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Working on SIP
This commit is contained in:
seogi_macbook
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from SimPEG import Problem, Utils, Maps, Mesh
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from SimPEG.EM.Base import BaseEMProblem
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from SimPEG.EM.Static.DC.FieldsDC import Fields, Fields_CC, Fields_N
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from SimPEG.Utils import sdiag
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import numpy as np
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from SimPEG.Utils import Zero
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from SimPEG.EM.Static.DC import getxBCyBC_CC
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from SurveySIP import Survey
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class ColeColePropMap(Maps.PropMap):
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"""
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Property Map for EM Problems. The electrical conductivity (\\(\\sigma\\)) is the default inversion property, and the default value of the magnetic permeability is that of free space (\\(\\mu = 4\\pi\\times 10^{-7} \\) H/m)
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"""
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eta = Maps.Property("Electrical Conductivity", defaultInvProp=True)
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tau = Maps.Property("Electrical Conductivity", defaultVal=0.1, propertyLink=('taui', Maps.ReciprocalMap))
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taui = Maps.Property("Electrical Conductivity", defaultVal=1., propertyLink=('tau', Maps.ReciprocalMap))
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c = Maps.Property("Electrical Conductivity", defaultVal=1.)
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class BaseSIPProblem(BaseEMProblem):
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surveyPair = Survey
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fieldsPair = Fields
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PropMap = ColeColePropMap
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Ainv = None
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sigma = None
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rho = None
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f = None
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Ainv = None
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def DebyeTime(t):
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peta = self.curModel.eta*np.exp(-self.curModel.taui*t)
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return peta
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def EtaDeriv(t):
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return np.exp(-self.curModel.taui*t)
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def TauiDeriv(t):
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return -self.curModel.eta*t*np.exp(-self.curModel.taui*t)
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def fields(self, m):
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self.curModel = m
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if self.f is None:
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self.f = self.fieldsPair(self.mesh, self.survey)
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if self.Ainv == None:
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A = self.getA()
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self.Ainv = self.Solver(A, **self.solverOpts)
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RHS = self.getRHS()
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u = self.Ainv * RHS
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Srcs = self.survey.srcList
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self.f[Srcs, self._solutionType] = u
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return self.f
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def forward(self, m, f=None):
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if f is None:
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f = self.fields(m)
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self.curModel = m
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Jv = self.dataPair(self.survey) #same size as the data
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# A = self.getA()
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JvAll = []
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for tind in range(len(self.survey.times)):
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#Pseudo-chareability
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v = DebyeTime(self.survey.times[tind])
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for src in self.survey.srcList:
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u_src = f[src, self._solutionType] # solution vector
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dA_dm_v = self.getADeriv(u_src, v)
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dRHS_dm_v = self.getRHSDeriv(src, v)
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du_dm_v = self.Ainv * ( - dA_dm_v + dRHS_dm_v )
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for rx in src.rxList:
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timeindex = rx.getTimeP(self.survey.times)
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if timeindex[tind]:
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df_dmFun = getattr(f, '_%sDeriv'%rx.projField, None)
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df_dm_v = df_dmFun(src, du_dm_v, v, adjoint=False)
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Jv[src, rx] = rx.evalDeriv(src, self.mesh, f, df_dm_v)
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JvAll.append(Utils.mkvc(Jv))
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# Conductivity (d u / d log sigma)
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if self._formulation is 'EB':
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return -np.hstack(JvAll)
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# Conductivity (d u / d log rho)
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if self._formulation is 'HJ':
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return np.hstack(JvAll)
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# def Jvec(self, m, v, f=None):
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# if f is None:
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# f = self.fields(m)
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# self.curModel = m
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# Jv = self.dataPair(self.survey) #same size as the data
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# x1 =
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# x2 =
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# # A = self.getA()
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# for src in self.survey.srcList:
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# u_src = f[src, self._solutionType] # solution vector
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# dA_dm_v = self.getADeriv(u_src, v)
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# dRHS_dm_v = self.getRHSDeriv(src, v)
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# du_dm_v = self.Ainv * ( - dA_dm_v + dRHS_dm_v )
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# for rx in src.rxList:
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# for tind in range(len(self.survey.times)):
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# df_dmFun = getattr(f, '_%sDeriv'%rx.projField, None)
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# df_dm_v = df_dmFun(src, du_dm_v, v, adjoint=False)
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# Jv[src, rx] = rx.evalDeriv(src, self.mesh, f, df_dm_v)
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# # Conductivity (d u / d log sigma)
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# if self._formulation is 'EB':
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# return -Utils.mkvc(Jv)
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# # Conductivity (d u / d log rho)
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# if self._formulation is 'HJ':
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# return Utils.mkvc(Jv)
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# def Jtvec(self, m, v, f=None):
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# if f is None:
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# f = self.fields(m)
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# self.curModel = m
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# # Ensure v is a data object.
