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SUBROUTINE DSTECT( N, A, B, SHIFT, NUM )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
INTEGER N, NUM
DOUBLE PRECISION SHIFT
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( * ), B( * )
* ..
*
* Purpose
* =======
*
* DSTECT 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
*
* Arguments
* =========
*
* N (input) INTEGER
* The dimension of the tridiagonal matrix T.
*
* A (input) DOUBLE PRECISION array, dimension (N)
* The diagonal entries of the tridiagonal matrix T.
*
* B (input) DOUBLE PRECISION array, dimension (N-1)
* The offdiagonal entries of the tridiagonal matrix T.
*
* SHIFT (input) DOUBLE PRECISION
* The shift, used as described under Purpose.
*
* NUM (output) INTEGER
* The number of eigenvalues of T less than or equal
* to SHIFT.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE, THREE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, THREE = 3.0D0 )
* ..
* .. Local Scalars ..
INTEGER I
DOUBLE PRECISION M1, M2, MX, OVFL, SOV, SSHIFT, SSUN, SUN, TMP,
$ TOM, U, UNFL
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, SQRT
* ..
* .. Executable Statements ..
*
* Get machine constants
*
UNFL = DLAMCH( 'Safe minimum' )
OVFL = DLAMCH( '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 DSTECT
*
END
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