mirror of
https://github.com/wassname/simpeg.git
synced 2026-07-06 05:16:51 +08:00
Result of SimPEG hackathon
- Incorporate field class on DC - Add IP forward modelling and inversion - Modify notebooks - change folder name form simpegDC to simpegDCIP
This commit is contained in:
seogi_macbook
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@@ -1,27 +1,70 @@
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from SimPEG import *
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class FieldsDC_CC(Problem.Fields):
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knownFields = {'phi_sol':'CC'}
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aliasFields = {
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'phi' : ['phi_sol','CC','_phi'],
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'e' : ['phi_sol','F','_e'],
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'j' : ['phi_sol','F','_j']
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}
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def __init__(self,mesh,survey,**kwargs):
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super(FieldsDC_CC, self).__init__(mesh, survey, **kwargs)
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def startup(self):
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self._cellGrad = self.survey.prob.mesh.cellGrad
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def _phi(self, phi_sol, srcList):
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phi = phi_sol
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for i, src in enumerate(srcList):
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phi_p = src.phi_p(self.survey.prob)
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if phi_p is not None:
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phi[:,i] += phi_p
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return phi
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def _e(self, phi_sol, srcList):
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e = -self._cellGrad*phi_sol
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for i, src in enumerate(srcList):
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e_p = src.e_p(self.survey.prob)
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if e_p is not None:
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e[:,i] += e_p
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return e
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def _j(self, phi_sol, srcList):
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j = -self.survey.prob.Msig*self._cellGrad*phi_sol
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for i, src in enumerate(srcList):
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j_p = src.j_p(self.survey.prob)
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if j_p is not None:
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j[:,i] += j_p
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return j
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class SrcDipole(Survey.BaseSrc):
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"""A dipole source, locA and locB are moved to the closest cell-centers"""
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current = 1
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loc = None
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_rhsDict = None
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# _rhsDict = None
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def __init__(self, rxList, locA, locB, **kwargs):
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self.loc = (locA, locB)
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super(SrcDipole, self).__init__(rxList, **kwargs)
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def getRhs(self, mesh):
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if getattr(self, '_rhsDict', None) is None:
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self._rhsDict = {}
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if mesh not in self._rhsDict:
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pts = [self.loc[0], self.loc[1]]
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inds = Utils.closestPoints(mesh, pts)
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q = np.zeros(mesh.nC)
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q[inds] = - self.current * ( np.r_[1., -1.] / mesh.vol[inds] )
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self._rhsDict[mesh] = q
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return self._rhsDict[mesh]
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def eval(self, prob):
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# Recompute rhs
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# if getattr(self, '_rhsDict', None) is None:
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# self._rhsDict = {}
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# if mesh not in self._rhsDict:
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pts = [self.loc[0], self.loc[1]]
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inds = Utils.closestPoints(prob.mesh, pts)
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q = np.zeros(prob.mesh.nC)
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q[inds] = - self.current * ( np.r_[1., -1.] / prob.mesh.vol[inds] )
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# self._rhsDict[mesh] = q
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# return self._rhsDict[mesh]
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return q
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class RxDipole(Survey.BaseRx):
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@@ -53,7 +96,7 @@ class SurveyDC(Survey.BaseSurvey):
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def __init__(self, srcList, **kwargs):
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self.srcList = srcList
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Survey.BaseSurvey.__init__(self, **kwargs)
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self._rhsDict = {}
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# self._rhsDict = {}
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self._Ps = {}
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def projectFields(self, u):
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@@ -64,13 +107,7 @@ class SurveyDC(Survey.BaseSurvey):
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d_\\text{pred} = Pu(m)
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"""
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P = self.getP(self.prob.mesh)
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return P*mkvc(u)
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def getRhs(self, mesh):
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if mesh not in self._rhsDict:
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RHS = np.array([src.getRhs(mesh) for src in self.srcList]).T
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self._rhsDict[mesh] = RHS
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return self._rhsDict[mesh]
