def test_parsing_of_matrix_expressions():
expr = M * N
assert parse_matrix_expression(expr) == CodegenArrayContraction(
CodegenArrayTensorProduct(M, N), (1, 2))
expr = Transpose(M)
assert parse_matrix_expression(expr) == CodegenArrayPermuteDims(M, [1, 0])
expr = M * Transpose(N)
assert parse_matrix_expression(expr) == CodegenArrayContraction(
CodegenArrayTensorProduct(M, CodegenArrayPermuteDims(N, [1, 0])),
(1, 2))
expr = 3 * M * N
res = parse_matrix_expression(expr)
rexpr = recognize_matrix_expression(res)
assert expr == rexpr
expr = 3 * M + N * M.T * M + 4 * k * N
res = parse_matrix_expression(expr)
rexpr = recognize_matrix_expression(res)
assert expr == rexpr
expr = Inverse(M) * N
rexpr = recognize_matrix_expression(parse_matrix_expression(expr))
assert expr == rexpr
expr = M**2
rexpr = recognize_matrix_expression(parse_matrix_expression(expr))
assert expr == rexpr
expr = M * (2 * N + 3 * M)
res = parse_matrix_expression(expr)
rexpr = recognize_matrix_expression(res)
assert expr.expand() == rexpr.doit()
expr = Trace(M)
result = CodegenArrayContraction(M, (0, 1))
assert parse_matrix_expression(expr) == result
def test_codegen_extra():
if not np:
skip("NumPy not installed")
M = MatrixSymbol("M", 2, 2)
N = MatrixSymbol("N", 2, 2)
P = MatrixSymbol("P", 2, 2)
Q = MatrixSymbol("Q", 2, 2)
ma = np.matrix([[1, 2], [3, 4]])
mb = np.matrix([[1,-2], [-1, 3]])
mc = np.matrix([[2, 0], [1, 2]])
md = np.matrix([[1,-1], [4, 7]])
cg = CodegenArrayTensorProduct(M, N)
f = lambdify((M, N), cg, 'numpy')
assert (f(ma, mb) == np.einsum(ma, [0, 1], mb, [2, 3])).all()
cg = CodegenArrayElementwiseAdd(M, N)
f = lambdify((M, N), cg, 'numpy')
assert (f(ma, mb) == ma+mb).all()
cg = CodegenArrayElementwiseAdd(M, N, P)
f = lambdify((M, N, P), cg, 'numpy')
assert (f(ma, mb, mc) == ma+mb+mc).all()
cg = CodegenArrayElementwiseAdd(M, N, P, Q)
f = lambdify((M, N, P, Q), cg, 'numpy')
assert (f(ma, mb, mc, md) == ma+mb+mc+md).all()
cg = CodegenArrayPermuteDims(M, [1, 0])
f = lambdify((M,), cg, 'numpy')
assert (f(ma) == ma.T).all()
cg = CodegenArrayPermuteDims(CodegenArrayTensorProduct(M, N), [1, 2, 3, 0])
f = lambdify((M, N), cg, 'numpy')
assert (f(ma, mb) == np.transpose(np.einsum(ma, [0, 1], mb, [2, 3]), (1, 2, 3, 0))).all()
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(M, N), (1, 2))
f = lambdify((M, N), cg, 'numpy')
assert (f(ma, mb) == np.diagonal(np.einsum(ma, [0, 1], mb, [2, 3]), axis1=1, axis2=2)).all()
def test_codegen_array_contraction_construction():
cg = CodegenArrayContraction(A)
assert cg == A
s = Sum(A[i] * B[i], (i, 0, 3))
cg = parse_indexed_expression(s)
assert cg == CodegenArrayContraction(CodegenArrayTensorProduct(A, B),
(0, 1))
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, B), (1, 0))
assert cg == CodegenArrayContraction(CodegenArrayTensorProduct(A, B),
(0, 1))
expr = M * N
result = CodegenArrayContraction(CodegenArrayTensorProduct(M, N), (1, 2))
assert parse_matrix_expression(expr) == result
elem = expr[i, j]
assert parse_indexed_expression(elem) == result
expr = M * N * M
result = CodegenArrayContraction(CodegenArrayTensorProduct(M, N, M),
(1, 2), (3, 4))
assert parse_matrix_expression(expr) == result
elem = expr[i, j]
result = CodegenArrayContraction(CodegenArrayTensorProduct(M, M, N),
(1, 4), (2, 5))
cg = parse_indexed_expression(elem)
cg = cg.sort_args_by_name()
assert cg == result
def tensorproduct(*args):
"""
Tensor product among scalars or array-like objects.
Examples
========
>>> from sympy.tensor.array import tensorproduct, Array
>>> from sympy.abc import x, y, z, t
>>> A = Array([[1, 2], [3, 4]])
>>> B = Array([x, y])
>>> tensorproduct(A, B)
[[[x, y], [2*x, 2*y]], [[3*x, 3*y], [4*x, 4*y]]]
>>> tensorproduct(A, x)
[[x, 2*x], [3*x, 4*x]]
>>> tensorproduct(A, B, B)
[[[[x**2, x*y], [x*y, y**2]], [[2*x**2, 2*x*y], [2*x*y, 2*y**2]]], [[[3*x**2, 3*x*y], [3*x*y, 3*y**2]], [[4*x**2, 4*x*y], [4*x*y, 4*y**2]]]]
Applying this function on two matrices will result in a rank 4 array.
>>> from sympy import Matrix, eye
>>> m = Matrix([[x, y], [z, t]])
>>> p = tensorproduct(eye(3), m)
>>> p
[[[[x, y], [z, t]], [[0, 0], [0, 0]], [[0, 0], [0, 0]]], [[[0, 0], [0, 0]], [[x, y], [z, t]], [[0, 0], [0, 0]]], [[[0, 0], [0, 0]], [[0, 0], [0, 0]], [[x, y], [z, t]]]]
"""
from sympy.tensor.array import SparseNDimArray, ImmutableSparseNDimArray
if len(args) == 0:
return S.One
if len(args) == 1:
return _arrayfy(args[0])
from sympy.codegen.array_utils import _CodegenArrayAbstract, CodegenArrayTensorProduct
from sympy.tensor.array.expressions.array_expressions import _ArrayExpr
if any(isinstance(arg, (_ArrayExpr, _CodegenArrayAbstract)) for arg in args):
return CodegenArrayTensorProduct(*args)
if len(args) > 2:
return tensorproduct(tensorproduct(args[0], args[1]), *args[2:])
# length of args is 2:
a, b = map(_arrayfy, args)
if not isinstance(a, NDimArray) or not isinstance(b, NDimArray):
return a*b
if isinstance(a, SparseNDimArray) and isinstance(b, SparseNDimArray):
lp = len(b)
new_array = {k1*lp + k2: v1*v2 for k1, v1 in a._sparse_array.items() for k2, v2 in b._sparse_array.items()}
return ImmutableSparseNDimArray(new_array, a.shape + b.shape)
product_list = [i*j for i in Flatten(a) for j in Flatten(b)]
return ImmutableDenseNDimArray(product_list, a.shape + b.shape)
def test_codegen_array_shape():
expr = CodegenArrayTensorProduct(M, N, P, Q)
assert expr.shape == (k, k, k, k, k, k, k, k)
Z = MatrixSymbol("Z", m, n)
expr = CodegenArrayTensorProduct(M, Z)
assert expr.shape == (k, k, m, n)
expr2 = CodegenArrayContraction(expr, (0, 1))
assert expr2.shape == (m, n)
expr2 = CodegenArrayDiagonal(expr, (0, 1))
assert expr2.shape == (m, n, k)
exprp = CodegenArrayPermuteDims(expr, [2, 1, 3, 0])
assert exprp.shape == (m, k, n, k)
expr3 = CodegenArrayTensorProduct(N, Z)
expr2 = CodegenArrayElementwiseAdd(expr, expr3)
assert expr2.shape == (k, k, m, n)
# Contraction along axes with discordant dimensions:
raises(ValueError, lambda: CodegenArrayContraction(expr, (1, 2)))
# Also diagonal needs the same dimensions:
raises(ValueError, lambda: CodegenArrayDiagonal(expr, (1, 2)))
# Diagonal requires at least to axes to compute the diagonal:
raises(ValueError, lambda: CodegenArrayDiagonal(expr, (1,)))
def test_nested_array_elementwise_add():
cg = CodegenArrayContraction(
CodegenArrayElementwiseAdd(CodegenArrayTensorProduct(M, N),
CodegenArrayTensorProduct(N, M)), (1, 2))
result = CodegenArrayElementwiseAdd(
CodegenArrayContraction(CodegenArrayTensorProduct(M, N), (1, 2)),
CodegenArrayContraction(CodegenArrayTensorProduct(N, M), (1, 2)))
assert cg == result
cg = CodegenArrayDiagonal(
CodegenArrayElementwiseAdd(CodegenArrayTensorProduct(M, N),
CodegenArrayTensorProduct(N, M)), (1, 2))
result = CodegenArrayElementwiseAdd(
CodegenArrayDiagonal(CodegenArrayTensorProduct(M, N), (1, 2)),
CodegenArrayDiagonal(CodegenArrayTensorProduct(N, M), (1, 2)))
assert cg == result
def test_permute_tensor_product():
cg1 = CodegenArrayPermuteDims(CodegenArrayTensorProduct(M, N, P, Q),
Permutation([2, 3, 1, 0, 5, 4, 6, 7]))
cg2 = CodegenArrayTensorProduct(N, CodegenArrayPermuteDims(M, [1, 0]),
CodegenArrayPermuteDims(P, [1, 0]), Q)
