SRC/claev2.f(3)

💖 NAME 💖

SRC/claev2.f — bestie, this is the SRC/claev2.f(3) page from the Library Functions Manual, and it's serving the claev2 subroutine. It's giving linear algebra icon energy. 💅

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

• subroutine claev2 (a, b, c, rt1, rt2, cs1, sn1) — CLA EV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

💅 Function/Subroutine Documentation 💅

🎀 subroutine claev2 🎀

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.

🦋 Purpose 🦋

Okay so bestie, here's the lore: CLA EV2 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, giving the decomposition

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

🍓 Parameters 🍓

• A — A is COMPLEX. The (1,1) element of the 2-by-2 matrix.
• B — B is COMPLEX. The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix.
• C — C is COMPLEX. 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.
• CS1 — CS1 is REAL. That's the whole note for this one in the source, bestie.
• 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 🔥

• 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 📌

Definition at line 120 of file claev2.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie. This one is from LAPACK, Version 3.12.0, and the source is SRC/claev2.f(3). The footer doesn't list a date, so consider this your no-date-but-full-detail moment. 💖✨ periodt.