ZGSVJ0(3)

💖 ZGSVJ0(3) 💖

okay bestie, this is the zgsvj0.f(3) page from the Library Functions Manual ✨ it's giving source-file realness, and we're keeping every detail cute and intact.

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🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgsvj0.f

that's the NAME section, bestie — just the path, no extra lore 💅

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🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines 🧚

subroutine ZGSVJ0 (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin,
    tol, nsweep, work, lwork, info)
     ZGSVJ0 pre-processor for the routine zgesvj.

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🌈 Function/Subroutine Documentation 🌈

subroutine ZGSVJ0 (character*1 jobv, integer m, integer n, complex*16,
    dimension( lda, * ) a, integer lda, complex*16, dimension( n ) d, double
    precision, dimension( n ) sva, integer mv, complex*16, dimension( ldv, *
    ) v, integer ldv, double precision eps, double precision sfmin, double
    precision tol, integer nsweep, complex*16, dimension( lwork ) work,
    integer lwork, integer info)
     ZGSVJ0 pre-processor for the routine zgesvj.

✨ Purpose ✨

ZGSVJ0 is called from ZGESVJ as a pre-processor and that is its main purpose. It applies Jacobi rotations in the same way as ZGESVJ 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 — COMPLEX*16 array, dimension (LDA,N). On entry, M-by-N matrix A, such that A*diag(D) represents the input matrix. On exit, A_onexit * diag(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 — COMPLEX*16 array, dimension (N). The array D accumulates the scaling factors from the complex 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 A_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 — COMPLEX*16 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 ABS(COS(angle(A(:,p),A(:,q)))) > TOL.
• NSWEEP — INTEGER. NSWEEP is the number of sweeps of Jacobi rotations to be performed.
• WORK — COMPLEX*16 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 🔥

ZGSVJ0 is used just to enable ZGESVJ to call a simplified version of itself to work on a submatrix of the original matrix.

🍓 Contributor 🍓

Zlatko Drmac (Zagreb, Croatia)

💀 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 zgsvj0.f.

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👑 Author 👑

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okay that's the whole thing, bestie 🫶 footer tea: LAPACK, Version 3.12.0, page /home/abui...RC/zgsvj0.f(3). There's no extra date printed on this one, so I'm not inventing one — periodt 💅✨