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sgerqf.f(3)				      LAPACK				      sgerqf.f(3)

NAME
       sgerqf.f -

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

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

       Purpose:

	    SGERQF computes an RQ factorization of a real M-by-N matrix A:
	    A = R * 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,
		     if m <= n, the upper triangle of the subarray
		     A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R;
		     if m >= n, the elements on and above the (m-n)-th subdiagonal
		     contain the M-by-N upper trapezoidal matrix R;
		     the remaining elements, with the array TAU, represent the
		     orthogonal matrix Q as a product of min(m,n) 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(1) H(2) . . . H(k), 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
	     A(m-k+i,1:n-k+i-1), and tau in TAU(i).

       Definition at line 139 of file sgerqf.f.

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

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