larra(3)

NAME
larra - larra: step in stemr

SYNOPSIS

  Functions
subroutine dlarra (n, d, e, e2, spltol, tnrm, nsplit, isplit, info)
DLARRA computes the splitting points with the specified threshold.
subroutine slarra (n, d, e, e2, spltol, tnrm, nsplit, isplit, info)
SLARRA computes the splitting points with the specified threshold.

Detailed Description

Function Documentation

  subroutine dlarra (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( * ) e2, double precision spltol, double precision tnrm, integer nsplit, integer, dimension( * ) isplit, integer info)

DLARRA computes the splitting points with the specified threshold.

Purpose:

     Compute the splitting points with threshold SPLTOL.
     DLARRA sets any 'small' off-diagonal elements to zero.

Parameters
    N

              N is INTEGER
              The order of the matrix. N > 0.

    D

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

    E

              E is DOUBLE PRECISION array, dimension (N)
              On entry, the first (N-1) entries contain the subdiagonal
              elements of the tridiagonal matrix T; E(N) need not be set.
              On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,
              are set to zero, the other entries of E are untouched.

    E2

              E2 is DOUBLE PRECISION array, dimension (N)
              On entry, the first (N-1) entries contain the SQUARES of the
              subdiagonal elements of the tridiagonal matrix T;
              E2(N) need not be set.
              On exit, the entries E2( ISPLIT( I ) ),
              1 <= I <= NSPLIT, have been set to zero

    SPLTOL

              SPLTOL is DOUBLE PRECISION
              The threshold for splitting. Two criteria can be used:
              SPLTOL<0 : criterion based on absolute off-diagonal value
              SPLTOL>0 : criterion that preserves relative accuracy

    TNRM

              TNRM is DOUBLE PRECISION
              The norm of the matrix.

    NSPLIT

              NSPLIT is INTEGER
              The number of blocks T splits into. 1 <= NSPLIT <= N.

    ISPLIT

              ISPLIT is INTEGER array, dimension (N)
              The splitting points, at which T breaks up into blocks.
              The first block consists of rows/columns 1 to ISPLIT(1),
              the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
              etc., and the NSPLIT-th consists of rows/columns
              ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.

    INFO

              INFO is INTEGER
              = 0:  successful exit

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Beresford Parlett, University of California, Berkeley, USA
     Jim Demmel, University of California, Berkeley, USA
     Inderjit Dhillon, University of Texas, Austin, USA
     Osni Marques, LBNL/NERSC, USA
     Christof Voemel, University of California, Berkeley, USA

Definition at line 134 of file dlarra.f.

  subroutine slarra (integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( * ) e2, real spltol, real tnrm, integer nsplit, integer, dimension( * ) isplit, integer info)

SLARRA computes the splitting points with the specified threshold.

Purpose:

     Compute the splitting points with threshold SPLTOL.
     SLARRA sets any 'small' off-diagonal elements to zero.

Parameters
    N

              N is INTEGER
              The order of the matrix. N > 0.

    D

              D is REAL array, dimension (N)
              On entry, the N diagonal elements of the tridiagonal
              matrix T.

    E

              E is REAL array, dimension (N)
              On entry, the first (N-1) entries contain the subdiagonal
              elements of the tridiagonal matrix T; E(N) need not be set.
              On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,
              are set to zero, the other entries of E are untouched.

    E2

              E2 is REAL array, dimension (N)
              On entry, the first (N-1) entries contain the SQUARES of the
              subdiagonal elements of the tridiagonal matrix T;
              E2(N) need not be set.
              On exit, the entries E2( ISPLIT( I ) ),
              1 <= I <= NSPLIT, have been set to zero

    SPLTOL

              SPLTOL is REAL
              The threshold for splitting. Two criteria can be used:
              SPLTOL<0 : criterion based on absolute off-diagonal value
              SPLTOL>0 : criterion that preserves relative accuracy

    TNRM

              TNRM is REAL
              The norm of the matrix.

    NSPLIT

              NSPLIT is INTEGER
              The number of blocks T splits into. 1 <= NSPLIT <= N.

    ISPLIT

              ISPLIT is INTEGER array, dimension (N)
              The splitting points, at which T breaks up into blocks.
              The first block consists of rows/columns 1 to ISPLIT(1),
              the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
              etc., and the NSPLIT-th consists of rows/columns
              ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.

    INFO

              INFO is INTEGER
              = 0:  successful exit

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Beresford Parlett, University of California, Berkeley, USA
     Jim Demmel, University of California, Berkeley, USA
     Inderjit Dhillon, University of Texas, Austin, USA
     Osni Marques, LBNL/NERSC, USA
     Christof Voemel, University of California, Berkeley, USA

Definition at line 134 of file slarra.f.

Author

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