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from sympy.matrices.expressions.factorizations import lu, LofCholesky, qr, svd
from sympy.assumptions.ask import (Q, ask)
from sympy.core.symbol import Symbol
from sympy.matrices.expressions.matexpr import MatrixSymbol
n = Symbol('n')
X = MatrixSymbol('X', n, n)
def test_LU():
L, U = lu(X)
assert L.shape == U.shape == X.shape
assert ask(Q.lower_triangular(L))
assert ask(Q.upper_triangular(U))
def test_Cholesky():
LofCholesky(X)
def test_QR():
Q_, R = qr(X)
assert Q_.shape == R.shape == X.shape
assert ask(Q.orthogonal(Q_))
assert ask(Q.upper_triangular(R))
def test_svd():
U, S, V = svd(X)
assert U.shape == S.shape == V.shape == X.shape
assert ask(Q.orthogonal(U))
assert ask(Q.orthogonal(V))
assert ask(Q.diagonal(S))
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