assert cg1 == cg2
# TODO: reverse operation starting with `CodegenArrayPermuteDims` and getting down to `bb`...
cg1 = CodegenArrayPermuteDims(CodegenArrayTensorProduct(M, N, P, Q),
Permutation([2, 3, 4, 5, 0, 1, 6, 7]))
cg2 = CodegenArrayTensorProduct(N, P, M, Q)
assert cg1 == cg2
cg1 = CodegenArrayPermuteDims(CodegenArrayTensorProduct(M, N, P, Q),
Permutation([2, 3, 4, 6, 5, 7, 0, 1]))
assert cg1.expr == CodegenArrayTensorProduct(N, P, Q, M)
assert cg1.permutation == Permutation([0, 1, 2, 4, 3, 5, 6, 7])
cg1 = CodegenArrayContraction(
CodegenArrayPermuteDims(CodegenArrayTensorProduct(N, Q, Q, M),
[2, 1, 5, 4, 0, 3, 6, 7]), [1, 2, 6])
cg2 = CodegenArrayPermuteDims(
CodegenArrayContraction(CodegenArrayTensorProduct(Q, Q, N, M),
(3, 5, 6)), [0, 2, 3, 1, 4])
assert cg1 == cg2
cg1 = CodegenArrayContraction(
CodegenArrayContraction(
CodegenArrayContraction(
CodegenArrayContraction(
CodegenArrayPermuteDims(
CodegenArrayTensorProduct(N, Q, Q, M),
[2, 1, 5, 4, 0, 3, 6, 7]), [1, 2, 6]), [1, 3, 4]),
[1]), [0])
cg2 = CodegenArrayContraction(CodegenArrayTensorProduct(M, N, Q, Q),
(0, 3, 5), (1, 4, 7), (2, ), (6, ))
assert cg1 == cg2
def test_array_expr_zero_array():
za1 = ZeroArray(k, l, m, n)
zm1 = ZeroMatrix(m, n)
za2 = ZeroArray(k, m, m, n)
zm2 = ZeroMatrix(m, m)
zm3 = ZeroMatrix(k, k)
assert CodegenArrayTensorProduct(M, N,
za1) == ZeroArray(k, k, k, k, k, l, m, n)
assert CodegenArrayTensorProduct(M, N, zm1) == ZeroArray(k, k, k, k, m, n)
assert CodegenArrayContraction(za1, (3, )) == ZeroArray(k, l, m)
assert CodegenArrayContraction(zm1, (1, )) == ZeroArray(m)
assert CodegenArrayContraction(za2, (1, 2)) == ZeroArray(k, n)
assert CodegenArrayContraction(zm2, (0, 1)) == 0
assert CodegenArrayDiagonal(za2, (1, 2)) == ZeroArray(k, n, m)
assert CodegenArrayDiagonal(zm2, (0, 1)) == ZeroArray(m)
assert CodegenArrayPermuteDims(za1, [2, 1, 3, 0]) == ZeroArray(m, l, n, k)
assert CodegenArrayPermuteDims(zm1, [1, 0]) == ZeroArray(n, m)
assert CodegenArrayElementwiseAdd(za1) == za1
assert CodegenArrayElementwiseAdd(zm1) == ZeroArray(m, n)
tp1 = CodegenArrayTensorProduct(MatrixSymbol("A", k, l),
MatrixSymbol("B", m, n))
assert CodegenArrayElementwiseAdd(tp1, za1) == tp1
tp2 = CodegenArrayTensorProduct(MatrixSymbol("C", k, l),
MatrixSymbol("D", m, n))
assert CodegenArrayElementwiseAdd(tp1, za1,
tp2) == CodegenArrayElementwiseAdd(
tp1, tp2)
assert CodegenArrayElementwiseAdd(M, zm3) == M
assert CodegenArrayElementwiseAdd(M, N,
zm3) == CodegenArrayElementwiseAdd(M, N)
def test_codegen_array_parse():
expr = M[i, j]
assert _codegen_array_parse(expr) == (M, (i, j))
expr = M[i, j]*N[k, l]
assert _codegen_array_parse(expr) == (CodegenArrayTensorProduct(M, N), (i, j, k, l))
expr = M[i, j]*N[j, k]
assert _codegen_array_parse(expr) == (CodegenArrayDiagonal(CodegenArrayTensorProduct(M, N), (1, 2)), (i, k, j))
expr = Sum(M[i, j]*N[j, k], (j, 0, k-1))
assert _codegen_array_parse(expr) == (CodegenArrayContraction(CodegenArrayTensorProduct(M, N), (1, 2)), (i, k))
expr = M[i, j] + N[i, j]
assert _codegen_array_parse(expr) == (CodegenArrayElementwiseAdd(M, N), (i, j))
expr = M[i, j] + N[j, i]
assert _codegen_array_parse(expr) == (CodegenArrayElementwiseAdd(M, CodegenArrayPermuteDims(N, Permutation([1,0]))), (i, j))
expr = M[i, j] + M[j, i]
assert _codegen_array_parse(expr) == (CodegenArrayElementwiseAdd(M, CodegenArrayPermuteDims(M, Permutation([1,0]))), (i, j))
expr = (M*N*P)[i, j]
assert _codegen_array_parse(expr) == (CodegenArrayContraction(CodegenArrayTensorProduct(M, N, P), (1, 2), (3, 4)), (i, j))
expr = expr.function # Disregard summation in previous expression
ret1, ret2 = _codegen_array_parse(expr)
assert ret1 == CodegenArrayDiagonal(CodegenArrayTensorProduct(M, N, P), (1, 2), (3, 4))
assert str(ret2) == "(i, j, _i_1, _i_2)"
expr = KroneckerDelta(i, j)*M[i, k]
assert _codegen_array_parse(expr) == (M, ({i, j}, k))
expr = KroneckerDelta(i, j)*KroneckerDelta(j, k)*M[i, l]
assert _codegen_array_parse(expr) == (M, ({i, j, k}, l))
expr = KroneckerDelta(j, k)*(M[i, j]*N[k, l] + N[i, j]*M[k, l])
assert _codegen_array_parse(expr) == (CodegenArrayDiagonal(CodegenArrayElementwiseAdd(
CodegenArrayTensorProduct(M, N),
CodegenArrayPermuteDims(CodegenArrayTensorProduct(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 _codegen_array_parse(expr) == (CodegenArrayDiagonal(CodegenArrayElementwiseAdd(
CodegenArrayTensorProduct(M, N),
CodegenArrayPermuteDims(CodegenArrayTensorProduct(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 _codegen_array_parse(expr) == (M, ({i,j,k,m,n}, 0))
expr = M[i, i]
assert _codegen_array_parse(expr) == (CodegenArrayDiagonal(M, (0, 1)), (i,))
def test_codegen_array_doit():
M = MatrixSymbol("M", 2, 2)
N = MatrixSymbol("N", 2, 2)
P = MatrixSymbol("P", 2, 2)
Q = MatrixSymbol("Q", 2, 2)
M = M.as_explicit()
N = N.as_explicit()
P = P.as_explicit()
Q = Q.as_explicit()
expr = CodegenArrayTensorProduct(M, N, P, Q)
assert expr.doit() == tensorproduct(M, N, P, Q)
expr2 = CodegenArrayContraction(expr, (0, 1))
assert expr2.doit() == tensorcontraction(tensorproduct(M, N, P, Q), (0, 1))
expr2 = CodegenArrayDiagonal(expr, (0, 1))
#assert expr2 = ... # TODO: not implemented
expr = CodegenArrayTensorProduct(M, N)
exprp = CodegenArrayPermuteDims(expr, [2, 1, 3, 0])
assert exprp.doit() == permutedims(tensorproduct(M, N), [2, 1, 3, 0])
expr = CodegenArrayElementwiseAdd(M, N)
assert expr.doit() == M + N
def test_diag2contraction_diagmatrix():
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(M, a), (1, 2))
res = _array_diag2contr_diagmatrix(cg)
assert res.shape == cg.shape
assert res == CodegenArrayContraction(CodegenArrayTensorProduct(M, OneArray(1), DiagMatrix(a)), (1, 3))
raises(ValueError, lambda: CodegenArrayDiagonal(CodegenArrayTensorProduct(a, M), (1, 2)))
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(a.T, M), (1, 2))
