DGSVJ0(3)

💅 DGSVJ0(3) — Library Functions Manual 💅

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🌸 NAME 🌸

This page is literally about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dgsvj0.f — yes, the whole path, we're keeping it. 🫶

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

       subroutine DGSVJ0 (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin,
           tol, nsweep, work, lwork, info)

DGSVJ0 pre-processor for the routine dgesvj. 💖

🦋 Function/Subroutine Documentation 🦋

   subroutine DGSVJ0 (character*1 jobv, integer m, integer n, double precision,
       dimension( lda, * ) a, integer lda, double precision, dimension( n ) d,
       double precision, dimension( n ) sva, integer mv, double precision,
       dimension( ldv, * ) v, integer ldv, double precision eps, double
       precision sfmin, double precision tol, integer nsweep, double precision,
       dimension( lwork ) work, integer lwork, integer info)

DGSVJ0 pre-processor for the routine dgesvj.

🎯 Purpose 🎯

DGSVJ0 is called from DGESVJ as a pre-processor and that is its main purpose. It applies Jacobi rotations in the same way as DGESVJ does, but it does not check convergence (stopping criterion). Few tuning parameters (marked by [TP]) are available for the implementer. 👑

🧸 Parameters 🧸

• JOBV — 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 postmultiplying the N-by-N array V. (See the description of V.)
  • = 'A': the product of the Jacobi rotations is accumulated by postmultiplying the MV-by-N array V. (See the descriptions of MV and V.)
  • = 'N': the Jacobi rotations are not accumulated.
• M — INTEGER. The number of rows of the input matrix A. M >= 0.
• N — INTEGER. The number of columns of the input matrix A. M >= N >= 0.
• A — DOUBLE PRECISION 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 — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• D — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 — INTEGER. If JOBV = 'A', then MV rows of V are post-multiplied by a sequence of Jacobi rotations. If JOBV = 'N', then MV is not referenced.
• V — DOUBLE PRECISION array, dimension (LDV,N). If JOBV = 'V' then N rows of V are post-multiplied by a sequence of Jacobi rotations. If JOBV = 'A' then MV rows of V are post-multiplied by a sequence of Jacobi rotations. If JOBV = 'N', then V is not referenced.
• LDV — INTEGER. The leading dimension of the array V, LDV >= 1. If JOBV = 'V', LDV >= N. If JOBV = 'A', LDV >= MV.
• EPS — DOUBLE PRECISION. EPS = DLAMCH('Epsilon').
• SFMIN — DOUBLE PRECISION. SFMIN = DLAMCH('Safe Minimum').
• TOL — DOUBLE PRECISION. 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)))) > TOL.
• NSWEEP — INTEGER. NSWEEP is the number of sweeps of Jacobi rotations to be performed.
• WORK — DOUBLE PRECISION array, dimension (LWORK).
• LWORK — INTEGER. LWORK is the dimension of WORK. LWORK >= M.
• INFO — 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.

🔎 Further Details:

DGSVJ0 is used just to enable DGESVJ 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 216 of file dgsvj0.f.

🤖 Author

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