dorgbr(l) [redhat man page]

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 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.

	       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)