from scipy import sparse as sp from sputils import sdiag from utils import sub2ind, ndgrid, mkvc import numpy as np class InnerProducts(object): """ Class creates the inner product matrices that you need! """ def __init__(self): raise Exception('InnerProducts is a base class providing inner product matrices for meshes and cannot run on its own. Inherit to your favorite Mesh class.') def getFaceInnerProduct(self, mu): if self._meshType == 'TENSOR': pass elif self._meshType == 'LOM': pass # todo: we should be doing something slightly different here! return getFaceInnerProduct(self, mu) def getEdgeInnerProduct(self, sigma): if self._meshType == 'TENSOR': pass elif self._meshType == 'LOM': pass # todo: we should be doing something slightly different here! return getEdgeInnerProduct(self, sigma) def getFaceInnerProduct(mesh, mu): m = np.array([mesh.nCx, mesh.nCy, mesh.nCz]) nc = mesh.nC i, j, k = np.int64(range(m[0])), np.int64(range(m[1])), np.int64(range(m[2])) iijjkk = ndgrid(i, j, k) ii, jj, kk = iijjkk[:, 0], iijjkk[:, 1], iijjkk[:, 2] def Pxxx(pos): ind1 = sub2ind(mesh.nFx, np.c_[ii + pos[0][0], jj + pos[0][1], kk + pos[0][2]]) ind2 = sub2ind(mesh.nFy, np.c_[ii + pos[1][0], jj + pos[1][1], kk + pos[1][2]]) + mesh.nF[0] ind3 = sub2ind(mesh.nFz, np.c_[ii + pos[2][0], jj + pos[2][1], kk + pos[2][2]]) + mesh.nF[0] + mesh.nF[1] IND = np.r_[ind1, ind2, ind3].flatten() return sp.coo_matrix((np.ones(3*nc), (range(3*nc), IND)), shape=(3*nc, np.sum(mesh.nF))).tocsr() # node(i,j,k+1) ------ edge2(i,j,k+1) ----- node(i,j+1,k+1) # / / # / / | # edge3(i,j,k) face1(i,j,k) edge3(i,j+1,k) # / / | # / / | # node(i,j,k) ------ edge2(i,j,k) ----- node(i,j+1,k) # | | | # | | node(i+1,j+1,k+1) # | | / # edge1(i,j,k) face3(i,j,k) edge1(i,j+1,k) # | | / # | | / # | |/ # node(i+1,j,k) ------ edge2(i+1,j,k) ----- node(i+1,j+1,k) # no | node | f1 | f2 | f3 # 000 | i ,j ,k | i , j, k | i, j , k | i, j, k # 100 | i+1,j ,k | i+1, j, k | i, j , k | i, j, k # 010 | i ,j+1,k | i , j, k | i, j+1, k | i, j, k # 110 | i+1,j+1,k | i+1, j, k | i, j+1, k | i, j, k # 001 | i ,j ,k | i , j, k | i, j , k | i, j, k+1 # 101 | i+1,j ,k | i+1, j, k | i, j , k | i, j, k+1 # 011 | i ,j+1,k | i , j, k | i, j+1, k | i, j, k+1 # 111 | i+1,j+1,k | i+1, j, k | i, j+1, k | i, j, k+1 P000 = Pxxx([[0, 0, 0], [0, 0, 0], [0, 0, 0]]) P100 = Pxxx([[1, 0, 0], [0, 0, 0], [0, 0, 0]]) P010 = Pxxx([[0, 0, 0], [0, 1, 0], [0, 0, 0]]) P110 = Pxxx([[1, 0, 0], [0, 1, 0], [0, 0, 