dgelqf man page on Scientific

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DGELQF(1)		 LAPACK routine (version 3.2)		     DGELQF(1)

NAME
       DGELQF - computes 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
       (MAX(1,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 routine (version 3.2)	 November 2008			     DGELQF(1)
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