mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-29 21:09:14 +08:00
adjoint hooked up for b formulation
This commit is contained in:
Lindsey Heagy
@@ -86,15 +86,12 @@ class Fields_b(Fields):
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_, S_e = src.eval(self.survey.prob, self.survey.prob.times[tInd])
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bSolution = self[[src],'bSolution',tInd]
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if adjoint:
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v = self.MeSigmaI.T * v
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_, S_eDeriv_v = src.evalDeriv(self.survey.prob.times[tInd], self, v=v, adjoint=adjoint)
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_, S_eDeriv = src.evalDeriv(self.survey.prob.times[tInd], self, adjoint=adjoint)
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if adjoint is True:
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return self.MeSigmaIDeriv(-S_e + self.edgeCurl.T * ( self.MfMui * bSolution ) ).T * v - S_eDeriv_v
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return self.MeSigmaIDeriv(-S_e + self.edgeCurl.T * ( self.MfMui * bSolution ) ).T * v - S_eDeriv(self.MeSigmaI.T * v)
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return self.MeSigmaIDeriv(-S_e + self.edgeCurl.T * ( self.MfMui * bSolution)) * v - self.MeSigmaI * S_eDeriv_v
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return self.MeSigmaIDeriv(-S_e + self.edgeCurl.T * ( self.MfMui * bSolution)) * v - self.MeSigmaI * S_eDeriv(v)
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def _eDeriv(self, tInd, src, dun_dm_v, v, adjoint=False):
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if adjoint is True:
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+39
-12
@@ -168,7 +168,8 @@ class BaseTDEMProblem(Problem.BaseTimeProblem, BaseEMProblem):
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df_duT_v[src, '%sDeriv'%self._fieldType, :] = np.zeros_like(u[src, self._fieldType, :])
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for rx in src.rxList:
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PT_v[src,'%sDeriv'%rx.projField,:] = rx.evalDeriv(src, self.mesh, self.timeMesh, Utils.mkvc(v[src,rx]), adjoint=True)
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PT_v[src,'%sDeriv'%rx.projField,:] = rx.evalDeriv(src, self.mesh, self.timeMesh, Utils.mkvc(v[src,rx]), adjoint=True) # this is +=
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# PT_v = np.reshape(curPT_v,(len(curPT_v)/self.timeMesh.nN, self.timeMesh.nN), order='F')
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df_duTFun = getattr(u, '_%sDeriv'%rx.projField, None)
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@@ -187,13 +188,14 @@ class BaseTDEMProblem(Problem.BaseTimeProblem, BaseEMProblem):
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AdiagTinv = None
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# Do the back-solve through time
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for tInd in reversed(range(self.nT)):
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for tIndP in reversed(range(self.nT + 1)):
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tInd = tIndP - 1
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if AdiagTinv is not None and (tInd <= self.nT and self.timeSteps[tInd] != self.timeSteps[tInd+1]): # if the previous timestep is the same --> no need to refactor the matrix
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AdiagTinv.clean()
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AdiagTinv = None
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# refactor if we need to
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if AdiagTinv is None:
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if AdiagTinv is None and tInd > -1:
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Adiag = self.getAdiag(tInd)
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AdiagTinv = self.Solver(Adiag.T, **self.solverOpts)
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@@ -204,25 +206,46 @@ class BaseTDEMProblem(Problem.BaseTimeProblem, BaseEMProblem):
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for isrc, src in enumerate(self.survey.srcList):
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# solve against df_duT_v
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if tInd >= self.nT-1:
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# last timestep (first to be solved)
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ATinv_df_duT_v[isrc,:] = AdiagTinv * df_duT_v[src,'%sDeriv'%self._fieldType,tInd+1]
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else:
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elif tInd > -1:
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ATinv_df_duT_v[isrc,:] = AdiagTinv * (Utils.mkvc(df_duT_v[src,'%sDeriv'%self._fieldType,tInd+1]) - Asubdiag.T * Utils.mkvc(ATinv_df_duT_v[isrc,:]))
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else:
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# AdiagTinv = I
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ATinv_df_duT_v[isrc,:] = (Utils.mkvc(df_duT_v[src,'%sDeriv'%self._fieldType,tInd+1]) - Asubdiag.T * Utils.mkvc(ATinv_df_duT_v[isrc,:]))
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un_src = u[src,ftype,tInd+1]
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dAT_dm_v = self.getAdiagDeriv(None, un_src, ATinv_df_duT_v[isrc,:], adjoint=True) # cell centered on time mesh
