SRC/slarrf.f(3)

🌸 SRC/slarrf.f 🌸

From the Library Functions Manual — LAPACK edition, bestie. This is the page for the slarrf source file, and it's giving subroutine with main character energy fr fr. 💅✨

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✨ 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.

🎀 Function/Subroutine Documentation 🎀

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.

🎯 Purpose:

Okay so here's the vibe: you hand SLARRF the initial representation L D L^T and its cluster of close eigenvalues (in a relative measure), namely W( CLSTRT ), W( CLSTRT+1 ), ... W( CLEND ). Then 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. That's the whole mission, and it ate. 💅🔥

🧮 Parameters

• N — N is INTEGER. The order of the matrix (subblock, if the matrix split). 🫶
• D — D is REAL array, dimension (N). The N diagonal elements of the diagonal matrix D.
• L — L is REAL array, dimension (N-1). The (N-1) subdiagonal elements of the unit bidiagonal matrix L.
• LD — LD is REAL array, dimension (N-1). The (N-1) elements L(i)*D(i).
• CLSTRT — CLSTRT is INTEGER. The index of the first eigenvalue in the cluster.
• CLEND — CLEND is INTEGER. The index of the last eigenvalue in the cluster.
• W — W is 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 eigenalues. (Their spelling, not mine, but we keep it 💀)
• WGAP — WGAP is REAL array, dimension; dimension is >= (CLEND-CLSTRT+1). The separation from the right neighbor eigenvalue in W.
• WERR — WERR is REAL array, dimension; dimension is >= (CLEND-CLSTRT+1). WERR contain the semiwidth of the uncertainty interval of the corresponding eigenvalue APPROXIMATION in W.
• SPDIAM — SPDIAM is REAL: estimate of the spectral diameter obtained from the Gerschgorin intervals.
• CLGAPL — CLGAPL is REAL. Short and sweet, bestie. 💅
• CLGAPR — CLGAPR is 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 — PIVMIN is REAL. The minimum pivot allowed in the Sturm sequence.
• SIGMA — SIGMA is REAL. The shift used to form L(+) D(+) L(+)^T.
• DPLUS — DPLUS is REAL array, dimension (N). The N diagonal elements of the diagonal matrix D(+).
• LPLUS — LPLUS is REAL array, dimension (N-1). The first (N-1) elements of LPLUS contain the subdiagonal elements of the unit bidiagonal matrix L(+).
• WORK — WORK is REAL array, dimension (2*N). Workspace.
• INFO — INFO is 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

Generated automatically by Doxygen for LAPACK from the source code.

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Sign-off: LAPACK, Version 3.12.0, page SRC/slarrf.f(3) — that's the footer, bestie (no extra date line on this one)! 💖✨🦋