dorgbr(3)

NAME

DORGBR - generate one of the real orthogonal matrices Q or

P**T determined by DGEBRD when reducing a real matrix A to bidi

agonal form

SYNOPSIS

SUBROUTINE DORGBR( VECT, M,  N,  K,  A,  LDA,  TAU,  WORK,
LWORK, INFO )
    CHARACTER      VECT
    INTEGER        INFO, K, LDA, LWORK, M, N
    DOUBLE          PRECISION A( LDA, * ), TAU( * ), WORK(
* )

PURPOSE

DORGBR generates one of the real orthogonal matrices Q or

P**T determined by DGEBRD when reducing a real matrix A to bidi

agonal form: A = Q * B * P**T. Q and P**T are defined as products

of elementary reflectors H(i) or G(i) respectively.

If VECT = 'Q', A is assumed to have been an M-by-K matrix,

and Q is of order M:
if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the

first n columns of Q, where m >= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q

as an M-by-M matrix.

If VECT = 'P', A is assumed to have been a K-by-N matrix,

and P**T is of order N:
if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns

the first m rows of P**T, where n >= m >= k;
if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR re

turns P**T as an N-by-N matrix.

ARGUMENTS

VECT (input) CHARACTER*1

Specifies whether the matrix Q or the matrix P**T

is required, as defined in the transformation applied by DGEBRD:
= 'Q': generate Q;
= 'P': generate P**T.

M (input) INTEGER

The number of rows of the matrix Q or P**T to be

returned. M >= 0.

N (input) INTEGER

The number of columns of the matrix Q or P**T to

be returned. N >= 0. If VECT = 'Q', M >= N >= min(M,K); if VECT

= 'P', N >= M >= min(N,K).

K (input) INTEGER

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

nal M-by-K matrix reduced by DGEBRD. If VECT = 'P', the number

of rows in the original K-by-N matrix reduced by DGEBRD. K >= 0.

A (input/output) DOUBLE PRECISION array, dimension

(LDA,N)

On entry, the vectors which define the elementary

reflectors, as returned by DGEBRD. On exit, the M-by-N matrix Q

or P**T.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(1,M).

TAU (input) DOUBLE PRECISION array, dimension

(min(M,K)) if VECT = 'Q' (min(N,K)) if VECT = 'P'

TAU(i) must contain the scalar factor of the elementary reflector

H(i) or G(i), which determines Q or P**T, as returned by DGEBRD

in its array argument TAUQ or TAUP.

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. LWORK >=

max(1,min(M,N)). For optimum performance LWORK >= min(M,N)*NB,

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

DORGBR(3)