import random from sympy.combinatorics import Permutation from sympy.combinatorics.permutations import _af_invert from sympy.testing.pytest import raises from sympy import symbols, sin, exp, log, cos, transpose, adjoint, conjugate, diff from sympy.tensor.array import Array, ImmutableDenseNDimArray, ImmutableSparseNDimArray, MutableSparseNDimArray from sympy.tensor.array.arrayop import tensorproduct, tensorcontraction, derive_by_array, permutedims, Flatten, \ tensordiagonal def test_import_NDimArray(): from sympy.tensor.array import NDimArray del NDimArray def test_tensorproduct(): x,y,z,t = symbols('x y z t') from sympy.abc import a,b,c,d assert tensorproduct() == 1 assert tensorproduct([x]) == Array([x]) assert tensorproduct([x], [y]) == Array([[x*y]]) assert tensorproduct([x], [y], [z]) == Array([[[x*y*z]]]) assert tensorproduct([x], [y], [z], [t]) == Array([[[[x*y*z*t]]]]) assert tensorproduct(x) == x assert tensorproduct(x, y) == x*y assert tensorproduct(x, y, z) == x*y*z assert tensorproduct(x, y, z, t) == x*y*z*t for ArrayType in [ImmutableDenseNDimArray, ImmutableSparseNDimArray]: A = ArrayType([x, y]) B = ArrayType([1, 2, 3]) C = ArrayType([a, b, c, d]) assert tensorproduct(A, B, C) == ArrayType([[[a*x, b*x, c*x, d*x], [2*a*x, 2*b*x, 2*c*x, 2*d*x], [3*a*x, 3*b*x, 3*c*x, 3*d*x]], [[a*y, b*y, c*y, d*y], [2*a*y, 2*b*y, 2*c*y, 2*d*y], [3*a*y, 3*b*y, 3*c*y, 3*d*y]]]) assert tensorproduct([x, y], [1, 2, 3]) == tensorproduct(A, B) assert tensorproduct(A, 2) == ArrayType([2*x, 2*y]) assert tensorproduct(A, [2]) == ArrayType([[2*x], [2*y]]) assert tensorproduct([2], A) == ArrayType([[2*x, 2*y]]) assert tensorproduct(a, A) == ArrayType([a*x, a*y]) assert tensorproduct(a, A, B) == ArrayType([[a*x, 2*a*x, 3*a*x], [a*y, 2*a*y, 3*a*y]]) assert tensorproduct(A, B, a) == ArrayType([[a*x, 2*a*x, 3*a*x], [a*y, 2*a*y, 3*a*y]]) assert tensorproduct(B, a, A) == ArrayType([[a*x, a*y], [2*a*x, 2*a*y], [3*a*x, 3*a*y]]) # tests for large scale sparse array for SparseArrayType in [ImmutableSparseNDimArray, MutableSparseNDimArray]: a = SparseArrayType({1:2, 3:4},(1000, 2000)) b = SparseArrayType({1:2, 3:4},(1000, 2000)) assert tensorproduct(a, b) == ImmutableSparseNDimArray({2000001: 4, 2000003: 8, 6000001: 8, 6000003: 16}, (1000, 2000, 1000, 2000)) def test_tensorcontraction(): from sympy.abc import a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x B = Array(range(18), (2, 3, 3)) assert tensorcontraction(B, (1, 2)) == Array([12, 39]) C1 = Array([a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x], (2, 3, 2, 2)) assert tensorcontraction(C1, (0, 2)) == Array([[a + o, b + p], [e + s, f + t], [i + w, j + x]]) assert tensorcontraction(C1, (0, 2, 3)) == Array([a + p, e + t, i + x]) assert tensorcontraction(C1, (2, 3)) == Array([[a + d, e + h, i + l], [m + p, q + t, u + x]]) def test_derivative_by_array(): from sympy.abc import i, j, t, x, y, z bexpr = x*y**2*exp(z)*log(t) sexpr = sin(bexpr) cexpr = cos(bexpr) a = Array([sexpr]) assert derive_by_array(sexpr, t) == x*y**2*exp(z)*cos(x*y**2*exp(z)*log(t))/t assert derive_by_array(sexpr, [x, y, z]) == Array([bexpr/x*cexpr, 2*y*bexpr/y**2*cexpr, bexpr*cexpr]) assert derive_by_array(a, [x, y, z]) == Array([[bexpr/x*cexpr], [2*y*bexpr/y**2*cexpr], [bexpr*cexpr]]) assert derive_by_array(sexpr, [[x, y], [z, t]]) == Array([[bexpr/x*cexpr, 2*y*bexpr/y**2*cexpr], [bexpr*cexpr, bexpr/log(t)/t*cexpr]]) assert derive_by_array(a, [[x, y], [z, t]]) == Array([[[bexpr/x*cexpr], [2*y*bexpr/y**2*cexpr]], [[bexpr*cexpr], [bexpr/log(t)/t*cexpr]]]) assert derive_by_array([[x, y], [z, t]], [x, y]) == Array([[[1, 0], [0, 0]], [[0, 1], [0, 0]]]) assert derive_by_array([[x, y], [z, t]], [[x, y], [z, t]]) == Array([[[[1, 0], [0, 0]], [[0, 1], [0, 0]]], [[[0, 0], [1, 0]], [[0, 0], [0, 1]]]]) assert diff(sexpr, t) == x*y**2*exp(z)*cos(x*y**2*exp(z)*log(t))/t assert diff(sexpr, Array([x, y, z])) == Array([bexpr/x*cexpr, 2*y*bexpr/y**2*cexpr, bexpr*cexpr]) assert diff(a, Array([x, y, z])) == Array([[bexpr/x*cexpr], [2*y*bexpr/y**2*cexpr], [bexpr*cexpr]]) assert diff(sexpr, Array([[x, y], [z, t]])) == Array([[bexpr/x*cexpr, 2*y*bexpr/y**2*cexpr], [bexpr*cexpr, bexpr/log(t)/t*cexpr]]) assert diff(a, Array([[x, y], [z, t]])) == Array([[[bexpr/x*cexpr], [2*y*bexpr/y**2*cexpr]], [[bexpr*cexpr], [bexpr/log(t)/t*cexpr]]]) assert diff(Array([[x, y], [z, t]]), Array([x, y])) == Array([[[1, 0], [0, 0]], [[0, 1], [0, 0]]]) assert diff(Array([[x, y], [z, t]]), Array([[x, y], [z, t]])) == Array([[[[1, 0], [0, 0]], [[0, 1], [0, 0]]], [[[0, 0], [1, 0]], [[0, 0], [0, 1]]]]) # test for large scale sparse array for SparseArrayType in [ImmutableSparseNDimArray, MutableSparseNDimArray]: b = MutableSparseNDimArray({0:i, 1:j}, (10000, 20000)) assert derive_by_array(b, i) == ImmutableSparseNDimArray({0: 1}, (10000, 20000)) assert derive_by_array(b, (i, j)) == ImmutableSparseNDimArray({0: 1, 200000001: 1}, (2, 10000, 20000)) #https://github.com/sympy/sympy/issues/20655 U = Array([x, y, z]) E = 2 assert derive_by_array(E, U) == ImmutableDenseNDimArray([0, 0, 0]) def test_issue_emerged_while_discussing_10972(): ua = Array([-1,0]) Fa = Array([[0, 1], [-1, 0]]) po = tensorproduct(Fa, ua, Fa, ua) assert tensorcontraction(po, (1, 2), (4, 5)) == Array([[0, 0], [0, 1]]) sa = symbols('a0:144') po = Array(sa, [2, 2, 3, 3, 2, 2]) assert tensorcontraction(po, (0, 1), (2, 3), (4, 5)) == sa[0] + sa[108] + sa[111] + sa[124] + sa[127] + sa[140] + sa[143] + sa[16] + sa[19] + sa[3] + sa[32] + sa[35] assert tensorcontraction(po, (0, 1, 4, 5), (2, 3)) == sa[0] + sa[111] + sa[127] + sa[143] + sa[16] + sa[32] assert tensorcontraction(po, (0, 1), (4, 