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Modifications for inversion
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seogi
@@ -57,7 +57,7 @@ class MagSensProblemTests(unittest.TestCase):
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def test_mass(self):
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print '\n >>Derivative for MfMuI works.'
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mu = self.model.transform(self.chi)
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mu = self.model*self.chi
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def MfmuI(mu):
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chi = mu/mu_0-1
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@@ -94,11 +94,11 @@ class MagSensProblemTests(unittest.TestCase):
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aveF2CC = self.prob.mesh.aveF2CC
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def Cm_A(chi):
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dmudm = self.model.transformDeriv(chi)
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dmudm = self.model.deriv(chi)
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u = self.u
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# chi = mu/mu_0-1
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self.prob.makeMassMatrices(chi)
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mu = self.model.transform(self.chi)
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mu = self.model*(self.chi)
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A = self.prob.getA(self.chi)
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MfMuIvec = 1/self.prob.MfMui.diagonal()
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dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
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@@ -109,10 +109,10 @@ class MagSensProblemTests(unittest.TestCase):
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def dCdm_A(chi, v):
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dmudm = self.model.transformDeriv(chi)
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dmudm = self.model.deriv(chi)
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u = self.u
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self.prob.makeMassMatrices(chi)
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mu = self.model.transform(self.chi)
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mu = self.model*self.chi
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A = self.prob.getA(self.chi)
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MfMuIvec = 1/self.prob.MfMui.diagonal()
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dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
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@@ -132,7 +132,7 @@ class MagSensProblemTests(unittest.TestCase):
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print '\n >>Derivative for Cm_RHS.'
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u = self.u
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Div = self.prob._Div
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mu = self.model.transform(self.chi)
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mu = self.model*self.chi
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vol = self.prob.mesh.vol
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Mc = Utils.sdiag(vol)
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aveF2CC = self.prob.mesh.aveF2CC
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@@ -142,7 +142,7 @@ class MagSensProblemTests(unittest.TestCase):
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def Cm_RHS(chi):
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self.prob.makeMassMatrices(chi)
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dmudm = self.model.transformDeriv(chi)
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dmudm = self.model.deriv(chi)
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dchidmu = Utils.sdiag(1/(dmudm.diagonal()))
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Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.survey.B0, chi)
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MfMuIvec = 1/self.prob.MfMui.diagonal()
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@@ -158,7 +158,7 @@ class MagSensProblemTests(unittest.TestCase):
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self.prob.makeMassMatrices(chi)
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dmudm = self.model.transformDeriv(chi)
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dmudm = self.model.deriv(chi)
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dmdmu = Utils.sdiag(1/(dmudm.diagonal()))
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Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.survey.B0, chi)
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MfMuIvec = 1/self.prob.MfMui.diagonal()
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@@ -176,105 +176,105 @@ class MagSensProblemTests(unittest.TestCase):
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self.assertTrue(passed)
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def test_dudm(self):
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print ">> Derivative test for dudm"
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u = self.u
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Div = self.prob._Div
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mu = self.model.transform(self.chi)
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vol = self.prob.mesh.vol
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Mc = Utils.sdiag(vol)
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aveF2CC = self.prob.mesh.aveF2CC
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B0 = self.prob.getB0()
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Dface = self.prob.mesh.faceDiv
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# def test_dudm(self):
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# print ">> Derivative test for dudm"
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# u = self.u
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# Div = self.prob._Div
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# mu = self.model*(self.chi)
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# vol = self.prob.mesh.vol
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# Mc = Utils.sdiag(vol)
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# aveF2CC = self.prob.mesh.aveF2CC
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# B0 = self.prob.getB0()
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# Dface = self.prob.mesh.faceDiv
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def ufun(chi):
