SLAEV2(3)

SLAEV2(3) — Library Functions Manual 💅✨

🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slaev2.f

Okay so bestie, this whole page is literally about that file right there. That's the main character. No cap. 🫶

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine SLAEV2 (a, b, c, rt1, rt2, cs1, sn1)

SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. It's giving math but make it cute. 💖

💖 Function/Subroutine Documentation 💖

subroutine SLAEV2 (real a, real b, real c, real rt1, real rt2, real cs1, real sn1)

SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. Lowkey iconic behavior. ✨

🌸 Purpose 🌸

!>
!> SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
!>    [  A   B  ]
!>    [  B   C  ].
!> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
!> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
!> eigenvector for RT1, giving the decomposition
!>
!>    [ CS1  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1  0  ]
!>    [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]     [  0  RT2 ].
!>

So yeah, it takes that symmetric 2-by-2 matrix and decomposes it. RT1 is the eigenvalue with the bigger absolute value, RT2 is the one with the smaller absolute value, and (CS1,SN1) is the unit right eigenvector for RT1. The way that matrix factors is honestly a 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) element and the conjugate of the (2,1) element 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. Main character eigenvalue energy, fr fr. 👑
• RT2 — RT2 is REAL. It's the eigenvalue of smaller absolute value.
• CS1 — CS1 is REAL. That's the whole note, bestie.
• SN1 — SN1 is REAL. The vector (CS1, SN1) is a unit right eigenvector for RT1.

💜 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.
!>
!>  CS1 and SN1 are accurate to a few ulps barring over/underflow.
!>
!>  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.
!>

Okay so the accuracy tea: RT1 is accurate to a few ulps barring over/underflow. RT2 may be inaccurate if there's massive cancellation in the determinant A*C-B*B, and higher precision or correctly rounded or correctly truncated arithmetic would be needed to compute RT2 accurately in all cases. CS1 and SN1 are accurate to a few ulps barring over/underflow. 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. Periodt. 💀✨

Definition at line 119 of file slaev2.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

---

LAPACK Version 3.12.0, from /home/abui...RC/slaev2.f(3) — mwah, bestie, that's the footer vibe 💋🎀