DGELQF computes an LQ factorization of a real M-by-N matrix A:


 A = L * Q.

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 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

          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(1,M).

TAU

          TAU is DOUBLE PRECISION array, dimension (min(M,N))


          The scalar factors of the elementary reflectors (see Further


          Details).

WORK

          WORK is DOUBLE PRECISION 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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016

  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**T


  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).