SGEQLF (3lapack)

compute a QL factorization of a real M-by-N matrix A

SYNOPSIS

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

      INTEGER        INFO, LDA, LWORK, M, N

      REAL           A( LDA, * ), TAU( * ), WORK( LWORK )

PURPOSE

  SGEQLF computes a QL factorization of a real M-by-N matrix A: A = Q * L.

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) REAL array, dimension (LDA,N)
          On entry, the M-by-N matrix A.  On exit, if m >= n, the lower
          triangle of the subarray A(m-n+1:m,1:n) contains the N-by-N lower
          triangular matrix L; if m <= n, the elements on and below the (n-
          m)-th superdiagonal contain the M-by-N lower trapezoidal matrix L;
          the remaining elements, with the array TAU, represent the
          orthogonal matrix Q as a product of elementary reflectors (see
          Further Details).  LDA     (input) INTEGER The leading dimension of
          the array A.  LDA >= max(1,M).

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

  WORK    (workspace/output) REAL 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,N).  For optimum
          performance LWORK >= N*NB, where NB is the optimal blocksize.

  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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
  A(1:m-k+i-1,n-k+i), and tau in TAU(i).