InexactGaussNewton(maxIter=20)
+    opt = Optimization.InexactGaussNewton(maxIter=35)
     invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
     beta = Directives.BetaSchedule()
     betaest = Directives.BetaEstimate_ByEig()
@@ -63,16 +73,18 @@ def run(N, plotIt=True):
 
     if plotIt:
         import matplotlib.pyplot as plt
-        plt.figure(1)
-        for i in range(prob.G.shape[0]):
-            plt.plot(prob.G[i,:])
 
-        plt.figure(2)
-        plt.plot(M.vectorCCx, survey.mtrue, 'b-')
-        plt.plot(M.vectorCCx, mrec, 'r-')
+        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(M.vectorCCx, survey.mtrue, 'b-')
+        axes[1].plot(M.vectorCCx, mrec, 'r-')
+        axes[1].legend(('True Model', 'Recovered Model'))
         plt.show()
 
     return prob, survey, mesh, mrec
 
 if __name__ == '__main__':
-    run(100)
+    run()

SimPEG/Examples/Mesh_Basic_PlotImage.py

@@ -0,0 +1,46 @@
+from SimPEG import *
+
+def run(plotIt=True):
+    """
+        Mesh: Basic: PlotImage
+        ======================
+
+        You can use M.PlotImage to plot images on all of the Meshes.
+
+
+    """
+    M = Mesh.TensorMesh([32,32])
+    v = Utils.ModelBuilder.randomModel(M.vnC, seed=789)
+    v = Utils.mkvc(v)
+
+    O = Mesh.TreeMesh([32,32])
+    O.refine(1)
+    def function(cell):
+        if (cell.center[0] < 0.75 and cell.center[0] > 0.25 and
+            cell.center[1] < 0.75 and cell.center[1] > 0.25):return 5
+        if (cell.center[0] < 0.9 and cell.center[0] > 0.1 and
+            cell.center[1] < 0.9 and cell.center[1] > 0.1):return 4
+        return 3
+    O.refine(function)
+
+    P = M.getInterpolationMat(O.gridCC, 'CC')
+
+    ov = P * v
+
+    if plotIt:
+        import matplotlib.pyplot as plt
+
+        fig, axes = plt.subplots(1,2,figsize=(10,5))
+
+        out = M.plotImage(v, grid=True, ax=axes[0])
+        cb = plt.colorbar(out[0], ax=axes[0]); cb.set_label("Random Field")
+        axes[0].set_title('TensorMesh')
+
+        out = O.plotImage(ov, grid=True, ax=axes[1], clim=[0,1])
+        cb = plt.colorbar(out[0], ax=axes[1]); cb.set_label("Random Field")
+        axes[1].set_title('TreeMesh')
+
+        plt.show()
+
+if __name__ == '__main__':
+    run()

SimPEG/Examples/Mesh_Basic_Types.py

@@ -0,0 +1,30 @@
+from SimPEG import *
+
+def run(plotIt=True):
+    """
+        Mesh: Basic: Types
+        ==================
+
+        Here we show SimPEG used to create three different types of meshes.
+
+    """
+    sz = [16,16]
+    tM = Mesh.TensorMesh(sz)
+    qM = Mesh.TreeMesh(sz)
+    qM.refine(lambda cell: 4 if np.sqrt(((np.r_[cell.center]-0.5)**2).sum()) < 0.4 else 3)
+    rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz,'rotate'))
+
+    if plotIt:
+        import matplotlib.pyplot as plt
+        fig, axes = plt.subplots(1,3,figsize=(14,5))
+        opts = {}
+        tM.plotGrid(ax=axes[0], **opts)
+        axes[0].set_title('TensorMesh')
+        qM.plotGrid(ax=axes[1], **opts)
+        axes[1].set_title('TreeMesh')
+        rM.plotGrid(ax=axes[2], **opts)
+        axes[2].set_title('CurvilinearMesh')
+        plt.show()
+
+if __name__ == '__main__':
+    run()

SimPEG/Examples/Mesh_Operators_CahnHilliard.py

@@ -0,0 +1,105 @@
+from SimPEG import *
+
+def run(plotIt=True, n=60):
+    """
+        Mesh: Operators: Cahn Hilliard
+        ==============================
+
+        This example is based on the example in the FiPy_ library.
+        Please see their documentation for more information about the Cahn-Hilliard equation.
+
+        The "Cahn-Hilliard" equation separates a field \\\\( \\\\phi \\\\) into 0 and 1 with smooth transitions.
+
+        .. math::
+
+            \\frac{\partial \phi}{\partial t} = \\nabla \cdot D \\nabla \left( \\frac{\partial f}{\partial \phi} - \epsilon^2 \\nabla^2 \phi \\right)
+
+        Where \\\\( f \\\\) is the energy function \\\\( f = ( a^2 / 2 )\\\\phi^2(1 - \\\\phi)^2 \\\\)
+        which drives \\\\( \\\\phi \\\\) towards either 0 or 1, this competes with the term
+        \\\\(\\\\epsilon^2 \\\\nabla^2 \\\\phi \\\\) which is a diffusion term that creates smooth changes in \\\\( \\\\phi \\\\).
+        The equation can be factored:
+
+        .. math::
+
+            \\frac{\partial \phi}{\partial t} = \\nabla \cdot D \\nabla \psi \\\\
+            \psi = \\frac{\partial^2 f}{\partial \phi^2} (\phi - \phi^{\\text{old}}) + \\frac{\partial f}{\partial \phi} - \epsilon^2 \\nabla^2 \phi
+
+        Here we will need the derivatives of \\\\( f \\\\):
+
+        .. math::
+
+            \\frac{\partial f}{\partial \phi} = (a^2/2)2\phi(1-\phi)(1-2\phi)
+            \\frac{\partial^2 f}{\partial \phi^2} = (a^2/2)2[1-6\phi(1-\phi)]
+
+        The implementation below uses backwards Euler in time with an exponentially increasing time step.
+        The initial \\\\( \\\\phi \\\\) is a normally distributed field with a standard deviation of 0.1 and mean of 0.5.
+        The grid is 60x60 and takes a few seconds to solve ~130 times. The results are seen below, and you can see the
+        field separating as the time increases.
+
+        .. _FiPy: http://www.ctcms.nist.gov/fipy/examples/cahnHilliard/generated/examples.cahnHilliard.mesh2DCoupled.html
+
+    """
+
+    np.random.seed(5)
+
+    # Here we are going to rearrange the equations:
+
+    # (phi_ - phi)/dt = A*(d2fdphi2*(phi_ - phi) + dfdphi - L*phi_)
+    # (phi_ - phi)/dt = A*(d2fdphi2*phi_ - d2fdphi2*phi + dfdphi - L*phi_)
+    # (phi_ - phi)/dt = A*d2fdphi2*phi_ + A*( - d2fdphi2*phi + dfdphi - L*phi_)
+    # phi_ - phi = dt*A*d2fdphi2*phi_ + dt*A*(- d2fdphi2*phi + dfdphi - L*phi_)
+    # phi_ - dt*A*d2fdphi2 * phi_ =  dt*A*(- d2fdphi2*phi + dfdphi - L*phi_) + phi
+    # (I - dt*A*d2fdphi2) * phi_ =  dt*A*(- d2fdphi2*phi + dfdphi - L*phi_) + phi
+    # (I - dt*A*d2fdphi2) * phi_ =  dt*A*dfdphi - dt*A*d2fdphi2*phi - dt*A*L*phi_ + phi
+    # (dt*A*d2fdphi2 - I) * phi_ =  dt*A*d2fdphi2*phi + dt*A*L*phi_ - phi - dt*A*dfdphi
+    # (dt*A*d2fdphi2 - I - dt*A*L) * phi_ =  (dt*A*d2fdphi2 - I)*phi - dt*A*dfdphi
+
+    h = [(0.25,n)]
+    M = Mesh.TensorMesh([h,h])
+
+    # Constants
+    D = a = epsilon = 1.
+    I = Utils.speye(M.nC)
+
+    # Operators
+    A = D * M.faceDiv * M.cellGrad
+    L = epsilon**2 * M.faceDiv * M.cellGrad
+
+    duration = 75
+    elapsed = 0.
+    dexp = -5
+    phi = np.random.normal(loc=0.5,scale=0.01,size=M.nC)
+    ii, jj = 0, 0
+    PHIS = []
+    capture = np.logspace(-1,np.log10(duration),8)
+    while elapsed < duration:
+        dt = min(100, np.exp(dexp))
+        elapsed += dt
+        dexp += 0.05
+
+        dfdphi   = a**2 * 2 * phi * (1 - phi) * (1 - 2 * phi)
+        d2fdphi2 = Utils.sdiag(a**2 * 2 * (1 - 6 * phi * (1 - phi)))
+
+        MAT = (dt*A*d2fdphi2 - I - dt*A*L)
+        rhs = (dt*A*d2fdphi2 - I)*phi - dt*A*dfdphi
+        phi = Solver(MAT)*rhs
+
+        if elapsed > capture[jj]:
+            PHIS += [(elapsed, phi.copy())]
+            jj += 1
+        if ii % 10 == 0: print ii, elapsed
+        ii += 1
+
+    if plotIt:
+        import matplotlib.pyplot as plt
+        fig, axes = plt.subplots(2,4,figsize=(14,6))
+        axes = np.array(axes).flatten().tolist()
+        for ii, ax in zip(np.linspace(0,len(PHIS)-1,len(axes)),axes):
+            ii = int(ii)
+            out = M.plotImage(PHIS[ii][1],ax=ax)
+            ax.axis('off')
+            ax.set_title('Elapsed Time: %4.1f'%PHIS[ii][0])
+        plt.show()
+
+if __name__ == '__main__':
+    run()

SimPEG/Examples/Mesh_QuadTree_Creation.py

@@ -0,0 +1,28 @@
+from SimPEG import *
+
+def run(plotIt=True):
+    """
+        Mesh: QuadTree: Creation
+        ========================
+
+        You can give the refine method a function, which is evaluated on every cell
+        of the TreeMesh.
+
+        Occasionally it is useful to initially refine to a constant level
+        (e.g. 3 in this 32x32 mesh). This means the function is first evaluated
+        on an 8x8 mesh (2^3).
+
+    """
+    M = Mesh.TreeMesh([32,32])
+    M.refine(3)
+    def function(cell):
+        xyz = cell.center
+        for i in range(3):
+            if np.abs(np.sin(xyz[0]*np.pi*2)*0.5 + 0.5 - xyz[1]) < 0.2*i:
+                return 6-i
+        return 0
+    M.refine(function);
+    if plotIt: M.plotGrid(showIt=True)
+
+if __name__ == '__main__':
+    run()

SimPEG/Examples/Mesh_QuadTree_FaceDiv.py

@@ -0,0 +1,49 @@
+from SimPEG import *
+
+def run(plotIt=True, n=60):
+    """
+        Mesh: QuadTree: FaceDiv
+        =======================
+
+
+
+    """
+
+
+    M = Mesh.TreeMesh([[(1,16)],[(1,16)]], levels=4)
+    M._refineCell([0,0,0])
+    M._refineCell([0,0,1])
+    M._refineCell([4,4,2])
+    M.__dirty__ = True
+    M.number()
+
+
+    if plotIt:
+        import matplotlib.pyplot as plt
+        fig, axes = plt.subplots(2,1,figsize=(10,10))
+
+        M.plotGrid(cells=True, nodes=False, ax=axes[0])
+        axes[0].axis('off')
+        axes[0].set_title('Simple QuadTree Mesh')
+        axes[0].set_xlim([-1,17])
+        axes[0].set_ylim([-1,17])
+
+        for ii, loc in zip(range(M.nC),M.gridCC):
+            axes[0].text(loc[0]+0.2,loc[1],'%d'%ii, color='r')
+
+        axes[0].plot(M.gridFx[:,0],M.gridFx[:,1], 'g>')
+        for ii, loc in zip(range(M.nFx),M.gridFx):
+            axes[0].text(loc[0]+0.2,loc[1],'%d'%ii, color='g')
+
+        axes[0].plot(M.gridFy[:,0],M.gridFy[:,1], 'm^')
+        for ii, loc in zip(range(M.nFy),M.gridFy):
+            axes[0].text(loc[0]+0.2,loc[1]+0.2,'%d'%(ii+M.nFx), color='m')
+
+        axes[1].spy(M.faceDiv)
+        axes[1].set_title('Face Divergence')
+        axes[1].set_ylabel('Cell Number')
+        axes[1].set_xlabel('Face Number')
+        plt.show()
+
+if __name__ == '__main__':
+    run()

SimPEG/Examples/Mesh_QuadTree_HangingNodes.py

@@ -0,0 +1,32 @@
+from SimPEG import *
+
+def run(plotIt=True):
+    """
+        Mesh: QuadTree: Hanging Nodes
+        =============================
+
+        You can give the refine method a function, which is evaluated on every cell
+        of the TreeMesh.
+
+        Occasionally it is useful to initially refine to a constant level
+        (e.g. 3 in this 32x32 mesh). This means the function is first evaluated
+        on an 8x8 mesh (2^3).
+
+    """
+    M = Mesh.TreeMesh([8,8])
+    def function(cell):
+        xyz = cell.center
+        dist = ((xyz - [0.25,0.25])**2).sum()**0.5
+        if dist < 0.25:
+            return 3
+        return 2
+    M.refine(function);
+    M.number()
+    if plotIt:
+        import matplotlib.pyplot as plt
+        M.plotGrid(nodes=True, cells=True, facesX=True)
+        plt.legend(('Grid', 'Cell Centers', 'Nodes', 'Hanging Nodes', 'X faces', 'Hanging X faces'))
+        plt.show()
+
+if __name__ == '__main__':
+    run()

SimPEG/Examples/Mesh_Tensor_Creation.py

@@ -0,0 +1,35 @@
+from SimPEG import *
+
+def run(plotIt=True):
+    """
+
+        Mesh: Tensor: Creation
+        ======================
+
+        For tensor meshes, there are some functions that can come
+        in handy. For example, creating mesh tensors can be a bit time
+        consuming, these can be created speedily by just giving numbers
+        and sizes of padding. See the example below, that follows this
+        notation::
+
+            h1 = (
+                   (cellSize, numPad, [, increaseFactor]),
+                   (cellSize, numCore),
+                   (cellSize, numPad, [, increaseFactor])
+                 )
+
+        .. note::
+
+            You can center your mesh by passing a 'C' for the x0[i] position.
+            A 'N' will make the entire mesh negative, and a '0' (or a 0) will
+            make the mesh start at zero.
+
+    """
+    h1 = [(10, 5, -1.3), (5, 20), (10, 3, 1.3)]
+    M = Mesh.TensorMesh([h1, h1], x0='CN')
+    if plotIt:
+        M.plotGrid(showIt=True)
+
+if __name__ == '__main__':
+    run()
+

SimPEG/Examples/__init__.py

@@ -1 +1,103 @@
-import Linear
+# Run this file to add imports.
+
+##### AUTOIMPORTS #####
+import EM_FDEM_1D_Inversion
+import FLOW_Richards_1D_Celia1990
+import Forward_BasicDirectCurrent
+import Inversion_Linear
+import Mesh_Basic_PlotImage
+import Mesh_Basic_Types
+import Mesh_Operators_CahnHilliard
+import Mesh_QuadTree_Creation
+import Mesh_QuadTree_FaceDiv
+import Mesh_QuadTree_HangingNodes
+import Mesh_Tensor_Creation
+
+__examples__ = ["EM_FDEM_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"]
+
+##### AUTOIMPORTS #####
+
+if __name__ == '__main__':
+    """
+
+        Run the following to create the examples documentation and add to the imports at the top.
+
+    """
+
+    import shutil, os
+    from SimPEG import Examples
+
+    # Create the examples dir in the docs folder.
+    docExamplesDir = os.path.sep.join(os.path.realpath(__file__).split(os.path.sep)[:-3] + ['docs', 'examples'])
+    shutil.rmtree(docExamplesDir)
+    os.makedirs(docExamplesDir)
+
+    # Get all the python examples in this folder
+    thispath = os.path.sep.join(__file__.split(os.path.sep)[:-1])
+    exfiles  = [f[:-3] for f in os.listdir(thispath) if os.path.isfile(os.path.join(thispath, f)) and f.endswith('.py') and not f.startswith('_')]
+
+    # Add the imports to the top in the AUTOIMPORTS section
+    f = file(__file__, 'r')
+    inimports = False
+    out = ''
+    for line in f:
+        if not inimports:
+            out += line
+
+        if line == "##### AUTOIMPORTS #####\n":
+            inimports = not inimports
+            if inimports:
+                out += '\n'.join(["import %s"%_ for _ in exfiles])
+                out += '\n\n__examples__ = ["' + '", "'.join(exfiles)+ '"]\n'
+                out += '\n##### AUTOIMPORTS #####\n'
+    f.close()
+
+    f = file(__file__, 'w')
+    f.write(out)
+    f.close()
+
+
+    def _makeExample(filePath, runFunction):
+        """Makes the example given a path of the file and the run function."""
+        filePath = os.path.realpath(filePath)
+        name = filePath.split(os.path.sep)[-1].rstrip('.pyc').rstrip('.py')
+
+        docstr = runFunction.__doc__
+        if docstr is None:
+            doc = '%s\n%s'%(name.replace('_',' '),'='*len(name))
+        else:
+            doc = '\n'.join([_[8:].rstrip() for _ in docstr.split('\n')])
+
+        out = """.. _examples_%s:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+%s
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.%s.run()
+
+.. literalinclude:: ../../SimPEG/Examples/%s.py
+    :language: python
+    :linenos:
+"""%(name,doc,name,name)
+
+        rst = os.path.sep.join((filePath.split(os.path.sep)[:-3] + ['docs', 'examples', name + '.rst']))
+
+        print 'Creating: %s.rst'%name
+        f = open(rst, 'w')
+        f.write(out)
+        f.close()
+
+    for ex in dir(Examples):
+        if ex.startswith('_'): continue
+        E = getattr(Examples,ex)
+        _makeExample(E.__file__, E.run)

