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sgelqf.f(3)				      LAPACK				      sgelqf.f(3)

NAME
       sgelqf.f -

SYNOPSIS
   Functions/Subroutines
       subroutine sgelqf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
	   SGELQF

Function/Subroutine Documentation
   subroutine sgelqf (integerM, integerN, real, dimension( lda, * )A, integerLDA, real,
       dimension( * )TAU, real, dimension( * )WORK, integerLWORK, integerINFO)
       SGELQF

       Purpose:

	    SGELQF computes an LQ factorization of a real M-by-N matrix A:
	    A = L * Q.

       Parameters:
	   M

		     M is INTEGER
		     The number of rows of the matrix A.  M >= 0.

	   N

		     N is INTEGER
		     The number of columns of the matrix A.  N >= 0.

	   A

		     A is REAL array, dimension (LDA,N)
		     On entry, the M-by-N matrix A.
		     On exit, the elements on and below the diagonal of the array
		     contain the m-by-min(m,n) lower trapezoidal matrix L (L is
		     lower triangular if m <= n); the elements above the diagonal,
		     with the array TAU, represent the orthogonal matrix Q as a
		     product of elementary reflectors (see Further Details).

	   LDA

		     LDA is INTEGER
		     The leading dimension of the array A.  LDA >= max(1,M).

	   TAU

		     TAU is REAL array, dimension (min(M,N))
		     The scalar factors of the elementary reflectors (see Further
		     Details).

	   WORK

		     WORK is REAL array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

	   LWORK

		     LWORK is INTEGER
		     The dimension of the array WORK.  LWORK >= max(1,M).
		     For optimum performance LWORK >= M*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

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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Further Details:

	     The matrix Q is represented as a product of elementary reflectors

		Q = H(k) . . . H(2) H(1), where k = min(m,n).

	     Each H(i) has the form

		H(i) = I - tau * v * v**T

	     where tau is a real scalar, and v is a real vector with
	     v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
	     and tau in TAU(i).

       Definition at line 136 of file sgelqf.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      sgelqf.f(3)
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