SLARRK(3)

💖 SLARRK(3) — slarrk.f 💖

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slarrk.f

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine SLARRK (n, iw, gl, gu, d, e2, pivmin, reltol, w, werr, info)

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

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🦋 Function/Subroutine Documentation 🦋

💅 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.
• GU — GU is REAL. The page says: “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.
• 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. 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 slarrk.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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