SRC/cgsvj1.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

🦋 NAME 🦋

SRC/cgsvj1.f — bestie, this is the source file for cgsvj1, and it lives in the Library Functions Manual (section 3). Consider this your official intro 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines

subroutine cgsvj1 (jobv, m, n, n1, a, lda, d, sva, mv, v, ldv, eps,
    sfmin, tol, nsweep, work, lwork, info)

Okay so real talk: CGSVJ1 is a pre-processor for the routine cgesvj, and it applies Jacobi rotations targeting only particular pivots. That's the whole vibe 🔥

💖 FUNCTION/SUBROUTINE DOCUMENTATION 💖

subroutine cgsvj1 (character*1 jobv, integer m, integer n, integer n1,
    complex, dimension( lda, * ) a, integer lda, complex, dimension( n ) d,
    real, dimension( n ) sva, integer mv, complex, dimension( ldv, * ) v,
    integer ldv, real eps, real sfmin, real tol, integer nsweep, complex,
    dimension( lwork ) work, integer lwork, integer info)

CGSVJ1 pre-processor for the routine cgesvj, applies Jacobi rotations targeting only particular pivots. Slay 💅

🌸 Purpose 🌸

So the tea is: CGSVJ1 is called from CGESVJ as a pre-processor, and honestly that is its main purpose. It applies Jacobi rotations in the same way as CGESVJ does, but — and this is the iconique part — it targets only particular pivots and it does not check convergence (stopping criterion). Few tuning parameters (marked by [TP]) are available for the implementer ✨

🧚 Further Details 🧚

CGSVJ1 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 tuning parameter. 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 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.

🍓 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. Literally the divider bestie ✂️

🍓 A

A is COMPLEX 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 COMPLEX 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 = 'A', then MV rows of V are post-multiplied by a sequence of Jacobi rotations.
  • If JOBV = 'N', then MV is not referenced.

🍓 V

V is COMPLEX 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 COMPLEX array, dimension (LWORK).

🍓 LWORK

LWORK is INTEGER. LWORK is the dimension of WORK. LWORK >= M.

🍓 INFO

INFO is INTEGER.

  • = 0: successful exit. Periodt. ✅
  • < 0: if INFO = -i, then the i-th argument had an illegal value 💀
Ngl, that < 0 case means somebody passed something cursed. Check your args bestie 🙈

🌟 Author 🌟

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

💜 Contributor 💜

Zlatko Drmac (Zagreb, Croatia) — main character energy fr fr 👑

Definition at line 234 of file cgsvj1.f.

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

Okay that's the whole page, no cap 🫶 This is LAPACK, Version 3.12.0, and it's SRC/cgsvj1.f(3) — go forth and rotate those pivots bestie, ily 💖✨🌸

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