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if tInd > -1:
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un_src = u[src,ftype,tInd+1]
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dAT_dm_v = self.getAdiagDeriv(tInd, un_src, ATinv_df_duT_v[isrc,:], adjoint=True) # cell centered on time mesh
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dRHST_dm_v = self.getRHSDeriv(tInd+1, src, ATinv_df_duT_v[isrc,:], adjoint=True) # on nodes of time mesh
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JTv = JTv + Utils.mkvc(-dAT_dm_v + dRHST_dm_v)
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# else:
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# print 'here'
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dRHST_dm_v = self.getRHSDeriv(tInd+1, src, ATinv_df_duT_v[isrc,:], adjoint=True) # on nodes of time mesh
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# un_src = u[src,ftype,tInd+1]
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# # dAT_dm_v = self.getAdiagDeriv(tInd, un_src, ATinv_df_duT_v[isrc,:], adjoint=True) # cell centered on time mesh
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# dRHST_dm_v0 = self.getRHSDeriv(tInd+1, src, ATinv_df_duT_v[isrc,:], adjoint=True) # on nodes of time mesh
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# dRHST_dm_v1 = self.getInitialFieldsDeriv( Utils.mkvc(df_duT_v[src,'%sDeriv'%self._fieldType,tInd+1]), adjoint=True)
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# JTv = JTv + Utils.mkvc(dRHST_dm_v0 + dRHST_dm_v1)
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# print 'here'
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# inFields = self.getInitialFieldsDeriv(u[src,ftype,tInd+1], Utils.mkvc(df_duT_v[src,'%sDeriv'%self._fieldType,tInd+1]), adjoint=True)
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# # - Asubdiag.T * Utils.mkvc(ATinv_df_duT_v[isrc,:]), adjoint=True)
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# print inFields.shape
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# JTv = JTv + inFields
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# dAsubdiag_dm_v = 0
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JTv = JTv + Utils.mkvc(-dAT_dm_v + dRHST_dm_v)
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# Missing the 0 step
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# adding du_dm^T * dF_du^T * P^T vfor time 0 (no dRHS_dm_v at time 0)
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for src in self.survey.srcList:
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for projField in set(rx.projField):
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JTv = JTv + self.getInitialFieldsDeriv(Utils.mkvc(df_duT_v[src,'%sDeriv'%self._fieldType,0]), adjoint=True)
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# Asubdiag = self.getAsubdiag(0)
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# for src in self.survey.srcList:
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# for projField in set(rx.projField):
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# v = AdiagTinv * (Utils.mkvc(df_duT_v[src,'%sDeriv'%self._fieldType,0]) - Asubdiag.T * Utils.mkvc(ATinv_df_duT_v[isrc,:]))
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# JTv = JTv - Utils.mkvc(self.getAdiagDeriv(0, u[src, ftype, tInd], v, adjoint = True))
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# # JTv = JTv + self.getInitialFieldsDeriv(Utils.mkvc(df_duT_v[src,'%sDeriv'%self._fieldType,0] - Asubdiag.T * Utils.mkvc(ATinv_df_duT_v[isrc,:])), adjoint=True)
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return Utils.mkvc(JTv)
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@@ -274,7 +297,10 @@ class BaseTDEMProblem(Problem.BaseTimeProblem, BaseEMProblem):
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ifieldsDeriv[:,i] = ifieldsDeriv[:,i] + getattr(src, '%sInitialDeriv'%self._fieldType, None)(self,v,adjoint)
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if adjoint is True:
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ifieldsDeriv = ifieldsDeriv.sum()
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ifieldsDeriv = np.zeros_like(self.curModel)
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print v.shape
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# ifieldsDeriv = self.getAdiagDeriv(None, u, v, adjoint)
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# ifieldsDeriv = ifieldsDeriv.sum()
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return ifieldsDeriv
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@@ -337,6 +363,7 @@ class Problem_b(BaseTDEMProblem):
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(\mathbf{I} + \mathbf{dt} \mathbf{C} \mathbf{M_{\sigma}^e}^{-1} \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f})
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"""
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assert tInd >= 0 and tInd < self.nT
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dt = self.timeSteps[tInd]
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C = self.mesh.edgeCurl
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@@ -23,7 +23,7 @@ def setUp(rxcomp='bz'):
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mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * activeMap
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rxOffset = 10.