res = _array_diag2contr_diagmatrix(cg)
assert res.shape == cg.shape
assert res == CodegenArrayContraction(CodegenArrayTensorProduct(OneArray(1), M, DiagMatrix(a.T)), (1, 4))
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(a.T, M, N, b.T), (1, 2), (4, 7))
res = _array_diag2contr_diagmatrix(cg)
assert res.shape == cg.shape
assert res == CodegenArrayContraction(
CodegenArrayTensorProduct(OneArray(1), M, N, OneArray(1), DiagMatrix(a.T), DiagMatrix(b.T)), (1, 7), (3, 9))
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(a, M, N, b.T), (0, 2), (4, 7))
res = _array_diag2contr_diagmatrix(cg)
assert res.shape == cg.shape
assert res == CodegenArrayContraction(
CodegenArrayTensorProduct(OneArray(1), M, N, OneArray(1), DiagMatrix(a), DiagMatrix(b.T)), (1, 6), (3, 9))
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(a, M, N, b.T), (0, 4), (3, 7))
res = _array_diag2contr_diagmatrix(cg)
assert res.shape == cg.shape
assert res == CodegenArrayContraction(
CodegenArrayTensorProduct(OneArray(1), M, N, OneArray(1), DiagMatrix(a), DiagMatrix(b.T)), (3, 6), (2, 9))
def test_remove_trivial_dims():
# Tensor Product:
assert _remove_trivial_dims(CodegenArrayTensorProduct(a, b)) == (a * b.T, [1, 3])
assert _remove_trivial_dims(CodegenArrayTensorProduct(a.T, b)) == (a * b.T, [0, 3])
assert _remove_trivial_dims(CodegenArrayTensorProduct(a, b.T)) == (a * b.T, [1, 2])
assert _remove_trivial_dims(CodegenArrayTensorProduct(a.T, b.T)) == (a * b.T, [0, 2])
assert _remove_trivial_dims(CodegenArrayTensorProduct(I, a.T, b.T)) == (a * b.T, [0, 1, 2, 4])
assert _remove_trivial_dims(CodegenArrayTensorProduct(a.T, I, b.T)) == (a * b.T, [0, 2, 3, 4])
assert _remove_trivial_dims(CodegenArrayTensorProduct(a, I)) == (a, [2, 3])
assert _remove_trivial_dims(CodegenArrayTensorProduct(I, a)) == (a, [0, 1])
assert _remove_trivial_dims(CodegenArrayTensorProduct(a.T, b.T, c, d)) == (
CodegenArrayTensorProduct(a * b.T, c * d.T), [0, 2, 5, 7])
assert _remove_trivial_dims(CodegenArrayTensorProduct(a.T, I, b.T, c, d, I)) == (
CodegenArrayTensorProduct(a * b.T, c * d.T, I), [0, 2, 3, 4, 7, 9])
# Addition:
cg = CodegenArrayElementwiseAdd(CodegenArrayTensorProduct(a, b), CodegenArrayTensorProduct(c, d))
assert _remove_trivial_dims(cg) == (a * b.T + c * d.T, [1, 3])
# Permute Dims:
cg = CodegenArrayPermuteDims(CodegenArrayTensorProduct(a, b), Permutation(3)(1, 2))
assert _remove_trivial_dims(cg) == (a * b.T, [2, 3])
cg = CodegenArrayPermuteDims(CodegenArrayTensorProduct(a, I, b), Permutation(5)(1, 2, 3, 4))
assert _remove_trivial_dims(cg) == (a * b.T, [2, 3, 4, 5])
cg = CodegenArrayPermuteDims(CodegenArrayTensorProduct(I, b, a), Permutation(5)(1, 2, 4, 5, 3))
assert _remove_trivial_dims(cg) == (b * a.T, [0, 1, 2, 3])
# Diagonal:
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(M, a), (1, 2))
assert _remove_trivial_dims(cg) == (cg, [])
# Contraction:
cg = CodegenArrayContraction(CodegenArrayTensorProduct(M, a), (1, 2))
assert _remove_trivial_dims(cg) == (cg, [])
def test_array_wrong_permutation_size():
cg = CodegenArrayTensorProduct(M, N)
raises(ValueError, lambda: CodegenArrayPermuteDims(cg, [1, 0]))
raises(ValueError, lambda: CodegenArrayPermuteDims(cg, [1, 0, 2, 3, 5, 4]))
def test_contraction_permutation_mix():
Me = M.subs(k, 3).as_explicit()
Ne = N.subs(k, 3).as_explicit()
cg1 = CodegenArrayContraction(CodegenArrayPermuteDims(CodegenArrayTensorProduct(M, N), Permutation([0, 2, 1, 3])), (2, 3))
cg2 = CodegenArrayContraction(CodegenArrayTensorProduct(M, N), (1, 3))
assert cg1 == cg2
assert recognize_matrix_expression(cg2) == M*N.T
cge1 = tensorcontraction(permutedims(tensorproduct(Me, Ne), Permutation([0, 2, 1, 3])), (2, 3))
cge2 = tensorcontraction(tensorproduct(Me, Ne), (1, 3))
assert cge1 == cge2
cg1 = CodegenArrayPermuteDims(CodegenArrayTensorProduct(M, N), Permutation([0, 1, 3, 2]))
cg2 = CodegenArrayTensorProduct(M, CodegenArrayPermuteDims(N, Permutation([1, 0])))
assert cg1 == cg2
assert recognize_matrix_expression(cg1) == CodegenArrayTensorProduct(M, N.T)
assert recognize_matrix_expression(cg2) == CodegenArrayTensorProduct(M, N.T)
cg1 = CodegenArrayContraction(
CodegenArrayPermuteDims(
CodegenArrayTensorProduct(M, N, P, Q), Permutation([0, 2, 3, 1, 4, 5, 7, 6])),
(1, 2), (3, 5)
)
cg2 = CodegenArrayContraction(
CodegenArrayTensorProduct(M, N, P, CodegenArrayPermuteDims(Q, Permutation([1, 0]))),
(1, 5), (2, 3)
)
assert cg1 == cg2
assert recognize_matrix_expression(cg1) == CodegenArrayTensorProduct(M*P.T*Trace(N), Q.T)
assert recognize_matrix_expression(cg2) == CodegenArrayTensorProduct(M*P.T*Trace(N), Q.T)
cg1 = CodegenArrayContraction(
CodegenArrayPermuteDims(
CodegenArrayTensorProduct(M, N, P, Q), Permutation([1, 0, 4, 6, 2, 7, 5, 3])),
(0, 1), (2, 6), (3, 7)
)
cg2 = CodegenArrayPermuteDims(
CodegenArrayContraction(
CodegenArrayTensorProduct(M, P, Q, N),
(0, 1), (2, 3), (4, 7)),
[1, 0]
)
assert cg1 == cg2
cg1 = CodegenArrayContraction(
CodegenArrayPermuteDims(
CodegenArrayTensorProduct(M, N, P, Q), Permutation([1, 0, 4, 6, 7, 2, 5, 3])),
(0, 1), (2, 6), (3, 7)
)
cg2 = CodegenArrayPermuteDims(
CodegenArrayContraction(
CodegenArrayTensorProduct(CodegenArrayPermuteDims(M, [1, 0]), N, P, Q),
(0, 1), (3, 6), (4, 5)
),
Permutation([1, 0])
)
assert cg1 == cg2
def test_parsing_of_matrix_expressions():
expr = M*N
assert parse_matrix_expression(expr) == CodegenArrayContraction(CodegenArrayTensorProduct(M, N), (1, 2))
expr = Transpose(M)
assert parse_matrix_expression(expr) == CodegenArrayPermuteDims(M, [1, 0])
expr = M*Transpose(N)
assert parse_matrix_expression(expr) == CodegenArrayContraction(CodegenArrayTensorProduct(M, CodegenArrayPermuteDims(N, [1, 0])), (1, 2))
expr = 3*M*N
res = parse_matrix_expression(expr)
rexpr = recognize_matrix_expression(res)
assert expr == rexpr
expr = 3*M + N*M.T*M + 4*k*N
