SRC/zlaein.f(3)

📦
version 3.12.1 · 4 versions
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SRC/zlaein.f(3) 💅✨

okay bestie, this page is from the Library Functions Manual, and the whole vibe is LAPACK's zlaein. It's giving “inverse iteration but make it eigenvectors.” 🦋

🌸 NAME 🌸

SRC/zlaein.f — literally the name on the page. No cap. 💖

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine zlaein (rightv, noinit, n, h, ldh, w, v, b, ldb, rwork, eps3, smlnum, info)

ZLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. Iconic behavior, honestly. 👑

💖 Function/Subroutine Documentation 💖

subroutine zlaein (logical rightv, logical noinit, integer n, complex*16, dimension( ldh, * ) h, integer ldh, complex*16 w, complex*16, dimension( * ) v, complex*16, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) rwork, double precision eps3, double precision smlnum, integer info)

ZLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. Yes, same flex as above — the docs say it twice, so we say it twice. 💅

🎀 Purpose 🎀

Bestie, ZLAEIN uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H. That's the whole mission. ✨

🌈 Parameters 🌈

  • RIGHTV — RIGHTV is LOGICAL. = .TRUE. : compute right eigenvector; = .FALSE.: compute left eigenvector. Choose your fighter. 🫶
  • NOINIT — NOINIT is LOGICAL. = .TRUE. : no initial vector supplied in V; = .FALSE.: initial vector supplied in V.
  • N — N is INTEGER. The order of the matrix H. N >= 0.
  • H — H is COMPLEX*16 array, dimension (LDH,N). The upper Hessenberg matrix H.
  • LDH — LDH is INTEGER. The leading dimension of the array H. LDH >= max(1,N).
  • W — W is COMPLEX*16. The eigenvalue of H whose corresponding right or left eigenvector is to be computed.
  • V — V is COMPLEX*16 array, dimension (N). On entry, if NOINIT = .FALSE., V must contain a starting vector for inverse iteration; otherwise V need not be set. On exit, V contains the computed eigenvector, normalized so that the component of largest magnitude has magnitude 1; here the magnitude of a complex number (x,y) is taken to be |x| + |y|. She's normalized and ready. 💅
  • B — B is COMPLEX*16 array, dimension (LDB,N).
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • RWORK — RWORK is DOUBLE PRECISION array, dimension (N).
  • EPS3 — EPS3 is DOUBLE PRECISION. A small machine-dependent value which is used to perturb close eigenvalues, and to replace zero pivots.
  • SMLNUM — SMLNUM is DOUBLE PRECISION. A machine-dependent value close to the underflow threshold.
  • INFO — INFO is INTEGER. = 0: successful exit; = 1: inverse iteration did not converge; V is set to the last iterate. So if you see 1, it's not a slay — it's the last iterate. 😭

👑 Author 👑

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Definition at line 147 of file zlaein.f.

🦋 Author 🦋

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okay bestie, that's the page! It's LAPACK Version 3.12.0, from source SRC/zlaein.f(3). Signing off with main character energy — periodt 💜✨

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