# larrb - Man Page

larrb: step in stemr

## Synopsis

### Functions

subroutine dlarrb (n, d, lld, ifirst, ilast, rtol1, rtol2, offset, w, wgap, werr, work, iwork, pivmin, spdiam, twist, info)
DLARRB provides limited bisection to locate eigenvalues for more accuracy.
subroutine slarrb (n, d, lld, ifirst, ilast, rtol1, rtol2, offset, w, wgap, werr, work, iwork, pivmin, spdiam, twist, info)
SLARRB provides limited bisection to locate eigenvalues for more accuracy.

## Function Documentation

### subroutine dlarrb (integer n, double precision, dimension( * ) d, double precision, dimension( * ) lld, integer ifirst, integer ilast, double precision rtol1, double precision rtol2, integer offset, double precision, dimension( * ) w, double precision, dimension( * ) wgap, double precision, dimension( * ) werr, double precision, dimension( * ) work, integer, dimension( * ) iwork, double precision pivmin, double precision spdiam, integer twist, integer info)

DLARRB provides limited bisection to locate eigenvalues for more accuracy.

Purpose:

``` Given the relatively robust representation(RRR) L D L^T, DLARRB
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 DOUBLE PRECISION array, dimension (N)
The N diagonal elements of the diagonal matrix D.```

LLD

```          LLD is DOUBLE PRECISION 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 DOUBLE PRECISION`

RTOL2

```          RTOL2 is DOUBLE PRECISION
Tolerance for the convergence of the bisection intervals.
An interval [LEFT,RIGHT] has converged if
RIGHT-LEFT < 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 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.```

WGAP

```          WGAP is DOUBLE PRECISION 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 = ILAST
then WGAP(IFIRST-OFFSET) must be set to ZERO.
On output, these gaps 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.```

SPDIAM

```          SPDIAM is DOUBLE PRECISION
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

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

Definition at line 193 of file dlarrb.f.

### subroutine slarrb (integer n, real, dimension( * ) d, real, dimension( * ) lld, integer ifirst, integer ilast, real rtol1, real rtol2, integer offset, real, dimension( * ) w, real, dimension( * ) wgap, real, dimension( * ) werr, real, dimension( * ) work, integer, dimension( * ) iwork, real pivmin, real spdiam, integer twist, integer info)

SLARRB provides limited bisection to locate eigenvalues for more accuracy.

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 < 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 through
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 = 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

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

Definition at line 193 of file slarrb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK