fixess.py

# -*- coding: utf-8 -*-
"""
MIT license
Created on Wed Feb 11 20:03:52 2015

@author: xevaquor
"""

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import fmin_bfgs


TrainingData = np.array([
                [1.,2.,2.],
                [1.,3.,2.],
                [1.,2.,3.],
                [1.,2.,1.],
                [1.,1.,2.],
                [1.,3.,3.],
                [1.,1.,1.],
                [1.,1.,3.],
                [1.,3.,1.],
                [1.,2.,4.],
                [1.,2.,0.],
                [1.,0.,2.],
                [1.,4.,2.]                
])

                
m,n = TrainingData.shape

Y = np.array([0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1])
                
def sigmoid(x):
    return 1/(1 + np.e**(-x))
    
def h(Theta, X):
    z = Theta[0] * X[0] + Theta[1] * X[1] + Theta[2] * X[2] +\
    Theta[3] * X[1]*X[2] +\
    Theta[4] * X[1]**2 + Theta[5] * X[2]**2 +\
    Theta[6] * X[1]**2 * X[2]**2 +\
    Theta[7] * X[1]**2 * X[2] + Theta[8] * X[1]**2 +\
    Theta[9] * X[1]**3 + Theta[10] * X[2]**3   
    return sigmoid(z)
    
#ostatecznie uznałem, że tak będzie czytelniej
def single_penalty(Theta, x, y):
    return -np.log(h(Theta, x)) if y == 1 else -np.log(1-h(Theta, x))                
        
def J(Theta):
    sum = 0.
    for i in range(m):
        sum += single_penalty(Theta, TrainingData[i,:], Y[i])
    return sum/m


initialTheta = [0,0,0,0,0,0,0,0,0,0,0]
theta = fmin_bfgs(J, initialTheta)
print(theta)      

zeros = TrainingData[:5]
ones = TrainingData[5:]

plt.scatter(zeros[:,1], zeros[:,2],s=120, marker='x', color='purple')
plt.scatter(ones[:,1], ones[:,2],s=120, marker='*', color='orange')

xscale = np.linspace(-3,6,500)
yscale = np.linspace(-3,6,500)


xmesh, ymesh = np.meshgrid(xscale, yscale)
zmesh = xmesh**2 + ymesh**2
for row in range(len(yscale)):
    for col in range(len(xscale)):
        xx = xmesh[row,col]
        yy = ymesh[row,col]
        zmesh[row,col] = h(theta, [1, xx,yy])
        
plt.contour(xmesh, ymesh, zmesh, [0.01, 0.5, 0.99] )
plt.xlabel('X1')
plt.ylabel('X2')
plt.xlim([-1,5])
plt.ylim([-1,5])
plt.gca().set_aspect('equal', adjustable='box')
#plt.savefig('6.png')