numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/SRC/dlarra.f | 5941B | -rw-r--r-- |
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*> \brief \b DLARRA computes the splitting points with the specified threshold. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLARRA + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarra.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarra.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarra.f"> *> [TXT]</a> *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM, * NSPLIT, ISPLIT, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, N, NSPLIT * DOUBLE PRECISION SPLTOL, TNRM * .. * .. Array Arguments .. * INTEGER ISPLIT( * ) * DOUBLE PRECISION D( * ), E( * ), E2( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> Compute the splitting points with threshold SPLTOL. *> DLARRA sets any "small" off-diagonal elements to zero. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix. N > 0. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (N) *> On entry, the N diagonal elements of the tridiagonal *> matrix T. *> \endverbatim *> *> \param[in,out] E *> \verbatim *> 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. *> \endverbatim *> *> \param[in,out] E2 *> \verbatim *> 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 *> \endverbatim *> *> \param[in] SPLTOL *> \verbatim *> 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 *> \endverbatim *> *> \param[in] TNRM *> \verbatim *> TNRM is DOUBLE PRECISION *> The norm of the matrix. *> \endverbatim *> *> \param[out] NSPLIT *> \verbatim *> NSPLIT is INTEGER *> The number of blocks T splits into. 1 <= NSPLIT <= N. *> \endverbatim *> *> \param[out] ISPLIT *> \verbatim *> 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. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup larra * *> \par Contributors: * ================== *> *> Beresford Parlett, University of California, Berkeley, USA \n *> Jim Demmel, University of California, Berkeley, USA \n *> Inderjit Dhillon, University of Texas, Austin, USA \n *> Osni Marques, LBNL/NERSC, USA \n *> Christof Voemel, University of California, Berkeley, USA * * ===================================================================== SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM, $ NSPLIT, ISPLIT, INFO ) * * -- LAPACK auxiliary routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER INFO, N, NSPLIT DOUBLE PRECISION SPLTOL, TNRM * .. * .. Array Arguments .. INTEGER ISPLIT( * ) DOUBLE PRECISION D( * ), E( * ), E2( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D0 ) * .. * .. Local Scalars .. INTEGER I DOUBLE PRECISION EABS, TMP1 * .. * .. Intrinsic Functions .. INTRINSIC ABS * .. * .. Executable Statements .. * INFO = 0 NSPLIT = 1 * * Quick return if possible * IF( N.LE.0 ) THEN RETURN END IF * * Compute splitting points 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 DLARRA * END