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dgelq2 examples
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Man Page Details
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NAME
       DGELQ2 - an LQ factorization of a real m by n matrix A

SYNOPSIS
       SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO )

           INTEGER        INFO, LDA, M, N

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

PURPOSE
       DGELQ2  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) DOUBLE PRECISION array, dimension (M)

       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).

