SRC/dlarrk.f(3)

okay bestie, this is the SRC/dlarrk.f(3) page from the Library Functions Manual — and it's all about DLARRK, an auxiliary LAPACK subroutine. It's giving eigenvalue-hunting main character energy. 💅✨

✨ NAME ✨

SRC/dlarrk.f

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

subroutine dlarrk (n, iw, gl, gu, d, e2, pivmin, reltol, w, werr, info)
    DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T
    to suitable accuracy.

🎀 Function/Subroutine Documentation 🎀

💅 subroutine dlarrk 💅

subroutine dlarrk (integer n, integer iw, double precision gl, double
    precision gu, double precision, dimension( * ) d, double precision,
    dimension( * ) e2, double precision pivmin, double precision reltol,
    double precision w, double precision werr, integer info)

DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy. 🔥

🦋 Purpose 🦋

okay so the purpose is literally this: DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy. It's auxiliary code — it gets called from DSTEMR.

To avoid overflow, the matrix must be scaled so that its largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest accuracy it should not be much smaller than that. 💜

See W. Kahan, Report CS41, Computer Science Dept., Stanford University, July 21, 1966.

💖 Parameters 💖

• N — N is INTEGER; it's the order of the tridiagonal matrix T, and N >= 0. ⭐
• IW — IW is INTEGER; it's the index of the eigenvalues to be returned.
• GL — GL is DOUBLE PRECISION. 🫶
• GU — GU is DOUBLE PRECISION; an upper and a lower bound on the eigenvalue.
• D — D is DOUBLE PRECISION array, dimension (N); these are the n diagonal elements of the tridiagonal matrix T.
• E2 — E2 is DOUBLE PRECISION array, dimension (N-1); these are the (n-1) squared off-diagonal elements of the tridiagonal matrix T.
• PIVMIN — PIVMIN is DOUBLE PRECISION; it's the minimum pivot allowed in the Sturm sequence for T.
• RELTOL — RELTOL is DOUBLE PRECISION; it's the minimum relative width of an interval. When an interval is narrower than RELTOL times the larger (in magnitude) endpoint, then it is considered to be sufficiently small, i.e., converged. Note: this should always be at least radix*machine epsilon. 🧚
• W — W is DOUBLE PRECISION. 🌸
• WERR — WERR is DOUBLE PRECISION; it's the error bound on the corresponding eigenvalue approximation in W.
• INFO — INFO is INTEGER; the values are:
  • = 0: Eigenvalue converged ✅
  • = -1: Eigenvalue did NOT converge 💀

🔮 Internal Parameters 🔮

FUDGE   DOUBLE PRECISION, default = 2
        A  to widen the Gershgorin intervals.

👑 Author 👑

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

Definition at line 143 of file dlarrk.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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that's the whole page, bestie: LAPACK · Version 3.12.0 · SRC/dlarrk.f(3) — mwah 💖✨