# -*- coding: utf-8 -*-
"""
Created on Fri Apr  4 02:53:30 2014

@author: user
"""

from numpy import dot, array

"""
a1=array(
[[2.,3.,1.,5.],
 [6.,13.,5.,19.],
 [2.,19.,10.,23.],
 [4.,10.,11.,31.]])

b1=array([1.,1.,1.,1.])

a1=array(
[[2.,-1.,0.],
 [-1.,2.,-1.],
 [0.,-1.,1.]])

b1=array([1.,0.,0.])
"""

a1=array(
[[0.,-1.,1.],
 [-1.,2.,-1.],
 [2.,-1.,0.]])

b1=array([0.,0., 1.])


def GaussElimin(a,b):
    n = len(b)
  # Faza eliminacji
  # niejsca "wyzerowane" pozostawiane są bez zmian
    for k in range(0,n-1):
        for i in range(k+1,n):
           if a[i,k] != 0.0:
               alfa = a[i,k]/a[k,k]
               a[i,k+1:n] = a[i,k+1:n] - alfa*a[k,k+1:n]
               b[i] = b[i] - alfa*b[k]
  #Faza podstawianie wsteczne
    for k in range(n-1,-1,-1):
        b[k] = (b[k] - dot(a[k,k+1:n],b[k+1:n]))/a[k,k]
    return b

print('wynik:',GaussElimin(a1,b1))
print('tablica a1 po elimonacji:')
print(a1)

"""
print('sprawdzenie dla wiersza [2.,-1.,0.]:', dot(array([2.,-1., 0.]),array([1.,1.,1.])))
print('sprawdzenie dla wiersza [-1.,2.,-1.]:', dot(array([-1.,2.,-1.]),array([1.,1.,1.])))
print('sprawdzenie dla wiersza [0.,-1.,1.]:', dot(array([0.,-1.,1.]),array([1.,1.,1.])))
"""