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# if not isinstance(v, self.dataPair):
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# v = self.dataPair(self.survey, v)
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# Jtv = np.zeros(m.size)
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# # AT = self.getA()
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# for src in self.survey.srcList:
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# u_src = f[src, self._solutionType]
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# for rx in src.rxList:
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# PTv = rx.evalDeriv(src, self.mesh, f, v[src, rx], adjoint=True) # wrt f, need possibility wrt m
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# df_duTFun = getattr(f, '_%sDeriv'%rx.projField, None)
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# df_duT, df_dmT = df_duTFun(src, None, PTv, adjoint=True)
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# ATinvdf_duT = self.Ainv * df_duT
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# dA_dmT = self.getADeriv(u_src, ATinvdf_duT, adjoint=True)
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# dRHS_dmT = self.getRHSDeriv(src, ATinvdf_duT, adjoint=True)
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# du_dmT = -dA_dmT + dRHS_dmT
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# Jtv += df_dmT + du_dmT
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# # Conductivity ((d u / d log sigma).T)
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# if self._formulation is 'EB':
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# return -Utils.mkvc(Jtv)
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# # Conductivity ((d u / d log rho).T)
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# if self._formulation is 'HJ':
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# return Utils.mkvc(Jtv)
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def getSourceTerm(self):
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"""
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takes concept of source and turns it into a matrix
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"""
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"""
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Evaluates the sources, and puts them in matrix form
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:rtype: (numpy.ndarray, numpy.ndarray)
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:return: q (nC or nN, nSrc)
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"""
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Srcs = self.survey.srcList
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if self._formulation is 'EB':
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n = self.mesh.nN
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# return NotImplementedError
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elif self._formulation is 'HJ':
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n = self.mesh.nC
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q = np.zeros((n, len(Srcs)))
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for i, src in enumerate(Srcs):
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q[:,i] = src.eval(self)
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return q
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@property
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def deleteTheseOnModelUpdate(self):
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toDelete = []
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return toDelete
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# assume log rho or log cond
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@property
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def MeSigma(self):
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"""
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Edge inner product matrix for \\(\\sigma\\). Used in the E-B formulation
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"""
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if getattr(self, '_MeSigma', None) is None:
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self._MeSigma = self.mesh.getEdgeInnerProduct(self.sigma)
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return self._MeSigma
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@property
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def MfRhoI(self):
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"""
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Inverse of :code:`MfRho`
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"""
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if getattr(self, '_MfRhoI', None) is None:
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self._MfRhoI = self.mesh.getFaceInnerProduct(self.rho, invMat=True)
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return self._MfRhoI
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def MfRhoIDeriv(self,u):
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"""
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Derivative of :code:`MfRhoI` with respect to the model.
