CXML
        	    
LAPACK version 3.0
sorgbr(3)

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

SYNTAX
  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( * )

DESCRIPTION
  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