import unittest import sys from SimPEG import * class TestCyl2DMesh(unittest.TestCase): def setUp(self): hx = np.r_[1,1,0.5] hz = np.r_[2,1] self.mesh = Mesh.CylMesh([hx, 1,hz]) def test_dim(self): self.assertTrue(self.mesh.dim == 3) def test_nC(self): self.assertTrue(self.mesh.nC == 6) self.assertTrue(self.mesh.nCx == 3) self.assertTrue(self.mesh.nCy == 1) self.assertTrue(self.mesh.nCz == 2) self.assertTrue(np.all(self.mesh.vnC == [3, 1, 2])) def test_nN(self): self.assertTrue(self.mesh.nN == 0) self.assertTrue(self.mesh.nNx == 3) self.assertTrue(self.mesh.nNy == 0) self.assertTrue(self.mesh.nNz == 3) self.assertTrue(np.all(self.mesh.vnN == [3, 0, 3])) def test_nF(self): self.assertTrue(self.mesh.nFx == 6) self.assertTrue(np.all(self.mesh.vnFx == [3, 1, 2])) self.assertTrue(self.mesh.nFy == 0) self.assertTrue(np.all(self.mesh.vnFy == [3, 0, 2])) self.assertTrue(self.mesh.nFz == 9) self.assertTrue(np.all(self.mesh.vnFz == [3, 1, 3])) self.assertTrue(self.mesh.nF == 15) self.assertTrue(np.all(self.mesh.vnF == [6, 0, 9])) def test_nE(self): self.assertTrue(self.mesh.nEx == 0) self.assertTrue(np.all(self.mesh.vnEx == [3, 0, 3])) self.assertTrue(self.mesh.nEy == 9) self.assertTrue(np.all(self.mesh.vnEy == [3, 1, 3])) self.assertTrue(self.mesh.nEz == 0) self.assertTrue(np.all(self.mesh.vnEz == [3, 0, 2])) self.assertTrue(self.mesh.nE == 9) self.assertTrue(np.all(self.mesh.vnE == [0, 9, 0])) def test_vectorsCC(self): v = np.r_[0.5, 1.5, 2.25] self.assertTrue(np.linalg.norm((v-self.mesh.vectorCCx)) == 0) v = np.r_[0] self.assertTrue(np.linalg.norm((v-self.mesh.vectorCCy)) == 0) v = np.r_[1, 2.5] self.assertTrue(np.linalg.norm((v-self.mesh.vectorCCz)) == 0) def test_vectorsN(self): v = np.r_[1, 2, 2.5] self.assertTrue(np.linalg.norm((v-self.mesh.vectorNx)) == 0) v = np.r_[0] self.assertTrue(np.linalg.norm((v-self.mesh.vectorNy)) == 0) v = np.r_[0, 2, 3.] self.assertTrue(np.linalg.norm((v-self.mesh.vectorNz)) == 0) def test_edge(self): edge = np.r_[1, 2, 2.5, 1, 2, 2.5, 1, 2, 2.5] * 2 * np.pi self.assertTrue(np.linalg.norm((edge-self.mesh.edge)) == 0) def test_area(self): r = np.r_[0, 1, 2, 2.5] a = r[1:]*2*np.pi areaX = np.r_[2*a,a] a = (r[1:]**2 - r[:-1]**2)*np.pi areaZ = np.r_[a,a,a] area = np.r_[areaX, areaZ] self.assertTrue(np.linalg.norm((area-self.mesh.area)) == 0) def test_vol(self): r = np.r_[0, 1, 2, 2.5] a = (r[1:]**2 - r[:-1]**2)*np.pi vol = np.r_[2*a,a] self.assertTrue(np.linalg.norm((vol-self.mesh.vol)) == 0) def test_gridSizes(self): self.assertTrue(self.mesh.gridCC.shape == (self.mesh.nC, 3)) self.assertTrue(self.mesh.gridN.shape == (9, 3)) self.assertTrue(self.mesh.gridFx.shape == (self.mesh.nFx, 3)) self.assertTrue(self.mesh.gridFy is None) self.assertTrue(self.mesh.gridFz.shape == (self.mesh.nFz, 3)) self.assertTrue(self.mesh.gridEx is None) self.assertTrue(self.mesh.gridEy.shape == (self.mesh.nEy, 