trial for secondary data

Conflicts:
	SimPEG/Problem.py

.travis.yml

@@ -33,7 +33,7 @@ before_install:
 
 # Install packages
 install:
-  - conda install --yes pip python=$TRAVIS_PYTHON_VERSION numpy scipy matplotlib cython ipython nose
+  - conda install --yes pip python=$TRAVIS_PYTHON_VERSION numpy scipy matplotlib cython ipython nose vtk
   - pip install nose-cov python-coveralls
 
   - git clone https://github.com/rowanc1/pymatsolver.git

SimPEG/Directives.py

@@ -206,17 +206,84 @@ class SaveOutputEveryIteration(_SaveEveryIteration):
         f.write(' %3d %1.4e %1.4e %1.4e %1.4e\n'%(self.opt.iter, self.invProb.beta, self.invProb.phi_d, self.invProb.phi_m, self.opt.f))
         f.close()
 
+class SaveOutputDictEveryIteration(_SaveEveryIteration):
+    """SaveOutputDictEveryIteration"""
+
+    def initialize(self):
+        print "SimPEG.SaveOutputDictEveryIteration will save your inversion progress as dictionary: '###-%s.npz'"%self.fileName
+
+    def endIter(self):
+        # Save the data.
+        ms = self.reg.Ws * ( self.reg.mapping * (self.invProb.curModel - self.reg.mref) )
+        phi_ms = 0.5*ms.dot(ms)
+        if self.reg.smoothModel == True:
+            mref = self.reg.mref
+        else:
+            mref = 0
+        mx = self.reg.Wx * ( self.reg.mapping * (self.invProb.curModel - mref) )
+        phi_mx = 0.5 * mx.dot(mx)
+        if self.prob.mesh.dim==2:
+            my = self.reg.Wy * ( self.reg.mapping * (self.invProb.curModel - mref) )
+            phi_my = 0.5 * my.dot(my)
+        else:
+            phi_my = 'NaN'
+        if self.prob.mesh.dim==3:
+            mz = self.reg.Wz * ( self.reg.mapping * (self.invProb.curModel - mref) )
+            phi_mz = 0.5 * mz.dot(mz)
+        else:
+            phi_mz = 'NaN'
+
+
+        # Save the file as a npz
+        np.savez('{:03d}-{:s}'.format(self.opt.iter,self.fileName), iter=self.opt.iter, beta=self.invProb.beta, phi_d=self.invProb.phi_d, phi_m=self.invProb.phi_m, phi_ms=phi_ms, phi_mx=phi_mx, phi_my=phi_my, phi_mz=phi_mz,f=self.opt.f, m=self.invProb.curModel,dpred=self.invProb.dpred)
 
 
 
-# class UpdateReferenceModel(Parameter):
+class update_IRLS(InversionDirective):
 
-#     mref0 = None
+     m = None
+     eps_min = None
+     factor = None
+     gamma = None
+     phi_m_last = None
      
-#     def nextIter(self):
-#         mref = getattr(self, 'm_prev', None)
-#         if mref is None:
-#             if self.debug: print 'UpdateReferenceModel is using mref0'
-#             mref = self.mref0
-#         self.m_prev = self.invProb.m_current
-#         return mref
+     def initialize(self):
+        
+         # Scale the regularization for changes in norm
+         if getattr(self, 'phi_m_last', None) is not None:
+             self.reg.gamma = 1.
+             phim_new = self.reg.eval(self.invProb.curModel)
+             self.gamma = self.phi_m_last / phim_new
+         
+         self.reg.gamma = self.gamma
+         
+     def endIter(self):
+         # Cool the threshold parameter 
+         if getattr(self, 'factor', None) is not None:
+             eps = self.reg.eps / self.factor
+             
+             if getattr(self, 'eps_min', None) is not None:
+                 self.reg.eps = np.max([self.eps_min,eps])
+             else:
+                 self.reg.eps = eps
+                 
+         
+         # Update the model used for the IRLS weights
+         if getattr(self, 'm', None) is None:
+             self.reg.m = self.invProb.curModel
+         
+         # Update the pre-conditioner
+         diagA = np.sum(self.prob.G**2.,axis=0) + self.invProb.beta*(self.reg.W.T*self.reg.W).diagonal() * (self.reg.mapping * np.ones(self.prob.mesh.nC))**2.
+         PC     = Utils.sdiag(diagA**-1.)
+
+         self.opt.approxHinv = PC
+         
+         phim_new = self.reg.eval(self.invProb.curModel)
+         self.reg.gamma = self.reg.gamma * self.invProb.phi_m_last / phim_new
+
+#==============================================================================
+#          import pylab as plt
+#          plt.figure()
+#          ax = plt.subplot(221)
+#          self.prob.mesh.plotSlice(self.invProb.curModel, ax = ax, normal = 'Z', ind=-5, clim = (0, 0.005))
+#==============================================================================

SimPEG/EM/FDEM/FDEM.py

@@ -50,7 +50,7 @@ class BaseFDEMProblem(BaseEMProblem):
             Srcs = self.survey.getSrcByFreq(freq)
             ftype = self._fieldType + 'Solution'
             F[Srcs, ftype] = sol
-
+            Ainv.clean()
         return F
 
     def Jvec(self, m, v, f=None):
@@ -89,6 +89,7 @@ class BaseFDEMProblem(BaseEMProblem):
 
                     Jv[src, rx] = P(Df_Dm)
 
+            Ainv.clean()
         return Utils.mkvc(Jv)
 
     def Jtvec(self, m, v, f=None):
@@ -140,6 +141,7 @@ class BaseFDEMProblem(BaseEMProblem):
                     else:
                         raise Exception('Must be real or imag')
             
+            ATinv.clean()
         return Jtv
 
     def getSourceTerm(self, freq):

SimPEG/EM/FDEM/SrcFDEM.py

@@ -277,10 +277,10 @@ class CircularLoop(BaseSrc):
             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)
+            a = MagneticLoopVectorPotential(self.loc, gridY, 'y', self.radius, mu=self.mu)
 
         else:
-            srcfct = MagneticDipoleVectorPotential
+            srcfct = MagneticLoopVectorPotential
             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)

SimPEG/EM/FDEM/SurveyFDEM.py

@@ -26,6 +26,13 @@ class Rx(SimPEG.Survey.BaseRx):
                     'byi':['b', 'Fy', 'imag'],
                     'bzi':['b', 'Fz', 'imag'],
 
+                    'bxr_sec':['bSecondary', 'Fx', 'real'],
+                    'byr_sec':['bSecondary', 'Fy', 'real'],
+                    'bzr_sec':['bSecondary', 'Fz', 'real'],
+                    'bxi_sec':['bSecondary', 'Fx', 'imag'],
+                    'byi_sec':['bSecondary', 'Fy', 'imag'],
+                    'bzi_sec':['bSecondary', 'Fz', 'imag'],
+
                     'jxr':['j', 'Fx', 'real'],
                     'jyr':['j', 'Fy', 'real'],
                     'jzr':['j', 'Fz', 'real'],
@@ -106,7 +113,7 @@ class Survey(SimPEG.Survey.BaseSurvey):
         SimPEG.Survey.BaseSurvey.__init__(self, **kwargs)
 
         _freqDict = {}
-        for src in srcList:
+        for src in self.srcList:
             if src.freq not in _freqDict:
                 _freqDict[src.freq] = []
             _freqDict[src.freq] += [src]

SimPEG/EM/TDEM/BaseTDEM.py

@@ -37,6 +37,14 @@ class BaseTDEMProblem(BaseTimeProblem, BaseEMProblem):
 
     _FieldsForward_pair = FieldsTDEM  #: used for the forward calculation only
 
+    waveformType = "STEPOFF"
+    current = None
+
+    def currentwaveform(self, wave):
+        self._timeSteps = np.diff(wave[:,0])
+        self.current = wave[:,1]
+        self.waveformType = "GENERAL"
+
     def fields(self, m):
         if self.verbose: print '%s\nCalculating fields(m)\n%s'%('*'*50,'*'*50)
         self.curModel = m

SimPEG/EM/TDEM/SurveyTDEM.py

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

SimPEG/Examples/DC_PseudoSection_Simulation.py

@@ -0,0 +1,179 @@
+from SimPEG import *
+import simpegDCIP as DC
+import scipy.interpolate as interpolation
+import matplotlib.pyplot as plt
+import time
+import re
+
+def run(loc=np.c_[[-50.,0.,-50.],[50.,0.,-50.]], sig=np.r_[1e-2,1e-1,1e-3], radi=np.r_[25.,25.], param = np.r_[30.,30.,5], stype = 'dpdp',  plotIt=True):
+    """
+    DC Forward Simulation
+    
+    Forward model conductive spheres in a half-space and plot a pseudo-section
+    
+    Created on Mon Feb 01 19:28:06 2016
+    
+    @fourndo
+    """
+    
+    # First we need to create a mesh and a model.
+    
+    # This is our mesh
+    dx    = 5.
+    
+    hxind = [(dx,15,-1.3), (dx, 75), (dx,15,1.3)]
+    hyind = [(dx,15,-1.3), (dx, 10), (dx,15,1.3)]
+    hzind = [(dx,15,-1.3),(dx, 15)]
+    
+    mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCN')
+    
+    
+    # Set background conductivity
+    model = np.ones(mesh.nC) * sig[0]
+    
+    # First anomaly
+    ind = Utils.ModelBuilder.getIndicesSphere(loc[:,0],radi[0],mesh.gridCC)
+    model[ind] = sig[1]
+    
+    # Second anomaly
+    ind = Utils.ModelBuilder.getIndicesSphere(loc[:,1],radi[1],mesh.gridCC)
+    model[ind] = sig[2]
+    
+    # Get index of the center
+    indy = int(mesh.nCy/2)
+
+    
+    # Plot the model for reference
+    # Define core mesh extent
+    xlim = 200
+    zlim = 125
+    
+    # Specify the survey type: "pdp" | "dpdp"
+    
+    
+    # Then specify the end points of the survey. Let's keep it simple for now and survey above the anomalies, top of the mesh
+    ends = [(-175,0),(175,0)]
+    ends = np.c_[np.asarray(ends),np.ones(2).T*mesh.vectorNz[-1]]
+    
+    # Snap the endpoints to the grid. Easier to create 2D section.
+    indx = Utils.closestPoints(mesh, ends )
+    locs = np.c_[mesh.gridCC[indx,0],mesh.gridCC[indx,1],np.ones(2).T*mesh.vectorNz[-1]]
+    
+    # We will handle the geometry of the survey for you and create all the combination of tx-rx along line
+    [Tx, Rx] = DC.gen_DCIPsurvey(locs, mesh, stype, param[0], param[1], param[2])
+    
+    # Define some global geometry
+    dl_len = np.sqrt( np.sum((locs[0,:] - locs[1,:])**2) ) 
+    dl_x = ( Tx[-1][0,1] - Tx[0][0,0] ) / dl_len
+    dl_y = ( Tx[-1][1,1] - Tx[0][1,0]  ) / dl_len
+    azm =  np.arctan(dl_y/dl_x)
+
+    #Set boundary conditions
+    mesh.setCellGradBC('neumann')
+    
+    # Define the differential operators needed for the DC problem
+    Div = mesh.faceDiv
+    Grad = mesh.cellGrad
+    Msig = Utils.sdiag(1./(mesh.aveF2CC.T*(1./model)))
+    
+    A = Div*Msig*Grad
+    
+    # Change one corner to deal with nullspace
+    A[0,0] = 1
+    A = sp.csc_matrix(A)
+    
+    # We will solve the system iteratively, so a pre-conditioner is helpful
+    # This is simply a Jacobi preconditioner (inverse of the main diagonal)
+    dA = A.diagonal()
+    P = sp.spdiags(1/dA,0,A.shape[0],A.shape[0])
+
+    # Now we can solve the system for all the transmitters
+    # We want to store the data
+    data = []
+    
+    # There is probably a more elegant way to do this, but we can just for-loop through the transmitters
+    for ii in range(len(Tx)):
+        
+        start_time = time.time() # Let's time the calculations
+        
+        #print("Transmitter %i / %i\r" % (ii+1,len(Tx)))
+        
+        # Select dipole locations for receiver
+        rxloc_M = np.asarray(Rx[ii][:,0:3])
+        rxloc_N = np.asarray(Rx[ii][:,3:])
+
+      
+        # For usual cases "dpdp" or "gradient"
+        if not re.match(stype,'pdp'): 
+            inds = Utils.closestPoints(mesh, np.asarray(Tx[ii]).T )
+            RHS = mesh.getInterpolationMat(np.asarray(Tx[ii]).T, 'CC').T*( [-1,1] / mesh.vol[inds] )   
+            
+        else: 
+            
+            # Create an "inifinity" pole
+            tx =  np.squeeze(Tx[ii][:,0:1])
+            tinf = tx + np.array([dl_x,dl_y,0])*dl_len*2
+            inds = Utils.closestPoints(mesh, np.c_[tx,tinf].T)
+            RHS = mesh.getInterpolationMat(np.asarray(Tx[ii]).T, 'CC').T*( [-1] / mesh.vol[inds] )  
+    
+    
+        # Iterative Solve
+        Ainvb = sp.linalg.bicgstab(P*A,P*RHS, tol=1e-5)
+    
+        # We now have the potential everywhere
+        phi = mkvc(Ainvb[0])
+        
+        # Solve for phi on pole locations
+        P1 = mesh.getInterpolationMat(rxloc_M, 'CC')
+        P2 = mesh.getInterpolationMat(rxloc_N, 'CC')
+            
+        # Compute the potential difference
+        dtemp = (P1*phi - P2*phi)*np.pi
+        
+        data.append( dtemp )     
+        print '\rTransmitter {0} of {1} -> Time:{2} sec'.format(ii,len(Tx),time.time()- start_time),
+        
+    print 'Transmitter {0} of {1}'.format(ii,len(Tx))
+    print 'Forward completed'
+    
+    
+    # Let's just convert the 3D format into 2D (distance along line) and plot
+    [Tx2d, Rx2d] = DC.convertObs_DC3D_to_2D(Tx,Rx)
+    
+
+    # Here is an example for the first tx-rx array
+    if plotIt:
+        fig = plt.figure()
+        ax = plt.subplot(2,1,1, aspect='equal')
+        mesh.plotSlice(np.log10(model), ax =ax, normal = 'Y', ind = indy,grid=True)
+        ax.set_title('E-W section at '+str(mesh.vectorCCy[indy])+' m')
+        plt.gca().set_aspect('equal', adjustable='box')
+
+        plt.scatter(Tx[0][0,:],Tx[0][2,:],s=40,c='g', marker='v')
+        plt.scatter(Rx[0][:,0::3],Rx[0][:,2::3],s=40,c='y')
+        plt.xlim([-xlim,xlim])
+        plt.ylim([-zlim,mesh.vectorNz[-1]+dx])
+        
+        
+        ax = plt.subplot(2,1,2, aspect='equal')   
+        
+        # Plot the location of the spheres for reference
+        circle1=plt.Circle((loc[0,0]-Tx[0][0,0],loc[2,0]),radi[0],color='w',fill=False, lw=3)
+        circle2=plt.Circle((loc[0,1]-Tx[0][0,0],loc[2,1]),radi[1],color='k',fill=False, lw=3)
+        ax.add_artist(circle1)
+        ax.add_artist(circle2)  
+        
+        # Add the speudo section
+        DC.plot_pseudoSection(Tx2d,Rx2d,data,mesh.vectorNz[-1],stype)
+        
+        plt.scatter(Tx2d[0][:],Tx[0][2,:],s=40,c='g', marker='v')
+        plt.scatter(Rx2d[0][:],Rx[0][:,2::3],s=40,c='y')
+        plt.plot(np.r_[Tx2d[0][0],Rx2d[-1][-1,-1]],np.ones(2)*mesh.vectorNz[-1], color='k')
+        plt.ylim([-zlim,mesh.vectorNz[-1]+dx])
+        
+        plt.show()
+        
+        return fig, ax
+        
+if __name__ == '__main__':
+    run()

