SLARRA(3)      LAPACK routine of NEC Numeric Library Collection      SLARRA(3)



NAME
       SLARRA

SYNOPSIS
       SUBROUTINE SLARRA (N, D, E, E2, SPLTOL, TNRM, NSPLIT, ISPLIT, INFO)



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




ARGUMENTS
           N         (input)
                     N is INTEGER
                     The order of the matrix. N > 0.

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

           E         (input/output)
                     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        (input/output)
                     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    (input)
                     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      (input)
                     TNRM is REAL
                     The norm of the matrix.

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

           ISPLIT    (output)
                     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      (output)
                     INFO is INTEGER
                     = 0:  successful exit



LAPACK routine                  31 October 2017                      SLARRA(3)