LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
slasq6.f
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1 *> \brief \b SLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download SLASQ6 + dependencies
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11 *> [TGZ]</a>
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slasq6.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
22 * DNM1, DNM2 )
23 *
24 * .. Scalar Arguments ..
25 * INTEGER I0, N0, PP
26 * REAL DMIN, DMIN1, DMIN2, DN, DNM1, DNM2
27 * ..
28 * .. Array Arguments ..
29 * REAL Z( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> SLASQ6 computes one dqd (shift equal to zero) transform in
39 *> ping-pong form, with protection against underflow and overflow.
40 *> \endverbatim
41 *
42 * Arguments:
43 * ==========
44 *
45 *> \param[in] I0
46 *> \verbatim
47 *> I0 is INTEGER
48 *> First index.
49 *> \endverbatim
50 *>
51 *> \param[in] N0
52 *> \verbatim
53 *> N0 is INTEGER
54 *> Last index.
55 *> \endverbatim
56 *>
57 *> \param[in] Z
58 *> \verbatim
59 *> Z is REAL array, dimension ( 4*N )
60 *> Z holds the qd array. EMIN is stored in Z(4*N0) to avoid
61 *> an extra argument.
62 *> \endverbatim
63 *>
64 *> \param[in] PP
65 *> \verbatim
66 *> PP is INTEGER
67 *> PP=0 for ping, PP=1 for pong.
68 *> \endverbatim
69 *>
70 *> \param[out] DMIN
71 *> \verbatim
72 *> DMIN is REAL
73 *> Minimum value of d.
74 *> \endverbatim
75 *>
76 *> \param[out] DMIN1
77 *> \verbatim
78 *> DMIN1 is REAL
79 *> Minimum value of d, excluding D( N0 ).
80 *> \endverbatim
81 *>
82 *> \param[out] DMIN2
83 *> \verbatim
84 *> DMIN2 is REAL
85 *> Minimum value of d, excluding D( N0 ) and D( N0-1 ).
86 *> \endverbatim
87 *>
88 *> \param[out] DN
89 *> \verbatim
90 *> DN is REAL
91 *> d(N0), the last value of d.
92 *> \endverbatim
93 *>
94 *> \param[out] DNM1
95 *> \verbatim
96 *> DNM1 is REAL
97 *> d(N0-1).
98 *> \endverbatim
99 *>
100 *> \param[out] DNM2
101 *> \verbatim
102 *> DNM2 is REAL
103 *> d(N0-2).
104 *> \endverbatim
105 *
106 * Authors:
107 * ========
108 *
109 *> \author Univ. of Tennessee
110 *> \author Univ. of California Berkeley
111 *> \author Univ. of Colorado Denver
112 *> \author NAG Ltd.
113 *
114 *> \ingroup auxOTHERcomputational
115 *
116 * =====================================================================
117  SUBROUTINE slasq6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
118  $ DNM1, DNM2 )
119 *
120 * -- LAPACK computational routine --
121 * -- LAPACK is a software package provided by Univ. of Tennessee, --
122 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
123 *
124 * .. Scalar Arguments ..
125  INTEGER I0, N0, PP
126  REAL DMIN, DMIN1, DMIN2, DN, DNM1, DNM2
127 * ..
128 * .. Array Arguments ..
129  REAL Z( * )
130 * ..
131 *
132 * =====================================================================
133 *
134 * .. Parameter ..
135  REAL ZERO
136  parameter( zero = 0.0e0 )
137 * ..
138 * .. Local Scalars ..
139  INTEGER J4, J4P2
140  REAL D, EMIN, SAFMIN, TEMP
141 * ..
142 * .. External Function ..
143  REAL SLAMCH
144  EXTERNAL slamch
145 * ..
146 * .. Intrinsic Functions ..
147  INTRINSIC min
148 * ..
149 * .. Executable Statements ..
