larrk(3)

💖 larrk(3) — Library Functions Manual 💖

okay bestie, welcome to larrk(3) from the Library Functions Manual — it's giving “tiny LAPACK helper page that is actually carrying the eigenvalue accuracy lore.” no cap. ✨

🌸 NAME 🌸

larrk — larrk: step in stemr, compute one eigval

🎀 SYNOPSIS 🎀

Functions

• 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.
• slarrk — subroutine slarrk (integer n, integer iw, real gl, real gu, real, dimension( * ) d, real, dimension( * ) e2, real pivmin, real reltol, real w, real werr, integer info) — SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.

✨ Detailed Description ✨

okay so the detailed description is literally this: the page documents two Fortran subroutines, dlarrk and slarrk, and their full deets are right below. 💅

🔥 Function 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

DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy. This is an auxiliary code to be 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. The order of the tridiagonal matrix T. N >= 0.
• IW — IW is INTEGER. The index of the eigenvalues to be returned.
• GL — GL is DOUBLE PRECISION. That is all it says here, bestie.
• GU — GU is DOUBLE PRECISION. An upper and a lower bound on the eigenvalue.
• D — D is DOUBLE PRECISION array, dimension (N). The n diagonal elements of the tridiagonal matrix T.
• E2 — E2 is DOUBLE PRECISION array, dimension (N-1). The (n-1) squared off-diagonal elements of the tridiagonal matrix T.
• PIVMIN — PIVMIN is DOUBLE PRECISION. The minimum pivot allowed in the Sturm sequence for T.
• RELTOL — RELTOL is DOUBLE PRECISION. 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. No extra description on this line.
• WERR — WERR is DOUBLE PRECISION. The error bound on the corresponding eigenvalue approximation in W.
• INFO — INFO is INTEGER.
  • = 0: Eigenvalue converged
  • = -1: Eigenvalue did NOT converge

Internal Parameters

• FUDGE — DOUBLE PRECISION, default = 2. The source description is literally A to widen the Gershgorin intervals. (yes, double space and all, bestie).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 143 of file dlarrk.f.

---

subroutine slarrk

subroutine slarrk (integer n, integer iw, real gl, real gu, real, dimension( * ) d, real, dimension( * ) e2, real pivmin, real reltol, real w, real werr, integer info)

SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy. 🌸

Purpose

SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy. This is an auxiliary code to be called from SSTEMR.

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. The order of the tridiagonal matrix T. N >= 0.
• IW — IW is INTEGER. The index of the eigenvalues to be returned.
• GL — GL is REAL. That is all it says here, bestie.
• GU — GU is REAL. An upper and a lower bound on the eigenvalue.
• D — D is REAL array, dimension (N). The n diagonal elements of the tridiagonal matrix T.
• E2 — E2 is REAL array, dimension (N-1). The (n-1) squared off-diagonal elements of the tridiagonal matrix T.
• PIVMIN — PIVMIN is REAL. The minimum pivot allowed in the Sturm sequence for T.
• RELTOL — RELTOL is REAL. 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 REAL. No extra description on this line.
• WERR — WERR is REAL. The error bound on the corresponding eigenvalue approximation in W.
• INFO — INFO is INTEGER.
  • = 0: Eigenvalue converged
  • = -1: Eigenvalue did NOT converge

Internal Parameters

• FUDGE — REAL, default = 2. The source description is literally A to widen the Gershgorin intervals. (yes, double space and all, bestie).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 143 of file slarrk.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

and that is the page, bestie — footer sign-off energy: LAPACK Version 3.12.0, larrk(3). 💅✨