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rx = EM.TDEM.Rx(np.array([[rxOffset, 0., -1e-2]]), np.logspace(-4,-3, 20), rxcomp)
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rx = EM.TDEM.Rx(np.array([[rxOffset, 0., -1e-2]]), np.logspace(-4,-3, 20), rxcomp) #,]
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src = EM.TDEM.SurveyTDEM.MagDipole([rx], loc=np.array([0., 0., 0.]))
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survey = EM.TDEM.Survey([src])
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@@ -45,13 +45,14 @@ def setUp(rxcomp='bz'):
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return prb, m, mesh
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class TDEM_DerivTests(unittest.TestCase):
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# ====== TEST A ========== #
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def test_Deriv_Pieces(self):
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def test_AderivTest(self):
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prb, m0, mesh = setUp()
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tInd = 0
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tInd = 2
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v = np.random.rand(mesh.nF)
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@@ -64,36 +65,78 @@ class TDEM_DerivTests(unittest.TestCase):
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return Av, ADeriv_dm
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def A_adjointTest():
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print '\n Testing A_adjoint'
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m = np.random.rand(prb.mapping.nP)
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v = np.random.rand(prb.mesh.nF)
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u = np.random.rand(prb.mesh.nF)
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prb.curModel = m0
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tInd = 0 # not actually used
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V1 = v.dot(prb.getAdiagDeriv(tInd, u, m))
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V2 = m.dot(prb.getAdiagDeriv(tInd, u, v, adjoint=True))
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passed = np.abs(V1-V2) < TOL * (np.abs(V1) + np.abs(V2))/2.
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print 'AdjointTest', V1, V2, passed
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self.assertTrue(passed)
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print '\n Testing ADeriv'
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Tests.checkDerivative(AderivTest, m0, plotIt=False, num=4, eps=1e-20)
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A_adjointTest()
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def test_A_adjointTest(self):
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prb, m0, mesh = setUp()
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tInd = 2
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print '\n Testing A_adjoint'
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m = np.random.rand(prb.mapping.nP)
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v = np.random.rand(prb.mesh.nF)
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u = np.random.rand(prb.mesh.nF)
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prb.curModel = m0
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tInd = 2 # not actually used
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V1 = v.dot(prb.getAdiagDeriv(tInd, u, m))
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V2 = m.dot(prb.getAdiagDeriv(tInd, u, v, adjoint=True))
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passed = np.abs(V1-V2) < TOL * (np.abs(V1) + np.abs(V2))/2.
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print 'AdjointTest', V1, V2, passed
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self.assertTrue(passed)
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# ====== TEST Fields Deriv Pieces ========== #
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def test_eDeriv_m_adjoint(self):
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prb, m0, mesh = setUp()
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tInd = 0
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v = np.random.rand(mesh.nF)
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print '\n Testing eDeriv_m Adjoint'
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prb, m0, mesh = setUp()
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f = prb.fields(m0)
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m = np.random.rand(prb.mapping.nP)
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e = np.random.randn(prb.mesh.nE)
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V1 = e.dot(f._eDeriv_m(1, prb.survey.srcList[0], m))
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V2 = m.dot(f._eDeriv_m(1, prb.survey.srcList[0], e, adjoint=True))
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tol = TOL * (np.abs(V1) + np.abs(V2)) / 2.
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passed = np.abs(V1-V2) < tol
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print ' ', V1, V2, np.abs(V1-V2), tol, passed
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self.assertTrue(passed)
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def test_eDeriv_u_adjoint(self):
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print '\n Testing eDeriv_u Adjoint'
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prb, m0, mesh = setUp()
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f = prb.fields(m0)
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b = np.random.rand(prb.mesh.nF)
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e = np.random.randn(prb.mesh.nE)
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V1 = e.dot(f._eDeriv_u(1, prb.survey.srcList[0], b))
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V2 = b.dot(f._eDeriv_u(1, prb.survey.srcList[0], e, adjoint=True))
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tol = TOL * (np.abs(V1) + np.abs(V2)) / 2.
