DLARRF(3)

💅 DLARRF(3) 💅

okay so bestie, this is DLARRF(3) from the LAPACK Library Functions Manual — and yes, it’s a Fortran subroutine page, so grab your iced coffee and let’s get into it. ✨

💖 NAME 💖

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

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine DLARRF (n, d, l, ld, clstrt, clend, w, wgap, werr, spdiam,
    clgapl, clgapr, pivmin, sigma, dplus, lplus, work, info)

DLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated.

🎀 FUNCTION/SUBROUTINE DOCUMENTATION 🎀

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

DLARRF finds a new relatively robust representation such that at least one of the eigenvalues is relatively isolated. 💅

🧚 Purpose 🧚

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 ), DLARRF 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. 🦋

💅 Parameters 💅

• N — INTEGER. The order of the matrix (subblock, if the matrix split).
• D — DOUBLE PRECISION array, dimension (N). The N diagonal elements of the diagonal matrix D.
• L — DOUBLE PRECISION array, dimension (N-1). The (N-1) subdiagonal elements of the unit bidiagonal matrix L.
• LD — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 — DOUBLE PRECISION array, dimension — dimension is >= (CLEND-CLSTRT+1). The separation from the right neighbor eigenvalue in W.
• WERR — DOUBLE PRECISION array, dimension — dimension is >= (CLEND-CLSTRT+1). WERR contain the semiwidth of the uncertainty interval of the corresponding eigenvalue APPROXIMATION in W.
• SPDIAM — DOUBLE PRECISION. Estimate of the spectral diameter obtained from the Gerschgorin intervals.
• CLGAPL — DOUBLE PRECISION. And that’s literally it — the page leaves this one on read, bestie. 🙈
• CLGAPR — DOUBLE PRECISION. 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 — DOUBLE PRECISION. The minimum pivot allowed in the Sturm sequence.
• SIGMA — DOUBLE PRECISION. The shift used to form L(+) D(+) L(+)^T.
• DPLUS — DOUBLE PRECISION array, dimension (N). The N diagonal elements of the diagonal matrix D(+).
• LPLUS — DOUBLE PRECISION array, dimension (N-1). The first (N-1) elements of LPLUS contain the subdiagonal elements of the unit bidiagonal matrix L(+).
• WORK — DOUBLE PRECISION 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 dlarrf.f.

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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