Intel® Math Kernel Library

Cosine-Sine Decomposition: LAPACK Computational Routines

This topic describes LAPACK computational routines for computing the cosine-sine decomposition (CS decomposition) of a partitioned unitary/orthogonal matrix. The algorithm computes a complete 2-by-2 CS decomposition, which requires simultaneous diagonalization of all the four blocks of a unitary/orthogonal matrix partitioned into a 2-by-2 block structure.

The computation has the following phases:

?gels

Uses QR or LQ factorization to solve a overdetermined or underdetermined linear system with full rank matrix.

?gelsy

Computes the minimum-norm solution to a linear least squares problem using a complete orthogonal factorization of A.

?gelss

Computes the minimum-norm solution to a linear least squares problem using the singular value decomposition of A.

?gelsd

Computes the minimum-norm solution to a linear least squares problem using the singular value decomposition of A and a divide and conquer method.

?getsls

Uses QR or LQ factorization to solve an overdetermined or underdetermined linear system with full rank matrix, with best performance for tall and skinny matrices.

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