# slarrk(3) [centos man page]

```slarrk.f(3)							      LAPACK							       slarrk.f(3)

NAME
slarrk.f -

SYNOPSIS
Functions/Subroutines
subroutine slarrk (N, IW, GL, GU, D, E2, PIVMIN, RELTOL, W, WERR, INFO)
SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.

Function/Subroutine Documentation
subroutine slarrk (integerN, integerIW, realGL, realGU, real, dimension( * )D, real, dimension( * )E2, realPIVMIN, realRELTOL, realW, realWERR,
integerINFO)
SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.

Purpose:

SLARRK computes one eigenvalue of a symmetric tridiagonal
matrix T to suitable accuracy. This is an auxiliary code to be
called from SSTEMR.

To avoid overflow, the matrix must be scaled so that its
largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
accuracy, it should not be much smaller than that.

See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
Matrix", Report CS41, Computer Science Dept., Stanford
University, July 21, 1966.

Parameters:
N

N is INTEGER
The order of the tridiagonal matrix T.  N >= 0.

IW

IW is INTEGER
The index of the eigenvalues to be returned.

GL

GL is REAL

GU

GU is REAL
An upper and a lower bound on the eigenvalue.

D

D is REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix T.

E2

E2 is REAL array, dimension (N-1)
The (n-1) squared off-diagonal elements of the tridiagonal matrix T.

PIVMIN

PIVMIN is REAL
The minimum pivot allowed in the Sturm sequence for T.

RELTOL

RELTOL is REAL
The minimum relative width of an interval.  When an interval
is narrower than RELTOL times the larger (in
magnitude) endpoint, then it is considered to be
sufficiently small, i.e., converged.  Note: this should
always be at least radix*machine epsilon.

W

W is REAL

WERR

WERR is REAL
The error bound on the corresponding eigenvalue approximation
in W.

INFO

INFO is INTEGER
= 0:	Eigenvalue converged
= -1:	Eigenvalue did NOT converge

Internal Parameters:

FUDGE   REAL	     , default = 2
A "fudge factor" to widen the Gershgorin intervals.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
September 2012

Definition at line 145 of file slarrk.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       slarrk.f(3)```

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```slarrk.f(3)							      LAPACK							       slarrk.f(3)

NAME
slarrk.f -

SYNOPSIS
Functions/Subroutines
subroutine slarrk (N, IW, GL, GU, D, E2, PIVMIN, RELTOL, W, WERR, INFO)
SLARRK

Function/Subroutine Documentation
subroutine slarrk (integerN, integerIW, realGL, realGU, real, dimension( * )D, real, dimension( * )E2, realPIVMIN, realRELTOL, realW, realWERR,
integerINFO)
SLARRK

Purpose:

SLARRK computes one eigenvalue of a symmetric tridiagonal
matrix T to suitable accuracy. This is an auxiliary code to be
called from SSTEMR.

To avoid overflow, the matrix must be scaled so that its
largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
accuracy, it should not be much smaller than that.

See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
Matrix", Report CS41, Computer Science Dept., Stanford
University, July 21, 1966.

Parameters:
N

N is INTEGER
The order of the tridiagonal matrix T.  N >= 0.

IW

IW is INTEGER
The index of the eigenvalues to be returned.

GL

GL is REAL

GU

GU is REAL
An upper and a lower bound on the eigenvalue.

D

D is REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix T.

E2

E2 is REAL array, dimension (N-1)
The (n-1) squared off-diagonal elements of the tridiagonal matrix T.

PIVMIN

PIVMIN is REAL
The minimum pivot allowed in the Sturm sequence for T.

RELTOL

RELTOL is REAL
The minimum relative width of an interval.  When an interval
is narrower than RELTOL times the larger (in
magnitude) endpoint, then it is considered to be
sufficiently small, i.e., converged.  Note: this should
always be at least radix*machine epsilon.

W

W is REAL

WERR

WERR is REAL
The error bound on the corresponding eigenvalue approximation
in W.

INFO

INFO is INTEGER
= 0:	Eigenvalue converged
= -1:	Eigenvalue did NOT converge

Internal Parameters:

FUDGE   REAL	     , default = 2
A "fudge factor" to widen the Gershgorin intervals.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
November 2011

Definition at line 145 of file slarrk.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       slarrk.f(3)```
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