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dormhr

```
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( LWORK )

PURPOSE
DORMHR 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 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', 1 <= ILO and
min(M,ILO) <= IHI <= M; if SIDE = 'R', 1 <= ILO and
min(N,ILO) <= IHI <= N;

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 reflec-
tor 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) 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 performance LWORK >= N*NB if SIDE = 'L',
and LWORK >= M*NB if SIDE = 'R', where NB is the
optimal blocksize.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal
value
```