dggsvp(3P) Sun Performance Library dggsvp(3P)NAMEdggsvp - compute orthogonal matrices U, V and Q such that N-K-L K L
U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
SYNOPSIS
SUBROUTINE DGGSVP(JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA,
TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, TAU, WORK, INFO)
CHARACTER * 1 JOBU, JOBV, JOBQ
INTEGER M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO
INTEGER IWORK(*)
DOUBLE PRECISION TOLA, TOLB
DOUBLE PRECISION A(LDA,*), B(LDB,*), U(LDU,*), V(LDV,*), Q(LDQ,*),
TAU(*), WORK(*)
SUBROUTINE DGGSVP_64(JOBU, JOBV, JOBQ, M, P, N, A, LDA, B, LDB, TOLA,
TOLB, K, L, U, LDU, V, LDV, Q, LDQ, IWORK, TAU, WORK, INFO)
CHARACTER * 1 JOBU, JOBV, JOBQ
INTEGER*8 M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO
INTEGER*8 IWORK(*)
DOUBLE PRECISION TOLA, TOLB
DOUBLE PRECISION A(LDA,*), B(LDB,*), U(LDU,*), V(LDV,*), Q(LDQ,*),
TAU(*), WORK(*)
F95 INTERFACE
SUBROUTINE GGSVP(JOBU, JOBV, JOBQ, [M], [P], [N], A, [LDA], B, [LDB],
TOLA, TOLB, K, L, U, [LDU], V, [LDV], Q, [LDQ], [IWORK], [TAU],
[WORK], [INFO])
CHARACTER(LEN=1) :: JOBU, JOBV, JOBQ
INTEGER :: M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL(8) :: TOLA, TOLB
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A, B, U, V, Q
SUBROUTINE GGSVP_64(JOBU, JOBV, JOBQ, [M], [P], [N], A, [LDA], B,
[LDB], TOLA, TOLB, K, L, U, [LDU], V, [LDV], Q, [LDQ], [IWORK],
[TAU], [WORK], [INFO])
CHARACTER(LEN=1) :: JOBU, JOBV, JOBQ
INTEGER(8) :: M, P, N, LDA, LDB, K, L, LDU, LDV, LDQ, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL(8) :: TOLA, TOLB
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A, B, U, V, Q
C INTERFACE
#include <sunperf.h>
void dggsvp(char jobu, char jobv, char jobq, int m, int p, int n, dou‐
ble *a, int lda, double *b, int ldb, double tola, double
tolb, int *k, int *l, double *u, int ldu, double *v, int ldv,
double *q, int ldq, int *info);
void dggsvp_64(char jobu, char jobv, char jobq, long m, long p, long n,
double *a, long lda, double *b, long ldb, double tola, double
tolb, long *k, long *l, double *u, long ldu, double *v, long
ldv, double *q, long ldq, long *info);
PURPOSEdggsvp computes orthogonal matrices U, V and Q such that
L ( 0 0 A23 )
M-K-L ( 0 0 0 )
N-K-L K L
= K ( 0 A12 A13 ) if M-K-L < 0;
M-K ( 0 0 A23 )
N-K-L K L
V'*B*Q = L ( 0 0 B13 )
P-L ( 0 0 0 )
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. K+L = the effective numerical rank of
the (M+P)-by-N matrix (A',B')'. Z' denotes the transpose of Z.
This decomposition is the preprocessing step for computing the General‐
ized Singular Value Decomposition (GSVD), see subroutine DGGSVD.
ARGUMENTS
JOBU (input)
= 'U': Orthogonal matrix U is computed;
= 'N': U is not computed.
JOBV (input)
= 'V': Orthogonal matrix V is computed;
= 'N': V is not computed.
JOBQ (input)
= 'Q': Orthogonal matrix Q is computed;
= 'N': Q is not computed.
M (input) The number of rows of the matrix A. M >= 0.
P (input) The number of rows of the matrix B. P >= 0.
N (input) The number of columns of the matrices A and B. N >= 0.
A (input/output)
On entry, the M-by-N matrix A. On exit, A contains the tri‐
angular (or trapezoidal) matrix described in the Purpose sec‐
tion.
LDA (input)
The leading dimension of the array A. LDA >= max(1,M).
B (input/output)
On entry, the P-by-N matrix B. On exit, B contains the tri‐
angular matrix described in the Purpose section.
LDB (input)
The leading dimension of the array B. LDB >= max(1,P).
TOLA (input)
TOLA and TOLB are the thresholds to determine the effective
numerical rank of matrix B and a subblock of A. Generally,
they are set to TOLA = MAX(M,N)*norm(A)*MACHEPS, TOLB =
MAX(P,N)*norm(B)*MACHEPS. The size of TOLA and TOLB may
affect the size of backward errors of the decomposition.
TOLB (input)
See the description of TOLA.
K (output)
On exit, K and L specify the dimension of the subblocks
described in Purpose. K + L = effective numerical rank of
(A',B')'.
L (output)
See the description of K.
U (output)
If JOBU = 'U', U contains the orthogonal matrix U. If JOBU =
'N', U is not referenced.
LDU (input)
The leading dimension of the array U. LDU >= max(1,M) if JOBU
= 'U'; LDU >= 1 otherwise.
V (output)
If JOBV = 'V', V contains the orthogonal matrix V. If JOBV =
'N', V is not referenced.
LDV (input)
The leading dimension of the array V. LDV >= max(1,P) if JOBV
= 'V'; LDV >= 1 otherwise.
Q (output)
If JOBQ = 'Q', Q contains the orthogonal matrix Q. If JOBQ =
'N', Q is not referenced.
LDQ (input)
The leading dimension of the array Q. LDQ >= max(1,N) if JOBQ
= 'Q'; LDQ >= 1 otherwise.
IWORK (workspace)
dimension(N)
TAU (workspace)
dimension(N)
WORK (workspace)
dimension(MAX(3*N,M,P))
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
FURTHER DETAILS
The subroutine uses LAPACK subroutine DGEQPF for the QR factorization
with column pivoting to detect the effective numerical rank of the a
matrix. It may be replaced by a better rank determination strategy.
6 Mar 2009 dggsvp(3P)