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"""
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dMfRhoI_dI = -self.MfRhoI**2
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dMf_drho = self.mesh.getFaceInnerProductDeriv(self.rho)(u)
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drho_dlogrho = Utils.sdiag(self.rho)
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return dMfRhoI_dI * ( dMf_drho * ( drho_dlogrho))
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# TODO: This should take a vector
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def MeSigmaDeriv(self, u):
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"""
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Derivative of MeSigma with respect to the model
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"""
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dsigma_dlogsigma = Utils.sdiag(self.sigma)
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return self.mesh.getEdgeInnerProductDeriv(self.sigma)(u) * dsigma_dlogsigma
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class Problem3D_CC(BaseSIPProblem):
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_solutionType = 'phiSolution'
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_formulation = 'HJ' # CC potentials means J is on faces
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fieldsPair = Fields_CC
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def __init__(self, mesh, **kwargs):
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BaseSIPProblem.__init__(self, mesh, **kwargs)
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self.setBC()
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def getA(self):
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"""
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Make the A matrix for the cell centered DC resistivity problem
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A = D MfRhoI D^\\top V
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"""
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D = self.Div
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G = self.Grad
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# TODO: this won't work for full anisotropy
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MfRhoI = self.MfRhoI
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A = D * MfRhoI * G
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# I think we should deprecate this for DC problem.
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# if self._makeASymmetric is True:
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# return V.T * A
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return A
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def getADeriv(self, u, v, adjoint= False):
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D = self.Div
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G = self.Grad
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MfRhoIDeriv = self.MfRhoIDeriv
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if adjoint:
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# if self._makeASymmetric is True:
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# v = V * v
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return(MfRhoIDeriv( G * u ).T) * ( D.T * v)
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# I think we should deprecate this for DC problem.
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# if self._makeASymmetric is True:
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# return V.T * ( D * ( MfRhoIDeriv( D.T * ( V * u ) ) * v ) )
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return D * (MfRhoIDeriv( G * u ) * v)
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def getRHS(self):
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"""
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RHS for the DC problem
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q
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"""
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RHS = self.getSourceTerm()
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# I think we should deprecate this for DC problem.
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# if self._makeASymmetric is True:
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# return self.Vol.T * RHS
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return RHS
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def getRHSDeriv(self, src, v, adjoint=False):
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"""
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Derivative of the right hand side with respect to the model
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"""
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# TODO: add qDeriv for RHS depending on m
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# qDeriv = src.evalDeriv(self, adjoint=adjoint)
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# return qDeriv
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return Zero()
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def setBC(self):
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if self.mesh.dim==3:
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fxm,fxp,fym,fyp,fzm,fzp = self.mesh.faceBoundaryInd
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gBFxm = self.mesh.gridFx[fxm,:]
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gBFxp = self.mesh.gridFx[fxp,:]
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gBFym = self.mesh.gridFy[fym,:]
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gBFyp = self.mesh.gridFy[fyp,:]
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gBFzm = self.mesh.gridFz[fzm,:]
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gBFzp = self.mesh.gridFz[fzp,:]
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# Setup Mixed B.C (alpha, beta, gamma)
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temp_xm, temp_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
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temp_ym, temp_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])
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temp_zm, temp_zp = np.ones_like(gBFzm[:,2]), np.ones_like(gBFzp[:,2])
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alpha_xm, alpha_xp = temp_xm*0., temp_xp*0.
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alpha_ym, alpha_yp = temp_ym*0., temp_yp*0.
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alpha_zm, alpha_zp = temp_zm*0., temp_zp*0.
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beta_xm, beta_xp = temp_xm, temp_xp
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beta_ym, beta_yp = temp_ym, temp_yp
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beta_zm, beta_zp = temp_zm, temp_zp
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gamma_xm, gamma_xp = temp_xm*0., temp_xp*0.
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gamma_ym, gamma_yp = temp_ym*0., temp_yp*0.
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gamma_zm, gamma_zp = temp_zm*0., temp_zp*0.
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alpha = [alpha_xm, alpha_xp, alpha_ym, alpha_yp, alpha_zm, alpha_zp]
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beta = [beta_xm, beta_xp, beta_ym, beta_yp, beta_zm, beta_zp]
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gamma = [gamma_xm, gamma_xp, gamma_ym, gamma_yp, gamma_zm, gamma_zp]
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elif self.mesh.dim==2:
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fxm,fxp,fym,fyp = self.mesh.faceBoundaryInd
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gBFxm = self.mesh.gridFx[fxm,:]
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gBFxp = self.mesh.gridFx[fxp,:]
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gBFym = self.mesh.gridFy[fym,:]
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gBFyp = self.mesh.gridFy[fyp,:]
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# Setup Mixed B.C (alpha, beta, gamma)
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temp_xm, temp_xp = np.ones_like(gBFxm[:,0]), np.ones_like(gBFxp[:,0])
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temp_ym, temp_yp = np.ones_like(gBFym[:,1]), np.ones_like(gBFyp[:,1])
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alpha_xm, alpha_xp = temp_xm*0., temp_xp*0.
