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DORGBR(3F)							    DORGBR(3F)

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( LWORK )

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).

									Page 1

DORGBR(3F)							    DORGBR(3F)

     K	     (input) INTEGER
	     If VECT = 'Q', the number of columns in the original 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, 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.

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0:  if INFO = -i, the i-th argument had an illegal value

									Page 2

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