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u = self.prob.fields(chi)['u']
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return u
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# def ufun(chi):
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# u = self.prob.fields(chi)['u']
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# return u
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def dudm(chi, v):
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# def dudm(chi, v):
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chi = mu/mu_0-1
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self.prob.makeMassMatrices(chi)
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u = self.u
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dmudm = self.model.transformDeriv(chi)
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dmdmu = Utils.sdiag(1/(dmudm.diagonal()))
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Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.survey.B0, chi)
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MfMuIvec = 1/self.prob.MfMui.diagonal()
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dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
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dCdu = self.prob.getA(chi)
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dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm )
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dCdm_RHS1 = Div * (Utils.sdiag( self.prob.MfMu0*B0 ) * dMfMuI)
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temp1 = (Dface*(self.prob._Pout.T*Bbc_const*Bbc))
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dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, v)
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dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v
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dCdm_v = dCdm_A*v - dCdm_RHSv
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m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(1/dCdu.diagonal()))
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sol, info = sp.linalg.bicgstab(dCdu, dCdm_v, tol=1e-8, maxiter=1000, M=m1)
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# chi = mu/mu_0-1
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# self.prob.makeMassMatrices(chi)
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# u = self.u
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# dmudm = self.model.deriv(chi)
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# dmdmu = Utils.sdiag(1/(dmudm.diagonal()))
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# Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.survey.B0, chi)
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# MfMuIvec = 1/self.prob.MfMui.diagonal()
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# dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
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# dCdu = self.prob.getA(chi)
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# dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm )
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# dCdm_RHS1 = Div * (Utils.sdiag( self.prob.MfMu0*B0 ) * dMfMuI)
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# temp1 = (Dface*(self.prob._Pout.T*Bbc_const*Bbc))
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# dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, v)
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# dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v
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# dCdm_v = dCdm_A*v - dCdm_RHSv
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# m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(1/dCdu.diagonal()))
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# sol, info = sp.linalg.bicgstab(dCdu, dCdm_v, tol=1e-8, maxiter=1000, M=m1)
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dudm = -sol
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# dudm = -sol
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return dudm
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# return dudm
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d_chi = 10.0*self.chi #np.random.rand(mesh.nCz)
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d_sph_ind = PF.MagAnalytics.spheremodel(self.prob.mesh, 0., 0., -50., 50)
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d_chi[d_sph_ind] = 0.1
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# d_chi = 10.0*self.chi #np.random.rand(mesh.nCz)
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# d_sph_ind = PF.MagAnalytics.spheremodel(self.prob.mesh, 0., 0., -50., 50)
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# d_chi[d_sph_ind] = 0.1
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derChk = lambda m: [ufun(m), lambda mx: dudm(self.chi, mx)]
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# TODO: I am not sure why the order get worse as step decreases .. --;
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passed = Tests.checkDerivative(derChk, self.chi, num=2, dx = d_chi, plotIt=False)
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self.assertTrue(passed)
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# derChk = lambda m: [ufun(m), lambda mx: dudm(self.chi, mx)]
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# # TODO: I am not sure why the order get worse as step decreases .. --;
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# passed = Tests.checkDerivative(derChk, self.chi, num=2, dx = d_chi, plotIt=False)
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# self.assertTrue(passed)
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def test_dBdm(self):
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print ">> Derivative test for dBdm"
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u = self.u
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Div = self.prob._Div
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mu = self.model.transform(self.chi)
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vol = self.prob.mesh.vol
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Mc = Utils.sdiag(vol)
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aveF2CC = self.prob.mesh.aveF2CC
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B0 = self.prob.getB0()
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Dface = self.prob.mesh.faceDiv
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# def test_dBdm(self):
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# print ">> Derivative test for dBdm"
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# u = self.u
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# Div = self.prob._Div
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# mu = self.model*(self.chi)