res = parse_matrix_expression(expr)
rexpr = recognize_matrix_expression(res)
assert expr == rexpr
expr = Inverse(M)*N
rexpr = recognize_matrix_expression(parse_matrix_expression(expr))
assert expr == rexpr
expr = M**2
rexpr = recognize_matrix_expression(parse_matrix_expression(expr))
assert expr == rexpr
expr = M*(2*N + 3*M)
res = parse_matrix_expression(expr)
rexpr = recognize_matrix_expression(res)
assert expr == rexpr
expr = Trace(M)
result = CodegenArrayContraction(M, (0, 1))
assert parse_matrix_expression(expr) == result
expr = 3*Trace(M)
result = CodegenArrayContraction(CodegenArrayTensorProduct(3, M), (0, 1))
assert parse_matrix_expression(expr) == result
expr = 3*Trace(Trace(M) * M)
result = CodegenArrayContraction(CodegenArrayTensorProduct(3, M, M), (0, 1), (2, 3))
assert parse_matrix_expression(expr) == result
expr = 3*Trace(M)**2
result = CodegenArrayContraction(CodegenArrayTensorProduct(3, M, M), (0, 1), (2, 3))
assert parse_matrix_expression(expr) == result
expr = HadamardProduct(M, N)
result = CodegenArrayDiagonal(CodegenArrayTensorProduct(M, N), (0, 2), (1, 3))
assert parse_matrix_expression(expr) == result
expr = HadamardPower(M, 2)
result = CodegenArrayDiagonal(CodegenArrayTensorProduct(M, M), (0, 2), (1, 3))
assert parse_matrix_expression(expr) == result
expr = M**2
assert isinstance(expr, MatPow)
assert parse_matrix_expression(expr) == CodegenArrayContraction(CodegenArrayTensorProduct(M, M), (1, 2))
def _(expr: MatrixSymbol, x: Expr):
m, n = expr.shape
if expr == x:
return CodegenArrayPermuteDims(
CodegenArrayTensorProduct(Identity(m), Identity(n)), [0, 2, 1, 3])
return ZeroArray(*(x.shape + expr.shape))
def test_codegen_array_diagonal():
cg = CodegenArrayDiagonal(M, (1, 0))
assert cg == CodegenArrayDiagonal(M, (0, 1))
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(M, N, P), (4, 1), (2, 0))
assert cg == CodegenArrayDiagonal(CodegenArrayTensorProduct(M, N, P), (1, 4), (0, 2))
def test_recognize_diagonalized_vectors():
a = MatrixSymbol("a", k, 1)
b = MatrixSymbol("b", k, 1)
A = MatrixSymbol("A", k, k)
B = MatrixSymbol("B", k, k)
C = MatrixSymbol("C", k, k)
X = MatrixSymbol("X", k, k)
x = MatrixSymbol("x", k, 1)
I1 = Identity(1)
I = Identity(k)
# Check matrix recognition over trivial dimensions:
cg = CodegenArrayTensorProduct(a, b)
assert recognize_matrix_expression(cg) == a*b.T
cg = CodegenArrayTensorProduct(I1, a, b)
assert recognize_matrix_expression(cg) == a*I1*b.T
# Recognize trace inside a tensor product:
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, B, C), (0, 3), (1, 2))
assert recognize_matrix_expression(cg) == Trace(A*B)*C
# Transform diagonal operator to contraction:
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(A, a), (1, 2))
assert cg.transform_to_product() == CodegenArrayContraction(CodegenArrayTensorProduct(A, DiagonalizeVector(a)), (1, 2))
assert recognize_matrix_expression(cg) == A*DiagonalizeVector(a)
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(a, b), (0, 2))
assert cg.transform_to_product() == CodegenArrayContraction(CodegenArrayTensorProduct(DiagonalizeVector(a), b), (0, 2))
assert recognize_matrix_expression(cg).doit() == DiagonalizeVector(a)*b
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(A, a), (0, 2))
assert cg.transform_to_product() == CodegenArrayContraction(CodegenArrayTensorProduct(A, DiagonalizeVector(a)), (0, 2))
assert recognize_matrix_expression(cg) == A.T*DiagonalizeVector(a)
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(I, x, I1), (0, 2), (3, 5))
assert cg.transform_to_product() == CodegenArrayContraction(CodegenArrayTensorProduct(I, DiagonalizeVector(x), I1), (0, 2))
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(I, x, A, B), (1, 2), (5, 6))
assert cg.transform_to_product() == CodegenArrayDiagonal(CodegenArrayContraction(CodegenArrayTensorProduct(I, DiagonalizeVector(x), A, B), (1, 2)), (3, 4))
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(x, I1), (1, 2))
assert isinstance(cg, CodegenArrayDiagonal)
assert cg.diagonal_indices == ((1, 2),)
assert recognize_matrix_expression(cg) == x
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(x, I), (0, 2))
assert cg.transform_to_product() == CodegenArrayContraction(CodegenArrayTensorProduct(DiagonalizeVector(x), I), (0, 2))
assert recognize_matrix_expression(cg).doit() == DiagonalizeVector(x)
cg = CodegenArrayDiagonal(x, (1,))
assert cg == x
# Ignore identity matrices with contractions:
cg = CodegenArrayContraction(CodegenArrayTensorProduct(I, A, I, I), (0, 2), (1, 3), (5, 7))
assert cg.split_multiple_contractions() == cg
assert recognize_matrix_expression(cg) == Trace(A)*I
cg = CodegenArrayContraction(CodegenArrayTensorProduct(Trace(A) * I, I, I), (1, 5), (3, 4))
assert cg.split_multiple_contractions() == cg
assert recognize_matrix_expression(cg).doit() == Trace(A)*I
# Add DiagonalizeVector when required:
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a), (1, 2))
assert cg.split_multiple_contractions() == cg
assert recognize_matrix_expression(cg) == A*a
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a, B), (1, 2, 4))
assert cg.split_multiple_contractions() == CodegenArrayContraction(CodegenArrayTensorProduct(A, DiagonalizeVector(a), B), (1, 2), (3, 4))
assert recognize_matrix_expression(cg) == A*DiagonalizeVector(a)*B
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a, B), (0, 2, 4))
assert cg.split_multiple_contractions() == CodegenArrayContraction(CodegenArrayTensorProduct(A, DiagonalizeVector(a), B), (0, 2), (3, 4))
assert recognize_matrix_expression(cg) == A.T*DiagonalizeVector(a)*B
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a, b, a.T, B), (0, 2, 4, 7, 9))
assert cg.split_multiple_contractions() == CodegenArrayContraction(CodegenArrayTensorProduct(A, DiagonalizeVector(a), DiagonalizeVector(b),
