import unittest from SimPEG import * from SimPEG import EM import sys from scipy.constants import mu_0 testDerivs = True testCrossCheck = True testAdjoint = True testEB = True testHJ = True verbose = False TOL = 1e-5 FLR = 1e-20 # "zero", so if residual below this --> pass regardless of order CONDUCTIVITY = 1e1 MU = mu_0 freq = 1e-1 addrandoms = True SrcType = 'RawVec' #or 'MAgDipole_Bfield', 'CircularLoop', 'RawVec' def getProblem(fdemType, comp): cs = 5. ncx, ncy, ncz = 6, 6, 6 npad = 3 hx = [(cs,npad,-1.3), (cs,ncx), (cs,npad,1.3)] hy = [(cs,npad,-1.3), (cs,ncy), (cs,npad,1.3)] hz = [(cs,npad,-1.3), (cs,ncz), (cs,npad,1.3)] mesh = Mesh.TensorMesh([hx,hy,hz],['C','C','C']) mapping = Maps.ExpMap(mesh) x = np.array([np.linspace(-30,-15,3),np.linspace(15,30,3)]) #don't sample right by the source XYZ = Utils.ndgrid(x,x,np.r_[0.]) Rx0 = EM.FDEM.RxFDEM(XYZ, comp) if SrcType is 'MagDipole': Src = EM.FDEM.SrcFDEM_MagDipole([Rx0], freq=freq, loc=np.r_[0.,0.,0.]) elif SrcType is 'MagDipole_Bfield': Src = EM.FDEM.SrcFDEM_MagDipole_Bfield([Rx0], freq=freq, loc=np.r_[0.,0.,0.]) elif SrcType is 'CircularLoop': Src2 = EM.FDEM.SrcFDEM_CircularLoop([Rx0], freq=freq, loc=np.r_[0.,0.,0.]) if verbose: print ' Fetching %s problem' % (fdemType) if fdemType == 'e': if SrcType is 'RawVec': S_m = np.zeros(mesh.nF) S_e = np.zeros(mesh.nE) S_m[Utils.closestPoints(mesh,[0.,0.,0.],'Fz') + np.sum(mesh.vnF[:1])] = 1. S_e[Utils.closestPoints(mesh,[0.,0.,0.],'Ez') + np.sum(mesh.vnE[:1])] = 1. Src = EM.FDEM.SrcFDEM_RawVec([Rx0], freq, S_m, S_e) survey = EM.FDEM.SurveyFDEM([Src]) prb = EM.FDEM.ProblemFDEM_e(mesh, mapping=mapping) elif fdemType == 'b': if SrcType is 'RawVec': S_m = np.zeros(mesh.nF) S_e = np.zeros(mesh.nE) S_m[Utils.closestPoints(mesh,[0.,0.,0.],'Fz') + np.sum(mesh.vnF[:1])] = 1. S_e[Utils.closestPoints(mesh,[0.,0.,0.],'Ez') + np.sum(mesh.vnE[:1])] = 1. Src = EM.FDEM.SrcFDEM_RawVec([Rx0], freq, S_m, S_e) survey = EM.FDEM.SurveyFDEM([Src]) prb = EM.FDEM.ProblemFDEM_b(mesh, mapping=mapping) elif fdemType == 'j': if SrcType is 'RawVec': S_m = np.zeros(mesh.nE) S_e = np.zeros(mesh.nF) S_m[Utils.closestPoints(mesh,[0.,0.,0.],'Ez') + np.sum(mesh.vnE[:1])] = 1. S_e[Utils.closestPoints(mesh,[0.,0.,0.],'Fz') + np.sum(mesh.vnF[:1])] = 1. Src = EM.FDEM.SrcFDEM_RawVec([Rx0], freq, S_m, S_e) survey = EM.FDEM.SurveyFDEM([Src]) prb = EM.FDEM.ProblemFDEM_j(mesh, mapping=mapping) elif fdemType == 'h': if SrcType is 'RawVec': S_m = np.zeros(mesh.nE) S_e = np.zeros(mesh.nF) S_m[Utils.closestPoints(mesh,[0.,0.,0.],'Ez') + np.sum(mesh.vnE[:1])] = 1. S_e[Utils.closestPoints(mesh,[0.,0.,0.],'Fz') + np.sum(mesh.vnF[:1])] = 1. Src = EM.FDEM.SrcFDEM_RawVec([Rx0], freq, S_m, S_e) survey = EM.FDEM.SurveyFDEM([Src]) prb = EM.FDEM.ProblemFDEM_h(mesh, mapping=mapping) else: raise NotImplementedError() prb.pair(survey) try: from pymatsolver import MumpsSolver prb.Solver = MumpsSolver except ImportError, e: pass return prb def adjointTest(fdemType, comp): prb = getProblem(fdemType, comp) print 'Adjoint %s formulation - %s' % (fdemType, comp) m = np.log(np.ones(prb.mapping.nP)*CONDUCTIVITY) mu = np.ones(prb.mesh.nC)*MU if addrandoms is True: m = m + np.random.randn(prb.mapping.nP)*np.log(CONDUCTIVITY)*1e-1 mu = mu + np.random.randn(prb.mesh.nC)*MU*1e-1 survey = prb.survey # prb.PropMap.PropModel.mu = mu # prb.PropMap.PropModel.mui = 1./mu u = prb.fields(m) v = np.random.rand(survey.nD) w = np.random.rand(prb.mesh.nC) vJw = v.dot(prb.Jvec(m, w, u)) wJtv = w.dot(prb.Jtvec(m, v, u)) tol = np.max([TOL*(10**int(np.log10(np.abs(vJw)))),FLR]) print vJw, wJtv, vJw - wJtv, tol, np.abs(vJw - wJtv) < tol return np.abs(vJw - wJtv) < tol def derivTest(fdemType, comp): prb = getProblem(fdemType, comp) print '%s formulation - %s' % (fdemType, comp) x0 = np.log(np.ones(prb.mapping.nP)*CONDUCTIVITY) mu = np.log(np.ones(prb.mesh.nC)*MU) if addrandoms is True: x0 = x0 + np.random.randn(prb.mapping.nP)*np.log(CONDUCTIVITY)*1e-1 mu = mu + np.random.randn(prb.mapping.nP)*MU*1e-1 # prb.PropMap.PropModel.mu = mu # prb.PropMap.PropModel.mui = 1./mu survey = prb.survey def fun(x): return survey.dpred(x), lambda x: prb.Jvec(x0, x) return Tests.checkDerivative(fun, x0, num=3, plotIt=False, eps=FLR) def crossCheckTest(fdemType, comp): l2norm = lambda r: np.sqrt(r.dot(r)) prb1 = getProblem(fdemType, comp) mesh = prb1.mesh print 'Cross Checking Forward: %s formulation - %s' % (fdemType, comp) m = np.log(np.ones(mesh.nC)*CONDUCTIVITY) mu = np.log(np.ones(mesh.nC)*MU) if addrandoms is True: m = m + np.random.randn(mesh.nC)*np.log(CONDUCTIVITY)*1e-1 mu = mu + np.random.randn(mesh.nC)*MU*1e-1 # prb1.PropMap.PropModel.mu = mu # prb1.PropMap.PropModel.mui = 1./mu survey1 = prb1.survey d1 = survey1.dpred(m) if verbose: print ' Problem 1 solved' if fdemType == 'e': prb2 = getProblem('b', comp) elif fdemType == 'b': prb2 = getProblem('e', comp) elif fdemType == 'j': prb2 = getProblem('h', comp) elif fdemType == 'h': prb2 = getProblem('j', comp) else: raise NotImplementedError() # prb2.mu = mu survey2 = prb2.survey d2 = survey2.dpred(m) if verbose: print ' Problem 2 solved' r = d2-d1 l2r = l2norm(r) tol = np.max([TOL*(10**int(np.log10(l2norm(d1)))),FLR]) print l2norm(d1), l2norm(d2), l2r , tol, l2r < tol return l2r < tol class FDEM_DerivTests(unittest.TestCase): if testDerivs: if testEB: def test_Jvec_exr_Eform(self): self.assertTrue(derivTest('e', 'exr')) def test_Jvec_eyr_Eform(self): self.assertTrue(derivTest('e', 'eyr')) def test_Jvec_ezr_Eform(self): self.assertTrue(derivTest('e', 'ezr')) def test_Jvec_exi_Eform(self): self.assertTrue(derivTest('e', 'exi')) def test_Jvec_eyi_Eform(self): self.assertTrue(derivTest('e', 'eyi')) def test_Jvec_ezi_Eform(self): self.assertTrue(derivTest('e', 'ezi')) def test_Jvec_bxr_Eform(self): self.assertTrue(derivTest('e', 'bxr')) def test_Jvec_byr_Eform(self): self.assertTrue(derivTest('e', 'byr')) def test_Jvec_bzr_Eform(self): self.assertTrue(derivTest('e', 'bzr')) def