simpeg/SimPEG/EM/Static/IP/ProblemIP.py

from SimPEG import Problem, Utils, Maps, Mesh
from SimPEG.EM.Base import BaseEMProblem
from SimPEG.EM.Static.DC.FieldsDC import Fields, Fields_CC, Fields_N
from SimPEG.Utils import sdiag
import numpy as np
from SimPEG.Utils import Zero
from SimPEG.EM.Static.DC import getxBCyBC_CC
from SurveyIP import Survey

class IPPropMap(Maps.PropMap):
    """
        Property Map for IP Problems. The electrical chargeability,
        (\\(\\eta\\)) is the default inversion property
    """
    eta = Maps.Property("Electrical Chargeability", defaultInvProp = True)

class BaseIPProblem(BaseEMProblem):

    surveyPair = Survey
    fieldsPair = Fields
    PropMap = IPPropMap
    Ainv = None
    sigma = None
    rho = None
    f = None
    Ainv = None

    def fields(self, m):
        self.curModel = m
        if self.f is None:
            self.f = self.fieldsPair(self.mesh, self.survey)
            if self.Ainv == None:
                A = self.getA()
                self.Ainv = self.Solver(A, **self.solverOpts)
            RHS = self.getRHS()
            u = self.Ainv * RHS
            Srcs = self.survey.srcList
            self.f[Srcs, self._solutionType] = u
        return self.f

    def Jvec(self, m, v, f=None):

        if f is None:
            f = self.fields(m)

        self.curModel = m

        Jv = self.dataPair(self.survey) #same size as the data

        A = self.getA()

        for src in self.survey.srcList:
            u_src = f[src, self._solutionType] # solution vector
            dA_dm_v = self.getADeriv(u_src, v)
            dRHS_dm_v = self.getRHSDeriv(src, v)
            du_dm_v = self.Ainv * ( - dA_dm_v + dRHS_dm_v )

            for rx in src.rxList:
                df_dmFun = getattr(f, '_%sDeriv'%rx.projField, None)
                df_dm_v = df_dmFun(src, du_dm_v, v, adjoint=False)
                Jv[src, rx] = rx.evalDeriv(src, self.mesh, f, df_dm_v)
        # Conductivity (d u / d log sigma)
        if self._formulation is 'EB':
            return -Utils.mkvc(Jv)
        # Conductivity (d u / d log rho)
        if self._formulation is 'HJ':
            return Utils.mkvc(Jv)

    def Jtvec(self, m, v, f=None):
        if f is None:
            f = self.fields(m)

        self.curModel = m

        # Ensure v is a data object.
        if not isinstance(v, self.dataPair):
            v = self.dataPair(self.survey, v)

        Jtv = np.zeros(m.size)
        AT = self.getA()

        for src in self.survey.srcList:
            u_src = f[src, self._solutionType]
            for rx in src.rxList:
                PTv = rx.evalDeriv(src, self.mesh, f, v[src, rx], adjoint=True) # wrt f, need possibility wrt m
                df_duTFun = getattr(f, '_%sDeriv'%rx.projField, None)
                df_duT, df_dmT = df_duTFun(src, None, PTv, adjoint=True)
                ATinvdf_duT = self.Ainv * df_duT
                dA_dmT = self.getADeriv(u_src, ATinvdf_duT, adjoint=True)
                dRHS_dmT = self.getRHSDeriv(src, ATinvdf_duT, adjoint=True)
                du_dmT = -dA_dmT + dRHS_dmT
                Jtv += (df_dmT + du_dmT).astype(float)
        # Conductivity ((d u / d log sigma).T)
        if self._formulation is 'EB':
            return -Utils.mkvc(Jtv)
        # Conductivity ((d u / d log rho).T)
        if self._formulation is 'HJ':
            return Utils.mkvc(Jtv)

    def getSourceTerm(self):
        """
        takes concept of source and turns it into a matrix
        """
        """
        Evaluates the sources, and puts them in matrix form

        :rtype: (numpy.ndarray, numpy.ndarray)
        :return: q (nC or nN, nSrc)
        """

        Srcs = self.survey.srcList

        if self._formulation is 'EB':
            n = self.mesh.nN
            # return NotImplementedError

        elif self._formulation is 'HJ':
            n = self.mesh.nC

        q = np.zeros((n, len(Srcs)))

        for i, src in enumerate(Srcs):
            q[:,i] = src.eval(self)
        return q

