sorgbr(3)

NAME

SORGBR - generate one of the real orthogonal matrices Q or

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

agonal form

SYNOPSIS

SUBROUTINE SORGBR( VECT, M,  N,  K,  A,  LDA,  TAU,  WORK,
LWORK, INFO )
    CHARACTER      VECT
    INTEGER        INFO, K, LDA, LWORK, M, N
    REAL           A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

SORGBR generates one of the real orthogonal matrices Q or

P**T determined by SGEBRD 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 SORGBR returns the

first n columns of Q, where m >= n >= k;
if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR 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 SORGBR 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 SORGBR 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 SGEBRD:
= '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 SGEBRD. If VECT = 'P', the number

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

A (input/output) REAL array, dimension (LDA,N)

On entry, the vectors which define the elementary

reflectors, as returned by SGEBRD. 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) REAL 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 SGEBRD

in its array argument TAUQ or TAUP.

WORK (workspace/output) REAL array, dimension (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

SORGBR(3)