SRC/claesy.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

🌸 NAME 🌸

okay bestie, this page is SRC/claesy.f(3) from the Library Functions Manual, and the name on the page is simply SRC/claesy.f. Slay.

✨ SYNOPSIS ✨

Functions/Subroutines

  • subroutine claesy (a, b, c, rt1, rt2, evscal, cs1, sn1) — 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. It's giving tiny matrix, huge main character energy.

Purpose 💡

So the purpose is literally this: CLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix

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

provided the norm of the matrix of eigenvectors is larger than some threshold value. That's the threshold condition, periodt.

RT1 is the eigenvalue of larger absolute value, and RT2 of 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. The ( 1, 1 ) element of input matrix.
  • B — B is COMPLEX. The ( 1, 2 ) element of input matrix. The ( 2, 1 ) element is also given by B, since the 2-by-2 matrix is symmetric.
  • C — C is COMPLEX. The ( 2, 2 ) element of 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.
  • SN1 — SN1 is COMPLEX. If EVSCAL .NE. 0, ( CS1, SN1 ) is the unit right eigenvector for RT1.
bestie note: EVSCAL being zero is the "eigenvectors were not computed" vibe, and it happens for one of those two reasons. No cap.

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 that's the whole page, bestie. the footer says LAPACK Version 3.12.0 and SRC/claesy.f(3); there is no date printed, so I'm not making one up. 💖✨🎀

📦 where this page comes from