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294 lines
8.9 KiB
Python
294 lines
8.9 KiB
Python
import unittest
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from SimPEG import *
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import simpegEM as EM
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class TDEM_bDerivTests(unittest.TestCase):
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def setUp(self):
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cs = 5.
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ncx = 20
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ncy = 6
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npad = 20
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hx = Utils.meshTensors(((0,cs), (ncx,cs), (npad,cs)))
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hy = Utils.meshTensors(((npad,cs), (ncy,cs), (npad,cs)))
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mesh = Mesh.Cyl1DMesh([hx,hy], -hy.sum()/2)
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active = mesh.vectorCCz<0.
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model = Model.ActiveModel(mesh, active, -8, nC=mesh.nCz)
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model = Model.ComboModel(mesh,
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[Model.LogModel, Model.Vertical1DModel, model])
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opts = {'txLoc':0.,
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'txType':'VMD_MVP',
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'rxLoc':np.r_[150., 0.],
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'rxType':'bz',
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'timeCh':np.logspace(-4,-2,20),
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}
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self.dat = EM.TDEM.SurveyTDEM1D(**opts)
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self.prb = EM.TDEM.ProblemTDEM_b(model)
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self.prb.setTimes([1e-5, 5e-5, 2.5e-4], [10, 10, 10])
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self.sigma = np.ones(mesh.nCz)*1e-8
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self.sigma[mesh.vectorCCz<0] = 1e-1
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self.sigma = np.log(self.sigma[active])
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self.prb.pair(self.dat)
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self.mesh = mesh
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def test_AhVec(self):
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"""
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Test that fields and AhVec produce consistent results
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"""
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prb = self.prb
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sigma = self.sigma
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u = prb.fields(sigma)
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Ahu = prb.AhVec(sigma, u)
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V1 = Ahu.get_b(0)
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V2 = 1/prb.getDt(0)*prb.MfMui*u.get_b(-1)
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self.assertTrue(np.linalg.norm(V1-V2)/np.linalg.norm(V2) < 1.e-6)
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V1 = Ahu.get_e(0)
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self.assertTrue(np.linalg.norm(V1) < 1.e-6)
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for i in range(1,u.nTimes):
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dt = prb.getDt(i)
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V1 = Ahu.get_b(i)
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V2 = 1/dt*prb.MfMui*u.get_b(i-1)
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self.assertTrue(np.linalg.norm(V1)/np.linalg.norm(V2) < 1.e-6)
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V1 = Ahu.get_e(i)
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V2 = prb.MeSigma*u.get_e(i)
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self.assertTrue(np.linalg.norm(V1)/np.linalg.norm(V2) < 1.e-6)
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def test_AhVecVSMat_OneTS(self):
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prb = self.prb
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prb.setTimes([1e-5], [1])
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sigma = self.sigma
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prb.makeMassMatrices(sigma)
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dt = prb.getDt(0)
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a11 = 1/dt*prb.MfMui*sp.eye(prb.mesh.nF)
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a12 = prb.MfMui*prb.mesh.edgeCurl
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a21 = prb.mesh.edgeCurl.T*prb.MfMui
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a22 = -prb.MeSigma
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A = sp.bmat([[a11,a12],[a21,a22]])
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f = prb.fields(sigma)
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u1 = A*f.fieldVec()
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u2 = prb.AhVec(sigma,f).fieldVec()
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self.assertTrue(np.linalg.norm(u1-u2)/np.linalg.norm(u1)<1e-12)
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def test_solveAhVSMat_OneTS(self):
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prb = self.prb
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prb.setTimes([1e-5], [1])
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sigma = self.sigma
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prb.makeMassMatrices(sigma)
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dt = prb.getDt(0)
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a11 = 1/dt*prb.MfMui*sp.eye(prb.mesh.nF)
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a12 = prb.MfMui*prb.mesh.edgeCurl
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a21 = prb.mesh.edgeCurl.T*prb.MfMui
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a22 = -prb.MeSigma