SimPEG/Exceptions.py

@@ -0,0 +1,13 @@
+
+
+class SimPEGException(Exception):
+
+    def __init__(self, reason=''):
+        self.reason = reason
+
+    def __str__(self):
+        return '%s: %s' %(self.__class__.__name__,  self.reason)
+
+
+class PairingException(SimPEGException):
+    pass

SimPEG/InvProblem.py

@@ -66,8 +66,8 @@ class BaseInvProblem(object):
         self.curModel = m0
 
         print """SimPEG.InvProblem is setting bfgsH0 to the inverse of the eval2Deriv.
-                    ***Done using same solver as the problem***"""
-        self.opt.bfgsH0 = self.prob.Solver(self.reg.eval2Deriv(self.curModel))
+                    ***Done using same Solver and solverOpts as the problem***"""
+        self.opt.bfgsH0 = self.prob.Solver(self.reg.eval2Deriv(self.curModel), **self.prob.solverOpts)
 
     @property
     def warmstart(self):

SimPEG/Maps.py

@@ -4,27 +4,32 @@ from Tests import checkDerivative
 from PropMaps import PropMap, Property
 from numpy.polynomial import polynomial
 from scipy.interpolate import UnivariateSpline
+from scipy.spatial import cKDTree
 
 class IdentityMap(object):
     """
     SimPEG Map
 
     """
-
     __metaclass__ = Utils.SimPEGMetaClass
 
-    mesh = None      #: A SimPEG Mesh
-
-    def __init__(self, mesh, **kwargs):
+    def __init__(self, mesh=None, nP=None, **kwargs):
         Utils.setKwargs(self, **kwargs)
+
+        if nP is not None:
+            assert type(nP) in [int, long], ' Number of parameters must be an integer.'
+
         self.mesh = mesh
+        self._nP  = nP
 
     @property
     def nP(self):
         """
             :rtype: int
-            :return: number of parameters in the model
+            :return: number of parameters that the mapping accepts
         """
+        if self._nP is not None:
+            return self._nP
         if self.mesh is None:
             return '*'
         return self.mesh.nC
@@ -32,11 +37,15 @@ class IdentityMap(object):
     @property
     def shape(self):
         """
-            The default shape is (mesh.nC, nP).
+            The default shape is (mesh.nC, nP) if the mesh is defined.
+            If this is a meshless mapping (i.e. nP is defined independently)
+            the shape will be the the shape (nP,nP).
 
             :rtype: (int,int)
             :return: shape of the operator as a tuple
         """
+        if self._nP is not None:
+            return (self.nP, self.nP)
         if self.mesh is None:
             return ('*', self.nP)
         return (self.mesh.nC, self.nP)
@@ -113,11 +122,12 @@ class IdentityMap(object):
             if not self.shape[1] == '*' and not self.shape[1] == val.shape[0]:
                 raise ValueError('Dimension mismatch in %s and np.ndarray%s.' % (str(self), str(val.shape)))
             return self._transform(val)
-        raise Exception('Unrecognized data type to multiply. Try a map or a numpy.ndarray!')
+        raise Exception('Unrecognized data type to multiply. Try a map or a numpy.ndarray! Not a %s'%type(val))
 
     def __str__(self):
         return "%s(%s,%s)" % (self.__class__.__name__, self.shape[0], self.shape[1])
 
+
 class ComboMap(IdentityMap):
     """Combination of various maps."""
 
@@ -449,6 +459,89 @@ class Mesh2Mesh(IdentityMap):
         return self.P
 
 
+class Mesh2MeshTopo(IdentityMap):
+    """
+        Takes a model on one mesh are translates it to another mesh
+        with consideration of topography
+
+    """
+    tree = None
+    nIterpPts = 6
+    P = None #: The CSR projection matrix.
+
+    def __init__(self, meshes, actinds, **kwargs):
+        Utils.setKwargs(self, **kwargs)
+
+        assert type(meshes) is list, "meshes must be a list of two meshes"
+        assert len(meshes) == 2, "meshes must be a list of two meshes"
+        assert type(actinds) is list, "actinds must be a list of two meshes"
+        assert len(actinds) == 2, "actinds must be a list of two meshes"
+        assert meshes[0].dim == meshes[1].dim, """The two meshes must be the same dimension"""
+
+        self.mesh  = meshes[0]
+        self.mesh2 = meshes[1]
+        self.actind = actinds[0]
+        self.actind2 = actinds[1]
+        self._createProjection()
+
+        # Old version using SimPEG interpolation
+        # self.P = self.mesh2.getInterpolationMat(self.mesh.gridCC,'CC',zerosOutside=True)
+
+    def genActiveindfromTopo(mesh, xyztopo):
+        #TODO: This possibly needs to be improved use vtk(?)
+        if mesh.dim==3:
+            nCxy = mesh.nCx*mesh.nCy
+            Zcc = mesh.gridCC[:,2].reshape((nCxy, mesh.nCz), order='F')
+            Ftopo = NearestNDInterpolator(xyztopo[:,:2], xyztopo[:,2])
+            XY = Utils.ndgrid(mesh.vectorCCx, mesh.vectorCCy)
+            XY.shape
+            topo = Ftopo(XY)
+            actind = []
+            for ixy in range(nCxy):
+                actind.append(topo[ixy] <= Zcc[ixy,:])
+        else:
+            raise NotImplementedError("Only 3D is working")
+
+        return Utils.mkvc(np.vstack(actind))
+
+    #Question .. is it only generated once?
+    def _createProjection(self):
+        """
+            KD Tree interpolation onto the active cells.
+        """
+        if self.tree==None:
+            self.tree = cKDTree(zip(self.mesh.gridCC[self.actind,0], self.mesh.gridCC[self.actind,1], self.mesh.gridCC[self.actind,2]))
+        d, inds = self.tree.query(zip(self.mesh2.gridCC[self.actind2,0],self.mesh2.gridCC[self.actind2,1],self.mesh2.gridCC[self.actind2,2]), k=self.nIterpPts)
+        # Not sure consideration of the volume ...
+        # vol = np.zeros((self.actind2.sum(), self.nIterpPts))
+        # for i in range(self.nIterpPts):
+        #     vol[:,i] = self.mesh.vol[inds[:,i]]
+        w = 1. / d**2
+        w = Utils.sdiag(1./np.sum(w, axis=1)) * (w)
+        I = Utils.mkvc(np.arange(inds.shape[0]).reshape([-1,1]).repeat(self.nIterpPts, axis=1))
+        J = Utils.mkvc(inds)
+        P = sp.coo_matrix( (Utils.mkvc(w),(I, J)), shape=(inds.shape[0], (self.actind).sum()) )
+        # self.P = Utils.sdiag(self.mesh2.vol[self.actind2])*P.tocsc()
+        self.P = P.tocsr()
+
+    @property
+    def shape(self):
+        """Number of parameters in the model."""
+        # return (self.mesh.nC, self.mesh2.nC)
+        return (self.actind2.sum(), self.actind.sum())
+
+    @property
+    def nP(self):
+        """Number of parameters in the model."""
+        # return self.mesh2.nC
+        return self.actind2.sum()
+
+    def _transform(self, m):
+        return self.P*m
+
+    def deriv(self, m):
+        return self.P
+
 class ActiveCells(IdentityMap):
     """
         Active model parameters.

