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
