def gaussQuad2(f, x, y, m): def jac(x, y, s, t): J = np.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 = np.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 = np.dot(N, x) yCoord = np.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
def gaussQuad2(f,x,y,m): def jac(x,y,s,t): J = zeros((2,2),type=Float64) 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),type=Float64) 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
def gaussQuad(f, a, b, m): c1 = (b + a) / 2.0 c2 = (b - a) / 2.0 x, A = gaussNodes(m) sum = 0.0 for i in range(len(x)): sum = sum + A[i] * f(c1 + c2 * x[i]) return c2 * sum
def gaussQuad(f,a,b,m): c1 = (b + a)/2.0 c2 = (b - a)/2.0 x,A = gaussNodes(m) sum = 0.0 for i in range(len(x)): sum = sum + A[i]*f(c1 + c2*x[i]) return c2*sum