slarrj(3) [centos man page]
slarrj.f(3) LAPACK slarrj.f(3) NAME
slarrj.f - SYNOPSIS
Functions/Subroutines subroutine slarrj (N, D, E2, IFIRST, ILAST, RTOL, OFFSET, W, WERR, WORK, IWORK, PIVMIN, SPDIAM, INFO) SLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T. Function/Subroutine Documentation subroutine slarrj (integerN, real, dimension( * )D, real, dimension( * )E2, integerIFIRST, integerILAST, realRTOL, integerOFFSET, real, dimension( * )W, real, dimension( * )WERR, real, dimension( * )WORK, integer, dimension( * )IWORK, realPIVMIN, realSPDIAM, integerINFO) SLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T. Purpose: Given the initial eigenvalue approximations of T, SLARRJ does bisection to refine the eigenvalues of T, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial guesses for these eigenvalues are input in W, the corresponding estimate of the error in these guesses in WERR. During bisection, intervals [left, right] are maintained by storing their mid-points and semi-widths in the arrays W and WERR respectively. Parameters: N N is INTEGER The order of the matrix. D D is REAL array, dimension (N) The N diagonal elements of T. E2 E2 is REAL array, dimension (N-1) The Squares of the (N-1) subdiagonal elements of T. IFIRST IFIRST is INTEGER The index of the first eigenvalue to be computed. ILAST ILAST is INTEGER The index of the last eigenvalue to be computed. RTOL RTOL is REAL Tolerance for the convergence of the bisection intervals. An interval [LEFT,RIGHT] has converged if RIGHT-LEFT.LT.RTOL*MAX(|LEFT|,|RIGHT|). OFFSET OFFSET is INTEGER Offset for the arrays W and WERR, i.e., the IFIRST-OFFSET through ILAST-OFFSET elements of these arrays are to be used. W W is REAL array, dimension (N) On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are estimates of the eigenvalues of L D L^T indexed IFIRST through ILAST. On output, these estimates are refined. WERR WERR is REAL array, dimension (N) On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are the errors in the estimates of the corresponding elements in W. On output, these errors are refined. WORK WORK is REAL array, dimension (2*N) Workspace. IWORK IWORK is INTEGER array, dimension (2*N) Workspace. PIVMIN PIVMIN is REAL The minimum pivot in the Sturm sequence for T. SPDIAM SPDIAM is REAL The spectral diameter of T. INFO INFO is INTEGER Error flag. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 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 167 of file slarrj.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 slarrj.f(3)
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slarrb.f(3) LAPACK slarrb.f(3) NAME
slarrb.f - SYNOPSIS
Functions/Subroutines subroutine slarrb (N, D, LLD, IFIRST, ILAST, RTOL1, RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK, PIVMIN, SPDIAM, TWIST, INFO) SLARRB Function/Subroutine Documentation subroutine slarrb (integerN, real, dimension( * )D, real, dimension( * )LLD, integerIFIRST, integerILAST, realRTOL1, realRTOL2, integerOFFSET, real, dimension( * )W, real, dimension( * )WGAP, real, dimension( * )WERR, real, dimension( * )WORK, integer, dimension( * )IWORK, realPIVMIN, realSPDIAM, integerTWIST, integerINFO) SLARRB Purpose: Given the relatively robust representation(RRR) L D L^T, SLARRB does "limited" bisection to refine the eigenvalues of L D L^T, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial guesses for these eigenvalues are input in W, the corresponding estimate of the error in these guesses and their gaps are input in WERR and WGAP, respectively. During bisection, intervals [left, right] are maintained by storing their mid-points and semi-widths in the arrays W and WERR respectively. Parameters: N N is INTEGER The order of the matrix. D D is REAL array, dimension (N) The N diagonal elements of the diagonal matrix D. LLD LLD is REAL array, dimension (N-1) The (N-1) elements L(i)*L(i)*D(i). IFIRST IFIRST is INTEGER The index of the first eigenvalue to be computed. ILAST ILAST is INTEGER The index of the last eigenvalue to be computed. RTOL1 RTOL1 is REAL RTOL2 RTOL2 is REAL Tolerance for the convergence of the bisection intervals. An interval [LEFT,RIGHT] has converged if RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) where GAP is the (estimated) distance to the nearest eigenvalue. OFFSET OFFSET is INTEGER Offset for the arrays W, WGAP and WERR, i.e., the IFIRST-OFFSET through ILAST-OFFSET elements of these arrays are to be used. W W is REAL array, dimension (N) On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are estimates of the eigenvalues of L D L^T indexed IFIRST throug ILAST. On output, these estimates are refined. WGAP WGAP is REAL array, dimension (N-1) On input, the (estimated) gaps between consecutive eigenvalues of L D L^T, i.e., WGAP(I-OFFSET) is the gap between eigenvalues I and I+1. Note that if IFIRST.EQ.ILAST then WGAP(IFIRST-OFFSET) must be set to ZERO. On output, these gaps are refined. WERR WERR is REAL array, dimension (N) On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are the errors in the estimates of the corresponding elements in W. On output, these errors are refined. WORK WORK is REAL array, dimension (2*N) Workspace. IWORK IWORK is INTEGER array, dimension (2*N) Workspace. PIVMIN PIVMIN is REAL The minimum pivot in the Sturm sequence. SPDIAM SPDIAM is REAL The spectral diameter of the matrix. TWIST TWIST is INTEGER The twist index for the twisted factorization that is used for the negcount. TWIST = N: Compute negcount from L D L^T - LAMBDA I = L+ D+ L+^T TWIST = 1: Compute negcount from L D L^T - LAMBDA I = U- D- U-^T TWIST = R: Compute negcount from L D L^T - LAMBDA I = N(r) D(r) N(r) INFO INFO is INTEGER Error flag. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 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 195 of file slarrb.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 slarrb.f(3)