DORMTR(l) ) DORMTR(l)NAME
DORMTR - overwrite the general real M-by-N matrix C with SIDE = 'L'
SIDE = 'R' TRANS = 'N'
SYNOPSIS
SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, WORK,
LWORK, INFO )
CHARACTER SIDE, TRANS, UPLO
INTEGER INFO, LDA, LDC, LWORK, M, N
DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK(
* )
PURPOSE
DORMTR 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 nq-1 ele‐
mentary reflectors, as returned by DSYTRD:
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
DSYTRD; = 'L': Lower triangle of A contains elementary reflec‐
tors from DSYTRD.
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) DOUBLE PRECISION array, dimension
(LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which
define the elementary reflectors, as returned by DSYTRD.
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) DOUBLE PRECISION 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
DSYTRD.
C (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (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 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) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
LAPACK version 3.0 15 June 2000 DORMTR(l)