SimPEG/Mesh/DiffOperators.py

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

SimPEG/Mesh/MeshIO.py

@@ -0,0 +1,416 @@
+import numpy as np, os
+from SimPEG import Utils
+
+class TensorMeshIO(object):
+
+    @classmethod
+    def readUBC(TensorMesh, fileName):
+        """
+            Read UBC GIF 3DTensor mesh and generate 3D Tensor mesh in simpegTD
+
+            Input:
+            :param fileName, path to the UBC GIF mesh file
+
+            Output:
+            :param SimPEG TensorMesh object
+        """
+
+        # Interal function to read cell size lines for the UBC mesh files.
+        def readCellLine(line):
+            for seg in line.split():
+                if '*' in seg:
+                    st = seg
+                    sp = seg.split('*')
+                    re = np.array(sp[0],dtype=int)*(' ' + sp[1])
+                    line = line.replace(st,re.strip())
+            return np.array(line.split(),dtype=float)
+
+        # Read the file as line strings, remove lines with comment = !
+        msh = np.genfromtxt(fileName,delimiter='\n',dtype=np.str,comments='!')
+
+        # Fist line is the size of the model
+        sizeM = np.array(msh[0].split(),dtype=float)
+        # Second line is the South-West-Top corner coordinates.
+        x0 = np.array(msh[1].split(),dtype=float)
+        # Read the cell sizes
+        h1 = readCellLine(msh[2])
+        h2 = readCellLine(msh[3])
+        h3temp = readCellLine(msh[4])
+        h3 = h3temp[::-1] # Invert the indexing of the vector to start from the bottom.
+        # Adjust the reference point to the bottom south west corner
+        x0[2] = x0[2] - np.sum(h3)
+        # Make the mesh
+        tensMsh = TensorMesh([h1,h2,h3],x0)
+        return tensMsh
+
+    @classmethod
+    def readVTK(TensorMesh, fileName):
+        """
+            Read VTK Rectilinear (vtr xml file) and return SimPEG Tensor mesh and model
+
+            Input:
+            :param vtrFileName, path to the vtr model file to write to
+
+            Output:
+            :return SimPEG TensorMesh object
+            :return SimPEG model dictionary
+
+        """
+        # Import
+        from vtk import vtkXMLRectilinearGridReader as vtrFileReader
+        from vtk.util.numpy_support import vtk_to_numpy
+
+        # Read the file
+        vtrReader = vtrFileReader()
+        vtrReader.SetFileName(fileName)
+        vtrReader.Update()
+        vtrGrid = vtrReader.GetOutput()
+        # Sort information
+        hx = np.abs(np.diff(vtk_to_numpy(vtrGrid.GetXCoordinates())))
+        xR = vtk_to_numpy(vtrGrid.GetXCoordinates())[0]
+        hy = np.abs(np.diff(vtk_to_numpy(vtrGrid.GetYCoordinates())))
+        yR = vtk_to_numpy(vtrGrid.GetYCoordinates())[0]
+        zD = np.diff(vtk_to_numpy(vtrGrid.GetZCoordinates()))
+        # Check the direction of hz
+        if np.all(zD < 0):
+            hz = np.abs(zD[::-1])
+            zR = vtk_to_numpy(vtrGrid.GetZCoordinates())[-1]
+        else:
+            hz = np.abs(zD)
+            zR = vtk_to_numpy(vtrGrid.GetZCoordinates())[0]
+        x0 = np.array([xR,yR,zR])
+
+        # Make the SimPEG object
+        tensMsh = TensorMesh([hx,hy,hz],x0)
+
+        # Grap the models
+        models = {}
+        for i in np.arange(vtrGrid.GetCellData().GetNumberOfArrays()):
+            modelName = vtrGrid.GetCellData().GetArrayName(i)
+            if np.all(zD < 0):
+                modFlip = vtk_to_numpy(vtrGrid.GetCellData().GetArray(i))
+                tM = tensMsh.r(modFlip,'CC','CC','M')
+                modArr = tensMsh.r(tM[:,:,::-1],'CC','CC','V')
+            else:
+                modArr = vtk_to_numpy(vtrGrid.GetCellData().GetArray(i))
+            models[modelName] = modArr
+
+        # Return the data
+        return tensMsh, models
+
+    def writeVTK(mesh, fileName, models=None):
+        """
+        Makes and saves a VTK rectilinear file (vtr) for a simpeg Tensor mesh and model.
+
+        Input:
+        :param str, path to the output vtk file
+        :param mesh, SimPEG TensorMesh object - mesh to be transfer to VTK
+        :param models, dictionary of numpy.array - Name('s) and array('s). Match number of cells
+
+        """
+        # Import
+        from vtk import vtkRectilinearGrid as rectGrid, vtkXMLRectilinearGridWriter as rectWriter, VTK_VERSION
+        from vtk.util.numpy_support import numpy_to_vtk
+
+        # Deal with dimensionalities
+        if mesh.dim >= 1:
+            vX = mesh.vectorNx
+            xD = mesh.nNx
+            yD,zD = 1,1
+            vY, vZ = np.array([0,0])
+        if mesh.dim >= 2:
+            vY = mesh.vectorNy
+            yD = mesh.nNy
+        if mesh.dim == 3:
+            vZ = mesh.vectorNz
+            zD = mesh.nNz
+        # Use rectilinear VTK grid.
+        # Assign the spatial information.
+        vtkObj = rectGrid()
+        vtkObj.SetDimensions(xD,yD,zD)
+        vtkObj.SetXCoordinates(numpy_to_vtk(vX,deep=1))
+        vtkObj.SetYCoordinates(numpy_to_vtk(vY,deep=1))
+        vtkObj.SetZCoordinates(numpy_to_vtk(vZ,deep=1))
+
+        # Assign the model('s) to the object
+        if models is not None:
+            for item in models.iteritems():
+                # Convert numpy array
+                vtkDoubleArr = numpy_to_vtk(item[1],deep=1)
+                vtkDoubleArr.SetName(item[0])
+                vtkObj.GetCellData().AddArray(vtkDoubleArr)
+            # Set the active scalar
+            vtkObj.GetCellData().SetActiveScalars(models.keys()[0])
+        # vtkObj.Update()
+
+        # Check the extension of the fileName
+        ext = os.path.splitext(fileName)[1]
+        if ext is '':
+            fileName = fileName + '.vtr'
+        elif ext not in '.vtr':
+            raise IOError('{:s} is an incorrect extension, has to be .vtr')
+        # Write the file.
+        vtrWriteFilter = rectWriter()
+        if float(VTK_VERSION.split('.')[0]) >=6:
+            vtrWriteFilter.SetInputData(vtkObj)
+        else:
+            vtuWriteFilter.SetInput(vtuObj)
+        vtrWriteFilter.SetFileName(fileName)
+        vtrWriteFilter.Update()
+
+
+    def readModelUBC(mesh, fileName):
+        """
+            Read UBC 3DTensor mesh model and generate 3D Tensor mesh model in simpeg
+
+            Input:
+            :param fileName, path to the UBC GIF mesh file to read
+            :param mesh, TensorMesh object, mesh that coresponds to the model
+
+            Output:
+            :return numpy array, model with TensorMesh ordered
+        """
+        f = open(fileName, 'r')
+        model = np.array(map(float, f.readlines()))
+        f.close()
+        model = np.reshape(model, (mesh.nCz, mesh.nCx, mesh.nCy), order = 'F')
+        model = model[::-1,:,:]
+        model = np.transpose(model, (1, 2, 0))
+        model = Utils.mkvc(model)
+        return model
+
+    def writeModelUBC(mesh, fileName, model):
+        """
+            Writes a model associated with a SimPEG TensorMesh
+            to a UBC-GIF format model file.
+
+            :param str fileName: File to write to
+            :param simpeg.Mesh.TensorMesh mesh: The mesh
+            :param numpy.ndarray model: The model
+        """
+
+        # Reshape model to a matrix
+        modelMat = mesh.r(model,'CC','CC','M')
+        # Transpose the axes
+        modelMatT = modelMat.transpose((2,0,1))
+        # Flip z to positive down
+        modelMatTR = Utils.mkvc(modelMatT[::-1,:,:])
+
+        np.savetxt(fileName, modelMatTR.ravel())
+
+    def writeUBC(mesh, fileName, models=None):
+        """
+            Writes a SimPEG TensorMesh to a UBC-GIF format mesh file.
+
+            :param str fileName: File to write to
+            :param simpeg.Mesh.TensorMesh mesh: The mesh
+
+        """
+        assert mesh.dim == 3
+        s = ''
+        s += '%i %i %i\n' %tuple(mesh.vnC)
+        origin = mesh.x0 + np.array([0,0,mesh.hz.sum()]) # Have to it in the same operation or use mesh.x0.copy(), otherwise the mesh.x0 is updated.
+        origin.dtype = float
+
+        s += '%.2f %.2f %.2f\n' %tuple(origin)
+        s += ('%.2f '*mesh.nCx+'\n')%tuple(mesh.hx)
+        s += ('%.2f '*mesh.nCy+'\n')%tuple(mesh.hy)
+        s += ('%.2f '*mesh.nCz+'\n')%tuple(mesh.hz[::-1])
+        f = open(fileName, 'w')
+        f.write(s)
+        f.close()
+
+        if models is None: return
+        assert type(models) is dict, 'models must be a dict'
+        for key in models:
+            assert type(key) is str, 'The dict key is a file name'
+            mesh.writeModelUBC(key, models[key])
+
+class TreeMeshIO(object):
+
+    def writeUBC(mesh, fileName, models=None):
+        """
+            Write UBC ocTree mesh and model files from a simpeg ocTree mesh and model.
+
+            :param str fileName: File to write to
+            :param simpeg.Mesh.TreeMesh mesh: The mesh
+            :param dictionary models: The models in a dictionary, where the keys is the name of the of the model file
+        """
+
+        # Calculate information to write in the file.
+        # Number of cells in the underlying mesh
+        nCunderMesh = np.array([h.size for h in mesh.h],dtype=np.int64)
+        # The top-south-west most corner of the mesh
+        tswCorn = mesh.x0 + np.array([0,0,np.sum(mesh.h[2])])
+        # Smallest cell size
+        smallCell = np.array([h.min() for h in mesh.h])
+        # Number of cells
+        nrCells = mesh.nC
+
+        ## Extract iformation about the cells.
+        # cell pointers
+        cellPointers = np.array([c._pointer for c in mesh])
+        # cell with
+        cellW = np.array([ mesh._levelWidth(i) for i in cellPointers[:,-1] ])
+        # Need to shift the pointers to work with UBC indexing
+        # UBC Octree indexes always the top-left-close (top-south-west) corner first and orders the cells in z(top-down),x,y vs x,y,z(bottom-up).
+        # Shift index up by 1
+        ubcCellPt = cellPointers[:,0:-1].copy() + np.array([1.,1.,1.])
+        # Need reindex the z index to be from the top-left-close corner and to be from the global top.
+        ubcCellPt[:,2] = ( nCunderMesh[-1] + 2) - (ubcCellPt[:,2] + cellW)
+
+        # Reorder the ubcCellPt
+        ubcReorder = np.argsort(ubcCellPt.view(','.join(3*['float'])),axis=0,order=['f2','f1','f0'])[:,0]
+        # Make a array with the pointers and the withs, that are order in the ubc ordering
+        indArr = np.concatenate((ubcCellPt[ubcReorder,:],cellW[ubcReorder].reshape((-1,1)) ),axis=1)
+
+        ## Write the UBC octree mesh file
+        with open(fileName,'w') as mshOut:
+            mshOut.write('{:.0f} {:.0f} {:.0f}\n'.format(nCunderMesh[0],nCunderMesh[1],nCunderMesh[2]))
+            mshOut.write('{:.4f} {:.4f} {:.4f}\n'.format(tswCorn[0],tswCorn[1],tswCorn[2]))
+            mshOut.write('{:.3f} {:.3f} {:.3f}\n'.format(smallCell[0],smallCell[1],smallCell[2]))
+            mshOut.write('{:.0f} \n'.format(nrCells))
+            np.savetxt(mshOut,indArr,fmt='%i')
+
+        ## Print the models
+        # Assign the model('s) to the object
+        if models is not None:
+            # indUBCvector = np.argsort(cX0[np.argsort(np.concatenate((cX0[:,0:2],cX0[:,2:3].max() - cX0[:,2:3]),axis=1).view(','.join(3*['float'])),axis=0,order=('f2','f1','f0'))[:,0]].view(','.join(3*['float'])),axis=0,order=('f2','f1','f0'))[:,0]
+            for item in models.iteritems():
+                # Save the data
+                np.savetxt(item[0],item[1][ubcReorder],fmt='%3.5e')
+
+    @classmethod
+    def readUBC(TreeMesh, meshFile):
+        """
+            Read UBC 3D OcTree mesh and/or modelFiles
+
+            Input:
+            :param str meshFile: path to the UBC GIF OcTree mesh file to read
+
+            Output:
+            :return SimPEG.Mesh.TreeMesh mesh: The octree mesh
+            :return list of ndarray's: models as a list of numpy array's
+        """
+
+        ## Read the file lines
+        fileLines = np.genfromtxt(meshFile,dtype=str,delimiter='\n')
+        # Extract the data
+        nCunderMesh = np.array(fileLines[0].split(),dtype=float)
+        # I think this is the case?
+        if np.unique(nCunderMesh).size >1:
+            raise Exception('SimPEG TreeMeshes have the same number of cell in all directions')
+        tswCorn = np.array(fileLines[1].split(),dtype=float)
+        smallCell = np.array(fileLines[2].split(),dtype=float)
+        nrCells = np.array(fileLines[3].split(),dtype=float)
+        # Read the index array
+        indArr = np.genfromtxt(fileLines[4::],dtype=np.int)
+
+        ## Calculate simpeg parameters
+        h1,h2,h3 = [np.ones(nr)*sz for nr,sz in zip(nCunderMesh,smallCell)]
+        x0 = tswCorn - np.array([0,0,np.sum(h3)])
+        # Need to convert the index array to a points list that complies with SimPEG TreeMesh.
+        # Shift to start at 0
+        simpegCellPt = indArr[:,0:-1].copy()
+        simpegCellPt[:,2] = ( nCunderMesh[-1] + 2) - (simpegCellPt[:,2] + indArr[:,3])
+        # Need reindex the z index to be from the bottom-left-close corner and to be from the global bottom.
+        simpegCellPt = simpegCellPt - np.array([1.,1.,1.])
+
+        # Calculate the cell level
+        simpegLevel = np.log2(np.min(nCunderMesh)) - np.log2(indArr[:,3])
+        # Make a pointer matrix
+        simpegPointers = np.concatenate((simpegCellPt,simpegLevel.reshape((-1,1))),axis=1)
+
+        ## Make the tree mesh
+        mesh = TreeMesh([h1,h2,h3],x0)
+        mesh._cells = set([mesh._index(p) for p in simpegPointers.tolist()])
+
+        # Figure out the reordering
+        mesh._simpegReorderUBC = np.argsort(np.array([mesh._index(i) for i in simpegPointers.tolist()]))
+        # mesh._simpegReorderUBC = np.argsort((np.array([[1,1,1,-1]])*simpegPointers).view(','.join(4*['float'])),axis=0,order=['f3','f2','f1','f0'])[:,0]
+
+        return mesh
+
+
+    def readModelUBC(mesh, fileName):
+        """
+            Read UBC OcTree model and get vector
+
+            Input:
+            :param fileName, path to the UBC GIF model file to read
+
+            Output:
+            :return numpy array, OcTree model
+        """
+
+        if type(fileName) is list:
+            out = {}
+            for f in fileName:
+                out[f] = mesh.readModelUBC(f)
+            return out
+
+        assert hasattr(mesh, '_simpegReorderUBC'), 'The file must have been loaded from a UBC format.'
+        assert mesh.dim == 3
+
+        modList = []
+        modArr = np.loadtxt(fileName)
+        if len(modArr.shape) == 1:
+            modList.append(modArr[mesh._simpegReorderUBC])
+        else:
+            modList.append(modArr[mesh._simpegReorderUBC,:])
+        return modList
+
+    def writeVTK(mesh, fileName, models=None):
+        """
+        Function to write a VTU file from a SimPEG TreeMesh and model.
+        """
+        import vtk
+        from vtk import vtkXMLUnstructuredGridWriter as Writer, VTK_VERSION
+        from vtk.util.numpy_support import numpy_to_vtk, numpy_to_vtkIdTypeArray
+
+        if str(type(mesh)).split()[-1][1:-2] not in 'SimPEG.Mesh.TreeMesh.TreeMesh':
+            raise IOError('mesh is not a SimPEG TreeMesh.')
+
+        # Make the data parts for the vtu object
+        # Points
+        mesh.number()
+        ptsMat = mesh._gridN + mesh.x0
+
+        vtkPts = vtk.vtkPoints()
+        vtkPts.SetData(numpy_to_vtk(ptsMat,deep=True))
+        # Cells
+        cellConn = np.array([c.nodes for c in mesh],dtype=np.int64)
+
+        cellsMat = np.concatenate((np.ones((cellConn.shape[0],1),dtype=np.int64)*cellConn.shape[1],cellConn),axis=1).ravel()
+        cellsArr = vtk.vtkCellArray()
+        cellsArr.SetNumberOfCells(cellConn.shape[0])
+        cellsArr.SetCells(cellConn.shape[0],numpy_to_vtkIdTypeArray(cellsMat,deep=True))
+
+        # Make the object
+        vtuObj = vtk.vtkUnstructuredGrid()
+        vtuObj.SetPoints(vtkPts)
+        vtuObj.SetCells(vtk.VTK_VOXEL,cellsArr)
+        # Add the level of refinement as a cell array
+        cellSides = np.array([np.array(vtuObj.GetCell(i).GetBounds()).reshape((3,2)).dot(np.array([-1, 1])) for i in np.arange(vtuObj.GetNumberOfCells())])
+        uniqueLevel, indLevel = np.unique(np.prod(cellSides,axis=1),return_inverse=True)
+        refineLevelArr = numpy_to_vtk(indLevel.max() - indLevel,deep=1)
+        refineLevelArr.SetName('octreeLevel')
+        vtuObj.GetCellData().AddArray(refineLevelArr)
+        # Assign the model('s) to the object
+        if models is not None:
+            for item in models.iteritems():
+                # Convert numpy array
+                vtkDoubleArr = numpy_to_vtk(item[1],deep=1)
+                vtkDoubleArr.SetName(item[0])
+                vtuObj.GetCellData().AddArray(vtkDoubleArr)
+
+        # Make the writer
+        vtuWriteFilter = Writer()
+        if float(VTK_VERSION.split('.')[0]) >=6:
+            vtuWriteFilter.SetInputData(vtuObj)
+        else:
+            vtuWriteFilter.SetInput(vtuObj)
+        vtuWriteFilter.SetFileName(fileName)
+        # Write the file
+        vtuWriteFilter.Update()
+