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alpha_ym, alpha_yp = temp_ym*0., temp_yp*0.
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beta_xm, beta_xp = temp_xm, temp_xp
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beta_ym, beta_yp = temp_ym, temp_yp
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gamma_xm, gamma_xp = temp_xm*0., temp_xp*0.
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gamma_ym, gamma_yp = temp_ym*0., temp_yp*0.
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alpha = [alpha_xm, alpha_xp, alpha_ym, alpha_yp]
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beta = [beta_xm, beta_xp, beta_ym, beta_yp]
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gamma = [gamma_xm, gamma_xp, gamma_ym, gamma_yp]
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x_BC, y_BC = getxBCyBC_CC(self.mesh, alpha, beta, gamma)
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V = self.Vol
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self.Div = V * self.mesh.faceDiv
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P_BC, B = self.mesh.getBCProjWF_simple()
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M = B*self.mesh.aveCC2F
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self.Grad = self.Div.T - P_BC*Utils.sdiag(y_BC)*M
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class Problem3D_N(BaseSIPProblem):
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_solutionType = 'phiSolution'
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_formulation = 'EB' # N potentials means B is on faces
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fieldsPair = Fields_N
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def __init__(self, mesh, **kwargs):
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BaseSIPProblem.__init__(self, mesh, **kwargs)
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def getA(self):
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"""
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Make the A matrix for the cell centered DC resistivity problem
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A = D MfRhoI D^\\top V
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"""
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# TODO: this won't work for full anisotropy
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MeSigma = self.MeSigma
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Grad = self.mesh.nodalGrad
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A = Grad.T * MeSigma * Grad
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# Handling Null space of A
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A[0,0] = A[0,0] + 1.
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return A
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def getADeriv(self, u, v, adjoint=False):
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"""
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Product of the derivative of our system matrix with respect to the model and a vector
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"""
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MeSigma = self.MeSigma
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Grad = self.mesh.nodalGrad
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if not adjoint:
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return Grad.T*(self.MeSigmaDeriv(Grad*u)*v)
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elif adjoint:
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return self.MeSigmaDeriv(Grad*u).T * (Grad*v)
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def getRHS(self):
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"""
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RHS for the DC problem
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q
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"""
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RHS = self.getSourceTerm()
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return RHS
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def getRHSDeriv(self, src, v, adjoint=False):
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"""
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Derivative of the right hand side with respect to the model
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"""
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# TODO: add qDeriv for RHS depending on m
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# qDeriv = src.evalDeriv(self, adjoint=adjoint)
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# return qDeriv
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return Zero()
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if __name__ == '__main__':
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cs = 12.5
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hx = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
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hy = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
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hz = [(cs,7, -1.3),(cs,20)]
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mesh = Mesh.TensorMesh([hx, hy, hz],x0="CCN")
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sigma = np.ones(mesh.nC)
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prob = BaseSIPProblem(mesh, sigma=sigma)
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@@ -0,0 +1,82 @@
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import SimPEG
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import numpy as np
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from SimPEG.Utils import Zero, closestPoints
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class BaseRx(SimPEG.Survey.BaseTimeRx):
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locs = None
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rxType = None
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knownRxTypes = {
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'phi':['phi',None],
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'ex':['e','x'],
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'ey':['e','y'],
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'ez':['e','z'],
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'jx':['j','x'],
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'jy':['j','y'],
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'jz':['j','z'],
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}
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def __init__(self, locs, times, rxType, **kwargs):
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SimPEG.Survey.BaseTimeRx.__init__(self, locs, times, rxType, **kwargs)
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@property
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def projField(self):
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"""Field Type projection (e.g. e b ...)"""
