GaussPoints.py

""" From "COMPUTATIONAL PHYSICS" & "COMPUTER PROBLEMS in PHYSICS"
    by RH Landau, MJ Paez, and CC Bordeianu (deceased)
    Copyright R Landau, Oregon State Unv, MJ Paez, Univ Antioquia, 
    C Bordeianu, Univ Bucharest, 2017. 
    Please respect copyright & acknowledge our work."""

# GaussPoints.py: N point Gaussian quadrature pts & Wts generation

import math
from numpy import *

def GaussPoints(Npts, a, b, x, w, eps):
    m = 0; i = 0; j = 0; t = 0.; t1 = 0.; pp = 0.
    p1 = 0.; p2 = 0.; p3 = 0.  
    m = int((Npts+1)/2)
    for i in range(1, m+1):
        t = math.cos(math.pi*(float(i)-0.25)/(float(Npts)+0.5))
        t1 = 1 
        while((abs(t-t1)) >=  eps):
            p1 = 1. ;  p2 = 0.  
            for j in range(1, Npts + 1):
                p3 = p2;   p2 = p1 
                p1 = ((2.*float(j)-1)*t*p2 - (float(j)-1.)*p3)/(float(j))
            pp = Npts*(t*p1 - p2)/(t*t - 1.) 
            t1 = t
            t = t1 - p1/pp
        x[i-1] =  -t
        x[Npts-i] = t 
        w[i-1] = 2./( (1.-t*t)*pp*pp) 
        w[Npts-i] = w[i-1]
        
    for j in range(0, Npts):               # Scale [-1,+1] to [a,b]
            x[j] = x[j]*(b-a)/2. + (b+a)/2. 
            w[j] = w[j]*(b-a)/2.