SimPEG/FLOW/Richards/Empirical.py

@@ -0,0 +1,578 @@
+from SimPEG import Mesh, Maps, Utils, np
+
+
+class NonLinearMap(object):
+    """
+    SimPEG NonLinearMap
+
+    """
+
+    __metaclass__ = Utils.SimPEGMetaClass
+
+    counter = None   #: A SimPEG.Utils.Counter object
+    mesh = None      #: A SimPEG Mesh
+
+    def __init__(self, mesh):
+        self.mesh = mesh
+
+    def _transform(self, u, m):
+        """
+            :param numpy.array u: fields
+            :param numpy.array m: model
+            :rtype: numpy.array
+            :return: transformed model
+
+            The *transform* changes the model into the physical property.
+
+        """
+        return m
+
+    def derivU(self, u, m):
+        """
+            :param numpy.array u: fields
+            :param numpy.array m: model
+            :rtype: scipy.csr_matrix
+            :return: derivative of transformed model
+
+            The *transform* changes the model into the physical property.
+            The *transformDerivU* provides the derivative of the *transform* with respect to the fields.
+        """
+        raise NotImplementedError('The transformDerivU is not implemented.')
+
+
+    def derivM(self, u, m):
+        """
+            :param numpy.array u: fields
+            :param numpy.array m: model
+            :rtype: scipy.csr_matrix
+            :return: derivative of transformed model
+
+            The *transform* changes the model into the physical property.
+            The *transformDerivU* provides the derivative of the *transform* with respect to the model.
+        """
+        raise NotImplementedError('The transformDerivM is not implemented.')
+
+    @property
+    def nP(self):
+        """Number of parameters in the model."""
+        return self.mesh.nC
+
+    def example(self):
+        raise NotImplementedError('The example is not implemented.')
+
+    def test(self, m=None):
+        raise NotImplementedError('The test is not implemented.')
+
+
+class RichardsMap(object):
+    """docstring for RichardsMap"""
+
+    mesh       = None  #: SimPEG mesh
+
+    @property
+    def thetaModel(self):
+        """Model for moisture content"""
+        return self._thetaModel
+
+    @property
+    def kModel(self):
+        """Model for hydraulic conductivity"""
+        return self._kModel
+
+    def __init__(self, mesh, thetaModel, kModel):
+        self.mesh = mesh
+        assert isinstance(thetaModel, NonLinearMap)
+        assert isinstance(kModel, NonLinearMap)
+
+        self._thetaModel = thetaModel
+        self._kModel = kModel
+
+    def theta(self, u, m):
+        return self.thetaModel.transform(u, m)
+
+    def thetaDerivM(self, u, m):
+        return self.thetaModel.transformDerivM(u, m)
+
+    def thetaDerivU(self, u, m):
+        return self.thetaModel.transformDerivU(u, m)
+
+    def k(self, u, m):
+        return self.kModel.transform(u, m)
+
+    def kDerivM(self, u, m):
+        return self.kModel.transformDerivM(u, m)
+
+    def kDerivU(self, u, m):
+        return self.kModel.transformDerivU(u, m)
+
+    def plot(self, m):
+        import matplotlib.pyplot as plt
+
+        m = m[0]
+        h = np.linspace(-100, 20, 1000)
+        ax = plt.subplot(121)
+        ax.plot(self.theta(h, m), h)
+        ax = plt.subplot(122)
+        ax.semilogx(self.k(h, m), h)
+
+    def _assertMatchesPair(self, pair):
+        assert isinstance(self, pair), "Mapping object must be an instance of a %s class."%(pair.__name__)
+
+
+
+def _ModelProperty(name, models, doc=None, default=None):
+
+    def fget(self):
+        model = models[0]
+        if getattr(self, model, None) is not None:
+            MOD = getattr(self, model)
+            return getattr(MOD, name, default)
+        return default
+
+    def fset(self, value):
+        for model in models:
+            if getattr(self, model, None) is not None:
+                MOD = getattr(self, model)
+                setattr(MOD, name, value)
+
+    return property(fget, fset=fset, doc=doc)
+
+
+class HaverkampParams(object):
+    """Holds some default parameterizations for the Haverkamp model."""
+    def __init__(self): pass
+    @property
+    def celia1990(self):
+        """
+            Parameters used in:
+
+                Celia, Michael A., Efthimios T. Bouloutas, and Rebecca L. Zarba.
+                "A general mass-conservative numerical solution for the unsaturated flow equation."
+                Water Resources Research 26.7 (1990): 1483-1496.
+
+        """
+        return {'alpha':1.611e+06, 'beta':3.96,
+                'theta_r':0.075, 'theta_s':0.287,
+                'Ks':9.44e-03, 'A':1.175e+06,
+                'gamma':4.74}
+
+
+class _haverkamp_theta(NonLinearMap):
+
+    theta_s = 0.430
+    theta_r = 0.078
+    alpha   = 0.036
+    beta    = 3.960
+
+    def __init__(self, mesh, **kwargs):
+        NonLinearMap.__init__(self, mesh)
+        Utils.setKwargs(self, **kwargs)
+
+    def setModel(self, m):
+        self._currentModel = m
+
+    def transform(self, u, m):
+        self.setModel(m)
+        f = (self.alpha*(self.theta_s  -    self.theta_r  )/
+                        (self.alpha    + abs(u)**self.beta) + self.theta_r)
+        if Utils.isScalar(self.theta_s):
+            f[u >= 0] = self.theta_s
+        else:
+            f[u >= 0] = self.theta_s[u >= 0]
+        return f
+
+    def transformDerivM(self, u, m):
+        self.setModel(m)
+
+    def transformDerivU(self, u, m):
+        self.setModel(m)
+        g = (self.alpha*((self.theta_s - self.theta_r)/
+             (self.alpha + abs(u)**self.beta)**2)
+             *(-self.beta*abs(u)**(self.beta-1)*np.sign(u)))
+        g[u >= 0] = 0
+        g = Utils.sdiag(g)
+        return g
+
+
+class _haverkamp_k(NonLinearMap):
+
+    A       = 1.175e+06
+    gamma   = 4.74
+    Ks      = np.log(24.96)
+
+    def __init__(self, mesh, **kwargs):
+        NonLinearMap.__init__(self, mesh)
+        Utils.setKwargs(self, **kwargs)
+
+    def setModel(self, m):
+        self._currentModel = m
+        #TODO: Fix me!
+        self.Ks = m
+
+    def transform(self, u, m):
+        self.setModel(m)
+        f = np.exp(self.Ks)*self.A/(self.A+abs(u)**self.gamma)
+        if Utils.isScalar(self.Ks):
+            f[u >= 0] = np.exp(self.Ks)
+        else:
+            f[u >= 0] = np.exp(self.Ks[u >= 0])
+        return f
+
+    def transformDerivM(self, u, m):
+        self.setModel(m)
+        #A
+        # dA = np.exp(self.Ks)/(self.A+abs(u)**self.gamma) - np.exp(self.Ks)*self.A/(self.A+abs(u)**self.gamma)**2
+        #gamma
+        # dgamma = -(self.A*np.exp(self.Ks)*np.log(abs(u))*abs(u)**self.gamma)/(self.A + abs(u)**self.gamma)**2
+
+        # This assumes that the the model is Ks
+        return Utils.sdiag(self.transform(u, m))
+
+    def transformDerivU(self, u, m):
+        self.setModel(m)
+        g = -(np.exp(self.Ks)*self.A*self.gamma*abs(u)**(self.gamma-1)*np.sign(u))/((self.A+abs(u)**self.gamma)**2)
+        g[u >= 0] = 0
+        g = Utils.sdiag(g)
+        return g
+
+class Haverkamp(RichardsMap):
+    """Haverkamp Model"""
+
+    alpha   = _ModelProperty('alpha',   ['thetaModel'], default=1.6110e+06)
+    beta    = _ModelProperty('beta',    ['thetaModel'], default=3.96)
+    theta_r = _ModelProperty('theta_r', ['thetaModel'], default=0.075)
+    theta_s = _ModelProperty('theta_s', ['thetaModel'], default=0.287)
+
+    Ks    = _ModelProperty('Ks',    ['kModel'], default=np.log(24.96))
+    A     = _ModelProperty('A',     ['kModel'], default=1.1750e+06)
+    gamma = _ModelProperty('gamma', ['kModel'], default=4.74)
+
+    def __init__(self, mesh, **kwargs):
+        RichardsMap.__init__(self, mesh,
+                               _haverkamp_theta(mesh),
+                               _haverkamp_k(mesh))
+        Utils.setKwargs(self, **kwargs)
+
+
+
+
+class _vangenuchten_theta(NonLinearMap):
+
+    theta_s = 0.430
+    theta_r = 0.078
+    alpha   = 0.036
+    n       = 1.560
+
+    def __init__(self, mesh, **kwargs):
+        NonLinearMap.__init__(self, mesh)
+        Utils.setKwargs(self, **kwargs)
+
+    def setModel(self, m):
+        self._currentModel = m
+
+    def transform(self, u, m):
+        self.setModel(m)
+        m = 1 - 1.0/self.n
+        f = ((  self.theta_s  -  self.theta_r  )/
+             ((1+abs(self.alpha*u)**self.n)**m)   +  self.theta_r)
+        if Utils.isScalar(self.theta_s):
+            f[u >= 0] = self.theta_s
+        else:
+            f[u >= 0] = self.theta_s[u >= 0]
+
+        return f
+
+    def transformDerivM(self, u, m):
+        self.setModel(m)
+
+    def transformDerivU(self, u, m):
+        g = -self.alpha*self.n*abs(self.alpha*u)**(self.n - 1)*np.sign(self.alpha*u)*(1./self.n - 1)*(self.theta_r - self.theta_s)*(abs(self.alpha*u)**self.n + 1)**(1./self.n - 2)
+        g[u >= 0] = 0
+        g = Utils.sdiag(g)
+        return g
+
+
+class _vangenuchten_k(NonLinearMap):
+
+    I       = 0.500
+    alpha   = 0.036
+    n       = 1.560
+    Ks      = np.log(24.96)
+
+    def __init__(self, mesh, **kwargs):
+        NonLinearMap.__init__(self, mesh)
+        Utils.setKwargs(self, **kwargs)
+
+    def setModel(self, m):
+        self._currentModel = m
+        #TODO: Fix me!
+        self.Ks = m
+
+    def transform(self, u, m):
+        self.setModel(m)
+
+        alpha = self.alpha
+        I = self.I
+        n = self.n
+        Ks = self.Ks
+        m = 1.0 - 1.0/n
+
+        theta_e = 1.0/((1.0+abs(alpha*u)**n)**m)
+        f = np.exp(Ks)*theta_e**I* ( ( 1.0 - ( 1.0 - theta_e**(1.0/m) )**m )**2 )
+        if Utils.isScalar(self.Ks):
+            f[u >= 0] = np.exp(self.Ks)
+        else:
+            f[u >= 0] = np.exp(self.Ks[u >= 0])
+        return f
+
+    def transformDerivM(self, u, m):
+        self.setModel(m)
+#         #alpha
+#         # dA = I*u*n*np.exp(Ks)*abs(alpha*u)**(n - 1)*np.sign(alpha*u)*(1.0/n - 1)*((abs(alpha*u)**n + 1)**(1.0/n - 1))**(I - 1)*((1 - 1.0/((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n) - 1)**2*(abs(alpha*u)**n + 1)**(1.0/n - 2) - (2*u*n*np.exp(Ks)*abs(alpha*u)**(n - 1)*np.sign(alpha*u)*(1.0/n - 1)*((abs(alpha*u)**n + 1)**(1.0/n - 1))**I*((1 - 1.0/((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n) - 1)*(abs(alpha*u)**n + 1)**(1.0/n - 2))/(((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1) + 1)*(1 - 1.0/((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1.0/n));
+#         #n
+#         # dn = 2*np.exp(Ks)*((np.log(1 - 1.0/((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))*(1 - 1.0/((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n))/n**2 + ((1.0/n - 1)*(((np.log(abs(alpha*u)**n + 1)*(abs(alpha*u)**n + 1)**(1.0/n - 1))/n**2 - abs(alpha*u)**n*np.log(abs(alpha*u))*(1.0/n - 1)*(abs(alpha*u)**n + 1)**(1.0/n - 2))/((1.0/n - 1)*((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1) + 1)) - np.log((abs(alpha*u)**n + 1)**(1.0/n - 1))/(n**2*(1.0/n - 1)**2*((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))))/(1 - 1.0/((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1.0/n))*((abs(alpha*u)**n + 1)**(1.0/n - 1))**I*((1 - 1.0/((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n) - 1) - I*np.exp(Ks)*((np.log(abs(alpha*u)**n + 1)*(abs(alpha*u)**n + 1)**(1.0/n - 1))/n**2 - abs(alpha*u)**n*np.log(abs(alpha*u))*(1.0/n - 1)*(abs(alpha*u)**n + 1)**(1.0/n - 2))*((abs(alpha*u)**n + 1)**(1.0/n - 1))**(I - 1)*((1 - 1.0/((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n) - 1)**2;
+#         #I
+#         # dI = np.exp(Ks)*np.log((abs(alpha*u)**n + 1)**(1.0/n - 1))*((abs(alpha*u)**n + 1)**(1.0/n - 1))**I*((1 - 1.0/((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n) - 1)**2;
+        return Utils.sdiag(self.transform(u, m)) # This assumes that the the model is Ks
+
+    def transformDerivU(self, u, m):
+        self.setModel(m)
+        alpha = self.alpha
+        I = self.I
+        n = self.n
+        Ks = self.Ks
+        m = 1.0 - 1.0/n
+
+        g = I*alpha*n*np.exp(Ks)*abs(alpha*u)**(n - 1.0)*np.sign(alpha*u)*(1.0/n - 1.0)*((abs(alpha*u)**n + 1)**(1.0/n - 1))**(I - 1)*((1 - 1.0/((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n) - 1)**2*(abs(alpha*u)**n + 1)**(1.0/n - 2) - (2*alpha*n*np.exp(Ks)*abs(alpha*u)**(n - 1)*np.sign(alpha*u)*(1.0/n - 1)*((abs(alpha*u)**n + 1)**(1.0/n - 1))**I*((1 - 1.0/((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1 - 1.0/n) - 1)*(abs(alpha*u)**n + 1)**(1.0/n - 2))/(((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1) + 1)*(1 - 1.0/((abs(alpha*u)**n + 1)**(1.0/n - 1))**(1.0/(1.0/n - 1)))**(1.0/n))
+        g[u >= 0] = 0
+        g = Utils.sdiag(g)
+        return g
+
+class VanGenuchten(RichardsMap):
+    """vanGenuchten Model"""
+
+    theta_r = _ModelProperty('theta_r', ['thetaModel'], default=0.075)
+    theta_s = _ModelProperty('theta_s', ['thetaModel'], default=0.287)
+
+    alpha   = _ModelProperty('alpha',   ['thetaModel', 'kModel'], default=0.036)
+    n       = _ModelProperty('n',       ['thetaModel', 'kModel'], default=1.560)
+
+    Ks    = _ModelProperty('Ks',    ['kModel'], default=np.log(24.96))
+    I     = _ModelProperty('I',     ['kModel'], default=0.500)
+
+    def __init__(self, mesh, **kwargs):
+        RichardsMap.__init__(self, mesh,
+                               _vangenuchten_theta(mesh),
+                               _vangenuchten_k(mesh))
+        Utils.setKwargs(self, **kwargs)
+
+
+class VanGenuchtenParams(object):
+    """
+        The RETC code for quantifying the hydraulic functions of unsaturated soils,
+        Van Genuchten, M Th, Leij, F J, Yates, S R
+
+        Table 3: Average values for selected soil water retention and hydraulic
+        conductivity parameters for 11 major soil textural groups
+        according to Rawls et al. [1982]
+
+    """
+    def __init__(self): pass
+    @property
+    def sand(self):
+        return {"theta_r": 0.020, "theta_s": 0.417, "alpha": 0.138*100., "n": 1.592, "Ks": 504.0/100./24./60./60.}
+    @property
+    def loamySand(self):
+        return {"theta_r": 0.035, "theta_s": 0.401, "alpha": 0.115*100., "n": 1.474, "Ks": 146.6/100./24./60./60.}
+    @property
+    def sandyLoam(self):
+        return {"theta_r": 0.041, "theta_s": 0.412, "alpha": 0.068*100., "n": 1.322, "Ks": 62.16/100./24./60./60.}
+    @property
+    def loam(self):
+        return {"theta_r": 0.027, "theta_s": 0.434, "alpha": 0.090*100., "n": 1.220, "Ks": 16.32/100./24./60./60.}
+    @property
+    def siltLoam(self):
+        return {"theta_r": 0.015, "theta_s": 0.486, "alpha": 0.048*100., "n": 1.211, "Ks": 31.68/100./24./60./60.}
+    @property
+    def sandyClayLoam(self):
+        return {"theta_r": 0.068, "theta_s": 0.330, "alpha": 0.036*100., "n": 1.250, "Ks": 10.32/100./24./60./60.}
+    @property
+    def clayLoam(self):
+        return {"theta_r": 0.075, "theta_s": 0.390, "alpha": 0.039*100., "n": 1.194, "Ks": 5.52/100./24./60./60.}
+    @property
+    def siltyClayLoam(self):
+        return {"theta_r": 0.040, "theta_s": 0.432, "alpha": 0.031*100., "n": 1.151, "Ks": 3.60/100./24./60./60.}
+    @property
+    def sandyClay(self):
+        return {"theta_r": 0.109, "theta_s": 0.321, "alpha": 0.034*100., "n": 1.168, "Ks": 2.88/100./24./60./60.}
+    @property
+    def siltyClay(self):
+        return {"theta_r": 0.056, "theta_s": 0.423, "alpha": 0.029*100., "n": 1.127, "Ks": 2.16/100./24./60./60.}
+    @property
+    def clay(self):
+        return {"theta_r": 0.090, "theta_s": 0.385, "alpha": 0.027*100., "n": 1.131, "Ks": 1.44/100./24./60./60.}
+
+
+    # From: INDIRECT METHODS FOR ESTIMATING THE HYDRAULIC PROPERTIES OF UNSATURATED SOILS
+    # @property
+    # def siltLoamGE3(self):
+    #     """Soil Index: 3310"""
+    #     return {"theta_r": 0.139, "theta_s": 0.394, "alpha": 0.00414, "n": 2.15}
+    # @property
+    # def yoloLightClayK_WC(self):
+    #     """Soil Index: None"""
+    #     return {"theta_r": 0.205, "theta_s": 0.499, "alpha": 0.02793, "n": 1.71}
+    # @property
+    # def yoloLightClayK_H(self):
+    #     """Soil Index: None"""
+    #     return {"theta_r": 0.205, "theta_s": 0.499, "alpha": 0.02793, "n": 1.71}
+    # @property
+    # def hygieneSandstone(self):
+    #     """Soil Index: 4130"""
+    #     return {"theta_r": 0.000, "theta_s": 0.256, "alpha": 0.00562, "n": 3.27}
+    # @property
+    # def lambcrgClay(self):
+    #     """Soil Index: 1003"""
+    #     return {"theta_r": 0.000, "theta_s": 0.502, "alpha": 0.140, "n": 1.93}
+    # @property
+    # def beitNetofaClaySoil(self):
+    #     """Soil Index: 1006"""
+    #     return {"theta_r": 0.000, "theta_s": 0.447, "alpha": 0.00156, "n": 1.17}
+    # @property
+    # def shiohotSiltyClay(self):
+    #     """Soil Index: 1101"""
+    #     return {"theta_r": 0.000, "theta_s": 0.456, "alpha": 183, "n":1.17}
+    # @property
+    # def siltColumbia(self):
+    #     """Soil Index: 2001"""
+    #     return {"theta_r": 0.146, "theta_s": 0.397,  "alpha": 0.0145, "n": 1.85}
+    # @property
+    # def siltMontCenis(self):
+    #     """Soil Index: 2002"""
+    #     return {"theta_r": 0.000, "theta_s": 0.425, "alpha": 0.0103, "n": 1.34}
+    # @property
+    # def slateDust(self):
+    #     """Soil Index: 2004"""
+    #     return {"theta_r": 0.000, "theta_s": 0.498, "alpha": 0.00981, "n": 6.75}
+    # @property
+    # def weldSiltyClayLoam(self):
+    #     """Soil Index: 3001"""
+    #     return {"theta_r": 0.159, "theta_s": 0.496, "alpha": 0.0136, "n": 5.45}
+    # @property
+    # def rideauClayLoam_Wetting(self):
+    #     """Soil Index: 3101a"""
+    #     return {"theta_r": 0.279, "theta_s": 0.419, "alpha": 0.0661, "n": 1.89}
+    # @property
+    # def rideauClayLoam_Drying(self):
+    #     """Soil Index: 3101b"""
+    #     return {"theta_r": 0.290, "theta_s": 0.419, "alpha": 0.0177, "n": 3.18}
+    # @property
+    # def caribouSiltLoam_Drying(self):
+    #     """Soil Index: 3301a"""
+    #     return {"theta_r": 0.000, "theta_s": 0.451, "alpha": 0.00845, "n": 1.29}
+    # @property
+    # def caribouSiltLoam_Wetting(self):
+    #     """Soil Index: 3301b"""
+    #     return {"theta_r": 0.000, "theta_s": 0.450, "alpha": 0.140, "n": 1.09}
+    # @property
+    # def grenvilleSiltLoam_Wetting(self):
+    #     """Soil Index: 3302a"""
+    #     return {"theta_r": 0.013, "theta_s": 0523,  "alpha": 0.0630, "n": 1.24}
+    # @property
+    # def grenvilleSiltLoam_Drying(self):
+    #     """Soil Index: 3302c"""
+    #     return {"theta_r": 0.000, "theta_s": 0.488, "alpha": 0.0112, "n": 1.23}
+    # @property
+    # def touchetSiltLoam(self):
+    #     """Soil Index: 3304"""
+    #     return {"theta_r": 0.183, "theta_s": 0.498, "alpha": 0.0104, "n": 5.78}
+    # @property
+    # def gilatLoam(self):
+    #     """Soil Index: 3402a"""
+    #     return {"theta_r": 0.000, "theta_s": 0.454, "alpha": 0.0291, "n": 1.47}
+    # @property
+    # def pachapaLoam(self):
+    #     """Soil Index: 3403"""
+    #     return {"theta_r": 0.000, "theta_s": 0.472, "alpha": 0.00829, "n": 1.62}
+    # @property
+    # def adelantoLoam(self):
+    #     """Soil Index: 3404"""
+    #     return {"theta_r": 0.000, "theta_s": 0.444, "alpha": 0.00710, "n": 1.26}
+    # @property
+    # def indioLoam(self):
+    #     """Soil Index: 3405a"""
+    #     return {"theta_r": 0.000, "theta_s": 0.507, "alpha": 0.00847, "n": 1.60}
+    # @property
+    # def guclphLoam(self):
+    #     """Soil Index: 3407a"""
+    #     return {"theta_r": 0.000, "theta_s": 0.563, "alpha": 0.0275, "n": 1.27}
+    # @property
+    # def guclphLoam(self):
+    #     """Soil Index: 3407b"""
+    #     return {"theta_r": 0.236, "theta_s": 0.435, "alpha": 0.0271, "n": 262}
+    # @property
+    # def rubiconSandyLoam(self):
+    #     """Soil Index: 3501a"""
+    #     return {"theta_r": 0.000, "theta_s": 0.393,  "alpha": 0.00972, "n": 2.18}
+    # @property
+    # def rubiconSandyLoam(self):
+    #     """Soil Index: 350lb"""
+    #     return {"theta_r": 0.000, "theta_s": 0.433, "alpha": 0.147, "n": 1.28}
+    # @property
+    # def pachapaFmeSandyClay(self):
+    #     """Soil Index: 3503a"""
+    #     return {"theta_r": 0.000, "theta_s": 0.340, "alpha": 0.0194, "n": 1.45}
+    # @property
+    # def gilatSandyLoam(self):
+    #     """Soil Index: 3504"""
+    #     return {"theta_r": 0.000, "theta_s": 0.432, "alpha": 0.0103, "n": 1.48}
+    # @property
+    # def plainfieldSand_210to250(self):
+    #     """Soil Index: 4101a"""
+    #     return {"theta_r": 0.000, "theta_s": 0.351, "alpha": 0.0236, "n": 12.30}
+    # @property
+    # def plainfieldSand_210to250(self):
+    #     """Soil Index: 4101b"""
+    #     return {"theta_r": 0.000, "theta_s": 0.312, "alpha": 0.0387, "n": 4.48}
+    # @property
+    # def plainfieldSand_177to210(self):
+    #     """Soil Index: 4102a"""
+    #     return {"theta_r": 0.000, "theta_s": 0.361, "alpha": 0.0207, "n": 10.0}
+    # @property
+    # def plainfieldSand_177to210(self):
+    #     """Soil Index: 4102b"""
+    #     return {"theta_r": 0.022, "theta_s": 0.309, "alpha": 0.0328, "n": 6.23}
+    # @property
+    # def plainfieldSand_149to177(self):
+    #     """Soil Index: 4103a"""
+    #     return {"theta_r": 0.000, "theta_s": 0.387, "alpha": 0.0173, "n": 7.80}
+    # @property
+    # def plainfieldSand_149to177(self):
+    #     """Soil Index: 4103b"""
+    #     return {"theta_r": 0.025, "theta_s": 0.321, "alpha": 0.0272, "n": 6.69}
+    # @property
+    # def plainfieldSand_l25to149(self):
+    #     """Soil Index: 4104a"""
+    #     return {"theta_r": 0.000, "theta_s": 03770, "alpha": 0.0145, "n": 10.60}
+    # @property
+    # def plainfieldSand_125to149(self):
+    #     """Soil Index: 4104b"""
+    #     return {"theta_r": 0.000, "theta_s": 0.342, "alpha": 0.0230, "n": 5.18}
+
+
+if __name__ == '__main__':
+    import matplotlib.pyplot as plt
+    M = Mesh.TensorMesh([10])
+    VGparams = VanGenuchtenParams()
+    leg = []
+    for p in dir(VGparams):
+        if p[0] == '_': continue
+        leg += [p]
+        params = getattr(VGparams, p)
+        model = VanGenuchten(M, **params)
+        ks = np.log(np.r_[params['Ks']])
+        model.plot(ks)
+
+    plt.legend(leg)
+
+    plt.show()

