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_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_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_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])
def as_explicit(self):
return tensordiagonal(self.expr.as_explicit(), *self.diagonal_indices)