SLANV2(3)

💖 NAME

okay so this is the Library Functions Manual page for /home/abui...RC/slanv2.f(3), and the actual file it’s about is literally:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slanv2.f

that’s it, that’s the NAME section, no cap. 💅

✨ SYNOPSIS

🧩 Functions/Subroutines

subroutine SLANV2 (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn)

SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form. periodt. 🦋

🌸 Function/Subroutine Documentation

subroutine SLANV2 (real a, real b, real c, real d, real rt1r, real rt1i, real rt2r, real rt2i, real cs, real sn)

SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form. yes, it’s the same sentence again — keeping both because the original does, bestie 💖

🎀 Purpose

the whole point, bestie, is this factorization:

     [ 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 REAL. 💖
• B — B is REAL. ✨
• C — C is REAL. 🎀
• D — D is REAL. On entry, the elements of the input matrix. On exit, they are overwritten by the elements of the standardised Schur form. 🦋
• RT1R — RT1R is REAL. 🌸
• RT1I — RT1I is REAL. 💅
• RT2R — RT2R is REAL. 🫶
• RT2I — RT2I is REAL. The real and imaginary parts of the eigenvalues. If the eigenvalues are a complex conjugate pair, RT1I > 0. 👑
• CS — CS is REAL. 🌈
• SN — SN is REAL. 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 126 of file slanv2.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code. (robot authors slay, I guess 🤖✨)

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okay that’s the whole page, bestie 🫶 — sign-off: LAPACK Version 3.12.0, source /home/abui...RC/slanv2.f(3). the footer doesn’t print a date, so no fake date from me, periodt. 💖