SimPEG/FLOW/Richards/RichardsProblem.py

@@ -0,0 +1,304 @@
+from SimPEG import *
+from Empirical import RichardsMap
+import time
+
+
+class RichardsRx(Survey.BaseTimeRx):
+    """Richards Receiver Object"""
+
+    knownRxTypes = ['saturation','pressureHead']
+
+    def projectFields(self, U, m, mapping, mesh, timeMesh):
+
+        if self.rxType == 'pressureHead':
+            u = np.concatenate(U)
+        elif self.rxType == 'saturation':
+            u = np.concatenate([mapping.theta(ui, m) for ui in U])
+
+        return self.getP(mesh, timeMesh) * u
+
+    def projectFieldsDeriv(self, U, m, mapping, mesh, timeMesh):
+
+        P = self.getP(mesh, timeMesh)
+        if self.rxType == 'pressureHead':
+            return P
+        elif self.rxType == 'saturation':
+            #TODO: if m is a parameter in the theta
+            #      distribution, we may need to do
+            #      some more chain rule here.
+            dT = sp.block_diag([mapping.thetaDerivU(ui, m) for ui in U])
+            return P*dT
+
+
+class RichardsSurvey(Survey.BaseSurvey):
+    """docstring for RichardsSurvey"""
+
+    rxList = None
+
+    def __init__(self, rxList, **kwargs):
+        self.rxList = rxList
+        Survey.BaseSurvey.__init__(self, **kwargs)
+
+    @property
+    def nD(self):
+        return np.array([rx.nD for rx in self.rxList]).sum()
+
+    @Utils.count
+    @Utils.requires('prob')
+    def dpred(self, m, u=None):
+        """
+            Create the projected data from a model.
+            The field, u, (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)
+
+            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))
+
+    @Utils.requires('prob')
+    def projectFields(self, U, m):
+        Ds = range(len(self.rxList))
+        for ii, rx in enumerate(self.rxList):
+            Ds[ii] = rx.projectFields(U, m,
+                                self.prob.mapping,
+                                self.prob.mesh,
+                                self.prob.timeMesh)
+
+        return np.concatenate(Ds)
+
+    @Utils.requires('prob')
+    def projectFieldsDeriv(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,
+                                self.prob.mapping,
+                                self.prob.mesh,
+                                self.prob.timeMesh)
+
+        return sp.vstack(Ds)
+
+class RichardsProblem(Problem.BaseTimeProblem):
+    """docstring for RichardsProblem"""
+
+    boundaryConditions = None
+    initialConditions  = None
+
+    surveyPair  = RichardsSurvey
+    mapPair = RichardsMap
+
+    debug=True
+
+    Solver = Solver
+    solverOpts = {}
+
+    def __init__(self, mesh, mapping=None, **kwargs):
+        Problem.BaseTimeProblem.__init__(self, mesh, mapping=mapping, **kwargs)
+
+    def getBoundaryConditions(self, ii, u_ii):
+        if type(self.boundaryConditions) is np.ndarray:
+            return self.boundaryConditions
+
+        time = self.timeMesh.vectorCCx[ii]
+
+        return self.boundaryConditions(time, u_ii)
+
+    @property
+    def method(self):
+        """Method must be either 'mixed' or 'head'. See notes in Celia et al., 1990."""
+        return getattr(self, '_method', 'mixed')
+    @method.setter
+    def method(self, value):
+        assert value in ['mixed','head'], "method must be 'mixed' or 'head'."
+        self._method = value
+
+    # Setting doNewton will clear the rootFinder, which will be reinitialized when called
+    doNewton = Utils.dependentProperty('_doNewton', False, ['_rootFinder'],
+                "Do a Newton iteration. If False, a Picard iteration will be completed.")
+
+    maxIterRootFinder = Utils.dependentProperty('_maxIterRootFinder', 30, ['_rootFinder'],
+                "Maximum iterations for rootFinder iteration.")
+    tolRootFinder = Utils.dependentProperty('_tolRootFinder', 1e-4, ['_rootFinder'],
+                "Maximum iterations for rootFinder iteration.")
+
+    @property
+    def rootFinder(self):
+        """Root-finding Algorithm"""
+        if getattr(self, '_rootFinder', None) is None:
+            self._rootFinder = Optimization.NewtonRoot(doLS=self.doNewton, maxIter=self.maxIterRootFinder, tol=self.tolRootFinder, Solver=self.Solver)
+        return self._rootFinder
+
+    @Utils.timeIt
+    def fields(self, m):
+        tic = time.time()
+        u = range(self.nT+1)
+        u[0] = self.initialConditions
+        for ii, dt in enumerate(self.timeSteps):
+            bc = self.getBoundaryConditions(ii, u[ii])
+            u[ii+1] = self.rootFinder.root(lambda hn1m, return_g=True: self.getResidual(m, u[ii], hn1m, dt, bc, return_g=return_g), u[ii])
+            if self.debug: print "Solving Fields (%4d/%d - %3.1f%% Done) %d Iterations, %4.2f seconds"%(ii+1, self.nT, 100.0*(ii+1)/self.nT, self.rootFinder.iter, time.time() - tic)
+        return u
+
+    @Utils.timeIt
+    def diagsJacobian(self, m, hn, hn1, dt, bc):
+
+        DIV  = self.mesh.faceDiv
+        GRAD = self.mesh.cellGrad
+        BC   = self.mesh.cellGradBC
+        AV   = self.mesh.aveF2CC.T
+        if self.mesh.dim == 1:
+            Dz = self.mesh.faceDivx
+        elif self.mesh.dim == 2:
+            Dz = sp.hstack((Utils.spzeros(self.mesh.nC,self.mesh.vnF[0]), self.mesh.faceDivy),format='csr')
+        elif self.mesh.dim == 3:
+            Dz = sp.hstack((Utils.spzeros(self.mesh.nC,self.mesh.vnF[0]+self.mesh.vnF[1]), self.mesh.faceDivz),format='csr')
+
+        dT   = self.mapping.thetaDerivU(hn, m)
+        dT1  = self.mapping.thetaDerivU(hn1, m)
+        K1   = self.mapping.k(hn1, m)
+        dK1  = self.mapping.kDerivU(hn1, m)
+        dKm1 = self.mapping.kDerivM(hn1, m)
+
+        # Compute part of the derivative of:
+        #
+        #       DIV*diag(GRAD*hn1+BC*bc)*(AV*(1.0/K))^-1
+
+        DdiagGh1 = DIV*Utils.sdiag(GRAD*hn1+BC*bc)
+        diagAVk2_AVdiagK2 = Utils.sdiag((AV*(1./K1))**(-2)) * AV*Utils.sdiag(K1**(-2))
+
+        # The matrix that we are computing has the form:
+        #
+        #   -                                      -   -  -     -  -
+        #  |  Adiag                                 | | h1 |   | b1 |
+        #  |   Asub    Adiag                        | | h2 |   | b2 |
+        #  |            Asub    Adiag               | | h3 | = | b3 |
+        #  |                 ...     ...            | | .. |   | .. |
+        #  |                         Asub    Adiag  | | hn |   | bn |
+        #   -                                      -   -  -     -  -
+
+        Asub = (-1.0/dt)*dT
+
+        Adiag = (
+                  (1.0/dt)*dT1
+                 -DdiagGh1*diagAVk2_AVdiagK2*dK1
+                 -DIV*Utils.sdiag(1./(AV*(1./K1)))*GRAD
+                 -Dz*diagAVk2_AVdiagK2*dK1
+                )
+
+        B = DdiagGh1*diagAVk2_AVdiagK2*dKm1 + Dz*diagAVk2_AVdiagK2*dKm1
+
+        return Asub, Adiag, B
+
+    @Utils.timeIt
+    def getResidual(self, m, hn, h, dt, bc, return_g=True):
+        """
+            Where h is the proposed value for the next time iterate (h_{n+1})
+        """
+        DIV  = self.mesh.faceDiv
+        GRAD = self.mesh.cellGrad
+        BC   = self.mesh.cellGradBC
+        AV   = self.mesh.aveF2CC.T
+        if self.mesh.dim == 1:
+            Dz = self.mesh.faceDivx
+        elif self.mesh.dim == 2:
+            Dz = sp.hstack((Utils.spzeros(self.mesh.nC,self.mesh.vnF[0]), self.mesh.faceDivy),format='csr')
+        elif self.mesh.dim == 3:
+            Dz = sp.hstack((Utils.spzeros(self.mesh.nC,self.mesh.vnF[0]+self.mesh.vnF[1]), self.mesh.faceDivz),format='csr')
+
+        T  = self.mapping.theta(h, m)
+        dT = self.mapping.thetaDerivU(h, m)
+        Tn = self.mapping.theta(hn, m)
+        K  = self.mapping.k(h, m)
+        dK = self.mapping.kDerivU(h, m)
+
+        aveK = 1./(AV*(1./K))
+
+        RHS = DIV*Utils.sdiag(aveK)*(GRAD*h+BC*bc) + Dz*aveK
+        if self.method == 'mixed':
+            r = (T-Tn)/dt - RHS
+        elif self.method == 'head':
+            r = dT*(h - hn)/dt - RHS
+
+        if not return_g: return r
+
+        J = dT/dt - DIV*Utils.sdiag(aveK)*GRAD
+        if self.doNewton:
+            DDharmAve = Utils.sdiag(aveK**2)*AV*Utils.sdiag(K**(-2)) * dK
+            J = J - DIV*Utils.sdiag(GRAD*h + BC*bc)*DDharmAve - Dz*DDharmAve
+
+        return r, J
+
+    @Utils.timeIt
+    def Jfull(self, m, u=None):
+        if u is None:
+            u = self.fields(m)
+
+        nn = len(u)-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)
+        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])
+        As = sp.vstack((zTop,sp.hstack((sp.block_diag(Asubs[1:]),zRight))))
+        A = As + Ad
+        B = np.array(sp.vstack(Bs).todense())
+
+        Ainv = self.Solver(A, **self.solverOpts)
+        P = self.survey.projectFieldsDeriv(u, m)
+        AinvB = Ainv * B
+        z = np.zeros((self.mesh.nC, B.shape[1]))
+        zAinvB = np.vstack((z, AinvB))
+        J = P * zAinvB
+        return J
+
+    @Utils.timeIt
+    def Jvec(self, m, v, u=None):
+        if u is None:
+            u = self.fields(m)
+
+        JvC = range(len(u)-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)
+        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)
+            Adiaginv = self.Solver(Adiag, **self.solverOpts)
+            JvC[ii] = Adiaginv * (B*v - Asub*JvC[ii-1])
+
+        P = self.survey.projectFieldsDeriv(u, 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)
+
+        P = self.survey.projectFieldsDeriv(u, 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)
+            #select the correct part of v
+            vpart = range((ii)*Adiag.shape[0], (ii+1)*Adiag.shape[0])
+            AdiaginvT = self.Solver(Adiag.T, **self.solverOpts)
+            JTvC = AdiaginvT * (PTv[vpart] - minus)
+            minus = Asub.T*JTvC  # this is now the super diagonal.
+            BJtv = BJtv + B.T*JTvC
+
+        return BJtv

SimPEG/FLOW/Richards/__init__.py

@@ -0,0 +1,2 @@
+import Empirical
+from RichardsProblem import *

SimPEG/FLOW/__init__.py

@@ -0,0 +1 @@
+import Richards

SimPEG/Maps.py

@@ -1,7 +1,9 @@
 import Utils, numpy as np, scipy.sparse as sp
+from scipy.sparse.linalg import LinearOperator
 from Tests import checkDerivative
 from PropMaps import PropMap, Property
-
+from numpy.polynomial import polynomial
+from scipy.interpolate import UnivariateSpline
 
 class IdentityMap(object):
     """
@@ -289,7 +291,7 @@ class FullMap(IdentityMap):
     """
     FullMap
 
-    Given a scalar, the FullMap maps the value to the 
+    Given a scalar, the FullMap maps the value to the
     full model space.
     """
 
@@ -314,8 +316,8 @@ class FullMap(IdentityMap):
             :rtype: numpy.array
             :return: derivative of transformed model
         """
-        return np.ones([self.mesh.nC,1])     
-      
+        return np.ones([self.mesh.nC,1])
+
 
 class Vertical1DMap(IdentityMap):
     """Vertical1DMap
@@ -469,11 +471,11 @@ class ActiveCells(IdentityMap):
         self.indActive = indActive
         self.indInactive = np.logical_not(indActive)
         if Utils.isScalar(valInactive):
-            valInactive = np.ones(self.nC)*float(valInactive)
-
-        valInactive[self.indActive] = 0
-        self.valInactive = valInactive
-
+            self.valInactive = np.ones(self.nC)*float(valInactive)
+        else:
+            self.valInactive = valInactive.copy()
+        self.valInactive[self.indActive] = 0
+        
         inds = np.nonzero(self.indActive)[0]
         self.P = sp.csr_matrix((np.ones(inds.size),(inds, range(inds.size))), shape=(self.nC, self.nP))
 
@@ -639,7 +641,7 @@ class ComplexMap(IdentityMap):
             return v[:nC] + v[nC:]*1j
         def adj(v):
             return np.r_[v.real,v.imag]
-        return Utils.SimPEGLinearOperator(shp,fwd,adj)
+        return LinearOperator(shp,matvec=fwd,rmatvec=adj)
 