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A = sp.bmat([[a11,a12],[a21,a22]])
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f = prb.fields(sigma)
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f.set_b(np.zeros((prb.mesh.nF,1)),0)
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f.set_e(np.random.rand(prb.mesh.nE,1),0)
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u1 = prb.solveAh(sigma,f).fieldVec().flatten()
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u2 = sp.linalg.spsolve(A.tocsr(),f.fieldVec())
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self.assertTrue(np.linalg.norm(u1-u2)<1e-8)
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def test_solveAhVsAhVec(self):
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prb = self.prb
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mesh = self.prb.mesh
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sigma = self.sigma
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self.prb.makeMassMatrices(sigma)
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f = EM.TDEM.FieldsTDEM(prb.mesh, 1, prb.times.size, 'b')
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for i in range(f.nTimes):
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f.set_b(np.zeros((mesh.nF, 1)), i)
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f.set_e(np.random.rand(mesh.nE, 1), i)
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Ahf = prb.AhVec(sigma, f)
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f_test = prb.solveAh(sigma, Ahf)
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u1 = f.fieldVec()
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u2 = f_test.fieldVec()
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self.assertTrue(np.linalg.norm(u1-u2)<1e-8)
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def test_DerivG(self):
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"""
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Test the derivative of c with respect to sigma
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"""
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# Random model and perturbation
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sigma = np.random.rand(self.prb.model.nP)
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f = self.prb.fields(sigma)
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dm = 1000*np.random.rand(self.prb.model.nP)
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h = 0.01
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derChk = lambda m: [self.prb.AhVec(m, f).fieldVec(), lambda mx: self.prb.Gvec(sigma, mx, u=f).fieldVec()]
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print '\ntest_DerivG'
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passed = Tests.checkDerivative(derChk, sigma, plotIt=False, dx=dm, num=6, eps=1e-20)
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self.assertTrue(passed)
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def test_Deriv_dUdM(self):
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prb = self.prb
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prb.setTimes([1e-5, 1e-4, 1e-3], [10, 10, 10])
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mesh = self.mesh
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sigma = self.sigma
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dm = 10*np.random.rand(prb.model.nP)
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f = prb.fields(sigma)
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derChk = lambda m: [self.prb.fields(m).fieldVec(), lambda mx: -prb.solveAh(sigma, prb.Gvec(sigma, mx, u=f)).fieldVec()]
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print '\n'
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print 'test_Deriv_dUdM'
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passed = Tests.checkDerivative(derChk, sigma, plotIt=False, dx=dm, num=6, eps=1e-20)
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self.assertTrue(passed)
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def test_Deriv_J(self):
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prb = self.prb
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prb.setTimes([1e-5, 1e-4, 1e-3], [10, 10, 10])
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mesh = self.mesh
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sigma = self.sigma
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# d_sig = 0.8*sigma #np.random.rand(mesh.nCz)
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d_sig = 10*np.random.rand(prb.model.nP)
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derChk = lambda m: [prb.survey.dpred(m), lambda mx: -prb.Jvec(sigma, mx)]
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print '\n'
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print 'test_Deriv_J'
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passed = Tests.checkDerivative(derChk, sigma, plotIt=False, dx=d_sig, num=6, eps=1e-20)
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self.assertTrue(passed)
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def test_projectAdjoint(self):
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prb = self.prb
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dat = self.dat
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mesh = self.mesh
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# Generate random fields and data
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f = EM.TDEM.FieldsTDEM(prb.mesh, 1, prb.times.size, 'b')
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for i in range(f.nTimes):
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f.set_b(np.random.rand(mesh.nF, 1), i)
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f.set_e(np.random.rand(mesh.nE, 1), i)
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d = np.random.rand(dat.prob.nTimes, dat.nTx)
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# Check that d.T*Q*f = f.T*Q.T*d
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V1 = d.T.dot(dat.projectFields(f))
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V2 = f.fieldVec().dot(dat.projectFieldsAdjoint(d).fieldVec())
