# sormhr (l) - Linux Man Pages

## NAME

SORMHR - overwrites the general real M-by-N matrix C with SIDE = aqLaq SIDE = aqRaq TRANS = aqNaq

## SYNOPSIS

SUBROUTINE SORMHR(
SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

CHARACTER SIDE, TRANS

INTEGER IHI, ILO, INFO, LDA, LDC, LWORK, M, N

REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )

## PURPOSE

SORMHR overwrites the general real M-by-N matrix C with TRANS = aqTaq: Q**T * C C * Q**T
where Q is a real orthogonal matrix of order nq, with nq = m if SIDE = aqLaq and nq = n if SIDE = aqRaq. Q is defined as the product of IHI-ILO elementary reflectors, as returned by SGEHRD:
Q = H(ilo) H(ilo+1) . . . H(ihi-1).

## ARGUMENTS

SIDE (input) CHARACTER*1
= aqLaq: apply Q or Q**T from the Left;
= aqRaq: apply Q or Q**T from the Right.
TRANS (input) CHARACTER*1

= aqNaq: No transpose, apply Q;
= aqTaq: Transpose, apply Q**T.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
ILO (input) INTEGER
IHI (input) INTEGER ILO and IHI must have the same values as in the previous call of SGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). If SIDE = aqLaq, then 1 <= ILO <= IHI <= M, if M > 0, and ILO = 1 and IHI = 0, if M = 0; if SIDE = aqRaq, then 1 <= ILO <= IHI <= N, if N > 0, and ILO = 1 and IHI = 0, if N = 0.
A (input) REAL array, dimension
(LDA,M) if SIDE = aqLaq (LDA,N) if SIDE = aqRaq The vectors which define the elementary reflectors, as returned by SGEHRD.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M) if SIDE = aqLaq; LDA >= max(1,N) if SIDE = aqRaq.
TAU (input) REAL array, dimension
(M-1) if SIDE = aqLaq (N-1) if SIDE = aqRaq TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEHRD.
C (input/output) REAL array, dimension (LDC,N)
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) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. If SIDE = aqLaq, LWORK >= max(1,N); if SIDE = aqRaq, LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = aqLaq, and LWORK >= M*NB if SIDE = aqRaq, 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) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value