SUBROUTINE SLARRA( N, D, E, E2, SPLTOL, TNRM, \$ NSPLIT, ISPLIT, INFO ) IMPLICIT NONE * * -- LAPACK auxiliary routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. INTEGER INFO, N, NSPLIT REAL SPLTOL, TNRM * .. * .. Array Arguments .. INTEGER ISPLIT( * ) REAL D( * ), E( * ), E2( * ) * .. * * Purpose * ======= * * Compute the splitting points with threshold SPLTOL. * SLARRA sets any "small" off-diagonal elements to zero. * * Arguments * ========= * * N (input) INTEGER * The order of the matrix. N > 0. * * D (input) REAL array, dimension (N) * On entry, the N diagonal elements of the tridiagonal * matrix T. * * E (input/output) 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) 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) 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) REAL * The norm of the matrix. * * NSPLIT (output) INTEGER * The number of blocks T splits into. 1 <= NSPLIT <= N. * * ISPLIT (output) 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) INTEGER * = 0: successful exit * * Further Details * =============== * * Based on contributions by * 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 * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E0 ) * .. * .. Local Scalars .. INTEGER I REAL EABS, TMP1 * .. * .. Intrinsic Functions .. INTRINSIC ABS * .. * .. Executable Statements .. * INFO = 0 * Compute splitting points NSPLIT = 1 IF(SPLTOL.LT.ZERO) THEN * Criterion based on absolute off-diagonal value TMP1 = ABS(SPLTOL)* TNRM DO 9 I = 1, N-1 EABS = ABS( E(I) ) IF( EABS .LE. TMP1) THEN E(I) = ZERO E2(I) = ZERO ISPLIT( NSPLIT ) = I NSPLIT = NSPLIT + 1 END IF 9 CONTINUE ELSE * Criterion that guarantees relative accuracy DO 10 I = 1, N-1 EABS = ABS( E(I) ) IF( EABS .LE. SPLTOL * SQRT(ABS(D(I)))*SQRT(ABS(D(I+1))) ) \$ THEN E(I) = ZERO E2(I) = ZERO ISPLIT( NSPLIT ) = I NSPLIT = NSPLIT + 1 END IF 10 CONTINUE ENDIF ISPLIT( NSPLIT ) = N RETURN * * End of SLARRA * END