def bulStoer(F, x, y, xStop, H, tol=1.0e-6):
X = []
Y = []
X.append(x)
Y.append(y)
while x < xStop:
H = min(H, xStop - x)
y = midpoint.integrate(F, x, y, x + H, tol) # Midpoint method
x = x + H
X.append(x)
Y.append(y)
return numpy.array(X), numpy.array(Y)
#!/usr/bin/env python3
import numpy as np
import midpoint
def intf(x):
return np.exp(x)
rangex = np.linspace(0, 10, 100, endpoint=True)
out = "{} integration, e^x on ({},{}): {}"
print(out.format(
"midpoint",
rangex[0], rangex[-1],
midpoint.integrate(intf, rangex)
))
from scipy.integrate import quad
print(out.format(
"scipy",
rangex[0], rangex[-1],
quad(intf, rangex[0], rangex[-1])
))
import numpy as np
import midpoint
import trapezoid
import time
def intf(x):
return np.exp(x)
rangex = np.linspace(0, 10, 100, endpoint=True)
out = "{} integration, e^x on ({},{}): {}\nelapsed: {}"
start = time.clock()
res = midpoint.integrate(intf, rangex)
elapsed = time.clock() - start
print(out.format("midpoint", rangex[0], rangex[-1], res, elapsed))
start = time.clock()
res = trapezoid.integrate(intf, rangex)
elapsed = time.clock() - start
print(out.format("trapezoid", rangex[0], rangex[-1], res, elapsed))
from scipy.integrate import quad
start = time.clock()
res = quad(intf, rangex[0], rangex[-1])
elapsed = time.clock() - start