CLAEV2(3)

💖 NAME

Header vibes first: this page is /home/abui...RC/claev2.f(3), and the manual is Library Functions Manual. The original NAME line gives the source path as /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/claev2.f — yes, the manpage wraps it after lapack-, but that's the path, bestie. 💅

✨ SYNOPSIS

🧚 Functions/Subroutines

• subroutine CLAEV2 (a, b, c, rt1, rt2, cs1, sn1) — CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

🦋 Function/Subroutine Documentation

subroutine CLAEV2 (complex a, complex b, complex c, real rt1, real rt2, real cs1, complex sn1)

CLA EV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix. (Okay not “CLA EV2” — CLAEV2, no cap, the space was just my brain buffering 😭)

💫 Purpose:

Okay so CLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix

[  A         B  ]
[  CONJG(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 — iconic — giving the decomposition

[ CS1  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
[-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ].

That's the whole eigen-slay, no cap. Obsessed. 🔥

🌸 Parameters

• A — A is COMPLEX; it's the (1,1) element of the 2-by-2 matrix. Periodt.
• B — B is COMPLEX; it's the (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix. iykyk.
• C — C is COMPLEX; 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 energy.
• RT2 — RT2 is REAL; it's the eigenvalue of smaller absolute value.
• CS1 — CS1 is REAL.
• SN1 — SN1 is COMPLEX; 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:

Vibe check on accuracy, bestie — lowkey important:

• 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.

Definition at line 120 of file claev2.f.

💜 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off, bestie: the footer's source/version is LAPACK Version 3.12.0, and the footer path is /home/abui...RC/claev2.f(3). Byeee, go slay your 2-by-2 Hermitian matrix 💖✨🦋 fr fr