test_Jvec_bxi_Eform(self): self.assertTrue(derivTest('e', 'bxi')) def test_Jvec_byi_Eform(self): self.assertTrue(derivTest('e', 'byi')) def test_Jvec_bzi_Eform(self): self.assertTrue(derivTest('e', 'bzi')) def test_Jvec_exr_Bform(self): self.assertTrue(derivTest('b', 'exr')) def test_Jvec_eyr_Bform(self): self.assertTrue(derivTest('b', 'eyr')) def test_Jvec_ezr_Bform(self): self.assertTrue(derivTest('b', 'ezr')) def test_Jvec_exi_Bform(self): self.assertTrue(derivTest('b', 'exi')) def test_Jvec_eyi_Bform(self): self.assertTrue(derivTest('b', 'eyi')) def test_Jvec_ezi_Bform(self): self.assertTrue(derivTest('b', 'ezi')) def test_Jvec_bxr_Bform(self): self.assertTrue(derivTest('b', 'bxr')) def test_Jvec_byr_Bform(self): self.assertTrue(derivTest('b', 'byr')) def test_Jvec_bzr_Bform(self): self.assertTrue(derivTest('b', 'bzr')) def test_Jvec_bxi_Bform(self): self.assertTrue(derivTest('b', 'bxi')) def test_Jvec_byi_Bform(self): self.assertTrue(derivTest('b', 'byi')) def test_Jvec_bzi_Bform(self): self.assertTrue(derivTest('b', 'bzi')) if testHJ: def test_Jvec_jxr_Jform(self): self.assertTrue(derivTest('j', 'jxr')) def test_Jvec_jyr_Jform(self): self.assertTrue(derivTest('j', 'jyr')) def test_Jvec_jzr_Jform(self): self.assertTrue(derivTest('j', 'jzr')) def test_Jvec_jxi_Jform(self): self.assertTrue(derivTest('j', 'jxi')) def test_Jvec_jyi_Jform(self): self.assertTrue(derivTest('j', 'jyi')) def test_Jvec_jzi_Jform(self): self.assertTrue(derivTest('j', 'jzi')) def test_Jvec_hxr_Jform(self): self.assertTrue(derivTest('j', 'hxr')) def test_Jvec_hyr_Jform(self): self.assertTrue(derivTest('j', 'hyr')) def test_Jvec_hzr_Jform(self): self.assertTrue(derivTest('j', 'hzr')) def test_Jvec_hxi_Jform(self): self.assertTrue(derivTest('j', 'hxi')) def test_Jvec_hyi_Jform(self): self.assertTrue(derivTest('j', 'hyi')) def test_Jvec_hzi_Jform(self): self.assertTrue(derivTest('j', 'hzi')) def test_Jvec_hxr_Hform(self): self.assertTrue(derivTest('h', 'hxr')) def test_Jvec_hyr_Hform(self): self.assertTrue(derivTest('h', 'hyr')) def test_Jvec_hzr_Hform(self): self.assertTrue(derivTest('h', 'hzr')) def test_Jvec_hxi_Hform(self): self.assertTrue(derivTest('h', 'hxi')) def test_Jvec_hyi_Hform(self): self.assertTrue(derivTest('h', 'hyi')) def test_Jvec_hzi_Hform(self): self.assertTrue(derivTest('h', 'hzi')) def test_Jvec_hxr_Hform(self): self.assertTrue(derivTest('h', 'jxr')) def test_Jvec_hyr_Hform(self): self.assertTrue(derivTest('h', 'jyr')) def test_Jvec_hzr_Hform(self): self.assertTrue(derivTest('h', 'jzr')) def test_Jvec_hxi_Hform(self): self.assertTrue(derivTest('h', 'jxi')) def test_Jvec_hyi_Hform(self): self.assertTrue(derivTest('h', 'jyi')) def test_Jvec_hzi_Hform(self): self.assertTrue(derivTest('h', 'jzi')) if testAdjoint: if testEB: def test_Jtvec_adjointTest_exr_Eform(self): self.assertTrue(adjointTest('e', 'exr')) def test_Jtvec_adjointTest_eyr_Eform(self): self.assertTrue(adjointTest('e', 'eyr')) def test_Jtvec_adjointTest_ezr_Eform(self): self.assertTrue(adjointTest('e', 