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