Man page - larrk(3)

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Manual

larrk

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine dlarrk (integer n, integer iw, double precision gl, doubleprecision gu, double precision, dimension( * ) d, double precision,dimension( * ) e2, double precision pivmin, double precision reltol,double precision w, double precision werr, integer info)
subroutine slarrk (integer n, integer iw, real gl, real gu, real,dimension( * ) d, real, dimension( * ) e2, real pivmin, real reltol,real w, real werr, integer info)
Author

NAME

larrk - larrk: step in stemr, compute one eigval

SYNOPSIS

Functions

subroutine dlarrk (n, iw, gl, gu, d, e2, pivmin, reltol, w, werr, info)
DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.
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.

Detailed Description

Function Documentation

subroutine dlarrk (integer n, integer iw, double precision gl, doubleprecision gu, double precision, dimension( * ) d, double precision,dimension( * ) e2, double precision pivmin, double precision reltol,double precision w, double precision werr, integer info)

DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.

Purpose:

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

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 DOUBLE PRECISION

GU

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

D

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

E2

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

PIVMIN

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

RELTOL

RELTOL is DOUBLE PRECISION
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 DOUBLE PRECISION

WERR

WERR is DOUBLE PRECISION
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 DOUBLE PRECISION, default = 2
A ’fudge factor’ to widen the Gershgorin intervals.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine slarrk (integer n, integer iw, real gl, real gu, real,dimension( * ) d, real, dimension( * ) e2, real pivmin, real reltol,real w, real werr, integer info)

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

Univ. of Colorado Denver

NAG Ltd.

Author

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