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DGEQRF(3F)							    DGEQRF(3F)


NAME    [Toc]    [Back]

     DGEQRF - compute a	QR factorization of a real M-by-N matrix A

SYNOPSIS    [Toc]    [Back]

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

	 INTEGER	INFO, LDA, LWORK, M, N

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

PURPOSE    [Toc]    [Back]

     DGEQRF computes a QR factorization	of a real M-by-N matrix	A:  A =	Q * R.

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, the elements on and
	     above the diagonal	of the array contain the min(M,N)-by-N upper
	     trapezoidal matrix	R (R is	upper triangular if m >= n); the
	     elements below the	diagonal, with the array TAU, represent	the
	     orthogonal	matrix Q as a product of min(m,n) 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(1) H(2) .	. . H(k), where	k = min(m,n).




									Page 1






DGEQRF(3F)							    DGEQRF(3F)



     Each H(i) has the form

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

     where tau is a real scalar, and v is a real vector	with
     v(1:i-1) =	0 and v(i) = 1;	v(i+1:m) is stored on exit in A(i+1:m,i), and
     tau in TAU(i).
DGEQRF(3F)							    DGEQRF(3F)


NAME    [Toc]    [Back]

     DGEQRF - compute a	QR factorization of a real M-by-N matrix A

SYNOPSIS    [Toc]    [Back]

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

	 INTEGER	INFO, LDA, LWORK, M, N

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

PURPOSE    [Toc]    [Back]

     DGEQRF computes a QR factorization	of a real M-by-N matrix	A:  A =	Q * R.

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, the elements on and
	     above the diagonal	of the array contain the min(M,N)-by-N upper
	     trapezoidal matrix	R (R is	upper triangular if m >= n); the
	     elements below the	diagonal, with the array TAU, represent	the
	     orthogonal	matrix Q as a product of min(m,n) 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(1) H(2) .	. . H(k), where	k = min(m,n).




									Page 1






DGEQRF(3F)							    DGEQRF(3F)



     Each H(i) has the form

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

     where tau is a real scalar, and v is a real vector	with
     v(1:i-1) =	0 and v(i) = 1;	v(i+1:m) is stored on exit in A(i+1:m,i), and
     tau in TAU(i).


									PPPPaaaaggggeeee 2222
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