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RedHat 9 (Linux i386) - man page for dorgbr (redhat section l)

DORGBR(l)					)					DORGBR(l)

NAME
       DORGBR  - generate one of the real orthogonal matrices Q or P**T determined by DGEBRD when
       reducing a real matrix A to bidiagonal 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 bidiagonal 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 returns 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 original M-by-K matrix reduced by DGE-
	       BRD.   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  DGE-
	       BRD.  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, 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 perfor-
	       mance 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 illegal value

LAPACK version 3.0			   15 June 2000 				DORGBR(l)


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