sgsvj1.f - Man Page

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.

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:

November 2017

Contributors:

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

Definition at line 238 of file sgsvj1.f.