SRC/dlaein.f(3)

🌸 SRC/dlaein.f(3) 🌸

Okay bestie, welcome to the Library Functions Manual page for SRC/dlaein.f — yes, that's the whole title and it's lowkey giving old-school Fortran glam. 💅

💖 NAME 💖

SRC/dlaein.f — that's the name, periodt. This page documents the DLAEIN subroutine.

✨ 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 🦋

Here's the full signature, copied exactly because we do not mess with Fortran:

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. No cap. ✨

🧚 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 — LOGICAL. = .TRUE.: compute right eigenvector; = .FALSE.: compute left eigenvector.
• NOINIT — LOGICAL. = .TRUE.: no initial vector supplied in (VR,VI). = .FALSE.: initial vector supplied in (VR,VI).
• N — INTEGER. The order of the matrix H. N >= 0.
• H — DOUBLE PRECISION array, dimension (LDH,N). The upper Hessenberg matrix H.
• LDH — INTEGER. The leading dimension of the array H. LDH >= max(1,N).
• WR — DOUBLE PRECISION.
• WI — DOUBLE PRECISION. The real and imaginary parts of the eigenvalue of H whose corresponding right or left eigenvector is to be computed.
• VR — DOUBLE PRECISION array, dimension (N).
• VI — 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 — DOUBLE PRECISION array, dimension (LDB,N).
• LDB — INTEGER. The leading dimension of the array B. LDB >= N+1.
• WORK — DOUBLE PRECISION array, dimension (N).
• EPS3 — DOUBLE PRECISION. A small machine-dependent value which is used to perturb close eigenvalues, and to replace zero pivots.
• SMLNUM — DOUBLE PRECISION. A machine-dependent value close to the underflow threshold.
• BIGNUM — DOUBLE PRECISION. A machine-dependent value close to the overflow threshold.
• INFO — 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.

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mwah 💋 okay bestie, that's the whole page. It's from LAPACK, Version 3.12.0, and the source is SRC/dlaein.f(3). Go slay those eigenvectors! 🫶✨