SRC/zgsvj0.f(3)

📦
version 3.12.1 · 7 versions
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💅 NAME 💅

Bestie, this is the page for SRC/zgsvj0.f, served fresh from the Library Functions Manual. It's the home of the zgsvj0 subroutine — aka the pre-processor bestie for zgesvj. 💖

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

  • subroutine zgsvj0 (...) — ZGSVJ0 pre-processor for the routine zgesvj.
subroutine zgsvj0 (jobv, m, n, a, lda, d, sva, mv, v, ldv, eps, sfmin, tol, nsweep, work, lwork, info)

💖 Function/Subroutine Documentation 💖

🫶 subroutine zgsvj0 🫶

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 gets called from ZGESVJ as a pre-processor — that's literally its main character purpose. It applies Jacobi rotations the same way ZGESVJ does, except it does not check convergence (the stopping criterion). A few tuning parameters (marked [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 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.

🦋 A 🦋

A is 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 🦋

LDA is INTEGER

The leading dimension of the array A. LDA >= max(1,M).

🧚 D 🧚

D is 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 🧚

SVA is 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 💜

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*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 🌸

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 DOUBLE PRECISION

EPS = DLAMCH('Epsilon')

⭐ SFMIN ⭐

SFMIN is DOUBLE PRECISION

SFMIN = DLAMCH('Safe Minimum')

🔥 TOL 🔥

TOL is 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 🔥

NSWEEP is INTEGER

NSWEEP is the number of sweeps of Jacobi rotations to be performed.

🎀 WORK 🎀

WORK is COMPLEX*16 array, dimension (LWORK)

🎀 LWORK 🎀

LWORK is INTEGER

LWORK is the dimension of WORK. LWORK >= 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.

🔥 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.

🌈 Author 🌈

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