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

## SYNOPSIS

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

CHARACTER SIDE, TRANS, UPLO

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

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

## PURPOSE

SORMTR 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 of order nq, with nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of nq-1 elementary reflectors, as returned by SSYTRD:
if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

## ARGUMENTS

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

= 'U': Upper triangle of A contains elementary reflectors from SSYTRD; = 'L': Lower triangle of A contains elementary reflectors from SSYTRD.
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.
A (input) REAL array, dimension
(LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by SSYTRD.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
TAU (input) REAL array, dimension
(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 SSYTRD.
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