dgelqf man page on YellowDog

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DGELQF(l)			       )			     DGELQF(l)

NAME
       DGELQF - compute an LQ factorization of a real M-by-N matrix A

SYNOPSIS
       SUBROUTINE DGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )

	   INTEGER	  INFO, LDA, LWORK, M, N

	   DOUBLE	  PRECISION A( LDA, * ), TAU( * ), WORK( * )

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

ARGUMENTS
       M       (input) INTEGER
	       The number of rows of the matrix A.  M >= 0.

       N       (input) INTEGER
	       The number of columns of the matrix A.  N >= 0.

       A       (input/output) DOUBLE PRECISION 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	    (input) INTEGER The leading dimen‐
	       sion of the array A.  LDA >= max(1,M).

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

       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,M).  For opti‐
	       mum performance LWORK >= M*NB, where NB is the  optimal	block‐
	       size.

	       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

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'

       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).

LAPACK version 3.0		 15 June 2000			     DGELQF(l)
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