SRC/slae2.f(3)

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version 3.12.1 · 7 versions
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💅 SRC/slae2.f(3) — the Library Functions Manual moment ✨

okay bestie, welcome to the SRC/slae2.f(3) page. she’s giving classic LAPACK, she’s giving eigenvalues, and she’s absolutely not gatekeeping. 🫶

🌸 NAME 🌸

SRC/slae2.f — that’s the name, and yes, she’s iconic. 💖

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

subroutine slae2 (a, b, c, rt1, rt2)

SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. no cap, that’s the whole slay. 🔥

🦋 Function/Subroutine Documentation 🦋

subroutine slae2 (real a, real b, real c, real rt1, real rt2)

SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. we’re so back. 👑

🌈 Purpose

SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix:

[  A   B  ]
[  B   C  ].

On return, RT1 is the eigenvalue of larger absolute value, and RT2 is the eigenvalue of smaller absolute value. periodt. 💅

🎀 Parameters

  • A — A is REAL. it’s the (1,1) element of the 2-by-2 matrix. 🫶
  • B — B is REAL. it’s the (1,2) and (2,1) elements of the 2-by-2 matrix. ✨
  • C — C is REAL. it’s the (2,2) element of the 2-by-2 matrix. 🌸
  • RT1 — RT1 is REAL. it’s the eigenvalue of larger absolute value. 👑
  • RT2 — RT2 is REAL. it’s the eigenvalue of smaller absolute value. 🎀

🌸 Author

the author squad is:

  • 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. 😭
  • 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 101 of file slae2.f.

👑 Author 👑

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sign-off from LAPACK, Version 3.12.0, on SRC/slae2.f(3) — that’s the footer, bestie. bye! 💖✨

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