SimPEG/Mesh/TensorMesh.py

@@ -3,6 +3,7 @@ from BaseMesh import BaseMesh, BaseRectangularMesh
 from View import TensorView
 from DiffOperators import DiffOperators
 from InnerProducts import InnerProducts
+from MeshIO import TensorMeshIO
 
 class BaseTensorMesh(BaseMesh):
 
@@ -215,7 +216,7 @@ class BaseTensorMesh(BaseMesh):
             inside = inside & (pts[:,i] >= tensor.min()-TOL) & (pts[:,i] <= tensor.max()+TOL)
         return inside
 
-    def getInterpolationMat(self, loc, locType, zerosOutside=False):
+    def getInterpolationMat(self, loc, locType='CC', zerosOutside=False):
         """ Produces interpolation matrix
 
         :param numpy.ndarray loc: Location of points to interpolate to
@@ -359,7 +360,7 @@ class BaseTensorMesh(BaseMesh):
 
 
 
-class TensorMesh(BaseTensorMesh, BaseRectangularMesh, TensorView, DiffOperators, InnerProducts):
+class TensorMesh(BaseTensorMesh, BaseRectangularMesh, TensorView, DiffOperators, InnerProducts, TensorMeshIO):
     """
     TensorMesh is a mesh class that deals with tensor product meshes.
 

SimPEG/Mesh/TreeMesh.py

@@ -100,11 +100,12 @@ except Exception, e:
 
 from InnerProducts import InnerProducts
 from TensorMesh import TensorMesh, BaseTensorMesh
+from MeshIO import TreeMeshIO
 import time
 
 MAX_BITS = 20
 
-class TreeMesh(BaseTensorMesh, InnerProducts):
+class TreeMesh(BaseTensorMesh, InnerProducts, TreeMeshIO):
 
     _meshType = 'TREE'
 
@@ -564,15 +565,18 @@ class TreeMesh(BaseTensorMesh, InnerProducts):
         return [p - (p % mod) for p in pointer[:-1]] + [pointer[-1]-1]
 
     def _cellN(self, p):
+        """Node location [x,y(,z)] of a single cell, closest to origin, given a pointer."""
         p = self._asPointer(p)
         return [hi[:p[ii]].sum() for ii, hi in enumerate(self.h)]
 
     def _cellH(self, p):
+        """Widths of a single cell given a pointer."""
         p = self._asPointer(p)
         w = self._levelWidth(p[-1])
         return [hi[p[ii]:p[ii]+w].sum() for ii, hi in enumerate(self.h)]
 
     def _cellC(self, p):
+        """Cell center of a single cell (without origin correction), given a pointer."""
         return (np.array(self._cellH(p))/2.0 + self._cellN(p)).tolist()
 
     def _levelWidth(self, level):
@@ -827,8 +831,10 @@ class TreeMesh(BaseTensorMesh, InnerProducts):
     def _numberCells(self, force=False):
         if not self.__dirtyCells__ and not force: return
         self._cc2i = dict()
+        self._i2cc = dict()
         for ii, c in enumerate(sorted(self._cells)):
             self._cc2i[c] = ii
+            self._i2cc[ii] = c
         self.__dirtyCells__ = False
 
     def _numberNodes(self, force=False):
@@ -1704,9 +1710,9 @@ class TreeMesh(BaseTensorMesh, InnerProducts):
         "Construct the averaging operator on cell faces to cell centers."
         if getattr(self, '_aveF2CC', None) is None:
             if self.dim == 2:
-                self._aveF2CC = 1./self.dim*sp.hstack([self.aveFx2CC, self.aveFy2CC])
+                self._aveF2CC = 1./self.dim*sp.hstack([self.aveFx2CC, self.aveFy2CC]).tocsr()
             elif self.dim == 3:
-                self._aveF2CC = 1./self.dim*sp.hstack([self.aveFx2CC, self.aveFy2CC, self.aveFz2CC])
+                self._aveF2CC = 1./self.dim*sp.hstack([self.aveFx2CC, self.aveFy2CC, self.aveFz2CC]).tocsr()
         return self._aveF2CC
 
     @property
@@ -1714,9 +1720,9 @@ class TreeMesh(BaseTensorMesh, InnerProducts):
         "Construct the averaging operator on cell faces to cell centers."
         if getattr(self, '_aveF2CCV', None) is None:
             if self.dim == 2:
-                self._aveF2CCV = sp.block_diag([self.aveFx2CC, self.aveFy2CC])
+                self._aveF2CCV = sp.block_diag([self.aveFx2CC, self.aveFy2CC]).tocsr()
             elif self.dim == 3:
-                self._aveF2CCV = sp.block_diag([self.aveFx2CC, self.aveFy2CC, self.aveFz2CC])
+                self._aveF2CCV = sp.block_diag([self.aveFx2CC, self.aveFy2CC, self.aveFz2CC]).tocsr()
         return self._aveF2CCV
 
     @property
@@ -2218,6 +2224,25 @@ class TreeMesh(BaseTensorMesh, InnerProducts):
         if showIt: plt.show()
         return tuple(out)
 
+    def __len__(self): return self.nC
+
+    def __getitem__(self, key):
+        if isinstance( key, slice ) :
+            #Get the start, stop, and step from the slice
+            return [self[ii] for ii in xrange(*key.indices(len(self)))]
+        elif isinstance( key, int ) :
+            if key < 0 : #Handle negative indices
+                key += len( self )
+            if key >= len( self ) :
+                raise IndexError, "The index (%d) is out of range."%key
+
+            self._numberCells() # no-op if numbered
+            index   = self._i2cc[key]
+            pointer = self._asPointer(index)
+            return Cell(self, index, pointer)
+        else:
+            raise TypeError, "Invalid argument type."
+
 
 class Cell(object):
     def __init__(self, mesh, index, pointer):
@@ -2225,6 +2250,35 @@ class Cell(object):
         self._index   = index
         self._pointer = pointer
 
+    @property
+    def nodes(self):
+        """The node index in _gridN (this may include hanging nodes)."""
+        M = self.mesh
+        M._numberNodes()
+        p = self._pointer
+        i = self._index
+        w = M._levelWidth(p[-1])
+
+        if M.dim == 2:
+            n = [
+                    i,
+                    M._index([ p[0] + w, p[1]   , p[2]]),
+                    M._index([ p[0]    , p[1]+ w, p[2]]),
+                    M._index([ p[0] + w, p[1]+ w, p[2]]),
+                ]
+        elif self.dim == 3:
+            n = [
+                    i,
+                    M._index([ p[0] + w, p[1]    , p[2]    ,p[3]]),
+                    M._index([ p[0]    , p[1] + w, p[2]    ,p[3]]),
+                    M._index([ p[0] + w, p[1] + w, p[2]    ,p[3]]),
+                    M._index([ p[0]    , p[1]    , p[2] + w,p[3]]),
+                    M._index([ p[0] + w, p[1]    , p[2] + w,p[3]]),
+                    M._index([ p[0]    , p[1] + w, p[2] + w,p[3]]),
+                    M._index([ p[0] + w, p[1] + w, p[2] + w,p[3]]),
+                ]
+        return [M._n2i[_] for _ in n]
+
     @property
     def center(self):
         if getattr(self, '_center', None) is None:
@@ -2282,121 +2336,3 @@ class NotBalancedException(TreeException):
     pass
 class CellLookUpException(TreeException):
     pass
-
-if __name__ == '__main__':
-
-
-    import matplotlib.pyplot as plt
-    import matplotlib
-    from mpl_toolkits.mplot3d import Axes3D
-    import matplotlib.colors as colors
-    import matplotlib.cm as cmx
-
-    def topo(x):
-        return np.sin(x*(2.*np.pi))*0.3 + 0.5
-
-    def function(cell):
-        r = cell.center - np.array([0.5]*len(cell.center))
-        dist = np.sqrt(r.dot(r))
-        # dist2 = np.abs(cell.center[-1] - topo(cell.center[0]))
-
-        # dist = min([dist1,dist2])
-        # if dist < 0.05:
-        #     return 5
-        if dist < 0.1:
-            return 5
-        if dist < 0.2:
-            return 4
-        if dist < 0.4:
-            return 3
-        return 2
-
-    # T = TreeMesh([[(1,128)],[(1,128)],[(1,128)]],levels=7)
-    # T = TreeMesh([128,128,128])
-    # T = TreeMesh([64,64],levels=6)
-    T = TreeMesh([4,4,4])
-    # T = TreeMesh([[(1,128)],[(1,128)]],levels=7)
-    # T.refine(lambda xc:2, balance=False)
-    # T._index([0,0,0])
-    # T._pointer(0)
-
-
-    # tic = time.time()
-    T.refine(function)#, balance=False)
-    # print time.time() - tic
-    # print T.nC
-    T.plotSlice(np.log(T.vol))#np.random.rand(T.nC))
-
-    plt.show()
-    blah
-
-    # T.plotImage(np.arange(len(T.vol)),showIt=True)
-
-    # print T.getFaceInnerProduct()
-    # print T.gridFz
-
-
-    # T._refineCell([8,0,1])
-    # T._refineCell([8,0,2])
-    # T._refineCell([12,0,2])
-    # T._refineCell([8,4,2])
-    # T._refineCell([6,0,3])
-    # T._refineCell([8,8,1])
-    # T._refineCell([0,0,0,1])
-    # T.__dirty__ = True
-
-
-    # print T.gridFx.shape[0], T.nFx
-
-
-
-    ax = plt.subplot(211)
-    ax.spy(T.edgeCurl)
-
-    # print Mesh.TensorMesh([2,2,2]).edgeCurl.todense()
-    # print T.edgeCurl.todense()
-    # print Mesh.TensorMesh([2,2,2]).edgeCurl.todense() - T.edgeCurl.todense()
-    # print T.gridEy - Mesh.TensorMesh([2,2,2]).gridEy
-
-    # print T.edge
-    # T.plotGrid(ax=ax)
-
-    # R = deflationMatrix(T._facesX, T._hangingFx, T._fx2i)
-    # print R
-
-    ax = plt.subplot(212)#, projection='3d')
-    ax.spy(Mesh.TensorMesh([2,2,2]).edgeCurl)
-
-    # ax = plt.subplot(313)
-    # ax.spy(T.faceDiv[:,:T.nFx] * R)
-
-
-    # T.balance()
-    # T.plotGrid(ax=ax)
-
-    # cx = T._getNextCell([0,0,1],direction=0,positive=True)
-    # print cx
-    # # print [T._asPointer(_) for _ in cx]
-    # cx = T._getNextCell([8,0,3],direction=0,positive=False)
-    # print T._asPointer(cx)
-    # cx = T._getNextCell([8,8,1],direction=1,positive=False)
-    # print cx, #[T._asPointer(_) for _ in cx]
-    # cm = T._getNextCell([64,80,4],direction=0,positive=False)
-    # cy = T._getNextCell([64,80,4],direction=1,positive=True)
-    # cp = T._getNextCell([64,80,4],direction=1,positive=False)
-
-    # ax.plot( T._cellN([4,0,1])[0],T._cellN([4,0,1])[1], 'yd')
-    # ax.plot( T._cellN(cx)[0],T._cellN(cx)[1], 'ys')
-    # ax.plot( T._cellN(cm)[0],T._cellN(cm)[1], 'ys')
-    # ax.plot( T._cellN(cy)[0],T._cellN(cy)[1], 'ys')
-    # ax.plot( T._cellN(cp[0])[0],T._cellN(cp[0])[1], 'ys')
-    # ax.plot( T._cellN(cp[1])[0],T._cellN(cp[1])[1], 'ys')
-
-
-
-
-
-    # print T.nN
-
-    plt.show()
-