DiagonalizeVector(a), B),
(0, 2), (3, 4), (5, 7), (6, 9))
assert recognize_matrix_expression(cg).doit() == A.T*DiagonalizeVector(a)*DiagonalizeVector(b)*DiagonalizeVector(a)*B.T
cg = CodegenArrayContraction(CodegenArrayTensorProduct(I1, I1, I1), (1, 2, 4))
assert cg.split_multiple_contractions() == CodegenArrayContraction(CodegenArrayTensorProduct(I1, I1, I1), (1, 2), (3, 4))
assert recognize_matrix_expression(cg).doit() == Identity(1)
cg = CodegenArrayContraction(CodegenArrayTensorProduct(I, I, I, I, A), (1, 2, 8), (5, 6, 9))
assert recognize_matrix_expression(cg.split_multiple_contractions()).doit() == A
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a, C, a, B), (1, 2, 4), (5, 6, 8))
assert cg.split_multiple_contractions() == CodegenArrayContraction(CodegenArrayTensorProduct(A, DiagonalizeVector(a), C, DiagonalizeVector(a), B), (1, 2), (3, 4), (5, 6), (7, 8))
assert recognize_matrix_expression(cg) == A*DiagonalizeVector(a)*C*DiagonalizeVector(a)*B
cg = CodegenArrayContraction(CodegenArrayTensorProduct(a, I1, b, I1, (a.T*b).applyfunc(cos)), (1, 2, 8), (5, 6, 9))
assert cg.split_multiple_contractions() == CodegenArrayContraction(CodegenArrayTensorProduct(a, I1, b, I1, (a.T*b).applyfunc(cos)), (1, 2), (3, 8), (5, 6), (7, 9))
assert recognize_matrix_expression(cg) == MatMul(a, I1, (a.T*b).applyfunc(cos), Transpose(I1), b.T)
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A.T, a, b, b.T, (A*X*b).applyfunc(cos)), (1, 2, 8), (5, 6, 9))
assert cg.split_multiple_contractions() == CodegenArrayContraction(
CodegenArrayTensorProduct(A.T, DiagonalizeVector(a), b, b.T, (A*X*b).applyfunc(cos)),
(1, 2), (3, 8), (5, 6, 9))
# assert recognize_matrix_expression(cg)
# Check no overlap of lines:
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a, C, a, B), (1, 2, 4), (5, 6, 8), (3, 7))
assert cg.split_multiple_contractions() == cg
cg = CodegenArrayContraction(CodegenArrayTensorProduct(a, b, A), (0, 2, 4), (1, 3))
assert cg.split_multiple_contractions() == cg
def test_codegen_array_flatten():
# Flatten nested CodegenArrayTensorProduct objects:
expr1 = CodegenArrayTensorProduct(M, N)
expr2 = CodegenArrayTensorProduct(P, Q)
expr = CodegenArrayTensorProduct(expr1, expr2)
assert expr == CodegenArrayTensorProduct(M, N, P, Q)
assert expr.args == (M, N, P, Q)
# Flatten mixed CodegenArrayTensorProduct and CodegenArrayContraction objects:
cg1 = CodegenArrayContraction(expr1, (1, 2))
cg2 = CodegenArrayContraction(expr2, (0, 3))
expr = CodegenArrayTensorProduct(cg1, cg2)
assert expr == CodegenArrayContraction(
CodegenArrayTensorProduct(M, N, P, Q), (1, 2), (4, 7))
expr = CodegenArrayTensorProduct(M, cg1)
assert expr == CodegenArrayContraction(CodegenArrayTensorProduct(M, M, N),
(3, 4))
# Flatten nested CodegenArrayContraction objects:
cgnested = CodegenArrayContraction(cg1, (0, 1))
assert cgnested == CodegenArrayContraction(CodegenArrayTensorProduct(M, N),
(0, 3), (1, 2))
cgnested = CodegenArrayContraction(CodegenArrayTensorProduct(cg1, cg2),
(0, 3))
assert cgnested == CodegenArrayContraction(
CodegenArrayTensorProduct(M, N, P, Q), (0, 6), (1, 2), (4, 7))
cg3 = CodegenArrayContraction(CodegenArrayTensorProduct(M, N, P, Q),
(1, 3), (2, 4))
cgnested = CodegenArrayContraction(cg3, (0, 1))
assert cgnested == CodegenArrayContraction(
CodegenArrayTensorProduct(M, N, P, Q), (0, 5), (1, 3), (2, 4))
cgnested = CodegenArrayContraction(cg3, (0, 3), (1, 2))
assert cgnested == CodegenArrayContraction(
CodegenArrayTensorProduct(M, N, P, Q), (0, 7), (1, 3), (2, 4), (5, 6))
cg4 = CodegenArrayContraction(CodegenArrayTensorProduct(M, N, P, Q),
(1, 5), (3, 7))
cgnested = CodegenArrayContraction(cg4, (0, 1))
assert cgnested == CodegenArrayContraction(
CodegenArrayTensorProduct(M, N, P, Q), (0, 2), (1, 5), (3, 7))
cgnested = CodegenArrayContraction(cg4, (0, 1), (2, 3))
assert cgnested == CodegenArrayContraction(
CodegenArrayTensorProduct(M, N, P, Q), (0, 2), (1, 5), (3, 7), (4, 6))
cg = CodegenArrayDiagonal(cg4)
assert cg == cg4
assert isinstance(cg, type(cg4))
# Flatten nested CodegenArrayDiagonal objects:
cg1 = CodegenArrayDiagonal(expr1, (1, 2))
cg2 = CodegenArrayDiagonal(expr2, (0, 3))
cg3 = CodegenArrayDiagonal(CodegenArrayTensorProduct(M, N, P, Q), (1, 3),
(2, 4))
cg4 = CodegenArrayDiagonal(CodegenArrayTensorProduct(M, N, P, Q), (1, 5),
(3, 7))
cgnested = CodegenArrayDiagonal(cg1, (0, 1))
assert cgnested == CodegenArrayDiagonal(CodegenArrayTensorProduct(M, N),
(1, 2), (0, 3))
cgnested = CodegenArrayDiagonal(cg3, (1, 2))
assert cgnested == CodegenArrayDiagonal(
CodegenArrayTensorProduct(M, N, P, Q), (1, 3), (2, 4), (5, 6))
cgnested = CodegenArrayDiagonal(cg4, (1, 2))
assert cgnested == CodegenArrayDiagonal(
CodegenArrayTensorProduct(M, N, P, Q), (1, 5), (3, 7), (2, 4))
def test_recognize_diagonalized_vectors():
a = MatrixSymbol("a", k, 1)
b = MatrixSymbol("b", k, 1)
A = MatrixSymbol("A", k, k)
B = MatrixSymbol("B", k, k)
C = MatrixSymbol("C", k, k)
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a), (1, 2))
assert cg.split_multiple_contractions() == cg
assert recognize_matrix_expression(cg) == A * a
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a, B), (1, 2, 4))
assert cg.split_multiple_contractions() == CodegenArrayContraction(
CodegenArrayTensorProduct(A, DiagonalizeVector(a), B), (1, 2), (3, 4))
assert recognize_matrix_expression(cg) == A * DiagonalizeVector(a) * B
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a, B), (0, 2, 4))
assert cg.split_multiple_contractions() == CodegenArrayContraction(
CodegenArrayTensorProduct(A, DiagonalizeVector(a), B), (0, 2), (3, 4))
assert recognize_matrix_expression(cg) == A.T * DiagonalizeVector(a) * B
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a, b, a.T, B),
(0, 2, 4, 7, 9))
assert cg.split_multiple_contractions() == CodegenArrayContraction(