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return self.knownRxTypes[self.rxType][0]
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def projGLoc(self, f):
|
||||
"""Grid Location projection (e.g. Ex Fy ...)"""
|
||||
comp = self.knownRxTypes[self.rxType][1]
|
||||
if comp is not None:
|
||||
return f._GLoc(self.rxType) + comp
|
||||
return f._GLoc(self.rxType)
|
||||
|
||||
def getTimeP(self, timesall):
|
||||
"""
|
||||
Returns the time projection matrix.
|
||||
|
||||
.. note::
|
||||
|
||||
This is not stored in memory, but is created on demand.
|
||||
"""
|
||||
time_inds = np.in1d(timesall, self.times)
|
||||
return time_inds
|
||||
|
||||
def evalDeriv(self, src, mesh, f, v, adjoint=False):
|
||||
P = self.getP(mesh, self.projGLoc(f))
|
||||
if not adjoint:
|
||||
return P*v
|
||||
elif adjoint:
|
||||
return P.T*v
|
||||
|
||||
|
||||
# DC.Rx.Dipole(locs)
|
||||
class Dipole(BaseRx):
|
||||
|
||||
def __init__(self, locsM, locsN, times, rxType = 'phi', **kwargs):
|
||||
assert locsM.shape == locsN.shape, 'locsM and locsN need to be the same size'
|
||||
locs = [locsM, locsN]
|
||||
# We may not need this ...
|
||||
BaseRx.__init__(self, locs, times, rxType)
|
||||
|
||||
@property
|
||||
def nD(self):
|
||||
"""Number of data in the receiver."""
|
||||
return self.locs[0].shape[0] * len(self.times)
|
||||
|
||||
# Not sure why ...
|
||||
# return int(self.locs[0].size / 2)
|
||||
|
||||
|
||||
def getP(self, mesh, Gloc):
|
||||
if mesh in self._Ps:
|
||||
return self._Ps[mesh]
|
||||
|
||||
P0 = mesh.getInterpolationMat(self.locs[0], Gloc)
|
||||
P1 = mesh.getInterpolationMat(self.locs[1], Gloc)
|
||||
P = P0 - P1
|
||||
|
||||
if self.storeProjections:
|
||||
self._Ps[mesh] = P
|
||||
|
||||
return P
|
||||
@@ -0,0 +1,32 @@
|
||||
import SimPEG
|
||||
from SimPEG.EM.Base import BaseEMSurvey
|
||||
from SimPEG import np, sp, Survey
|
||||
from SimPEG.Utils import Zero, Identity
|
||||
from SimPEG.EM.Static.DC.SrcDC import BaseSrc
|
||||
from SimPEG.EM.Static.SIP.RxSIP import BaseRx
|
||||
|
||||
class Survey(BaseEMSurvey):
|
||||
rxPair = BaseRx
|
||||
srcPair = BaseSrc
|
||||
times = None
|
||||
|
||||
def __init__(self, srcList, **kwargs):
|
||||
self.srcList = srcList
|
||||
BaseEMSurvey.__init__(self, srcList, **kwargs)
|
||||
self.getUniqueTimes()
|
||||
|
||||
def getUniqueTimes(self):
|
||||
time_rx = []
|
||||
for src in self.srcList:
|
||||
for rx in src.rxList:
|
||||
time_rx.append(rx.times)
|
||||
self.times = np.unique(np.hstack(time_rx))
|
||||
|
||||
def dpred(self, m, f=None):
|
||||
"""
|
||||
Predicted data.
|
||||
|
||||
.. math::
|
||||
d_\\text{pred} = Pf(m)
|
||||
"""
|
||||
return self.prob.Jvec(m, m, f=f)
|
||||
@@ -0,0 +1,2 @@
|
||||
from ProblemSIP import Problem3D_CC, Problem3D_N
|
||||
from SurveySIP import Survey
|
||||
@@ -1,2 +1,3 @@
|
||||
import DC
|
||||
import IP
|
||||
import SIP
|
||||
|
||||
Reference in New Issue
Block a user