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  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

  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  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

Author

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