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passed = np.abs(V1-V2) < tol
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print ' ', V1, V2, np.abs(V1-V2), tol, passed
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self.assertTrue(passed)
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# ====== TEST Jvec ========== #
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def JvecTest(self, rxcomp):
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prb, m, mesh = setUp(rxcomp)
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derChk = lambda m: [prb.survey.dpred(m), lambda mx: prb.Jvec(m, mx)]
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print '\n'
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print 'test_Jvec_%s' %(rxcomp)
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Tests.checkDerivative(derChk, m, plotIt=False, num=2, eps=1e-20)
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if testDeriv:
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def JvecTest(self, rxcomp):
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prb, m, mesh = setUp(rxcomp)
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derChk = lambda m: [prb.survey.dpred(m), lambda mx: prb.Jvec(m, mx)]
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print '\n'
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print 'test_Jvec_%s' %(rxcomp)
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Tests.checkDerivative(derChk, m, plotIt=False, num=2, eps=1e-20)
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def test_Jvec_b_bx(self):
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self.JvecTest('bx')
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@@ -103,33 +146,38 @@ class TDEM_DerivTests(unittest.TestCase):
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def test_Jvec_b_ey(self):
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self.JvecTest('ey')
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else:
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pass
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# ====== TEST Jtvec ========== #
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def adjointJvecVsJtvecTest(self, rxcomp='bz'):
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print '\nAdjoint Testing Jvec, Jtvec %s' %(rxcomp)
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prb, m0, mesh = setUp(rxcomp)
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m = np.random.rand(prb.mapping.nP)
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d = np.random.randn(prb.survey.nD)
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V1 = d.dot(prb.Jvec(m0, m))
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V2 = m.dot(prb.Jtvec(m0, d))
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tol = TOL * (np.abs(V1) + np.abs(V2)) / 2.
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passed = np.abs(V1-V2) < tol
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print ' ', V1, V2, np.abs(V1-V2), tol, passed
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self.assertTrue(passed)
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if testAdjoint:
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def test_Jvec_b_bx(self):
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self.adjointJvecVsJtvecTest('bx')
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def test_Jvec_b_bz(self):
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self.adjointJvecVsJtvecTest('bz')
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def JvecVsJtvecTest(self, rxcomp='bz'):
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print '\nAdjoint Testing Jvec, Jtvec %s' %(rxcomp)
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prb, m0, mesh = setUp(rxcomp)
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m = np.random.rand(prb.mapping.nP)
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d = np.random.randn(prb.survey.nD)
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V1 = d.dot(prb.Jvec(m0, m))
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V2 = m.dot(prb.Jtvec(m0, d))
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tol = TOL * (np.abs(V1) + np.abs(V2)) / 2.
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passed = np.abs(V1-V2) < tol
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print ' ', V1, V2, np.abs(V1-V2), tol, passed
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self.assertTrue(passed)
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def test_Jvec_adjoint_b_bx(self):
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self.JvecVsJtvecTest('bx')
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def test_Jvec_adjoint_b_bz(self):
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self.JvecVsJtvecTest('bz')
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def test_Jvec_adjoint_b_ey(self):
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self.JvecVsJtvecTest('ey')
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def test_Jvec_b_ey(self):
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self.adjointJvecVsJtvecTest('ey')
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if __name__ == '__main__':
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@@ -6,11 +6,9 @@ plotIt = False
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testDeriv = True
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testAdjoint = True
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TOL = 1e-6
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TOL = 1e-5
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class TDEM_bDerivTests(unittest.TestCase):
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def setUp(self):
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def setUp(self, rxcomp='bz'):
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cs = 5.
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ncx = 20
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@@ -25,46 +23,58 @@ class TDEM_bDerivTests(unittest.TestCase):
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mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * activeMap
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rxOffset = 40.
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rx = EM.TDEM.Rx(np.array([[rxOffset, 0., 0.]]), np.logspace(-4,-3, 20), 'bz')
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rx = EM.TDEM.Rx(np.array([[rxOffset, 0., 0.]]), np.logspace(-4,-3, 20), rxcomp)
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src = EM.TDEM.SurveyTDEM.MagDipole( [rx], loc=np.array([0., 0., 0.]))
