ssvdct.f

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*> \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 November 2011
*
*> \ingroup single_eig
*
*  =====================================================================
      SUBROUTINE ssvdct( N, S, E, SHIFT, NUM )
*
*  -- LAPACK test routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. 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