'ezr')) def test_Jtvec_adjointTest_exi_Eform(self): self.assertTrue(adjointTest('e', 'exi')) def test_Jtvec_adjointTest_eyi_Eform(self): self.assertTrue(adjointTest('e', 'eyi')) def test_Jtvec_adjointTest_ezi_Eform(self): self.assertTrue(adjointTest('e', 'ezi')) def test_Jtvec_adjointTest_bxr_Eform(self): self.assertTrue(adjointTest('e', 'bxr')) def test_Jtvec_adjointTest_byr_Eform(self): self.assertTrue(adjointTest('e', 'byr')) def test_Jtvec_adjointTest_bzr_Eform(self): self.assertTrue(adjointTest('e', 'bzr')) def test_Jtvec_adjointTest_bxi_Eform(self): self.assertTrue(adjointTest('e', 'bxi')) def test_Jtvec_adjointTest_byi_Eform(self): self.assertTrue(adjointTest('e', 'byi')) def test_Jtvec_adjointTest_bzi_Eform(self): self.assertTrue(adjointTest('e', 'bzi')) def test_Jtvec_adjointTest_exr_Bform(self): self.assertTrue(adjointTest('b', 'exr')) def test_Jtvec_adjointTest_eyr_Bform(self): self.assertTrue(adjointTest('b', 'eyr')) def test_Jtvec_adjointTest_ezr_Bform(self): self.assertTrue(adjointTest('b', 'ezr')) def test_Jtvec_adjointTest_exi_Bform(self): self.assertTrue(adjointTest('b', 'exi')) def test_Jtvec_adjointTest_eyi_Bform(self): self.assertTrue(adjointTest('b', 'eyi')) def test_Jtvec_adjointTest_ezi_Bform(self): self.assertTrue(adjointTest('b', 'ezi')) def test_Jtvec_adjointTest_bxr_Bform(self): self.assertTrue(adjointTest('b', 'bxr')) def test_Jtvec_adjointTest_byr_Bform(self): self.assertTrue(adjointTest('b', 'byr')) def test_Jtvec_adjointTest_bzr_Bform(self): self.assertTrue(adjointTest('b', 'bzr')) def test_Jtvec_adjointTest_bxi_Bform(self): self.assertTrue(adjointTest('b', 'bxi')) def test_Jtvec_adjointTest_byi_Bform(self): self.assertTrue(adjointTest('b', 'byi')) def test_Jtvec_adjointTest_bzi_Bform(self): self.assertTrue(adjointTest('b', 'bzi')) if testHJ: def test_Jtvec_adjointTest_jxr_Jform(self): self.assertTrue(adjointTest('j', 'jxr')) def test_Jtvec_adjointTest_jyr_Jform(self): self.assertTrue(adjointTest('j', 'jyr')) def test_Jtvec_adjointTest_jzr_Jform(self): self.assertTrue(adjointTest('j', 'jzr')) def test_Jtvec_adjointTest_jxi_Jform(self): self.assertTrue(adjointTest('j', 'jxi')) def test_Jtvec_adjointTest_jyi_Jform(self): self.assertTrue(adjointTest('j', 'jyi')) def test_Jtvec_adjointTest_jzi_Jform(self): self.assertTrue(adjointTest('j', 'jzi')) def test_Jtvec_adjointTest_hxr_Jform(self): self.assertTrue(adjointTest('j', 'hxr')) def test_Jtvec_adjointTest_hyr_Jform(self): self.assertTrue(adjointTest('j', 'hyr')) def test_Jtvec_adjointTest_hzr_Jform(self): self.assertTrue(adjointTest('j', 'hzr')) def test_Jtvec_adjointTest_hxi_Jform(self): self.assertTrue(adjointTest('j', 'hxi')) def test_Jtvec_adjointTest_hyi_Jform(self): self.assertTrue(adjointTest('j', 'hyi')) def test_Jtvec_adjointTest_hzi_Jform(self): self.assertTrue(adjointTest('j', 'hzi')) def test_Jtvec_adjointTest_hxr_Hform(self): self.assertTrue(adjointTest('h', 'hxr')) def test_Jtvec_adjointTest_hyr_Hform(self): self.assertTrue(adjointTest('h', 