LAPACK

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 is INTEGER


          The order of the matrix. N > 0.



          D is DOUBLE PRECISION array, dimension (N)


          On entry, the N diagonal elements of the tridiagonal


          matrix T.



          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 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.