dorgbr(3P) Sun Performance Library dorgbr(3P)NAMEdorgbr - generate one of the real orthogonal matrices Q or P**T deter‐
mined by DGEBRD when reducing a real matrix A to bidiagonal form
SYNOPSIS
SUBROUTINE DORGBR(VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CHARACTER * 1 VECT
INTEGER M, N, K, LDA, LWORK, INFO
DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)
SUBROUTINE DORGBR_64(VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
CHARACTER * 1 VECT
INTEGER*8 M, N, K, LDA, LWORK, INFO
DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)
F95 INTERFACE
SUBROUTINE ORGBR(VECT, M, [N], K, A, [LDA], TAU, [WORK], [LWORK],
[INFO])
CHARACTER(LEN=1) :: VECT
INTEGER :: M, N, K, LDA, LWORK, INFO
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE ORGBR_64(VECT, M, [N], K, A, [LDA], TAU, [WORK], [LWORK],
[INFO])
CHARACTER(LEN=1) :: VECT
INTEGER(8) :: M, N, K, LDA, LWORK, INFO
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void dorgbr(char vect, int m, int n, int k, double *a, int lda, double
*tau, int *info);
void dorgbr_64(char vect, long m, long n, long k, double *a, long lda,
double *tau, long *info);
PURPOSEdorgbr generates one of the real orthogonal matrices Q or P**T deter‐
mined by DGEBRD when reducing a real matrix A to bidiagonal form: A = Q
* B * P**T. Q and P**T are defined as products of elementary reflec‐
tors H(i) or G(i) respectively.
If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q is of
order M:
if m >= k, Q = H(1)H(2) . . . H(k) and DORGBR returns the first n col‐
umns of Q, where m >= n >= k;
if m < k, Q = H(1)H(2) . . . H(m-1) and DORGBR returns Q as an M-by-M
matrix.
If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T is
of order N:
if k < n, P**T = G(k) . . . G(2)G(1) and DORGBR returns the first m
rows of P**T, where n >= m >= k;
if k >= n, P**T = G(n-1) . . . G(2)G(1) and DORGBR returns P**T as an
N-by-N matrix.
ARGUMENTS
VECT (input)
Specifies whether the matrix Q or the matrix P**T is
required, as defined in the transformation applied by DGEBRD:
= 'Q': generate Q;
= 'P': generate P**T.
M (input) The number of rows of the matrix Q or P**T to be returned. M
>= 0.
N (input) The number of columns of the matrix Q or P**T to be returned.
N >= 0. If VECT = 'Q', M >= N >= min(M,K); if VECT = 'P', N
>= M >= min(N,K).
K (input) If VECT = 'Q', the number of columns in the original M-by-K
matrix reduced by DGEBRD. If VECT = 'P', the number of rows
in the original K-by-N matrix reduced by DGEBRD. K >= 0.
A (input/output)
On entry, the vectors which define the elementary reflectors,
as returned by DGEBRD. On exit, the M-by-N matrix Q or P**T.
LDA (input)
The leading dimension of the array A. LDA >= max(1,M).
TAU (input)
(min(M,K)) if VECT = 'Q' (min(N,K)) if VECT = 'P' TAU(i) must
contain the scalar factor of the elementary reflector H(i) or
G(i), which determines Q or P**T, as returned by DGEBRD in
its array argument TAUQ or TAUP.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The dimension of the array WORK. LWORK >= max(1,min(M,N)).
For optimum performance LWORK >= min(M,N)*NB, where NB is the
optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
6 Mar 2009 dorgbr(3P)