3)) self.assertTrue(self.mesh.gridEz is None) def test_gridCC(self): x = np.r_[0.5,1.5,2.25,0.5,1.5,2.25] y = np.zeros(6) z = np.r_[1,1,1,2.5,2.5,2.5] G = np.c_[x,y,z] self.assertTrue(np.linalg.norm((G-self.mesh.gridCC).ravel()) == 0) def test_gridN(self): x = np.r_[1,2,2.5,1,2,2.5,1,2,2.5] y = np.zeros(9) z = np.r_[0,0,0,2,2,2,3,3,3.] G = np.c_[x,y,z] self.assertTrue(np.linalg.norm((G-self.mesh.gridN).ravel()) == 0) def test_gridFx(self): x = np.r_[1,2,2.5,1,2,2.5] y = np.zeros(6) z = np.r_[1,1,1,2.5,2.5,2.5] G = np.c_[x,y,z] self.assertTrue(np.linalg.norm((G-self.mesh.gridFx).ravel()) == 0) def test_gridFz(self): x = np.r_[0.5,1.5,2.25,0.5,1.5,2.25,0.5,1.5,2.25] y = np.zeros(9) z = np.r_[0,0,0,2,2,2,3,3,3.] G = np.c_[x,y,z] self.assertTrue(np.linalg.norm((G-self.mesh.gridFz).ravel()) == 0) def test_gridEy(self): x = np.r_[1,2,2.5,1,2,2.5,1,2,2.5] y = np.zeros(9) z = np.r_[0,0,0,2,2,2,3,3,3.] G = np.c_[x,y,z] self.assertTrue(np.linalg.norm((G-self.mesh.gridEy).ravel()) == 0) def test_lightOperators(self): self.assertTrue(self.mesh.nodalGrad is None) def test_getInterpMatCartMesh_Cells(self): Mr = Mesh.TensorMesh([100,100,2], x0='CC0') Mc = Mesh.CylMesh([np.ones(10)/5,1,10],x0='0C0',cartesianOrigin=[-0.2,-0.2,0]) mc = np.arange(Mc.nC) xr = np.linspace(0,0.4,50) xc = np.linspace(0,0.4,50) + 0.2 Pr = Mr.getInterpolationMat(np.c_[xr,np.ones(50)*-0.2,np.ones(50)*0.5],'CC') Pc = Mc.getInterpolationMat(np.c_[xc,np.zeros(50),np.ones(50)*0.5],'CC') Pc2r = Mc.getInterpolationMatCartMesh(Mr, 'CC') assert np.abs(Pr*(Pc2r*mc) - Pc*mc).max() < 1e-3 def test_getInterpMatCartMesh_Faces(self): Mr = Mesh.TensorMesh([100,100,2], x0='CC0') Mc = Mesh.CylMesh([np.ones(10)/5,1,10],x0='0C0',cartesianOrigin=[-0.2,-0.2,0]) Pf = Mc.getInterpolationMatCartMesh(Mr, 'F') mf = np.ones(Mc.nF) frect = Pf * mf fxcc = Mr.aveFx2CC*Mr.r(frect, 'F', 'Fx') fycc = Mr.aveFy2CC*Mr.r(frect, 'F', 'Fy') fzcc = Mr.r(frect, 'F', 'Fz') indX = Utils.closestPoints(Mr, [0.45, -0.2, 0.5]) indY = Utils.closestPoints(Mr, [-0.2, 0.45, 0.5]) TOL = 1e-2 assert np.abs(float(fxcc[indX]) - 1) < TOL assert np.abs(float(fxcc[indY]) - 0) < TOL assert np.abs(float(fycc[indX]) - 0) < TOL assert np.abs(float(fycc[indY]) - 1) < TOL assert np.abs((fzcc - 1).sum()) < TOL mag = (fxcc**2 + fycc**2)**0.5 dist = ((Mr.gridCC[:,0] + 0.2)**2 + (Mr.gridCC[:,1] + 0.2)**2)**0.5 assert np.abs(mag[dist > 0.1].max() - 1) < TOL assert np.abs(mag[dist > 0.1].min() - 1) < TOL def test_getInterpMatCartMesh_Edges(self): Mr = Mesh.TensorMesh([100,100,2], x0='CC0') Mc = Mesh.CylMesh([np.ones(10)/5,1,10],x0='0C0',cartesianOrigin=[-0.2,-0.2,0]) Pe = Mc.getInterpolationMatCartMesh(Mr, 'E') me = np.ones(Mc.nE) erect = Pe * me excc = Mr.aveEx2CC*Mr.r(erect, 'E', 'Ex') eycc = Mr.aveEy2CC*Mr.r(erect, 'E', 'Ey') ezcc = Mr.r(erect, 'E', 'Ez') indX = Utils.closestPoints(Mr, [0.45, -0.2, 0.5]) indY = Utils.closestPoints(Mr, [-0.2, 