SRC/dlae2.f(3)

💅 SRC/dlae2.f(3)

okay bestie, welcome to the Library Functions Manual page for SRC/dlae2.f — this is the one about computing eigenvalues of a 2-by-2 symmetric matrix, and it is lowkey iconic ✨

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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. periodt 💅

🌸 Purpose 🌸

okay so DLAE2 computes the eigenvalues of this 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. no cap 🫶

🦋 Parameters 🦋

• A — DOUBLE PRECISION; the (1,1) element of the 2-by-2 matrix. slay.
• B — DOUBLE PRECISION; the (1,2) and (2,1) elements of the 2-by-2 matrix.
• C — DOUBLE PRECISION; the (2,2) element of the 2-by-2 matrix.
• RT1 — DOUBLE PRECISION; the eigenvalue of larger absolute value.
• RT2 — DOUBLE PRECISION; 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 at line 101 of file dlae2.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 that’s the whole page, bestie — source/version is LAPACK Version 3.12.0, and the page is SRC/dlae2.f(3); the footer doesn’t show a date, so no date to report 🫶✨