/home/abui...RC/dlae2.f(3)

💅 dlae2.f — Library Functions Manual, bestie edition

ok so the whole file path situation is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlae2.f and honestly? that's her full government name. she lives in the LAPACK library's function manual section, and she's about to eat. ✨

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🦋 SYNOPSIS 🦋

Functions/Subroutines

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

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🌸 Function/Subroutine 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. that's it, that's the whole vibe. 🎀

Purpose:

!>
!> 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.
!>

so like, you hand her this cute lil symmetric 2-by-2 matrix and she hands you back the eigenvalues. RT1 is the one with the larger absolute value and RT2 is the one with the smaller absolute value. main character and supporting character, lowkey. 👑

Parameters

• A — 👑 A is DOUBLE PRECISION. The (1,1) element of the 2-by-2 matrix.
• B — 🦋 B is DOUBLE PRECISION. The (1,2) and (2,1) elements of the 2-by-2 matrix. yes bestie, both of them — she's symmetric, that's the whole point.
• C — 🌸 C is DOUBLE PRECISION. The (2,2) element of the 2-by-2 matrix.
• RT1 — ✨ RT1 is DOUBLE PRECISION. The eigenvalue of larger absolute value.
• RT2 — 💜 RT2 is DOUBLE PRECISION. The eigenvalue of smaller absolute value.

Author

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

(an absolute icon collective, no cap 🫶)

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.
!>

ok let me translate this because it's giving lore:

• RT1 is accurate to a few ulps, barring over/underflow. she's reliable. she shows up. 💅
• RT2 may be inaccurate if there's massive cancellation in the determinant A*C-B*B. to compute RT2 accurately in all cases you'd need higher precision or correctly rounded or correctly truncated arithmetic. so like... RT2 is the flaky friend and that's just how it is, ngl 😭
• Overflow is possible only if RT1 is within a factor of 5 of overflow. that's the whole condition, fr fr.
• Underflow is harmless if the input data is 0 or exceeds underflow_threshold / macheps. 💀

🚨 real talk though — that RT2 inaccuracy is the kind of caveat you do not gloss over. if your determinant A*C-B*B is cancelling hard, RT2 can be off. periodt.

Definition at line 101 of file dlae2.f.

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🧚 Author

Generated automatically by Doxygen for LAPACK from the source code. (she didn't write her own bio, the robot did it for her, iconic behavior honestly 🎀)

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LAPACK · Version 3.12.0 · /home/abui...RC/dlae2.f(3)

and that's the page bestie, tysm for reading, mwah 💖✨🦋🌈🍓