CodegenArrayTensorProduct(A,
DiagonalizeVector(a), DiagonalizeVector(b),
DiagonalizeVector(a), B), (0, 2), (3, 4),
(5, 7), (6, 9))
assert recognize_matrix_expression(cg).doit() == A.T * DiagonalizeVector(
a) * DiagonalizeVector(b) * DiagonalizeVector(a) * B.T
I1 = Identity(1)
cg = CodegenArrayContraction(CodegenArrayTensorProduct(I1, I1, I1),
(1, 2, 4))
assert cg.split_multiple_contractions() == CodegenArrayContraction(
CodegenArrayTensorProduct(I1, I1, I1), (1, 2), (3, 4))
assert recognize_matrix_expression(cg).doit() == Identity(1)
I = Identity(k)
cg = CodegenArrayContraction(CodegenArrayTensorProduct(I, I, I, I, A),
(1, 2, 8), (5, 6, 9))
assert recognize_matrix_expression(
cg.split_multiple_contractions()).doit() == A
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a, C, a, B),
(1, 2, 4), (5, 6, 8))
assert cg.split_multiple_contractions() == CodegenArrayContraction(
CodegenArrayTensorProduct(A, DiagonalizeVector(a), C,
DiagonalizeVector(a), B), (1, 2), (3, 4),
(5, 6), (7, 8))
assert recognize_matrix_expression(
cg) == A * DiagonalizeVector(a) * C * DiagonalizeVector(a) * B
cg = CodegenArrayContraction(
CodegenArrayTensorProduct(a, I1, b, I1, (a.T * b).applyfunc(cos)),
(1, 2, 8), (5, 6, 9))
assert cg.split_multiple_contractions() == CodegenArrayContraction(
CodegenArrayTensorProduct(a, I1, b, I1, (a.T * b).applyfunc(cos)),
(1, 2), (3, 8), (5, 6), (7, 9))
assert recognize_matrix_expression(cg) == MatMul(a, I1,
(a.T * b).applyfunc(cos),
Transpose(I1), b.T)
# Check no overlap of lines:
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a, C, a, B),
(1, 2, 4), (5, 6, 8), (3, 7))
raises(ValueError, lambda: cg.split_multiple_contractions())
cg = CodegenArrayContraction(CodegenArrayTensorProduct(a, b, A), (0, 2, 4),
(1, 3))
raises(ValueError, lambda: cg.split_multiple_contractions())
def test_diag2contraction_diagmatrix():
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(M, a), (1, 2))
res = _array_diag2contr_diagmatrix(cg)
assert res.shape == cg.shape
assert res == CodegenArrayContraction(
CodegenArrayTensorProduct(M, OneArray(1), DiagMatrix(a)), (1, 3))
raises(
ValueError,
lambda: CodegenArrayDiagonal(CodegenArrayTensorProduct(a, M), (1, 2)))
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(a.T, M), (1, 2))
res = _array_diag2contr_diagmatrix(cg)
assert res.shape == cg.shape
assert res == CodegenArrayContraction(
CodegenArrayTensorProduct(OneArray(1), M, DiagMatrix(a.T)), (1, 4))
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(a.T, M, N, b.T),
(1, 2), (4, 7))
res = _array_diag2contr_diagmatrix(cg)
assert res.shape == cg.shape
assert res == CodegenArrayContraction(
CodegenArrayTensorProduct(OneArray(1), M, N, OneArray(1),
DiagMatrix(a.T), DiagMatrix(b.T)), (1, 7),
(3, 9))
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(a, M, N, b.T), (0, 2),
(4, 7))
res = _array_diag2contr_diagmatrix(cg)
assert res.shape == cg.shape
assert res == CodegenArrayContraction(
CodegenArrayTensorProduct(OneArray(1),
M, N, OneArray(1), DiagMatrix(a),
DiagMatrix(b.T)), (1, 6), (3, 9))
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(a, M, N, b.T), (0, 4),
(3, 7))
res = _array_diag2contr_diagmatrix(cg)
assert res.shape == cg.shape
assert res == CodegenArrayContraction(
CodegenArrayTensorProduct(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 = CodegenArrayDiagonal(CodegenArrayTensorProduct(x, A.T, I1), (0, 2))
assert _array_diag2contr_diagmatrix(cg).shape == cg.shape
assert array2matrix(cg).shape == cg.shape
def test_recognize_products_support_function():
A = MatrixSymbol("A", k, k)
B = MatrixSymbol("B", k, k)
C = MatrixSymbol("C", k, k)
D = MatrixSymbol("D", k, k)
X = MatrixSymbol("X", k, k)
Y = MatrixSymbol("Y", k, k)
assert _support_function_tp1_recognize([], [2 * k]) == 2 * k
assert _support_function_tp1_recognize([(1, 2)],
[A, 2 * k, B, 3]) == 6 * k * A * B
assert _support_function_tp1_recognize([(0, 3), (1, 2)],
[A, B]) == Trace(A * B)
assert _support_function_tp1_recognize([(1, 2)], [A, B]) == A * B
assert _support_function_tp1_recognize([(0, 2)], [A, B]) == A.T * B
assert _support_function_tp1_recognize([(1, 3)], [A, B]) == A * B.T
assert _support_function_tp1_recognize([(0, 3)], [A, B]) == A.T * B.T
assert _support_function_tp1_recognize(
[(1, 2),
(5, 6)], [A, B, C, D]) == CodegenArrayTensorProduct(A * B, C * D)
assert _support_function_tp1_recognize(
[(1, 4), (3, 6)], [A, B, C, D]) == CodegenArrayPermuteDims(
CodegenArrayTensorProduct(A * C, B * D), [0, 2, 1, 3])
assert _support_function_tp1_recognize([(0, 3), (1, 4)],
[A, B, C]) == B * A * C
assert _support_function_tp1_recognize(
[(9, 10), (1, 2), (5, 6), (3, 4),
(7, 8)], [X, Y, A, B, C, D]) == X * Y * A * B * C * D
assert _support_function_tp1_recognize(
[(9, 10), (1, 2), (5, 6), (3, 4)],
[X, Y, A, B, C, D]) == CodegenArrayTensorProduct(X * Y * A * B, C * D)
assert _support_function_tp1_recognize(
[(1, 7), (3, 8),
(4, 11)], [X, Y, A, B, C, D]) == CodegenArrayPermuteDims(
CodegenArrayTensorProduct(X * B.T, Y * C, D * A),
[0, 2, 5, 1, 3, 4])
assert _support_function_tp1_recognize(
[(0, 1), (3, 6), (5, 8)], [X, A, B, C, D]) == CodegenArrayPermuteDims(
CodegenArrayTensorProduct(Trace(X) * A * C, B * D), [0, 2, 1, 3])
assert _support_function_tp1_recognize([(1, 2), (3, 4), (5, 6), (7, 8)],
[A, A, B, C, D]) == A**2 * B * C * D
assert _support_function_tp1_recognize(
[(1, 2), (3, 4), (5, 6), (7, 8)], [X, A, B, C, D]) == X * A * B * C * D
assert _support_function_tp1_recognize(
[(1, 6), (3, 8), (5, 10)],
[X, Y, A, B, C, D]) == CodegenArrayPermuteDims(
CodegenArrayTensorProduct(X * B, Y * C, A * D), [0, 2, 4, 1, 3, 5])
assert _support_function_tp1_recognize(
[(1, 4), (3, 6)], [A, B, C, D]) == CodegenArrayPermuteDims(
CodegenArrayTensorProduct(A * C, B * D), [0, 2, 1, 3])
assert _support_function_tp1_recognize(