SimPEG/Optimization.py

@@ -990,4 +990,18 @@ class ProjectedGNCG(BFGS, Minimize, Remember):
                     cgFlag = 1
                 # End CG Iterations
                     
+            # Take a gradient step on the active cells if exist
+            if temp != self.xc.size:
+        
+                rhs_a = (Active) * -self.g
+                
+                dm_i = max( abs( delx ) )
+                dm_a = max( abs(rhs_a) )           
+    
+                delx = delx + rhs_a * dm_i / dm_a /10.
+                    
+            # Only keep gradients going in the right direction on the active set
+            indx = ((self.xc<=self.lower) & (delx < 0)) | ((self.xc>=self.upper) & (delx > 0))
+            delx[indx] = 0.
+
             return delx

SimPEG/Problem.py

@@ -1,6 +1,6 @@
 import Utils, Survey, Models, numpy as np, scipy.sparse as sp
 Solver = Utils.SolverUtils.Solver
-import Maps, Mesh
+import Maps, Mesh, Exceptions
 from Fields import Fields, TimeFields
 
 class BaseProblem(object):
@@ -18,10 +18,14 @@ class BaseProblem(object):
     Solver = Solver   #: A SimPEG Solver class.
     solverOpts = {}   #: Sovler options as a kwarg dict
 
-    mesh    = None    #: A SimPEG.Mesh instance.
-
     PropMap = None    #: A SimPEG PropertyMap class.
 
+    def __init__(self, mesh, mapping=None, **kwargs):
+        Utils.setKwargs(self, **kwargs)
+        assert isinstance(mesh, Mesh.BaseMesh), "mesh must be a SimPEG.Mesh object."
+        self.mesh = mesh
+        self.mapping = mapping or Maps.IdentityMap(mesh)
+
     @property
     def mapping(self):
         "A SimPEG.Map instance or a property map is PropMap is not None"
@@ -32,14 +36,9 @@ class BaseProblem(object):
             val._assertMatchesPair(self.mapPair)
             self._mapping = val
         else:
+            self._propMapMapping = val
             self._mapping = self.PropMap(val)
 
-    def __init__(self, mesh, mapping=None, **kwargs):
-        Utils.setKwargs(self, **kwargs)
-        assert isinstance(mesh, Mesh.BaseMesh), "mesh must be a SimPEG.Mesh object."
-        self.mesh = mesh
-        self.mapping = mapping or Maps.IdentityMap(mesh)
-
     @property
     def survey(self):
         """
@@ -47,13 +46,22 @@ class BaseProblem(object):
         """
         return getattr(self, '_survey', None)
 
-    def pair(self, d):
+    def pair(self, survey):
         """Bind a survey to this problem instance using pointers."""
-        assert isinstance(d, self.surveyPair), "Data object must be an instance of a %s class."%(self.surveyPair.__name__)
-        if d.ispaired:
+        assert isinstance(survey, self.surveyPair), "Survey must be an instance of a %s class."%(self.surveyPair.__name__)
+        if survey.ispaired:
             raise Exception("The survey object is already paired to a problem. Use survey.unpair()")
-        self._survey = d
-        d._prob = self
+        try:
+            self._survey = survey
+            self._validatePairing()
+        except Exceptions.PairingException, e:
+            self._survey = None
+            raise e
+        survey._prob = self
+
+    def _validatePairing(self):
+        """Called when the pair is done, raise a SimPEG.Exceptions.PairingException if unsuccessful"""
+        pass
 
     def unpair(self):
         """Unbind a survey from this problem instance."""
@@ -222,4 +230,191 @@ class BaseTimeProblem(BaseProblem):
             del self._timeMesh
 
 
+class GlobalProblem(BaseProblem):
+    """
+
+        The GlobalProblem allows you to run a whole bunch of SubProblems,
+        potentially in parallel, potentially of different meshes.
+
+        This is handy for working with lots of sources,
+
+    """
+
+    surveyKwargs = {}
+    probKwargs   = {}
+
+    def __init__(self, SubProblem, globalMesh, mapping=None, **kwargs):
+
+        # assert isclass??(SubProblem, BaseProblem), "SubProblem must be a SimPEG.Problem.BaseProblem object."
+        self.surveyPair = SubProblem.surveyPair
+        self.PropMap = SubProblem.PropMap
+        self.mapPair = SubProblem.mapPair
+        self.SubProblem = SubProblem
+
+        Utils.setKwargs(self, **kwargs)
+        assert isinstance(globalMesh, Mesh.BaseMesh), "globalMesh must be a SimPEG.Mesh object."
+        self.globalMesh = globalMesh
+        self.mapping = mapping or Maps.IdentityMap()
+
+    @property
+    def groups(self):
+        """
+            List of lists/integers to say how the sources are grouped.
+
+            e.g.
+
+            survey.srcList = [s0,s1,s2,s3,s4]
+            groups = [ [0,4], [1,3], 2 ]
+        """
+        if getattr(self, '_groups', None) is None:
+            if not self.ispaired: return None
+            self._groups = range(self.survey.nSrc)
+        return self._groups
+    @groups.setter
+    def groups(self, val):
+        assert type(val) is list, 'This should be an list of groups'
+        if self.ispaired:
+            for g in val:
+                assert type(g) in [int, list], 'Must be an integer or a list'
+                if type(g) is int:
+                    assert g >= 0 and g < self.survey.nSrc, '%d is outside the number of sources in the surveys list'%g
+                if type(g) is list:
+                    for sg in g:
+                        assert type(g) is int, 'Must be an integer or a list'
+                        assert g >= 0 and g < self.survey.nSrc, '%d is outside the number of sources in the surveys list'%g
+            assert len(val) == len(self.survey.srcList), 'The groups must be the same length as the srcList in the survey'
+        self._groups = val
+        self._nGroups = None
+
+    @property
+    def meshes(self):
+        if getattr(self, '_meshes', None) is None:
+            if not self.ispaired: return None
+            self._meshes = [self.globalMesh]*self.nGroups
+        return self._meshes
+    @meshes.setter
+    def meshes(self, val):
+        assert type(val) is list
+        if self.ispaired:
+            assert len(val) == self.nGroups
+        self._meshes = val
+
+    @property
+    def nGroups(self):
+        if getattr(self, '_groups', None) is None:
+            return None
+        return len(self.groups)
+
+    def _validatePairing(self):
+        try:
+            self.groups = self.groups # check the assumptions for the grouping
+        except Exception, e:
+            raise Exceptions.PairingException(reason='The grouping does not match the survey')
+        if self.nGroups is not len(self.meshes):
+            raise Exceptions.PairingException(reason='The meshes are not the the same length as the number of groups')
+
+    def getSubProblemandSubSurvey(self, subMap, ind):
+        #This is a core place that we can proceed parallelization
+        assert self.ispaired, 'You must be paired to a survey'
+        assert type(ind) in [int,long] and ind >= 0 and ind < self.nGroups, 'ind must be an index into the group list'
+
+        subMesh = self.meshes[ind]
+        # subMap  = Maps.IdentityMap(subMesh) # this is probably a mesh2mesh mapping?
+        # subMap  = self.getSubMap(subMesh, ind)
+
+        if self.PropMap is None:
+            prob = self.SubProblem(subMesh, mapping=subMap * self.mapping, **self.probKwargs)
+        else:
+            # This will not work with a fancier propmap...
+            prob = self.SubProblem(subMesh, mapping=subMap * self._propMapMapping, **self.probKwargs)
+
+        survey = self.survey.__class__(srcList=self.survey.srcList[self.groups[ind]], **self.surveyKwargs)
+        prob.pair(survey)
+
+        return prob, survey
+
+    # Not sure we need this here ... 
+
+    def getSubMap(self, subMesh, ind):
+        """The sub"""
+        mesh2mesh = Maps.IdentityMap(subMesh) # this is probably a mesh2mesh mapping?
+
+        if self.PropMap is None:
+            subMap = mesh2mesh * self.mapping
+        else:
+            subMap = mesh2mesh * self._propMapMapping
+
+        return subMap
+
+if __name__ == '__main__':
+
+
+    from SimPEG import *
+    from SimPEG import EM
+    from scipy.constants import mu_0
+    from pymatsolver import MumpsSolver
+
+    cs = 10.
+    ncx, ncy, ncz = 10, 10, 10
+    npad = 4
+    freq = 1e2
+
+    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], 'CCC')
+
+    mapping = Maps.ExpMap(mesh)
+
+    x = np.linspace(-10,10,5)
+    XYZ = Utils.ndgrid(x,np.r_[0],np.r_[0])
+    rxList = EM.FDEM.Rx(XYZ, 'exi')
+    Src0 = EM.FDEM.Src.MagDipole([rxList],loc=np.r_[0.,0.,0.], freq=freq)
+    Src1 = EM.FDEM.Src.MagDipole([rxList],loc=np.r_[0.,0.,0.], freq=freq)
+
+
+    prb0 = EM.FDEM.Problem_b(mesh, mapping=mapping, Solver=MumpsSolver)
+    survey = EM.FDEM.Survey([Src0])
+    prb0.pair(survey)
+    prb1 = EM.FDEM.Problem_b(mesh, mapping=mapping, Solver=MumpsSolver)
+    survey = EM.FDEM.Survey([Src1])
+    prb1.pair(survey)
+
+
+
+    sig = 1e-1
+    sigma = np.ones(mesh.nC)*sig
+    sigma[mesh.gridCC[:,2] > 0] = 1e-8
+    m = np.log(sigma)
+
+    GP = GlobalProblem(EM.FDEM.Problem_b, mesh, mapping=mapping, meshes=[mesh,mesh])
+    survey = EM.FDEM.Survey([Src0, Src1])
+    GP.pair(survey)
+
+    gp1 = GP.getSubProblem(0)
+    gp1.Solver = MumpsSolver
+
+    pu = prb0.fields(m)
+    gpu = gp1.fields(m)
+
+    bfz = mesh.r(pu[Src0, 'b'],'F','Fz','M')
+    bfz = mesh.r(gpu[Src0, 'b'],'F','Fz','M')
+    x = np.linspace(-55,55,12)
+    XYZ = Utils.ndgrid(x,np.r_[0],np.r_[0])
+    P = mesh.getInterpolationMat(XYZ, 'Fz')
+
+    # an = EM.Analytics.FDEM.hzAnalyticDipoleF(x, Src0.freq, sig)
+
+    # diff = np.log10(np.abs(P*np.imag(pu[Src0, 'b']) - mu_0*np.imag(an)))
+    # diff = np.log10(np.abs(P*np.imag(gpu[Src0, 'b']) - mu_0*np.imag(an)))
+
+    import matplotlib.pyplot as plt
+    plt.plot(x,np.log10(np.abs(P*np.imag(pu[Src0, 'b']))), 'r-s')
+    plt.plot(x,np.log10(np.abs(P*np.imag(gpu[Src0, 'b']))), 'b')
+    # plt.plot(x,np.log10(np.abs(mu_0*np.imag(an))), 'r')
+    # plt.plot(x,diff,'g')
+    plt.show()
+
+
+
 

SimPEG/Regularization.py

@@ -20,12 +20,13 @@ class BaseRegularization(object):
     mesh    = None    #: A SimPEG.Mesh instance.
     mref = None       #: Reference model.
 