     inverse = deriv
 
@@ -696,4 +698,304 @@ class CircleMap(IdentityMap):
         g3 = a*(-X + x)*(-sig1 + sig2)/(np.pi*(a**2*(-r + np.sqrt((X - x)**2 + (Y - y)**2))**2 + 1)*np.sqrt((X - x)**2 + (Y - y)**2))
         g4 = a*(-Y + y)*(-sig1 + sig2)/(np.pi*(a**2*(-r + np.sqrt((X - x)**2 + (Y - y)**2))**2 + 1)*np.sqrt((X - x)**2 + (Y - y)**2))
         g5 = -a*(-sig1 + sig2)/(np.pi*(a**2*(-r + np.sqrt((X - x)**2 + (Y - y)**2))**2 + 1))
-        return np.c_[g1,g2,g3,g4,g5]
+        return sp.csr_matrix(np.c_[g1,g2,g3,g4,g5])
+
+
+class PolyMap(IdentityMap):
+
+    """PolyMap
+
+        Parameterize the model space using a polynomials in a wholespace.
+
+        ..math::
+            
+            y = \mathbf{V} c
+
+        Define the model as:
+
+        ..math::
+
+            m = [\sigma_1, \sigma_2, c]
+
+    """
+    def __init__(self, mesh, order, logSigma=True, normal='X'):
+        IdentityMap.__init__(self, mesh)
+        self.logSigma = logSigma
+        self.order = order
+        self.normal = normal
+
+    slope = 1e4
+
+    @property
+    def nP(self):
+        if np.isscalar(self.order):
+            nP = self.order+3
+        else:
+            nP =(self.order[0]+1)*(self.order[1]+1)+2
+        return nP
+
+    def _transform(self, m):
+        # Set model parameters
+        alpha = self.slope
+        sig1,sig2 = m[0],m[1]
+        c = m[2:]
+        if self.logSigma:
+            sig1, sig2 = np.exp(sig1), np.exp(sig2)
+        #2D
+        if self.mesh.dim == 2:
+            X = self.mesh.gridCC[:,0]
+            Y = self.mesh.gridCC[:,1]
+            if self.normal =='X':
+                f = polynomial.polyval(Y, c) - X
+            elif self.normal =='Y':
+                f = polynomial.polyval(X, c) - Y
+            else:
+                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]            
+            if self.normal =='X':
+                f = polynomial.polyval2d(Y, Z, c.reshape((self.order[0]+1,self.order[1]+1))) - X
+            elif self.normal =='Y':
+                f = polynomial.polyval2d(X, Z, c.reshape((self.order[0]+1,self.order[1]+1))) - Y
+            elif self.normal =='Z':
+                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"))
+                    
+
+        return sig1+(sig2-sig1)*(np.arctan(alpha*f)/np.pi+0.5)
+    
+    def deriv(self, m):
+        alpha = self.slope
+        sig1,sig2, c = m[0],m[1],m[2:]
+        if self.logSigma:
+            sig1, sig2 = np.exp(sig1), np.exp(sig2)
+        #2D
+        if self.mesh.dim == 2:            
+            X = self.mesh.gridCC[:,0]
+            Y = self.mesh.gridCC[:,1]
+
+            if self.normal =='X':
+                f = polynomial.polyval(Y, c) - X
+                V = polynomial.polyvander(Y, len(c)-1)        
+            elif self.normal =='Y':
+                f = polynomial.polyval(X, c) - Y
+                V = polynomial.polyvander(X, len(c)-1)        
+            else:
+                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]
+
+            if self.normal =='X':
+                f = polynomial.polyval2d(Y, Z, c.reshape((self.order[0]+1,self.order[1]+1))) - X
+                V = polynomial.polyvander2d(Y, Z, self.order)        
+            elif self.normal =='Y':
+                f = polynomial.polyval2d(X, Z, c.reshape((self.order[0]+1,self.order[1]+1))) - Y
+                V = polynomial.polyvander2d(X, Z, self.order)        
+            elif self.normal =='Z':
+                f = polynomial.polyval2d(X, Y, c.reshape((self.order[0]+1,self.order[1]+1))) - Z
+                V = polynomial.polyvander2d(X, Y, self.order)        
+            else:
+                raise(Exception("Input for normal = X or Y or Z"))
+
+        if self.logSigma:
+            g1 = -(np.arctan(alpha*f)/np.pi + 0.5)*sig1 + sig1
+            g2 = (np.arctan(alpha*f)/np.pi + 0.5)*sig2
+        else:
+            g1 = -(np.arctan(alpha*f)/np.pi + 0.5) + 1.0
+            g2 = (np.arctan(alpha*f)/np.pi + 0.5)
+
+        g3 = Utils.sdiag(alpha*(sig2-sig1)/(1.+(alpha*f)**2)/np.pi)*V
+
+        return sp.csr_matrix(np.c_[g1,g2,g3])  
+
+class SplineMap(IdentityMap):
+
+    """SplineMap
+
+        Parameterize the boundary of two geological units using a spline interpolation 
+
+        ..math::
+            
+            g = f(x)-y
+
+        Define the model as:
+
+        ..math::
+
+            m = [\sigma_1, \sigma_2, y]
+
+    """
+    def __init__(self, mesh, pts, ptsv=None,order=3, logSigma=True, normal='X'):
+        IdentityMap.__init__(self, mesh)
+        self.logSigma = logSigma
+        self.order = order
+        self.normal = normal
+        self.pts= pts
+        self.npts = np.size(pts)
+        self.ptsv = ptsv
+        self.spl = None
+
+    slope = 1e4
+    @property
+    def nP(self):
+        if self.mesh.dim == 2:
+            return np.size(self.pts)+2
+        elif self.mesh.dim == 3: 
+            return np.size(self.pts)*2+2
+        else:
+            raise(Exception("Only supports 2D and 3D"))
+
+    def _transform(self, m):
+        # Set model parameters
+        alpha = self.slope
+        sig1,sig2 = m[0],m[1]
+        c = m[2:]
+        if self.logSigma:
+            sig1, sig2 = np.exp(sig1), np.exp(sig2)
+        #2D
+        if self.mesh.dim == 2:
+            X = self.mesh.gridCC[:,0]
+            Y = self.mesh.gridCC[:,1]
+            self.spl = UnivariateSpline(self.pts, c, k=self.order, s=0)
+            if self.normal =='X':                
+                f = self.spl(Y) - X
+            elif self.normal =='Y':
+                f = self.spl(X) - Y
+            else:
+                raise(Exception("Input for normal = X or Y or Z"))
+
+        # 3D: 
+        # Comments: 
+        # Make two spline functions and link them using linear interpolation.
+        # This is not quite direct extension of 2D to 3D case
+        # Using 2D interpolation  is possible
+
+        elif self.mesh.dim == 3: 
+            X = self.mesh.gridCC[:,0]
+            Y = self.mesh.gridCC[:,1]            
+            Z = self.mesh.gridCC[:,2]
+
+            npts = np.size(self.pts)            
+            if np.mod(c.size, 2):
+                raise(Exception("Put even points!"))
+            
+            self.spl = {"splb":UnivariateSpline(self.pts, c[:npts], k=self.order, s=0),
+                        "splt":UnivariateSpline(self.pts, c[npts:], k=self.order, s=0)}
+
+            if self.normal =='X':
+                zb = self.ptsv[0]
+                zt = self.ptsv[1]
+                flines = (self.spl["splt"](Y)-self.spl["splb"](Y))*(Z-zb)/(zt-zb) + self.spl["splb"](Y)
+                f = flines - X
+            # elif self.normal =='Y':
+            # elif self.normal =='Z':
+            else:
+                raise(Exception("Input for normal = X or Y or Z"))
+        else:
+            raise(Exception("Only supports 2D and 3D"))
+                    
+
+        return sig1+(sig2-sig1)*(np.arctan(alpha*f)/np.pi+0.5)
+
+    def deriv(self, m):
+        alpha = self.slope
+        sig1,sig2, c = m[0],m[1],m[2:]
+        if self.logSigma:
+            sig1, sig2 = np.exp(sig1), np.exp(sig2)
+        #2D
+        if self.mesh.dim == 2:            
+            X = self.mesh.gridCC[:,0]
+            Y = self.mesh.gridCC[:,1]
+
+            if self.normal =='X':
+                f = self.spl(Y) - X
+            elif self.normal =='Y':
+                f = self.spl(X) - Y
+            else:
+                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]
+            if self.normal =='X':
+                zb = self.ptsv[0]
+                zt = self.ptsv[1]
+                flines = (self.spl["splt"](Y)-self.spl["splb"](Y))*(Z-zb)/(zt-zb) + self.spl["splb"](Y)
+                f = flines - X            
+            # elif self.normal =='Y':
+            # elif self.normal =='Z':
+            else:
+                raise(Exception("Not Implemented for Y and Z, your turn :)"))
+
+        if self.logSigma:
+            g1 = -(np.arctan(alpha*f)/np.pi + 0.5)*sig1 + sig1
+            g2 = (np.arctan(alpha*f)/np.pi + 0.5)*sig2
+        else:
+            g1 = -(np.arctan(alpha*f)/np.pi + 0.5) + 1.0
+            g2 = (np.arctan(alpha*f)/np.pi + 0.5)
+
+        
+        if self.mesh.dim ==2:
+            g3 = np.zeros((self.mesh.nC, self.npts))
+            if self.normal =='Y':
+                # Here we use perturbation to compute sensitivity
+                # TODO: bit more generalization of this ...
+                # Modfications for X and Z directions ...
+                for i in range(np.size(self.pts)):
+                    ctemp = c[i]
+                    ind = np.argmin(abs(self.mesh.vectorCCy-ctemp))
+                    ca = c.copy()
+                    cb = c.copy()
+                    dy = self.mesh.hy[ind]*1.5
+                    ca[i] = ctemp+dy
+                    cb[i] = ctemp-dy                
+                    spla = UnivariateSpline(self.pts, ca, k=self.order, s=0)
+                    splb = UnivariateSpline(self.pts, cb, k=self.order, s=0)
+                    fderiv = (spla(X)-splb(X))/(2*dy)
+                    g3[:,i] = Utils.sdiag(alpha*(sig2-sig1)/(1.+(alpha*f)**2)/np.pi)*fderiv
+
+        elif self.mesh.dim==3:
+            g3 = np.zeros((self.mesh.nC, self.npts*2))
+            if self.normal =='X':
+                # Here we use perturbation to compute sensitivity
+                for i in range(self.npts*2):                    
+                    ctemp = c[i]
+                    ind = np.argmin(abs(self.mesh.vectorCCy-ctemp))
+                    ca = c.copy()
+                    cb = c.copy()
+                    dy = self.mesh.hy[ind]*1.5
+                    ca[i] = ctemp+dy
+                    cb[i] = ctemp-dy
+                    #treat bottom boundary
+                    if i< self.npts:
+                        splba = UnivariateSpline(self.pts, ca[:self.npts], k=self.order, s=0)
+                        splbb = UnivariateSpline(self.pts, cb[:self.npts], k=self.order, s=0)
+                        flinesa = (self.spl["splt"](Y)-splba(Y))*(Z-zb)/(zt-zb) + splba(Y) - X
+                        flinesb = (self.spl["splt"](Y)-splbb(Y))*(Z-zb)/(zt-zb) + splbb(Y) - X
+                    #treat top boundary                        
+                    else:
+                        splta = UnivariateSpline(self.pts, ca[self.npts:], k=self.order, s=0)
+                        spltb = UnivariateSpline(self.pts, ca[self.npts:], k=self.order, s=0)
+                        flinesa = (self.spl["splt"](Y)-splta(Y))*(Z-zb)/(zt-zb) + splta(Y) - X
+                        flinesb = (self.spl["splt"](Y)-spltb(Y))*(Z-zb)/(zt-zb) + spltb(Y) - X                        
+                    fderiv = (flinesa-flinesb)/(2*dy)                                
+                    g3[:,i] = Utils.sdiag(alpha*(sig2-sig1)/(1.+(alpha*f)**2)/np.pi)*fderiv
+        else :
+            raise(Exception("Not Implemented for Y and Z, your turn :)"))
+        return sp.csr_matrix(np.c_[g1,g2,g3])  
+
+
+
+
+
+            

SimPEG/Mesh/BaseMesh.py

@@ -27,6 +27,7 @@ class BaseMesh(object):
         # Ensure x0 & n are 1D vectors
         self._n = np.array(n, dtype=int).ravel()
         self._x0 = np.array(x0, dtype=float).ravel()
+        self._dim = len(self._x0)
 
     @property
     def x0(self):
@@ -46,7 +47,7 @@ class BaseMesh(object):
         :rtype: int
         :return: dim
         """
-        return len(self._n)
+        return self._dim
 
     @property
     def nC(self):

SimPEG/Mesh/CylMesh.py

@@ -2,12 +2,12 @@ import numpy as np
 import scipy.sparse as sp
 from scipy.constants import pi
 from SimPEG.Utils import mkvc, ndgrid, sdiag, kron3, speye, spzeros, ddx, av, avExtrap
-from TensorMesh import BaseTensorMesh
+from TensorMesh import BaseTensorMesh, BaseRectangularMesh
 from InnerProducts import InnerProducts
 from View import CylView
 
 
-class CylMesh(BaseTensorMesh, InnerProducts, CylView):
+class CylMesh(BaseTensorMesh, BaseRectangularMesh, InnerProducts, CylView):
     """
         CylMesh is a mesh class for cylindrical problems
 

SimPEG/Mesh/TensorMesh.py

@@ -1,10 +1,10 @@
 from SimPEG import Utils, np, sp
-from BaseMesh import BaseRectangularMesh
+from BaseMesh import BaseMesh, BaseRectangularMesh
 from View import TensorView
 from DiffOperators import DiffOperators
 from InnerProducts import InnerProducts
 
-class BaseTensorMesh(BaseRectangularMesh):
+class BaseTensorMesh(BaseMesh):
 
     __metaclass__ = Utils.SimPEGMetaClass
 
@@ -42,7 +42,10 @@ class BaseTensorMesh(BaseRectangularMesh):
                 else:
                     raise Exception("x0[%i] must be a scalar or '0' to be zero, 'C' to center, or 'N' to be negative." % i)
 
-        BaseRectangularMesh.__init__(self, np.array([x.size for x in h]), x0)
+        if isinstance(self, BaseRectangularMesh):
+            BaseRectangularMesh.__init__(self, np.array([x.size for x in h]), x0)
+        else:
+            BaseMesh.__init__(self, np.array([x.size for x in h]), x0)
 
         # Ensure h contains 1D vectors
         self._h = [Utils.mkvc(x.astype(float)) for x in h]
@@ -356,7 +359,7 @@ class BaseTensorMesh(BaseRectangularMesh):
 
 
 
-class TensorMesh(BaseTensorMesh, TensorView, DiffOperators, InnerProducts):
+class TensorMesh(BaseTensorMesh, BaseRectangularMesh, TensorView, DiffOperators, InnerProducts):
     """
     TensorMesh is a mesh class that deals with tensor product meshes.
 
@@ -413,34 +416,34 @@ class TensorMesh(BaseTensorMesh, TensorView, DiffOperators, InnerProducts):
                         break
 
                 if n == 1:
-                    outStr = outStr + ' {0:.2f},'.format(h)
+                    outStr += ' {0:.2f},'.format(h)
                 else:
-                    outStr = outStr + ' {0:d}*{1:.2f},'.format(n,h)
+                    outStr += ' {0:d}*{1:.2f},'.format(n,h)
 
             return outStr[:-1]
 
         if self.dim == 1:
-            outStr = outStr + '\n   x0: {0:.2f}'.format(self.x0[0])
-            outStr = outStr + '\n  nCx: {0:d}'.format(self.nCx)
-            outStr = outStr + printH(self.hx, outStr='\n   hx:')
+            outStr += '\n   x0: {0:.2f}'.format(self.x0[0])
+            outStr += '\n  nCx: {0:d}'.format(self.nCx)
+            outStr += printH(self.hx, outStr='\n   hx:')
             pass
         elif self.dim == 2:
-            outStr = outStr + '\n   x0: {0:.2f}'.format(self.x0[0])
-            outStr = outStr + '\n   y0: {0:.2f}'.format(self.x0[1])
-            outStr = outStr + '\n  nCx: {0:d}'.format(self.nCx)
-            outStr = outStr + '\n  nCy: {0:d}'.format(self.nCy)
-            outStr = outStr + printH(self.hx, outStr='\n   hx:')
-            outStr = outStr + printH(self.hy, outStr='\n   hy:')
+            outStr += '\n   x0: {0:.2f}'.format(self.x0[0])
+            outStr += '\n   y0: {0:.2f}'.format(self.x0[1])
+            outStr += '\n  nCx: {0:d}'.format(self.nCx)
+            outStr += '\n  nCy: {0:d}'.format(self.nCy)
+            outStr += printH(self.hx, outStr='\n   hx:')
+            outStr += printH(self.hy, outStr='\n   hy:')
         elif self.dim == 3:
-            outStr = outStr + '\n   x0: {0:.2f}'.format(self.x0[0])
-            outStr = outStr + '\n   y0: {0:.2f}'.format(self.x0[1])
-            outStr = outStr + '\n   z0: {0:.2f}'.format(self.x0[2])
-            outStr = outStr + '\n  nCx: {0:d}'.format(self.nCx)
-            outStr = outStr + '\n  nCy: {0:d}'.format(self.nCy)
-            outStr = outStr + '\n  nCz: {0:d}'.format(self.nCz)
-            outStr = outStr + printH(self.hx, outStr='\n   hx:')
-            outStr = outStr + printH(self.hy, outStr='\n   hy:')
-            outStr = outStr + printH(self.hz, outStr='\n   hz:')
+            outStr += '\n   x0: {0:.2f}'.format(self.x0[0])
+            outStr += '\n   y0: {0:.2f}'.format(self.x0[1])
+            outStr += '\n   z0: {0:.2f}'.format(self.x0[2])
+            outStr += '\n  nCx: {0:d}'.format(self.nCx)
+            outStr += '\n  nCy: {0:d}'.format(self.nCy)
+            outStr += '\n  nCz: {0:d}'.format(self.nCz)
+            outStr += printH(self.hx, outStr='\n   hx:')
+            outStr += printH(self.hy, outStr='\n   hy:')
+            outStr += printH(self.hz, outStr='\n   hz:')
 
         return outStr
 

SimPEG/Mesh/TreeUtils.pyx

@@ -0,0 +1,85 @@
+# from __future__ import division
+# import numpy as np
+# cimport numpy as np
+# from libcpp.vector cimport vector
+
+
+"""
+    The Z-order curve is generated by interleaving the bits of an offset.
+
+    See also:
+
+        https://github.com/cortesi/scurve
+        Aldo Cortesi <aldo@corte.si>
+
+"""
+
+def bitrange(long x, int width, int start, int end):
+    """
+        Extract a bit range as an integer.
+        (start, end) is inclusive lower bound, exclusive upper bound.
+    """
+    return x >> (width-end) & ((2**(end-start))-1)
+
+def index(int dimension, int bits, int levelBits, list p, int level):
+    cdef long idx = 0
+    cdef int iwidth
+    cdef int i
+    cdef long b
+    cdef int bitoff
+
+    p = [_ for _ in p]
+
+    p.reverse()
+    iwidth = bits * dimension
+    for i in range(iwidth):
+        bitoff = bits-(i/dimension)-1
+        poff = dimension-(i%dimension)-1
+        b = bitrange(p[poff], bits, bitoff, bitoff+1) << i
+        idx |= b
+
+    return (idx << levelBits) + level
+
+def point(int dimension, int bits, int levelBits, long idx):
+    cdef list p
+    cdef int iwidth
+    cdef int i, n
+    cdef long b
+
+    n   = idx & (2**levelBits-1)
+    idx = idx >> levelBits
+
+    p = [0]*dimension
+    iwidth = bits * dimension
+    for i in range(iwidth):
+        b = bitrange(idx, iwidth, i, i+1) << (iwidth-i-1)/dimension
+        p[i%dimension] |= b
+    p.reverse()
+    return p + [n]
+
+
+# def _refineCell(int dimension, int bits, self, pointer):
+#     self._structureChange()
+#     pointer = self._asPointer(pointer)
+#     ind = self._asIndex(pointer)
+#     assert ind in self
+#     h = self._levelWidth(pointer[-1])/2 # halfWidth
+#     nL = pointer[-1] + 1 # new level
+#     add = lambda p:p[0]+p[1]
+#     added = []
+#     def addCell(p):
+#         i = self._index(p+[nL])
+#         self._treeInds.add(i)
+#         added.append(i)
+
+#     addCell(map(add, zip(pointer[:-1], [0,0,0])))
+#     addCell(map(add, zip(pointer[:-1], [h,0,0])))
+#     addCell(map(add, zip(pointer[:-1], [0,h,0])))
+#     addCell(map(add, zip(pointer[:-1], [h,h,0])))
+#     if self.dim == 3:
+#         addCell(map(add, zip(pointer[:-1], [0,0,h])))
+#         addCell(map(add, zip(pointer[:-1], [h,0,h])))
+#         addCell(map(add, zip(pointer[:-1], [0,h,h])))
+#         addCell(map(add, zip(pointer[:-1], [h,h,h])))
+#     self._treeInds.remove(ind)
+#     return added

SimPEG/Mesh/View.py

@@ -173,7 +173,7 @@ class TensorView(object):
                   ax=None, clim=None, showIt=False,
                   pcolorOpts={},
                   streamOpts={'color':'k'},
-                  gridOpts={'color':'k'}
+                  gridOpts={'color':'k', 'alpha':0.5}
                   ):
 
         """
@@ -216,6 +216,7 @@ class TensorView(object):
         if ind is None: ind = int(szSliceDim/2)
         assert type(ind) in [int, long], 'ind must be an integer'
 
+        assert not (v.dtype == complex and view == 'vec'), 'Can not plot a complex vector.'
         # The slicing and plotting code!!
 
         def getIndSlice(v):

SimPEG/Survey.py

@@ -367,7 +367,7 @@ class BaseSurvey(object):
 
         """
         if getattr(self, 'dobs', None) is not None and not force:
-            raise Exception('Survey already has dobs.')
+            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)
         noise = std*abs(self.dtrue)*np.random.randn(*self.dtrue.shape)

SimPEG/Tests.py

@@ -4,6 +4,7 @@ from numpy.linalg import norm
 from SimPEG.Utils import mkvc, sdiag, diagEst
 from SimPEG import Utils
 from SimPEG.Mesh import TensorMesh, CurvilinearMesh, CylMesh
+from SimPEG.Mesh.TreeMesh import TreeMesh as Tree
 import numpy as np
 import scipy.sparse as sp
 import unittest
@@ -132,6 +133,34 @@ class OrderTest(unittest.TestCase):
                 self.M = CurvilinearMesh([X, Y, Z])
             return 1./nc
 
+        elif 'Tree' in self._meshType:
+            nc *= 2
+            if 'uniform' in self._meshType or 'notatree' in self._meshType:
+                h = [nc, nc, nc]
+            elif 'random' in self._meshType:
+                h1 = np.random.rand(nc)*nc*0.5 + nc*0.5
+                h2 = np.random.rand(nc)*nc*0.5 + nc*0.5
+                h3 = np.random.rand(nc)*nc*0.5 + nc*0.5
+                h = [hi/np.sum(hi) for hi in [h1, h2, h3]]  # normalize
+            else:
+                raise Exception('Unexpected meshType')
+
+            levels = int(np.log(nc)/np.log(2))
+            self.M = Tree(h[:self.meshDimension], levels=levels)
+            def function(cell):
+                if 'notatree' in self._meshType:
+                    return levels - 1
+                r = cell.center - np.array([0.5]*len(cell.center))
+                dist = np.sqrt(r.dot(r))
+                if dist < 0.2:
+                    return levels
+                return levels - 1
+            self.M.refine(function,balance=False)
+            self.M.number(balance=False)
+            # self.M.plotGrid(showIt=True)
+            max_h = max([np.max(hi) for hi in self.M.h])
+            return max_h
+
     def getError(self):
         """For given h, generate A[h], f and A(f) and return norm of error."""
         return 1.

