diff --git a/SimPEG/getFaceInnerProducts.py b/SimPEG/getFaceInnerProducts.py new file mode 100644 index 00000000..961013c8 --- /dev/null +++ b/SimPEG/getFaceInnerProducts.py @@ -0,0 +1,87 @@ +from scipy import sparse as sp +from sputils import sdiag +from utils import sub2ind, ndgrid, mkvc +import numpy as np + + +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 | e1 | e2 | e3 + # 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 = 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 + + return A + +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) diff --git a/SimPEG/getInnerProducts.py b/SimPEG/getInnerProducts.py new file mode 100644 index 00000000..94c02826 --- /dev/null +++ b/SimPEG/getInnerProducts.py @@ -0,0 +1,165 @@ +from scipy import sparse as sp +from sputils import sdiag +from utils import sub2ind, ndgrid, mkvc +import numpy as np + + +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 | e1 | e2 | e3 + # 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 = 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 + + 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 = np.r_[v, v, v] + V = sdiag(v3)*Sigma*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 + + return A + + + +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)