dtgsja (l) - Linux Manuals
dtgsja: computes the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B
NAME
DTGSJA - computes the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and BSYNOPSIS
- SUBROUTINE DTGSJA(
- JOBU, JOBV, JOBQ, M, P, N, K, L, A, LDA, B, LDB, TOLA, TOLB, ALPHA, BETA, U, LDU, V, LDV, Q, LDQ, WORK, NCYCLE, INFO )
- CHARACTER JOBQ, JOBU, JOBV
- INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, NCYCLE, P
- DOUBLE PRECISION TOLA, TOLB
- DOUBLE PRECISION A( LDA, * ), ALPHA( * ), B( LDB, * ), BETA( * ), Q( LDQ, * ), U( LDU, * ), V( LDV, * ), WORK( * )
PURPOSE
DTGSJA computes the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B. On entry, it is assumed that matrices A and B have the following forms, which may be obtained by the preprocessing subroutine DGGSVP from a general M-by-N matrix A and P-by-N matrix B:A
M-K-L
A
M-K
B
P-L
where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, otherwise A23 is (M-K)-by-L upper trapezoidal.
On exit,
where U, V and Q are orthogonal matrices, Zaq denotes the transpose of Z, R is a nonsingular upper triangular matrix, and D1 and D2 are ``diagonalaqaq matrices, which are of the following structures: If M-K-L >= 0,