150 *
151  IF( ( n0-i0-1 ).LE.0 )
152  $ RETURN
153 *
154  safmin = slamch( 'Safe minimum' )
155  j4 = 4*i0 + pp - 3
156  emin = z( j4+4 )
157  d = z( j4 )
158  dmin = d
159 *
160  IF( pp.EQ.0 ) THEN
161  DO 10 j4 = 4*i0, 4*( n0-3 ), 4
162  z( j4-2 ) = d + z( j4-1 )
163  IF( z( j4-2 ).EQ.zero ) THEN
164  z( j4 ) = zero
165  d = z( j4+1 )
166  dmin = d
167  emin = zero
168  ELSE IF( safmin*z( j4+1 ).LT.z( j4-2 ) .AND.
169  $ safmin*z( j4-2 ).LT.z( j4+1 ) ) THEN
170  temp = z( j4+1 ) / z( j4-2 )
171  z( j4 ) = z( j4-1 )*temp
172  d = d*temp
173  ELSE
174  z( j4 ) = z( j4+1 )*( z( j4-1 ) / z( j4-2 ) )
175  d = z( j4+1 )*( d / z( j4-2 ) )
176  END IF
177  dmin = min( dmin, d )
178  emin = min( emin, z( j4 ) )
179  10 CONTINUE
180  ELSE
181  DO 20 j4 = 4*i0, 4*( n0-3 ), 4
182  z( j4-3 ) = d + z( j4 )
183  IF( z( j4-3 ).EQ.zero ) THEN
184  z( j4-1 ) = zero
185  d = z( j4+2 )
186  dmin = d
187  emin = zero
188  ELSE IF( safmin*z( j4+2 ).LT.z( j4-3 ) .AND.
189  $ safmin*z( j4-3 ).LT.z( j4+2 ) ) THEN
190  temp = z( j4+2 ) / z( j4-3 )
191  z( j4-1 ) = z( j4 )*temp
192  d = d*temp
193  ELSE
194  z( j4-1 ) = z( j4+2 )*( z( j4 ) / z( j4-3 ) )
195  d = z( j4+2 )*( d / z( j4-3 ) )
196  END IF
197  dmin = min( dmin, d )
198  emin = min( emin, z( j4-1 ) )
199  20 CONTINUE
200  END IF
201 *
202 * Unroll last two steps.
203 *
204  dnm2 = d
205  dmin2 = dmin
206  j4 = 4*( n0-2 ) - pp
207  j4p2 = j4 + 2*pp - 1
208  z( j4-2 ) = dnm2 + z( j4p2 )
209  IF( z( j4-2 ).EQ.zero ) THEN
210  z( j4 ) = zero
211  dnm1 = z( j4p2+2 )
212  dmin = dnm1
213  emin = zero
214  ELSE IF( safmin*z( j4p2+2 ).LT.z( j4-2 ) .AND.
215  $ safmin*z( j4-2 ).LT.z( j4p2+2 ) ) THEN
216  temp = z( j4p2+2 ) / z( j4-2 )
217  z( j4 ) = z( j4p2 )*temp
218  dnm1 = dnm2*temp
219  ELSE
220  z( j4 ) = z( j4p2+2 )*( z( j4p2 ) / z( j4-2 ) )
221  dnm1 = z( j4p2+2 )*( dnm2 / z( j4-2 ) )
222  END IF
223  dmin = min( dmin, dnm1 )
224 *
225  dmin1 = dmin
226  j4 = j4 + 4
227  j4p2 = j4 + 2*pp - 1
228  z( j4-2 ) = dnm1 + z( j4p2 )
229  IF( z( j4-2 ).EQ.zero ) THEN
230  z( j4 ) = zero
231  dn = z( j4p2+2 )
232  dmin = dn
233  emin = zero
234  ELSE IF( safmin*z( j4p2+2 ).LT.z( j4-2 ) .AND.
235  $ safmin*z( j4-2 ).LT.z( j4p2+2 ) ) THEN
236  temp = z( j4p2+2 ) / z( j4-2 )
237  z( j4 ) = z( j4p2 )*temp
238  dn = dnm1*temp
239  ELSE
240  z( j4 ) = z( j4p2+2 )*( z( j4p2 ) / z( j4-2 ) )
241  dn = z( j4p2+2 )*( dnm1 / z( j4-2 ) )
242  END IF
243  dmin = min( dmin, dn )
244 *
245  z( j4+2 ) = dn
246  z( 4*n0-pp ) = emin
247  RETURN
248 *
249 * End of SLASQ6
250 *
251  END
subroutine slasq6(I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, DNM1, DNM2)
SLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr.
Definition: slasq6.f:119