sgsvj1.f(3)							      LAPACK							       sgsvj1.f(3)

NAME

       sgsvj1.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sgsvj1 (JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO)
	   SGSVJ1 pre-processor for the routine sgesvj, applies Jacobi rotations targeting only particular pivots.

Function/Subroutine Documentation
   subroutine sgsvj1 (character*1JOBV, integerM, integerN, integerN1, real, dimension( lda, * )A, integerLDA, real, dimension( n )D, real,
       dimension( n )SVA, integerMV, real, dimension( ldv, * )V, integerLDV, realEPS, realSFMIN, realTOL, integerNSWEEP, real, dimension( lwork
       )WORK, integerLWORK, integerINFO)
       SGSVJ1 pre-processor for the routine sgesvj, applies Jacobi rotations targeting only particular pivots.

       Purpose:

	    SGSVJ1 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
	    ~~~~~~~~~~~~~~~
	    SGSVJ1 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.

       Parameters:
	   JOBV

		     JOBV is 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

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

	   N

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

	   N1

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

	   A

		     A is 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

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

	   D

		     D is 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

		     SVA is 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

		     MV is 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

		     V is 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

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

	   EPS

		     EPS is REAL
		     EPS = SLAMCH('Epsilon')

	   SFMIN

		     SFMIN is REAL
		     SFMIN = SLAMCH('Safe Minimum')

	   TOL

		     TOL is 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 ABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.

	   NSWEEP

		     NSWEEP is INTEGER
		     NSWEEP is the number of sweeps of Jacobi rotations to be
		     performed.

	   WORK

		     WORK is REAL array, dimension LWORK.

	   LWORK

		     LWORK is INTEGER
		     LWORK is the dimension of WORK. LWORK .GE. M.

	   INFO

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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Contributors:
	   Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)

       Definition at line 236 of file sgsvj1.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       sgsvj1.f(3)