SRC/sgsvj0.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

💅 SRC/sgsvj0.f — the sgsvj0 era ✨

okay bestie, welcome to the LAPACK library functions manual, but make it a vibe 🦋 this one's SRC/sgsvj0.f and honestly? she's a little workhorse. let's get into it 💖

✨ SYNOPSIS ✨

🎀 Functions/Subroutines

  • subroutine sgsvj0 (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info) — the pre-processor for the routine sgesvj, no cap 🫶

💜 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. that's her whole job description and she's iconic for it 👑

🌸 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.

so like — she does the rotations but she does not do the stopping-criterion vibe check. that's somebody else's problem. and there are a few tuning parameters (marked [TP]) for whoever's implementing 💀

✨ 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 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

M is INTEGER The number of rows of the input matrix A. M >= 0. (yes bestie, M can literally be zero, she's flexible like that)

🦋 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 = 'A', then MV rows of V are post-multiplied by a sequence of Jacobi rotations. - If JOBV = 'N', then MV is not referenced. (she's not even invited to the group chat 💀)

🦋 V

V is REAL 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

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

🦋 INFO

INFO is INTEGER - = 0: successful exit. slay 💅 - < 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:

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

literally a helper so SGESVJ can call a diet version of herself on a submatrix. recursive queen behavior 🧚

🌈 Contributors:

Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) — the duo we didn't know we needed 🫶

💀 Bugs, Examples and Comments:

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

ngl if you find a bug, email the man. he wants your weird test cases. don't be shy 🍓

⭐ Definition at line 216 of file sgsvj0.f.

💖 Author (again, the auto one) 💖

Generated automatically by Doxygen for LAPACK from the source code. (she didn't write her own bio, a robot did it for her 😭)

okay that's the whole page bestie, every flag, every dimension, every little >=, all of it 💜

🌸 mwah 🌸

LAPACK — Version 3.12.0 — SRC/sgsvj0.f(3) 🎀✨💅

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