import unittest from SimPEG import * from SimPEG.Tests.TestUtils import OrderTest, checkDerivative from scipy.sparse.linalg import dsolve from simpegFLOW import Richards TOL = 1E-8 class TestModels(unittest.TestCase): def test_BaseHaverkamp_Theta(self): mesh = Mesh.TensorMesh([50]) hav = Richards.Empirical._haverkamp_theta(mesh) m = np.random.randn(50) def wrapper(u): return hav.transform(u, m), hav.transformDerivU(u, m) passed = checkDerivative(wrapper, np.random.randn(50), plotIt=False) self.assertTrue(passed,True) def test_vangenuchten_theta(self): mesh = Mesh.TensorMesh([50]) hav = Richards.Empirical._vangenuchten_theta(mesh) m = np.random.randn(50) def wrapper(u): return hav.transform(u, m), hav.transformDerivU(u, m) passed = checkDerivative(wrapper, np.random.randn(50), plotIt=False) self.assertTrue(passed,True) def test_BaseHaverkamp_k(self): mesh = Mesh.TensorMesh([50]) hav = Richards.Empirical._haverkamp_k(mesh) m = np.random.randn(50) def wrapper(u): return hav.transform(u, m), hav.transformDerivU(u, m) passed = checkDerivative(wrapper, np.random.randn(50), plotIt=False) self.assertTrue(passed,True) hav = Richards.Empirical._haverkamp_k(mesh) u = np.random.randn(50) def wrapper(m): return hav.transform(u, m), hav.transformDerivM(u, m) passed = checkDerivative(wrapper, np.random.randn(50), plotIt=False) self.assertTrue(passed,True) def test_vangenuchten_k(self): mesh = Mesh.TensorMesh([50]) hav = Richards.Empirical._vangenuchten_k(mesh) m = np.random.randn(50) def wrapper(u): return hav.transform(u, m), hav.transformDerivU(u, m) passed = checkDerivative(wrapper, np.random.randn(50), plotIt=False) self.assertTrue(passed,True) hav = Richards.Empirical._vangenuchten_k(mesh) u = np.random.randn(50) def wrapper(m): return hav.transform(u, m), hav.transformDerivM(u, m) passed = checkDerivative(wrapper, np.random.randn(50), plotIt=False) self.assertTrue(passed,True) class RichardsTests1D(unittest.TestCase): def setUp(self): M = Mesh.TensorMesh([np.ones(20)]) M.setCellGradBC('dirichlet') params = Richards.Empirical.HaverkampParams().celia1990 params['Ks'] = np.log(params['Ks']) E = Richards.Empirical.Haverkamp(M, **params) bc = np.array([-61.5,-20.7]) h = np.zeros(M.nC) + bc[0] prob = Richards.RichardsProblem(M, mapping=E, timeSteps=[(40,3),(60,3)], boundaryConditions=bc, initialConditions=h, doNewton=False, method='mixed') locs = np.r_[5.,10,15] times = prob.times[3:5] rxSat = Richards.RichardsRx(locs, times, 'saturation') rxPre = Richards.RichardsRx(locs, times, 'pressureHead') survey = Richards.RichardsSurvey([rxSat, rxPre]) prob.pair(survey) self.h0 = h self.M = M self.Ks = params['Ks'] self.prob = prob self.survey = survey def test_Richards_getResidual_Newton(self): self.prob.doNewton = True m = self.Ks passed = checkDerivative(lambda hn1: self.prob.getResidual(m, self.h0, hn1, self.prob.timeSteps[0], self.prob.boundaryConditions), self.h0, plotIt=False) self.assertTrue(passed,True) def test_Richards_getResidual_Picard(self): self.prob.doNewton = False m = self.Ks passed = checkDerivative(lambda hn1: self.prob.getResidual(m, self.h0, hn1, self.prob.timeSteps[0], self.prob.boundaryConditions), self.h0, plotIt=False, expectedOrder=1) self.assertTrue(passed,True) def test_Adjoint(self): v = np.random.rand(self.survey.nD) z = np.random.rand(self.M.nC) Hs = self.prob.fields(self.Ks) vJz = v.dot(self.prob.Jvec(self.Ks,z,u=Hs)) zJv = z.dot(self.prob.Jtvec(self.Ks,v,u=Hs)) tol = TOL*(10**int(np.log10(zJv))) passed = np.abs(vJz - zJv) < tol print 'Richards Adjoint Test - PressureHead' print '%4.4e === %4.4e, diff=%4.4e < %4.e'%(vJz, zJv,np.abs(vJz - zJv),tol) self.assertTrue(passed,True) def test_Sensitivity(self): mTrue = self.Ks*np.ones(self.M.nC) derChk = lambda m: [self.survey.dpred(m), lambda v: self.prob.Jvec(m, v)] print 'Testing Richards Derivative' passed = checkDerivative(derChk, mTrue, num=4, plotIt=False) self.assertTrue(passed,True) def test_Sensitivity_full(self): mTrue = self.Ks*np.ones(self.M.nC) J = self.prob.Jfull(mTrue) derChk = lambda m: [self.survey.dpred(m), J] print 'Testing Richards Derivative' passed = checkDerivative(derChk, mTrue, num=4, plotIt=False) self.assertTrue(passed,True) # class RichardsTests2D(object): # def setUp(self): # M = mesh.TensorMesh([np.ones(8),np.ones(30)]) # Ks = 9.4400e-03 # E = Richards.Haverkamp(Ks=np.log(Ks), A=1.1750e+06, gamma=4.74, alpha=1.6110e+06, theta_s=0.287, theta_r=0.075, beta=3.96) # bc = np.array([-61.5,-20.7]) # bc = np.r_[np.zeros(M.nCy*2),np.ones(M.nCx)*bc[0],np.ones(M.nCx)*bc[1]] # h = np.zeros(M.nC) + bc[0] # prob = Richards.RichardsProblem(M,E, timeStep=60, timeEnd=180, boundaryConditions=bc, initialConditions=h, doNewton=False, method='mixed') # XY = utils.ndgrid(np.array([5,7.]),np.array([5,15,25.])) # q = M.getInterpolationMat(XY,'CC') # P = sp.kron(sp.identity(prob.numIts),q) # prob.P = P # self.h0 = h # self.M = M # self.Ks = Ks # self.prob = prob # def test_Richards_getResidual_Newton(self): # self.prob.doNewton = True # passed = checkDerivative(lambda hn1: self.prob.getResidual(self.h0,hn1), self.h0, plotIt=False) # self.assertTrue(passed,True) # def test_Richards_getResidual_Picard(self): # self.prob.doNewton = False # passed = checkDerivative(lambda hn1: self.prob.getResidual(self.h0,hn1), self.h0, plotIt=False, expectedOrder=1) # self.assertTrue(passed,True) # def test_Adjoint_PressureHead(self): # self.prob.dataType = 'pressureHead' # Ks = self.Ks # v = np.random.rand(self.prob.P.shape[0]) # z = np.random.rand(self.M.nC) # Hs = self.prob.field(np.log(Ks)) # vJz = v.dot(self.prob.J(np.log(Ks),z,u=Hs)) # zJv = z.dot(self.prob.Jt(np.log(Ks),v,u=Hs)) # tol = TOL*(10**int(np.log10(zJv))) # passed = np.abs(vJz - zJv) < tol # print 'Richards Adjoint Test - PressureHead' # print '%4.4e === %4.4e, diff=%4.4e < %4.e'%(vJz, zJv,np.abs(vJz - zJv),tol) # self.assertTrue(passed,True) # def test_Adjoint_Saturation(self): # self.prob.dataType = 'saturation' # Ks = self.Ks # v = np.random.rand(self.prob.P.shape[0]) # z = np.random.rand(self.M.nC) # Hs = self.prob.field(np.log(Ks)) # vJz = v.dot(self.prob.J(np.log(Ks),z,u=Hs)) # zJv = z.dot(self.prob.Jt(np.log(Ks),v,u=Hs)) # tol = TOL #*(10**int(np.log10(zJv))) # passed = np.abs(vJz - zJv) < tol # print 'Richards Adjoint Test - Saturation' # print '%4.4e === %4.4e, diff=%4.4e < %4.e'%(vJz, zJv,np.abs(vJz - zJv),tol) # self.assertTrue(passed,True) # def test_Sensitivity(self): # self.prob.dataType = 'pressureHead' # mTrue = np.ones(self.M.nC)*self.Ks # stdev = 0.01 # The standard deviation for the noise # dobs = self.prob.createSyntheticSurvey(mTrue,std=stdev)[0] # self.prob.dobs = dobs # self.prob.std = dobs*0 + stdev # Hs = self.prob.field(mTrue) # opt = inverse.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6) # reg = regularization.Regularization(self.M) # inv = inverse.Inversion(self.prob, reg, opt, beta0=1e4) # derChk = lambda m: [inv.dataObj(m), inv.dataObjDeriv(m)] # print 'Testing Richards Derivative' # passed = checkDerivative(derChk, mTrue, num=5, plotIt=False) # self.assertTrue(passed,True) if __name__ == '__main__': unittest.main()