CGEQL2 (3lapack)

compute a QL factorization of a complex m by n matrix A

SYNOPSIS

  SUBROUTINE CGEQL2( M, N, A, LDA, TAU, WORK, INFO )

      INTEGER        INFO, LDA, M, N

      COMPLEX        A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

  CGEQL2 computes a QL factorization of a complex 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) COMPLEX 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 unitary
          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) COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).

  WORK    (workspace) COMPLEX array, dimension (N)

  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 complex scalar, and v is a complex 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).