from scipy.sparse import linalg from scipy import sparse from sputils import * from utils import * from sputils import * from numpy import * from getEdgeTangent import * from inv3X3BlockDiagonal import * from getCellVolume import getCellVolume def subarray(T, i1, i2, i3): return take(take(take(T, i1, 0), i2, 1), i3, 2) def getEdgeInnerProduct(X, Y, Z, sigma): """A = getEdgeInnerProduct(X, Y, Z, sigma) 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 """ m = array(shape(X))-1 nc = prod(m) me1 = m + array([0, 1, 1]); ne1 = prod(me1) me2 = m + array([1, 0, 1]); ne2 = prod(me2) me3 = m + array([1, 1, 0]); ne3 = prod(me3) e1x,e1y,e1z,e2x,e2y,e2z,e3x,e3y,e3z,norme1,norme2,norme3 = getEdgeTangent(X,Y,Z) i = int64(linspace(0,m[0]-1,m[0])) j = int64(linspace(0,m[1]-1,m[1])) k = int64(linspace(0,m[2]-1,m[2])) ii,jj,kk = ndgrid(i,j,k) ii = mkvc(ii); jj = mkvc(jj); kk = mkvc(kk) ## -------- # no | node | e1 | e2 | e3 # 000 | i ,j ,k | i ,j ,k | i ,j ,k | i ,j ,k ind1 = sub2ind(me1,hstack3(ii,jj,kk)) ind2 = sub2ind(me2,hstack3(ii,jj,kk)) + ne1 ind3 = sub2ind(me3,hstack3(ii,jj,kk)) + ne1 + ne2 IND = vstack((vstack((ind1,ind2)),ind3)) IND = array(IND).flatten() P000 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr() invT000 = inv3X3BlockDiagonal(subarray(e1x,i,j,k) , subarray(e1y,i,j,k), subarray(e1z,i,j,k), subarray(e2x,i,j,k) , subarray(e2y,i,j,k), subarray(e2z,i,j,k) , subarray(e3x,i,j,k) , subarray(e3y,i,j,k), subarray(e3z,i,j,k) ) ## -------- # no | node | e1 | e2 | e3 # 100 | i+1,j ,k | i ,j ,k | i+1,j ,k | i+1,j ,k ind1 = sub2ind(me1,hstack3(ii,jj,kk)) ind2 = sub2ind(me2,hstack3(ii+1,jj,kk)) + ne1 ind3 = sub2ind(me3,hstack3(ii+1,jj,kk)) + ne1 + ne2 IND = vstack((vstack((ind1,ind2)),ind3)) IND = array(IND).flatten() P100 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr() invT100 = inv3X3BlockDiagonal(subarray(e1x,i,j,k), subarray(e1y,i,j,k), subarray(e1z,i,j,k), subarray(e2x,i+1,j,k), subarray(e2y,i+1,j,k), subarray(e2z,i+1,j,k), subarray(e3x,i+1,j,k) , subarray(e3y,i+1,j,k), subarray(e3z,i+1,j,k)) ## -------- # no | node | e1 | e2 | e3 # 010 | i ,j+1,k | i ,j+1,k | i ,j ,k | i ,j+1,k ind1 = sub2ind(me1,hstack3(ii,jj+1,kk)) ind2 = sub2ind(me2,hstack3(ii,jj,kk)) + ne1 ind3 = sub2ind(me3,hstack3(ii,jj+1,kk)) + ne1 + ne2 IND = vstack((vstack((ind1,ind2)),ind3)) IND = array(IND).flatten() P010 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr() invT010 = inv3X3BlockDiagonal(subarray(e1x,i,j+1,k) , subarray(e1y,i,j+1,k) , subarray(e1z,i,j+1,k) , subarray(e2x,i,j,k) , subarray(e2y,i,j,k) , subarray(e2z,i,j,k) , subarray(e3x,i,j+1,k) , subarray(e3y,i,j+1,k) ,subarray( e3z,i,j+1,k) ) ## -------- # no | node | e1 | e2 | e3 # 110 | i+1,j+1,k | i ,j+1,k | i+1,j ,k | i+1,j+1,k ind1 = sub2ind(me1,hstack3(ii,jj+1,kk)) ind2 = sub2ind(me2,hstack3(ii+1,jj,kk)) + ne1 ind3 = sub2ind(me3,hstack3(ii+1,jj+1,kk)) + ne1 + ne2 IND = vstack((vstack((ind1,ind2)),ind3)) IND = array(IND).flatten() P110 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr() invT110 = inv3X3BlockDiagonal(subarray(e1x,i,j+1,k) ,subarray(e1y,i,j+1,k) , subarray(e1z,i,j+1,k) , subarray(e2x,i+1,j,k) ,subarray(e2y,i+1,j,k) , subarray(e2z,i+1,j,k), subarray(e3x,i+1,j+1,k) ,subarray(e3y,i+1,j+1,k) , subarray(e3z,i+1,j+1,k) ) ###### ## -------- # no | node | e1 | e2 | e3 # 001 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k ind1 = sub2ind(me1,hstack3(ii,jj,kk+1)) ind2 = sub2ind(me2,hstack3(ii,jj,kk+1)) + ne1 ind3 = sub2ind(me3,hstack3(ii,jj,kk)) + ne1 + ne2 IND = vstack((vstack((ind1,ind2)),ind3)) IND = array(IND).flatten() P001 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr() invT001 = inv3X3BlockDiagonal(subarray(e1x,i,j,k+1) ,subarray(e1y,i,j,k+1) , subarray(e1z,i,j,k+1) , subarray(e2x,i,j,k+1) , subarray(e2y,i,j,k+1) , subarray(e2z,i,j,k+1) , subarray(e3x,i,j,k) , subarray(e3y,i,j,k) , subarray(e3z,i,j,k) ) ## -------- # no | node | e1 | e2 | e3 # 101 | i+1,j ,k+1 | i ,j ,k+1 | i+1,j ,k+1 | i+1,j ,k+1 ind1 = sub2ind(me1,hstack3(ii,jj,kk+1)) ind2 = sub2ind(me2,hstack3(ii+1,jj,kk+1)) + ne1 ind3 = sub2ind(me3,hstack3(ii+1,jj,kk)) + ne1 + ne2 IND = vstack((vstack((ind1,ind2)),ind3)) IND = array(IND).flatten() P101 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr() invT101 = inv3X3BlockDiagonal(subarray(e1x,i,j,k+1), subarray(e1y,i,j,k+1), subarray(e1z,i,j,k+1) , subarray(e2x,i+1,j,k+1), subarray(e2y,i+1,j,k+1) , subarray(e2z,i+1,j,k+1) , subarray(e3x,i+1,j,k), subarray(e3y,i+1,j,k) , subarray(e3z,i+1,j,k) ) ## -------- # no | node | e1 | e2 | e3 # 011 | i ,j+1,k+1 | i ,j+1,k+1 | i ,j ,k+1 | i ,j+1,k+1 ind1 = sub2ind(me1,hstack3(ii,jj+1,kk+1)) ind2 = sub2ind(me2,hstack3(ii,jj,kk+1)) + ne1 ind3 = sub2ind(me3,hstack3(ii,jj+1,kk)) + ne1 + ne2 IND = vstack((vstack((ind1,ind2)),ind3)) IND = array(IND).flatten() P011 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr() invT011 = inv3X3BlockDiagonal(subarray(e1x,i,j+1,k+1) , subarray(e1y,i,j+1,k+1) , subarray(e1z,i,j+1,k+1) , subarray(e2x,i,j,k+1) , subarray(e2y,i,j,k+1) , subarray(e2z,i,j,k+1) , subarray(e3x,i,j+1,k) , subarray(e3y,i,j+1,k) , subarray(e3z,i,j+1,k) ) ## -------- # no | node | e1 | e2 | e3 # 111 | i+1,j+1,k+1 | i ,j+1,k+1 | i+1,j ,k+1 | i+1,j+1,k+1 ind1 = sub2ind(me1,hstack3(ii,jj+1,kk+1)) ind2 = sub2ind(me2,hstack3(ii+1,jj,kk+1)) + ne1 ind3 = sub2ind(me3,hstack3(ii+1,jj+1,kk)) + ne1 + ne2 IND = vstack((vstack((ind1,ind2)),ind3)) IND = array(IND).flatten() P111 = sparse.coo_matrix((ones(3*nc),(linspace(0,3*nc-1,3*nc),IND)),shape=(3*nc,ne1+ne2+ne3)).tocsr() invT111 = inv3X3BlockDiagonal(subarray(e1x,i,j+1,k+1) , subarray(e1y,i,j+1,k+1) , subarray(e1z,i,j+1,k+1) , subarray(e2x,i+1,j,k+1) , subarray(e2y,i+1,j,k+1) , subarray(e2z,i+1,j,k+1) , subarray(e3x,i+1,j+1,k) , subarray(e3y,i+1,j+1,k) , subarray(e3z,i+1,j+1,k) ) # Cell volume v = mkvc(getCellVolume(X,Y,Z)) #mkvc(getVolume(X,Y,Z)) vsig = v*mkvc(sigma) v3 = vstack((vstack((vsig,vsig)),vsig)) v3 = v3.flatten() V = sdiag(v3) A = P000.T*invT000.T*V*invT000*P000 + P001.T*invT001.T*V*invT001*P001 + P010.T*invT010.T*V*invT010*P010 + P011.T*invT011.T*V*invT011*P011 + P100.T*invT100.T*V*invT100*P100 + P101.T*invT101.T*V*invT101*P101 + P110.T*invT110.T*V*invT110*P110 + P111.T*invT111.T*V*invT111*P111 A = 0.125*A return A if __name__ == '__main__': X,Y,Z = ndgrid(linspace(0,2,3),linspace(0,2,3),linspace(0,2,3)) Z[2,2,2] = 2.5; Z[0,0,0] = -0.5 X[2,2,2] = 2.5; X[0,0,0] = -0.5 sig = ones([2,2,2]) A = getEdgeInnerProduct(X,Y,Z,sig)