Previous: dormql Up: ../lapack-d.html Next: dormr2

# dormqr

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

SYNOPSIS
SUBROUTINE DORMQR( 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
DORMQR 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 DGEQRF. 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,K)
The i-th column must contain the vector which
defines the elementary reflector H(i), for i =
1,2,...,k, as returned by DGEQRF in the first k

columns 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.  If SIDE =
'L', LDA >= max(1,M); if SIDE = 'R', LDA >=
max(1,N).

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

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
```