LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ dsvdct()

subroutine dsvdct ( integer  N,
double precision, dimension( * )  S,
double precision, dimension( * )  E,
double precision  SHIFT,
integer  NUM 
)

DSVDCT

Purpose:
 DSVDCT 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
Parameters
[in]N
          N is INTEGER
          The dimension of the bidiagonal matrix B.
[in]S
          S is DOUBLE PRECISION array, dimension (N)
          The diagonal entries of the bidiagonal matrix B.
[in]E
          E is DOUBLE PRECISION array of dimension (N-1)
          The superdiagonal entries of the bidiagonal matrix B.
[in]SHIFT
          SHIFT is DOUBLE PRECISION
          The shift, used as described under Purpose.
[out]NUM
          NUM is INTEGER
          The number of eigenvalues of T less than or equal to SHIFT.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 86 of file dsvdct.f.

87 *
88 * -- LAPACK test routine --
89 * -- LAPACK is a software package provided by Univ. of Tennessee, --
90 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
91 *
92 * .. Scalar Arguments ..
93  INTEGER N, NUM
94  DOUBLE PRECISION SHIFT
95 * ..
96 * .. Array Arguments ..
97  DOUBLE PRECISION E( * ), S( * )
98 * ..
99 *
100 * =====================================================================
101 *
102 * .. Parameters ..
103  DOUBLE PRECISION ONE
104  parameter( one = 1.0d0 )
105  DOUBLE PRECISION ZERO
106  parameter( zero = 0.0d0 )
107 * ..
108 * .. Local Scalars ..
109  INTEGER I
110  DOUBLE PRECISION M1, M2, MX, OVFL, SOV, SSHIFT, SSUN, SUN, TMP,
111  $ TOM, U, UNFL
112 * ..
113 * .. External Functions ..
114  DOUBLE PRECISION DLAMCH
115  EXTERNAL dlamch
116 * ..
117 * .. Intrinsic Functions ..
118  INTRINSIC abs, max, sqrt
119 * ..
120 * .. Executable Statements ..
121 *
122 * Get machine constants
123 *
124  unfl = 2*dlamch( 'Safe minimum' )
125  ovfl = one / unfl
126 *
127 * Find largest entry
128 *
129  mx = abs( s( 1 ) )
130  DO 10 i = 1, n - 1
131  mx = max( mx, abs( s( i+1 ) ), abs( e( i ) ) )
132  10 CONTINUE
133 *
134  IF( mx.EQ.zero ) THEN
135  IF( shift.LT.zero ) THEN
136  num = 0
137  ELSE
138  num = 2*n
139  END IF
140  RETURN
141  END IF
142 *
143 * Compute scale factors as in Kahan's report
144 *
145  sun = sqrt( unfl )
146  ssun = sqrt( sun )
147  sov = sqrt( ovfl )
148  tom = ssun*sov
149  IF( mx.LE.one ) THEN
150  m1 = one / mx
151  m2 = tom
152  ELSE
153  m1 = one
154  m2 = tom / mx
155  END IF
156 *
157 * Begin counting
158 *
159  u = one
160  num = 0
161  sshift = ( shift*m1 )*m2
162  u = -sshift
163  IF( u.LE.sun ) THEN
164  IF( u.LE.zero ) THEN
165  num = num + 1
166  IF( u.GT.-sun )
167  $ u = -sun
168  ELSE
169  u = sun
170  END IF
171  END IF
172  tmp = ( s( 1 )*m1 )*m2
173  u = -tmp*( tmp / u ) - sshift
174  IF( u.LE.sun ) THEN
175  IF( u.LE.zero ) THEN
176  num = num + 1
177  IF( u.GT.-sun )
178  $ u = -sun
179  ELSE
180  u = sun
181  END IF
182  END IF
183  DO 20 i = 1, n - 1
184  tmp = ( e( i )*m1 )*m2
185  u = -tmp*( tmp / u ) - sshift
186  IF( u.LE.sun ) THEN
187  IF( u.LE.zero ) THEN
188  num = num + 1
189  IF( u.GT.-sun )
190  $ u = -sun
191  ELSE
192  u = sun
193  END IF
194  END IF
195  tmp = ( s( i+1 )*m1 )*m2
196  u = -tmp*( tmp / u ) - sshift
197  IF( u.LE.sun ) THEN
198  IF( u.LE.zero ) THEN
199  num = num + 1
200  IF( u.GT.-sun )
201  $ u = -sun
202  ELSE
203  u = sun
204  END IF
205  END IF
206  20 CONTINUE
207  RETURN
208 *
209 * End of DSVDCT
210 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
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