0]]) P001 = Pxxx([[0, 0, 0], [0, 0, 0], [0, 0, 1]]) P101 = Pxxx([[1, 0, 0], [0, 0, 0], [0, 0, 1]]) P011 = Pxxx([[0, 0, 0], [0, 1, 0], [0, 0, 1]]) P111 = Pxxx([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) if mu.size == mesh.nC: # Isotropic! mu = mkvc(mu) # ensure it is a vector. Mu = sdiag(np.r_[mu, mu, mu]) elif mu.shape[1] == 3: # Diagonal tensor Mu = sdiag(np.r_[mu[:, 0], mu[:, 1], mu[:, 2]]) elif mu.shape[1] == 6: # Fully anisotropic row1 = sp.hstack((sdiag(mu[:, 0]), sdiag(mu[:, 3]), sdiag(mu[:, 4]))) row2 = sp.hstack((sdiag(mu[:, 3]), sdiag(mu[:, 1]), sdiag(mu[:, 5]))) row3 = sp.hstack((sdiag(mu[:, 4]), sdiag(mu[:, 5]), sdiag(mu[:, 2]))) Mu = sp.vstack((row1, row2, row3)) # Cell volume v = np.sqrt(mesh.vol) v3 = (0.125)**(0.5)*np.r_[v, v, v] #V = sdiag(v3)*mu*sdiag(v3) # to keep symmetry #A = P000.T*V*P000 + P001.T*V*P001 + P010.T*V*P010 + P011.T*V*P011 + P100.T*V*P100 + P101.T*V*P101 + P110.T*V*P110 + P111.T*V*P111 #A = 0.125*A P000 = sdiag(v3)*P000; P001 = sdiag(v3)*P001; P010 = sdiag(v3)*P010; P011 = sdiag(v3)*P011 P100 = sdiag(v3)*P100; P101 = sdiag(v3)*P101; P110 = sdiag(v3)*P110; P111 = sdiag(v3)*P111 A = P000.T*Mu*P000 + P001.T*Mu*P001 + P010.T*Mu*P010 + P011.T*Mu*P011 + P100.T*Mu*P100 + P101.T*Mu*P101 + P110.T*Mu*P110 + P111.T*Mu*P111 #P = sp.vstack((sdiag(v3)*P000,sdiag(v3)*P001,sdiag(v3)*P010,sdiag(v3)*P011, # sdiag(v3)*P100,sdiag(v3)*P101,sdiag(v3)*P110,sdiag(v3)*P111)) #A = 0.125*(P.T * sp.kron(sp.eye(8),Sigma) * P) P = [P000,P001,P010,P011,P100,P101,P110,P111] return A, P return A def getEdgeInnerProduct(mesh, sigma): m = np.array([mesh.nCx, mesh.nCy, mesh.nCz]) nc = mesh.nC i, j, k = np.int64(range(m[0])), np.int64(range(m[1])), np.int64(range(m[2])) iijjkk = ndgrid(i, j, k) ii, jj, kk = iijjkk[:, 0], iijjkk[:, 1], iijjkk[:, 2] def Pxxx(pos): ind1 = sub2ind(mesh.nEx, np.c_[ii + pos[0][0], jj + pos[0][1], kk + pos[0][2]]) ind2 = sub2ind(mesh.nEy, np.c_[ii + pos[1][0], jj + pos[1][1], kk + pos[1][2]]) + mesh.nE[0] ind3 = sub2ind(mesh.nEz, np.c_[ii + pos[2][0], jj + pos[2][1], kk + pos[2][2]]) + mesh.nE[0] + mesh.nE[1] IND = np.r_[ind1, ind2, ind3].flatten() return sp.coo_matrix((np.ones(3*nc), (range(3*nc), IND)), shape=(3*nc, np.sum(mesh.nE))).tocsr() # node(i,j,k+1) ------ edge2(i,j,k+1) ----- node(i,j+1,k+1) # / / # / / | # edge3(i,j,k) face1(i,j,k) edge3(i,j+1,k) # / / | # / / | # node(i,j,k) ------ edge2(i,j,k) ----- node(i,j+1,k) # | | | # | | node(i+1,j+1,k+1) # | | / # edge1(i,j,k) face3(i,j,k) edge1(i,j+1,k) # | | / # | | / # | |/ # node(i+1,j,k) ------ edge2(i+1,j,k) ----- node(i+1,j+1,k) # no | node | e1 | e2 | e3 # 000 | i ,j ,k | i ,j ,k | i ,j ,k | i ,j ,k # 100 | i+1,j ,k | i ,j ,k | i+1,j ,k | i+1,j ,k # 010 | i ,j+1,k | i ,j+1,k | i ,j ,k | i ,j+1,k # 110 | i+1,j+1,k | i ,j+1,k | i+1,j ,k | i+1,j+1,k # 001 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k # 101 | i+1,j ,k+1 | i ,j ,k+1 | i+1,j ,k+1 | i+1,j ,k # 011 | i ,j+1,k+1 | i ,j+1,k+1 | i ,j ,k+1 | i ,j+1,k # 111 | i+1,j+1,k+1 | i ,j+1,k+1 | i+1,j ,k+1 | i+1,j+1,k P000 = Pxxx([[0, 0, 0], [0, 0, 0], [0, 0, 0]]) P100 = Pxxx([[0, 0, 0], [1, 0, 0], [1, 0, 0]]) P010 = Pxxx([[0, 1, 0], [0, 0, 0], [0, 1, 0]]) P110 = Pxxx([[0, 1, 0], [1, 0, 0], [1, 1, 0]]) P001 = Pxxx([[0, 0, 1], [0, 0, 1], [0, 0, 0]]) P101 = Pxxx([[0, 0, 1], [1, 0, 1], [1, 0, 0]]) P011 = Pxxx([[0, 1, 1], [0, 0, 1], [0, 1, 0]]) P111 = Pxxx([[0, 1, 1], [1, 0, 1], [1, 1, 0]]) if sigma.size == mesh.nC: # Isotropic! sigma = mkvc(sigma) # ensure it is a vector. Sigma = sdiag(np.r_[sigma, sigma, sigma]) elif sigma.shape[1] == 3: # Diagonal tensor Sigma = sdiag(np.r_[sigma[:, 0], sigma[:, 1], sigma[:, 2]]) elif sigma.shape[1] == 6: # Fully anisotropic row1 = sp.hstack((sdiag(sigma[:, 0]), sdiag(sigma[:, 3]), sdiag(sigma[:, 4]))) row2 = sp.hstack((sdiag(sigma[:, 3]), sdiag(sigma[:, 1]), sdiag(sigma[:, 5]))) row3 = sp.hstack((sdiag(sigma[:, 4]), sdiag(sigma[:, 5]), sdiag(sigma[:, 2]))) Sigma = sp.vstack((row1, row2, row3)) # Cell volume v = np.sqrt(mesh.vol) v3 = (0.125)**(0.5)*np.r_[v, v, v] P000 = sdiag(v3)*P000; P001 = sdiag(v3)*P001; P010 = sdiag(v3)*P010; P011 = sdiag(v3)*P011 P100 = sdiag(v3)*P100; P101 = sdiag(v3)*P101; P110 = sdiag(v3)*P110; P111 = sdiag(v3)*P111 #V = sdiag(v3)*Sigma*sdiag(v3) # to keep symmetry A = P000.T*Sigma*P000 + P001.T*Sigma*P001 + P010.T*Sigma*P010 + P011.T*Sigma*P011 + P100.T*Sigma*P100 + P101.T*Sigma*P101 + P110.T*Sigma*P110 + P111.T*Sigma*P111 #P = sp.vstack((sdiag(v3)*P000,sdiag(v3)*P001,sdiag(v3)*P010,sdiag(v3)*P011, # sdiag(v3)*P100,sdiag(v3)*P101,sdiag(v3)*P110,sdiag(v3)*P111)) #A = 0.125*(P.T * sp.kron(sp.eye(8),Sigma) * P) P = [P000,P001,P010,P011,P100,P101,P110,P111] return A, P if __name__ == '__main__': from TensorMesh import TensorMesh h = [np.array([1, 2, 3, 4]), np.array([1, 2, 1, 4, 2]), np.array([1, 1, 4, 1])] mesh = TensorMesh(h) mu = np.ones((mesh.nC, 6)) A = getFaceInnerProduct(mesh,mu) B, P = getEdgeInnerProduct(mesh,mu)