LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dlarrk()

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.

Download DLARRK + dependencies [TGZ] [ZIP] [TXT]

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
[in]N
!>          N is INTEGER
!>          The order of the tridiagonal matrix T.  N >= 0.
!>
[in]IW
!>          IW is INTEGER
!>          The index of the eigenvalues to be returned.
!>
[in]GL
!>          GL is DOUBLE PRECISION
!>
[in]GU
!>          GU is DOUBLE PRECISION
!>          An upper and a lower bound on the eigenvalue.
!>
[in]D
!>          D is DOUBLE PRECISION array, dimension (N)
!>          The n diagonal elements of the tridiagonal matrix T.
!>
[in]E2
!>          E2 is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) squared off-diagonal elements of the tridiagonal matrix T.
!>
[in]PIVMIN
!>          PIVMIN is DOUBLE PRECISION
!>          The minimum pivot allowed in the Sturm sequence for T.
!>
[in]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.
!>
[out]W
!>          W is DOUBLE PRECISION
!>
[out]WERR
!>          WERR is DOUBLE PRECISION
!>          The error bound on the corresponding eigenvalue approximation
!>          in W.
!>
[out]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.