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DGSVJ1(1LAPACK routine (version 3.2)				     DGSVJ1(1)

NAME
       DGSVJ1  - is called from SGESVJ as a pre-processor and that is its main
       purpose

SYNOPSIS
       SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,

	   +		  EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )

	   IMPLICIT	  NONE

	   DOUBLE	  PRECISION EPS, SFMIN, TOL

	   INTEGER	  INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP

	   CHARACTER*1	  JOBV

	   DOUBLE	  PRECISION A( LDA, * ), D( N ), SVA( N ), V(  LDV,  *
			  ),

	   +		  WORK( LWORK )

PURPOSE
       DGSVJ1  is  called  from SGESVJ as a pre-processor and that is its main
       purpose. It applies Jacobi rotations in the same way  as	 SGESVJ	 does,
       but it targets only particular pivots and it does not check convergence
       (stopping criterion). Few  tunning  parameters  (marked	by  [TP])  are
       available for the implementer.
       Further Details
       DGSVJ1  applies	few  sweeps of Jacobi rotations in the column space of
       the input M-by-N matrix A. The pivot pairs are  taken  from  the	 (1,2)
       off-diagonal block in the corresponding N-by-N Gram matrix A^T * A. The
       block-entries (tiles) of the (1,2) off-diagonal block are marked by the
       [x]'s in the following scheme:
	  | *	*   * [x] [x] [x]|
	  |  *	  *    *  [x]  [x] [x]|	   Row-cycling in the nblr-by-nblc [x]
       blocks.
	  | *	*   * [x] [x] [x]|     Row-cyclic  pivoting  inside  each  [x]
       block.
	  |[x] [x] [x] *   *   * |
	  |[x] [x] [x] *   *   * |
	  |[x] [x] [x] *   *   * |
       In  terms  of  the  columns  of	A,  the	 first	N1 columns are rotated
       'against' the remaining N-N1 columns,  trying  to  increase  the	 angle
       between the corresponding subspaces. The off-diagonal block is N1-by(N-
       N1) and it is tiled using quadratic tiles of side KBL. Here, KBL	 is  a
       tunning	parmeter.   The	 number	 of  sweeps is given in NSWEEP and the
       orthogonality threshold is given in TOL.
       Contributors
       ~~~~~~~~~~~~
       Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)

ARGUMENTS
       JOBV    (input) CHARACTER*1
	       Specifies whether the output from this  procedure  is  used  to
	       compute the matrix V:
	       =  'V':	the  product of the Jacobi rotations is accumulated by
	       postmulyiplying the N-by-N array V.  (See  the  description  of
	       V.)   = 'A': the product of the Jacobi rotations is accumulated
	       by postmulyiplying the MV-by-N array V.	(See the  descriptions
	       of MV and V.)  = 'N': the Jacobi rotations are not accumulated.

       M       (input) INTEGER
	       The number of rows of the input matrix A.  M >= 0.

       N       (input) INTEGER
	       The number of columns of the input matrix A.  M >= N >= 0.

       N1      (input) INTEGER
	       N1  specifies  the  2 x 2 block partition, the first N1 columns
	       are rotated 'against' the remaining N-N1 columns of A.

       A       (input/output) REAL array, dimension (LDA,N)
	       On entry, M-by-N matrix A, such that A*diag(D)  represents  the
	       input  matrix.	On  exit,  A_onexit  * D_onexit represents the
	       input matrix A*diag(D) post-multiplied by a sequence of	Jacobi
	       rotations, where the rotation threshold and the total number of
	       sweeps are given in TOL and  NSWEEP,  respectively.   (See  the
	       descriptions of N1, D, TOL and NSWEEP.)

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

       D       (input/workspace/output) REAL array, dimension (N)
	       The  array  D  accumulates  the	scaling	 factors from the fast
	       scaled Jacobi rotations.	 On entry,  A*diag(D)  represents  the
	       input  matrix.  On exit, A_onexit*diag(D_onexit) represents the
	       input matrix post-multiplied by a sequence of Jacobi rotations,
	       where the rotation threshold and the total number of sweeps are
	       given in TOL and NSWEEP, respectively.  (See  the  descriptions
	       of N1, A, TOL and NSWEEP.)

       SVA     (input/workspace/output) REAL array, dimension (N)
	       On  entry,  SVA	contains the Euclidean norms of the columns of
	       the matrix A*diag(D).  On  exit,	 SVA  contains	the  Euclidean
	       norms of the columns of the matrix onexit*diag(D_onexit).

       MV      (input) INTEGER
	       If  JOBV	 .EQ.  'A',  then MV rows of V are post-multipled by a
	       sequence of Jacobi rotations.  If JOBV = 'N',   then MV is  not
	       referenced.

       V       (input/output) REAL array, dimension (LDV,N)
	       If  JOBV	 .EQ.  'V'  then  N  rows of V are post-multipled by a
	       sequence of Jacobi rotations.  If JOBV .EQ. 'A' then MV rows of
	       V  are  post-multipled  by  a sequence of Jacobi rotations.  If
	       JOBV = 'N',   then V is not referenced.

       LDV     (input) INTEGER
	       The leading dimension of the array V,  LDV >=  1.   If  JOBV  =
	       'V', LDV .GE. N.	 If JOBV = 'A', LDV .GE. MV.

       EPS     (input) INTEGER
	       EPS = SLAMCH('Epsilon')

       SFMIN   (input) INTEGER
	       SFMIN = SLAMCH('Safe Minimum')

       TOL     (input) REAL
	       TOL  is	the threshold for Jacobi rotations. For a pair A(:,p),
	       A(:,q) of pivot columns, the Jacobi rotation is
	       applied only if DABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.

       NSWEEP  (input) INTEGER
	       NSWEEP is the number of sweeps of Jacobi rotations to  be  per‐
	       formed.

       WORK    (workspace) REAL array, dimension LWORK.

       LWORK   (input) INTEGER
	       LWORK is the dimension of WORK. LWORK .GE. M.

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

 LAPACK routine (version 3.2)	 November 2008			     DGSVJ1(1)
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