slarrj (3) - Linux Man Pages
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.
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.
N is INTEGER The order of the matrix.
D is REAL array, dimension (N) The N diagonal elements of T.
E2 is REAL array, dimension (N-1) The Squares of the (N-1) subdiagonal elements of T.
IFIRST is INTEGER The index of the first eigenvalue to be computed.
ILAST is INTEGER The index of the last eigenvalue to be computed.
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 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 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 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 is REAL array, dimension (2*N) Workspace.
IWORK is INTEGER array, dimension (2*N) Workspace.
PIVMIN is REAL The minimum pivot in the Sturm sequence for T.
SPDIAM is REAL The spectral diameter of T.
INFO is INTEGER Error flag.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
- September 2012
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
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