0.45, 0.5]) TOL = 1e-2 assert np.abs(float(excc[indX]) - 0) < TOL assert np.abs(float(excc[indY]) + 1) < TOL assert np.abs(float(eycc[indX]) - 1) < TOL assert np.abs(float(eycc[indY]) - 0) < TOL assert np.abs(ezcc.sum()) < TOL mag = (excc**2 + eycc**2)**0.5 dist = ((Mr.gridCC[:,0] + 0.2)**2 + (Mr.gridCC[:,1] + 0.2)**2)**0.5 assert np.abs(mag[dist > 0.1].max() - 1) < TOL assert np.abs(mag[dist > 0.1].min() - 1) < TOL MESHTYPES = ['uniformCylMesh'] call2 = lambda fun, xyz: fun(xyz[:, 0], xyz[:, 2]) call3 = lambda fun, xyz: fun(xyz[:, 0], xyz[:, 1], xyz[:, 2]) cyl_row2 = lambda g, xfun, yfun: np.c_[call2(xfun, g), call2(yfun, g)] cyl_row3 = lambda g, xfun, yfun, zfun: np.c_[call3(xfun, g), call3(yfun, g), call3(zfun, g)] cylF2 = lambda M, fx, fy: np.vstack((cyl_row2(M.gridFx, fx, fy), cyl_row2(M.gridFz, fx, fy))) class TestFaceDiv2D(Tests.OrderTest): name = "FaceDiv" meshTypes = MESHTYPES meshDimension = 2 def getError(self): funR = lambda r, z: np.sin(2.*np.pi*r) funZ = lambda r, z: np.sin(2.*np.pi*z) sol = lambda r, t, z: (2*np.pi*r*np.cos(2*np.pi*r) + np.sin(2*np.pi*r))/r + 2*np.pi*np.cos(2*np.pi*z) Fc = cylF2(self.M, funR, funZ) Fc = np.c_[Fc[:,0],np.zeros(self.M.nF),Fc[:,1]] F = self.M.projectFaceVector(Fc) divF = self.M.faceDiv.dot(F) divF_ana = call3(sol, self.M.gridCC) err = np.linalg.norm((divF-divF_ana), np.inf) return err def test_order(self): self.orderTest() class TestEdgeCurl2D(Tests.OrderTest): name = "EdgeCurl" meshTypes = MESHTYPES meshDimension = 2 def getError(self): # To Recreate or change the functions: # import sympy # r,t,z = sympy.symbols('r,t,z') # fR = 0 # fZ = 0 # fT = sympy.sin(2.*sympy.pi*z) # print 1/r*sympy.diff(fZ,t) - sympy.diff(fT,z) # print sympy.diff(fR,z) - sympy.diff(fZ,r) # print 1/r*(sympy.diff(r*fT,r) - sympy.diff(fR,t)) funT = lambda r, t, z: np.sin(2.*np.pi*z) solR = lambda r, z: -2.0*np.pi*np.cos(2.0*np.pi*z) solZ = lambda r, z: np.sin(2.0*np.pi*z)/r E = call3(funT, self.M.gridEy) curlE = self.M.edgeCurl.dot(E) Fc = cylF2(self.M, solR, solZ) Fc = np.c_[Fc[:,0],np.zeros(self.M.nF),Fc[:,1]] curlE_ana = self.M.projectFaceVector(Fc) err = np.linalg.norm((curlE-curlE_ana), np.inf) return err def test_order(self): self.orderTest() # class TestInnerProducts2D(Tests.OrderTest): # """Integrate an function over a unit cube domain using edgeInnerProducts and faceInnerProducts.""" # meshTypes = MESHTYPES # meshDimension = 2 # meshSizes = [4, 8, 16, 32, 64, 128] # def getError(self): # funR = lambda r, t, z: np.cos(2.0*np.pi*z) # funT = lambda r, t, z: 0*t # funZ = lambda r, t, z: np.sin(2.0*np.pi*r) # call = lambda fun, xyz: fun(xyz[:, 0], xyz[:, 1], xyz[:, 2]) # sigma1 = lambda r, t, z: z+1 # sigma2 = lambda r, t, z: r*z+50 # sigma3 = lambda r, t, z: 3+t*r # sigma4 = lambda r, t, z: 0.1*r*t*z # sigma5 = lambda r, t, z: 0.2*z*r*t # sigma6 = lambda r, t, z: 0.1*t # Gc = self.M.gridCC # if