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from sympy.matrices.expressions.slice import MatrixSlice
from sympy.matrices.expressions import MatrixSymbol
from sympy.abc import a, b, c, d, k, l, m, n
from sympy.testing.pytest import raises, XFAIL
from sympy.functions.elementary.integers import floor
from sympy.assumptions import assuming, Q
X = MatrixSymbol('X', n, m)
Y = MatrixSymbol('Y', m, k)
def test_shape():
B = MatrixSlice(X, (a, b), (c, d))
assert B.shape == (b - a, d - c)
def test_entry():
B = MatrixSlice(X, (a, b), (c, d))
assert B[0,0] == X[a, c]
assert B[k,l] == X[a+k, c+l]
raises(IndexError, lambda : MatrixSlice(X, 1, (2, 5))[1, 0])
assert X[1::2, :][1, 3] == X[1+2, 3]
assert X[:, 1::2][3, 1] == X[3, 1+2]
def test_on_diag():
assert not MatrixSlice(X, (a, b), (c, d)).on_diag
assert MatrixSlice(X, (a, b), (a, b)).on_diag
def test_inputs():
assert MatrixSlice(X, 1, (2, 5)) == MatrixSlice(X, (1, 2), (2, 5))
assert MatrixSlice(X, 1, (2, 5)).shape == (1, 3)
def test_slicing():
assert X[1:5, 2:4] == MatrixSlice(X, (1, 5), (2, 4))
assert X[1, 2:4] == MatrixSlice(X, 1, (2, 4))
assert X[1:5, :].shape == (4, X.shape[1])
assert X[:, 1:5].shape == (X.shape[0], 4)
assert X[::2, ::2].shape == (floor(n/2), floor(m/2))
assert X[2, :] == MatrixSlice(X, 2, (0, m))
assert X[k, :] == MatrixSlice(X, k, (0, m))
def test_exceptions():
X = MatrixSymbol('x', 10, 20)
raises(IndexError, lambda: X[0:12, 2])
raises(IndexError, lambda: X[0:9, 22])
raises(IndexError, lambda: X[-1:5, 2])
@XFAIL
def test_symmetry():
X = MatrixSymbol('x', 10, 10)
Y = X[:5, 5:]
with assuming(Q.symmetric(X)):
assert Y.T == X[5:, :5]
def test_slice_of_slice():
X = MatrixSymbol('x', 10, 10)
assert X[2, :][:, 3][0, 0] == X[2, 3]
assert X[:5, :5][:4, :4] == X[:4, :4]
assert X[1:5, 2:6][1:3, 2] == X[2:4, 4]
assert X[1:9:2, 2:6][1:3, 2] == X[3:7:2, 4]
def test_negative_index():
X = MatrixSymbol('x', 10, 10)
assert X[-1, :] == X[9, :]
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