def test_arrayexpr_convert_indexed_to_array_and_back_to_matrix():
expr = a.T * b
elem = expr[0, 0]
cg = convert_indexed_to_array(elem)
assert cg == ArrayElement(
ArrayContraction(ArrayTensorProduct(a, b), (0, 2)), [0, 0])
expr = M[i, j] + N[i, j]
p1, p2 = _convert_indexed_to_array(expr)
assert convert_array_to_matrix(p1) == M + N
expr = M[i, j] + N[j, i]
p1, p2 = _convert_indexed_to_array(expr)
assert convert_array_to_matrix(p1) == M + N.T
expr = M[i, j] * N[k, l] + N[i, j] * M[k, l]
p1, p2 = _convert_indexed_to_array(expr)
assert convert_array_to_matrix(p1) == ArrayAdd(ArrayTensorProduct(M, N),
ArrayTensorProduct(N, M))
expr = (M * N * P)[i, j]
p1, p2 = _convert_indexed_to_array(expr)
assert convert_array_to_matrix(p1) == M * N * P
expr = Sum(M[i, j] * (N * P)[j, m], (j, 0, k - 1))
p1, p2 = _convert_indexed_to_array(expr)
assert convert_array_to_matrix(p1) == M * N * P
expr = Sum((P[j, m] + P[m, j]) * (M[i, j] * N[m, n] + N[i, j] * M[m, n]),
(j, 0, k - 1), (m, 0, k - 1))
p1, p2 = _convert_indexed_to_array(expr)
assert convert_array_to_matrix(
p1) == M * P * N + M * P.T * N + N * P * M + N * P.T * M
def test_arrayexpr_convert_index_to_array_support_function():
expr = M[i, j]
assert _convert_indexed_to_array(expr) == (M, (i, j))
expr = M[i, j] * N[k, l]
assert _convert_indexed_to_array(expr) == (ArrayTensorProduct(M, N),
(i, j, k, l))
expr = M[i, j] * N[j, k]
assert _convert_indexed_to_array(expr) == (ArrayDiagonal(
ArrayTensorProduct(M, N), (1, 2)), (i, k, j))
expr = Sum(M[i, j] * N[j, k], (j, 0, k - 1))
assert _convert_indexed_to_array(expr) == (ArrayContraction(
ArrayTensorProduct(M, N), (1, 2)), (i, k))
expr = M[i, j] + N[i, j]
assert _convert_indexed_to_array(expr) == (ArrayAdd(M, N), (i, j))
expr = M[i, j] + N[j, i]
assert _convert_indexed_to_array(expr) == (ArrayAdd(
M, PermuteDims(N, Permutation([1, 0]))), (i, j))
expr = M[i, j] + M[j, i]
assert _convert_indexed_to_array(expr) == (ArrayAdd(
M, PermuteDims(M, Permutation([1, 0]))), (i, j))
expr = (M * N * P)[i, j]
assert _convert_indexed_to_array(expr) == (_array_contraction(
ArrayTensorProduct(M, N, P), (1, 2), (3, 4)), (i, j))
expr = expr.function # Disregard summation in previous expression
ret1, ret2 = _convert_indexed_to_array(expr)
assert ret1 == ArrayDiagonal(ArrayTensorProduct(M, N, P), (1, 2), (3, 4))
assert str(ret2) == "(i, j, _i_1, _i_2)"
expr = KroneckerDelta(i, j) * M[i, k]
assert _convert_indexed_to_array(expr) == (M, ({i, j}, k))
expr = KroneckerDelta(i, j) * KroneckerDelta(j, k) * M[i, l]
assert _convert_indexed_to_array(expr) == (M, ({i, j, k}, l))
expr = KroneckerDelta(j, k) * (M[i, j] * N[k, l] + N[i, j] * M[k, l])
assert _convert_indexed_to_array(expr) == (_array_diagonal(
_array_add(
ArrayTensorProduct(M, N),
_permute_dims(ArrayTensorProduct(M, N),
Permutation(0, 2)(1, 3))),
(1, 2)), (i, l, frozenset({j, k})))
expr = KroneckerDelta(j, m) * KroneckerDelta(
m, k) * (M[i, j] * N[k, l] + N[i, j] * M[k, l])
assert _convert_indexed_to_array(expr) == (_array_diagonal(
_array_add(
ArrayTensorProduct(M, N),
_permute_dims(ArrayTensorProduct(M, N),
Permutation(0, 2)(1, 3))),
(1, 2)), (i, l, frozenset({j, m, k})))
expr = KroneckerDelta(i, j) * KroneckerDelta(j, k) * KroneckerDelta(
k, m) * M[i, 0] * KroneckerDelta(m, n)
assert _convert_indexed_to_array(expr) == (M, ({i, j, k, m, n}, 0))
expr = M[i, i]
assert _convert_indexed_to_array(expr) == (ArrayDiagonal(M, (0, 1)), (i, ))