DORMTR(3f)

NAME
DORMTR - 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 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 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 reflectors 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 (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