dormhr(3P) Sun Performance Library dormhr(3P)NAMEdormhr - overwrite the general real M-by-N matrix C with Q*C or Q**T*C
or C*Q**T or C*Q.
SYNOPSIS
SUBROUTINE DORMHR(SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC,
WORK, LWORK, INFO)
CHARACTER * 1 SIDE, TRANS
INTEGER M, N, ILO, IHI, LDA, LDC, LWORK, INFO
DOUBLE PRECISION A(LDA,*), TAU(*), C(LDC,*), WORK(*)
SUBROUTINE DORMHR_64(SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C,
LDC, WORK, LWORK, INFO)
CHARACTER * 1 SIDE, TRANS
INTEGER*8 M, N, ILO, IHI, LDA, LDC, LWORK, INFO
DOUBLE PRECISION A(LDA,*), TAU(*), C(LDC,*), WORK(*)
F95 INTERFACE
SUBROUTINE ORMHR(SIDE, [TRANS], [M], [N], ILO, IHI, A, [LDA], TAU, C,
[LDC], [WORK], [LWORK], [INFO])
CHARACTER(LEN=1) :: SIDE, TRANS
INTEGER :: M, N, ILO, IHI, LDA, LDC, LWORK, INFO
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A, C
SUBROUTINE ORMHR_64(SIDE, [TRANS], [M], [N], ILO, IHI, A, [LDA], TAU,
C, [LDC], [WORK], [LWORK], [INFO])
CHARACTER(LEN=1) :: SIDE, TRANS
INTEGER(8) :: M, N, ILO, IHI, LDA, LDC, LWORK, INFO
REAL(8), DIMENSION(:) :: TAU, WORK
REAL(8), DIMENSION(:,:) :: A, C
C INTERFACE
#include <sunperf.h>
void dormhr(char side, char trans, int m, int n, int ilo, int ihi, dou‐
ble *a, int lda, double *tau, double *c, int ldc, int *info);
void dormhr_64(char side, char trans, long m, long n, long ilo, long
ihi, double *a, long lda, double *tau, double *c, long ldc,
long *info);
PURPOSEdormhr 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
where Q is a real orthogonal matrix of order nq, with nq = m if SIDE =
'L' and nq = n if SIDE = 'R'. Q is defined as the product of IHI-ILO
elementary reflectors, as returned by DGEHRD:
Q = H(ilo) H(ilo+1) . . . H(ihi-1).
ARGUMENTS
SIDE (input)
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS (input)
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**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.
ILO (input)
ILO and IHI must have the same values as in the previous call
of DGEHRD. Q is equal to the unit matrix except in the subma‐
trix Q(ilo+1:ihi,ilo+1:ihi). If SIDE = 'L', then 1 <= ILO <=
IHI <= M, if M > 0, and ILO = 1 and IHI = 0, if M = 0; if
SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and ILO = 1
and IHI = 0, if N = 0.
IHI (input)
See the description of ILO.
A (input) (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which
define the elementary reflectors, as returned by DGEHRD.
LDA (input)
The leading dimension of the array A. LDA >= max(1,M) if
SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
TAU (input)
(M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain
the scalar factor of the elementary reflector H(i), as
returned by DGEHRD.
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.
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 dormhr(3P)