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return P*mkvc(u[self.srcList, 'phi_sol'])
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def getP(self, mesh):
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if mesh in self._Ps:
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@@ -82,9 +119,7 @@ class SurveyDC(Survey.BaseSurvey):
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return self._Ps[mesh]
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class ProblemDC(Problem.BaseProblem):
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class ProblemDC_CC(Problem.BaseProblem):
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"""
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**ProblemDC**
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@@ -94,6 +129,8 @@ class ProblemDC(Problem.BaseProblem):
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surveyPair = SurveyDC
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Solver = Solver
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fieldsPair = FieldsDC_CC
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Ainv = None
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def __init__(self, mesh, **kwargs):
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Problem.BaseProblem.__init__(self, mesh)
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@@ -143,13 +180,25 @@ class ProblemDC(Problem.BaseProblem):
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self._A = self._A.tocsc()
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return self._A
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def getRHS(self):
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# if self.mesh not in self._rhsDict:
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RHS = np.array([src.eval(self) for src in self.survey.srcList]).T
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# self._rhsDict[mesh] = RHS
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# return self._rhsDict[mesh]
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return RHS
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def fields(self, m):
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F = self.fieldsPair(self.mesh, self.survey)
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self.curModel = m
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A = self.A
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Ainv = self.Solver(A, **self.solverOpts)
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Q = self.survey.getRhs(self.mesh)
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Phi = Ainv * Q
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return Phi
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self.Ainv = self.Solver(A, **self.solverOpts)
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RHS = self.getRHS()
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Phi = self.Ainv * RHS
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Srcs = self.survey.srcList
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F[Srcs, 'phi_sol'] = Phi
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return F
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def Jvec(self, m, v, u=None):
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"""
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@@ -178,10 +227,9 @@ class ProblemDC(Problem.BaseProblem):
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sigma = self.curModel.transform # $\sigma = \mathcal{M}(\m)$
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if u is None:
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# Run forward simulation if $u$ not provided
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u = self.fields(self.curModel)
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u = self.fields(self.curModel)[self.survey.srcList, 'phi_sol']
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else:
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shp = (self.mesh.nC, self.survey.nSrc)
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u = u.reshape(shp, order='F')
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u = u[self.survey.srcList, 'phi_sol']
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D = self.mesh.faceDiv
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G = self.mesh.cellGrad
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@@ -199,9 +247,12 @@ class ProblemDC(Problem.BaseProblem):
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# Take derivative of $C(m,u)$ w.r.t. $u$
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dCdu = self.A
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# Solve for $\deriv{u}{m}$
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dCdu_inv = self.Solver(dCdu, **self.solverOpts)
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# dCdu_inv = self.Solver(dCdu, **self.solverOpts)
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if self.Ainv is None:
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self.Ainv = self.Solver(dCdu, **self.solverOpts)
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P = self.survey.getP(self.mesh)
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J_x_v = - P * mkvc( dCdu_inv * dCdm_x_v )
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J_x_v = - P * mkvc( self.Ainv * dCdm_x_v )
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return J_x_v
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def Jtvec(self, m, v, u=None):
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@@ -209,10 +260,12 @@ class ProblemDC(Problem.BaseProblem):
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self.curModel = m
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sigma = self.curModel.transform # $\sigma = \mathcal{M}(\m)$
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if u is None:
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u = self.fields(self.curModel)
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# Run forward simulation if $u$ not provided
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u = self.fields(self.curModel)[self.survey.srcList, 'phi_sol']
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else:
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u = u[self.survey.srcList, 'phi_sol']
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shp = (self.mesh.nC, self.survey.nSrc)
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u = u.reshape(shp, order='F')
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shp = u.shape
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P = self.survey.getP(self.mesh)
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PT_x_v = (P.T*v).reshape(shp, order='F')
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@@ -221,9 +274,13 @@ class ProblemDC(Problem.BaseProblem):
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A = self.A
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mT_dm = self.mapping.deriv(m)
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# We probably always need this due to the linesearch .. (?)
