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RedHat 9 (Linux i386) - man page for cgeql2 (redhat section l)

CGEQL2(l)					)					CGEQL2(l)

NAME
       CGEQL2 - 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 sub-
	       array 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 trape-
	       zoidal 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).

LAPACK version 3.0			   15 June 2000 				CGEQL2(l)


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