Contents
dormbr - VECT = 'Q', DORMBR overwrites the general real M-
by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
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, double *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);
dormbr 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
SGEBRD when reducing a real matrix A to bidiagonal form: A =
Q * B * P**T. Q and P**T are defined as products of elemen-
tary 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).
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 origi-
nal matrix reduced by SGEBRD. If VECT = 'P', the
number of rows in the original matrix reduced by
SGEBRD. 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 SGEBRD.
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 ele-
mentary reflector H(i) or G(i) which determines Q
or P, as returned by SGEBRD 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 performance 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 ille-
gal value