import numpy as np
import math

def GMMRanking(matrix):
    rowMul = list()

    for row in matrix:
        mult = 1
        for item in np.asarray(row[0])[0]:
            mult *= item
        rowMul.append(np.power(mult,1/len(matrix)))

    rowSum = np.asarray(rowMul).sum()
    rowMul = np.asarray(np.matrix(rowMul).transpose()) / rowSum
    return rowMul

def Satty(matrix):
    size = len(matrix)
    lmax = max(np.linalg.eigvals(matrix))
    return (lmax - size) / (size - 1)

def Geom(matrix):
    matrixSum = 0
    matrix = GMMRanking(matrix)
    scalar = 2/((len(matrix)-1)*(len(matrix)-2))
    for row in matrix:
        for item in row:
            matrixSum += np.power(np.log(item),2)

    return scalar * matrixSum

def Koczkodaj(matrix):
    n = len(matrix)
    def K(i,j,k):
        return (matrix[i,j]/(matrix[i,k]*matrix[k,j]))

    def minimum(i,j,k):
        return min(math.fabs(1-K(i,j,k)),math.fabs(1-(1/K(i,j,k))))

    trp = [ minimum(i,j,k) for i in range(0,n-2) for j in range(1,n-1) for k in range(2,n)]
    return max(trp)

A = np.matrix([[1,7,3],[(1/7),1,2],[(1/3),(1/2),1]])
B = np.matrix([[1,(1/5),7,1],[5,1,(1/2),2],[(1/7),2,1,3],[1,(1/2),(1/3),1]])
C = np.matrix([[1,2,5,1,7],[(1/2),1,3,(1/2),5],[(1/5),(1/3),1,(1/5),2],[1,2,5,1,7],[(1/7),(1/5),(1/2),(1/7),1]])

print("Wskazniki macierzy A: ")
print("Satty'ego : ", Satty(A))
print("Geometryczny : ", Geom(A))
print("Koczkodaj : ", Koczkodaj(A))

print("Wskazniki macierzy B: ")
print("Satty'ego : ", Satty(B))
print("Geometryczny : ", Geom(B))
print("Koczkodaj : ", Koczkodaj(B))

print("Wskazniki macierzy C: ")
print("Satty'ego : ", Satty(C))
print("Geometryczny : ", Geom(C))
print("Koczkodaj : ", Koczkodaj(C))