CLAESY(3)

📦 version 3.12.0, in opensuse-leap 16.0

okay so bestie, this is the claesy.f(3) page from the Library Functions Manual — and it's literally about a tiny 2-by-2 complex symmetric matrix glow-up ✨

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/claesy.f

✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

  • subroutine CLAESY (a, b, c, rt1, rt2, evscal, cs1, sn1) — our main character 💅. CLAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix.

🫶 Function/Subroutine Documentation 🫶

subroutine CLAESY (complex a, complex b, complex c, complex rt1, complex rt2, complex evscal, complex cs1, complex sn1)

CLAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix.

🎀 Purpose 🎀

okay so CLAESY does the eigendecomposition of a 2-by-2 symmetric matrix

( ( A, B );( B, C ) )

but only when the norm of the matrix of eigenvectors is larger than some threshold value 👀.

RT1 is the eigenvalue of larger absolute value, and RT2 is the one with smaller absolute value. If the eigenvectors are computed, then on return ( CS1, SN1 ) is the unit eigenvector for RT1, hence:

!> [  CS1     SN1   ] . [ A  B ] . [ CS1    -SN1   ] = [ RT1  0  ]
!> [ -SN1     CS1   ]   [ B  C ]   [ SN1     CS1   ]   [  0  RT2 ]

🍓 Parameters 🍓

  • A — A is COMPLEX. It's the ( 1, 1 ) element of the input matrix.
  • B — B is COMPLEX. It's the ( 1, 2 ) element of the input matrix. The ( 2, 1 ) element is also given by B, because the 2-by-2 matrix is symmetric.
  • C — C is COMPLEX. It's the ( 2, 2 ) element of the input matrix.
  • RT1 — RT1 is COMPLEX. The eigenvalue of larger modulus.
  • RT2 — RT2 is COMPLEX. The eigenvalue of smaller modulus.
  • EVSCAL — EVSCAL is COMPLEX. The complex value by which the eigenvector matrix was scaled to make it orthonormal. If EVSCAL is zero, the eigenvectors were not computed. This means one of two things: the 2-by-2 matrix could not be diagonalized, or the norm of the matrix of eigenvectors before scaling was larger than the threshold value THRESH (set below). 😭
  • CS1 — CS1 is COMPLEX. That's it, bestie — no extra description given.
  • SN1 — SN1 is COMPLEX. If EVSCAL .NE. 0, then ( CS1, SN1 ) is the unit right eigenvector for RT1.

👑 Author 👑

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

Definition at line 114 of file claesy.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

okay bye bestie 💖 this whole page is from LAPACK Version 3.12.0, and the footer path is /home/abui...RC/claesy.f(3) — there's no date listed, so no cap, we're not inventing one 🫶✨

📦 where this page comes from