laesy(3)

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version 3.12.1 · 9 versions
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💖 laesy(3) — Library Functions Manual 💖

Okay bestie, welcome to the laesy page. It's giving LAPACK linear algebra, but make it cute. No cap, every detail is staying. 💅

✨ NAME ✨

laesy — laesy: 2x2 eig

🌸 SYNOPSIS 🌸

Here are the two functions on deck, bestie:

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

🦋 Detailed Description 🦋

This is where the function docs live, so buckle up. 💖

🔥 Function Documentation 🔥

🎀 subroutine claesy 🎀

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

What it does: CLAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix.

✨ Purpose ✨

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.

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.

👑 Author 👑

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

📌 Definition 📌

Definition at line 114 of file claesy.f.

🎀 subroutine zlaesy 🎀

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)

What it does: ZLAESY computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix.

✨ Purpose ✨

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 ]

💜 Parameters 💜

  • A — A is COMPLEX*16 — the ( 1, 1 ) element of input matrix.
  • B — B is COMPLEX*16 — 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*16 — the ( 2, 2 ) element of 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, ( CS1, SN1 ) is the unit right eigenvector for RT1.

👑 Author 👑

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

📌 Definition 📌

Definition at line 114 of file zlaesy.f.

🌈 Author 🌈

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Ok bye bestie! 🫶 This was laesy(3), source/version: LAPACK, Version 3.12.0. Date: not listed in this page's footer, so I'm not making one up. It was generated automatically by Doxygen for LAPACK from the source code. Slay. 💅✨

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