DLAEV2(3)

🌸 DLAEV2(3) — Library Functions Manual 🌸

okay bestie, welcome to the DLAEV2(3) page — it lives in the Library Functions Manual, and it's literally all about one iconic Fortran source file. 💅 No cap, this one is a tiny little linear-algebra moment, and the way it handles a 2-by-2 matrix? main character energy. 🌈

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💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlaev2.f

That's the filepath this whole page is serving, bestie. 🫶

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine DLAEV2 (a, b, c, rt1, rt2, cs1, sn1)

DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. periodt. 🌈

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🦋 Function/Subroutine Documentation 🦋

🧚 subroutine DLAEV2 🧚

subroutine DLAEV2 (double precision a, double precision b, double precision c, double precision rt1, double precision rt2, double precision cs1, double precision sn1)

DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. 💖

🎯 Purpose

okay so the whole vibe is: DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix

    [  A   B  ]
    [  B   C  ].

On return, RT1 is the eigenvalue of larger absolute value, RT2 is the eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right eigenvector for RT1, giving the decomposition

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

🍓 Parameters 🍓

• A — A is DOUBLE PRECISION. It's the (1,1) element of the 2-by-2 matrix. ✨
• B — B is DOUBLE PRECISION. It's the (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix. 🦋
• C — C is DOUBLE PRECISION. It's the (2,2) element of the 2-by-2 matrix. 🌸
• RT1 — RT1 is DOUBLE PRECISION. It's the eigenvalue of larger absolute value. 👑
• RT2 — RT2 is DOUBLE PRECISION. It's the eigenvalue of smaller absolute value. 💜
• CS1 — CS1 is DOUBLE PRECISION. That's it, bestie — the page gives no extra description here. 💀
• SN1 — SN1 is DOUBLE PRECISION. The vector (CS1, SN1) is a unit right eigenvector for RT1. 🎀

👑 Author 👑

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

🔍 Further Details 🔍

• RT1 is accurate to a few ulps barring over/underflow. 💅
• RT2 may be inaccurate if there is massive cancellation in the determinant A*C-B*B; higher precision or correctly rounded or correctly truncated arithmetic would be needed to compute RT2 accurately in all cases. 😭
• CS1 and SN1 are accurate to a few ulps barring over/underflow. 🦋
• Overflow is possible only if RT1 is within a factor of 5 of overflow. Underflow is harmless if the input data is 0 or exceeds underflow_threshold / macheps. 🌊

📍 Definition at line 119 of file dlaev2.f.

📝 Author 📝

Generated automatically by Doxygen for LAPACK from the source code. 🤖💖

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okay bestie, that's the whole page! The footer clocks in with LAPACK Version 3.12.0 and the path /home/abui...RC/dlaev2.f(3) — and there's no separate date on this page. Byeee, go slay some 2-by-2 matrices! 💖✨🎀🦋