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rx2 = EM.TDEM.Rx(np.array([[rxOffset-10, 0., 0.]]), np.logspace(-5,-4, 25), 'bz')
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rx2 = EM.TDEM.Rx(np.array([[rxOffset-10, 0., 0.]]), np.logspace(-5,-4, 25), rxcomp)
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src2 = EM.TDEM.SurveyTDEM.MagDipole( [rx2], loc=np.array([0., 0., 0.]))
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survey = EM.TDEM.Survey([src,src2])
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self.prb = EM.TDEM.Problem_b(mesh, mapping=mapping)
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# self.prb.timeSteps = [1e-5]
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self.prb.timeSteps = [(1e-05, 10), (5e-05, 10), (2.5e-4, 10)]
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# self.prb.timeSteps = [(1e-05, 100)]
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prb = EM.TDEM.Problem_b(mesh, mapping=mapping)
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# prb.timeSteps = [1e-5]
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prb.timeSteps = [(1e-05, 10), (5e-05, 10), (2.5e-4, 10)]
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# prb.timeSteps = [(1e-05, 100)]
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try:
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from pymatsolver import MumpsSolver
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self.prb.Solver = MumpsSolver
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prb.Solver = MumpsSolver
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except ImportError, e:
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self.prb.Solver = SolverLU
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prb.Solver = SolverLU
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self.m = np.log(1e-1)*np.ones(self.prb.mapping.nP) + 1e-2*np.random.randn(self.prb.mapping.nP)
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m = np.log(1e-1)*np.ones(prb.mapping.nP) + 1e-2*np.random.randn(prb.mapping.nP)
|
||||
|
||||
prb.pair(survey)
|
||||
|
||||
return mesh, prb, m
|
||||
|
||||
class TDEM_bDerivTests(unittest.TestCase):
|
||||
|
||||
self.prb.pair(survey)
|
||||
self.mesh = mesh
|
||||
|
||||
if testDeriv:
|
||||
def test_Deriv_J(self):
|
||||
def Deriv_J(self, rxcomp='bz'):
|
||||
|
||||
mesh, prb, m0 = setUp(rxcomp)
|
||||
|
||||
prb = self.prb
|
||||
prb.timeSteps = [(1e-05, 10), (0.0001, 10), (0.001, 10)]
|
||||
mesh = self.mesh
|
||||
|
||||
derChk = lambda m: [prb.survey.dpred(m), lambda mx: prb.Jvec(self.m, mx)]
|
||||
derChk = lambda m: [prb.survey.dpred(m), lambda mx: prb.Jvec(m0, mx)]
|
||||
print '\n'
|
||||
print 'test_Deriv_J'
|
||||
Tests.checkDerivative(derChk, self.m, plotIt=False, num=3, eps=1e-20)
|
||||
print 'test_Deriv_J %s'%rxcomp
|
||||
Tests.checkDerivative(derChk, m0, plotIt=False, num=3, eps=1e-20)
|
||||
|
||||
def test_Jvec_bx(self):
|
||||
self.Deriv_J('bx')
|
||||
|
||||
def test_Jvec_bz(self):
|
||||
self.Deriv_J('bz')
|
||||
|
||||
def test_Jvec_ey(self):
|
||||
self.Deriv_J('ey')
|
||||
|
||||
if testAdjoint:
|
||||
def test_adjointJvecVsJtvec(self):
|
||||
mesh = self.mesh
|
||||
prb = self.prb
|
||||
m0 = self.m
|
||||
def adjointJvecVsJtvec(self, rxcomp='bz'):
|
||||
print ' \n Testing Adjoint %s' %rxcomp
|
||||
mesh, prb, m0 = setUp(rxcomp)
|
||||
|
||||
m = np.random.rand(prb.mapping.nP)
|
||||
d = np.random.rand(prb.survey.nD)
|
||||
@@ -77,6 +87,15 @@ class TDEM_bDerivTests(unittest.TestCase):
|
||||
print ' ', V1, V2, np.abs(V1-V2), tol, passed
|
||||
self.assertTrue(passed)
|
||||
|
||||
def test_JvecVsJtvec_bx(self):
|
||||
self.adjointJvecVsJtvec('bx')
|
||||
|
||||
def test_JvecVsJtvec_bz(self):
|
||||
self.adjointJvecVsJtvec('bz')
|
||||
|
||||
def test_JvecVsJtvec_ey(self):
|
||||
self.adjointJvecVsJtvec('ey')
|
||||
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
|
||||
Reference in New Issue
Block a user