lanv2(3)

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💅 lanv2(3) — Library Functions Manual 💅

Okay so welcome to lanv2(3) from the Library Functions Manual, bestie. This is the LAPACK page for a 2x2 Schur factor, and we're keeping every single technical crumb while making it feel like a group chat. 🫶

💖 NAME 💖

lanv2 — lanv2: 2x2 Schur factor

✨ SYNOPSIS ✨

🧚 Functions 🧚

  • 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.
  • 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.

🌈 Detailed Description 🌈

No extra prose lives under this heading in the original — it's lowkey just the runway to the function docs. 💅

🔥 Function 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: 🎀

Okay so here's the whole point, bestie: 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.

🧚 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 📍

Definition at line 126 of file dlanv2.f.

💖 subroutine slanv2 💖

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.

🎀 Purpose: 🎀

Okay so here's the whole point again, bestie: SLANV2 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.

🧚 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 📍

Definition at line 126 of file slanv2.f.

💅 Author 💅

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That's the whole page, bestie! Footer vibes: LAPACK, Version 3.12.0, page lanv2(3). Stay slay, and may your Schur form always be standardised. 💖✨

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