numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/EIG/sstech.f | 5975B | -rw-r--r-- |
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*> \brief \b SSTECH * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SSTECH( N, A, B, EIG, TOL, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, N * REAL TOL * .. * .. Array Arguments .. * REAL A( * ), B( * ), EIG( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> Let T be the tridiagonal matrix with diagonal entries A(1) ,..., *> A(N) and offdiagonal entries B(1) ,..., B(N-1)). SSTECH checks to *> see if EIG(1) ,..., EIG(N) are indeed accurate eigenvalues of T. *> It does this by expanding each EIG(I) into an interval *> [SVD(I) - EPS, SVD(I) + EPS], merging overlapping intervals if *> any, and using Sturm sequences to count and verify whether each *> resulting interval has the correct number of eigenvalues (using *> SSTECT). Here EPS = TOL*MACHEPS*MAXEIG, where MACHEPS is the *> machine precision and MAXEIG is the absolute value of the largest *> eigenvalue. If each interval contains the correct number of *> eigenvalues, INFO = 0 is returned, otherwise INFO is the index of *> the first eigenvalue in the first bad interval. *> \endverbatim * * Arguments: * ========== * *> \param[in] N *> \verbatim *> N is INTEGER *> The dimension of the tridiagonal matrix T. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is REAL array, dimension (N) *> The diagonal entries of the tridiagonal matrix T. *> \endverbatim *> *> \param[in] B *> \verbatim *> B is REAL array, dimension (N-1) *> The offdiagonal entries of the tridiagonal matrix T. *> \endverbatim *> *> \param[in] EIG *> \verbatim *> EIG is REAL array, dimension (N) *> The purported eigenvalues to be checked. *> \endverbatim *> *> \param[in] TOL *> \verbatim *> TOL is REAL *> Error tolerance for checking, a multiple of the *> machine precision. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> 0 if the eigenvalues are all correct (to within *> 1 +- TOL*MACHEPS*MAXEIG) *> >0 if the interval containing the INFO-th eigenvalue *> contains the incorrect number of eigenvalues. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup single_eig * * ===================================================================== SUBROUTINE SSTECH( N, A, B, EIG, TOL, WORK, INFO ) * * -- LAPACK test 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 REAL TOL * .. * .. Array Arguments .. REAL A( * ), B( * ), EIG( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E0 ) * .. * .. Local Scalars .. INTEGER BPNT, COUNT, I, ISUB, J, NUML, NUMU, TPNT REAL EMIN, EPS, LOWER, MX, TUPPR, UNFLEP, UPPER * .. * .. External Functions .. REAL SLAMCH EXTERNAL SLAMCH * .. * .. External Subroutines .. EXTERNAL SSTECT * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Executable Statements .. * * Check input parameters * INFO = 0 IF( N.EQ.0 ) $ RETURN IF( N.LT.0 ) THEN INFO = -1 RETURN END IF IF( TOL.LT.ZERO ) THEN INFO = -5 RETURN END IF * * Get machine constants * EPS = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' ) UNFLEP = SLAMCH( 'Safe minimum' ) / EPS EPS = TOL*EPS * * Compute maximum absolute eigenvalue, error tolerance * MX = ABS( EIG( 1 ) ) DO 10 I = 2, N MX = MAX( MX, ABS( EIG( I ) ) ) 10 CONTINUE EPS = MAX( EPS*MX, UNFLEP ) * * Sort eigenvalues from EIG into WORK * DO 20 I = 1, N WORK( I ) = EIG( I ) 20 CONTINUE DO 40 I = 1, N - 1 ISUB = 1 EMIN = WORK( 1 ) DO 30 J = 2, N + 1 - I IF( WORK( J ).LT.EMIN ) THEN ISUB = J EMIN = WORK( J ) END IF 30 CONTINUE IF( ISUB.NE.N+1-I ) THEN WORK( ISUB ) = WORK( N+1-I ) WORK( N+1-I ) = EMIN END IF 40 CONTINUE * * TPNT points to singular value at right endpoint of interval * BPNT points to singular value at left endpoint of interval * TPNT = 1 BPNT = 1 * * Begin loop over all intervals * 50 CONTINUE UPPER = WORK( TPNT ) + EPS LOWER = WORK( BPNT ) - EPS * * Begin loop merging overlapping intervals * 60 CONTINUE IF( BPNT.EQ.N ) $ GO TO 70 TUPPR = WORK( BPNT+1 ) + EPS IF( TUPPR.LT.LOWER ) $ GO TO 70 * * Merge * BPNT = BPNT + 1 LOWER = WORK( BPNT ) - EPS GO TO 60 70 CONTINUE * * Count singular values in interval [ LOWER, UPPER ] * CALL SSTECT( N, A, B, LOWER, NUML ) CALL SSTECT( N, A, B, UPPER, NUMU ) COUNT = NUMU - NUML IF( COUNT.NE.BPNT-TPNT+1 ) THEN * * Wrong number of singular values in interval * INFO = TPNT GO TO 80 END IF TPNT = BPNT + 1 BPNT = TPNT IF( TPNT.LE.N ) $ GO TO 50 80 CONTINUE RETURN * * End of SSTECH * END