def test_arrayexpr_convert_array_to_matrix_diag2contraction_diagmatrix():
cg = _array_diagonal(_array_tensor_product(M, a), (1, 2))
res = _array_diag2contr_diagmatrix(cg)
assert res.shape == cg.shape
assert res == _array_contraction(
_array_tensor_product(M, OneArray(1), DiagMatrix(a)), (1, 3))
raises(ValueError, lambda: _array_diagonal(_array_tensor_product(a, M),
(1, 2)))
cg = _array_diagonal(_array_tensor_product(a.T, M), (1, 2))
res = _array_diag2contr_diagmatrix(cg)
assert res.shape == cg.shape
assert res == _array_contraction(
_array_tensor_product(OneArray(1), M, DiagMatrix(a.T)), (1, 4))
cg = _array_diagonal(_array_tensor_product(a.T, M, N, b.T), (1, 2), (4, 7))
res = _array_diag2contr_diagmatrix(cg)
assert res.shape == cg.shape
assert res == _array_contraction(
_array_tensor_product(OneArray(1), M, N, OneArray(1), DiagMatrix(a.T),
DiagMatrix(b.T)), (1, 7), (3, 9))
cg = _array_diagonal(_array_tensor_product(a, M, N, b.T), (0, 2), (4, 7))
res = _array_diag2contr_diagmatrix(cg)
assert res.shape == cg.shape
assert res == _array_contraction(
_array_tensor_product(OneArray(1), M, N, OneArray(1), DiagMatrix(a),
DiagMatrix(b.T)), (1, 6), (3, 9))
cg = _array_diagonal(_array_tensor_product(a, M, N, b.T), (0, 4), (3, 7))
res = _array_diag2contr_diagmatrix(cg)
assert res.shape == cg.shape
assert res == _array_contraction(
_array_tensor_product(OneArray(1), M, N, OneArray(1), DiagMatrix(a),
DiagMatrix(b.T)), (3, 6), (2, 9))
I1 = Identity(1)
x = MatrixSymbol("x", k, 1)
A = MatrixSymbol("A", k, k)
cg = _array_diagonal(_array_tensor_product(x, A.T, I1), (0, 2))
assert _array_diag2contr_diagmatrix(cg).shape == cg.shape
assert _array2matrix(cg).shape == cg.shape
def test_arrayexpr_convert_array_to_diagonalized_vector():
# Check matrix recognition over trivial dimensions:
cg = ArrayTensorProduct(a, b)
assert convert_array_to_matrix(cg) == a * b.T
cg = ArrayTensorProduct(I1, a, b)
assert convert_array_to_matrix(cg) == a * b.T
# Recognize trace inside a tensor product:
cg = ArrayContraction(ArrayTensorProduct(A, B, C), (0, 3), (1, 2))
assert convert_array_to_matrix(cg) == Trace(A * B) * C
# Transform diagonal operator to contraction:
cg = ArrayDiagonal(ArrayTensorProduct(A, a), (1, 2))
assert _array_diag2contr_diagmatrix(cg) == ArrayContraction(ArrayTensorProduct(A, OneArray(1), DiagMatrix(a)), (1, 3))
assert convert_array_to_matrix(cg) == A * DiagMatrix(a)
cg = ArrayDiagonal(ArrayTensorProduct(a, b), (0, 2))
assert _array_diag2contr_diagmatrix(cg) == PermuteDims(
ArrayContraction(ArrayTensorProduct(DiagMatrix(a), OneArray(1), b), (0, 3)), [1, 2, 0]
)
assert convert_array_to_matrix(cg) == b.T * DiagMatrix(a)
cg = ArrayDiagonal(ArrayTensorProduct(A, a), (0, 2))
assert _array_diag2contr_diagmatrix(cg) == ArrayContraction(ArrayTensorProduct(A, OneArray(1), DiagMatrix(a)), (0, 3))
assert convert_array_to_matrix(cg) == A.T * DiagMatrix(a)
cg = ArrayDiagonal(ArrayTensorProduct(I, x, I1), (0, 2), (3, 5))
assert _array_diag2contr_diagmatrix(cg) == ArrayContraction(ArrayTensorProduct(I, OneArray(1), I1, DiagMatrix(x)), (0, 5))
assert convert_array_to_matrix(cg) == DiagMatrix(x)
cg = ArrayDiagonal(ArrayTensorProduct(I, x, A, B), (1, 2), (5, 6))
assert _array_diag2contr_diagmatrix(cg) == ArrayDiagonal(ArrayContraction(ArrayTensorProduct(I, OneArray(1), A, B, DiagMatrix(x)), (1, 7)), (5, 6))
