Generalized Singular Value Decomposition: LAPACK Computational Routines

This topic describes LAPACK computational routines used for finding the generalized singular value decomposition (GSVD) of two matrices A and B as

U^HAQ = D₁*(0 R),

V^HBQ = D₂*(0 R),

where U, V, and Q are orthogonal/unitary matrices, R is a nonsingular upper triangular matrix, and D₁, D₂ are “diagonal” matrices of the structure detailed in the routines description section.

Table “Computational Routines for Generalized Singular Value Decomposition” lists LAPACK routines that perform generalized singular value decomposition of matrices.

Computational Routines for Generalized Singular Value Decomposition
Routine name	Operation performed
ggsvp	Computes the preprocessing decomposition for the generalized SVD
ggsvp3	Performs preprocessing for a generalized SVD.
ggsvd3	Computes generalized SVD.
tgsja	Computes the generalized SVD of two upper triangular or trapezoidal matrices

You can use routines listed in the above table as well as the driver routine ggsvd to find the GSVD of a pair of general rectangular matrices.