schemes.py 文件源码

def _gauss_from_coefficients_sympy(alpha, beta):
    assert isinstance(alpha[0], sympy.Rational)
    # Construct the triadiagonal matrix [sqrt(beta), alpha, sqrt(beta)]
    A = _sympy_tridiag(alpha, [sympy.sqrt(bta) for bta in beta])

    # Extract points and weights from eigenproblem
    x = []
    w = []
    for item in A.eigenvects():
        val, multiplicity, vec = item
        assert multiplicity == 1
        assert len(vec) == 1
        vec = vec[0]
        x.append(val)
        norm2 = sum([v**2 for v in vec])
        # simplifiction takes really long
        # w.append(sympy.simplify(beta[0] * vec[0]**2 / norm2))
        w.append(beta[0] * vec[0]**2 / norm2)
    # sort by x
    order = sorted(range(len(x)), key=lambda i: x[i])
    x = [x[i] for i in order]
    w = [w[i] for i in order]
    return x, w