def test_array_expr_construction_with_functions():
tp = tensorproduct(M, N)
assert tp == ArrayTensorProduct(M, N)
expr = tensorproduct(A, eye(2))
assert expr == ArrayTensorProduct(A, eye(2))
# Contraction:
expr = tensorcontraction(M, (0, 1))
assert expr == ArrayContraction(M, (0, 1))
expr = tensorcontraction(tp, (1, 2))
assert expr == ArrayContraction(tp, (1, 2))
expr = tensorcontraction(tensorcontraction(tp, (1, 2)), (0, 1))
assert expr == ArrayContraction(tp, (0, 3), (1, 2))
# Diagonalization:
expr = tensordiagonal(M, (0, 1))
assert expr == ArrayDiagonal(M, (0, 1))
expr = tensordiagonal(tensordiagonal(tp, (0, 1)), (0, 1))
assert expr == ArrayDiagonal(tp, (0, 1), (2, 3))
# Permutation of dimensions:
expr = permutedims(M, [1, 0])
assert expr == PermuteDims(M, [1, 0])
expr = permutedims(PermuteDims(tp, [1, 0, 2, 3]), [0, 1, 3, 2])
assert expr == PermuteDims(tp, [1, 0, 3, 2])
def test_array_as_explicit_matrix_symbol():
A = MatrixSymbol("A", 3, 3)
B = MatrixSymbol("B", 3, 3)
texpr = tensorproduct(A, B)
assert isinstance(texpr, ArrayTensorProduct)
assert texpr.as_explicit() == tensorproduct(A.as_explicit(),
B.as_explicit())
texpr = tensorcontraction(A, (0, 1))
assert isinstance(texpr, ArrayContraction)
assert texpr.as_explicit() == A[0, 0] + A[1, 1] + A[2, 2]
texpr = tensordiagonal(A, (0, 1))
assert isinstance(texpr, ArrayDiagonal)
assert texpr.as_explicit() == ImmutableDenseNDimArray(
[A[0, 0], A[1, 1], A[2, 2]])
texpr = permutedims(A, [1, 0])
assert isinstance(texpr, PermuteDims)
assert texpr.as_explicit() == permutedims(A.as_explicit(), [1, 0])
expr = ArrayAdd(ArrayTensorProduct(A, B), ArrayTensorProduct(B, A))
assert expr.as_explicit(
) == expr.args[0].as_explicit() + expr.args[1].as_explicit()
def test_tensordiagonal():
from sympy.matrices.dense import eye
expr = Array(range(9)).reshape(3, 3)
raises(ValueError, lambda: tensordiagonal(expr, [0], [1]))
raises(ValueError, lambda: tensordiagonal(expr, [0, 0]))
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]))
def test_array_as_explicit_call():
assert ZeroArray(3, 2, 4).as_explicit() == ImmutableDenseNDimArray.zeros(
3, 2, 4)
assert OneArray(3, 2, 4).as_explicit() == ImmutableDenseNDimArray(
[1 for i in range(3 * 2 * 4)]).reshape(3, 2, 4)
k = Symbol("k")
X = ArraySymbol("X", (k, 3, 2))
raises(ValueError, lambda: X.as_explicit())
raises(ValueError, lambda: ZeroArray(k, 2, 3).as_explicit())
raises(ValueError, lambda: OneArray(2, k, 2).as_explicit())
A = ArraySymbol("A", (3, 3))
B = ArraySymbol("B", (3, 3))
texpr = tensorproduct(A, B)
assert isinstance(texpr, ArrayTensorProduct)
assert texpr.as_explicit() == tensorproduct(A.as_explicit(),
B.as_explicit())
texpr = tensorcontraction(A, (0, 1))
assert isinstance(texpr, ArrayContraction)
assert texpr.as_explicit() == A[0, 0] + A[1, 1] + A[2, 2]
texpr = tensordiagonal(A, (0, 1))
assert isinstance(texpr, ArrayDiagonal)
assert texpr.as_explicit() == ImmutableDenseNDimArray(
[A[0, 0], A[1, 1], A[2, 2]])
texpr = permutedims(A, [1, 0])
assert isinstance(texpr, PermuteDims)
assert texpr.as_explicit() == permutedims(A.as_explicit(), [1, 0])
def test_arrayexpr_contraction_permutation_mix():
Me = M.subs(k, 3).as_explicit()
Ne = N.subs(k, 3).as_explicit()
cg1 = _array_contraction(PermuteDims(_array_tensor_product(M, N), Permutation([0, 2, 1, 3])), (2, 3))
cg2 = _array_contraction(_array_tensor_product(M, N), (1, 3))
assert cg1 == cg2
cge1 = tensorcontraction(permutedims(tensorproduct(Me, Ne), Permutation([0, 2, 1, 3])), (2, 3))
cge2 = tensorcontraction(tensorproduct(Me, Ne), (1, 3))
assert cge1 == cge2
cg1 = _permute_dims(_array_tensor_product(M, N), Permutation([0, 1, 3, 2]))
cg2 = _array_tensor_product(M, _permute_dims(N, Permutation([1, 0])))
assert cg1 == cg2
cg1 = _array_contraction(
