ACP.py

#we have a matrix Z (n x p) with n people and p character

import numpy as np
import matplotlib as mp
from numpy import linalg as la
import decimal


"Create the scalars which enable to centerize Z "
def Center(Z):
    n = len(Z);
    A = Z;
    p = 1.0/n;
    X = np.zeros(n);
    for j in range(0, n):
        sum = 0.0;
        for i in range(0, n):
            sum += p * Z[i][j];
        X[j] = sum;
    return X;


"compute variance"
def Variance(Z):
    n = len(Z);
    X = Center(Z);
    S = np.zeros(n, dtype=np.dtype(decimal.Decimal));
    for j in range (0, n):
        sum = 0.0;
        for i in range(0,n):
            sum += (Z[i][j] - X[j])
        S[j] = np.sqrt(sum);
    return S



def Centerize(Z):
    A = Z;
    n = len(Z);
    X = Center(Z);

    for j in range (0, n):
        for i in range (0, n):
            A[i][j] -= X[j]
    return A




def Reduce(Z):
    n = len(Z);
    A = Z;
    X = Variance(Z);
    for i in range(0,n):
        for j in range (0, n):
            A[i][j] = A[i][j]/X[j];
        
    return A;


def ACP(Z):
    tmp = Centerize(Z);
    #tmp = Reduce(tmp);

    a = np.shape(tmp)[0];
    b = np.shape(tmp)[1];
    
    #SVD decomposition
    U, A, V = np.linalg.svd(tmp);

    S = np.zeros((a, b));
    mini = min(a, b);
    S[:mini, :mini ]= np.diag(A);

    #Factorial coord of peoples (Scores)
    Xi = np.dot(U, S);

    #Factorial coord of variables (loadings)
    Phi = np.dot(V, np.transpose(S));

    return Xi, Phi, A;





#Test

Z = [[1,2,3,4,5],[1,2,3,4,5],[6,7,8,9,10],[2,4,3,5,8]];
print Z;
print "Center(Z): "
print Center(Z);
print "Variance(Z): "
print Variance(Z);
print "Centerize(Z): "
print Centerize(Z);


U, S, V = np.linalg.svd(Z, full_matrices=False);

print U;
print S;
print V;

print "Xi"
print ACP(Z)[0]

print "Phi"
print  ACP(Z)[1]

print "A"
print ACP(Z)[2]


Xi = ACP(Z)[0];
Phi = ACP(Z)[1];


#X =  [row[1] for row in Xi]
#Y =  [row[1] for row in Phi]

n = np.shape(Z)[0];
X = np.zeros(n);

for i in range (0, n):
    X[i] = i+1;


import matplotlib.pyplot as plt
plt.plot(X, ACP(Z)[2], 'ro')
plt.plot( ACP(Z)[0], 'bo')
plt.plot( ACP(Z)[1], 'go')

plt.axis([-(n+2), n+2, -10, 10])
plt.show()