Gauss-Legendre integration in Python，,''' I = gaus

Gauss-Legendre integration in Python，,''' I = gaus

''' I = gaussQuad2(f,xc,yc,m).    Gauss-Legendre integration of f(x,y) over a    quadrilateral using integration order m.    {xc},{yc} are the corner coordinates of the quadrilateral.'''from gaussNodes import *from numpy import zeros,dotdef gaussQuad2(f,x,y,m):    def jac(x,y,s,t):        J = zeros((2,2))        J[0,0] = -(1.0 - t)*x[0] + (1.0 - t)*x[1]  \                + (1.0 + t)*x[2] - (1.0 + t)*x[3]        J[0,1] = -(1.0 - t)*y[0] + (1.0 - t)*y[1]  \                + (1.0 + t)*y[2] - (1.0 + t)*y[3]        J[1,0] = -(1.0 - s)*x[0] - (1.0 + s)*x[1]  \                + (1.0 + s)*x[2] + (1.0 - s)*x[3]        J[1,1] = -(1.0 - s)*y[0] - (1.0 + s)*y[1]  \                + (1.0 + s)*y[2] + (1.0 - s)*y[3]        return (J[0,0]*J[1,1] - J[0,1]*J[1,0])/16.0    def map(x,y,s,t):        N = zeros(4)        N[0] = (1.0 - s)*(1.0 - t)/4.0        N[1] = (1.0 + s)*(1.0 - t)/4.0        N[2] = (1.0 + s)*(1.0 + t)/4.0        N[3] = (1.0 - s)*(1.0 + t)/4.0        xCoord = dot(N,x)        yCoord = dot(N,y)        return xCoord,yCoord    s,A = gaussNodes(m)    sum = 0.0    for i in range(m):        for j in range(m):            xCoord,yCoord = map(x,y,s[i],s[j])            sum = sum + A[i]*A[j]*jac(x,y,s[i],s[j])  \                       *f(xCoord,yCoord)    return sum