-    def __init__(self, mesh, mapping=None, **kwargs):
+    def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
         Utils.setKwargs(self, **kwargs)
         self.mesh = mesh
         assert isinstance(mesh, Mesh.BaseMesh), "mesh must be a SimPEG.Mesh object."
         self.mapping = mapping or self.mapPair(mesh)
         self.mapping._assertMatchesPair(self.mapPair)
+        self.indActive = indActive
 
     @property
     def parent(self):
@@ -112,8 +113,6 @@ class BaseRegularization(object):
         return mD.T * ( self.W.T * ( self.W * ( mD * v) ) )
 
 
-
-
 class Tikhonov(BaseRegularization):
     """
     """
@@ -126,9 +125,182 @@ class Tikhonov(BaseRegularization):
     alpha_yy = Utils.dependentProperty('_alpha_yy', 0.0, ['_W', '_Wyy'], "Weight for the second derivative in the y direction")
     alpha_zz = Utils.dependentProperty('_alpha_zz', 0.0, ['_W', '_Wzz'], "Weight for the second derivative in the z direction")
 
+    def __init__(self, mesh, mapping=None, indActive = None, **kwargs):
+        BaseRegularization.__init__(self, mesh, mapping=mapping, **kwargs)
+        self.indActive = indActive
+
+    @property
+    def Ws(self):
+        """Regularization matrix Ws"""
+        if getattr(self,'_Ws', None) is None:
+            self._Ws = Utils.sdiag((self.mesh.vol*self.alpha_s)**0.5)
+            if self.indActive is not None:
+                Pac = Utils.speye(self.mesh.nC)[:,self.indActive]
+                self._Ws = Pac.T * self._Ws * Pac
+        return self._Ws
+
+    @property
+    def Wx(self):
+        """Regularization matrix Wx"""
+        if getattr(self, '_Wx', None) is None:
+            Ave_x_vol = self.mesh.aveF2CC[:,:self.mesh.nFx].T*self.mesh.vol
+            self._Wx = Utils.sdiag((Ave_x_vol*self.alpha_x)**0.5)*self.mesh.cellGradx
+
+            if self.indActive is not None:
+                indActive_Fx = (self.mesh.aveFx2CC.T * self.indActive) == 1
+                Pac = Utils.speye(self.mesh.nC)[:,self.indActive]
+                Pafx = Utils.speye(self.mesh.nFx)[:,indActive_Fx]
+                self._Wx = Pafx.T*self._Wx*Pac
+
+        return self._Wx
+
+    @property
+    def Wy(self):
+        """Regularization matrix Wy"""
+        if getattr(self, '_Wy', None) is None:
+            Ave_y_vol = self.mesh.aveF2CC[:,self.mesh.nFx:np.sum(self.mesh.vnF[:2])].T*self.mesh.vol
+            self._Wy = Utils.sdiag((Ave_y_vol*self.alpha_y)**0.5)*self.mesh.cellGrady
+
+            if self.indActive is not None:
+                indActive_Fy = (self.mesh.aveFy2CC.T * self.indActive) == 1
+                Pac = Utils.speye(self.mesh.nC)[:,self.indActive]
+                Pafy = Utils.speye(self.mesh.nFy)[:,indActive_Fy]
+                self._Wy = Pafy.T*self._Wy*Pac
+
+        return self._Wy
+
+    @property
+    def Wz(self):
+        """Regularization matrix Wz"""
+        if getattr(self, '_Wz', None) is None:
+            Ave_z_vol = self.mesh.aveF2CC[:,np.sum(self.mesh.vnF[:2]):].T*self.mesh.vol
+            self._Wz = Utils.sdiag((Ave_z_vol*self.alpha_z)**0.5)*self.mesh.cellGradz
+
+            if self.indActive is not None:
+                indActive_Fz = (self.mesh.aveFz2CC.T * self.indActive) == 1
+                Pac = Utils.speye(self.mesh.nC)[:,self.indActive]
+                Pafz = Utils.speye(self.mesh.nFz)[:,indActive_Fz]
+                self._Wz = Pafz.T*self._Wz*Pac
+
+        return self._Wz
+
+    @property
+    def Wxx(self):
+        """Regularization matrix Wxx"""
+        if getattr(self, '_Wxx', None) is None:
+            self._Wxx = Utils.sdiag((self.mesh.vol*self.alpha_xx)**0.5)*self.mesh.faceDivx*self.mesh.cellGradx
+
+            if self.indActive is not None:
+                Pac = Utils.speye(self.mesh.nC)[:,self.indActive]
+                self._Wxx = Pac.T*self._Wxx*Pac
+
+        return self._Wxx
+
+    @property
+    def Wyy(self):
+        """Regularization matrix Wyy"""
+        if getattr(self, '_Wyy', None) is None:
+            self._Wyy = Utils.sdiag((self.mesh.vol*self.alpha_yy)**0.5)*self.mesh.faceDivy*self.mesh.cellGrady
+
+            if self.indActive is not None:
+                Pac = Utils.speye(self.mesh.nC)[:,self.indActive]
+                self._Wyy = Pac.T*self._Wyy*Pac
+
+        return self._Wyy
+
+    @property
+    def Wzz(self):
+        """Regularization matrix Wzz"""
+        if getattr(self, '_Wzz', None) is None:
+            self._Wzz = Utils.sdiag((self.mesh.vol*self.alpha_zz)**0.5)*self.mesh.faceDivz*self.mesh.cellGradz
+
+            if self.indActive is not None:
+                Pac = Utils.speye(self.mesh.nC)[:,self.indActive]
+                self._Wzz = Pac.T*self._Wzz*Pac
+
+        return self._Wzz
+
+    @property
+    def Wsmooth(self):
+        """Full smoothness regularization matrix W"""
+        if getattr(self, '_Wsmooth', None) is None:
+            wlist = (self.Wx, self.Wxx)
+            if self.mesh.dim > 1:
+                wlist += (self.Wy, self.Wyy)
+            if self.mesh.dim > 2:
+                wlist += (self.Wz, self.Wzz)
+            self._Wsmooth = sp.vstack(wlist)
+        return self._Wsmooth
+
+    @property
+    def W(self):
+        """Full regularization matrix W"""
+        if getattr(self, '_W', None) is None:
+            wlist = (self.Ws, self.Wsmooth)
+            self._W = sp.vstack(wlist)
+        return self._W
+
+    @Utils.timeIt
+    def eval(self, m):
+        if self.smoothModel == True:
+            r1 = self.Wsmooth * ( self.mapping * (m) )
+            r2 = self.Ws * ( self.mapping * (m - self.mref) )
+            return 0.5*(r1.dot(r1)+r2.dot(r2))
+        elif self.smoothModel == False:
+            r = self.W * ( self.mapping * (m - self.mref) )
+            return 0.5*r.dot(r)
+
+
+    @Utils.timeIt
+    def evalDeriv(self, m):
+        """
+
+        The regularization is:
+
+        .. math::
+
+            R(m) = \\frac{1}{2}\mathbf{(m-m_\\text{ref})^\\top W^\\top W(m-m_\\text{ref})}
+
+        So the derivative is straight forward:
+
+        .. math::
+
+            R(m) = \mathbf{W^\\top W (m-m_\\text{ref})}
+
+        """
+        if self.smoothModel == True:
+            mD1 = self.mapping.deriv(m)
+            mD2 = self.mapping.deriv(m - self.mref)
+            r1 = self.Wsmooth * ( self.mapping * (m))
+            r2 = self.Ws * ( self.mapping * (m - self.mref) )
+            out1 = mD1.T * ( self.Wsmooth.T * r1 )
+            out2 = mD2.T * ( self.Ws.T * r2 )
+            out = out1+out2
+        elif self.smoothModel == False:
+            mD = self.mapping.deriv(m - self.mref)
+            r = self.W * ( self.mapping * (m - self.mref) )
+            out = mD.T * ( self.W.T * r )
+        return out
+
+class Simple(BaseRegularization):
+    """
+        Only for tensor mesh
+    """     
+    
+    smoothModel = True  #: SMOOTH and SMOOTH_MOD_DIF options
+    alpha_s  = Utils.dependentProperty('_alpha_s', 1.0, ['_W', '_Ws'], "Smallness weight")
+    alpha_x  = Utils.dependentProperty('_alpha_x', 1.0, ['_W', '_Wx'], "Weight for the first derivative in the x direction")
+    alpha_y  = Utils.dependentProperty('_alpha_y', 1.0, ['_W', '_Wy'], "Weight for the first derivative in the y direction")
+    alpha_z  = Utils.dependentProperty('_alpha_z', 1.0, ['_W', '_Wz'], "Weight for the first derivative in the z direction")
+    alpha_xx = Utils.dependentProperty('_alpha_xx', 0.0, ['_W', '_Wxx'], "Weight for the second derivative in the x direction")
+    alpha_yy = Utils.dependentProperty('_alpha_yy', 0.0, ['_W', '_Wyy'], "Weight for the second derivative in the y direction")
+    alpha_zz = Utils.dependentProperty('_alpha_zz', 0.0, ['_W', '_Wzz'], "Weight for the second derivative in the z direction")
+
     def __init__(self, mesh, mapping=None, **kwargs):
         BaseRegularization.__init__(self, mesh, mapping=mapping, **kwargs)
 
+    
+        
     @property
     def Ws(self):
         """Regularization matrix Ws"""
@@ -140,24 +312,21 @@ class Tikhonov(BaseRegularization):
     def Wx(self):
         """Regularization matrix Wx"""
         if getattr(self, '_Wx', None) is None:
-            Ave_x_vol = self.mesh.aveF2CC[:,:self.mesh.nFx].T*self.mesh.vol
-            self._Wx = Utils.sdiag((Ave_x_vol*self.alpha_x)**0.5)*self.mesh.cellGradx
+            self._Wx = Utils.sdiag((self.mesh.vol*self.alpha_x)**0.5)*self.mesh.unitCellGradx
         return self._Wx
 
     @property
     def Wy(self):
         """Regularization matrix Wy"""
         if getattr(self, '_Wy', None) is None:
-            Ave_y_vol = self.mesh.aveF2CC[:,self.mesh.nFx:np.sum(self.mesh.vnF[:2])].T*self.mesh.vol
-            self._Wy = Utils.sdiag((Ave_y_vol*self.alpha_y)**0.5)*self.mesh.cellGrady
+            self._Wy = Utils.sdiag((self.mesh.vol*self.alpha_y)**0.5)*self.mesh.unitCellGrady
         return self._Wy
 
     @property
     def Wz(self):
         """Regularization matrix Wz"""
         if getattr(self, '_Wz', None) is None:
-            Ave_z_vol = self.mesh.aveF2CC[:,np.sum(self.mesh.vnF[:2]):].T*self.mesh.vol
-            self._Wz = Utils.sdiag((Ave_z_vol*self.alpha_z)**0.5)*self.mesh.cellGradz
+            self._Wz = Utils.sdiag((self.mesh.vol*self.alpha_z)**0.5)*self.mesh.unitCellGradz
         return self._Wz
 
     @property
@@ -243,3 +412,109 @@ class Tikhonov(BaseRegularization):
             out = mD.T * ( self.W.T * r )
         return out
 
+class SparseRegularization(Simple):
+    
+    eps = 1e-1
+
+    m = None
+    gamma = 1.
+    p = 0.
+    qx = 2.
+    qy = 2.
+    qz = 2.
+    
+    def __init__(self, mesh, mapping=None, **kwargs):
+        Simple.__init__(self, mesh, mapping=mapping, **kwargs)
+        
+    
+    @property
+    def Wsmooth(self):
+        """Full smoothness regularization matrix W"""
+        if getattr(self, '_Wsmooth', None) is None:
+            wlist = (self.Wx, self.Wxx)
+            if self.mesh.dim > 1:
+                wlist += (self.Wy, self.Wyy)
+            if self.mesh.dim > 2:
+                wlist += (self.Wz, self.Wzz)
+            self._Wsmooth = sp.vstack(wlist)
+        return self._Wsmooth
+
+    @property
+    def W(self):
+        """Full regularization matrix W"""
+        if getattr(self, '_W', None) is None:
+            wlist = (self.Ws, self.Wsmooth)
+            self._W = sp.vstack(wlist)
+        return self._W
+    
+    @property
+    def Ws(self):
+        """Regularization matrix Ws"""
+        if getattr(self, 'm', None) is None:
+            self.Rs = Utils.speye(self.mesh.nC)            
+            
+        else:
+            f_m = self.m
+            self.rs = self.R(f_m , self.p, self.eps)
+            #print "Min rs: " + str(np.max(self.rs)) + "Max rs: " + str(np.min(self.rs))
+            self.Rs = Utils.sdiag( self.rs )
+            
+        self._Ws = Utils.sdiag((self.mesh.vol*self.alpha_s*self.gamma)**0.5)*self.Rs
+            
+        return self._Ws
+
+    @property
+    def Wx(self):
+        """Regularization matrix Wx"""
+        
+        if getattr(self, 'm', None) is None:
+            self.Rx = Utils.speye(self.mesh.unitCellGradx.shape[0])            
+            
+        else:
+            f_m = self.mesh.unitCellGradx * self.m
+            self.rx = self.R( f_m , self.qx, self.eps)
+            self.Rx = Utils.sdiag( self.rx )
+            
+        if getattr(self, '_Wx', None) is None:
+            self._Wx = Utils.sdiag((self.mesh.vol*self.alpha_x*self.gamma)**0.5)*self.Rx*self.mesh.unitCellGradx
+        return self._Wx
+
+    @property
+    def Wy(self):
+        """Regularization matrix Wy"""
+        
+        if getattr(self, 'm', None) is None:
+            self.Ry = Utils.speye(self.mesh.unitCellGrady.shape[0])            
+            
+        else:
+            f_m = self.mesh.unitCellGrady * self.m
+            self.ry = self.R( f_m , self.qy, self.eps)
+            self.Ry = Utils.sdiag( self.ry )
+            
+        if getattr(self, '_Wy', None) is None:
+            self._Wy = Utils.sdiag((self.mesh.vol*self.alpha_y*self.gamma)**0.5)*self.Ry*self.mesh.unitCellGrady
+        return self._Wy
+
+    @property
+    def Wz(self):
+        """Regularization matrix Wz"""
+
+        if getattr(self, 'm', None) is None:
+            self.Rz = Utils.speye(self.mesh.unitCellGradz.shape[0])            
+            
+        else:
+            f_m = self.mesh.unitCellGradz * self.m
+            self.rz = self.R( f_m , self.qz, self.eps)
+            self.Rz = Utils.sdiag( self.rz )
+        
+        if getattr(self, '_Wz', None) is None:
+            self._Wz = Utils.sdiag((self.mesh.vol*self.alpha_z*self.gamma)**0.5)*self.Rz*self.mesh.unitCellGradz
+        return self._Wz    
+
+    
+    def R(self, f_m , p, dec):
+
+        eta = (self.eps**(1-p/2.))**0.5
+        r = eta / (f_m**2.+self.eps**2.)**((1-p/2.)/2.)
+
+        return r