SimPEG/Tests/test_TreeMesh.py

@@ -1,505 +0,0 @@
-from SimPEG.Mesh import TensorMesh
-from SimPEG.Mesh.TreeMesh import TreeMesh, TreeFace, TreeCell
-import numpy as np
-import unittest
-import matplotlib.pyplot as plt
-
-TOL = 1e-10
-
-class TestOcTreeObjects(unittest.TestCase):
-
-    def setUp(self):
-        self.M  = TreeMesh([2,1,1])
-        self.M.number()
-
-        self.Mr = TreeMesh([2,1,1])
-        self.Mr.children[0,0,0].refine()
-        self.Mr.number()
-
-        def q(s):
-            if s[0] == 'M':
-                m = self.M
-                s = s[1:]
-            else:
-                m = self.Mr
-            c = m.sortedCells[int(s[1])]
-            if len(s) == 2: return c
-            if s[2] == 'f' and len(s) == 5: return c.faceDict[s[2:]]
-            if s[2] == 'f': return getattr(c.faceDict[s[2:5]], 'edg' +s[5:])
-            if s[2] == 'e': return getattr(c,s[2:])
-            if s[2] == 'n': return getattr(c,'node'+s[3:])
-
-        self.q = q
-
-    def test_counts(self):
-        self.assertTrue(self.M.nC == 2)
-        self.assertTrue(self.M.nFx == 3)
-        self.assertTrue(self.M.nFy == 4)
-        self.assertTrue(self.M.nFz == 4)
-        self.assertTrue(self.M.nF == 11)
-        self.assertTrue(self.M.nEx == 8)
-        self.assertTrue(self.M.nEy == 6)
-        self.assertTrue(self.M.nEz == 6)
-        self.assertTrue(self.M.nE == 20)
-        self.assertTrue(self.M.nN == 12)
-
-        self.assertTrue(self.Mr.nC == 9)
-        self.assertTrue(self.Mr.nFx == 13)
-        self.assertTrue(self.Mr.nFy == 14)
-        self.assertTrue(self.Mr.nFz == 14)
-        self.assertTrue(self.Mr.nF == 41)
-
-
-        for cell in self.Mr.sortedCells:
-            for e in cell.edgeDict:
-                self.assertTrue(cell.edgeDict[e].edgeType==e[1].lower())
-
-        self.assertTrue(self.Mr.nN == 31)
-        self.assertTrue(self.Mr.nEx == 22)
-        self.assertTrue(self.Mr.nEy == 20)
-        self.assertTrue(self.Mr.nEz == 20)
-
-    def test_sizes(self):
-        q = self.q
-
-        for key in ['Mc0','Mc1']:
-            self.assertTrue(q(key).vol == 0.5)
-            self.assertTrue(q(key+'fXm').area == 1.)
-            self.assertTrue(q(key+'fXp').area == 1.)
-            self.assertTrue(q(key+'fYm').area == 0.5)
-            self.assertTrue(q(key+'fYp').area == 0.5)
-            self.assertTrue(q(key+'fZm').area == 0.5)
-            self.assertTrue(q(key+'fZp').area == 0.5)
-
-    def test_pointersM(self):
-        q = self.q
-
-        self.assertTrue(q('Mc0fXp') is q('Mc1fXm'))
-        self.assertTrue(q('Mc0fXpe0') is q('Mc1fXme0'))
-        self.assertTrue(q('Mc0fXpe1') is q('Mc1fXme1'))
-        self.assertTrue(q('Mc0fXpe2') is q('Mc1fXme2'))
-        self.assertTrue(q('Mc0fXpe3') is q('Mc1fXme3'))
-        self.assertTrue(q('Mc0fYp') is not q('c1fYm'))
-        self.assertTrue(q('Mc0fXm') is not q('c1fXm'))
-
-        # Test connectivity of shared edges
-        self.assertTrue(q('Mc0fZpe3') is not q('c1fZpe0'))
-        self.assertTrue(q('Mc0fZpe3') is not q('c1fZpe1'))
-        self.assertTrue(q('Mc0fZpe3') is q('Mc1fZpe2'))
-        self.assertTrue(q('Mc0fZpe3') is not q('c1fZpe3'))
-
-        self.assertTrue(q('Mc0fZme3') is not q('c1fZme0'))
-        self.assertTrue(q('Mc0fZme3') is not q('c1fZme1'))
-        self.assertTrue(q('Mc0fZme3') is q('Mc1fZme2'))
-        self.assertTrue(q('Mc0fZme3') is not q('c1fZme3'))
-
-        self.assertTrue(q('Mc0fYpe3') is not q('c1fYpe0'))
-        self.assertTrue(q('Mc0fYpe3') is not q('c1fYpe1'))
-        self.assertTrue(q('Mc0fYpe3') is q('Mc1fYpe2'))
-        self.assertTrue(q('Mc0fYpe3') is not q('c1fYpe3'))
-
-        self.assertTrue(q('Mc0fYme3') is not q('c1fYme0'))
-        self.assertTrue(q('Mc0fYme3') is not q('c1fYme1'))
-        self.assertTrue(q('Mc0fYme3') is q('Mc1fYme2'))
-        self.assertTrue(q('Mc0fYme3') is not q('c1fYme3'))
-
-        self.assertTrue(q('Mc0fZme3') is q('Mc1fXme0'))
-        self.assertTrue(q('Mc0fZpe3') is q('Mc1fXme1'))
-        self.assertTrue(q('Mc0fYme3') is q('Mc1fXme2'))
-        self.assertTrue(q('Mc0fYpe3') is q('Mc1fXme3'))
-
-        self.assertTrue(q('Mc0fZme3') is q('Mc0fXpe0'))
-        self.assertTrue(q('Mc0fZpe3') is q('Mc0fXpe1'))
-        self.assertTrue(q('Mc0fYme3') is q('Mc0fXpe2'))
-        self.assertTrue(q('Mc0fYpe3') is q('Mc0fXpe3'))
-
-        self.assertTrue(q('Mc1fZme2') is q('Mc1fXme0'))
-        self.assertTrue(q('Mc1fZpe2') is q('Mc1fXme1'))
-        self.assertTrue(q('Mc1fYme2') is q('Mc1fXme2'))
-        self.assertTrue(q('Mc1fYpe2') is q('Mc1fXme3'))
-
-        self.assertTrue(q('Mc1fZme2') is q('Mc0fXpe0'))
-        self.assertTrue(q('Mc1fZpe2') is q('Mc0fXpe1'))
-        self.assertTrue(q('Mc1fYme2') is q('Mc0fXpe2'))
-        self.assertTrue(q('Mc1fYpe2') is q('Mc0fXpe3'))
-
-
-    def test_nodePointers(self):
-        q = self.q
-        c0 = self.Mr.sortedCells[0]
-        c0n0 = c0.node0
-        self.assertTrue(c0n0 is q('c0n0'))
-        self.assertTrue(np.all(q('c0n0').center == np.r_[0,0,0.]))
-        self.assertTrue(q('c0n0').num == 0)
-        self.assertTrue(q('c0n1').num == 1)
-        self.assertTrue(q('c0n2').num == 4)
-        self.assertTrue(q('c0n3').num == 5)
-        self.assertTrue(q('c0n4').num == 11)
-        self.assertTrue(q('c0n5').num == 12)
-        self.assertTrue(q('c0n6').num == 14)
-        self.assertTrue(q('c0n7').num == 15)
-
-    def test_pointersMr(self):
-        q = self.q
-
-        c0    = self.Mr.sortedCells[0]
-        c0fXm = c0.fXm
-        c0eX0 = c0.eX0
-        c0fYme0 = c0.fYm.edge0
-        self.assertTrue(c0 is q('c0'))
-        self.assertTrue(c0fXm is q('c0fXm'))
-        self.assertTrue(c0eX0 is q('c0eX0'))
-        self.assertTrue(c0fYme0 is q('c0fYme0'))
-
-        self.assertTrue(q('c0').depth == 1)
-        self.assertTrue(q('c1').depth == 1)
-        self.assertTrue(q('c2').depth == 0)
-
-        # Make sure we know where the center of the cells are.
-        self.assertTrue(np.all(q('c0').center == np.r_[0.125,0.25,0.25]))
-        self.assertTrue(np.all(q('c1').center == np.r_[0.375,0.25,0.25]))
-        self.assertTrue(np.all(q('c2').center == np.r_[0.75,0.5,0.5]))
-        self.assertTrue(np.all(q('c3').center == np.r_[0.125,0.75,0.25]))
-        self.assertTrue(np.all(q('c4').center == np.r_[0.375,0.75,0.25]))
-        self.assertTrue(np.all(q('c5').center == np.r_[0.125,0.25,0.75]))
-        self.assertTrue(np.all(q('c6').center == np.r_[0.375,0.25,0.75]))
-        self.assertTrue(np.all(q('c7').center == np.r_[0.125,0.75,0.75]))
-        self.assertTrue(np.all(q('c8').center == np.r_[0.375,0.75,0.75]))
-
-        # Test X face connectivity and locations and stuff...
-        self.assertTrue(np.all(q('c0fXm').center == np.r_[0,0.25,0.25]))
-        self.assertTrue(np.all(q('c0fXp').center == np.r_[0.25,0.25,0.25]))
-        self.assertTrue(q('c0fXp') is q('c1fXm'))
-        self.assertTrue(np.all(q('c1fXp').center == np.r_[0.5,0.25,0.25]))
-        self.assertTrue(np.all(q('c2fXm').center == np.r_[0.5,0.5,0.5]))
-        self.assertTrue(q('c2fXm').branchdepth == 1)
-        self.assertTrue(q('c2fXm').children[0,0] is q('c1fXp'))
-        self.assertTrue(np.all(q('c3fXm').center == np.r_[0,0.75,0.25]))
-        self.assertTrue(np.all(q('c3fXp').center == np.r_[0.25,0.75,0.25]))
-        self.assertTrue(q('c4fXm') is q('c3fXp'))
-        self.assertTrue(q('c2fXm').children[1,0] is q('c4fXp'))
-
-        #Test some internal stuff (edges held by cell should be same as inside)
-        for key in ['Mc0', 'Mc1'] + ['c%d'%i for i in range(9)]:
-            self.assertTrue(q(key+'eX0') is q(key+'fZme0'))
-            self.assertTrue(q(key+'eX1') is q(key+'fZme1'))
-            self.assertTrue(q(key+'eX2') is q(key+'fZpe0'))
-            self.assertTrue(q(key+'eX3') is q(key+'fZpe1'))
-
-            self.assertTrue(q(key+'eX0') is q(key+'fYme0'))
-            self.assertTrue(q(key+'eX1') is q(key+'fYpe0'))
-            self.assertTrue(q(key+'eX2') is q(key+'fYme1'))
-            self.assertTrue(q(key+'eX3') is q(key+'fYpe1'))
-
-            self.assertTrue(q(key+'eY0') is q(key+'fXme0'))
-            self.assertTrue(q(key+'eY1') is q(key+'fXpe0'))
-            self.assertTrue(q(key+'eY2') is q(key+'fXme1'))
-            self.assertTrue(q(key+'eY3') is q(key+'fXpe1'))
-
-            self.assertTrue(q(key+'eY0') is q(key+'fZme2'))
-            self.assertTrue(q(key+'eY1') is q(key+'fZme3'))
-            self.assertTrue(q(key+'eY2') is q(key+'fZpe2'))
-            self.assertTrue(q(key+'eY3') is q(key+'fZpe3'))
-
-            self.assertTrue(q(key+'eZ0') is q(key+'fXme2'))
-            self.assertTrue(q(key+'eZ1') is q(key+'fXpe2'))
-            self.assertTrue(q(key+'eZ2') is q(key+'fXme3'))
-            self.assertTrue(q(key+'eZ3') is q(key+'fXpe3'))
-
-            self.assertTrue(q(key+'eZ0') is q(key+'fYme2'))
-            self.assertTrue(q(key+'eZ1') is q(key+'fYme3'))
-            self.assertTrue(q(key+'eZ2') is q(key+'fYpe2'))
-            self.assertTrue(q(key+'eZ3') is q(key+'fYpe3'))
-
-        #Test some edge stuff
-        self.assertTrue(np.all(q('c0eX0').center == np.r_[0.125,0,0]))
-        self.assertTrue(np.all(q('c0eX1').center == np.r_[0.125,0.5,0]))
-        self.assertTrue(np.all(q('c0eX2').center == np.r_[0.125,0,0.5]))
-        self.assertTrue(np.all(q('c0eX3').center == np.r_[0.125,0.5,0.5]))
-
-        self.assertTrue(np.all(q('c5eX0').center == np.r_[0.125,0,0.5]))
-        self.assertTrue(np.all(q('c5eX1').center == np.r_[0.125,0.5,0.5]))
-        self.assertTrue(q('c5eX0') is q('c0eX2'))
-        self.assertTrue(q('c5eX1') is q('c0eX3'))
-
-        self.assertTrue(np.all(q('c0eY0').center == np.r_[0,0.25,0]))
-        self.assertTrue(np.all(q('c0eY1').center == np.r_[0.25,0.25,0]))
-        self.assertTrue(np.all(q('c0eY2').center == np.r_[0,0.25,0.5]))
-        self.assertTrue(np.all(q('c0eY3').center == np.r_[0.25,0.25,0.5]))
-
-        self.assertTrue(np.all(q('c1eY0').center == np.r_[0.25,0.25,0]))
-        self.assertTrue(np.all(q('c1eY2').center == np.r_[0.25,0.25,0.5]))
-        self.assertTrue(q('c1eY0') is q('c0eY1'))
-        self.assertTrue(q('c1eY2') is q('c0eY3'))
-
-
-        self.assertTrue(np.all(q('c0eZ0').center == np.r_[0,0,0.25]))
-        self.assertTrue(np.all(q('c0eZ1').center == np.r_[0.25,0,0.25]))
-        self.assertTrue(np.all(q('c0eZ2').center == np.r_[0,0.5,0.25]))
-        self.assertTrue(np.all(q('c0eZ3').center == np.r_[0.25,0.5,0.25]))
-
-        self.assertTrue(np.all(q('c3eZ0').center == np.r_[0,0.5,0.25]))
-        self.assertTrue(np.all(q('c3eZ1').center == np.r_[0.25,0.5,0.25]))
-        self.assertTrue(q('c3eZ0') is q('c0eZ2'))
-        self.assertTrue(q('c3eZ1') is q('c0eZ3'))
-
-
-        self.assertTrue(q('c0fXp') is q('c1fXm'))
-        self.assertTrue(q('c0fYp') is not q('c1fYm'))
-        self.assertTrue(q('c0fXm') is not q('c1fXm'))
-
-        self.assertTrue(q('c1fXp') is q('c2fXm').children[0,0])
-
-        self.assertTrue(q('c1fYp') is q('c4fYm'))
-        self.assertTrue(q('c1fZp') is q('c6fZm'))
-
-        self.assertTrue(q('c6fXp') is q('c2fXm').children[0,1])
-
-        self.assertTrue(q('c4fXp') is q('c2fXm').children[1,0])
-
-
-    def test_gridCC(self):
-        x = np.r_[0.25,0.75]
-        y = np.r_[0.5,0.5]
-        z = np.r_[0.5,0.5]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.M.gridCC).flatten()) == 0)
-
-        x = np.r_[0.125,0.375,0.75,0.125,0.375,0.125,0.375,0.125,0.375]
-        y = np.r_[0.25,0.25,0.5,0.75,0.75,0.25,0.25,0.75,0.75]
-        z = np.r_[0.25,0.25,0.5,0.25,0.25,0.75,0.75,0.75,0.75]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.Mr.gridCC).flatten()) == 0)
-
-    def test_gridN(self):
-        x = np.r_[0,0.5,1,0,0.5,1,0,0.5,1,0,0.5,1]
-        y = np.r_[0,0,0,1,1,1,0,0,0,1,1,1.]
-        z = np.r_[0,0,0,0,0,0,1,1,1,1,1,1.]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.M.gridN).flatten()) == 0)
-
-        x = np.r_[0,0.25,0.5,1,0,0.25,0.5,0,0.25,0.5,1,0,0.25,0.5,0,0.25,0.5,0,0.25,0.5,0,0.25,0.5,1,0,0.25,0.5,0,0.25,0.5,1]
-        y = np.r_[0,0,0,0,0.5,0.5,0.5,1,1,1,1,0,0,0,0.5,0.5,0.5,1,1,1,0,0,0,0,0.5,0.5,0.5,1,1,1,1]
-        z = np.r_[0,0,0,0,0,0,0,0,0,0,0,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,1,1,1,1,1,1,1,1,1,1,1]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.Mr.gridN).flatten()) == 0)
-
-    def test_gridFx(self):
-        x = np.r_[0.0,0.5,1.0]
-        y = np.r_[0.5,0.5,0.5]
-        z = np.r_[0.5,0.5,0.5]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.M.gridFx).flatten()) == 0)
-
-        x = np.r_[0.0,0.25,0.5,1.0,0.0,0.25,0.5,0.0,0.25,0.5,0.0,0.25,0.5]
-        y = np.r_[0.25,0.25,0.25,0.5,0.75,0.75,0.75,0.25,0.25,0.25,0.75,0.75,0.75]
-        z = np.r_[0.25,0.25,0.25,0.5,0.25,0.25,0.25,0.75,0.75,0.75,0.75,0.75,0.75]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.Mr.gridFx).flatten()) == 0)
-
-    def test_gridFy(self):
-        x = np.r_[0.25,0.75,0.25,0.75]
-        y = np.r_[0,0,1.,1.]
-        z = np.r_[0.5,0.5,0.5,0.5]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.M.gridFy).flatten()) == 0)
-
-        x = np.r_[0.125,0.375,0.75,0.125,0.375,0.125,0.375,0.75,0.125,0.375,0.125,0.375,0.125,0.375]
-        y = np.r_[0,0,0,0.5,0.5,1,1,1,0,0,0.5,0.5,1,1]
-        z = np.r_[0.25,0.25,0.5,0.25,0.25,0.25,0.25,0.5,0.75,0.75,0.75,0.75,0.75,0.75]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.Mr.gridFy).flatten()) == 0)
-
-    def test_gridFz(self):
-        x = np.r_[0.25,0.75,0.25,0.75]
-        y = np.r_[0.5,0.5,0.5,0.5]
-        z = np.r_[0,0,1.,1.]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.M.gridFz).flatten()) == 0)
-
-        x = np.r_[0.125,0.375,0.75,0.125,0.375,0.125,0.375,0.125,0.375,0.125,0.375,0.75,0.125,0.375]
-        y = np.r_[0.25,0.25,0.5,0.75,0.75,0.25,0.25,0.75,0.75,0.25,0.25,0.5,0.75,0.75]
-        z = np.r_[0,0,0,0,0,0.5,0.5,0.5,0.5,1,1,1,1,1]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.Mr.gridFz).flatten()) == 0)
-
-
-    def test_gridEx(self):
-        x = np.r_[0.25,0.75,0.25,0.75,0.25,0.75,0.25,0.75]
-        y = np.r_[0,0,1.,1.,0,0,1.,1.]
-        z = np.r_[0,0,0,0,1.,1.,1.,1.]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.M.gridEx).flatten()) == 0)
-
-        x = np.r_[0.125,0.375,0.75,0.125,0.375,0.125,0.375,0.75,0.125,0.375,0.125,0.375,0.125,0.375,0.125,0.375,0.75,0.125,0.375,0.125,0.375,0.75]
-        y = np.r_[0,0,0,0.5,0.5,1,1,1,0,0,0.5,0.5,1,1,0,0,0,0.5,0.5,1,1,1]
-        z = np.r_[0,0,0,0,0,0,0,0,0.5,0.5,0.5,0.5,0.5,0.5,1,1,1,1,1,1,1,1]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.Mr.gridEx).flatten()) == 0)
-
-    def test_gridEy(self):
-        x = np.r_[0,0.5,1,0,0.5,1]
-        y = np.r_[0.5,0.5,0.5,0.5,0.5,0.5]
-        z = np.r_[0,0,0,1.,1.,1.]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.M.gridEy).flatten()) == 0)
-
-        x = np.r_[0,0.25,0.5,1,0,0.25,0.5,0,0.25,0.5,0,0.25,0.5,0,0.25,0.5,1,0,0.25,0.5]
-        y = np.r_[0.25,0.25,0.25,0.5,0.75,0.75,0.75,0.25,0.25,0.25,0.75,0.75,0.75,0.25,0.25,0.25,0.5,0.75,0.75,0.75]
-        z = np.r_[0,0,0,0,0,0,0,0.5,0.5,0.5,0.5,0.5,0.5,1,1,1,1,1,1,1]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.Mr.gridEy).flatten()) == 0)
-
-    def test_gridEz(self):
-        x = np.r_[0,0.5,1,0,0.5,1]
-        y = np.r_[0,0,0,1.,1.,1.]
-        z = np.r_[0.5,0.5,0.5,0.5,0.5,0.5]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.M.gridEz).flatten()) == 0)
-
-        x = np.r_[0,0.25,0.5,1,0  ,0.25,0.5,0,0.25,0.5,1,0,0.25,0.5,0  ,0.25,0.5,0  ,0.25,0.5]
-        y = np.r_[0,0   ,0  ,0,0.5,0.5 ,0.5,1,1   ,1  ,1,0,0   ,0  ,0.5,0.5 ,0.5,1  ,1   ,1  ]
-        z = np.r_[0.25,0.25,0.25,0.5,0.25,0.25,0.25,0.25,0.25,0.25,0.5,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75,0.75]
-        self.assertTrue(np.linalg.norm((np.c_[x,y,z]-self.Mr.gridEz).flatten()) == 0)
-
-
-class TestQuadTreeObjects(unittest.TestCase):
-
-    def setUp(self):
-        self.M  = TreeMesh([2,1])
-        self.Mr = TreeMesh([2,1])
-        self.Mr.children[0,0].refine()
-        self.Mr.number()
-        # self.Mr.plotGrid(showIt=True)
-
-    def test_pointersM(self):
-        c0    = self.M.children[0,0]
-        c0fXm = c0.fXm
-        c0fXp = c0.fXp
-        c0fYm = c0.fYm
-        c0fYp = c0.fYp
-
-        c1    = self.M.children[1,0]
-        c1fXm = c1.fXm
-        c1fXp = c1.fXp
-        c1fYm = c1.fYm
-        c1fYp = c1.fYp
-
-        self.assertTrue(c0fXp is c1fXm)
-        self.assertTrue(c0fYp is not c1fYm)
-        self.assertTrue(c0fXm is not c1fXm)
-
-        self.assertTrue(c0fXm.area == 1)
-        self.assertTrue(c0fYm.area == 0.5)
-
-        self.assertTrue(c0.node1 is c1.node0)
-        self.assertTrue(c0.node3 is c1.node2)
-        self.assertTrue(self.M.nN == 6)
-
-
-    def test_pointersMr(self):
-        c0    = self.Mr.sortedCells[0]
-        c0fXm = c0.fXm
-        c0fXp = c0.fXp
-        c0fYm = c0.fYm
-        c0fYp = c0.fYp
-
-        c1    = self.Mr.sortedCells[1]
-        c1fXm = c1.fXm
-        c1fXp = c1.fXp
-        c1fYm = c1.fYm
-        c1fYp = c1.fYp
-
-        c2    = self.Mr.sortedCells[2]
-        c2fXm = c2.fXm
-        c2fXp = c2.fXp
-        c2fYm = c2.fYm
-        c2fYp = c2.fYp
-
-        c4    = self.Mr.sortedCells[4]
-        c4fXm = c4.fXm
-        c4fXp = c4.fXp
-        c4fYm = c4.fYm
-        c4fYp = c4.fYp
-
-        self.assertTrue(c0fXp is c1fXm)
-        self.assertTrue(c1fXp.node0 is c2fXm.node0)
-        self.assertTrue(c1fXp.node0 is c2fXm.node0)
-        self.assertTrue(c4fYm is c1fYp)
-        self.assertTrue(c4fXp.node1 is c2fXm.node1)
-        self.assertTrue(c4fXp.node0 is c1fYp.node1)
-        self.assertTrue(c0fXp.node1 is c4fYm.node0)
-
-        self.assertTrue(self.Mr.nN == 11)
-
-        self.assertTrue(np.all(c1fXp.node0.x0 == np.r_[0.5,0]))
-        self.assertTrue(np.all(c1fYp.node0.x0 == np.r_[0.25,0.5]))
-
-
-class TestQuadTreeMesh(unittest.TestCase):
-
-    def setUp(self):
-        M = TreeMesh([np.ones(x) for x in [3,2]])
-        for ii in range(1):
-            M.children[ii,ii].refine()
-        self.M = M
-        M.number()
-        # M.plotGrid(showIt=True)
-
-    def test_MeshSizes(self):
-        self.assertTrue(self.M.nC==9)
-        self.assertTrue(self.M.nF==25)
-        self.assertTrue(self.M.nFx==12)
-        self.assertTrue(self.M.nFy==13)
-        self.assertTrue(self.M.nE==25)
-        self.assertTrue(self.M.nEx==13)
-        self.assertTrue(self.M.nEy==12)
-
-    def test_gridCC(self):
-        x = np.r_[0.25,0.75,1.5,2.5,0.25,0.75,0.5,1.5,2.5]
-        y = np.r_[0.25,0.25,0.5,0.5,0.75,0.75,1.5,1.5,1.5]
-        self.assertTrue(np.linalg.norm((np.c_[x,y]-self.M.gridCC).flatten()) == 0)
-
-    def test_gridN(self):
-        x = np.r_[0,0.5,1,2,3,0,0.5,1,0,0.5,1,2,3,0,1,2,3]
-        y = np.r_[0,0,0,0,0,.5,.5,.5,1,1,1,1,1,2,2,2,2]
-        self.assertTrue(np.linalg.norm((np.c_[x,y]-self.M.gridN).flatten()) == 0)
-
-    def test_gridFx(self):
-        x = np.r_[0.0,0.5,1.0,2.0,3.0,0.0,0.5,1.0,0.0,1.0,2.0,3.0]
-        y = np.r_[0.25,0.25,0.25,0.5,0.5,0.75,0.75,0.75,1.5,1.5,1.5,1.5]
-        self.assertTrue(np.linalg.norm((np.c_[x,y]-self.M.gridFx).flatten()) == 0)
-
-    def test_gridFy(self):
-        x = np.r_[0.25,0.75,1.5,2.5,0.25,0.75,0.25,0.75,1.5,2.5,0.5,1.5,2.5]
-        y = np.r_[0,0,0,0,0.5,0.5,1,1,1,1,2,2,2]
-        self.assertTrue(np.linalg.norm((np.c_[x,y]-self.M.gridFy).flatten()) == 0)
-
-    def test_gridEx(self):
-        x = np.r_[0.25,0.75,1.5,2.5,0.25,0.75,0.25,0.75,1.5,2.5,0.5,1.5,2.5]
-        y = np.r_[0,0,0,0,0.5,0.5,1,1,1,1,2,2,2]
-        self.assertTrue(np.linalg.norm((np.c_[x,y]-self.M.gridEx).flatten()) == 0)
-
-    def test_gridEy(self):
-        x = np.r_[0.0,0.5,1.0,2.0,3.0,0.0,0.5,1.0,0.0,1.0,2.0,3.0]
-        y = np.r_[0.25,0.25,0.25,0.5,0.5,0.75,0.75,0.75,1.5,1.5,1.5,1.5]
-        self.assertTrue(np.linalg.norm((np.c_[x,y]-self.M.gridEy).flatten()) == 0)
-
-
-class SimpleOctreeOperatorTests(unittest.TestCase):
-
-    def setUp(self):
-        h1 = np.random.rand(5)
-        h2 = np.random.rand(7)
-        h3 = np.random.rand(3)
-        self.tM = TensorMesh([h1,h2,h3])
-        self.oM = TreeMesh([h1,h2,h3])
-        self.tM2 = TensorMesh([h1,h2])
-        self.oM2 = TreeMesh([h1,h2])
-
-    def test_faceDiv(self):
-        self.assertAlmostEqual((self.tM.faceDiv - self.oM.faceDiv).toarray().sum(), 0)
-        self.assertAlmostEqual((self.tM2.faceDiv - self.oM2.faceDiv).toarray().sum(), 0)
-
-    def test_nodalGrad(self):
-        self.assertAlmostEqual((self.tM.nodalGrad - self.oM.nodalGrad).toarray().sum(), 0)
-        self.assertAlmostEqual((self.tM2.nodalGrad - self.oM2.nodalGrad).toarray().sum(), 0)
-
-    def test_edgeCurl(self):
-        self.assertAlmostEqual((self.tM.edgeCurl - self.oM.edgeCurl).toarray().sum(), 0)
-        # self.assertAlmostEqual((self.tM2.edgeCurl - self.oM2.edgeCurl).toarray().sum(), 0)
-
-    def test_InnerProducts(self):
-        self.assertAlmostEqual((self.tM.getFaceInnerProduct() - self.oM.getFaceInnerProduct()).toarray().sum(), 0)
-        self.assertAlmostEqual((self.tM2.getFaceInnerProduct() - self.oM2.getFaceInnerProduct()).toarray().sum(), 0)
-        self.assertAlmostEqual((self.tM2.getEdgeInnerProduct() - self.oM2.getEdgeInnerProduct()).toarray().sum(), 0)
-        self.assertAlmostEqual((self.tM.getEdgeInnerProduct() - self.oM.getEdgeInnerProduct()).toarray().sum(), 0)
-
-
-if __name__ == '__main__':
-    unittest.main()

