dormbr(3)

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( * )

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 elementary re

flectors 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 ma

trix: 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

If VECT = 'Q', the number of columns in the origi

nal matrix reduced by DGEBRD. If VECT = 'P', the number of rows

in the original matrix reduced by DGEBRD. K >= 0.

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 ele

mentary reflector H(i) or G(i) which determines Q or P, as re

turned 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/output) DOUBLE PRECISION array, dimen

sion (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 ille

gal value

LAPACK version 3.0 15 June 2000

DORMBR(3)