SRC/claein.f(3)

🌸 NAME 🌸

okay so this is the SRC/claein.f page, from the Library Functions Manual, and it's literally page SRC/claein.f(3) — yes bestie, we're in the Fortran/LAPACK corner of the group chat. 💅

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine claein — the way that this subroutine ate: CLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.

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

💅 Function/Subroutine Documentation 💅

Here's the full signature, no cap:

   subroutine claein (logical rightv, logical noinit, integer n, complex,
       dimension( ldh, * ) h, integer ldh, complex w, complex, dimension( * )
       v, complex, dimension( ldb, * ) b, integer ldb, real, dimension( * )
       rwork, real eps3, real smlnum, integer info)

And the one-liner again, because it's iconic: CLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.

🦋 Purpose 🦋

okay so the actual purpose, in the original tea: CLAEIN uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper Hessenberg matrix H. ✨

🌈 Parameters 🌈

• RIGHTV — RIGHTV is LOGICAL.
  • = .TRUE. : compute right eigenvector;
  • = .FALSE.: compute left eigenvector.
• 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 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. The eigenvalue of H whose corresponding right or left eigenvector is to be computed.
• V — V is COMPLEX 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|.
• B — B is COMPLEX array, dimension (LDB,N).
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• RWORK — RWORK is REAL array, dimension (N).
• EPS3 — EPS3 is REAL. A small machine-dependent value which is used to perturb close eigenvalues, and to replace zero pivots.
• SMLNUM — SMLNUM is REAL. 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.

👑 Author 👑

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

Definition at line 147 of file claein.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

---

okay that's the whole page bestie 🫶 — signing off with the footer tea: LAPACK, Version 3.12.0, SRC/claein.f(3). slay, periodt. 💖✨