dgeqlf man page on IRIX

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DGEQLF(3F)							    DGEQLF(3F)

NAME
     DGEQLF - compute a QL factorization of a real M-by-N matrix A

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

	 INTEGER	INFO, LDA, LWORK, M, N

	 DOUBLE		PRECISION A( LDA, * ), TAU( * ), WORK( LWORK )

PURPOSE
     DGEQLF computes a QL factorization of a real 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) DOUBLE PRECISION 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 orthogonal 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) DOUBLE PRECISION array, dimension (min(M,N))
	     The scalar factors of the elementary reflectors (see Further
	     Details).

     WORK    (workspace/output) DOUBLE PRECISION 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.

     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

									Page 1

DGEQLF(3F)							    DGEQLF(3F)

	H(i) = I - tau * v * v'

     where tau is a real scalar, and v is a real 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).

									Page 2

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