Singular Value Decomposition.

For an m-by-n matrix A with m >= n, the singular value decomposition is an
m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and an n-by-n
orthogonal matrix V so that A = U*S*V'.

The singular values, sigma[k] = S[k][k], are ordered so that sigma[0] >=
sigma[1] >= ... >= sigma[n-1].

The singular value decompostion always exists, so the constructor will never
fail. The matrix condition number and the effective numerical rank can be
computed from this decomposition.

Origin : JAMA http://math.nist.gov/javanumerics/jama/ placed in public domain.

Construct the singular value decomposition
param  Arg Rectangular matrix
Structure to access U, S and V.

Return the left singular vectors
return  U

Return the right singular vectors
return  V

Return the one-dimensional array of singular values
return  diagonal of S.

Return the diagonal matrix of singular values
return  S

Two norm
return  max(S)

Two norm condition number
return  max(S)/min(S)

Effective numerical matrix rank
return  Number of nonnegligible singular values.