peirce1957.py 文件源码

def __init__(self, m):
        k = 4*m + 3
        self.degree = k
        theta = 2*numpy.pi * numpy.arange(1, k+2) / (k+1)
        p, w = numpy.polynomial.legendre.leggauss(m+1)
        # scale points to [r0, r1] (where r0 = 0, r1 = 1 for now)
        p = numpy.sqrt(0.5*(p + 1.0))
        p_theta = numpy.dstack(numpy.meshgrid(p, theta)).reshape(-1, 2).T
        self.points = numpy.column_stack([
            p_theta[0] * numpy.cos(p_theta[1]),
            p_theta[0] * numpy.sin(p_theta[1]),
            ])

        # When integrating between 0 and 1, the weights are exactly the
        # Gauss-Legendre weights, scaled according to the disk area.
        self.weights = numpy.tile(0.5 * numpy.pi / (k+1) * w, k+1)
        return