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# dormbr

```
NAME
DORMBR - VECT = 'Q', DORMBR overwrites the general real M-
by-N matrix C with  SIDE = 'L' SIDE = 'R' TRANS = 'N'

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

CHARACTER      SIDE, TRANS, VECT

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

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

PURPOSE
If VECT = 'Q', DORMBR 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

If VECT = 'P', DORMBR overwrites the general real M-by-N
matrix C with
SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      P * C          C * P
TRANS = 'T':      P**T * C       C * P**T

Here Q and P**T are the orthogonal matrices determined by
DGEBRD when reducing a real matrix A to bidiagonal form: A =
Q * B * P**T. Q and P**T are defined as products of elemen-
tary reflectors H(i) and G(i) respectively.

Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq
is the order of the orthogonal matrix Q or P**T that is
applied.

If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq-1).

If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq-1).

ARGUMENTS
VECT    (input) CHARACTER*1
= 'Q': apply Q or Q**T;
= 'P': apply P or P**T.

SIDE    (input) CHARACTER*1

= 'L': apply Q, Q**T, P or P**T from the Left;
= 'R': apply Q, Q**T, P or P**T from the Right.

TRANS   (input) CHARACTER*1
= 'N':  No transpose, apply Q  or P;
= 'T':  Transpose, apply Q**T or P**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
K >= 0.  If VECT = 'Q', the number of columns in the
original matrix reduced by DGEBRD.  If VECT = 'P',
the number of rows in the original matrix reduced by
DGEBRD.

A       (input) DOUBLE PRECISION array, dimension
(LDA,min(nq,K)) if VECT = 'Q' (LDA,nq)        if
VECT = 'P' The vectors which define the elementary
reflectors H(i) and G(i), whose products determine
the matrices Q and P, as returned by DGEBRD.

LDA     (input) INTEGER
The leading dimension of the array A.  If VECT =
'Q', LDA >= max(1,nq); if VECT = 'P', LDA >=
max(1,min(nq,K)).

TAU     (input) DOUBLE PRECISION array, dimension (min(nq,K))
TAU(i) must contain the scalar factor of the elemen-
tary reflector H(i) or G(i) which determines Q or P,
as returned by DGEBRD in the array argument TAUQ or
TAUP.

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 or P*C
or P**T*C or C*P or C*P**T.

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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