dormhr(3)

NAME

DORMHR - overwrite the general real M-by-N matrix C with

SIDE = 'L' SIDE = 'R' TRANS = 'N'

SYNOPSIS

SUBROUTINE  DORMHR(  SIDE,  TRANS, M, N, ILO, IHI, A, LDA,
TAU, C, LDC, WORK, LWORK, INFO )
    CHARACTER      SIDE, TRANS
    INTEGER        IHI, ILO, INFO, LDA, LDC, LWORK, M, N
    DOUBLE         PRECISION A( LDA, * ),  C(  LDC,  *  ),
TAU( * ), WORK( * )

PURPOSE

DORMHR 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 IHI-ILO elementary reflectors, as returned by DGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).

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.

ILO (input) INTEGER

IHI (input) INTEGER ILO and IHI must have the

same values as in the previous call of DGEHRD. Q is equal to the

unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). If

SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and ILO = 1 and

IHI = 0, if M = 0; if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N

> 0, and ILO = 1 and IHI = 0, if 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

DGEHRD.

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 DGEHRD.

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

DORMHR(3)