test_matexpr.py 文件源码

def test_MatrixElement_with_values():
    x, y, z, w = symbols("x y z w")
    M = Matrix([[x, y], [z, w]])
    i, j = symbols("i, j")
    Mij = M[i, j]
    assert isinstance(Mij, MatrixElement)
    Ms = SparseMatrix([[2, 3], [4, 5]])
    msij = Ms[i, j]
    assert isinstance(msij, MatrixElement)
    for oi, oj in [(0, 0), (0, 1), (1, 0), (1, 1)]:
        assert Mij.subs({i: oi, j: oj}) == M[oi, oj]
        assert msij.subs({i: oi, j: oj}) == Ms[oi, oj]
    A = MatrixSymbol("A", 2, 2)
    assert A[0, 0].subs(A, M) == x
    assert A[i, j].subs(A, M) == M[i, j]
    assert M[i, j].subs(M, A) == A[i, j]

    assert isinstance(M[3*i - 2, j], MatrixElement)
    assert M[3*i - 2, j].subs({i: 1, j: 0}) == M[1, 0]
    assert isinstance(M[i, 0], MatrixElement)
    assert M[i, 0].subs(i, 0) == M[0, 0]
    assert M[0, i].subs(i, 1) == M[0, 1]

    assert M[i, j].diff(x) == Matrix([[1, 0], [0, 0]])[i, j]

    raises(ValueError, lambda: M[i, 2])
    raises(ValueError, lambda: M[i, -1])
    raises(ValueError, lambda: M[2, i])
    raises(ValueError, lambda: M[-1, i])