ZLAESY(3)

💅 ZLAESY(3) — Library Functions Manual 💅

hiii bestie 🫶 you found the zlaesy.f(3) page, and she's here to serve eigenvalues and eigenvectors for a 2-by-2 complex symmetric matrix. The manual name is Library Functions Manual, and no cap, we're about to get into it ✨

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🎀 NAME 🎀

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

That's the whole name section, bestie. The path ate and left literally no crumbs 💅

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✨ SYNOPSIS ✨

Functions/Subroutines is the section vibe, and the icon of the hour is:

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

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

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🦋 Function/Subroutine Documentation 🦋

Here's the full signature with all the complex*16 energy:

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)

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

🌸 Purpose 🌸

Ok so the source's Purpose block is giving exact math realness. Verbatim, because we do not mess with the sacred matrix:

!>
!> 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.
!>
!> 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 ]
!>

Translation for the group chat: RT1 is the eigenvalue with larger absolute value, RT2 is the one with smaller absolute value. If the eigenvectors get computed, then on return ( CS1, SN1 ) is the unit eigenvector for RT1, and the matrix equation above holds. Slay 💅

🍓 Parameters 🍓

• A — A is COMPLEX*16, and she's the ( 1, 1 ) element of the input matrix. Iconic.
• B — B is COMPLEX*16, and she's 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. periodt.
• C — C is COMPLEX*16, and she's the ( 2, 2 ) element of the input matrix.
• RT1 — RT1 is COMPLEX*16: the eigenvalue of larger modulus.
• RT2 — RT2 is COMPLEX*16: the eigenvalue of smaller modulus.
• EVSCAL — 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 — CS1 is COMPLEX*16.
• SN1 — SN1 is COMPLEX*16. 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 zlaesy.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. Not me, not you — Doxygen did that. 💅

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Final footer vibe: LAPACK Version 3.12.0, /home/abui...RC/zlaesy.f(3) — mwah, bestie 💋✨