Provided by: liblapack-doc_3.12.0-3build1.1_all 
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, double precision, dimension(
* ) e2, integer ifirst, integer ilast, double precision rtol, integer offset, double
precision, dimension( * ) w, double precision, dimension( * ) werr, double precision,
dimension( * ) work, integer, dimension( * ) iwork, double precision pivmin, double
precision 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 L^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 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.
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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