lae2(3)

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version 3.12.1 · 9 versions
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🌸 lae2(3) 🌸

okay so welcome to the Library Functions Manual page for lae2, bestie 💅 this one is literally all about a 2x2 eig situation and a step in steqr, stemr. it's giving linear algebra but make it cute ✨

🌸 NAME 🌸

lae2 - lae2: 2x2 eig, step in steqr, stemr

✨ SYNOPSIS ✨

🎀 Functions 🎀

  • subroutine dlae2 (a, b, c, rt1, rt2) — DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.
  • subroutine slae2 (a, b, c, rt1, rt2) — SLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

🦋 DETAILED DESCRIPTION 🦋

the full deets live in the function documentation right below, bestie — no gatekeeping here 🫶

💖 FUNCTION DOCUMENTATION 💖

💅 subroutine dlae2 (double precision a, double precision b, double precision c, double precision rt1, double precision rt2) 💅

DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix.

✨ Purpose ✨

okay so DLAE2 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 DOUBLE PRECISION; it's the (1,1) element of the 2-by-2 matrix.
  • B — B is DOUBLE PRECISION; it's the (1,2) and (2,1) elements of the 2-by-2 matrix.
  • C — C is DOUBLE PRECISION; it's the (2,2) element of the 2-by-2 matrix.
  • RT1 — RT1 is DOUBLE PRECISION; it's the eigenvalue of larger absolute value.
  • RT2 — RT2 is DOUBLE PRECISION; it's 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.
  • 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 📌

Definition at line 101 of file dlae2.f.

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

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

✨ Purpose ✨

okay so 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. slay ✨

🎀 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 🌈

  • 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 📌

Definition at line 101 of file slae2.f.

👑 AUTHOR 👑

Generated automatically by Doxygen for LAPACK from the source code.

💖 ok that's the whole manual page, bestie — LAPACK Version 3.12.0, lae2(3), generated automatically by Doxygen for LAPACK from the source code. byeeee 🫶✨

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