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rowanc1
312 lines
11 KiB
Python
312 lines
11 KiB
Python
import unittest
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from SimPEG import *
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from simpegPF import BaseMag
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import matplotlib.pyplot as plt
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import simpegPF as PF
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from scipy.constants import mu_0
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class MagSensProblemTests(unittest.TestCase):
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def setUp(self):
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hxind = ((5,25,1.3),(21, 25.),(5,25,1.3))
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hyind = ((5,25,1.3),(21, 25.),(5,25,1.3))
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hzind = ((5,25,1.3),(20, 25.),(5,25,1.3))
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hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)
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M = Mesh.TensorMesh([hx, hy, hz], [-hx.sum()/2,-hy.sum()/2,-hz.sum()/2])
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chibkg = 0.001
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chiblk = 0.01
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chi = np.ones(M.nC)*chibkg
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Inc = 90.
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Dec = 0.
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Btot = 51000
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b0 = PF.MagAnalytics.IDTtoxyz(Inc, Dec, Btot)
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sph_ind = PF.MagAnalytics.spheremodel(M, 0., 0., 0., 100)
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chi[sph_ind] = chiblk
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model = PF.BaseMag.BaseMagMap(M)
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survey = BaseMag.BaseMagSurvey()
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survey.setBackgroundField(Inc, Dec, Btot)
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xr = np.linspace(-300, 300, 41)
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yr = np.linspace(-300, 300, 41)
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X, Y = np.meshgrid(xr, yr)
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Z = np.ones((xr.size, yr.size))*150
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rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
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survey.rxLoc = rxLoc
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prob = PF.Magnetics.MagneticsDiffSecondary(M, mapping=model)
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prob.pair(survey)
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dpre = survey.dpred(chi)
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fields = prob.fields(chi)
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self.u = fields['u']
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self.B = fields['B']
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self.survey = survey
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self.model = model
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self.prob = prob
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self.M = M
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self.chi = chi
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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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def MfmuI(mu):
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chi = mu/mu_0-1
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self.prob.makeMassMatrices(chi)
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vol = self.prob.mesh.vol
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aveF2CC = self.prob.mesh.aveF2CC
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MfMuI = self.prob.MfMuI.diagonal()
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return MfMuI
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def dMfmuI(mu, v):
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chi = mu/mu_0-1
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self.prob.makeMassMatrices(chi)
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vol = self.prob.mesh.vol
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aveF2CC = self.prob.mesh.aveF2CC
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MfMuI = self.prob.MfMuI.diagonal()
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dMfMuI = Utils.sdiag(MfMuI**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
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return dMfMuI*v
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d_mu = mu*0.8
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derChk = lambda m: [MfmuI(m), lambda mx: dMfmuI(self.chi, mx)]
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passed = Tests.checkDerivative(derChk, mu, num=4, dx = d_mu, plotIt=False)
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self.assertTrue(passed)
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def test_dCdm_Av(self):
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print '\n >>Derivative for Cm_A.'
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Div = self.prob._Div
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vol = self.prob.mesh.vol
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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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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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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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Cm_A = A*u
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return Cm_A
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def dCdm_A(chi, v):
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dmudm = self.model.transformDeriv(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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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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Cm_A = A*u
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dCdm_A = Div * ( Utils.sdiag( Div.T * u )* dMfMuI *dmudm )
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return dCdm_A*v
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d_chi = self.chi*0.8
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derChk = lambda m: [Cm_A(m), lambda mx: dCdm_A(self.chi, mx)]
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passed = Tests.checkDerivative(derChk, self.chi, num=4, dx = d_chi, plotIt=False)
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self.assertTrue(passed)
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def test_dCdmu_RHS(self):
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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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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 Cm_RHS(chi):
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self.prob.makeMassMatrices(chi)
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dmudm = self.model.transformDeriv(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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dMfMuI = Utils.sdiag(MfMuIvec**2)*aveF2CC.T*Utils.sdiag(vol*1./mu**2)
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RHS1 = Div*self.prob.MfMuI*self.prob.MfMu0*B0
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RHS2 = Mc*Dface*self.prob._Pout.T*Bbc
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RHS = RHS1 + RHS2 + Div*B0
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return RHS
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def dCdm_RHS(chi, v):
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self.prob.makeMassMatrices(chi)
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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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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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return dCdm_RHSv
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d_chi = self.chi*0.8
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derChk = lambda m: [Cm_RHS(m), lambda mx: dCdm_RHS(self.chi, mx)]
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passed = Tests.checkDerivative(derChk, self.chi, num=4, dx = d_chi, plotIt=False)
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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 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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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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dudm = -sol
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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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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 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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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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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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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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def test_Jvec(self):
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print ">> Derivative test for Jvec"
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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: (self.survey.dpred(m), lambda v: self.prob.Jvec(m, v))
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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_Jtvec(self):
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print ">> Derivative test for Jtvec"
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dobs = self.survey.dpred(self.chi)
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def misfit(m):
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dpre = self.survey.dpred(m)
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misfit = 0.5*np.linalg.norm(dpre-dobs)**2
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residual = dpre-dobs
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dmisfit = self.prob.Jtvec(self.chi, residual)
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return misfit, dmisfit
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# TODO: I am not sure why the order get worse as step decreases .. --;
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passed = Tests.checkDerivative(misfit, self.chi, num=4, plotIt=False)
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self.assertTrue(passed)
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if __name__ == '__main__':
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unittest.main()
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