[(0, 4), (1, 7), (2, 5),
(3, 8)], [X, A, B, C, D]) == C * X.T * B * A * D
assert _support_function_tp1_recognize(
[(0, 4), (1, 7), (2, 5),
(3, 8)], [X, A, B, C, D]) == C * X.T * B * A * D
def test_codegen_permutedims_sink():
cg = CodegenArrayPermuteDims(CodegenArrayTensorProduct(M, N), [0, 1, 3, 2])
sunk = cg.nest_permutation()
assert sunk == CodegenArrayTensorProduct(
M, CodegenArrayPermuteDims(N, [1, 0]))
assert recognize_matrix_expression(sunk) == [M, N.T]
cg = CodegenArrayPermuteDims(CodegenArrayTensorProduct(M, N), [1, 0, 3, 2])
sunk = cg.nest_permutation()
assert sunk == CodegenArrayTensorProduct(
CodegenArrayPermuteDims(M, [1, 0]), CodegenArrayPermuteDims(N, [1, 0]))
assert recognize_matrix_expression(sunk) == [M.T, N.T]
cg = CodegenArrayPermuteDims(CodegenArrayTensorProduct(M, N), [3, 2, 1, 0])
sunk = cg.nest_permutation()
assert sunk == CodegenArrayTensorProduct(
CodegenArrayPermuteDims(N, [1, 0]), CodegenArrayPermuteDims(M, [1, 0]))
assert recognize_matrix_expression(sunk) == [N.T, M.T]
cg = CodegenArrayPermuteDims(
CodegenArrayContraction(CodegenArrayTensorProduct(M, N), (1, 2)),
[1, 0])
sunk = cg.nest_permutation()
assert sunk == CodegenArrayContraction(
CodegenArrayPermuteDims(CodegenArrayTensorProduct(M, N), [[0, 3]]),
(1, 2))
cg = CodegenArrayPermuteDims(CodegenArrayTensorProduct(M, N), [1, 0, 3, 2])
sunk = cg.nest_permutation()
assert sunk == CodegenArrayTensorProduct(
CodegenArrayPermuteDims(M, [1, 0]), CodegenArrayPermuteDims(N, [1, 0]))
cg = CodegenArrayPermuteDims(
CodegenArrayContraction(CodegenArrayTensorProduct(M, N, P), (1, 2),
(3, 4)), [1, 0])
sunk = cg.nest_permutation()
assert sunk == CodegenArrayContraction(
CodegenArrayPermuteDims(CodegenArrayTensorProduct(M, N, P), [[0, 5]]),
(1, 2), (3, 4))
def test_codegen_extra():
if not tf:
skip("TensorFlow not installed")
graph = tf.Graph()
with graph.as_default():
session = tf.compat.v1.Session()
M = MatrixSymbol("M", 2, 2)
N = MatrixSymbol("N", 2, 2)
P = MatrixSymbol("P", 2, 2)
Q = MatrixSymbol("Q", 2, 2)
ma = tf.constant([[1, 2], [3, 4]])
mb = tf.constant([[1, -2], [-1, 3]])
mc = tf.constant([[2, 0], [1, 2]])
md = tf.constant([[1, -1], [4, 7]])
cg = CodegenArrayTensorProduct(M, N)
assert tensorflow_code(cg) == \
'tensorflow.linalg.einsum("ab,cd", M, N)'
f = lambdify((M, N), cg, 'tensorflow')
y = session.run(f(ma, mb))
c = session.run(tf.einsum("ij,kl", ma, mb))
assert (y == c).all()
cg = CodegenArrayElementwiseAdd(M, N)
assert tensorflow_code(cg) == 'tensorflow.math.add(M, N)'
f = lambdify((M, N), cg, 'tensorflow')
y = session.run(f(ma, mb))
c = session.run(ma + mb)
assert (y == c).all()
cg = CodegenArrayElementwiseAdd(M, N, P)
assert tensorflow_code(cg) == \
'tensorflow.math.add(tensorflow.math.add(M, N), P)'
f = lambdify((M, N, P), cg, 'tensorflow')
y = session.run(f(ma, mb, mc))
c = session.run(ma + mb + mc)
assert (y == c).all()
cg = CodegenArrayElementwiseAdd(M, N, P, Q)
assert tensorflow_code(cg) == \
'tensorflow.math.add(' \
'tensorflow.math.add(tensorflow.math.add(M, N), P), Q)'
f = lambdify((M, N, P, Q), cg, 'tensorflow')
y = session.run(f(ma, mb, mc, md))
c = session.run(ma + mb + mc + md)
assert (y == c).all()
cg = CodegenArrayPermuteDims(M, [1, 0])
assert tensorflow_code(cg) == 'tensorflow.transpose(M, [1, 0])'
f = lambdify((M, ), cg, 'tensorflow')
y = session.run(f(ma))
c = session.run(tf.transpose(ma))
assert (y == c).all()
cg = CodegenArrayPermuteDims(CodegenArrayTensorProduct(M, N),
[1, 2, 3, 0])
assert tensorflow_code(cg) == \
'tensorflow.transpose(' \
'tensorflow.linalg.einsum("ab,cd", M, N), [1, 2, 3, 0])'
f = lambdify((M, N), cg, 'tensorflow')
y = session.run(f(ma, mb))
c = session.run(tf.transpose(tf.einsum("ab,cd", ma, mb), [1, 2, 3, 0]))
assert (y == c).all()
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(M, N), (1, 2))
assert tensorflow_code(cg) == \
'tensorflow.linalg.einsum("ab,bc->acb", M, N)'
f = lambdify((M, N), cg, 'tensorflow')
y = session.run(f(ma, mb))
c = session.run(tf.einsum("ab,bc->acb", ma, mb))
assert (y == c).all()
def test_recognize_diagonalized_vectors():
a = MatrixSymbol("a", k, 1)
b = MatrixSymbol("b", k, 1)
A = MatrixSymbol("A", k, k)
B = MatrixSymbol("B", k, k)
C = MatrixSymbol("C", k, k)
X = MatrixSymbol("X", k, k)
x = MatrixSymbol("x", k, 1)
I1 = Identity(1)
I = Identity(k)
# Check matrix recognition over trivial dimensions:
cg = CodegenArrayTensorProduct(a, b)
assert recognize_matrix_expression(cg) == a * b.T
cg = CodegenArrayTensorProduct(I1, a, b)
assert recognize_matrix_expression(cg) == a * I1 * b.T
# Recognize trace inside a tensor product:
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, B, C), (0, 3),
(1, 2))
assert recognize_matrix_expression(cg) == Trace(A * B) * C
# Transform diagonal operator to contraction:
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(A, a), (1, 2))
assert cg.transform_to_product() == CodegenArrayContraction(
CodegenArrayTensorProduct(A, DiagMatrix(a)), (1, 2))
assert recognize_matrix_expression(cg) == A * DiagMatrix(a)
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(a, b), (0, 2))
assert cg.transform_to_product() == CodegenArrayContraction(
CodegenArrayTensorProduct(DiagMatrix(a), b), (0, 2))
assert recognize_matrix_expression(cg).doit() == DiagMatrix(a) * b
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(A, a), (0, 2))
assert cg.transform_to_product() == CodegenArrayContraction(
CodegenArrayTensorProduct(A, DiagMatrix(a)), (0, 2))
assert recognize_matrix_expression(cg) == A.T * DiagMatrix(a)
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(I, x, I1), (0, 2),
(3, 5))
assert cg.transform_to_product() == CodegenArrayContraction(
CodegenArrayTensorProduct(I, DiagMatrix(x), I1), (0, 2))
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(I, x, A, B), (1, 2),
(5, 6))
