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# dormrq

```
NAME
DORMRQ - overwrite the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R' TRANS = 'N'

SYNOPSIS
SUBROUTINE DORMRQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C,
LDC, WORK, LWORK, INFO )

CHARACTER      SIDE, TRANS

INTEGER        INFO, K, LDA, LDC, LWORK, M, N

DOUBLE         PRECISION A( LDA, * ), C( LDC, * ), TAU(
* ), WORK( LWORK )

PURPOSE
DORMRQ 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 defined as the product
of k elementary reflectors

Q = H(1) H(2) . . . H(k)

as returned by DGERQF. Q is of order M if SIDE = 'L' and of
order N if SIDE = 'R'.

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.

K       (input) INTEGER
The number of elementary reflectors whose product
defines the matrix Q.  If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.

A       (input) DOUBLE PRECISION array, dimension
(LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-
th row must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as

returned by DGERQF in the last k rows of its array
argument A.  A is modified by the routine but
restored on exit.

LDA     (input) INTEGER
The leading dimension of the array A. LDA >=
max(1,K).

TAU     (input) DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elemen-
tary reflector H(i), as returned by DGERQF.

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
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