numpy中高斯-勒让德正交的不同间隔

要更改间隔，请使用以下方法将x值从[-1，1]转换为[a，b]：

t = 0.5*(x + 1)*(b - a) + a

然后将正交公式缩放为（b-a）/ 2：

gauss = sum(w * f(t)) * 0.5*(b - a)

这是您的示例的修改版本：

import numpy as npfrom scipy import integrate# Define function and intervala = 0.0b = np.pi/2f = lambda x: np.cos(x)# Gauss-Legendre (default interval is [-1, 1])deg = 6x, w = np.polynomial.legendre.leggauss(deg)# Translate x values from the interval [-1, 1] to [a, b]t = 0.5*(x + 1)*(b - a) + agauss = sum(w * f(t)) * 0.5*(b - a)# For comparisonquad, quad_err = integrate.quad(f, a, b)print 'The QUADPACK solution: {0:.12} with error: {1:.12}'.format(quad, quad_err)print 'Gauss-Legendre solution: {0:.12}'.format(gauss)print 'Difference between QUADPACK and Gauss-Legendre: ', abs(gauss - quad)

它打印：

QUADPACK解决方案：1.0，错误：1.11022302463e-14高斯-勒根德雷解决方案：1.0QUADPACK和Gauss-Legendre之间的差异：4.62963001269e-14