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dCdu = A.T
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Ainv = self.Solver(dCdu, **self.solverOpts)
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w = Ainv * PT_x_v
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self.Ainv = self.Solver(dCdu, **self.solverOpts)
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# if self.Ainv is None:
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# self.Ainv = self.Solver(dCdu, **self.solverOpts)
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w = self.Ainv * PT_x_v
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Jtv = 0
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for i, ui in enumerate(u.T): # loop over each column
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@@ -0,0 +1,182 @@
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from SimPEG import *
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from BaseDC import SurveyDC, FieldsDC_CC
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class SurveyIP(SurveyDC):
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"""
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**SurveyDC**
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Geophysical DC resistivity data.
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"""
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def __init__(self, srcList, **kwargs):
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self.srcList = srcList
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Survey.BaseSurvey.__init__(self, **kwargs)
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self._Ps = {}
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def dpred(self, m, u=None):
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"""
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Predicted data.
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.. math::
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d_\\text{pred} = Pu(m)
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"""
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return self.prob.forward(m)
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class ProblemIP(Problem.BaseProblem):
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"""
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**ProblemIP**
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Geophysical IP resistivity problem.
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"""
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surveyPair = SurveyDC
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Solver = Solver
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sigma = None
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Ainv = None
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u = None
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def __init__(self, mesh, **kwargs):
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Problem.BaseProblem.__init__(self, mesh)
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self.mesh.setCellGradBC('neumann')
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Utils.setKwargs(self, **kwargs)
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# deleteTheseOnModelUpdate = ['_A', '_Msig', '_dMdsig']
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@property
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def Msig(self):
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if getattr(self, '_Msig', None) is None:
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# sigma = self.curModel.transform
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sigma = self.sigma
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Av = self.mesh.aveF2CC
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self._Msig = Utils.sdiag(1/(self.mesh.dim * Av.T * (1/sigma)))
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return self._Msig
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@property
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def dMdsig(self):
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if getattr(self, '_dMdsig', None) is None:
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# sigma = self.curModel.transform
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sigma = self.sigma
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Av = self.mesh.aveF2CC
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dMdprop = self.mesh.dim * Utils.sdiag(self.Msig.diagonal()**2) * Av.T * Utils.sdiag(1./sigma**2)
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self._dMdsig = lambda Gu: Utils.sdiag(Gu) * dMdprop
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return self._dMdsig
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@property
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def A(self):
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"""
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Makes the matrix A(m) for the DC resistivity problem.
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:param numpy.array m: model
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:rtype: scipy.csc_matrix
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:return: A(m)
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.. math::
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c(m,u) = A(m)u - q = G\\text{sdiag}(M(mT(m)))Du - q = 0
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Where M() is the mass matrix and mT is the model transform.
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"""
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if getattr(self, '_A', None) is None:
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D = self.mesh.faceDiv
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G = self.mesh.cellGrad
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self._A = D*self.Msig*G
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# Remove the null space from the matrix.