_permute_dims(
_array_tensor_product(M, N, P, Q), Permutation([0, 2, 3, 1, 4, 5, 7, 6])),
(1, 2), (3, 5)
)
cg2 = _array_contraction(
_array_tensor_product(M, N, P, _permute_dims(Q, Permutation([1, 0]))),
(1, 5), (2, 3)
)
assert cg1 == cg2
cg1 = _array_contraction(
_permute_dims(
_array_tensor_product(M, N, P, Q), Permutation([1, 0, 4, 6, 2, 7, 5, 3])),
(0, 1), (2, 6), (3, 7)
)
cg2 = _permute_dims(
_array_contraction(
_array_tensor_product(M, P, Q, N),
(0, 1), (2, 3), (4, 7)),
[1, 0]
)
assert cg1 == cg2
cg1 = _array_contraction(
_permute_dims(
_array_tensor_product(M, N, P, Q), Permutation([1, 0, 4, 6, 7, 2, 5, 3])),
(0, 1), (2, 6), (3, 7)
)
cg2 = _permute_dims(
_array_contraction(
_array_tensor_product(_permute_dims(M, [1, 0]), N, P, Q),
(0, 1), (3, 6), (4, 5)
),
Permutation([1, 0])
)
assert cg1 == cg2
def test_array_symbol_and_element():
A = ArraySymbol("A", (2, ))
A0 = ArrayElement(A, (0, ))
A1 = ArrayElement(A, (1, ))
assert A[0] == A0
assert A[1] != A0
assert A.as_explicit() == ImmutableDenseNDimArray([A0, A1])
A2 = tensorproduct(A, A)
assert A2.shape == (2, 2)
# TODO: not yet supported:
# assert A2.as_explicit() == Array([[A[0]*A[0], A[1]*A[0]], [A[0]*A[1], A[1]*A[1]]])
A3 = tensorcontraction(A2, (0, 1))
assert A3.shape == ()
# TODO: not yet supported:
# assert A3.as_explicit() == Array([])
A = ArraySymbol("A", (2, 3, 4))
Ae = A.as_explicit()
assert Ae == ImmutableDenseNDimArray(
[[[ArrayElement(A, (i, j, k)) for k in range(4)] for j in range(3)]
for i in range(2)])
p = _permute_dims(A, Permutation(0, 2, 1))
assert isinstance(p, PermuteDims)
def test_array_expr_construction_with_functions():
tp = tensorproduct(M, N)
assert tp == ArrayTensorProduct(M, N)
expr = tensorproduct(A, eye(2))
assert expr == ArrayTensorProduct(A, eye(2))
# Contraction:
expr = tensorcontraction(M, (0, 1))
assert expr == ArrayContraction(M, (0, 1))
expr = tensorcontraction(tp, (1, 2))
assert expr == ArrayContraction(tp, (1, 2))
expr = tensorcontraction(tensorcontraction(tp, (1, 2)), (0, 1))
assert expr == ArrayContraction(tp, (0, 3), (1, 2))
# Diagonalization:
expr = tensordiagonal(M, (0, 1))
assert expr == ArrayDiagonal(M, (0, 1))
expr = tensordiagonal(tensordiagonal(tp, (0, 1)), (0, 1))
assert expr == ArrayDiagonal(tp, (0, 1), (2, 3))
# Permutation of dimensions:
expr = permutedims(M, [1, 0])
assert expr == PermuteDims(M, [1, 0])
expr = permutedims(PermuteDims(tp, [1, 0, 2, 3]), [0, 1, 3, 2])
assert expr == PermuteDims(tp, [1, 0, 3, 2])
expr = PermuteDims(tp, index_order_new=["a", "b", "c", "d"], index_order_old=["d", "c", "b", "a"])
assert expr == PermuteDims(tp, [3, 2, 1, 0])
arr = Array(range(32)).reshape(2, 2, 2, 2, 2)
expr = PermuteDims(arr, index_order_new=["a", "b", "c", "d", "e"], index_order_old=['b', 'e', 'a', 'd', 'c'])
assert expr == PermuteDims(arr, [2, 0, 4, 3, 1])
assert expr.as_explicit() == permutedims(arr, index_order_new=["a", "b", "c", "d", "e"], index_order_old=['b', 'e', 'a', 'd', 'c'])
def test_array_expr_as_explicit_with_explicit_component_arrays():
# Test if .as_explicit() works with explicit-component arrays
# nested in array expressions:
from sympy.abc import x, y, z, t
A = Array([[x, y], [z, t]])
assert ArrayTensorProduct(A, A).as_explicit() == tensorproduct(A, A)
assert ArrayDiagonal(A, (0, 1)).as_explicit() == tensordiagonal(A, (0, 1))
assert ArrayContraction(A, (0, 1)).as_explicit() == tensorcontraction(A, (0, 1))
assert ArrayAdd(A, A).as_explicit() == A + A
assert ArrayElementwiseApplyFunc(sin, A).as_explicit() == A.applyfunc(sin)
assert PermuteDims(A, [1, 0]).as_explicit() == permutedims(A, [1, 0])
assert Reshape(A, [4]).as_explicit() == A.reshape(4)
def test_arrayexpr_nested_permutations():
cg = _permute_dims(_permute_dims(M, (1, 0)), (1, 0))