self.sigmaTest == 1: # sigma = np.c_[call(sigma1, Gc)] # analytic = 144877./360 # Found using sympy. z=5 # elif self.sigmaTest == 2: # sigma = np.c_[call(sigma1, Gc), call(sigma2, Gc)] # analytic = 189959./120 # Found using sympy. z=5 # elif self.sigmaTest == 3: # sigma = np.r_[call(sigma1, Gc), call(sigma2, Gc), call(sigma3, Gc)] # analytic = 781427./360 # Found using sympy. z=5 # if self.location == 'edges': # E = call(funT, self.M.gridEy) # A = self.M.getEdgeInnerProduct(sigma) # numeric = E.T.dot(A.dot(E)) # elif self.location == 'faces': # Fr = call(funR, self.M.gridFx) # Fz = call(funZ, self.M.gridFz) # A = self.M.getFaceInnerProduct(sigma) # F = np.r_[Fr,Fz] # numeric = F.T.dot(A.dot(F)) # print numeric # err = np.abs(numeric - analytic) # return err # def test_order1_faces(self): # self.name = "2D Face Inner Product - Isotropic" # self.location = 'faces' # self.sigmaTest = 1 # self.orderTest() class TestCyl3DMesh(unittest.TestCase): def setUp(self): hx = np.r_[1,1,0.5] hy = np.r_[np.pi, np.pi] hz = np.r_[2,1] self.mesh = Mesh.CylMesh([hx, hy,hz]) def test_dim(self): self.assertTrue(self.mesh.dim == 3) def test_nC(self): self.assertTrue(self.mesh.nCx == 3) self.assertTrue(self.mesh.nCy == 2) self.assertTrue(self.mesh.nCz == 2) self.assertTrue(np.all(self.mesh.vnC == [3, 2, 2])) def test_nN(self): self.assertTrue(self.mesh.nN == 24) self.assertTrue(self.mesh.nNx == 4) self.assertTrue(self.mesh.nNy == 2) self.assertTrue(self.mesh.nNz == 3) self.assertTrue(np.all(self.mesh.vnN == [4, 2, 3])) def test_nF(self): self.assertTrue(self.mesh.nFx == 12) self.assertTrue(np.all(self.mesh.vnFx == [3, 2, 2])) self.assertTrue(self.mesh.nFy == 12) self.assertTrue(np.all(self.mesh.vnFy == [3, 2, 2])) self.assertTrue(self.mesh.nFz == 18) self.assertTrue(np.all(self.mesh.vnFz == [3, 2, 3])) self.assertTrue(self.mesh.nF == 42) self.assertTrue(np.all(self.mesh.vnF == [12, 12, 18])) def test_nE(self): self.assertTrue(self.mesh.nEx == 18) self.assertTrue(np.all(self.mesh.vnEx == [3, 2, 3])) self.assertTrue(self.mesh.nEy == 18) self.assertTrue(np.all(self.mesh.vnEy == [3, 2, 3])) self.assertTrue(self.mesh.nEz == 12 + 2) self.assertTrue(self.mesh.vnEz is None) self.assertTrue(self.mesh.nE == 50) self.assertTrue(np.all(self.mesh.vnE == [18, 18, 14])) def test_vectorsCC(self): v = np.r_[0.5, 1.5, 2.25] self.assertTrue(np.linalg.norm((v-self.mesh.vectorCCx)) == 0) v = np.r_[0, np.pi] self.assertTrue(np.linalg.norm((v-self.mesh.vectorCCy)) == 0) v = np.r_[1, 2.5] self.assertTrue(np.linalg.norm((v-self.mesh.vectorCCz)) == 0) def test_vectorsN(self): v = np.r_[0, 1, 2, 2.5] self.assertTrue(np.linalg.norm((v-self.mesh.vectorNx)) == 0) v = np.r_[np.pi/2, 1.5*np.pi] self.assertTrue(np.linalg.norm((v-self.mesh.vectorNy)) == 0) v = np.r_[0, 2, 3] self.assertTrue(np.linalg.norm((v-self.mesh.vectorNz)) == 0) if __name__ == '__main__': unittest.main()