test_line_segment.py 文件源码

def test_cheb2_scheme(scheme):
    def integrate_exact(k):
        # \int_-1^1 x^k * sqrt(1 - x^2)
        if k == 0:
            return 0.5 * numpy.pi
        if k % 2 == 1:
            return 0.0
        return numpy.sqrt(numpy.pi) * ((-1)**k + 1) \
            * math.gamma(0.5*(k+1)) / math.gamma(0.5*k+2) \
            / 4

    degree = check_degree_1d(
            lambda poly: quadpy.line_segment.integrate(
                    poly, numpy.array([[-1.0], [1.0]]), scheme
                    ),
            integrate_exact,
            scheme.degree + 1
            )
    assert degree >= scheme.degree
    return