Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3  -  overwrites  the  general  real m by n matrix C with   Q * C if SIDE = 'L' and
TRANS = 'N', or   Q**T* C if SIDE = 'L' and TRANS = 'C', or   C * Q  if  SIDE  =  'R'  and
TRANS = 'N', or   C * Q**T if SIDE = 'R' and TRANS = 'C',

```

#### SYNOPSIS

```       SUBROUTINE DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO )

CHARACTER      SIDE, TRANS

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

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

```

#### PURPOSE

```       DORMR3 overwrites the general real m by n matrix C with
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 DTZRZF. 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': apply Q  (No transpose)
= 'T': apply Q**T (Transpose)

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.

L       (input) INTEGER
The number of columns of the matrix A containing
the meaningful part of the Householder reflectors.
If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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
DTZRZF 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 DTZRZF.

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
(N) if SIDE = 'L',
(M) if SIDE = 'R'

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

```

#### FURTHERDETAILS

```        Based on contributions by
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

LAPACK routine (version 3.3.1)             April 2011                            DORMR3(3lapack)
```