DLANV2(3)

💅 NAME 💅

ok so bestie, this page is literally about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlanv2.f — that's the file, that's the whole name entry, we move 🫶 (and it's from the Library Functions Manual, iykyk ✨)

---

✨ SYNOPSIS ✨

🎀 Functions/Subroutines

• subroutine DLANV2 (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn) — DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form. that's it, that's the girl 💅

---

👑 Function/Subroutine Documentation 👑

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. no cap, that's literally her whole job 🌸

💖 Purpose:

!>
!> DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
!> matrix in standard form:
!>
!>      [ 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.
!>

ok so like — it's giving rotation sandwich 🥪 you got the matrix, you got the two rotation matrices hugging it on both sides, and what falls out is either case 1) where CC = 0 and AA and DD slay as real eigenvalues, or case 2) where AA = DD and BB*CC < 0 so AA + or - sqrt(BB*CC) are complex conjugate eigenvalues. both are valid, both are iconic, we don't pick favorites 🔥

🦋 Parameters 🦋

• A — A is DOUBLE PRECISION. that's the whole description bestie, she speaks for herself 💀
• B — B is DOUBLE PRECISION. same energy 🎀
• C — C is DOUBLE PRECISION. yup, still the same vibe 🌈
• 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. so she comes in as one thing and leaves as another — main character transformation arc, honestly ⭐
• 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. periodt, that positivity is not optional 💅
• CS — CS is DOUBLE PRECISION. 🫶
• SN — SN is DOUBLE PRECISION. Parameters of the rotation matrix. the rotation needs her girls and these are them ✨

---

🌸 Author 🌸

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

a whole collab, the group project that actually ate 🔥

---

💀 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).
!>

so V. Sima from the Research Institute for Informatics, Bucharest, Romania, came in and did the work — reduced the risk of cancellation errors when computing real eigenvalues, and made sure, if possible, that abs(RT1R) >= abs(RT2R). note the "if possible" bestie, we're not promising anything, we're just trying our best 😭👑

---

Definition at line 126 of file dlanv2.f. go look, it's right there 🎀

---

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. no human wrote this footer, a robot did, and honestly? she served 🤖💅

---

💖 cute little sign-off time: this was LAPACK, Version 3.12.0, and the header said /home/abui...RC/dlanv2.f(3) and the footer said the same thing, so like… full circle bestie 🌈🦋 mwah, go factor something 💜