test_triangle_orth.py 文件源码

def op(i, j, x, y):
    p0, a, b, c = orthopy.line.recurrence_coefficients.jacobi(
            i, 0, 0,
            # standardization='monic'
            standardization='p(1)=(n+alpha over n)'
            )
    val1 = orthopy.line.tools.evaluate_orthogonal_polynomial(
            (x-y)/(x+y), p0, a, b, c
            )

    val1 = numpy.polyval(scipy.special.jacobi(i, 0, 0), (x-y)/(x+y))

    # treat x==0, y==0 separately
    if isinstance(val1, numpy.ndarray):
        idx = numpy.where(numpy.logical_and(x == 0, y == 0))[0]
        val1[idx] = numpy.polyval(scipy.special.jacobi(i, 0, 0), 0.0)
    else:
        if numpy.isnan(val1):
            val1 = numpy.polyval(scipy.special.jacobi(i, 0, 0), 0.0)

    p0, a, b, c = orthopy.line.recurrence_coefficients.jacobi(
            j, 2*i+1, 0,
            # standardization='monic'
            standardization='p(1)=(n+alpha over n)'
            )
    val2 = orthopy.line.tools.evaluate_orthogonal_polynomial(
            1-2*(x+y), p0, a, b, c
            )
    # val2 = numpy.polyval(scipy.special.jacobi(j, 2*i+1, 0), 1-2*(x+y))

    flt = numpy.vectorize(float)
    return flt(
        numpy.sqrt(2*i + 1) * val1 * (x+y)**i
        * numpy.sqrt(2*j + 2*i + 2) * val2
        )