Function SV_decomp (o2scl_linalg)

O2scl : Function List

template<class mat_t, class mat2_t, class vec_t, class vec2_t>
void o2scl_linalg::SV_decomp(size_t M, size_t N, mat_t &A, mat2_t &V, vec_t &S, vec2_t &work)

Factorise a general matrix into its SV decomposition using the Golub-Reinsch algorithm.

This factors matrix A of size (M,N) into

\[ A = U~D~V^T \]

where U is a column-orthogonal matrix of size (M,N) (stored in A), D is a diagonal matrix of size (N,N) (stored in the vector S of size N), and V is a orthogonal matrix of size (N,N). The vector work is a workspace vector of size N. The matrices U and V are constructed so that

\[ U^T~U = I \qquad \mathrm{and} \qquad V^T~V = V~V^T = I \]

This algorithm requres \( M \geq N \).

Todo:

Test N=1 case, N=2 case, and non-square matrices.