test_transforms.py 文件源码

def test_cosine_transform():
    from sympy import sinh, cosh, Si, Ci

    t = symbols("t")
    w = symbols("w")
    a = symbols("a")
    f = Function("f")

    # Test unevaluated form
    assert cosine_transform(f(t), t, w) == CosineTransform(f(t), t, w)
    assert inverse_cosine_transform(
        f(w), w, t) == InverseCosineTransform(f(w), w, t)

    assert cosine_transform(1/sqrt(t), t, w) == 1/sqrt(w)
    assert inverse_cosine_transform(1/sqrt(w), w, t) == 1/sqrt(t)

    assert cosine_transform(1/(
        a**2 + t**2), t, w) == sqrt(2)*sqrt(pi)*exp(-a*w)/(2*a)

    assert cosine_transform(t**(
        -a), t, w) == 2**(-a + S(1)/2)*w**(a - 1)*gamma((-a + 1)/2)/gamma(a/2)
    assert inverse_cosine_transform(2**(-a + S(
        1)/2)*w**(a - 1)*gamma(-a/2 + S(1)/2)/gamma(a/2), w, t) == t**(-a)

    assert cosine_transform(
        exp(-a*t), t, w) == sqrt(2)*a/(sqrt(pi)*(a**2 + w**2))
    assert inverse_cosine_transform(
        sqrt(2)*a/(sqrt(pi)*(a**2 + w**2)), w, t) == exp(-a*t)

    assert cosine_transform(exp(-a*sqrt(t))*cos(a*sqrt(
        t)), t, w) == a*exp(-a**2/(2*w))/(2*w**(S(3)/2))

    assert cosine_transform(1/(a + t), t, w) == sqrt(2)*(
        (-2*Si(a*w) + pi)*sin(a*w)/2 - cos(a*w)*Ci(a*w))/sqrt(pi)
    assert inverse_cosine_transform(sqrt(2)*meijerg(((S(1)/2, 0), ()), (
        (S(1)/2, 0, 0), (S(1)/2,)), a**2*w**2/4)/(2*pi), w, t) == 1/(a + t)

    assert cosine_transform(1/sqrt(a**2 + t**2), t, w) == sqrt(2)*meijerg(
        ((S(1)/2,), ()), ((0, 0), (S(1)/2,)), a**2*w**2/4)/(2*sqrt(pi))
    assert inverse_cosine_transform(sqrt(2)*meijerg(((S(1)/2,), ()), ((0, 0), (S(1)/2,)), a**2*w**2/4)/(2*sqrt(pi)), w, t) == 1/(t*sqrt(a**2/t**2 + 1))