LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ ssvdct()

 subroutine ssvdct ( integer N, real, dimension( * ) S, real, dimension( * ) E, real SHIFT, integer NUM )

SSVDCT

Purpose:
``` 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```
Parameters
 [in] N ``` N is INTEGER The dimension of the bidiagonal matrix B.``` [in] S ``` S is REAL array, dimension (N) The diagonal entries of the bidiagonal matrix B.``` [in] E ``` E is REAL array of dimension (N-1) The superdiagonal entries of the bidiagonal matrix B.``` [in] SHIFT ``` SHIFT is REAL The shift, used as described under Purpose.``` [out] NUM ``` NUM is INTEGER The number of eigenvalues of T less than or equal to SHIFT.```

Definition at line 86 of file ssvdct.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  REAL SHIFT
95 * ..
96 * .. Array Arguments ..
97  REAL E( * ), S( * )
98 * ..
99 *
100 * =====================================================================
101 *
102 * .. Parameters ..
103  REAL ONE
104  parameter( one = 1.0e0 )
105  REAL ZERO
106  parameter( zero = 0.0e0 )
107 * ..
108 * .. Local Scalars ..
109  INTEGER I
110  REAL M1, M2, MX, OVFL, SOV, SSHIFT, SSUN, SUN, TMP,
111  \$ TOM, U, UNFL
112 * ..
113 * .. External Functions ..
114  REAL SLAMCH
115  EXTERNAL slamch
116 * ..
117 * .. Intrinsic Functions ..
118  INTRINSIC abs, max, sqrt
119 * ..
120 * .. Executable Statements ..
121 *
122 * Get machine constants
123 *
124  unfl = 2*slamch( '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 SSVDCT
210 *
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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