'hyr')) def test_Jtvec_adjointTest_hzr_Hform(self): self.assertTrue(adjointTest('h', 'hzr')) def test_Jtvec_adjointTest_hxi_Hform(self): self.assertTrue(adjointTest('h', 'hxi')) def test_Jtvec_adjointTest_hyi_Hform(self): self.assertTrue(adjointTest('h', 'hyi')) def test_Jtvec_adjointTest_hzi_Hform(self): self.assertTrue(adjointTest('h', 'hzi')) def test_Jtvec_adjointTest_hxr_Hform(self): self.assertTrue(adjointTest('h', 'jxr')) def test_Jtvec_adjointTest_hyr_Hform(self): self.assertTrue(adjointTest('h', 'jyr')) def test_Jtvec_adjointTest_hzr_Hform(self): self.assertTrue(adjointTest('h', 'jzr')) def test_Jtvec_adjointTest_hxi_Hform(self): self.assertTrue(adjointTest('h', 'jxi')) def test_Jtvec_adjointTest_hyi_Hform(self): self.assertTrue(adjointTest('h', 'jyi')) def test_Jtvec_adjointTest_hzi_Hform(self): self.assertTrue(adjointTest('h', 'jzi')) if testCrossCheck: if testEB: def test_EB_CrossCheck_exr_Eform(self): self.assertTrue(crossCheckTest('e', 'exr')) def test_EB_CrossCheck_eyr_Eform(self): self.assertTrue(crossCheckTest('e', 'eyr')) def test_EB_CrossCheck_ezr_Eform(self): self.assertTrue(crossCheckTest('e', 'ezr')) def test_EB_CrossCheck_exi_Eform(self): self.assertTrue(crossCheckTest('e', 'exi')) def test_EB_CrossCheck_eyi_Eform(self): self.assertTrue(crossCheckTest('e', 'eyi')) def test_EB_CrossCheck_ezi_Eform(self): self.assertTrue(crossCheckTest('e', 'ezi')) def test_EB_CrossCheck_bxr_Eform(self): self.assertTrue(crossCheckTest('e', 'bxr')) def test_EB_CrossCheck_byr_Eform(self): self.assertTrue(crossCheckTest('e', 'byr')) def test_EB_CrossCheck_bzr_Eform(self): self.assertTrue(crossCheckTest('e', 'bzr')) def test_EB_CrossCheck_bxi_Eform(self): self.assertTrue(crossCheckTest('e', 'bxi')) def test_EB_CrossCheck_byi_Eform(self): self.assertTrue(crossCheckTest('e', 'byi')) def test_EB_CrossCheck_bzi_Eform(self): self.assertTrue(crossCheckTest('e', 'bzi')) if testHJ: def test_HJ_CrossCheck_jxr_Jform(self): self.assertTrue(crossCheckTest('j', 'jxr')) def test_HJ_CrossCheck_jyr_Jform(self): self.assertTrue(crossCheckTest('j', 'jyr')) def test_HJ_CrossCheck_jzr_Jform(self): self.assertTrue(crossCheckTest('j', 'jzr')) def test_HJ_CrossCheck_jxi_Jform(self): self.assertTrue(crossCheckTest('j', 'jxi')) def test_HJ_CrossCheck_jyi_Jform(self): self.assertTrue(crossCheckTest('j', 'jyi')) def test_HJ_CrossCheck_jzi_Jform(self): self.assertTrue(crossCheckTest('j', 'jzi')) def test_HJ_CrossCheck_hxr_Jform(self): self.assertTrue(crossCheckTest('j', 'hxr')) def test_HJ_CrossCheck_hyr_Jform(self): self.assertTrue(crossCheckTest('j', 'hyr')) def test_HJ_CrossCheck_hzr_Jform(self): self.assertTrue(crossCheckTest('j', 'hzr')) def test_HJ_CrossCheck_hxi_Jform(self): self.assertTrue(crossCheckTest('j', 'hxi')) def test_HJ_CrossCheck_hyi_Jform(self): self.assertTrue(crossCheckTest('j', 'hyi')) def test_HJ_CrossCheck_hzi_Jform(self): self.assertTrue(crossCheckTest('j', 'hzi')) if __name__ == '__main__': unittest.main()