SLARRF(3)

SLARRF(3) — Library Functions Manual 💅

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slarrf.f — that's the file, bestie. This page is SLARRF(3) from the Library Functions Manual, and it's all about the SLARRF routine.

🌈 SYNOPSIS 🌈

Functions/Subroutines

• subroutine SLARRF (n, d, l, ld, clstrt, clend, w, wgap, werr, spdiam, clgapl, clgapr, pivmin, sigma, dplus, lplus, work, info) — SLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated. periodt.

💖 Function/Subroutine Documentation 💖

subroutine SLARRF

subroutine SLARRF (integer n, real, dimension( * ) d, real, dimension( * ) l, real, dimension( * ) ld, integer clstrt, integer clend, real, dimension( * ) w, real, dimension( * ) wgap, real, dimension( * ) werr, real spdiam, real clgapl, real clgapr, real pivmin, real sigma, real, dimension( * ) dplus, real, dimension( * ) lplus, real, dimension( * ) work, integer info)

SLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated. no cap, that's the whole mission.

Purpose:

okay so given the initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ..., W( CLEND ), SLARRF finds a new relatively robust representation L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the eigenvalues of L(+) D(+) L(+)^T is relatively isolated. it's giving eigenvalue isolation era and we love that for it.

Parameters

• N — INTEGER. The order of the matrix (subblock, if the matrix split). bestie, that's the size vibe.
• D — REAL array, dimension (N). The N diagonal elements of the diagonal matrix D.
• L — REAL array, dimension (N-1). The (N-1) subdiagonal elements of the unit bidiagonal matrix L.
• LD — REAL array, dimension (N-1). The (N-1) elements L(i)*D(i).
• CLSTRT — INTEGER. The index of the first eigenvalue in the cluster.
• CLEND — INTEGER. The index of the last eigenvalue in the cluster.
• W — REAL array, dimension dimension is >= (CLEND-CLSTRT+1). The eigenvalue APPROXIMATIONS of L D L^T in ascending order. W( CLSTRT ) through W( CLEND ) form the cluster of relatively close eigenvalues.
• WGAP — REAL array, dimension dimension is >= (CLEND-CLSTRT+1). The separation from the right neighbor eigenvalue in W.
• WERR — REAL array, dimension dimension is >= (CLEND-CLSTRT+1). WERR contain the semiwidth of the uncertainty interval of the corresponding eigenvalue APPROXIMATION in W.
• SPDIAM — REAL. estimate of the spectral diameter obtained from the Gerschgorin intervals.
• CLGAPL — REAL. (the original literally just says this, bestie — no extra description, and we're not inventing one.)
• CLGAPR — REAL. absolute gap on each end of the cluster. Set by the calling routine to protect against shifts too close to eigenvalues outside the cluster.
• PIVMIN — REAL. The minimum pivot allowed in the Sturm sequence.
• SIGMA — REAL. The shift used to form L(+) D(+) L(+)^T.
• DPLUS — REAL array, dimension (N). The N diagonal elements of the diagonal matrix D(+).
• LPLUS — REAL array, dimension (N-1). The first (N-1) elements of LPLUS contain the subdiagonal elements of the unit bidiagonal matrix L(+).
• WORK — REAL array, dimension (2*N). Workspace.
• INFO — INTEGER. Signals processing OK (=0) or failure (=1).

Author

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

Contributors:

• Beresford Parlett, University of California, Berkeley, USA
• Jim Demmel, University of California, Berkeley, USA
• Inderjit Dhillon, University of Texas, Austin, USA
• Osni Marques, LBNL/NERSC, USA
• Christof Voemel, University of California, Berkeley, USA

Definition at line 189 of file slarrf.f.

Author

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that's the whole page, bestie 💖 — LAPACK Version 3.12.0, /home/abui...RC/slarrf.f(3). stay iconic, slay, and keep that main character energy. 💅