SimPEG/Survey.py

@@ -1,6 +1,5 @@
 import Utils, numpy as np, scipy.sparse as sp, uuid
 
-
 class BaseRx(object):
     """SimPEG Receiver Object"""
 
@@ -223,6 +222,8 @@ class BaseSurvey(object):
 
     @srcList.setter
     def srcList(self, value):
+        if isinstance(value, self.srcPair):
+            value = [value]
         assert type(value) is list, 'srcList must be a list'
         assert np.all([isinstance(src, self.srcPair) for src in value]), 'All sources must be instances of %s' % self.srcPair.__name__
         assert len(set(value)) == len(value), 'The srcList must be unique'
@@ -374,3 +375,11 @@ class BaseSurvey(object):
         self.dobs = self.dtrue+noise
         self.std = self.dobs*0 + std
         return self.dobs
+
+class LinearSurvey(BaseSurvey):
+    def projectFields(self, u):
+        return u
+    
+    @property
+    def nD(self):
+        return self.prob.G.shape[0]

SimPEG/Utils/ModelBuilder.py

@@ -118,6 +118,44 @@ def defineElipse(ccMesh, center=[0,0,0], anisotropy=[1,1,1], slope=10., theta=0.
     D = np.sqrt(np.sum(G**2,axis=1))
     return -np.arctan((D-1)*slope)*(2./np.pi)/2.+0.5
 
+def getIndicesSphere(center,radius,ccMesh):
+    """
+        Creates a vector containing the sphere indices in the cell centers mesh.
+        Returns a tuple
+
+        The sphere is defined by the points
+
+        p0, describe the position of the center of the cell
+
+        r, describe the radius of the sphere.
+
+        ccMesh represents the cell-centered mesh
+
+        The points p0 must live in the the same dimensional space as the mesh.
+
+    """
+
+    # Validation: mesh and point (p0) live in the same dimensional space
+    dimMesh = np.size(ccMesh[0,:])
+    assert len(center) == dimMesh, "Dimension mismatch. len(p0) != dimMesh"
+
+    if dimMesh == 1:
+       # Define the reference points
+        
+        ind  = np.abs(center[0] - ccMesh[:,0]) < radius
+
+    elif dimMesh == 2:
+       # Define the reference points
+
+        ind = np.sqrt( ( center[0] - ccMesh[:,0] )**2 + ( center[1] - ccMesh[:,1] )**2 ) < radius
+
+    elif dimMesh == 3:
+        # Define the points
+        ind = np.sqrt( ( center[0] - ccMesh[:,0] )**2 + ( center[1] - ccMesh[:,1] )**2 + ( center[2] - ccMesh[:,2] )**2 ) < radius
+
+    # Return a tuple
+    return ind
+
 def defineTwoLayers(ccMesh,depth,vals=[0,1]):
     """
     Define a two layered model.  Depth of the first layer must be specified.

SimPEG/Utils/SolverUtils.py

@@ -26,7 +26,14 @@ def SolverWrapD(fun, factorize=True, checkAccuracy=True, accuracyTol=1e-6):
 
     def __init__(self, A, **kwargs):
         self.A = A.tocsc()
+
+        self.checkAccuracy = kwargs.get("checkAccuracy", checkAccuracy)
+        if kwargs.has_key("checkAccuracy"): del kwargs["checkAccuracy"]
+        self.accuracyTol = kwargs.get("accuracyTol", accuracyTol)
+        if kwargs.has_key("accuracyTol"): del kwargs["accuracyTol"]
+
         self.kwargs = kwargs
+
         if factorize:
             self.solver = fun(self.A, **kwargs)
 
@@ -57,8 +64,8 @@ def SolverWrapD(fun, factorize=True, checkAccuracy=True, accuracyTol=1e-6):
                 else:
                     X[:,i] = fun(self.A, b[:,i], **self.kwargs)
 
-        if checkAccuracy:
-            _checkAccuracy(self.A, b, X, accuracyTol)
+        if self.checkAccuracy:
+            _checkAccuracy(self.A, b, X, self.accuracyTol)
         return X
 
     def clean(self):
@@ -81,6 +88,12 @@ def SolverWrapI(fun, checkAccuracy=True, accuracyTol=1e-5):
 
     def __init__(self, A, **kwargs):
         self.A = A
+
+        self.checkAccuracy = kwargs.get("checkAccuracy", checkAccuracy)
+        if kwargs.has_key("checkAccuracy"): del kwargs["checkAccuracy"]
+        self.accuracyTol = kwargs.get("accuracyTol", accuracyTol)
+        if kwargs.has_key("accuracyTol"): del kwargs["accuracyTol"]
+
         self.kwargs = kwargs
 
     def __mul__(self, b):
@@ -108,8 +121,8 @@ def SolverWrapI(fun, checkAccuracy=True, accuracyTol=1e-5):
                 else:
                     X[:,i] = out
 
-        if checkAccuracy:
-            _checkAccuracy(self.A, b, X, accuracyTol)
+        if self.checkAccuracy:
+            _checkAccuracy(self.A, b, X, self.accuracyTol)
         return X
 
     def clean(self):

SimPEG/Utils/__init__.py

@@ -1,6 +1,6 @@
 from matutils import *
 from codeutils import *
-from meshutils import exampleLrmGrid, meshTensor, closestPoints, readUBCTensorMesh, writeUBCTensorMesh, writeUBCTensorModel, readVTRFile, writeVTRFile
+from meshutils import *
 from curvutils import volTetra, faceInfo, indexCube
 from interputils import interpmat
 from CounterUtils import *

SimPEG/Utils/codeutils.py

@@ -17,7 +17,7 @@ def memProfileWrapper(towrap, *funNames):
 
         For example::
 
-            foo_mem = memProfile(foo,'my_func')
+            foo_mem = memProfileWrapper(foo,['my_func'])
             fooi = foo_mem()
             for i in range(5):
                 fooi.my_func()

SimPEG/Utils/meshutils.py

@@ -102,223 +102,6 @@ def closestPoints(mesh, pts, gridLoc='CC'):
 
     return nodeInds
 
-def readUBCTensorMesh(fileName):
-    """
-        Read UBC GIF 3DTensor mesh and generate 3D Tensor mesh in simpegTD
-
-        Input:
-        :param fileName, path to the UBC GIF mesh file
-
-        Output:
-        :param SimPEG TensorMesh object
-        :return
-    """
-
-    # Interal function to read cell size lines for the UBC mesh files.
-    def readCellLine(line):
-        for seg in line.split():
-            if '*' in seg:
-                st = seg
-                sp = seg.split('*')
-                re = np.array(sp[0],dtype=int)*(' ' + sp[1])
-                line = line.replace(st,re.strip())
-        return np.array(line.split(),dtype=float)
-
-    # Read the file as line strings, remove lines with comment = !
-    msh = np.genfromtxt(fileName,delimiter='\n',dtype=np.str,comments='!')
-
-    # Fist line is the size of the model
-    sizeM = np.array(msh[0].split(),dtype=float)
-    # Second line is the South-West-Top corner coordinates.
-    x0 = np.array(msh[1].split(),dtype=float)
-    # Read the cell sizes
-    h1 = readCellLine(msh[2])
-    h2 = readCellLine(msh[3])
-    h3temp = readCellLine(msh[4])
-    h3 = h3temp[::-1] # Invert the indexing of the vector to start from the bottom.
-    # Adjust the reference point to the bottom south west corner
-    x0[2] = x0[2] - np.sum(h3)
-    # Make the mesh
-    from SimPEG import Mesh
-    tensMsh = Mesh.TensorMesh([h1,h2,h3],x0)
-    return tensMsh
-
-def readUBCTensorModel(fileName, mesh):
-    """
-        Read UBC 3DTensor mesh model and generate 3D Tensor mesh model in simpeg
-
-        Input:
-        :param fileName, path to the UBC GIF mesh file to read
-        :param mesh, TensorMesh object, mesh that coresponds to the model
-
-        Output:
-        :return numpy array, model with TensorMesh ordered
-    """
-    f = open(fileName, 'r')
-    model = np.array(map(float, f.readlines()))
-    f.close()
-    model = np.reshape(model, (mesh.nCz, mesh.nCx, mesh.nCy), order = 'F')
-    model = model[::-1,:,:]
-    model = np.transpose(model, (1, 2, 0))
-    model = mkvc(model)
-
-    return model
-
-def writeUBCTensorMesh(fileName, mesh):
-    """
-        Writes a SimPEG TensorMesh to a UBC-GIF format mesh file.
-
-        :param str fileName: File to write to
-        :param simpeg.Mesh.TensorMesh mesh: The mesh
-
-    """
-    assert mesh.dim == 3
-    s = ''
-    s += '%i %i %i\n' %tuple(mesh.vnC)
-    origin = mesh.x0 + np.array([0,0,mesh.hz.sum()]) # Have to it in the same operation or use mesh.x0.copy(), otherwise the mesh.x0 is updated.
-    origin.dtype = float
-
-    s += '%.2f %.2f %.2f\n' %tuple(origin)
-    s += ('%.2f '*mesh.nCx+'\n')%tuple(mesh.hx)
-    s += ('%.2f '*mesh.nCy+'\n')%tuple(mesh.hy)
-    s += ('%.2f '*mesh.nCz+'\n')%tuple(mesh.hz[::-1])
-    f = open(fileName, 'w')
-    f.write(s)
-    f.close()
-
-def writeUBCTensorModel(fileName, mesh, model):
-    """
-        Writes a model associated with a SimPEG TensorMesh
-        to a UBC-GIF format model file.
-
-        :param str fileName: File to write to
-        :param simpeg.Mesh.TensorMesh mesh: The mesh
-        :param numpy.ndarray model: The model
-    """
-
-    # Reshape model to a matrix
-    modelMat = mesh.r(model,'CC','CC','M')
-    # Transpose the axes
-    modelMatT = modelMat.transpose((2,0,1))
-    # Flip z to positive down
-    modelMatTR = mkvc(modelMatT[::-1,:,:])
-
-    np.savetxt(fileName, modelMatTR.ravel())
-
-
-def readVTRFile(fileName):
-    """
-        Read VTK Rectilinear (vtr xml file) and return SimPEG Tensor mesh and model
-
-        Input:
-        :param vtrFileName, path to the vtr model file to write to
-
-        Output:
-        :return SimPEG TensorMesh object
-        :return SimPEG model dictionary
-
-    """
-    # Import
-    from vtk import vtkXMLRectilinearGridReader as vtrFileReader
-    from vtk.util.numpy_support import vtk_to_numpy
-
-    # Read the file
-    vtrReader = vtrFileReader()
-    vtrReader.SetFileName(fileName)
-    vtrReader.Update()
-    vtrGrid = vtrReader.GetOutput()
-    # Sort information
-    hx = np.abs(np.diff(vtk_to_numpy(vtrGrid.GetXCoordinates())))
-    xR = vtk_to_numpy(vtrGrid.GetXCoordinates())[0]
-    hy = np.abs(np.diff(vtk_to_numpy(vtrGrid.GetYCoordinates())))
-    yR = vtk_to_numpy(vtrGrid.GetYCoordinates())[0]
-    zD = np.diff(vtk_to_numpy(vtrGrid.GetZCoordinates()))
-    # Check the direction of hz
-    if np.all(zD < 0):
-        hz = np.abs(zD[::-1])
-        zR = vtk_to_numpy(vtrGrid.GetZCoordinates())[-1]
-    else:
-        hz = np.abs(zD)
-        zR = vtk_to_numpy(vtrGrid.GetZCoordinates())[0]
-    x0 = np.array([xR,yR,zR])
-
-    # Make the SimPEG object
-    from SimPEG import Mesh
-    tensMsh = Mesh.TensorMesh([hx,hy,hz],x0)
-
-    # Grap the models
-    modelDict = {}
-    for i in np.arange(vtrGrid.GetCellData().GetNumberOfArrays()):
-        modelName = vtrGrid.GetCellData().GetArrayName(i)
-        if np.all(zD < 0):
-            modFlip = vtk_to_numpy(vtrGrid.GetCellData().GetArray(i))
-            tM = tensMsh.r(modFlip,'CC','CC','M')
-            modArr = tensMsh.r(tM[:,:,::-1],'CC','CC','V')
-        else:
-            modArr = vtk_to_numpy(vtrGrid.GetCellData().GetArray(i))
-        modelDict[modelName] = modArr
-
-    # Return the data
-    return tensMsh, modelDict
-
-def writeVTRFile(fileName,mesh,model=None):
-    """
-    Makes and saves a VTK rectilinear file (vtr) for a simpeg Tensor mesh and model.
-
-    Input:
-    :param str, path to the output vtk file
-    :param mesh, SimPEG TensorMesh object - mesh to be transfer to VTK
-    :param model, dictionary of numpy.array - Name('s) and array('s). Match number of cells
-
-    """
-    # Import
-    from vtk import vtkRectilinearGrid as rectGrid, vtkXMLRectilinearGridWriter as rectWriter
-    from vtk.util.numpy_support import numpy_to_vtk
-
-    # Deal with dimensionalities
-    if mesh.dim >= 1:
-        vX = mesh.vectorNx
-        xD = mesh.nNx
-        yD,zD = 1,1
-        vY, vZ = np.array([0,0])
-    if mesh.dim >= 2:
-        vY = mesh.vectorNy
-        yD = mesh.nNy
-    if mesh.dim == 3:
-        vZ = mesh.vectorNz
-        zD = mesh.nNz
-    # Use rectilinear VTK grid.
-    # Assign the spatial information.
-    vtkObj = rectGrid()
-    vtkObj.SetDimensions(xD,yD,zD)
-    vtkObj.SetXCoordinates(numpy_to_vtk(vX,deep=1))
-    vtkObj.SetYCoordinates(numpy_to_vtk(vY,deep=1))
-    vtkObj.SetZCoordinates(numpy_to_vtk(vZ,deep=1))
-
-    # Assign the model('s) to the object
-    for item in model.iteritems():
-        # Convert numpy array
-        vtkDoubleArr = numpy_to_vtk(item[1],deep=1)
-        vtkDoubleArr.SetName(item[0])
-        vtkObj.GetCellData().AddArray(vtkDoubleArr)
-    # Set the active scalar
-    vtkObj.GetCellData().SetActiveScalars(model.keys()[0])
-    vtkObj.Update()
-
-
-    # Check the extension of the fileName
-    ext = os.path.splitext(fileName)[1]
-    if ext is '':
-        fileName = fileName + '.vtr'
-    elif ext not in '.vtr':
-        raise IOError('{:s} is an incorrect extension, has to be .vtr')
-    # Write the file.
-    vtrWriteFilter = rectWriter()
-    vtrWriteFilter.SetInput(vtkObj)
-    vtrWriteFilter.SetFileName(fileName)
-    vtrWriteFilter.Update()
-
-
 def ExtractCoreMesh(xyzlim, mesh, meshType='tensor'):
     """
         Extracts Core Mesh from Global mesh