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self._A[-1,-1] /= self.mesh.vol[-1]
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self._A = self._A.tocsc()
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return self._A
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def getRHS(self):
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# if self.mesh not in self._rhsDict:
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RHS = np.array([src.eval(self) for src in self.survey.srcList]).T
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# self._rhsDict[mesh] = RHS
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# return self._rhsDict[mesh]
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return RHS
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def fields(self, m):
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if self.u is None:
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A = self.A
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if self.Ainv == None:
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self.Ainv = self.Solver(A, **self.solverOpts)
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Q = self.getRHS()
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self.u = self.Ainv * Q
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return self.u
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def forward(self, m, u=None):
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# Set current model; clear dependent property $\mathbf{A(m)}$
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self.curModel = m
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# sigma = self.curModel.transform # $\sigma = \mathcal{M}(\m)$
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sigma = self.sigma
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if self.u is None:
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# Run forward simulation if $u$ not provided
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u = self.fields(sigma)
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shp = (self.mesh.nC, self.survey.nSrc)
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u = self.u.reshape(shp, order='F')
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D = self.mesh.faceDiv
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G = self.mesh.cellGrad
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# Derivative of model transform, $\deriv{\sigma}{\m}$
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# dsigdm_x_v = self.curModel.transformDeriv * v
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dsigdm_x_v = Utils.sdiag(sigma) * self.curModel.transformDeriv * m
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# Take derivative of $C(m,u)$ w.r.t. $m$
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dCdm_x_v = np.empty_like(u)
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# loop over fields for each source
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for i in range(self.survey.nSrc):
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# Derivative of inner product, $\left(\mathbf{M}_{1/\sigma}^f\right)^{-1}$
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dAdsig = D * self.dMdsig( G * u[:,i] )
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dCdm_x_v[:, i] = dAdsig * dsigdm_x_v
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# Take derivative of $C(m,u)$ w.r.t. $u$
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if self.Ainv == None:
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self.Ainv = self.Solver(A, **self.solverOpts)
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# dCdu = self.A
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# Solve for $\deriv{u}{m}$
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# dCdu_inv = self.Solver(dCdu, **self.solverOpts)
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P = self.survey.getP(self.mesh)
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J_x_v = - P * mkvc( self.Ainv * dCdm_x_v )
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return -J_x_v
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def Jvec(self, m, v, u=None):
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return self.forward(v)
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def Jtvec(self, m, v, u=None):
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self.curModel = m
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# sigma = self.curModel.transform # $\sigma = \mathcal{M}(\m)$
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sigma = self.sigma
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if self.u is None:
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u = self.fields(sigma)
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else:
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u = self.u
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shp = (self.mesh.nC, self.survey.nSrc)
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u = u.reshape(shp, order='F')
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P = self.survey.getP(self.mesh)
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PT_x_v = (P.T*v).reshape(shp, order='F')
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D = self.mesh.faceDiv
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G = self.mesh.cellGrad
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A = self.A
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mT_dm = Utils.sdiag(sigma)*self.mapping.deriv(m)
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# mT_dm = self.mapping.deriv(m)
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# dCdu = A.T
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# Ainv = self.Solver(dCdu, **self.solverOpts)
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# if self.Ainv == None:
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self.Ainv = self.Solver(A.T, **self.solverOpts)
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w = self.Ainv * PT_x_v
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Jtv = 0
