def splineInteg(x,y,integType):
y2a = cubicSpline(x,y,integType)
n = len(x)
sum = 0
for i in range(n-1):
h = x[i+1]-x[i]
sum = sum + h*(y[i+1]+y[i])/2.0
sum = sum - h*h*h*(y2a[i+1]+y2a[i])/24.0
return sum
for i in range(3, 15):
x = linspace(0, 15, 2 ** i)
y = map(total_integ, x)
ans = splineInteg(array(x), array(y), "knotanot")
error.append(ANS - ans)
figure(1)
loglog(pow(2, array(range(3, 15))), abs(array(error)), "k")
title("error vs no. of function calls")
x = linspace(0, 10, 100)
y = map(total_integ, x)
xtest = linspace(0, 10, 500)
x = array(x)
y = array(y)
xtest = array(xtest)
y2a = cubicSpline(x, y, "knotanot")
ytest = splintList(x, y, y2a, xtest)
figure(2)
title("spline interpolated function")
semilogy(xtest, ytest, "k")
x1 = linspace(0, 1, 64)
y1 = map(total_integ, x1)
tans = splineInteg(array(x1), array(y1), "knotanot")
print tans
error = []
for i in range(3, 15):
x = linspace(1, 15, 2 ** i)
y = map(total_integ, x)
ans = splineInteg(array(x), array(y), "knotanot")
error.append(ANS - ans[0] - tans)
figure(1)