SRC/zlaesy.f(3)

💅 SRC/zlaesy.f(3) — Library Functions Manual 💅

💖 NAME 💖

SRC/zlaesy.f

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

okay so bestie, ZLAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix. Periodt. 🫶

💫 Function/Subroutine Documentation 💫

subroutine zlaesy (complex*16 a, complex*16 b, complex*16 c, complex*16 rt1,
    complex*16 rt2, complex*16 evscal, complex*16 cs1, complex*16 sn1)

Not me being obsessed with a subroutine, but here we are. This one computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix. It’s giving main character energy. 👑

💫 Purpose 💫

Okay so ZLAESY 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. Vibe check passed. ✨

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 ]

The way that matrix equation ate, honestly. 💅

🎀 Parameters 🎀

• A — is COMPLEX*16. The ( 1, 1 ) element of the input matrix. 💅
• B — is COMPLEX*16. The ( 1, 2 ) element of the input matrix. The ( 2, 1 ) element is also given by B, since the 2-by-2 matrix is symmetric. 🦋
• C — is COMPLEX*16. The ( 2, 2 ) element of the input matrix. 🎀
• RT1 — is COMPLEX*16. The eigenvalue of larger modulus. 👑
• RT2 — is COMPLEX*16. The eigenvalue of smaller modulus. 🌸
• EVSCAL — is COMPLEX*16. 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 — is COMPLEX*16. 💜
• SN1 — is COMPLEX*16. If EVSCAL .NE. 0, ( 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 zlaesy.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

---

Okay bestie, that’s the whole page. Cute sign-off time: source is SRC/zlaesy.f, version is LAPACK Version 3.12.0; no date was listed in this footer, so we’re not inventing one. Mwah 💋✨