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for i, ui in enumerate(u.T): # loop over each column
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Jtv += self.dMdsig( G * ui ).T * ( D.T * w[:,i] )
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Jtv = - mT_dm.T * ( Jtv )
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return -Jtv
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@@ -1,5 +1,5 @@
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from SimPEG import *
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import simpegDC as DC
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import simpegDCIP as DC
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import matplotlib.pyplot as plt
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@@ -26,7 +26,7 @@ def run(plotIt=False):
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rx = DC.RxDipole(xyz_rxP, xyz_rxN)
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src = DC.SrcDipole([rx], [-200, 0, -12.5], [+200, 0, -12.5])
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survey = DC.SurveyDC([src])
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problem = DC.ProblemDC(mesh)
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problem = DC.ProblemDC_CC(mesh)
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problem.pair(survey)
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try:
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from pymatsolver import MumpsSolver
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@@ -1,5 +1,5 @@
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from SimPEG import *
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import simpegDC as DC
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import simpegDCIP as DC
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import matplotlib.pyplot as plt
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@@ -55,7 +55,7 @@ def example(aSpacing=2.5, nElecs=10, plotIt=False):
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srcList = getSrcList(nElecs, aSpacing, in2D=True)
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survey = DC.SurveyDC(srcList)
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problem = DC.ProblemDC(mesh)
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problem = DC.ProblemDC_CC(mesh)
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problem.pair(survey)
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return mesh, survey, problem
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+2
-2
@@ -38,8 +38,8 @@ class DCProblemTests(unittest.TestCase):
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u = np.random.rand(self.mesh.nC*self.survey.nSrc)
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v = np.random.rand(self.mesh.nC)
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w = np.random.rand(self.survey.dobs.shape[0])
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wtJv = w.dot(self.p.Jvec(self.m0, v, u=u))
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vtJtw = v.dot(self.p.Jtvec(self.m0, w, u=u))
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wtJv = w.dot(self.p.Jvec(self.m0, v))
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vtJtw = v.dot(self.p.Jtvec(self.m0, w))
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passed = np.abs(wtJv - vtJtw) < 1e-10
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print 'Adjoint Test', np.abs(wtJv - vtJtw), passed
|
||||
self.assertTrue(passed)
|
||||
-1
@@ -8,6 +8,5 @@ class DCAnalyticTests(unittest.TestCase):
|
||||
self.assertTrue(DC.Examples.Verification.run() < 0.1)
|
||||
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
unittest.main()
|
||||
@@ -0,0 +1,57 @@
|
||||
import unittest
|
||||
import simpegDC as DC
|
||||
from SimPEG import *
|
||||
from pymatsolver import MumpsSolver
|
||||
|
||||
class IPforwardTests(unittest.TestCase):
|
||||
|
||||
def test_IPforward(self):
|
||||
|
||||
cs = 12.5
|
||||
nc = 500/cs+1
|
||||
hx = [(cs,7, -1.3),(cs,nc),(cs,7, 1.3)]
|
||||
hy = [(cs,7, -1.3),(cs,int(nc/2+1)),(cs,7, 1.3)]
|
||||
hz = [(cs,7, -1.3),(cs,int(nc/2+1))]
|
||||
mesh = Mesh.TensorMesh([hx, hy, hz], 'CCN')
|
||||
sighalf = 1e-2
|
||||
sigma = np.ones(mesh.nC)*sighalf
|
||||
p0 = np.r_[-50., 50., -50.]
|
||||
p1 = np.r_[ 50.,-50., -150.]
|
||||
blk_ind = Utils.ModelBuilder.getIndecesBlock(p0, p1, mesh.gridCC)
|
||||
sigma[blk_ind] = 1e-3
|
||||
eta = np.zeros_like(sigma)
|
||||
eta[blk_ind] = 0.1
|
||||
sigmaInf = sigma.copy()
|
||||
sigma0 = sigma*(1-eta)
|
||||
|
||||
nElecs = 11
|
||||
x_temp = np.linspace(-250, 250, nElecs)
|
||||
aSpacing = x_temp[1]-x_temp[0]
|
||||
y_temp = 0.
|
||||
xyz = Utils.ndgrid(x_temp, np.r_[y_temp], np.r_[0.])
|
||||
srcList = DC.Examples.WennerArray.getSrcList(nElecs,aSpacing)
|
||||
survey = DC.SurveyDC(srcList)
|
||||
|
||||
imap = Maps.IdentityMap(mesh)
|
||||
problem = DC.ProblemDC_CC(mesh, mapping= imap )
|
||||
problem.Solver = MumpsSolver
|
||||
problem.pair(survey)
|
||||
|
||||
phi0 = survey.dpred(sigma0)
|
||||
phiInf = survey.dpred(sigmaInf)
|
||||
|
||||
phiIP_true = phi0-phiInf
|
||||
|
||||
surveyIP = DC.SurveyIP(srcList)
|
||||
problemIP = DC.ProblemIP(mesh, sigma=sigma)
|
||||
problemIP.pair(surveyIP)
|
||||
problemIP.Solver = MumpsSolver
|
||||
phiIP_approx = surveyIP.dpred(eta)
|
||||
|
||||
err = np.linalg.norm(phiIP_true-phiIP_approx) / np.linalg.norm(phiIP_true)
|
||||
|
||||
self.assertTrue(err < 0.02)
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
unittest.main()
|
||||
@@ -0,0 +1,80 @@
|
||||
import unittest
|
||||
from SimPEG import *
|
||||
import simpegDC as DC
|
||||
from pymatsolver import MumpsSolver
|
||||
|
||||
|
||||
|
||||
class IPProblemTests(unittest.TestCase):
|
||||
|
||||
def setUp(self):
|
||||
|
||||
cs = 12.5
|
||||
nc = 500/cs+1
|
||||
hx = [(cs,0, -1.3),(cs,nc),(cs,0, 1.3)]
|
||||
hy = [(cs,0, -1.3),(cs,int(nc/2+1)),(cs,0, 1.3)]
|
||||
hz = [(cs,0, -1.3),(cs,int(nc/2+1))]
|
||||
mesh = Mesh.TensorMesh([hx, hy, hz], 'CCN')
|
||||
sighalf = 1e-2
|
||||
sigma = np.ones(mesh.nC)*sighalf
|
||||
p0 = np.r_[-50., 50., -50.]
