dormtr(3)

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 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 re

flectors from DSYTRD; = 'L': Lower triangle of A contains elemen

tary 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, dimen

sion (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 ille

gal value

LAPACK version 3.0 15 June 2000

DORMTR(3)