5)) == Array([[sa[0] + sa[108] + sa[111] + sa[3], sa[112] + sa[115] + sa[4] + sa[7], sa[11] + sa[116] + sa[119] + sa[8]], [sa[12] + sa[120] + sa[123] + sa[15], sa[124] + sa[127] + sa[16] + sa[19], sa[128] + sa[131] + sa[20] + sa[23]], [sa[132] + sa[135] + sa[24] + sa[27], sa[136] + sa[139] + sa[28] + sa[31], sa[140] + sa[143] + sa[32] + sa[35]]]) assert tensorcontraction(po, (0, 1), (2, 3)) == Array([[sa[0] + sa[108] + sa[124] + sa[140] + sa[16] + sa[32], sa[1] + sa[109] + sa[125] + sa[141] + sa[17] + sa[33]], [sa[110] + sa[126] + sa[142] + sa[18] + sa[2] + sa[34], sa[111] + sa[127] + sa[143] + sa[19] + sa[3] + sa[35]]]) def test_array_permutedims(): sa = symbols('a0:144') for ArrayType in [ImmutableDenseNDimArray, ImmutableSparseNDimArray]: m1 = ArrayType(sa[:6], (2, 3)) assert permutedims(m1, (1, 0)) == transpose(m1) assert m1.tomatrix().T == permutedims(m1, (1, 0)).tomatrix() assert m1.tomatrix().T == transpose(m1).tomatrix() assert m1.tomatrix().C == conjugate(m1).tomatrix() assert m1.tomatrix().H == adjoint(m1).tomatrix() assert m1.tomatrix().T == m1.transpose().tomatrix() assert m1.tomatrix().C == m1.conjugate().tomatrix() assert m1.tomatrix().H == m1.adjoint().tomatrix() raises(ValueError, lambda: permutedims(m1, (0,))) raises(ValueError, lambda: permutedims(m1, (0, 0))) raises(ValueError, lambda: permutedims(m1, (1, 2, 0))) # Some tests with random arrays: dims = 6 shape = [random.randint(1,5) for i in range(dims)] elems = [random.random() for i in range(tensorproduct(*shape))] ra = ArrayType(elems, shape) perm = list(range(dims)) # Randomize the permutation: random.shuffle(perm) # Test inverse permutation: assert permutedims(permutedims(ra, perm), _af_invert(perm)) == ra # Test that permuted shape corresponds to action by `Permutation`: assert permutedims(ra, perm).shape == tuple(Permutation(perm)(shape)) z = ArrayType.zeros(4,5,6,7) assert permutedims(z, (2, 3, 1, 0)).shape == (6, 7, 5, 4) assert permutedims(z, [2, 3, 1, 0]).shape == (6, 7, 5, 4) assert permutedims(z, Permutation([2, 3, 1, 0])).shape == (6, 7, 5, 4) po = ArrayType(sa, [2, 2, 3, 3, 2, 2]) raises(ValueError, lambda: permutedims(po, (1, 1))) raises(ValueError, lambda: po.transpose()) raises(ValueError, lambda: po.adjoint()) assert permutedims(po, reversed(range(po.rank()))) == ArrayType( [[[[[[sa[0], sa[72]], [sa[36], sa[108]]], [[sa[12], sa[84]], [sa[48], sa[120]]], [[sa[24], sa[96]], [sa[60], sa[132]]]], [[[sa[4], sa[76]], [sa[40], sa[112]]], [[sa[16], sa[88]], [sa[52], sa[124]]], [[sa[28], sa[100]], [sa[64], sa[136]]]], [[[sa[8], sa[80]], [sa[44], sa[116]]], [[sa[20], sa[92]], [sa[56], sa[128]]], [[sa[32], sa[104]], [sa[68], sa[140]]]]], [[[[sa[2], sa[74]], [sa[38], sa[110]]], [[sa[14], sa[86]], [sa[50], sa[122]]], [[sa[26], sa[98]], [sa[62], sa[134]]]], [[[sa[6], sa[78]], [sa[42], sa[114]]], [[sa[18], sa[90]], [sa[54], sa[126]]], [[sa[30], sa[102]], [sa[66], sa[138]]]], [[[sa[10], sa[82]], [sa[46], sa[118]]], [[sa[22], sa[94]], [sa[58], sa[130]]], [[sa[34], sa[106]], [sa[70], sa[142]]]]]], [[[[[sa[1], sa[73]], [sa[37], sa[109]]], [[sa[13], sa[85]], [sa[49], sa[121]]], [[sa[25], sa[97]], [sa[61], sa[133]]]], [[[sa[5], sa[77]], [sa[41], sa[113]]], [[sa[17], sa[89]], [sa[53], sa[125]]], [[sa[29], sa[101]], [sa[65], sa[137]]]], [[[sa[9], sa[81]], [sa[45], sa[117]]], [[sa[21], sa[93]], [sa[57], sa[129]]], [[sa[33], sa[105]], [sa[69], sa[141]]]]], [[[[sa[3], sa[75]], [sa[39], sa[111]]], [[sa[15], sa[87]], [sa[51], sa[123]]], [[sa[27], sa[99]], [sa[63], sa[135]]]], [[[sa[7], sa[79]], [sa[43], sa[115]]], [[sa[19], sa[91]], [sa[55], sa[127]]], [[sa[31], sa[103]], [sa[67], sa[139]]]], [[[sa[11], sa[83]], [sa[47], sa[119]]], [[sa[23], sa[95]], [sa[59], sa[131]]], [[sa[35], sa[107]], [sa[71], sa[143]]]]]]]) assert permutedims(po, (1, 0, 2, 3, 4, 5)) == ArrayType( [[[[[[sa[0], sa[1]], [sa[2], sa[3]]], [[sa[4], sa[5]], [sa[6], sa[7]]], [[sa[8], sa[9]], [sa[10], sa[11]]]], [[[sa[12], sa[13]], [sa[14], sa[15]]], [[sa[16], sa[17]], [sa[18], sa[19]]], [[sa[20], sa[21]], [sa[22], sa[23]]]], [[[sa[24], sa[25]], [sa[26], sa[27]]], [[sa[28], sa[29]], [sa[30], sa[31]]], [[sa[32], sa[33]], [sa[34], sa[35]]]]], [[[[sa[72], sa[73]], [sa[74], sa[75]]], [[sa[76], sa[77]], [sa[78], sa[79]]], [[sa[80], sa[81]], [sa[82], sa[83]]]], [[[sa[84], sa[85]], [sa[86], sa[87]]], [[sa[88], sa[89]], [sa[90], sa[91]]], [[sa[92], sa[93]], [sa[94], sa[95]]]], [[[sa[96], sa[97]], [sa[98], sa[99]]], [[sa[100], sa[101]], [sa[102], sa[103]]], [[sa[104], sa[105]], [sa[106], sa[107]]]]]], [[[[[sa[36], sa[37]], [sa[38], sa[39]]], [[sa[40], sa[41]], [sa[42], sa[43]]], [[sa[44], sa[45]], [sa[46], sa[47]]]], [[[sa[48], sa[49]], [sa[50], sa[51]]], [[sa[52], sa[53]], [sa[54], sa[55]]], [[sa[56], sa[57]], [sa[58], sa[59]]]], [[[sa[60], sa[61]], [sa[62], sa[63]]], [[sa[64], sa[65]], [sa[66], sa[67]]], [[sa[68], sa[69]], [sa[70], sa[71]]]]], [ [[[sa[108], sa[109]], [sa[110], sa[111]]], [[sa[112], sa[113]], [sa[114], sa[115]]], [[sa[116], sa[117]], [sa[118], sa[119]]]], [[[sa[120], sa[121]], [sa[122], sa[123]]], [[sa[124], sa[125]], [sa[126], sa[127]]], [[sa[128], sa[129]], [sa[130], sa[131]]]], [[[sa[132], sa[133]], [sa[134], sa[135]]], [[sa[136], sa[137]], [sa[138], sa[139]]], [[sa[140], sa[141]], [sa[142], sa[143]]]]]]]) assert permutedims(po, (0, 2, 1, 4, 3, 5)) == ArrayType( [[[[[[sa[0], sa[1]], [sa[4], sa[5]], [sa[8], sa[9]]], [[sa[2], sa[3]], [sa[6], sa[7]], [sa[10], sa[11]]]], [[[sa[36], sa[37]], [sa[40], sa[41]], [sa[44], sa[45]]], [[sa[38], sa[39]], [sa[42], sa[43]], [sa[46], sa[47]]]]], [[[[sa[12], sa[13]], [sa[16], sa[17]], [sa[20], sa[21]]], [[sa[14], sa[15]], [sa[18], sa[19]], [sa[22], sa[23]]]], [[[sa[48], sa[49]], [sa[52], sa[53]], [sa[56], sa[57]]], [[sa[50], sa[51]], [sa[54], sa[55]], [sa[58], sa[59]]]]], [[[[sa[24], sa[25]], [sa[28], sa[29]], [sa[32], sa[33]]], [[sa[26], sa[27]], [sa[30], sa[31]], [sa[34], sa[35]]]], [[[sa[60], sa[61]], [sa[64], sa[65]], [sa[68], sa[69]]], [[sa[62], sa[63]], [sa[66], sa[67]], [sa[70], sa[71]]]]]], [[[[[sa[72], sa[73]], [sa[76], sa[77]], [sa[80], sa[81]]], [[sa[74], sa[75]], [sa[78], sa[79]], [sa[82], sa[83]]]], [[[sa[108], sa[109]], [sa[112], sa[113]], [sa[116], sa[117]]], [[sa[110], sa[111]], [sa[114], sa[115]], [sa[118], sa[119]]]]], [[[[sa[84], sa[85]], [sa[88], sa[89]], [sa[92], sa[93]]], [[sa[86], sa[87]], [sa[90], sa[91]], [sa[94], sa[95]]]], [[[sa[120], sa[121]], [sa[124], sa[125]], [sa[128], sa[129]]], [[sa[122], sa[123]], [sa[126], sa[127]], [sa[130], sa[131]]]]], [[[[sa[96], sa[97]], [sa[100], sa[101]], [sa[104], sa[105]]], [[sa[98], sa[99]], [sa[102], sa[103]], [sa[106], sa[107]]]], [[[sa[132], sa[133]], [sa[136], sa[137]], [sa[140], sa[141]]], [[sa[134], sa[135]], [sa[138], sa[139]], [sa[142], sa[143]]]]]]]) po2 = po.reshape(4, 9, 2, 2) assert po2 == ArrayType([[[[sa[0], sa[1]], [sa[2], sa[3]]], [[sa[4], sa[5]], [sa[6], sa[7]]], [[sa[8], sa[9]], [sa[10], sa[11]]], [[sa[12], sa[13]], [sa[14], sa[15]]], [[sa[16], sa[17]], [sa[18], sa[19]]], [[sa[20], sa[21]], [sa[22], sa[23]]], [[sa[24], sa[25]], [sa[26], sa[27]]], [[sa[28], sa[29]], [sa[30], sa[31]]], [[sa[32], sa[33]], [sa[34], sa[35]]]], [[[sa[36], sa[37]], [sa[38], sa[39]]], [[sa[40], sa[41]], [sa[42], sa[43]]], [[sa[44], sa[45]], [sa[46], sa[47]]], [[sa[48], sa[49]], [sa[50], sa[51]]], [[sa[52], sa[53]], [sa[54], sa[55]]], [[sa[56], sa[57]], [sa[58], sa[59]]], [[sa[60], sa[61]], [sa[62], sa[63]]], [[sa[64], sa[65]], [sa[66], sa[67]]], [[sa[68], sa[69]], [sa[70], sa[71]]]], [[[sa[72], sa[73]], [sa[74], sa[75]]], [[sa[76], sa[77]], [sa[78], sa[79]]], [[sa[80], sa[81]], [sa[82], sa[83]]], [[sa[84], sa[85]], [sa[86], sa[87]]], [[sa[88], sa[89]], [sa[90], sa[91]]], [[sa[92], sa[93]], [sa[94], sa[95]]], [[sa[96], sa[97]], [sa[98], sa[99]]], [[sa[100], sa[101]], [sa[102], sa[103]]], [[sa[104], sa[105]], [sa[106], sa[107]]]], [[[sa[108], sa[109]], [sa[110], sa[111]]], [[sa[112], sa[113]], [sa[114], sa[115]]], [[sa[116], sa[117]], [sa[118], sa[119]]], [[sa[120], sa[121]], [sa[122], sa[123]]], [[sa[124], sa[125]], [sa[126], sa[127]]], [[sa[128], sa[129]], [sa[130], sa[131]]], [[sa[132], sa[133]], [sa[134], sa[135]]], [[sa[136], sa[137]], [sa[138], sa[139]]], [[sa[140], sa[141]], [sa[142], sa[143]]]]]) assert permutedims(po2, (3, 2, 0, 1)) == ArrayType([[[[sa[0], sa[4], sa[8], sa[12], sa[16], sa[20], sa[24], sa[28], sa[32]], [sa[36], sa[40], sa[44], sa[48], sa[52], sa[56], sa[60], sa[64], sa[68]], [sa[72], sa[76], sa[80], sa[84], sa[88], sa[92], sa[96], sa[100], sa[104]], [sa[108], sa[112], sa[116], sa[120], sa[124], sa[128], sa[132], sa[136], sa[140]]], [[sa[2], sa[6], sa[10], sa[14], sa[18], sa[22], sa[26], sa[30], sa[34]], [sa[38], sa[42], sa[46], sa[50], sa[54], sa[58], sa[62], sa[66], sa[70]], [sa[74], sa[78], sa[82], sa[86], sa[90], sa[94], sa[98], sa[102], sa[106]], [sa[110], sa[114], sa[118], sa[122], sa[126], sa[130], sa[134], sa[138], sa[142]]]], [[[sa[1], sa[5], sa[9], sa[13], sa[17], sa[21], sa[25], sa[29], sa[33]], [sa[37], sa[41], sa[45], sa[49], sa[53], sa[57], sa[61], sa[65], sa[69]], [sa[73], sa[77], sa[81], sa[85], sa[89], sa[93], sa[97], sa[101], sa[105]], [sa[109], sa[113], sa[117], sa[121], sa[125], sa[129], sa[133], sa[137], sa[141]]], [[sa[3], sa[7], sa[11], sa[15], sa[19], sa[23], sa[27], sa[31], sa[35]], [sa[39], sa[43], sa[47], sa[51], sa[55], sa[59], sa[63], sa[67], sa[71]], [sa[75], sa[79], sa[83], sa[87], sa[91], sa[95], sa[99], sa[103], sa[107]], [sa[111], sa[115], sa[119], sa[123], sa[127], sa[131], sa[135], sa[139], sa[143]]]]]) # test for large scale sparse array for SparseArrayType in [ImmutableSparseNDimArray, MutableSparseNDimArray]: A = SparseArrayType({1:1, 10000:2}, (10000, 20000, 10000)) assert permutedims(A, (0, 1, 2)) == A assert permutedims(A, (1, 0, 2)) == SparseArrayType({1: 1, 100000000: 2}, (20000, 10000, 10000)) B = SparseArrayType({1:1, 20000:2}, (10000, 20000)) assert B.transpose() == SparseArrayType({10000: 1, 1: 2}, (20000, 10000)) def test_flatten(): from sympy import Matrix for ArrayType in [ImmutableDenseNDimArray, ImmutableSparseNDimArray, Matrix]: A = ArrayType(range(24)).reshape(4, 6) assert [i for i in Flatten(A)] == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23] for i, v in enumerate(Flatten(A)): i == v def test_tensordiagonal(): from sympy import eye expr = Array(range(9)).reshape(3, 3) raises(ValueError, lambda: tensordiagonal(expr, [0], [1])) assert tensordiagonal(eye(3), [0, 1]) == Array([1, 1, 1]) assert tensordiagonal(expr, [0, 1]) == Array([0, 4, 8]) x, y, z = symbols("x y z") expr2 = tensorproduct([x, y, z], expr) assert tensordiagonal(expr2, [1, 2]) == Array([[0, 4*x, 8*x], [0, 4*y, 8*y], [0, 4*z, 8*z]]) assert tensordiagonal(expr2, [0, 1]) == Array([[0, 3*y, 6*z], [x, 4*y, 7*z], [2*x, 5*y, 8*z]]) assert tensordiagonal(expr2, [0, 1, 2]) == Array([0, 4*y, 8*z]) # assert tensordiagonal(expr2, [0]) == permutedims(expr2, [1, 2, 0]) # assert tensordiagonal(expr2, [1]) == permutedims(expr2, [0, 2, 1]) # assert tensordiagonal(expr2, [2]) == expr2 # assert tensordiagonal(expr2, [1], [2]) == expr2 # assert tensordiagonal(expr2, [0], [1]) == permutedims(expr2, [2, 0, 1]) a, b, c, X, Y, Z = symbols("a b c X Y Z") expr3 = tensorproduct([x, y, z], [1, 2, 3], [a, b, c], [X, Y, Z]) assert tensordiagonal(expr3, [0, 1, 2, 3]) == Array([x*a*X, 2*y*b*Y, 3*z*c*Z]) assert tensordiagonal(expr3, [0, 1], [2, 3]) == tensorproduct([x, 2*y, 3*z], [a*X, b*Y, c*Z]) # assert tensordiagonal(expr3, [0], [1, 2], [3]) == tensorproduct([x, y, z], [a, 2*b, 3*c], [X, Y, Z]) assert tensordiagonal(tensordiagonal(expr3, [2, 3]), [0, 1]) == tensorproduct([a*X, b*Y, c*Z], [x, 2*y, 3*z]) raises(ValueError, lambda: tensordiagonal([[1, 2, 3], [4, 5, 6]], [0, 1])) raises(ValueError, lambda: tensordiagonal(expr3.reshape(3, 3, 9), [1, 2]))