    @property
    def deleteTheseOnModelUpdate(self):
        toDelete = []
        return toDelete

    # assume log rho or log cond
    @property
    def MeSigma(self):
        """
            Edge inner product matrix for \\(\\sigma\\). Used in the E-B formulation
        """
        if getattr(self, '_MeSigma', None) is None:
            self._MeSigma = self.mesh.getEdgeInnerProduct(self.sigma)
        return self._MeSigma

    @property
    def MfRhoI(self):
        """
            Inverse of :code:`MfRho`
        """
        if getattr(self, '_MfRhoI', None) is None:
            self._MfRhoI = self.mesh.getFaceInnerProduct(self.rho, invMat=True)
        return self._MfRhoI

    def MfRhoIDeriv(self,u):
        """
            Derivative of :code:`MfRhoI` with respect to the model.
        """

        dMfRhoI_dI = -self.MfRhoI**2
        dMf_drho = self.mesh.getFaceInnerProductDeriv(self.rho)(u)
        drho_dlogrho = Utils.sdiag(self.rho)*self.curModel.etaDeriv
        return dMfRhoI_dI * ( dMf_drho * ( drho_dlogrho))

    # TODO: This should take a vector
    def MeSigmaDeriv(self, u):
        """
            Derivative of MeSigma with respect to the model
        """
        dsigma_dlogsigma = Utils.sdiag(self.sigma)*self.curModel.etaDeriv
        return self.mesh.getEdgeInnerProductDeriv(self.sigma)(u) * dsigma_dlogsigma

class Problem3D_CC(BaseIPProblem):

    _solutionType = 'phiSolution'
    _formulation  = 'HJ' # CC potentials means J is on faces
    fieldsPair    = Fields_CC

    def __init__(self, mesh, **kwargs):
        BaseIPProblem.__init__(self, mesh, **kwargs)
        self.setBC()

    def getA(self):
        """

        Make the A matrix for the cell centered DC resistivity problem

        A = D MfRhoI G

        """

        D = self.Div
        G = self.Grad
        MfRhoI = self.MfRhoI
        A = D * MfRhoI * G

        # I think we should deprecate this for DC problem.
        # if self._makeASymmetric is True:
        #     return V.T * A
        return A

    def getADeriv(self, u, v, adjoint= False):

        D = self.Div
        G = self.Grad
        MfRhoIDeriv = self.MfRhoIDeriv

        if adjoint:
            # if self._makeASymmetric is True:
            #     v = V * v
            return(MfRhoIDeriv( G * u ).T) * ( D.T * v)

        # I think we should deprecate this for DC problem.
        # if self._makeASymmetric is True:
        #     return V.T * ( D * ( MfRhoIDeriv( D.T * ( V * u ) ) * v ) )
        return D * (MfRhoIDeriv( G * u ) * v)

    def getRHS(self):
        """
        RHS for the DC problem

        q
        """

        RHS = self.getSourceTerm()

        # I think we should deprecate this for DC problem.
        # if self._makeASymmetric is True:
        #     return self.Vol.T * RHS

        return RHS

    def getRHSDeriv(self, src, v, adjoint=False):
        """
        Derivative of the right hand side with respect to the model
        """
        # TODO: add qDeriv for RHS depending on m
        # qDeriv = src.evalDeriv(self, adjoint=adjoint)
        # return qDeriv
        return Zero()

    def setBC(self):
        if self.mesh.dim==3:
            fxm,fxp,fym,fyp,fzm,fzp = self.mesh.faceBoundaryInd
            gBFxm = self.mesh.gridFx[fxm,:]
            gBFxp = self.mesh.gridFx[fxp,:]
            gBFym = self.mesh.gridFy[fym,:]
            gBFyp = self.mesh.gridFy[fyp,:]
            gBFzm = self.mesh.gridFz[fzm,:]
            gBFzp = self.mesh.gridFz[fzp,:]

            # Setup Mixed B.C (alpha, beta, gamma)
            temp_xm, temp_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
            temp_ym, temp_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])
            temp_zm, temp_zp = np.ones_like(gBFzm[:,2]), np.ones_like(gBFzp[:,2])

            alpha_xm, alpha_xp = temp_xm*0., temp_xp*0.
            alpha_ym, alpha_yp = temp_ym*0., temp_yp*0.
            alpha_zm, alpha_zp = temp_zm*0., temp_zp*0.

