# sgsvj0.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine **sgsvj0** (JOBV, M, **N**, A, **LDA**, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO)**SGSVJ0** pre-processor for the routine sgesvj.

## Function/Subroutine Documentation

### subroutine sgsvj0 (character*1 JOBV, integer M, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( n ) D, real, dimension( n ) SVA, integer MV, real, dimension( ldv, * ) V, integer LDV, real EPS, real SFMIN, real TOL, integer NSWEEP, real, dimension( lwork ) WORK, integer LWORK, integer INFO)

**SGSVJ0** pre-processor for the routine sgesvj.

**Purpose:**

SGSVJ0 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 does not check convergence (stopping criterion). Few tuning parameters (marked by [TP]) are available for the implementer.

**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.

*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 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 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

**Further Details:**SGSVJ0 is used just to enable SGESVJ to call a simplified version of itself to work on a submatrix of the original matrix.

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

**Bugs, Examples and Comments:**

Please report all bugs and send interesting test examples and comments to drmac@math.hr. Thank you.

Definition at line 220 of file sgsvj0.f.

## Author

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## Referenced By

The man page sgsvj0(3) is an alias of sgsvj0.f(3).