Fast SVD and PCA

Fast truncated SVD and PCA rectangular matrices

Truncated Singular Value Decomposition (SVD) and Principal Component Analysis (PCA) that are much faster compared to using the Matlab svd and svds functions for rectangular matrices.
svdecon is a faster alternative to svd(X,'econ') for long or thin matrices.
svdsecon is a faster alternative to svds(X,k) for dense long or thin matrices where k << size(X,1) and size(X,2).
PCA versions of the two svd functions are also implemented.
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function [U,S,V] = svdecon(X)
function [U,S,V] = svdecon(X,k)

Input:
X : m x n matrix
k : gets the first k singular values (if k not given then k = min(m,n))

Output:
X = U*S*V'
U : m x k
S : k x k
V : n x k

Description:
svdecon(X) is equivalent to svd(X,'econ')
svdecon(X,k) is equivalent to svds(X,k) where k < min(m,n)
This is faster than svdsecon when k is not much smaller than min(m,n)

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function [U,S,V] = svdsecon(X,k)

Input:
X : m x n matrix
k : gets the first k singular values, k << min(m,n)

Output:
X = U*S*V' approximately (up to k)
U : m x k
S : k x k
V : n x k

Description:
svdsecon(X,k) is equivalent to svds(X,k) where k < min(m,n)
This function is useful if k << min(m,n) (see doc eigs)

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function [U,T,mu] = pcaecon(X,k)

Input:
X : m x n matrix
Each column of X is a feature vector
k : extracts the first k principal components

Output:
X = U*T approximately (up to k)
T = U'*X
U : m x k
T : k x n

Description:
Principal Component Analysis (PCA)
Requires that k < min(m,n)

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function [U,T,mu] = pcasecon(X,k)

Input:
X : m x n matrix
Each column of X is a feature vector
k : extracts the first k principal components, k << min(m,n)

Output:
X = U*T approximately (up to k)
T = U'*X
U : m x k
T : k x n

Description:
Principal Component Analysis (PCA)
Requires that k < min(m,n)
This function is useful if k << min(m,n) (see doc eigs)