assert cg == M
times = 3
plist1 = [list(range(6)) for i in range(times)]
plist2 = [list(range(6)) for i in range(times)]
for i in range(times):
random.shuffle(plist1[i])
random.shuffle(plist2[i])
plist1.append([2, 5, 4, 1, 0, 3])
plist2.append([3, 5, 0, 4, 1, 2])
plist1.append([2, 5, 4, 0, 3, 1])
plist2.append([3, 0, 5, 1, 2, 4])
plist1.append([5, 4, 2, 0, 3, 1])
plist2.append([4, 5, 0, 2, 3, 1])
Me = M.subs(k, 3).as_explicit()
Ne = N.subs(k, 3).as_explicit()
Pe = P.subs(k, 3).as_explicit()
cge = tensorproduct(Me, Ne, Pe)
for permutation_array1, permutation_array2 in zip(plist1, plist2):
p1 = Permutation(permutation_array1)
p2 = Permutation(permutation_array2)
cg = _permute_dims(
_permute_dims(
_array_tensor_product(M, N, P),
p1),
p2
)
result = _permute_dims(
_array_tensor_product(M, N, P),
p2*p1
)
assert cg == result
# Check that `permutedims` behaves the same way with explicit-component arrays:
result1 = _permute_dims(_permute_dims(cge, p1), p2)
result2 = _permute_dims(cge, p2*p1)
assert result1 == result2
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_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_symbol_and_element():
A = ArraySymbol("A", (2,))
A0 = ArrayElement(A, (0,))
A1 = ArrayElement(A, (1,))
assert A[0] == A0
assert A[1] != A0
assert A.as_explicit() == ImmutableDenseNDimArray([A0, A1])
A2 = tensorproduct(A, A)
assert A2.shape == (2, 2)
# TODO: not yet supported:
# assert A2.as_explicit() == Array([[A[0]*A[0], A[1]*A[0]], [A[0]*A[1], A[1]*A[1]]])
A3 = tensorcontraction(A2, (0, 1))
assert A3.shape == ()
# TODO: not yet supported:
# assert A3.as_explicit() == Array([])
A = ArraySymbol("A", (2, 3, 4))
Ae = A.as_explicit()
assert Ae == ImmutableDenseNDimArray(
[[[ArrayElement(A, (i, j, k)) for k in range(4)] for j in range(3)] for i in range(2)])
p = _permute_dims(A, Permutation(0, 2, 1))
assert isinstance(p, PermuteDims)
A = ArraySymbol("A", (2,))
raises(IndexError, lambda: A[()])
raises(IndexError, lambda: A[0, 1])
raises(ValueError, lambda: A[-1])
raises(ValueError, lambda: A[2])
O = OneArray(3, 4)
Z = ZeroArray(m, n)
raises(IndexError, lambda: O[()])
raises(IndexError, lambda: O[1, 2, 3])
raises(ValueError, lambda: O[3, 0])
raises(ValueError, lambda: O[0, 4])
assert O[1, 2] == 1
assert Z[1, 2] == 0
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
A = Array([x, y])
B = Array([1, 2, 3])
C = Array([a, b, c, d])
assert tensorproduct(A, B, C) == Array(
[[[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) == Array([2 * x, 2 * y])
assert tensorproduct(A, [2]) == Array([[2 * x], [2 * y]])
assert tensorproduct([2], A) == Array([[2 * x, 2 * y]])
assert tensorproduct(a, A) == Array([a * x, a * y])
assert tensorproduct(a, A, B) == Array([[a * x, 2 * a * x, 3 * a * x],
[a * y, 2 * a * y, 3 * a * y]])
assert tensorproduct(A, B, a) == Array([[a * x, 2 * a * x, 3 * a * x],
[a * y, 2 * a * y, 3 * a * y]])
assert tensorproduct(B, a, A) == Array([[a * x, a * y],
[2 * a * x, 2 * a * y],
[3 * a * x, 3 * a * y]])
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_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_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
A = Array([x, y])
B = Array([1, 2, 3])
C = Array([a, b, c, d])
assert tensorproduct(A, B, C) == Array([[[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) == Array([2*x, 2*y])
assert tensorproduct(A, [2]) == Array([[2*x], [2*y]])
assert tensorproduct([2], A) == Array([[2*x, 2*y]])
assert tensorproduct(a, A) == Array([a*x, a*y])
assert tensorproduct(a, A, B) == Array([[a*x, 2*a*x, 3*a*x], [a*y, 2*a*y, 3*a*y]])
assert tensorproduct(A, B, a) == Array([[a*x, 2*a*x, 3*a*x], [a*y, 2*a*y, 3*a*y]])
assert tensorproduct(B, a, A) == Array([[a*x, a*y], [2*a*x, 2*a*y], [3*a*x, 3*a*y]])