DLAEIN(3)

🎀 NAME 🎀

okay so bestie, this page is all about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlaein.f, and it lives in the Library Functions Manual 💅. That full path is lowkey a lot, but we keep it exact — no cap.

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

• subroutine DLAEIN (rightv, noinit, n, h, ldh, wr, wi, vr, vi, b, ldb, work, eps3, smlnum, bignum, info) — DLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. 👑

🧚 Function/Subroutine Documentation 🧚

subroutine DLAEIN (logical rightv, logical noinit, integer n, double
    precision, dimension( ldh, * ) h, integer ldh, double precision wr,
    double precision wi, double precision, dimension( * ) vr, double
    precision, dimension( * ) vi, double precision, dimension( ldb, * ) b,
    integer ldb, double precision, dimension( * ) work, double precision
    eps3, double precision smlnum, double precision bignum, integer info)

DLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration. ✨

💖 Purpose 💖

DLAEIN uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real 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 (VR,VI). = .FALSE.: initial vector supplied in (VR,VI). 🎀
• N — N is INTEGER. The order of the matrix H. N >= 0. 👑
• H — H is DOUBLE PRECISION array, dimension (LDH,N). The upper Hessenberg matrix H. 🌈
• LDH — LDH is INTEGER. The leading dimension of the array H. LDH >= max(1,N). ✨
• WR — WR is DOUBLE PRECISION. 🦋
• WI — WI is DOUBLE PRECISION. The real and imaginary parts of the eigenvalue of H whose corresponding right or left eigenvector is to be computed. 💜
• VR — VR is DOUBLE PRECISION array, dimension (N). 🎀
• VI — VI is DOUBLE PRECISION array, dimension (N). On entry, if NOINIT = .FALSE. and WI = 0.0, VR must contain a real starting vector for inverse iteration using the real eigenvalue WR; if NOINIT = .FALSE. and WI.ne.0.0, VR and VI must contain the real and imaginary parts of a complex starting vector for inverse iteration using the complex eigenvalue (WR,WI); otherwise VR and VI need not be set. On exit, if WI = 0.0 (real eigenvalue), VR contains the computed real eigenvector; if WI.ne.0.0 (complex eigenvalue), VR and VI contain the real and imaginary parts of the computed complex eigenvector. The eigenvector is 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|. VI is not referenced if WI = 0.0. 🫶
• B — B is DOUBLE PRECISION array, dimension (LDB,N). 🌸
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= N+1. 🔥
• WORK — WORK 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. 🍓
• BIGNUM — BIGNUM is DOUBLE PRECISION. A machine-dependent value close to the overflow threshold. 🌈
• INFO — INFO is INTEGER. = 0: successful exit; = 1: inverse iteration did not converge; VR is set to the last iterate, and so is VI if WI.ne.0.0. 💀

👑 Author 👑

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

📍 Definition at line 170 of file dlaein.f.

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code. 🧚

okay bestie, that’s the whole page 💖. Signing off with the footer deets exactly as printed: LAPACK, Version 3.12.0, /home/abui...RC/dlaein.f(3) 💅✨.