docs/flow/index.rst

@@ -41,7 +41,7 @@ Here we reproduce the results from Celia et al. (1990):
 Richards
 ========
 
-.. automodule:: simpegFLOW.Richards.Empirical
+.. automodule:: SimPEG.FLOW.Richards.Empirical
     :show-inheritance:
     :members:
     :undoc-members:

tests/base/test_regularization.py

@@ -4,11 +4,17 @@ from SimPEG import *
 from scipy.sparse.linalg import dsolve
 import inspect
 
+TOL = 1e-20
 
 class RegularizationTests(unittest.TestCase):
 
     def setUp(self):
-        self.mesh2 = Mesh.TensorMesh([3, 2])
+        hx, hy, hz = np.random.rand(10), np.random.rand(9), np.random.rand(8)
+        hx, hy, hz = hx/hx.sum(), hy/hy.sum(), hz/hz.sum()
+        mesh1 = Mesh.TensorMesh([hx])
+        mesh2 = Mesh.TensorMesh([hx, hy])
+        mesh3 = Mesh.TensorMesh([hx, hy, hz])
+        self.meshlist = [mesh1,mesh2, mesh3]
 
     def test_regularization(self):
         for R in dir(Regularization):
@@ -16,18 +22,63 @@ class RegularizationTests(unittest.TestCase):
             if not inspect.isclass(r): continue
             if not issubclass(r, Regularization.BaseRegularization):
                 continue
-            # if 'Regularization' not in R: continue
-            mapping = r.mapPair(self.mesh2)
-            reg = r(self.mesh2, mapping=mapping)
-            m = np.random.rand(mapping.nP)
-            reg.mref = m[:]*np.mean(m)
 
-            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)
+            for i, mesh in enumerate(self.meshlist):
+
+                print 'Testing %iD'%mesh.dim
+
+                mapping = r.mapPair(mesh)
+                reg = r(mesh, mapping=mapping)
+                m = np.random.rand(mapping.nP)
+                reg.mref = np.ones_like(m)*np.mean(m)
+
+                print 'Check: phi_m (mref) = %f' %reg.eval(reg.mref)
+                passed = reg.eval(reg.mref) < TOL
+                self.assertTrue(passed)
+
+                print 'Check:', R
+                passed = Tests.checkDerivative(lambda m : [reg.eval(m), reg.evalDeriv(m)], m, plotIt=False)
+                self.assertTrue(passed)
+
+                print 'Check 2 Deriv:', R
+                passed = Tests.checkDerivative(lambda m : [reg.evalDeriv(m), reg.eval2Deriv(m)], m, plotIt=False)
+                self.assertTrue(passed)
+
+    def test_regularization_ActiveCells(self):
+        for R in dir(Regularization):
+            r = getattr(Regularization, R)
+            if not inspect.isclass(r): continue
+            if not issubclass(r, Regularization.BaseRegularization):
+                continue
+
+            for i, mesh in enumerate(self.meshlist):
+
+                print 'Testing Active Cells %iD'%(mesh.dim)
+
+                if mesh.dim == 1:
+                    indAct = Utils.mkvc(mesh.gridCC <= 0.8)
+                elif mesh.dim == 2:
+                    indAct = Utils.mkvc(mesh.gridCC[:,-1] <= 2*np.sin(2*np.pi*mesh.gridCC[:,0])+0.5)
+                elif mesh.dim == 3:
+                    indAct = Utils.mkvc(mesh.gridCC[:,-1] <= 2*np.sin(2*np.pi*mesh.gridCC[:,0])+0.5 * 2*np.sin(2*np.pi*mesh.gridCC[:,1])+0.5)
+
+                mapping = Maps.IdentityMap(nP=indAct.nonzero()[0].size)
+
+                reg = r(mesh, mapping=mapping, indActive=indAct)
+                m = np.random.rand(mesh.nC)[indAct]
+                reg.mref = np.ones_like(m)*np.mean(m)
+
+                print 'Check: phi_m (mref) = %f' %reg.eval(reg.mref)
+                passed = reg.eval(reg.mref) < TOL
+                self.assertTrue(passed)
+
+                print 'Check:', R
+                passed = Tests.checkDerivative(lambda m : [reg.eval(m), reg.evalDeriv(m)], m, plotIt=False)
+                self.assertTrue(passed)
+
+                print 'Check 2 Deriv:', R
+                passed = Tests.checkDerivative(lambda m : [reg.evalDeriv(m), reg.eval2Deriv(m)], m, plotIt=False)
+                self.assertTrue(passed)
 
 
 if __name__ == '__main__':

tests/mesh/test_MeshIO.py

@@ -0,0 +1,100 @@
+import numpy as np
+import unittest, os
+import SimPEG as simpeg
+from SimPEG.Mesh import TensorMesh, TreeMesh
+
+
+class TestTensorMeshIO(unittest.TestCase):
+
+    def setUp(self):
+        h = np.ones(16)
+        mesh = TensorMesh([h,2*h,3*h])
+        self.mesh = mesh
+
+    def test_UBCfiles(self):
+
+        mesh = self.mesh
+        # Make a vector
+        vec = np.arange(mesh.nC)
+        # Write and read
+        mesh.writeUBC('temp.msh', {'arange.txt':vec})
+        meshUBC = TensorMesh.readUBC('temp.msh')
+        vecUBC  = meshUBC.readModelUBC('arange.txt')
+
+        # The mesh
+        assert mesh.__str__() == meshUBC.__str__()
+        assert np.sum(mesh.gridCC - meshUBC.gridCC) == 0
+        assert np.sum(vec - vecUBC) == 0
+        assert np.all(np.array(mesh.h) - np.array(meshUBC.h) == 0)
+
+
+        vecUBC  = mesh.readModelUBC('arange.txt')
+        assert np.sum(vec - vecUBC) == 0
+
+        mesh.writeModelUBC('arange2.txt', vec + 1)
+        vec2UBC  = mesh.readModelUBC('arange2.txt')
+        assert np.sum(vec + 1 - vec2UBC) == 0
+
+        print 'IO of UBC tensor mesh files is working'
+        os.remove('temp.msh')
+        os.remove('arange.txt')
+        os.remove('arange2.txt')
+
+    def test_VTKfiles(self):
+        mesh = self.mesh
+        vec = np.arange(mesh.nC)
+
+        mesh.writeVTK('temp.vtr', {'arange.txt':vec})
+        meshVTR, models = TensorMesh.readVTK('temp.vtr')
+
+        assert mesh.__str__() == meshVTR.__str__()
+        assert np.all(np.array(mesh.h) - np.array(meshVTR.h) == 0)
+
+        assert 'arange.txt' in models
+        vecVTK = models['arange.txt']
+        assert np.sum(vec - vecVTK) == 0
+
+        print 'IO of VTR tensor mesh files is working'
+        os.remove('temp.vtr')
+
+
+class TestOcTreeMeshIO(unittest.TestCase):
+
+    def setUp(self):
+        h = np.ones(16)
+        mesh = TreeMesh([h,2*h,3*h])
+        mesh.refine(3)
+        mesh._refineCell([0,0,0,3])
+        mesh._refineCell([0,2,0,3])
+        self.mesh = mesh
+
+    def test_UBCfiles(self):
+
+        mesh = self.mesh
+        # Make a vector
+        vec = np.arange(mesh.nC)
+        # Write and read
+        mesh.writeUBC('temp.msh', {'arange.txt':vec})
+        meshUBC = TreeMesh.readUBC('temp.msh')
+        vecUBC  = meshUBC.readModelUBC('arange.txt')
+
+        # The mesh
+        assert mesh.__str__() == meshUBC.__str__()
+        assert np.sum(mesh.gridCC - meshUBC.gridCC) == 0
+        assert np.sum(vec - vecUBC) == 0
+        assert np.all(np.array(mesh.h) - np.array(meshUBC.h) == 0)
+        print 'IO of UBC octree files is working'
+        os.remove('temp.msh')
+        os.remove('arange.txt')
+
+    def test_VTUfiles(self):
+        mesh = self.mesh
+        vec = np.arange(mesh.nC)
+        mesh.writeVTK('temp.vtu',{'arange':vec})
+        print 'Writing of VTU files is working'
+        os.remove('temp.vtu')
+
+
+
+if __name__ == '__main__':
+    unittest.main()

tests/mesh/test_TreeMesh.py

@@ -26,6 +26,27 @@ class TestSimpleQuadTree(unittest.TestCase):
 
         assert np.allclose(np.r_[M._areaFxFull, M._areaFyFull], M._deflationMatrix('F') * M.area)
 
+    def test_getitem(self):
+        M = Mesh.TreeMesh([4,4])
+        M.refine(1)
+        assert M.nC == 4
+        assert len(M) == M.nC
+        assert np.allclose(M[0].center, [0.25,0.25])
+        actual = [[0,0],[0.5,0],[0,0.5],[0.5,0.5]]
+        for i, n in enumerate(M[0].nodes):
+            assert np.allclose(M._gridN[n,:], actual[i])
+
+    def test_getitem3D(self):
+        M = Mesh.TreeMesh([4,4,4])
+        M.refine(1)
+        assert M.nC == 8
+        assert len(M) == M.nC
+        assert np.allclose(M[0].center, [0.25,0.25,0.25])
+        actual = [[0,0,0],[0.5,0,0],[0,0.5,0],[0.5,0.5,0],
+                  [0,0,0.5],[0.5,0,0.5],[0,0.5,0.5],[0.5,0.5,0.5]]
+        for i, n in enumerate(M[0].nodes):
+            assert np.allclose(M._gridN[n,:], actual[i])
+
     def test_refine(self):
         M = Mesh.TreeMesh([4,4,4])
         M.refine(1)