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  man pages->IRIX man pages -> complib/sgerqf (3)              
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SGERQF(3F)							    SGERQF(3F)


NAME    [Toc]    [Back]

     SGERQF - compute an RQ factorization of a real M-by-N matrix A

SYNOPSIS    [Toc]    [Back]

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

	 INTEGER	INFO, LDA, LWORK, M, N

	 REAL		A( LDA,	* ), TAU( * ), WORK( LWORK )

PURPOSE    [Toc]    [Back]

     SGERQF computes an	RQ factorization of a real M-by-N matrix A:  A = R *
     Q.

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) REAL array,	dimension (LDA,N)
	     On	entry, the M-by-N matrix A.  On	exit, if m <= n, the upper
	     triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M upper
	     triangular	matrix R; if m >= n, the elements on and above the
	     (m-n)-th subdiagonal contain the M-by-N upper trapezoidal matrix
	     R;	the remaining elements,	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) REAL array, dimension (min(M,N))
	     The scalar	factors	of the elementary reflectors (see Further
	     Details).

     WORK    (workspace/output)	REAL 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,M).  For optimum
	     performance LWORK >= M*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






SGERQF(3F)							    SGERQF(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(n-k+i+1:n) = 0 and v(n-k+i) = 1;	v(1:n-k+i-1) is	stored on exit in
     A(m-k+i,1:n-k+i-1), and tau in TAU(i).
SGERQF(3F)							    SGERQF(3F)


NAME    [Toc]    [Back]

     SGERQF - compute an RQ factorization of a real M-by-N matrix A

SYNOPSIS    [Toc]    [Back]

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

	 INTEGER	INFO, LDA, LWORK, M, N

	 REAL		A( LDA,	* ), TAU( * ), WORK( LWORK )

PURPOSE    [Toc]    [Back]

     SGERQF computes an	RQ factorization of a real M-by-N matrix A:  A = R *
     Q.

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) REAL array,	dimension (LDA,N)
	     On	entry, the M-by-N matrix A.  On	exit, if m <= n, the upper
	     triangle of the subarray A(1:m,n-m+1:n) contains the M-by-M upper
	     triangular	matrix R; if m >= n, the elements on and above the
	     (m-n)-th subdiagonal contain the M-by-N upper trapezoidal matrix
	     R;	the remaining elements,	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) REAL array, dimension (min(M,N))
	     The scalar	factors	of the elementary reflectors (see Further
	     Details).

     WORK    (workspace/output)	REAL 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,M).  For optimum
	     performance LWORK >= M*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






SGERQF(3F)							    SGERQF(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(n-k+i+1:n) = 0 and v(n-k+i) = 1;	v(1:n-k+i-1) is	stored on exit in
     A(m-k+i,1:n-k+i-1), and tau in TAU(i).


									PPPPaaaaggggeeee 2222
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