cgeqlf man page on Scientific

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CGEQLF(1)		 LAPACK routine (version 3.2)		     CGEQLF(1)

NAME
       CGEQLF - computes 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	dimen‐
	       sion 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 (MAX(1,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 opti‐
	       mum  performance	 LWORK >= N*NB, where NB is the optimal block‐
	       size.  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 routine (version 3.2)	 November 2008			     CGEQLF(1)
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