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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( * )
* ..
*
* Purpose
* =======
*
*>\details \b 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 3.1) --
* -- 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
|
