Man page - larrj(3)

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larrj

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine dlarrj (integer n, double precision, dimension( * ) d, doubleprecision, dimension( * ) e2, integer ifirst, integer ilast, doubleprecision rtol, integer offset, double precision, dimension( * ) w,double precision, dimension( * ) werr, double precision, dimension( * )work, integer, dimension( * ) iwork, double precision pivmin, doubleprecision spdiam, integer info)
subroutine slarrj (integer n, real, dimension( * ) d, real, dimension( * )e2, integer ifirst, integer ilast, real rtol, integer offset, real,dimension( * ) w, real, dimension( * ) werr, real, dimension( * ) work,integer, dimension( * ) iwork, real pivmin, real spdiam, integer info)
Author

NAME

larrj - larrj: step in stemr, refine eigval estimates

SYNOPSIS

Functions

subroutine dlarrj (n, d, e2, ifirst, ilast, rtol, offset, w, werr, work, iwork, pivmin, spdiam, info)
DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.
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.

Detailed Description

Function Documentation

subroutine dlarrj (integer n, double precision, dimension( * ) d, doubleprecision, dimension( * ) e2, integer ifirst, integer ilast, doubleprecision rtol, integer offset, double precision, dimension( * ) w,double precision, dimension( * ) werr, double precision, dimension( * )work, integer, dimension( * ) iwork, double precision pivmin, doubleprecision spdiam, integer info)

DLARRJ performs refinement of the initial estimates of the eigenvalues of the matrix T.

Purpose:

Given the initial eigenvalue approximations of T, DLARRJ
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 DOUBLE PRECISION array, dimension (N)
The N diagonal elements of T.

E2

E2 is DOUBLE PRECISION 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 DOUBLE PRECISION
Tolerance for the convergence of the bisection intervals.
An interval [LEFT,RIGHT] has converged if
RIGHT-LEFT < 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 DOUBLE PRECISION array, dimension (N)
On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are
estimates of the eigenvalues of L D LĖ†T indexed IFIRST through
ILAST.
On output, these estimates are refined.

WERR

WERR is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (2*N)
Workspace.

IWORK

IWORK is INTEGER array, dimension (2*N)
Workspace.

PIVMIN

PIVMIN is DOUBLE PRECISION
The minimum pivot in the Sturm sequence for T.

SPDIAM

SPDIAM is DOUBLE PRECISION
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.

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

subroutine slarrj (integer n, real, dimension( * ) d, real, dimension( * )e2, integer ifirst, integer ilast, real rtol, integer offset, real,dimension( * ) w, real, dimension( * ) werr, real, dimension( * ) work,integer, dimension( * ) iwork, real pivmin, real spdiam, integer info)

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 < 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 LĖ†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.

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

Author

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