            beta_xm, beta_xp = temp_xm, temp_xp
            beta_ym, beta_yp = temp_ym, temp_yp
            beta_zm, beta_zp = temp_zm, temp_zp

            gamma_xm, gamma_xp = temp_xm*0., temp_xp*0.
            gamma_ym, gamma_yp = temp_ym*0., temp_yp*0.
            gamma_zm, gamma_zp = temp_zm*0., temp_zp*0.

            alpha = [alpha_xm, alpha_xp, alpha_ym, alpha_yp, alpha_zm, alpha_zp]
            beta =  [beta_xm, beta_xp, beta_ym, beta_yp, beta_zm, beta_zp]
            gamma = [gamma_xm, gamma_xp, gamma_ym, gamma_yp, gamma_zm, gamma_zp]

        elif self.mesh.dim==2:

            fxm,fxp,fym,fyp = self.mesh.faceBoundaryInd
            gBFxm = self.mesh.gridFx[fxm,:]
            gBFxp = self.mesh.gridFx[fxp,:]
            gBFym = self.mesh.gridFy[fym,:]
            gBFyp = self.mesh.gridFy[fyp,:]

            # Setup Mixed B.C (alpha, beta, gamma)
            temp_xm, temp_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
            temp_ym, temp_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])

            alpha_xm, alpha_xp = temp_xm*0., temp_xp*0.
            alpha_ym, alpha_yp = temp_ym*0., temp_yp*0.

            beta_xm, beta_xp = temp_xm, temp_xp
            beta_ym, beta_yp = temp_ym, temp_yp

            gamma_xm, gamma_xp = temp_xm*0., temp_xp*0.
            gamma_ym, gamma_yp = temp_ym*0., temp_yp*0.

            alpha = [alpha_xm, alpha_xp, alpha_ym, alpha_yp]
            beta =  [beta_xm, beta_xp, beta_ym, beta_yp]
            gamma = [gamma_xm, gamma_xp, gamma_ym, gamma_yp]

        x_BC, y_BC = getxBCyBC_CC(self.mesh, alpha, beta, gamma)
        V = self.Vol
        self.Div = V * self.mesh.faceDiv
        P_BC, B = self.mesh.getBCProjWF_simple()
        M = B*self.mesh.aveCC2F
        self.Grad = self.Div.T - P_BC*Utils.sdiag(y_BC)*M


class Problem3D_N(BaseIPProblem):

    _solutionType = 'phiSolution'
    _formulation  = 'EB' # N potentials means B is on faces
    fieldsPair    = Fields_N

    def __init__(self, mesh, **kwargs):
        BaseIPProblem.__init__(self, mesh, **kwargs)

    def getA(self):
        """

        Make the A matrix for the cell centered DC resistivity problem

        A = G.T MeSigma G

        """

        MeSigma = self.MeSigma
        Grad = self.mesh.nodalGrad
        A = Grad.T * MeSigma * Grad

        # Handling Null space of A
        A[0,0] = A[0,0] + 1.

        return A

    def getADeriv(self, u, v, adjoint=False):
        """

        Product of the derivative of our system matrix with respect to the model and a vector

        """
        MeSigma = self.MeSigma
        Grad = self.mesh.nodalGrad
        if not adjoint:
            return Grad.T*(self.MeSigmaDeriv(Grad*u)*v)
        elif adjoint:
            return self.MeSigmaDeriv(Grad*u).T * (Grad*v)


    def getRHS(self):
        """
        RHS for the DC problem

        q
        """

        RHS = self.getSourceTerm()
        return RHS

    def getRHSDeriv(self, src, v, adjoint=False):
        """
        Derivative of the right hand side with respect to the model
        """
        # TODO: add qDeriv for RHS depending on m
        # qDeriv = src.evalDeriv(self, adjoint=adjoint)
        # return qDeriv
        return Zero()

if __name__ == '__main__':


    cs = 12.5
    hx = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
    hy = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
    hz = [(cs,7, -1.3),(cs,20)]
    mesh = Mesh.TensorMesh([hx, hy, hz],x0="CCN")
    sigma = np.ones(mesh.nC)
    prob = BaseIPProblem(mesh, sigma=sigma)