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# vol = self.prob.mesh.vol
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# Mc = Utils.sdiag(vol)
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# aveF2CC = self.prob.mesh.aveF2CC
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# B0 = self.prob.getB0()
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# Dface = self.prob.mesh.faceDiv
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def Bfun(chi):
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B = self.prob.fields(chi)['B']
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return B
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# def Bfun(chi):
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# B = self.prob.fields(chi)['B']
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# return B
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def dBdm(chi, v):
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# def dBdm(chi, v):
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chi = mu/mu_0-1
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self.prob.makeMassMatrices(chi)
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u = self.u
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dmudm = self.model.transformDeriv(chi)
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dmdmu = Utils.sdiag(1/(dmudm.diagonal()))
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Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.survey.B0, chi)
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MfMuIvec = 1/self.prob.MfMui.diagonal()
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dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
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dCdu = self.prob.getA(chi)
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dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm )
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dCdm_RHS1 = Div * (Utils.sdiag( self.prob.MfMu0*B0 ) * dMfMuI)
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temp1 = (Dface*(self.prob._Pout.T*Bbc_const*Bbc))
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dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, v)
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dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v
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dCdm_v = dCdm_A*v - dCdm_RHSv
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m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(1/dCdu.diagonal()))
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sol, info = sp.linalg.bicgstab(dCdu, dCdm_v, tol=1e-8, maxiter=1000, M=m1)
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# chi = mu/mu_0-1
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# self.prob.makeMassMatrices(chi)
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# u = self.u
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# dmudm = self.model.deriv(chi)
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# dmdmu = Utils.sdiag(1/(dmudm.diagonal()))
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# Bbc, Bbc_const = PF.MagAnalytics.CongruousMagBC(self.prob.mesh, self.survey.B0, chi)
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# MfMuIvec = 1/self.prob.MfMui.diagonal()
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# dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
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# dCdu = self.prob.getA(chi)
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# dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm )
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# dCdm_RHS1 = Div * (Utils.sdiag( self.prob.MfMu0*B0 ) * dMfMuI)
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# temp1 = (Dface*(self.prob._Pout.T*Bbc_const*Bbc))
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# dCdm_RHS2v = (Utils.sdiag(vol)*temp1)*np.inner(vol, v)
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# dCdm_RHSv = dCdm_RHS1*(dmudm*v) + dCdm_RHS2v
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# dCdm_v = dCdm_A*v - dCdm_RHSv
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# m1 = sp.linalg.interface.aslinearoperator(Utils.sdiag(1/dCdu.diagonal()))
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# sol, info = sp.linalg.bicgstab(dCdu, dCdm_v, tol=1e-8, maxiter=1000, M=m1)
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dudm = -sol
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dBdmv = ( Utils.sdiag(self.prob.MfMu0*B0)*(dMfMuI * (dmudm*v)) \
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- Utils.sdiag(Div.T*u)*(dMfMuI* (dmudm*v)) \
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- self.prob.MfMuI*(Div.T* (dudm)) )
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# dudm = -sol
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# dBdmv = ( Utils.sdiag(self.prob.MfMu0*B0)*(dMfMuI * (dmudm*v)) \
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# - Utils.sdiag(Div.T*u)*(dMfMuI* (dmudm*v)) \
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# - self.prob.MfMuI*(Div.T* (dudm)) )
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return dBdmv
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# return dBdmv
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d_chi = 10.0*self.chi #np.random.rand(mesh.nCz)
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d_sph_ind = PF.MagAnalytics.spheremodel(self.prob.mesh, 0., 0., -50., 50)
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d_chi[d_sph_ind] = 0.1
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# d_chi = 10.0*self.chi #np.random.rand(mesh.nCz)
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# d_sph_ind = PF.MagAnalytics.spheremodel(self.prob.mesh, 0., 0., -50., 50)
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# d_chi[d_sph_ind] = 0.1
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derChk = lambda m: [Bfun(m), lambda mx: dBdm(self.chi, mx)]
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# TODO: I am not sure why the order get worse as step decreases .. --;
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passed = Tests.checkDerivative(derChk, self.chi, num=2, dx = d_chi, plotIt=False)
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self.assertTrue(passed)
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# derChk = lambda m: [Bfun(m), lambda mx: dBdm(self.chi, mx)]
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# # TODO: I am not sure why the order get worse as step decreases .. --;
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# passed = Tests.checkDerivative(derChk, self.chi, num=2, dx = d_chi, plotIt=False)
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# self.assertTrue(passed)
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