SRC/dlanv2.f(3)

🌸 NAME 🌸

okay so this is SRC/dlanv2.f(3) from the Library Functions Manual — the page for SRC/dlanv2.f, aka the dlanv2 subroutine. 💅

✨ SYNOPSIS ✨

🛠️ Functions/Subroutines

• dlanv2 — DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

subroutine dlanv2 (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn)

💖 Function/Subroutine Documentation 💖

📞 subroutine dlanv2

subroutine dlanv2 (double precision a, double precision b, double precision c, double precision d, double precision rt1r, double precision rt1i, double precision rt2r, double precision rt2i, double precision cs, double precision sn)

DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form. 🫶

🎯 Purpose

bestie, here’s the whole glow-up it’s doing:

      [ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]
      [ C  D ]   [ SN  CS ] [ CC  DD ] [-SN  CS ]

where either

1. CC = 0 so that AA and DD are real eigenvalues of the matrix, or
2. AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex conjugate eigenvalues.

🧮 Parameters

• A — A is DOUBLE PRECISION. 🌸
• B — B is DOUBLE PRECISION. 🦋
• C — C is DOUBLE PRECISION. 🎀
• D — D is DOUBLE PRECISION. On entry, the elements of the input matrix. On exit, they are overwritten by the elements of the standardised Schur form. 💫
• RT1R — RT1R is DOUBLE PRECISION. ⭐
• RT1I — RT1I is DOUBLE PRECISION. 💜
• RT2R — RT2R is DOUBLE PRECISION. 🌈
• RT2I — RT2I is DOUBLE PRECISION. The real and imaginary parts of the eigenvalues. If the eigenvalues are a complex conjugate pair, RT1I > 0. 🔥
• CS — CS is DOUBLE PRECISION. 👑
• SN — SN is DOUBLE PRECISION. Parameters of the rotation matrix. 💅

👑 Author

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

🔍 Further Details

Modified by V. Sima, Research Institute for Informatics, Bucharest, Romania, to reduce the risk of cancellation errors, when computing real eigenvalues, and to ensure, if possible, that abs(RT1R) >= abs(RT2R). 😭✨

📍 Definition at line

Definition at line 126 of file dlanv2.f.

🌈 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that’s the whole page — footer version/date stamp: LAPACK Version 3.12.0, source SRC/dlanv2.f(3). mwah 💋