*> \brief \b SSTECT * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SSTECT( N, A, B, SHIFT, NUM ) * * .. Scalar Arguments .. * INTEGER N, NUM * REAL SHIFT * .. * .. Array Arguments .. * REAL A( * ), B( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SSTECT counts the number NUM of eigenvalues of a tridiagonal *> matrix T which are less than or equal to SHIFT. T has *> diagonal entries A(1), ... , A(N), and offdiagonal entries *> B(1), ..., B(N-1). *> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal *> Matrix", Report CS41, Computer Science Dept., Stanford *> University, July 21, 1966 *> \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] SHIFT *> \verbatim *> SHIFT is REAL *> The shift, used as described under Purpose. *> \endverbatim *> *> \param[out] NUM *> \verbatim *> NUM is INTEGER *> The number of eigenvalues of T less than or equal *> to SHIFT. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup single_eig * * ===================================================================== SUBROUTINE SSTECT( N, A, B, SHIFT, NUM ) * * -- 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 N, NUM REAL SHIFT * .. * .. Array Arguments .. REAL A( * ), B( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE, THREE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, THREE = 3.0E0 ) * .. * .. Local Scalars .. INTEGER I REAL M1, M2, MX, OVFL, SOV, SSHIFT, SSUN, SUN, TMP, $ TOM, U, UNFL * .. * .. External Functions .. REAL SLAMCH EXTERNAL SLAMCH * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, SQRT * .. * .. Executable Statements .. * * Get machine constants * UNFL = SLAMCH( 'Safe minimum' ) OVFL = SLAMCH( 'Overflow' ) * * Find largest entry * MX = ABS( A( 1 ) ) DO 10 I = 1, N - 1 MX = MAX( MX, ABS( A( I+1 ) ), ABS( B( I ) ) ) 10 CONTINUE * * Handle easy cases, including zero matrix * IF( SHIFT.GE.THREE*MX ) THEN NUM = N RETURN END IF IF( SHIFT.LT.-THREE*MX ) THEN NUM = 0 RETURN END IF * * Compute scale factors as in Kahan's report * At this point, MX .NE. 0 so we can divide by it * SUN = SQRT( UNFL ) SSUN = SQRT( SUN ) SOV = SQRT( OVFL ) TOM = SSUN*SOV IF( MX.LE.ONE ) THEN M1 = ONE / MX M2 = TOM ELSE M1 = ONE M2 = TOM / MX END IF * * Begin counting * NUM = 0 SSHIFT = ( SHIFT*M1 )*M2 U = ( A( 1 )*M1 )*M2 - SSHIFT IF( U.LE.SUN ) THEN IF( U.LE.ZERO ) THEN NUM = NUM + 1 IF( U.GT.-SUN ) $ U = -SUN ELSE U = SUN END IF END IF DO 20 I = 2, N TMP = ( B( I-1 )*M1 )*M2 U = ( ( A( I )*M1 )*M2-TMP*( TMP / U ) ) - SSHIFT IF( U.LE.SUN ) THEN IF( U.LE.ZERO ) THEN NUM = NUM + 1 IF( U.GT.-SUN ) $ U = -SUN ELSE U = SUN END IF END IF 20 CONTINUE RETURN * * End of SSTECT * END