SimPEG/Tests/test_example_linear.py

@@ -1,13 +0,0 @@
-import unittest
-import sys
-from SimPEG.Examples import Linear
-import numpy as np
-
-class TestLinear(unittest.TestCase):
-
-    def test_running(self):
-        Linear.run(100, plotIt=False)
-        self.assertTrue(True)
-
-if __name__ == '__main__':
-    unittest.main()

SimPEG/Utils/SolverUtils.py

@@ -37,12 +37,20 @@ def SolverWrapD(fun, factorize=True, checkAccuracy=True, accuracyTol=1e-6):
         if len(b.shape) == 1 or b.shape[1] == 1:
             b = b.flatten()
             # Just one RHS
+
+            if b.dtype is np.dtype('O'):
+                b = b.astype(type(b[0]))
+
             if factorize:
                 X = self.solver.solve(b, **self.kwargs)
             else:
                 X = fun(self.A, b, **self.kwargs)
         else: # Multiple RHSs
+            if b.dtype is np.dtype('O'):
+                b = b.astype(type(b[0,0]))
+
             X = np.empty_like(b)
+
             for i in range(b.shape[1]):
                 if factorize:
                     X[:,i] = self.solver.solve(b[:,i])
@@ -110,9 +118,10 @@ def SolverWrapI(fun, checkAccuracy=True, accuracyTol=1e-5):
     return type(fun.__name__+'_Wrapped', (object,), {"__init__": __init__, "clean": clean, "__mul__": __mul__})
 
 
-Solver   = SolverWrapD(sp.linalg.spsolve, factorize=False)
-SolverLU = SolverWrapD(sp.linalg.splu, factorize=True)
-SolverCG = SolverWrapI(sp.linalg.cg)
+from scipy.sparse import linalg
+Solver   = SolverWrapD(linalg.spsolve, factorize=False)
+SolverLU = SolverWrapD(linalg.splu, factorize=True)
+SolverCG = SolverWrapI(linalg.cg)
 
 
 class SolverDiag(object):

SimPEG/Utils/__init__.py

@@ -7,4 +7,4 @@ from ipythonutils import easyAnimate as animate
 from CounterUtils import *
 import ModelBuilder
 import SolverUtils
-
+from coordutils import *

SimPEG/Utils/codeutils.py

@@ -3,10 +3,7 @@ import time
 import numpy as np
 from functools import wraps
 
-
-class SimPEGMetaClass(type):
-    def __new__(cls, name, bases, attrs):
-        return super(SimPEGMetaClass, cls).__new__(cls, name, bases, attrs)
+SimPEGMetaClass = type
 
 def memProfileWrapper(towrap, *funNames):
     """

SimPEG/Utils/coordutils.py

@@ -0,0 +1,62 @@
+import numpy as np
+from SimPEG.Utils import mkvc
+
+def rotationMatrixFromNormals(v0,v1,tol=1e-20):
+    """
+        Performs the minimum number of rotations to define a rotation from the direction indicated by the vector n0 to the direction indicated by n1.
+        The axis of rotation is n0 x n1
+        https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula
+
+        :param numpy.array v0: vector of length 3
+        :param numpy.array v1: vector of length 3
+        :param tol = 1e-20: tolerance. If the norm of the cross product between the two vectors is below this, no rotation is performed
+        :rtype: numpy.array, 3x3
+        :return: rotation matrix which rotates the frame so that n0 is aligned with n1
+
+    """
+
+    # ensure both n0, n1 are vectors of length 1
+    assert len(v0) == 3, "Length of n0 should be 3"
+    assert len(v1) == 3, "Length of n1 should be 3"
+
+    # ensure both are true normals
+    n0 = v0*1./np.linalg.norm(v0)
+    n1 = v1*1./np.linalg.norm(v1)
+
+    n0dotn1 = n0.dot(n1) 
+
+    # define the rotation axis, which is the cross product of the two vectors
+    rotAx = np.cross(n0,n1)
+
+    if np.linalg.norm(rotAx) < tol:
+        return np.eye(3,dtype=float)
+
+    rotAx *= 1./np.linalg.norm(rotAx)
+
+    cosT = n0dotn1/(np.linalg.norm(n0)*np.linalg.norm(n1))
+    sinT = np.sqrt(1.-n0dotn1**2)
+
+    ux = np.array([[0., -rotAx[2], rotAx[1]], [rotAx[2], 0., -rotAx[0]], [-rotAx[1], rotAx[0], 0.]],dtype=float)
+
+    return np.eye(3,dtype=float) + sinT*ux + (1.-cosT)*(ux.dot(ux))
+
+
+def rotatePointsFromNormals(XYZ,n0,n1,x0=np.r_[0.,0.,0.]):
+    """
+        rotates a grid so that the vector n0 is aligned with the vector n1
+
+        :param numpy.array n0: vector of length 3, should have norm 1
+        :param numpy.array n1: vector of length 3, should have norm 1
+        :param numpy.array x0: vector of length 3, point about which we perform the rotation 
+        :rtype: numpy.array, 3x3
+        :return: rotation matrix which rotates the frame so that n0 is aligned with n1
+    """
+
+    R = rotationMatrixFromNormals(n0, n1)
+
+    assert XYZ.shape[1] == 3, "Grid XYZ should be 3 wide"
+    assert len(x0) == 3, "x0 should have length 3"
+
+    X0 = np.ones([XYZ.shape[0],1])*mkvc(x0)
+
+    return (XYZ - X0).dot(R.T) + X0 # equivalent to (R*(XYZ - X0)).T + X0

SimPEG/Utils/interputils.py

@@ -124,13 +124,13 @@ if not _interpCython:
             ind_x1, ind_x2, wx1, wx2 = _interp_point_1D(x, locs[i, 0])
             ind_y1, ind_y2, wy1, wy2 = _interp_point_1D(y, locs[i, 1])
 
-            inds += [( ind_x1,  ind_y2),
-                     ( ind_x1,  ind_y1),
+            inds += [( ind_x1,  ind_y1),
+                     ( ind_x1,  ind_y2),
                      ( ind_x2,  ind_y1),
                      ( ind_x2,  ind_y2)]
 
-            vals += [wx1*wy2,
-                     wx1*wy1,
+            vals += [wx1*wy1,
+                     wx1*wy2,
                      wx2*wy1,
                      wx2*wy2]
 
@@ -152,8 +152,8 @@ if not _interpCython:
             ind_y1, ind_y2, wy1, wy2 = _interp_point_1D(y, locs[i, 1])
             ind_z1, ind_z2, wz1, wz2 = _interp_point_1D(z, locs[i, 2])
 
-            inds += [( ind_x1,  ind_y2,  ind_z1),
-                     ( ind_x1,  ind_y1,  ind_z1),
+            inds += [( ind_x1,  ind_y1,  ind_z1),
+                     ( ind_x1,  ind_y2,  ind_z1),
                      ( ind_x2,  ind_y1,  ind_z1),
                      ( ind_x2,  ind_y2,  ind_z1),
                      ( ind_x1,  ind_y1,  ind_z2),
@@ -161,8 +161,8 @@ if not _interpCython:
                      ( ind_x2,  ind_y1,  ind_z2),
                      ( ind_x2,  ind_y2,  ind_z2)]
 
-            vals += [wx1*wy2*wz1,
-                     wx1*wy1*wz1,
+            vals += [wx1*wy1*wz1,
+                     wx1*wy2*wz1,
                      wx2*wy1*wz1,
                      wx2*wy2*wz1,
                      wx1*wy1*wz2,

SimPEG/Utils/interputils_cython.pyx

@@ -71,12 +71,12 @@ def _interpmat2D(np.ndarray[np.float64_t, ndim=2] locs,
         ind_x1, ind_x2, wx1, wx2 = _interp_point_1D(x, locs[i, 0])
         ind_y1, ind_y2, wy1, wy2 = _interp_point_1D(y, locs[i, 1])
 
-        inds += [( ind_x1,  ind_y2),
-                 ( ind_x1,  ind_y1),
+        inds += [( ind_x1,  ind_y1),
+                 ( ind_x1,  ind_y2),
                  ( ind_x2,  ind_y1),
                  ( ind_x2,  ind_y2)]
 
-        vals += [wx1*wy2, wx1*wy1, wx2*wy1, wx2*wy2]
+        vals += [wx1*wy1, wx1*wy2, wx2*wy1, wx2*wy2]
 
     return inds, vals
 
@@ -98,8 +98,8 @@ def _interpmat3D(np.ndarray[np.float64_t, ndim=2] locs,
         ind_y1, ind_y2, wy1, wy2 = _interp_point_1D(y, locs[i, 1])
         ind_z1, ind_z2, wz1, wz2 = _interp_point_1D(z, locs[i, 2])
 
-        inds += [( ind_x1,  ind_y2,  ind_z1),
-                 ( ind_x1,  ind_y1,  ind_z1),
+        inds += [( ind_x1,  ind_y1,  ind_z1),
+                 ( ind_x1,  ind_y2,  ind_z1),
                  ( ind_x2,  ind_y1,  ind_z1),
                  ( ind_x2,  ind_y2,  ind_z1),
                  ( ind_x1,  ind_y1,  ind_z2),
@@ -107,8 +107,8 @@ def _interpmat3D(np.ndarray[np.float64_t, ndim=2] locs,
                  ( ind_x2,  ind_y1,  ind_z2),
                  ( ind_x2,  ind_y2,  ind_z2)]
 
-        vals += [wx1*wy2*wz1,
-                 wx1*wy1*wz1,
+        vals += [wx1*wy1*wz1,
+                 wx1*wy2*wz1,
                  wx2*wy1*wz1,
                  wx2*wy2*wz1,
                  wx1*wy1*wz2,

SimPEG/Utils/matutils.py

@@ -342,10 +342,10 @@ def invPropertyTensor(M, tensor, returnMatrix=False):
 
 
 def diagEst(matFun, n, k=None, approach='Probing'):
-    """ 
+    """
     Estimate the diagonal of a matrix, A. Note that the matrix may be a function which returns A times a vector.
 
