larrk(3)

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

    !>          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  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 , 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  to widen the Gershgorin intervals.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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