assert cg.transform_to_product() == CodegenArrayDiagonal(
CodegenArrayContraction(
CodegenArrayTensorProduct(I, DiagMatrix(x), A, B), (1, 2)), (3, 4))
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(x, I1), (1, 2))
assert isinstance(cg, CodegenArrayDiagonal)
assert cg.diagonal_indices == ((1, 2), )
assert recognize_matrix_expression(cg) == x
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(x, I), (0, 2))
assert cg.transform_to_product() == CodegenArrayContraction(
CodegenArrayTensorProduct(DiagMatrix(x), I), (0, 2))
assert recognize_matrix_expression(cg).doit() == DiagMatrix(x)
cg = CodegenArrayDiagonal(x, (1, ))
assert cg == x
# Ignore identity matrices with contractions:
cg = CodegenArrayContraction(CodegenArrayTensorProduct(I, A, I, I), (0, 2),
(1, 3), (5, 7))
assert cg.split_multiple_contractions() == cg
assert recognize_matrix_expression(cg) == Trace(A) * I
cg = CodegenArrayContraction(CodegenArrayTensorProduct(Trace(A) * I, I, I),
(1, 5), (3, 4))
assert cg.split_multiple_contractions() == cg
assert recognize_matrix_expression(cg).doit() == Trace(A) * I
# Add DiagMatrix when required:
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a), (1, 2))
assert cg.split_multiple_contractions() == cg
assert recognize_matrix_expression(cg) == A * a
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a, B), (1, 2, 4))
assert cg.split_multiple_contractions() == CodegenArrayContraction(
CodegenArrayTensorProduct(A, DiagMatrix(a), B), (1, 2), (3, 4))
assert recognize_matrix_expression(cg) == A * DiagMatrix(a) * B
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a, B), (0, 2, 4))
assert cg.split_multiple_contractions() == CodegenArrayContraction(
CodegenArrayTensorProduct(A, DiagMatrix(a), B), (0, 2), (3, 4))
assert recognize_matrix_expression(cg) == A.T * DiagMatrix(a) * B
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a, b, a.T, B),
(0, 2, 4, 7, 9))
assert cg.split_multiple_contractions() == CodegenArrayContraction(
CodegenArrayTensorProduct(A, DiagMatrix(a), DiagMatrix(b),
DiagMatrix(a), B), (0, 2), (3, 4), (5, 7),
(6, 9))
assert recognize_matrix_expression(
cg).doit() == A.T * DiagMatrix(a) * DiagMatrix(b) * DiagMatrix(a) * B.T
cg = CodegenArrayContraction(CodegenArrayTensorProduct(I1, I1, I1),
(1, 2, 4))
assert cg.split_multiple_contractions() == CodegenArrayContraction(
CodegenArrayTensorProduct(I1, I1, I1), (1, 2), (3, 4))
assert recognize_matrix_expression(cg).doit() == Identity(1)
cg = CodegenArrayContraction(CodegenArrayTensorProduct(I, I, I, I, A),
(1, 2, 8), (5, 6, 9))
assert recognize_matrix_expression(
cg.split_multiple_contractions()).doit() == A
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a, C, a, B),
(1, 2, 4), (5, 6, 8))
assert cg.split_multiple_contractions() == CodegenArrayContraction(
CodegenArrayTensorProduct(A, DiagMatrix(a), C, DiagMatrix(a), B),
(1, 2), (3, 4), (5, 6), (7, 8))
assert recognize_matrix_expression(
cg) == A * DiagMatrix(a) * C * DiagMatrix(a) * B
cg = CodegenArrayContraction(
CodegenArrayTensorProduct(a, I1, b, I1, (a.T * b).applyfunc(cos)),
(1, 2, 8), (5, 6, 9))
assert cg.split_multiple_contractions().dummy_eq(
CodegenArrayContraction(
CodegenArrayTensorProduct(a, I1, b, I1, (a.T * b).applyfunc(cos)),
(1, 2), (3, 8), (5, 6), (7, 9)))
assert recognize_matrix_expression(cg).dummy_eq(
MatMul(a, I1, (a.T * b).applyfunc(cos), Transpose(I1), b.T))
cg = CodegenArrayContraction(
CodegenArrayTensorProduct(A.T, a, b, b.T, (A * X * b).applyfunc(cos)),
(1, 2, 8), (5, 6, 9))
assert cg.split_multiple_contractions().dummy_eq(
CodegenArrayContraction(
CodegenArrayTensorProduct(A.T, DiagMatrix(a), b, b.T,
(A * X * b).applyfunc(cos)), (1, 2),
(3, 8), (5, 6, 9)))
# assert recognize_matrix_expression(cg)
# Check no overlap of lines:
cg = CodegenArrayContraction(CodegenArrayTensorProduct(A, a, C, a, B),
(1, 2, 4), (5, 6, 8), (3, 7))
assert cg.split_multiple_contractions() == cg
cg = CodegenArrayContraction(CodegenArrayTensorProduct(a, b, A), (0, 2, 4),
(1, 3))
assert cg.split_multiple_contractions() == cg
def test_codegen_extra():
if not torch:
skip("Torch not installed")
M = MatrixSymbol("M", 2, 2)
N = MatrixSymbol("N", 2, 2)
P = MatrixSymbol("P", 2, 2)
Q = MatrixSymbol("Q", 2, 2)
ma = torch.tensor([[1, 2], [3, 4]])
mb = torch.tensor([[1, -2], [-1, 3]])
mc = torch.tensor([[2, 0], [1, 2]])
md = torch.tensor([[1, -1], [4, 7]])
cg = CodegenArrayTensorProduct(M, N)
assert torch_code(cg) == 'torch.einsum("ab,cd", [M, N])'
f = lambdify((M, N), cg, 'torch')
y = f(ma, mb)
c = torch.einsum("ij,kl", ma, mb)
assert (y == c).all()
cg = CodegenArrayElementwiseAdd(M, N)
assert torch_code(cg) == 'torch.add(M, N)'
f = lambdify((M, N), cg, 'torch')
y = f(ma, mb)
c = ma + mb
assert (y == c).all()
cg = CodegenArrayElementwiseAdd(M, N, P)
assert torch_code(cg) == 'torch.add(torch.add(M, N), P)'
f = lambdify((M, N, P), cg, 'torch')
y = f(ma, mb, mc)
c = ma + mb + mc
assert (y == c).all()
cg = CodegenArrayElementwiseAdd(M, N, P, Q)
assert torch_code(cg) == 'torch.add(torch.add(torch.add(M, N), P), Q)'
f = lambdify((M, N, P, Q), cg, 'torch')
y = f(ma, mb, mc, md)
c = ma + mb + mc + md
assert (y == c).all()
cg = CodegenArrayPermuteDims(M, [1, 0])
assert torch_code(cg) == 'M.permute(1, 0)'
f = lambdify((M, ), cg, 'torch')
y = f(ma)
c = ma.T
assert (y == c).all()
cg = CodegenArrayPermuteDims(CodegenArrayTensorProduct(M, N), [1, 2, 3, 0])
assert torch_code(
cg) == 'torch.einsum("ab,cd", [M, N]).permute(1, 2, 3, 0)'
f = lambdify((M, N), cg, 'torch')
y = f(ma, mb)
c = torch.einsum("ab,cd", ma, mb).permute(1, 2, 3, 0)
assert (y == c).all()
cg = CodegenArrayDiagonal(CodegenArrayTensorProduct(M, N), (1, 2))
assert torch_code(cg) == 'torch.einsum("ab,bc->acb", [M, N])'
f = lambdify((M, N), cg, 'torch')
y = f(ma, mb)
c = torch.einsum("ab,bc->acb", ma, mb)
assert (y == c).all()
