zgeql2(l) [redhat man page]

ZGEQL2(l)								 )								 ZGEQL2(l)

NAME

       ZGEQL2 - compute a QL factorization of a complex m by n matrix A

SYNOPSIS

       SUBROUTINE ZGEQL2( M, N, A, LDA, TAU, WORK, INFO )

	   INTEGER	  INFO, LDA, M, N

	   COMPLEX*16	  A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

       ZGEQL2 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*16 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*16 array, dimension (min(M,N))
	       The scalar factors of the elementary reflectors (see Further Details).

       WORK    (workspace) COMPLEX*16 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 							 ZGEQL2(l)

zgeql2.f(3)							      LAPACK							       zgeql2.f(3)

NAME

       zgeql2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zgeql2 (M, N, A, LDA, TAU, WORK, INFO)
	   ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Function/Subroutine Documentation
   subroutine zgeql2 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( *
       )WORK, integerINFO)
       ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

       Purpose:

	    ZGEQL2 computes a QL factorization of a complex m by n matrix A:
	    A = Q * L.

       Parameters:
	   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 COMPLEX*16 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

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

	   TAU

		     TAU is COMPLEX*16 array, dimension (min(M,N))
		     The scalar factors of the elementary reflectors (see Further
		     Details).

	   WORK

		     WORK is COMPLEX*16 array, dimension (N)

	   INFO

		     INFO is INTEGER
		     = 0: successful exit
		     < 0: if INFO = -i, the i-th argument had an illegal value

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       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**H

	     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).

       Definition at line 124 of file zgeql2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       zgeql2.f(3)