/home/abui...RC/slae2.f(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 NAME 💅

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slae2.f

Okay bestie, real talk: this page is from the Library Functions Manual, and it's the .3 page for /home/abui...RC/slae2.f(3). So we're deep in the LAPACK build tree, looking at one single Fortran source file — slae2.f — and this is literally its whole documentation. Small file, main character energy. ✨

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • subroutine SLAE2 (a, b, c, rt1, rt2) — SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix. That's it, that's the gig. No cap. 💅

🎀 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. Iconic behavior, honestly. 🦋

✨ Purpose ✨

Okay so picture this matrix, right, and she's symmetric:

[  A   B  ]
[  B   C  ]

SLAE2 computes the eigenvalues of that exact 2-by-2 symmetric matrix. On return, RT1 is the eigenvalue of larger absolute value, and RT2 is the eigenvalue of smaller absolute value. Two eigenvalues, one subroutine, zero drama. 🫶

🍓 Parameters 🍓

  • A — A is REAL. She's the (1,1) element of the 2-by-2 matrix. 💖
  • B — B is REAL. The (1,2) and (2,1) elements of the 2-by-2 matrix — yes, both of them, because symmetry said "you're doing double duty today" and B said "slay". 🔥
  • C — C is REAL. The (2,2) element of the 2-by-2 matrix. 🌸
  • RT1 — RT1 is REAL. The eigenvalue of larger absolute value. 👑
  • RT2 — RT2 is REAL. The eigenvalue of smaller absolute value. 🌈

💜 Author 💜

  • 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. Like, she's precise bestie, but only if nothing overflows or underflows — vibe check applies.
  • 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. So no, she can't always be perfect, and that's on cancellation.
  • 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.
⚠️ Bestie please read the Further Details again before you trust RT2 blindly. Massive cancellation in A*C-B*B is the enemy fr fr. 💀

Definition at line 101 of file slae2.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code. Not a human, just a robot doing her little documentation chores. 🤖💅

🌟 And that's the whole page!! This absolutely iconic little page came to you courtesy of LAPACK, Version 3.12.0, and she lives at /home/abui...RC/slae2.f(3). Go compute some eigenvalues, queen. 👑💖
📦 where this page comes from