-    Three different approaches have been implemented, 
+    Three different approaches have been implemented,
         1. Probing : uses cyclic permutations of vectors with ones and zeros (default)
         2. Ones : random +/- 1 entries
         3. Random : random vectors
@@ -362,7 +362,7 @@ def diagEst(matFun, n, k=None, approach='Probing'):
 
     if type(matFun).__name__=='ndarray':
         A = matFun
-        matFun = lambda v: A.dot(v) 
+        matFun = lambda v: A.dot(v)
 
     if k is None:
         k = np.floor(n/10.)
@@ -396,11 +396,62 @@ def diagEst(matFun, n, k=None, approach='Probing'):
 
     return d
 
+class Zero(object):
+    def __add__(self, v):return v
+    def __radd__(self, v):return v
+    def __iadd__(self, v):return v
+    def __sub__(self, v):return -v
+    def __rsub__(self, v):return v
+    def __isub__(self, v):return v
+    def __mul__(self, v):return self
+    def __rmul__(self, v):return self
+    def __div__(self, v): return self
+    def __truediv__(self, v): return self
+    def __rdiv__(self, v): raise ZeroDivisionError('Cannot divide by zero.')
+    def __pos__(self):return self
+    def __neg__(self):return self
+    def __lt__(self, v):return 0 < v
+    def __le__(self, v):return 0 <= v
+    def __eq__(self, v):return v == 0
+    def __ne__(self, v):return not (0 == v)
+    def __ge__(self, v):return 0 >= v
+    def __gt__(self, v):return 0 > v
+
+class Identity(object):
+    _positive = True
+    def __init__(self, positive=True):
+        self._positive = positive is True
+
+    def __pos__(self):return self
+    def __neg__(self):return Identity(not self._positive)
+
+    def __add__(self, v):
+        if sp.issparse(v):
+            return v + speye(v.shape[0]) if self._positive else v - speye(v.shape[0])
+        return v + 1 if self._positive else v - 1
+    def __radd__(self, v):
+        return self.__add__(v)
+
+    def __sub__(self, v): return self+-v
+    def __rsub__(self, v):return -self+v
+
+    def __mul__(self, v): return v if self._positive else -v
+    def __rmul__(self, v):return v if self._positive else -v
+
+    def __div__(self, v):
+        if sp.issparse(v): raise NotImplementedError('Sparse arrays not divisibile.')
+        return 1/v if self._positive else -1/v
+    def __truediv__(self, v):
+        if sp.issparse(v): raise NotImplementedError('Sparse arrays not divisibile.')
+        return 1.0/v if self._positive else -1.0/v
+    def __rdiv__(self, v):
+        return v if self._positive else -v
+
+    def __lt__(self, v):return 1 <  v if self._positive else -1 <  v
+    def __le__(self, v):return 1 <= v if self._positive else -1 <= v
+    def __eq__(self, v):return v == 1 if self._positive else v == -1
+    def __ne__(self, v):return (not (1 == v))if self._positive else (not (-1 == v))
+    def __ge__(self, v):return 1 >= v if self._positive else -1 >= v
+    def __gt__(self, v):return 1 >  v if self._positive else -1 >  v
 
-from scipy.sparse.linalg import LinearOperator
 
-class SimPEGLinearOperator(LinearOperator):
-    """Extends scipy.sparse.linalg.LinearOperator to have a .T function."""
-    @property
-    def T(self):
-        return self.__class__((self.shape[1],self.shape[0]),self.rmatvec,rmatvec=self.matvec,matmat=self.matmat)

SimPEG/Utils/meshutils.py

@@ -149,7 +149,7 @@ def readUBCTensorModel(fileName, mesh):
 
         Input:
         :param fileName, path to the UBC GIF mesh file to read
-        :param mesh, TensorMesh object, mesh that coresponds to the model 
+        :param mesh, TensorMesh object, mesh that coresponds to the model
 
         Output:
         :return numpy array, model with TensorMesh ordered
@@ -170,7 +170,7 @@ def writeUBCTensorMesh(fileName, mesh):
 
         :param str fileName: File to write to
         :param simpeg.Mesh.TensorMesh mesh: The mesh
-        
+
     """
     assert mesh.dim == 3
     s = ''
@@ -216,7 +216,7 @@ def readVTRFile(fileName):
         Output:
         :return SimPEG TensorMesh object
         :return SimPEG model dictionary
-        
+
     """
     # Import
     from vtk import vtkXMLRectilinearGridReader as vtrFileReader
@@ -324,56 +324,56 @@ def ExtractCoreMesh(xyzlim, mesh, meshType='tensor'):
         Extracts Core Mesh from Global mesh
         xyzlim: 2D array [ndim x 2]
         mesh: SimPEG mesh
-        This function ouputs: 
+        This function ouputs:
             - actind: corresponding boolean index from global to core
-            - meshcore: core SimPEG mesh  
+            - meshcore: core SimPEG mesh
         Warning: 1D and 2D has not been tested
     """
     from SimPEG import Mesh
     if mesh.dim ==1:
         xyzlim = xyzlim.flatten()
         xmin, xmax = xyzlim[0], xyzlim[1]
-        
-        xind = np.logical_and(mesh.vectorCCx>xmin, mesh.vectorCCx<xmax)        
-        
+
+        xind = np.logical_and(mesh.vectorCCx>xmin, mesh.vectorCCx<xmax)
+
         xc = mesh.vectorCCx[xind]
 
         hx = mesh.hx[xind]
-        
+
         x0 = [xc[0]-hx[0]*0.5, yc[0]-hy[0]*0.5]
-        
+
         meshCore = Mesh.TensorMesh([hx, hy] ,x0=x0)
-        
+
         actind = (mesh.gridCC[:,0]>xmin) & (mesh.gridCC[:,0]<xmax)
-        
+
     elif mesh.dim ==2:
         xmin, xmax = xyzlim[0,0], xyzlim[0,1]
         ymin, ymax = xyzlim[1,0], xyzlim[1,1]
 
         yind = np.logical_and(mesh.vectorCCy>ymin, mesh.vectorCCy<ymax)
-        zind = np.logical_and(mesh.vectorCCz>zmin, mesh.vectorCCz<zmax)        
+        zind = np.logical_and(mesh.vectorCCz>zmin, mesh.vectorCCz<zmax)
 
         xc = mesh.vectorCCx[xind]
         yc = mesh.vectorCCy[yind]
 
         hx = mesh.hx[xind]
         hy = mesh.hy[yind]
-        
+
         x0 = [xc[0]-hx[0]*0.5, yc[0]-hy[0]*0.5]
-        
+
         meshCore = Mesh.TensorMesh([hx, hy] ,x0=x0)
-        
+
         actind = (mesh.gridCC[:,0]>xmin) & (mesh.gridCC[:,0]<xmax) \
                & (mesh.gridCC[:,1]>ymin) & (mesh.gridCC[:,1]<ymax) \
-        
+
     elif mesh.dim==3:
         xmin, xmax = xyzlim[0,0], xyzlim[0,1]
         ymin, ymax = xyzlim[1,0], xyzlim[1,1]
         zmin, zmax = xyzlim[2,0], xyzlim[2,1]
-        
+
         xind = np.logical_and(mesh.vectorCCx>xmin, mesh.vectorCCx<xmax)
         yind = np.logical_and(mesh.vectorCCy>ymin, mesh.vectorCCy<ymax)
-        zind = np.logical_and(mesh.vectorCCz>zmin, mesh.vectorCCz<zmax)        
+        zind = np.logical_and(mesh.vectorCCz>zmin, mesh.vectorCCz<zmax)
 
         xc = mesh.vectorCCx[xind]
         yc = mesh.vectorCCy[yind]
@@ -382,19 +382,19 @@ def ExtractCoreMesh(xyzlim, mesh, meshType='tensor'):
         hx = mesh.hx[xind]
         hy = mesh.hy[yind]
         hz = mesh.hz[zind]
-        
+
         x0 = [xc[0]-hx[0]*0.5, yc[0]-hy[0]*0.5, zc[0]-hz[0]*0.5]
-        
+
         meshCore = Mesh.TensorMesh([hx, hy, hz] ,x0=x0)
-        
+
         actind = (mesh.gridCC[:,0]>xmin) & (mesh.gridCC[:,0]<xmax) \
                & (mesh.gridCC[:,1]>ymin) & (mesh.gridCC[:,1]<ymax) \
                & (mesh.gridCC[:,2]>zmin) & (mesh.gridCC[:,2]<zmax)
-                
+
     else:
         raise(Exception("Not implemented!"))
-    
-    
+
+
     return actind, meshCore
 
 

SimPEG/__init__.py

@@ -15,7 +15,7 @@ import Directives
 import Inversion
 import Tests
 
-__version__   = '0.1.3'
+__version__   = '0.1.4'
 __author__    = 'Rowan Cockett'
 __license__   = 'MIT'
 __copyright__ = 'Copyright 2014 Rowan Cockett'

docs/api_Examples.rst

@@ -3,8 +3,15 @@
 Examples
 ********
 
-Forward problem
-===============
+.. toctree::
+    :maxdepth: 1
+    :glob:
+
+    examples/*
+
+
+External Notebooks
+==================
 
 * `Example 1: Direct Current <http://www.seogi.me/s/notebooks/DCEx.html>`_
 * `Example 2: Seismic-Acoustic <http://www.seogi.me/s/notebooks/SeismicEx.html>`_

docs/api_Mesh.rst

@@ -23,23 +23,9 @@ the implementations.
 
 .. plot::
 
-    from SimPEG import Mesh, Utils, np
-    import matplotlib.pyplot as plt
-    sz = [10,10]
-    tM = Mesh.TensorMesh(sz)
-    qM = Mesh.TreeMesh(sz)
-    qM.refine(lambda X: 1 if np.sqrt(((X-0.5)**2).sum()) < 0.3 else 0)
-    rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz,'rotate'))
+    from SimPEG import Examples
+    Examples.Mesh_ThreeMeshes.run()
 
-    fig, axes = plt.subplots(1,3,figsize=(14,5))
-    opts = {}
-    tM.plotGrid(ax=axes[0], **opts)
-    axes[0].set_title('TensorMesh')
-    qM.plotGrid(ax=axes[1], **opts)
-    axes[1].set_title('TreeMesh')
-    rM.plotGrid(ax=axes[2], **opts)
-    axes[2].set_title('CurvilinearMesh')
-    plt.show()
 
 
 Variable Locations and Terminology

docs/api_Tests.rst

@@ -3,6 +3,6 @@
 Testing SimPEG
 ==============
 
-.. automodule:: SimPEG.Tests.TestUtils
+.. automodule:: SimPEG.Tests
     :members:
     :undoc-members:

docs/conf.py

@@ -51,9 +51,9 @@ copyright = u'2013, SimPEG Developers'
 # built documents.
 #
 # The short X.Y version.
-version = '0.1.3'
+version = '0.1.4'
 # The full version, including alpha/beta/rc tags.
-release = '0.1.3'
+release = '0.1.4'
 
 # The language for content autogenerated by Sphinx. Refer to documentation
 # for a list of supported languages.

docs/em/api_FDEM.rst

@@ -0,0 +1,159 @@
+.. _api_FDEM:
+
+.. math::
+    \renewcommand{\div}{\nabla\cdot\,}
+    \newcommand{\grad}{\vec \nabla}
+    \newcommand{\curl}{{\vec \nabla}\times\,}
+
+
+Frequency Domain Electromagnetics
+*********************************
+
+Electromagnetic (EM) geophysical methods are used in a variety of applications from resource exploration, including for hydrocarbons and minerals, to environmental applications, such as groundwater monitoring. The primary physical property of interest in EM is electrical conductivity, which describes the ease with which electric current flows through a material.
+
+
+Background
+==========
+
+Electromagnetic phenomena are governed by Maxwell's equations. They describe the behavior of EM fields and fluxes. Electromagnetic theory for geophysical applications by Ward and Hohmann (1988) is a highly recommended resource on this topic.
+
+Fourier Transform Convention
+----------------------------
+In order to examine Maxwell's equations in the frequency domain, we must first define our choice of harmonic time-dependence by choosing a Fourier transform convention. We use the \\(e^{i \\omega t} \\) convention, so we define our Fourier Transform pair as
+
+.. math ::
+	F(\omega) = \int_{-\infty}^{\infty} f(t) e^{- i \omega t} dt \\
+
+	f(t) = \frac{1}{2\pi}\int_{-\infty}^{\infty} F(\omega) e^{i \omega t} d \omega
+
+where \\(\\omega\\) is angular frequency, \\(t\\) is time, \\(F(\\omega)\\) is the function defined in the frequency domain and \\(f(t)\\) is the function defined in the time domain.
+
+
+Maxwell's Equations
+===================
+In the frequency domain, Maxwell's equations are given by
+
+.. math ::
+	\curl \vec{E} = - i \omega \vec{B} \\
+
+	\curl \vec{H} = \vec{J} + i \omega \vec{D} + \vec{S} \\
+
+	\div \vec{B} = 0 \\
+
+	\div \vec{D} = \rho_f
+
+where:
+
+	- \\(\\vec{E}\\) : electric field (\\(V/m\\))
+	- \\(\\vec{H}\\) : magnetic field (\\(A/m\\))
+	- \\(\\vec{B}\\) : magnetic flux density (\\(Wb/m^2\\))
+	- \\(\\vec{D}\\) : electric displacement / electric flux density (\\(C/m^2\\))
+	- \\(\\vec{J}\\) : electric current density (\\(A/m^2\\))
+	- \\(\\rho_f\\) : free charge density
+
+The source term is \\(\\vec{S}\\)
+
+
+Constitutive Relations
+----------------------
+The fields and fluxes are related through the constitutive relations. At each frequency, they are given by
+
+.. math ::
+	\vec{J} = \sigma \vec{E} \\
+
+	\vec{B} = \mu \vec{H} \\
+
+	\vec{D} = \varepsilon \vec{E}
+
+where:
+
+- \\(\\sigma\\) : electrical conductivity \\(S/m\\)
+- \\(\\mu\\) : magnetic permeability \\(H/m\\)
+- \\(\\varepsilon\\) : dielectric permittivity \\(F/m\\)
+
+\\(\\sigma\\), \\(\\mu\\), \\(\\varepsilon\\) are physical properties which depend on the material. \\(\\sigma\\) describes how easily electric current passes through a material, \\(\\mu\\) describes how easily a material is magnetized, and \\(\\varepsilon\\) describes how easily a material is electrically polarized. In most geophysical applications of EM, \\(\\sigma\\) is the the primary physical property of interest, and \\(\\mu\\), \\(\\varepsilon\\) are assumed to have their free-space values \\(\\mu_0 = 4\\pi \\times 10^{-7} H/m \\), \\(\\varepsilon_0 = 8.85 \\times 10^{-12} F/m\\)
+
+
+Quasi-static Approximation
+--------------------------
+
+For the frequency range typical of most geophysical surveys, the contribution of the electric displacement is negligible compared to the electric current density. In this case, we use the Quasi-static approximation and assume that this term can be neglected, giving
+
+.. math ::
+	\nabla \times \vec{E} = -i \omega \vec{B} \\
+	\nabla \times \vec{H} = \vec{J} + \vec{S}
+
+
+Implementation in SimPEG.EM
+===========================
+
+We consider two formulations in SimPEG.EM, both first-order and both in terms of one field and one flux. We allow for the definition of magnetic and electric sources (see for example: Ward and Hohmann, starting on page 144). The E-B formulation is in terms of the electric field and the magnetic flux:
+
+.. math ::
+	\nabla \times \vec{E} + i \omega \vec{B} = \vec{S}_m \\
+	\nabla \times \mu^{-1} \vec{B} - \sigma \vec{E} = \vec{S}_e
+
+The H-J formulation is in terms of the current density and the magnetic field:
+
+.. math ::
+	\nabla \times \sigma^{-1} \vec{J} + i \omega \mu \vec{H} = \vec{S}_m \\
+	\nabla \times \vec{H} - \vec{J} = \vec{S}_e
+
+
+Discretizing
+------------
+For both formulations, we use a finite volume discretization
+and discretize fields on cell edges, fluxes on cell faces and
+physical properties in cell centers. This is particularly
+important when using symmetry to reduce the dimensionality of a problem
+(for instance on a 2D CylMesh, there are \\(r\\), \\(z\\) faces and \\(\\theta\\) edges)
+
+.. figure:: ../images/finitevolrealestate.png
+	:align: center
+	:scale: 60 %
+
+For the two formulations, the discretization of the physical properties, fields and fluxes are summarized below.
+
+.. figure:: ../images/ebjhdiscretizations.png
+	:align: center
+	:scale: 60 %
+
+Note that resistivity is the inverse of conductivity, \\(\\rho = \\sigma^{-1}\\).
+
+
+E-B Formulation:
+****************
+
+.. math ::
+	\mathbf{C} \mathbf{e} + i \omega \mathbf{b} = \mathbf{s_m} \\
+	\mathbf{C^T} \mathbf{M^f_{\mu^{-1}}} \mathbf{b} - \mathbf{M^e_\sigma} \mathbf{e} = \mathbf{M^e} \mathbf{s_e}
+
+H-J Formulation:
+****************
+
+.. math ::
+	\mathbf{C^T} \mathbf{M^f_\rho} \mathbf{j} + i \omega \mathbf{M^e_\mu} \mathbf{h} = \mathbf{M^e} \mathbf{s_m} \\
+	\mathbf{C} \mathbf{h} - \mathbf{j} = \mathbf{s_e}
+
+
+.. Forward Problem
+.. ===============
+
+.. Inverse Problem
+.. ===============
+
+API
+===
+.. automodule:: SimPEG.EM.FDEM.FDEM
+    :show-inheritance:
+    :members:
+    :undoc-members:
+
+
+FDEM Survey
+-----------
+
+.. automodule:: SimPEG.EM.FDEM.SurveyFDEM
+    :show-inheritance:
+    :members:
+    :undoc-members:

docs/em/api_TDEM.rst

@@ -0,0 +1,88 @@
+.. _api_TDEM:
+
+
+.. math::
+
+    \renewcommand{\div}{\nabla\cdot\,}
+    \newcommand{\grad}{\vec \nabla}
+    \newcommand{\curl}{{\vec \nabla}\times\,}
+    \newcommand {\J}{{\vec J}}
+    \renewcommand{\H}{{\vec H}}
+    \newcommand {\E}{{\vec E}}
+    \newcommand{\dcurl}{{\mathbf C}}
+    \newcommand{\dgrad}{{\mathbf G}}
+    \newcommand{\Acf}{{\mathbf A_c^f}}
+    \newcommand{\Ace}{{\mathbf A_c^e}}
+    \renewcommand{\S}{{\mathbf \Sigma}}
+    \newcommand{\St}{{\mathbf \Sigma_\tau}}
+    \newcommand{\T}{{\mathbf T}}
+    \newcommand{\Tt}{{\mathbf T_\tau}}
+    \newcommand{\diag}[1]{\,{\sf diag}\left( #1 \right)}
+    \newcommand{\M}{{\mathbf M}}
+    \newcommand{\MfMui}{{\M^f_{\mu^{-1}}}}
+    \newcommand{\MeSig}{{\M^e_\sigma}}
+    \newcommand{\MeSigInf}{{\M^e_{\sigma_\infty}}}
+    \newcommand{\MeSigO}{{\M^e_{\sigma_0}}}
+    \newcommand{\Me}{{\M^e}}
+    \newcommand{\Mes}[1]{{\M^e_{#1}}}
+    \newcommand{\Mee}{{\M^e_e}}
+    \newcommand{\Mej}{{\M^e_j}}
+    \newcommand{\BigO}[1]{\mathcal{O}\bigl(#1\bigr)}
+    \newcommand{\bE}{\mathbf{E}}
+    \newcommand{\bH}{\mathbf{H}}
+    \newcommand{\B}{\vec{B}}
+    \newcommand{\D}{\vec{D}}
+    \renewcommand{\H}{\vec{H}}
+    \newcommand{\s}{\vec{s}}
+    \newcommand{\bfJ}{\bf{J}}
+    \newcommand{\vecm}{\vec m}
+    \renewcommand{\Re}{\mathsf{Re}}
+    \renewcommand{\Im}{\mathsf{Im}}
+    \renewcommand {\j}  { {\vec j} }
+    \newcommand {\h}  { {\vec h} }
+    \renewcommand {\b}  { {\vec b} }
+    \newcommand {\e}  { {\vec e} }
+    \newcommand {\c}  { {\vec c} }
+    \renewcommand {\d}  { {\vec d} }
+    \renewcommand {\u}  { {\vec u} }
+    \newcommand{\I}{\vec{I}}
+
+
+TDEM - B formulation
+====================
+
+.. automodule:: SimPEG.EM.TDEM.TDEM_b
+    :show-inheritance:
+    :members:
+    :undoc-members:
+
+
+Field Storage
+=============
+
+.. autoclass:: SimPEG.EM.TDEM.SurveyTDEM.FieldsTDEM
+    :show-inheritance:
+    :members:
+    :undoc-members:
+    :inherited-members:
+
+
+TDEM Survey Classes
+===================
+
+.. autoclass:: SimPEG.EM.TDEM.SurveyTDEM.SurveyTDEM
+    :show-inheritance:
+    :members:
+    :undoc-members:
+    :inherited-members:
+
+
+Base Classes
+============
+
+.. automodule:: SimPEG.EM.TDEM.BaseTDEM
+    :show-inheritance:
+    :members:
+    :undoc-members:
+    :inherited-members:
+

