In [5]:

    

import numpy as np
import matplotlib.pyplot as plt

%pylab inline


    

    




Populating the interactive namespace from numpy and matplotlib

In [6]:

    

x0 = 0  # starting point
h = 0.5  # step

def func(x):
    return - (3 - np.power(x, 2)) * x  # our function


    

In [7]:

    

fig, ax = plt.subplots()
x = np.linspace(-3, 3, 100)
y = func(x)
ax.plot(x, y)
ax.grid(True)


    

In [9]:

    

def optimize_svenn(x0, h):
    f0 = func(x0)
    f0_add = func(x0 + h)
    f0_sub = func(x0 - h)
    
    xk1 = lambda xk0, t, k: (xk0 + 2.0 ** k * t)

    if (f0 >= f0_sub) and (f0 >= f0_add):
        return (None, None)
    elif (f0 <= f0_sub) and (f0 <= f0_add):
        return (x0 - h, x0 + h)
    elif (f0 <= f0_sub) and (f0 >= f0_add):
        a = x0
    elif (f0 >= f0_sub) and (f0 <= f0_add):
        h = -h
        b = x0
    
    k = 1
    x1 = x0 + h
    x2 = xk1(x1, h, k)
    f1 = func(x1)
    f2 = func(x2)
     
    while f2 < f1:
        if (h > 0):
            a = x1
        else:
            b = x1
        k += 1
        
        x1, f1 = x2, f2
        x2 = xk1(x1, h, k)
        f2 = func(x2)
        
    if (h > 0):
        b = x2
    else:
        a = x2
        
    return a, b


a, b = optimize_svenn(x0, h)

if a is not None and b is not None:
    fa, fb = func(a), func(b)
    ax.plot([a], [fa], "ro")
    ax.text(a, fa - 2, "a")
    ax.plot([b], [fb], "ro")
    ax.text(b, fb - 2, "b")
    print "a = {0}".format(a)
    print "b = {0}".format(b)
else:
    print "Function is not unimodal"
    
fig


    

    




a = 0
b = 1.5






    
Out[9]:

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