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https://github.com/wassname/simpeg.git
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rowanc1
222 lines
6.9 KiB
Python
222 lines
6.9 KiB
Python
import unittest
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from SimPEG import *
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import simpegEM as EM
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from scipy.constants import mu_0
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from simpegEM.Utils.Ana import hzAnalyticDipoleT
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import matplotlib.pyplot as plt
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class TDEM_bTests(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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model = Model.Vertical1DModel(mesh)
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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.DataTDEM1D(**opts)
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self.prb = EM.TDEM.ProblemTDEM_b(mesh, model)
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self.prb.setTimes([1e-5, 5e-5, 2.5e-4], [150, 150, 150])
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self.sigma = np.ones(mesh.nCz)*1e-8
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self.sigma[mesh.vectorCCz<0] = 0.1
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self.prb.pair(self.dat)
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def test_analitic_b(self):
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bz_calc = self.dat.dpred(self.sigma)
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bz_ana = mu_0*hzAnalyticDipoleT(self.dat.rxLoc[0], self.prb.times, self.sigma[0])
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diff = np.linalg.norm(bz_calc.flatten() - bz_ana.flatten())/np.linalg.norm(bz_ana.flatten())
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self.assertTrue(diff<0.05)
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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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model = Model.Vertical1DModel(mesh)
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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.DataTDEM1D(**opts)
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self.prb = EM.TDEM.ProblemTDEM_b(mesh, 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] = 0.1
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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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sigma = np.ones(self.prb.mesh.nCz)*1e-8
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sigma[self.prb.mesh.vectorCCz<0] = 0.1
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u = self.prb.fields(sigma)
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Ahu = self.prb.AhVec(sigma, u)
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self.assertTrue(np.linalg.norm(Ahu.get_b(0)-1/self.prb.getDt(0)*u.get_b(-1))/np.linalg.norm(u.get_b(0)) < 1.e-2)
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self.assertTrue(np.linalg.norm(Ahu.get_e(0))/np.linalg.norm(u.get_e(0)) < 1.e-2)
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for i in range(1,u.nTimes):
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self.assertTrue(np.linalg.norm(Ahu.get_b(i))/np.linalg.norm(u.get_b(i)) < 1.e-2)
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self.assertTrue(np.linalg.norm(Ahu.get_e(i))/np.linalg.norm(u.get_e(i)) < 1.e-2)
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def test_AhVecVSMat_OneTS(self):
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self.prb.setTimes([1e-5], [1])
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sigma = np.ones(self.prb.mesh.nCz)*1e-8
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sigma[self.prb.mesh.vectorCCz<0] = 0.1
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self.prb.makeMassMatrices(sigma)
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dt = self.prb.getDt(0)
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a11 = 1/dt*sp.eye(self.prb.mesh.nF)
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a12 = self.prb.mesh.edgeCurl
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a21 = self.prb.mesh.edgeCurl.T*self.prb.MfMui
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a22 = -self.prb.MeSigma
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A = sp.bmat([[a11,a12],[a21,a22]])
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f = self.prb.fields(sigma)
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u1 = A*f.fieldVec()
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u2 = self.prb.AhVec(sigma,f).fieldVec()
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self.assertTrue(np.linalg.norm(u1-u2)<1e-12)
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def test_solveAhVSMat_OneTS(self):
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self.prb.setTimes([1e-5], [1])
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sigma = np.ones(self.prb.mesh.nCz)*1e-8
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sigma[self.prb.mesh.vectorCCz<0] = 0.1
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self.prb.makeMassMatrices(sigma)
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dt = self.prb.getDt(0)
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a11 = 1/dt*sp.eye(self.prb.mesh.nF)
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a12 = self.prb.mesh.edgeCurl
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a21 = self.prb.mesh.edgeCurl.T*self.prb.MfMui
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a22 = -self.prb.MeSigma
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A = sp.bmat([[a11,a12],[a21,a22]])
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f = self.prb.fields(sigma)
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f.set_b(np.zeros((self.prb.mesh.nF,1)),0)
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f.set_e(np.random.rand(self.prb.mesh.nE,1),0)
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u1 = self.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 = np.ones(self.prb.mesh.nCz)*1e-8
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sigma[self.prb.mesh.vectorCCz<0] = 0.1
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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.mesh.nCz)
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f = self.prb.fields(sigma)
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dm = np.random.rand(self.prb.mesh.nCz)
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h = 1.
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a = np.linalg.norm(self.prb.AhVec(sigma+h*dm, f).fieldVec() - self.prb.AhVec(sigma, f).fieldVec())
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b = np.linalg.norm(self.prb.AhVec(sigma+h*dm, f).fieldVec() - self.prb.AhVec(sigma, f).fieldVec() - h*self.prb.G(sigma, dm, u=f).fieldVec())
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# Assuming that the gradient is exact to machine precision
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self.assertTrue(b<1e-16)
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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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d_sig = sigma.copy() #np.random.rand(mesh.nCz)
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d_sig[d_sig==1e-8] = 0
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num = 10
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error = np.zeros(num)
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order = 0
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hv = np.logspace(-1.2,-3, num)
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for i, h in enumerate(hv):
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f = prb.fields(sigma)
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fstep = prb.fields(sigma + h*d_sig)
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dcdm = prb.G(sigma, h*d_sig, u=f) # TODO: make negative!?!?
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dudm = prb.solveAh(sigma, dcdm)
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linear = np.linalg.norm(f.fieldVec() - fstep.fieldVec())
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quad = np.linalg.norm(f.fieldVec() - fstep.fieldVec() - dudm.fieldVec())
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error[i] = quad
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if i > 0:
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order = np.log(error[i]/error[i-1])/np.log(hv[i]/hv[i-1])
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# print np.log(linearB/quadB)/np.log(h)
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print h, linear, quad, order
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self.assertTrue(order > 1.8)
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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[d_sig==1e-8] = 0
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derChk = lambda m: [prb.data.dpred(m), lambda mx: -prb.J(sigma, mx)]
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passed = Tests.checkDerivative(derChk, sigma, plotIt=False, dx=d_sig, num=2, eps=1e-20)
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self.assertTrue(passed)
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if __name__ == '__main__':
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unittest.main()
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