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DGEQLF(3F)							    DGEQLF(3F)


NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

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

	 INTEGER	INFO, LDA, LWORK, M, N

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

PURPOSE    [Toc]    [Back]

     DGEQLF computes a QL factorization	of a real M-by-N matrix	A:  A =	Q * L.

ARGUMENTS    [Toc]    [Back]

     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).
DGEQLF(3F)							    DGEQLF(3F)


NAME    [Toc]    [Back]

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

SYNOPSIS    [Toc]    [Back]

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

	 INTEGER	INFO, LDA, LWORK, M, N

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

PURPOSE    [Toc]    [Back]

     DGEQLF computes a QL factorization	of a real M-by-N matrix	A:  A =	Q * L.

ARGUMENTS    [Toc]    [Back]

     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).


									PPPPaaaaggggeeee 2222
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