# Code from Chapter 6 of Machine Learning: An Algorithmic Perspective (2nd Edition)
# by Stephen Marsland (http://stephenmonika.net)

# You are free to use, change, or redistribute the code in any way you wish for
# non-commercial purposes, but please maintain the name of the original author.
# This code comes with no warranty of any kind.

# Stephen Marsland, 2008, 2014

# An algorithm to compute PCA. Not as fast as the NumPy implementation
import numpy as np

def pca(data,nRedDim=0,normalise=1):
    
    # Centre data
    m = np.mean(data,axis=0)
    data -= m

    # Covariance matrix
    C = np.cov(np.transpose(data))

    # Compute eigenvalues and sort into descending order
    evals,evecs = np.linalg.eig(C) 
    indices = np.argsort(evals)
    indices = indices[::-1]
    evecs = evecs[:,indices]
    evals = evals[indices]

    if nRedDim>0:
        evecs = evecs[:,:nRedDim]
    
    if normalise:
        for i in range(np.shape(evecs)[1]):
            evecs[:,i] / np.linalg.norm(evecs[:,i]) * np.sqrt(evals[i])

    # Produce the new data matrix
    x = np.dot(np.transpose(evecs),np.transpose(data))
    # Compute the original data again
    y=np.transpose(np.dot(evecs,x))+m
    return x,y,evals,evecs