SORMRQ(3) overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

## SYNOPSIS

SUBROUTINE SORMRQ(
SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO )

CHARACTER SIDE, TRANS

INTEGER INFO, K, LDA, LDC, LWORK, M, N

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

## PURPOSE

SORMRQ overwrites the general real M-by-N matrix C with TRANS = 'T': Q**T * C C * Q**T
where Q is a real orthogonal matrix defined as the product of k elementary reflectors

Q = H(1) H(2) . . . H(k)
as returned by SGERQF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

## ARGUMENTS

SIDE (input) CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS (input) CHARACTER*1

= 'N': No transpose, apply Q;
= 'T': 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.
K (input) INTEGER
The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.
A (input) REAL array, dimension
(LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGERQF in the last k rows of its array argument A. A is modified by the routine but restored on exit.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,K).
TAU (input) REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGERQF.
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 = '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) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value