docs/em/api_TDEM_derivation.rst

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

docs/em/api_Utils.rst

@@ -0,0 +1,34 @@
+simpegEM Utilities
+******************
+
+SimPEG for EM provides a few EM specific utility codes,
+sources, and analytic functions.
+
+Analytic Functions - Time
+=========================
+
+.. automodule:: SimPEG.EM.Utils.Ana.TEM
+    :show-inheritance:
+    :members:
+    :undoc-members:
+    :inherited-members:
+
+
+Analytic Functions - Frequency
+==============================
+
+.. automodule:: SimPEG.EM.Utils.Ana.FEM
+    :show-inheritance:
+    :members:
+    :undoc-members:
+    :inherited-members:
+
+
+Sources
+=======
+
+.. automodule:: SimPEG.EM.Utils.Sources.magneticDipole
+    :show-inheritance:
+    :members:
+    :undoc-members:
+    :inherited-members:

docs/em/index.rst

@@ -0,0 +1,45 @@
+
+Electromagnetics
+================
+
+`SimPEG.EM` uses SimPEG as the framework for the forward and inverse
+electromagnetics geophysical problems.
+
+Time Domian Electromagnetics
+----------------------------
+
+.. toctree::
+   :maxdepth: 2
+
+    api_TDEM_derivation
+
+
+Code for Time Domian Electromagnetics
+-------------------------------------
+
+.. toctree::
+   :maxdepth: 2
+
+    api_TDEM
+
+Frequency Domian Electromagnetics
+---------------------------------
+
+.. toctree::
+   :maxdepth: 2
+
+   api_ForwardProblem
+   api_FDEM
+
+
+Utility Codes
+-------------
+
+.. toctree::
+   :maxdepth: 2
+
+   api_Utils
+
+
+
+

docs/examples/EM_FDEM_1D_Inversion.rst

@@ -0,0 +1,26 @@
+.. _examples_EM_FDEM_1D_Inversion:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+
+EM: FDEM: 1D: Inversion
+=======================
+
+Here we will create and run a FDEM 1D inversion.
+
+
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.EM_FDEM_1D_Inversion.run()
+
+.. literalinclude:: ../../SimPEG/Examples/EM_FDEM_1D_Inversion.py
+    :language: python
+    :linenos:

docs/examples/FLOW_Richards_1D_Celia1990.rst

@@ -0,0 +1,52 @@
+.. _examples_FLOW_Richards_1D_Celia1990:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+
+FLOW: Richards: 1D: Celia1990
+=============================
+
+There are two different forms of Richards equation that differ
+on how they deal with the non-linearity in the time-stepping term.
+
+The most fundamental form, referred to as the
+'mixed'-form of Richards Equation Celia1990_
+
+.. math::
+
+    \frac{\partial \theta(\psi)}{\partial t} - \nabla \cdot k(\psi) \nabla \psi - \frac{\partial k(\psi)}{\partial z} = 0
+    \quad \psi \in \Omega
+
+where \\(\\theta\\) is water content, and \\(\\psi\\) is pressure head.
+This formulation of Richards equation is called the
+'mixed'-form because the equation is parameterized in \\(\\psi\\)
+but the time-stepping is in terms of \\(\\theta\\).
+
+As noted in Celia1990_ the 'head'-based form of Richards
+equation can be written in the continuous form as:
+
+.. math::
+
+    \frac{\partial \theta}{\partial \psi}\frac{\partial \psi}{\partial t} - \nabla \cdot k(\psi) \nabla \psi - \frac{\partial k(\psi)}{\partial z} = 0 \quad \psi \in \Omega
+
+However, it can be shown that this does not conserve mass in the discrete formulation.
+
+Here we reproduce the results from Celia1990_ demonstrating the head-based formulation and the mixed-formulation.
+
+.. _Celia1990: http://www.webpages.uidaho.edu/ch/papers/Celia.pdf
+
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.FLOW_Richards_1D_Celia1990.run()
+
+.. literalinclude:: ../../SimPEG/Examples/FLOW_Richards_1D_Celia1990.py
+    :language: python
+    :linenos:

docs/examples/Forward_BasicDirectCurrent.rst

@@ -0,0 +1,21 @@
+.. _examples_Forward_BasicDirectCurrent:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+Forward BasicDirectCurrent
+==========================
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.Forward_BasicDirectCurrent.run()
+
+.. literalinclude:: ../../SimPEG/Examples/Forward_BasicDirectCurrent.py
+    :language: python
+    :linenos:

docs/examples/Inversion_Linear.rst

@@ -0,0 +1,26 @@
+.. _examples_Inversion_Linear:
+
+.. --------------------------------- ..
+..                                   ..
+..    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_Linear.run()
+
+.. literalinclude:: ../../SimPEG/Examples/Inversion_Linear.py
+    :language: python
+    :linenos:

docs/examples/Mesh_Basic_PlotImage.rst

@@ -0,0 +1,27 @@
+.. _examples_Mesh_Basic_PlotImage:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+
+Mesh: Basic: PlotImage
+======================
+
+You can use M.PlotImage to plot images on all of the Meshes.
+
+
+
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.Mesh_Basic_PlotImage.run()
+
+.. literalinclude:: ../../SimPEG/Examples/Mesh_Basic_PlotImage.py
+    :language: python
+    :linenos:

docs/examples/Mesh_Basic_Types.rst

@@ -0,0 +1,26 @@
+.. _examples_Mesh_Basic_Types:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+
+Mesh: Basic: Types
+==================
+
+Here we show SimPEG used to create three different types of meshes.
+
+
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.Mesh_Basic_Types.run()
+
+.. literalinclude:: ../../SimPEG/Examples/Mesh_Basic_Types.py
+    :language: python
+    :linenos:

docs/examples/Mesh_Operators_CahnHilliard.rst

@@ -0,0 +1,57 @@
+.. _examples_Mesh_Operators_CahnHilliard:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+
+Mesh: Operators: Cahn Hilliard
+==============================
+
+This example is based on the example in the FiPy_ library.
+Please see their documentation for more information about the Cahn-Hilliard equation.
+
+The "Cahn-Hilliard" equation separates a field \\( \\phi \\) into 0 and 1 with smooth transitions.
+
+.. math::
+
+    \frac{\partial \phi}{\partial t} = \nabla \cdot D \nabla \left( \frac{\partial f}{\partial \phi} - \epsilon^2 \nabla^2 \phi \right)
+
+Where \\( f \\) is the energy function \\( f = ( a^2 / 2 )\\phi^2(1 - \\phi)^2 \\)
+which drives \\( \\phi \\) towards either 0 or 1, this competes with the term
+\\(\\epsilon^2 \\nabla^2 \\phi \\) which is a diffusion term that creates smooth changes in \\( \\phi \\).
+The equation can be factored:
+
+.. math::
+
+    \frac{\partial \phi}{\partial t} = \nabla \cdot D \nabla \psi \\
+    \psi = \frac{\partial^2 f}{\partial \phi^2} (\phi - \phi^{\text{old}}) + \frac{\partial f}{\partial \phi} - \epsilon^2 \nabla^2 \phi
+
+Here we will need the derivatives of \\( f \\):
+
+.. math::
+
+    \frac{\partial f}{\partial \phi} = (a^2/2)2\phi(1-\phi)(1-2\phi)
+    \frac{\partial^2 f}{\partial \phi^2} = (a^2/2)2[1-6\phi(1-\phi)]
+
+The implementation below uses backwards Euler in time with an exponentially increasing time step.
+The initial \\( \\phi \\) is a normally distributed field with a standard deviation of 0.1 and mean of 0.5.
+The grid is 60x60 and takes a few seconds to solve ~130 times. The results are seen below, and you can see the
+field separating as the time increases.
+
+.. _FiPy: http://www.ctcms.nist.gov/fipy/examples/cahnHilliard/generated/examples.cahnHilliard.mesh2DCoupled.html
+
+
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.Mesh_Operators_CahnHilliard.run()
+
+.. literalinclude:: ../../SimPEG/Examples/Mesh_Operators_CahnHilliard.py
+    :language: python
+    :linenos:

docs/examples/Mesh_QuadTree_Creation.rst

@@ -0,0 +1,31 @@
+.. _examples_Mesh_QuadTree_Creation:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+
+Mesh: QuadTree: Creation
+========================
+
+You can give the refine method a function, which is evaluated on every cell
+of the TreeMesh.
+
+Occasionally it is useful to initially refine to a constant level
+(e.g. 3 in this 32x32 mesh). This means the function is first evaluated
+on an 8x8 mesh (2^3).
+
+
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.Mesh_QuadTree_Creation.run()
+
+.. literalinclude:: ../../SimPEG/Examples/Mesh_QuadTree_Creation.py
+    :language: python
+    :linenos:

docs/examples/Mesh_QuadTree_FaceDiv.rst

@@ -0,0 +1,26 @@
+.. _examples_Mesh_QuadTree_FaceDiv:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+
+Mesh: QuadTree: FaceDiv
+=======================
+
+
+
+
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.Mesh_QuadTree_FaceDiv.run()
+
+.. literalinclude:: ../../SimPEG/Examples/Mesh_QuadTree_FaceDiv.py
+    :language: python
+    :linenos:

docs/examples/Mesh_QuadTree_HangingNodes.rst

@@ -0,0 +1,31 @@
+.. _examples_Mesh_QuadTree_HangingNodes:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+
+Mesh: QuadTree: Hanging Nodes
+=============================
+
+You can give the refine method a function, which is evaluated on every cell
+of the TreeMesh.
+
+Occasionally it is useful to initially refine to a constant level
+(e.g. 3 in this 32x32 mesh). This means the function is first evaluated
+on an 8x8 mesh (2^3).
+
+
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.Mesh_QuadTree_HangingNodes.run()
+
+.. literalinclude:: ../../SimPEG/Examples/Mesh_QuadTree_HangingNodes.py
+    :language: python
+    :linenos:

docs/examples/Mesh_Tensor_Creation.rst

@@ -0,0 +1,43 @@
+.. _examples_Mesh_Tensor_Creation:
+
+.. --------------------------------- ..
+..                                   ..
+..    THIS FILE IS AUTO GENEREATED   ..
+..                                   ..
+..    SimPEG/Examples/__init__.py    ..
+..                                   ..
+.. --------------------------------- ..
+
+
+
+Mesh: Tensor: Creation
+======================
+
+For tensor meshes, there are some functions that can come
+in handy. For example, creating mesh tensors can be a bit time
+consuming, these can be created speedily by just giving numbers
+and sizes of padding. See the example below, that follows this
+notation::
+
+    h1 = (
+           (cellSize, numPad, [, increaseFactor]),
+           (cellSize, numCore),
+           (cellSize, numPad, [, increaseFactor])
+         )
+
+.. note::
+
+    You can center your mesh by passing a 'C' for the x0[i] position.
+    A 'N' will make the entire mesh negative, and a '0' (or a 0) will
+    make the mesh start at zero.
+
+
+
+.. plot::
+
+    from SimPEG import Examples
+    Examples.Mesh_Tensor_Creation.run()
+
+.. literalinclude:: ../../SimPEG/Examples/Mesh_Tensor_Creation.py
+    :language: python
+    :linenos:

docs/flow/index.rst

@@ -0,0 +1,47 @@
+.. _api_Richards:
+
+
+Richards Equation
+*****************
+
+There are two different forms of Richards equation that differ
+on how they deal with the non-linearity in the time-stepping term.
+
+The most fundamental form, referred to as the
+'mixed'-form of Richards Equation [Celia et al., 1990]
+
+.. math::
+
+    \frac{\partial \theta(\psi)}{\partial t} - \nabla \cdot k(\psi) \nabla \psi - \frac{\partial k(\psi)}{\partial z} = 0
+    \quad \psi \in \Omega
+
+where theta is water content, and psi is pressure head.
+This formulation of Richards equation is called the
+'mixed'-form because the equation is parameterized in psi
+but the time-stepping is in terms of theta.
+
+As noted in [Celia et al., 1990] the 'head'-based form of Richards
+equation can be written in the continuous form as:
+
+.. math::
+
+    \frac{\partial \theta}{\partial \psi}\frac{\partial \psi}{\partial t} - \nabla \cdot k(\psi) \nabla \psi - \frac{\partial k(\psi)}{\partial z} = 0
+    \quad \psi \in \Omega
+
+However, it can be shown that this does not conserve mass in the discrete formulation.
+
+
+Here we reproduce the results from Celia et al. (1990):
+
+.. plot::
+
+    from SimPEG.FLOW.Examples import Celia1990
+    Celia1990.run()
+
+Richards
+========
+
+.. automodule:: simpegFLOW.Richards.Empirical
+    :show-inheritance:
+    :members:
+    :undoc-members:

docs/index.rst

@@ -79,6 +79,15 @@ Utility Codes
    api_Tests
 
 
+Packages
+********
+
+.. toctree::
+   :maxdepth: 3
+
+   em/index
+   flow/index
+
 Developer's Documentation
 *************************
 

setup.py

@@ -5,10 +5,15 @@ SimPEG is a python package for simulation and gradient based
 parameter estimation in the context of geophysical applications.
 """
 
+import numpy as np
+
+import os
+import sys
+import subprocess
+
 from distutils.core import setup
 from setuptools import find_packages
-from Cython.Build import cythonize
-import numpy as np
+from distutils.extension import Extension
 
 CLASSIFIERS = [
 'Development Status :: 4 - Beta',
@@ -26,6 +31,44 @@ CLASSIFIERS = [
 'Natural Language :: English',
 ]
 
+args = sys.argv[1:]
+
+# Make a `cleanall` rule to get rid of intermediate and library files
+if "cleanall" in args:
+    print "Deleting cython files..."
+    # Just in case the build directory was created by accident,
+    # note that shell=True should be OK here because the command is constant.
+    subprocess.Popen("rm -rf build", shell=True, executable="/bin/bash")
+    subprocess.Popen("find . -name \*.c -type f -delete", shell=True, executable="/bin/bash")
+    subprocess.Popen("find . -name \*.so -type f -delete", shell=True, executable="/bin/bash")
+    # Now do a normal clean
+    sys.argv[sys.argv.index('cleanall')] = "clean"
+
+# We want to always use build_ext --inplace
+if args.count("build_ext") > 0 and args.count("--inplace") == 0:
+    sys.argv.insert(sys.argv.index("build_ext")+1, "--inplace")
+
+try:
+    from Cython.Build import cythonize
+    from Cython.Distutils import build_ext
+    cythonKwargs = dict(cmdclass={'build_ext': build_ext})
+    USE_CYTHON = True
+except Exception, e:
+    USE_CYTHON = False
+    cythonKwargs = dict()
+
+ext = '.pyx' if USE_CYTHON else '.c'
+
+cython_files = [
+                    "SimPEG/Utils/interputils_cython",
+                    "SimPEG/Mesh/TreeUtils"
+               ]
+extensions = [Extension(f, [f+ext]) for f in cython_files]
+
+if USE_CYTHON and "cleanall" not in args:
+    from Cython.Build import cythonize
+    extensions = cythonize(extensions)
+
 import os, os.path
 
 with open("README.rst") as f:
@@ -33,10 +76,11 @@ with open("README.rst") as f:
 
 setup(
     name = "SimPEG",
-    version = "0.1.3",
+    version = "0.1.4",
     packages = find_packages(),
     install_requires = ['numpy>=1.7',
-                        'scipy>=0.13'
+                        'scipy>=0.13',
+                        'Cython'
                        ],
     author = "Rowan Cockett",
     author_email = "rowan@3ptscience.com",
@@ -50,5 +94,6 @@ setup(
     platforms = ["Windows", "Linux", "Solaris", "Mac OS-X", "Unix"],
     use_2to3 = False,
     include_dirs=[np.get_include()],
-    ext_modules = cythonize('SimPEG/Utils/interputils_cython.pyx')
+    ext_modules = extensions,
+    **cythonKwargs
 )

tests/__init__.py

@@ -1,6 +1,3 @@
-from TestUtils import checkDerivative, Rosenbrock, OrderTest, getQuadratic
-
-
 if __name__ == '__main__':
     import os
     import glob

tests/base/__init__.py

@@ -0,0 +1,11 @@
+if __name__ == '__main__':
+    import os
+    import glob
+    import unittest
+    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/base/test_PropMaps.py

@@ -8,9 +8,9 @@ class MyPropMap(Maps.PropMap):
     mu    = Maps.Property("Mu", defaultVal=mu_0)
 
 class MyReciprocalPropMap(Maps.PropMap):
-    sigma = Maps.Property("Electrical Conductivity", defaultInvProp=True, propertyLink=('rho',   Maps.ReciprocalMap))
-    rho   = Maps.Property("Electrical Resistivity",                       propertyLink=('sigma', Maps.ReciprocalMap))
-    mu    = Maps.Property("Mu", defaultVal=mu_0, propertyLink=('mui',   Maps.ReciprocalMap))
+    sigma  = Maps.Property("Electrical Conductivity", defaultInvProp=True, propertyLink=('rho',   Maps.ReciprocalMap))
+    rho    = Maps.Property("Electrical Resistivity",                       propertyLink=('sigma', Maps.ReciprocalMap))
+    mu     = Maps.Property("Mu", defaultVal=mu_0,    propertyLink=('mui',  Maps.ReciprocalMap))
     mui    = Maps.Property("Mu", defaultVal=1./mu_0, propertyLink=('mu',   Maps.ReciprocalMap))
 
 

tests/base/test_maps.py

@@ -1,7 +1,6 @@
 import numpy as np
 import unittest
 from SimPEG import *
-from TestUtils import checkDerivative
 from scipy.sparse.linalg import dsolve
 
 TOL = 1e-14

tests/base/test_regularization.py

@@ -1,7 +1,6 @@
 import numpy as np
 import unittest
 from SimPEG import *
-from TestUtils import checkDerivative
 from scipy.sparse.linalg import dsolve
 import inspect
 
@@ -18,12 +17,16 @@ class RegularizationTests(unittest.TestCase):
             if not issubclass(r, Regularization.BaseRegularization):
                 continue
             # if 'Regularization' not in R: continue
-            print 'Check:', R
             mapping = r.mapPair(self.mesh2)
             reg = r(self.mesh2, mapping=mapping)
             m = np.random.rand(mapping.nP)
             reg.mref = m[:]*np.mean(m)
-            passed = checkDerivative(lambda m : [reg.eval(m), reg.evalDeriv(m)], m, plotIt=False)
+
+            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)