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dgelqf examples
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Man Page Details
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NAME
       DGELQF - 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).