|
||||
p1 = np.r_[ 50.,-50., -150.]
|
||||
blk_ind = Utils.ModelBuilder.getIndecesBlock(p0, p1, mesh.gridCC)
|
||||
sigma[blk_ind] = 1e-3
|
||||
eta = np.zeros_like(sigma)
|
||||
eta[blk_ind] = 0.1
|
||||
|
||||
nElecs = 5
|
||||
x_temp = np.linspace(-250, 250, nElecs)
|
||||
aSpacing = x_temp[1]-x_temp[0]
|
||||
y_temp = 0.
|
||||
xyz = Utils.ndgrid(x_temp, np.r_[y_temp], np.r_[0.])
|
||||
srcList = DC.Examples.WennerArray.getSrcList(nElecs,aSpacing)
|
||||
survey = DC.SurveyIP(srcList)
|
||||
imap = Maps.IdentityMap(mesh)
|
||||
problem = DC.ProblemIP(mesh, sigma=sigma, mapping= imap)
|
||||
problem.pair(survey)
|
||||
problem.Solver = MumpsSolver
|
||||
|
||||
mSynth = eta
|
||||
survey.makeSyntheticData(mSynth)
|
||||
|
||||
# Now set up the problem to do some minimization
|
||||
dmis = DataMisfit.l2_DataMisfit(survey)
|
||||
reg = Regularization.Tikhonov(mesh)
|
||||
opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6)
|
||||
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e4)
|
||||
inv = Inversion.BaseInversion(invProb)
|
||||
|
||||
self.inv = inv
|
||||
self.reg = reg
|
||||
self.p = problem
|
||||
self.mesh = mesh
|
||||
self.m0 = mSynth
|
||||
self.survey = survey
|
||||
self.dmis = dmis
|
||||
|
||||
def test_misfit(self):
|
||||
derChk = lambda m: [self.survey.dpred(m), lambda mx: self.p.Jvec(self.m0, mx)]
|
||||
passed = Tests.checkDerivative(derChk, self.m0*0, plotIt=False)
|
||||
self.assertTrue(passed)
|
||||
|
||||
def test_adjoint(self):
|
||||
# Adjoint Test
|
||||
u = np.random.rand(self.mesh.nC*self.survey.nSrc)
|
||||
v = np.random.rand(self.mesh.nC)
|
||||
w = np.random.rand(self.survey.dobs.shape[0])
|
||||
wtJv = w.dot(self.p.Jvec(self.m0, v))
|
||||
vtJtw = v.dot(self.p.Jtvec(self.m0, w))
|
||||
passed = np.abs(wtJv - vtJtw) < 1e-10
|
||||
print 'Adjoint Test', np.abs(wtJv - vtJtw), passed
|
||||
self.assertTrue(passed)
|
||||
|
||||
def test_dataObj(self):
|
||||
derChk = lambda m: [self.dmis.eval(m), self.dmis.evalDeriv(m)]
|
||||
passed = Tests.checkDerivative(derChk, self.m0, plotIt=False)
|
||||
self.assertTrue(passed)
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
unittest.main()
|
||||
@@ -1,2 +1,3 @@
|
||||
from BaseDC import *
|
||||
from BaseIP import *
|
||||
import Examples
|
||||
Reference in New Issue
Block a user