*> \brief \b SSVDCT * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SSVDCT( N, S, E, SHIFT, NUM ) * * .. Scalar Arguments .. * INTEGER N, NUM * REAL SHIFT * .. * .. Array Arguments .. * REAL E( * ), S( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SSVDCT counts the number NUM of eigenvalues of a 2*N by 2*N *> tridiagonal matrix T which are less than or equal to SHIFT. T is *> formed by putting zeros on the diagonal and making the off-diagonals *> equal to S(1), E(1), S(2), E(2), ... , E(N-1), S(N). If SHIFT is *> positive, NUM is equal to N plus the number of singular values of a *> bidiagonal matrix B less than or equal to SHIFT. Here B has diagonal *> entries S(1), ..., S(N) and superdiagonal entries E(1), ... E(N-1). *> If SHIFT is negative, NUM is equal to the number of singular values *> of B greater than or equal to -SHIFT. *> *> 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 bidiagonal matrix B. *> \endverbatim *> *> \param[in] S *> \verbatim *> S is REAL array, dimension (N) *> The diagonal entries of the bidiagonal matrix B. *> \endverbatim *> *> \param[in] E *> \verbatim *> E is REAL array of dimension (N-1) *> The superdiagonal entries of the bidiagonal matrix B. *> \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. * *> \date December 2016 * *> \ingroup single_eig * * ===================================================================== SUBROUTINE SSVDCT( N, S, E, SHIFT, NUM ) * * -- LAPACK test routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER N, NUM REAL SHIFT * .. * .. Array Arguments .. REAL E( * ), S( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E0 ) REAL ZERO PARAMETER ( ZERO = 0.0E0 ) * .. * .. 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 = 2*SLAMCH( 'Safe minimum' ) OVFL = ONE / UNFL * * Find largest entry * MX = ABS( S( 1 ) ) DO 10 I = 1, N - 1 MX = MAX( MX, ABS( S( I+1 ) ), ABS( E( I ) ) ) 10 CONTINUE * IF( MX.EQ.ZERO ) THEN IF( SHIFT.LT.ZERO ) THEN NUM = 0 ELSE NUM = 2*N END IF RETURN END IF * * Compute scale factors as in Kahan's report * 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 * U = ONE NUM = 0 SSHIFT = ( SHIFT*M1 )*M2 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 TMP = ( S( 1 )*M1 )*M2 U = -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 DO 20 I = 1, N - 1 TMP = ( E( I )*M1 )*M2 U = -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 TMP = ( S( I+1 )*M1 )*M2 U = -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 SSVDCT * END