LAPACK

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.

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.