# TODO: this is returning a wrong result:
# convert_array_to_matrix(cg)
cg = ArrayDiagonal(ArrayTensorProduct(I1, a, b), (1, 3, 5))
assert convert_array_to_matrix(cg) == a*b.T
cg = ArrayDiagonal(ArrayTensorProduct(I1, a, b), (1, 3))
assert _array_diag2contr_diagmatrix(cg) == ArrayContraction(ArrayTensorProduct(OneArray(1), a, b, I1), (2, 6))
assert convert_array_to_matrix(cg) == a*b.T
cg = ArrayDiagonal(ArrayTensorProduct(x, I1), (1, 2))
assert isinstance(cg, ArrayDiagonal)
assert cg.diagonal_indices == ((1, 2),)
assert convert_array_to_matrix(cg) == x
cg = ArrayDiagonal(ArrayTensorProduct(x, I), (0, 2))
assert _array_diag2contr_diagmatrix(cg) == ArrayContraction(ArrayTensorProduct(OneArray(1), I, DiagMatrix(x)), (1, 3))
assert convert_array_to_matrix(cg).doit() == DiagMatrix(x)
raises(ValueError, lambda: ArrayDiagonal(x, (1,)))
# Ignore identity matrices with contractions:
cg = ArrayContraction(ArrayTensorProduct(I, A, I, I), (0, 2), (1, 3), (5, 7))
assert cg.split_multiple_contractions() == cg
assert convert_array_to_matrix(cg) == Trace(A) * I
cg = ArrayContraction(ArrayTensorProduct(Trace(A) * I, I, I), (1, 5), (3, 4))
assert cg.split_multiple_contractions() == cg
assert convert_array_to_matrix(cg).doit() == Trace(A) * I
# Add DiagMatrix when required:
cg = ArrayContraction(ArrayTensorProduct(A, a), (1, 2))
assert cg.split_multiple_contractions() == cg
assert convert_array_to_matrix(cg) == A * a
cg = ArrayContraction(ArrayTensorProduct(A, a, B), (1, 2, 4))
assert cg.split_multiple_contractions() == ArrayContraction(ArrayTensorProduct(A, DiagMatrix(a), OneArray(1), B), (1, 2), (3, 5))
assert convert_array_to_matrix(cg) == A * DiagMatrix(a) * B
cg = ArrayContraction(ArrayTensorProduct(A, a, B), (0, 2, 4))
assert cg.split_multiple_contractions() == ArrayContraction(ArrayTensorProduct(A, DiagMatrix(a), OneArray(1), B), (0, 2), (3, 5))
assert convert_array_to_matrix(cg) == A.T * DiagMatrix(a) * B
cg = ArrayContraction(ArrayTensorProduct(A, a, b, a.T, B), (0, 2, 4, 7, 9))
assert cg.split_multiple_contractions() == ArrayContraction(ArrayTensorProduct(A, DiagMatrix(a), OneArray(1),
DiagMatrix(b), OneArray(1), DiagMatrix(a), OneArray(1), B),
(0, 2), (3, 5), (6, 9), (8, 12))
assert convert_array_to_matrix(cg) == A.T * DiagMatrix(a) * DiagMatrix(b) * DiagMatrix(a) * B.T
cg = ArrayContraction(ArrayTensorProduct(I1, I1, I1), (1, 2, 4))
assert cg.split_multiple_contractions() == ArrayContraction(ArrayTensorProduct(I1, I1, OneArray(1), I1), (1, 2), (3, 5))
assert convert_array_to_matrix(cg) == 1
cg = ArrayContraction(ArrayTensorProduct(I, I, I, I, A), (1, 2, 8), (5, 6, 9))
assert convert_array_to_matrix(cg.split_multiple_contractions()).doit() == A
cg = ArrayContraction(ArrayTensorProduct(A, a, C, a, B), (1, 2, 4), (5, 6, 8))
expected = ArrayContraction(ArrayTensorProduct(A, DiagMatrix(a), OneArray(1), C, DiagMatrix(a), OneArray(1), B), (1, 3), (2, 5), (6, 7), (8, 10))
assert cg.split_multiple_contractions() == expected
assert convert_array_to_matrix(cg) == A * DiagMatrix(a) * C * DiagMatrix(a) * B
cg = ArrayContraction(ArrayTensorProduct(a, I1, b, I1, (a.T*b).applyfunc(cos)), (1, 2, 8), (5, 6, 9))
expected = ArrayContraction(ArrayTensorProduct(a, I1, OneArray(1), b, I1, OneArray(1), (a.T*b).applyfunc(cos)),
(1, 3), (2, 10), (6, 8), (7, 11))
assert cg.split_multiple_contractions().dummy_eq(expected)
assert convert_array_to_matrix(cg).doit().dummy_eq(MatMul(a, (a.T * b).applyfunc(cos), b.T))