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self.assertLess((V1-V2)/np.abs(V1), 1e-6)
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def test_adjointAhVsAht(self):
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prb = self.prb
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mesh = self.mesh
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sigma = self.sigma
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f1 = EM.TDEM.FieldsTDEM(prb.mesh, 1, prb.nTimes, 'b')
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for i in range(f1.nTimes):
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f1.set_b(np.random.rand(mesh.nF, 1), i)
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f1.set_e(np.random.rand(mesh.nE, 1), i)
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f2 = EM.TDEM.FieldsTDEM(prb.mesh, 1, prb.nTimes, 'b')
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for i in range(f2.nTimes):
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f2.set_b(np.random.rand(mesh.nF, 1), i)
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f2.set_e(np.random.rand(mesh.nE, 1), i)
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V1 = f2.fieldVec().dot(prb.AhVec(sigma, f1).fieldVec())
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V2 = f1.fieldVec().dot(prb.AhtVec(sigma, f2).fieldVec())
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self.assertLess(np.abs(V1-V2)/np.abs(V1), 1e-6)
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def test_solveAhtVsAhtVec(self):
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prb = self.prb
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mesh = self.mesh
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sigma = np.random.rand(prb.model.nP)
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f1 = EM.TDEM.FieldsTDEM(mesh, 1, prb.nTimes, 'b')
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for i in range(f1.nTimes):
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f1.set_b(np.random.rand(mesh.nF, 1), i)
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f1.set_e(np.random.rand(mesh.nE, 1), i)
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f2 = prb.solveAht(sigma, f1)
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f3 = prb.AhtVec(sigma, f2)
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V1 = np.linalg.norm(f3.fieldVec()-f1.fieldVec())
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V2 = np.linalg.norm(f1.fieldVec())
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self.assertLess(V1/V2, 1e-6)
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def test_adjointsolveAhVssolveAht(self):
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prb = self.prb
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mesh = self.mesh
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sigma = self.sigma
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f1 = EM.TDEM.FieldsTDEM(prb.mesh, 1, prb.nTimes, 'b')
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for i in range(f1.nTimes):
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f1.set_b(np.random.rand(mesh.nF, 1), i)
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f1.set_e(np.random.rand(mesh.nE, 1), i)
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f2 = EM.TDEM.FieldsTDEM(prb.mesh, 1, prb.nTimes, 'b')
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for i in range(f2.nTimes):
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f2.set_b(np.random.rand(mesh.nF, 1), i)
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f2.set_e(np.random.rand(mesh.nE, 1), i)
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V1 = f2.fieldVec().dot(prb.solveAh(sigma, f1).fieldVec())
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V2 = f1.fieldVec().dot(prb.solveAht(sigma, f2).fieldVec())
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self.assertLess(np.abs(V1-V2)/np.abs(V1), 1e-6)
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def test_adjointGvecVsGtvec(self):
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mesh = self.mesh
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prb = self.prb
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m = np.random.rand(prb.model.nP)
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sigma = np.random.rand(prb.model.nP)
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u = EM.TDEM.FieldsTDEM(prb.mesh, 1, prb.nTimes, 'b')
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for i in range(u.nTimes):
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u.set_b(np.random.rand(mesh.nF, 1), i)
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u.set_e(np.random.rand(mesh.nE, 1), i)
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v = EM.TDEM.FieldsTDEM(prb.mesh, 1, prb.nTimes, 'b')
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for i in range(v.nTimes):
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v.set_b(np.random.rand(mesh.nF, 1), i)
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v.set_e(np.random.rand(mesh.nE, 1), i)
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V1 = m.dot(prb.Gtvec(sigma, v, u))
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V2 = v.fieldVec().dot(prb.Gvec(sigma, m, u).fieldVec())
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self.assertLess(np.abs(V1-V2)/np.abs(V1), 1e-6)
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def test_adjointJvecVsJtvec(self):
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mesh = self.mesh
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prb = self.prb
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sigma = self.sigma
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m = np.random.rand(prb.model.nP)
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d = np.random.rand(prb.nTimes)
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V1 = d.dot(prb.Jvec(sigma, m))
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V2 = m.dot(prb.Jtvec(sigma, d))
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self.assertLess(np.abs(V1-V2)/np.abs(V1), 1e-6)
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if __name__ == '__main__':
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unittest.main()
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