redhat man page for sorgbr

SORGBR(l)								 )								 SORGBR(l)

NAME
       SORGBR - generate one of the real orthogonal matrices Q or P**T determined by SGEBRD when reducing a real matrix A to bidiagonal 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 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 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 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 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 original 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 illegal value

LAPACK version 3.0						   15 June 2000 							 SORGBR(l)