dormbr(3P) Sun Performance Library dormbr(3P)NAMEdormbr - overwrites the general real M-by-N matrix C with Q*C or Q**T*C
or C*Q**T or C*Q or P*C or P**T*C or C*P or C*P**T.
SYNOPSIS
SUBROUTINE DORMBR(VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
WORK, LWORK, INFO)
CHARACTER * 1 VECT, SIDE, TRANS
INTEGER M, N, K, LDA, LDC, LWORK, INFO
DOUBLE PRECISION A(LDA,*), TAU(*), C(LDC,*), WORK(*)
SUBROUTINE DORMBR_64(VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
WORK, LWORK, INFO)
CHARACTER * 1 VECT, SIDE, TRANS
INTEGER*8 M, N, K, LDA, LDC, LWORK, INFO
DOUBLE PRECISION A(LDA,*), TAU(*), C(LDC,*), WORK(*)
F95 INTERFACE
SUBROUTINE ORMBR(VECT, SIDE, [TRANS], [M], [N], K, A, [LDA], TAU, C,
[LDC], [WORK], [LWORK], [INFO])
CHARACTER(LEN=1) :: VECT, SIDE, TRANS
INTEGER :: M, N, K, LDA, LDC, LWORK, INFO
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A, C
SUBROUTINE ORMBR_64(VECT, SIDE, [TRANS], [M], [N], K, A, [LDA], TAU,
C, [LDC], [WORK], [LWORK], [INFO])
CHARACTER(LEN=1) :: VECT, SIDE, TRANS
INTEGER(8) :: M, N, K, LDA, LDC, LWORK, INFO
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A, C
C INTERFACE
#include <sunperf.h>
void dormbr(char vect, char side, char trans, int m, int n, int k, dou‐
ble *a, int lda, double *tau, double *c, int ldc, int *info);
void dormbr_64(char vect, char side, char trans, long m, long n, long
k, double *a, long lda, double *tau, double *c, long ldc,
long *info);
PURPOSE
If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': P * C C * P
TRANS = 'T': P**T * C C * P**T
Here Q and P**T are the orthogonal matrices determined 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 reflectors H(i) and G(i)
respectively.
Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the order
of the orthogonal matrix Q or P**T that is applied.
If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: if nq >= k,
Q = H(1)H(2) . . . H(k);
if nq < k, Q = H(1)H(2) . . . H(nq-1).
If VECT = 'P', A is assumed to have been a K-by-NQ matrix: if k < nq, P
= G(1)G(2) . . . G(k);
if k >= nq, P = G(1)G(2) . . . G(nq-1).
ARGUMENTS
VECT (input)
= 'Q': apply Q or Q**T;
= 'P': apply P or P**T.
SIDE (input)
= 'L': apply Q, Q**T, P or P**T from the Left;
= 'R': apply Q, Q**T, P or P**T from the Right.
TRANS (input)
= 'N': No transpose, apply Q or P;
= 'T': Transpose, apply Q**T or P**T.
TRANS is defaulted to 'N' for F95 INTERFACE.
M (input) The number of rows of the matrix C. M >= 0.
N (input) The number of columns of the matrix C. N >= 0.
K (input) If VECT = 'Q', the number of columns in the original matrix
reduced by DGEBRD. If VECT = 'P', the number of rows in the
original matrix reduced by DGEBRD. K >= 0.
A (input) (LDA,min(nq,K)) if VECT = 'Q' (LDA,nq) if VECT = 'P'
The vectors which define the elementary reflectors H(i) and
G(i), whose products determine the matrices Q and P, as
returned by DGEBRD.
LDA (input)
The leading dimension of the array A. If VECT = 'Q', LDA >=
max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)).
TAU (input)
TAU(i) must contain the scalar factor of the elementary
reflector H(i) or G(i) which determines Q or P, as returned
by DGEBRD in the array argument TAUQ or TAUP.
C (input/output)
On entry, the M-by-N matrix C. On exit, C is overwritten by
Q*C or Q**T*C or C*Q**T or C*Q or P*C or P**T*C or C*P or
C*P**T.
LDC (input)
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The dimension of the array WORK. If SIDE = 'L', LWORK >=
max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum per‐
formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if
SIDE = 'R', 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 dormbr(3P)
