Library Functions Manual

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, double precision 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 , Report CS41, Computer Science Dept., Stanford
!> University, July 21, 1966.
!>

Parameters

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

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

!>          GL is DOUBLE PRECISION
!>

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

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

!>          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 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  to widen the Gershgorin intervals.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 143 of file dlarrk.f.

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.