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---
:name: dlarrb
:md5sum: 94581ce130ae520a534c65b282147970
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- d:
:type: doublereal
:intent: input
:dims:
- n
- lld:
:type: doublereal
:intent: input
:dims:
- n-1
- ifirst:
:type: integer
:intent: input
- ilast:
:type: integer
:intent: input
- rtol1:
:type: doublereal
:intent: input
- rtol2:
:type: doublereal
:intent: input
- offset:
:type: integer
:intent: input
- w:
:type: doublereal
:intent: input/output
:dims:
- n
- wgap:
:type: doublereal
:intent: input/output
:dims:
- n-1
- werr:
:type: doublereal
:intent: input/output
:dims:
- n
- work:
:type: doublereal
:intent: workspace
:dims:
- 2*n
- iwork:
:type: integer
:intent: workspace
:dims:
- 2*n
- pivmin:
:type: doublereal
:intent: input
- spdiam:
:type: doublereal
:intent: input
- twist:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DLARRB( N, D, LLD, IFIRST, ILAST, RTOL1, RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK, PIVMIN, SPDIAM, TWIST, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* Given the relatively robust representation(RRR) L D L^T, DLARRB\n\
* does \"limited\" bisection to refine the eigenvalues of L D L^T,\n\
* W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial\n\
* guesses for these eigenvalues are input in W, the corresponding estimate\n\
* of the error in these guesses and their gaps are input in WERR\n\
* and WGAP, respectively. During bisection, intervals\n\
* [left, right] are maintained by storing their mid-points and\n\
* semi-widths in the arrays W and WERR respectively.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix.\n\
*\n\
* D (input) DOUBLE PRECISION array, dimension (N)\n\
* The N diagonal elements of the diagonal matrix D.\n\
*\n\
* LLD (input) DOUBLE PRECISION array, dimension (N-1)\n\
* The (N-1) elements L(i)*L(i)*D(i).\n\
*\n\
* IFIRST (input) INTEGER\n\
* The index of the first eigenvalue to be computed.\n\
*\n\
* ILAST (input) INTEGER\n\
* The index of the last eigenvalue to be computed.\n\
*\n\
* RTOL1 (input) DOUBLE PRECISION\n\
* RTOL2 (input) DOUBLE PRECISION\n\
* Tolerance for the convergence of the bisection intervals.\n\
* An interval [LEFT,RIGHT] has converged if\n\
* RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )\n\
* where GAP is the (estimated) distance to the nearest\n\
* eigenvalue.\n\
*\n\
* OFFSET (input) INTEGER\n\
* Offset for the arrays W, WGAP and WERR, i.e., the IFIRST-OFFSET\n\
* through ILAST-OFFSET elements of these arrays are to be used.\n\
*\n\
* W (input/output) DOUBLE PRECISION array, dimension (N)\n\
* On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are\n\
* estimates of the eigenvalues of L D L^T indexed IFIRST throug\n\
* ILAST.\n\
* On output, these estimates are refined.\n\
*\n\
* WGAP (input/output) DOUBLE PRECISION array, dimension (N-1)\n\
* On input, the (estimated) gaps between consecutive\n\
* eigenvalues of L D L^T, i.e., WGAP(I-OFFSET) is the gap between\n\
* eigenvalues I and I+1. Note that if IFIRST.EQ.ILAST\n\
* then WGAP(IFIRST-OFFSET) must be set to ZERO.\n\
* On output, these gaps are refined.\n\
*\n\
* WERR (input/output) DOUBLE PRECISION array, dimension (N)\n\
* On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are\n\
* the errors in the estimates of the corresponding elements in W.\n\
* On output, these errors are refined.\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension (2*N)\n\
* Workspace.\n\
*\n\
* IWORK (workspace) INTEGER array, dimension (2*N)\n\
* Workspace.\n\
*\n\
* PIVMIN (input) DOUBLE PRECISION\n\
* The minimum pivot in the Sturm sequence.\n\
*\n\
* SPDIAM (input) DOUBLE PRECISION\n\
* The spectral diameter of the matrix.\n\
*\n\
* TWIST (input) INTEGER\n\
* The twist index for the twisted factorization that is used\n\
* for the negcount.\n\
* TWIST = N: Compute negcount from L D L^T - LAMBDA I = L+ D+ L+^T\n\
* TWIST = 1: Compute negcount from L D L^T - LAMBDA I = U- D- U-^T\n\
* TWIST = R: Compute negcount from L D L^T - LAMBDA I = N(r) D(r) N(r)\n\
*\n\
* INFO (output) INTEGER\n\
* Error flag.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Beresford Parlett, University of California, Berkeley, USA\n\
* Jim Demmel, University of California, Berkeley, USA\n\
* Inderjit Dhillon, University of Texas, Austin, USA\n\
* Osni Marques, LBNL/NERSC, USA\n\
* Christof Voemel, University of California, Berkeley, USA\n\
*\n\
* =====================================================================\n\
*\n"
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