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DGEQPF(3F)							    DGEQPF(3F)


NAME    [Toc]    [Back]

     DGEQPF - compute a	QR factorization with column pivoting of a real	M-by-N
     matrix A

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	DGEQPF(	M, N, A, LDA, JPVT, TAU, WORK, INFO )

	 INTEGER	INFO, LDA, M, N

	 INTEGER	JPVT( *	)

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

PURPOSE    [Toc]    [Back]

     DGEQPF computes a QR factorization	with column pivoting of	a real M-by-N
     matrix A: A*P = 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 upper	triangle of
	     the array contains	the min(M,N)-by-N upper	triangular matrix R;
	     the elements below	the diagonal, together with the	array TAU,
	     represent the orthogonal matrix Q as a product of min(m,n)
	     elementary	reflectors.

     LDA     (input) INTEGER
	     The leading dimension of the array	A. LDA >= max(1,M).

     JPVT    (input/output) INTEGER array, dimension (N)
	     On	entry, if JPVT(i) .ne. 0, the i-th column of A is permuted to
	     the front of A*P (a leading column); if JPVT(i) = 0, the i-th
	     column of A is a free column.  On exit, if	JPVT(i)	= k, then the
	     i-th column of A*P	was the	k-th column of A.

     TAU     (output) DOUBLE PRECISION array, dimension	(min(M,N))
	     The scalar	factors	of the elementary reflectors.

     WORK    (workspace) DOUBLE	PRECISION array, dimension (3*N)

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0:  if INFO = -i, the i-th argument had an illegal value






									Page 1






DGEQPF(3F)							    DGEQPF(3F)



FURTHER	DETAILS
     The matrix	Q is represented as a product of elementary reflectors

	Q = H(1) H(2) .	. . H(n)

     Each H(i) has the form

	H = 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).

     The matrix	P is represented in jpvt as follows: If
	jpvt(j)	= i
     then the jth column of P is the ith canonical unit	vector.
DGEQPF(3F)							    DGEQPF(3F)


NAME    [Toc]    [Back]

     DGEQPF - compute a	QR factorization with column pivoting of a real	M-by-N
     matrix A

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	DGEQPF(	M, N, A, LDA, JPVT, TAU, WORK, INFO )

	 INTEGER	INFO, LDA, M, N

	 INTEGER	JPVT( *	)

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

PURPOSE    [Toc]    [Back]

     DGEQPF computes a QR factorization	with column pivoting of	a real M-by-N
     matrix A: A*P = 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 upper	triangle of
	     the array contains	the min(M,N)-by-N upper	triangular matrix R;
	     the elements below	the diagonal, together with the	array TAU,
	     represent the orthogonal matrix Q as a product of min(m,n)
	     elementary	reflectors.

     LDA     (input) INTEGER
	     The leading dimension of the array	A. LDA >= max(1,M).

     JPVT    (input/output) INTEGER array, dimension (N)
	     On	entry, if JPVT(i) .ne. 0, the i-th column of A is permuted to
	     the front of A*P (a leading column); if JPVT(i) = 0, the i-th
	     column of A is a free column.  On exit, if	JPVT(i)	= k, then the
	     i-th column of A*P	was the	k-th column of A.

     TAU     (output) DOUBLE PRECISION array, dimension	(min(M,N))
	     The scalar	factors	of the elementary reflectors.

     WORK    (workspace) DOUBLE	PRECISION array, dimension (3*N)

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0:  if INFO = -i, the i-th argument had an illegal value






									Page 1






DGEQPF(3F)							    DGEQPF(3F)



FURTHER	DETAILS
     The matrix	Q is represented as a product of elementary reflectors

	Q = H(1) H(2) .	. . H(n)

     Each H(i) has the form

	H = 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).

     The matrix	P is represented in jpvt as follows: If
	jpvt(j)	= i
     then the jth column of P is the ith canonical unit	vector.


									PPPPaaaaggggeeee 2222
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