cgeqlf.f(3) [debian man page]

cgeqlf.f(3)							      LAPACK							       cgeqlf.f(3)

NAME

       cgeqlf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine cgeqlf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
	   CGEQLF

Function/Subroutine Documentation
   subroutine cgeqlf (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension( * )WORK,
       integerLWORK, integerINFO)
       CGEQLF

       Purpose:

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

	   WORK

		     WORK is COMPLEX 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,N).
		     For optimum performance LWORK >= N*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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       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 139 of file cgeqlf.f.

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

Version 3.4.1							  Sun May 26 2013						       cgeqlf.f(3)

Check Out this Related Man Page

CGEQLF(l)								 )								 CGEQLF(l)

NAME

       CGEQLF - compute a QL factorization of a complex M-by-N matrix A

SYNOPSIS

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

	   INTEGER	  INFO, LDA, LWORK, M, N

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

PURPOSE

       CGEQLF 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/output) COMPLEX 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.

	       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    (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 							 CGEQLF(l)

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