# dormrq.f(3) [debian man page]

```dormrq.f(3)							      LAPACK							       dormrq.f(3)

NAME
dormrq.f -

SYNOPSIS
Functions/Subroutines
recursive subroutine dormrq (SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMRQ

Function/Subroutine Documentation
recursive subroutine dormrq (characterSIDE, characterTRANS, integerM, integerN, integerK, double precision, dimension( lda, * )A, integerLDA,
double precision, dimension( * )TAU, double precision, dimension( ldc, * )C, integerLDC, double precision, dimension( * )WORK,
integerLWORK, integerINFO)
DORMRQ

Purpose:

DORMRQ 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 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'.

Parameters:
SIDE

SIDE is CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.

TRANS

TRANS is CHARACTER*1
= 'N':  No transpose, apply Q;
= 'T':  Transpose, apply Q**T.

M

M is INTEGER
The number of rows of the matrix C. M >= 0.

N

N is INTEGER
The number of columns of the matrix C. N >= 0.

K

K is 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

A is 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.

LDA

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

TAU

TAU is DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGERQF.

C

C is 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

LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).

WORK

WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is 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

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

Author:
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:
November 2011

Definition at line 169 of file dormrq.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       dormrq.f(3)```

## Check Out this Related Man Page

```DORMRQ(l)								 )								 DORMRQ(l)

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( * )

PURPOSE
DORMRQ 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 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 elementary 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/output) 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.

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

LAPACK version 3.0						   15 June 2000 							 DORMRQ(l)```
Man Page