summaryrefslogtreecommitdiff
path: root/SRC/dlasq5.f
blob: 0eb1fd30a4732ca876dfda8702b11942e40d2b7d (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
*> \brief \b DLASQ5 computes one dqds transform in ping-pong form. Used by sbdsqr and sstegr.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLASQ5 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq5.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq5.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq5.f">
*> [TXT]</a>
*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2, DN,
*                          DNM1, DNM2, IEEE, EPS )
*
*       .. Scalar Arguments ..
*       LOGICAL            IEEE
*       INTEGER            I0, N0, PP
*       DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU, SIGMA, EPS
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   Z( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DLASQ5 computes one dqds transform in ping-pong form, one
*> version for IEEE machines another for non IEEE machines.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] I0
*> \verbatim
*>          I0 is INTEGER
*>        First index.
*> \endverbatim
*>
*> \param[in] N0
*> \verbatim
*>          N0 is INTEGER
*>        Last index.
*> \endverbatim
*>
*> \param[in] Z
*> \verbatim
*>          Z is DOUBLE PRECISION array, dimension ( 4*N )
*>        Z holds the qd array. EMIN is stored in Z(4*N0) to avoid
*>        an extra argument.
*> \endverbatim
*>
*> \param[in] PP
*> \verbatim
*>          PP is INTEGER
*>        PP=0 for ping, PP=1 for pong.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is DOUBLE PRECISION
*>        This is the shift.
*> \endverbatim
*>
*> \param[in] SIGMA
*> \verbatim
*>          SIGMA is DOUBLE PRECISION
*>        This is the accumulated shift up to this step.
*> \endverbatim
*>
*> \param[out] DMIN
*> \verbatim
*>          DMIN is DOUBLE PRECISION
*>        Minimum value of d.
*> \endverbatim
*>
*> \param[out] DMIN1
*> \verbatim
*>          DMIN1 is DOUBLE PRECISION
*>        Minimum value of d, excluding D( N0 ).
*> \endverbatim
*>
*> \param[out] DMIN2
*> \verbatim
*>          DMIN2 is DOUBLE PRECISION
*>        Minimum value of d, excluding D( N0 ) and D( N0-1 ).
*> \endverbatim
*>
*> \param[out] DN
*> \verbatim
*>          DN is DOUBLE PRECISION
*>        d(N0), the last value of d.
*> \endverbatim
*>
*> \param[out] DNM1
*> \verbatim
*>          DNM1 is DOUBLE PRECISION
*>        d(N0-1).
*> \endverbatim
*>
*> \param[out] DNM2
*> \verbatim
*>          DNM2 is DOUBLE PRECISION
*>        d(N0-2).
*> \endverbatim
*>
*> \param[in] IEEE
*> \verbatim
*>          IEEE is LOGICAL
*>        Flag for IEEE or non IEEE arithmetic.
*> \endverbatim
*>
*> \param[in] EPS
*> \verbatim
*>          EPS is DOUBLE PRECISION
*>        This is the value of epsilon used.
*> \endverbatim
*>
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup auxOTHERcomputational
*
*  =====================================================================
      SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, SIGMA, DMIN, DMIN1, DMIN2,
     $                   DN, DNM1, DNM2, IEEE, EPS )
*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      LOGICAL            IEEE
      INTEGER            I0, N0, PP
      DOUBLE PRECISION   DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU,
     $                   SIGMA, EPS
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   Z( * )
*     ..
*
*  =====================================================================
*
*     .. Parameter ..
      DOUBLE PRECISION   ZERO, HALF
      PARAMETER          ( ZERO = 0.0D0, HALF = 0.5 )
*     ..
*     .. Local Scalars ..
      INTEGER            J4, J4P2
      DOUBLE PRECISION   D, EMIN, TEMP, DTHRESH
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MIN
*     ..
*     .. Executable Statements ..
*
      IF( ( N0-I0-1 ).LE.0 )
     $   RETURN
*
      DTHRESH = EPS*(SIGMA+TAU)
      IF( TAU.LT.DTHRESH*HALF ) TAU = ZERO
      IF( TAU.NE.ZERO ) THEN
      J4 = 4*I0 + PP - 3
      EMIN = Z( J4+4 )
      D = Z( J4 ) - TAU
      DMIN = D
      DMIN1 = -Z( J4 )
*
      IF( IEEE ) THEN
*
*        Code for IEEE arithmetic.
*
         IF( PP.EQ.0 ) THEN
            DO 10 J4 = 4*I0, 4*( N0-3 ), 4
               Z( J4-2 ) = D + Z( J4-1 )
               TEMP = Z( J4+1 ) / Z( J4-2 )
               D = D*TEMP - TAU
               DMIN = MIN( DMIN, D )
               Z( J4 ) = Z( J4-1 )*TEMP
               EMIN = MIN( Z( J4 ), EMIN )
   10       CONTINUE
         ELSE
            DO 20 J4 = 4*I0, 4*( N0-3 ), 4
               Z( J4-3 ) = D + Z( J4 )
               TEMP = Z( J4+2 ) / Z( J4-3 )
               D = D*TEMP - TAU
               DMIN = MIN( DMIN, D )
               Z( J4-1 ) = Z( J4 )*TEMP
               EMIN = MIN( Z( J4-1 ), EMIN )
   20       CONTINUE
         END IF
*
*        Unroll last two steps.
*
         DNM2 = D
         DMIN2 = DMIN
         J4 = 4*( N0-2 ) - PP
         J4P2 = J4 + 2*PP - 1
         Z( J4-2 ) = DNM2 + Z( J4P2 )
         Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
         DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
         DMIN = MIN( DMIN, DNM1 )
*
         DMIN1 = DMIN
         J4 = J4 + 4
         J4P2 = J4 + 2*PP - 1
         Z( J4-2 ) = DNM1 + Z( J4P2 )
         Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
         DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
         DMIN = MIN( DMIN, DN )
*
      ELSE
*
*        Code for non IEEE arithmetic.
*
         IF( PP.EQ.0 ) THEN
            DO 30 J4 = 4*I0, 4*( N0-3 ), 4
               Z( J4-2 ) = D + Z( J4-1 )
               IF( D.LT.ZERO ) THEN
                  RETURN
               ELSE
                  Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) )
                  D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU
               END IF
               DMIN = MIN( DMIN, D )
               EMIN = MIN( EMIN, Z( J4 ) )
   30       CONTINUE
         ELSE
            DO 40 J4 = 4*I0, 4*( N0-3 ), 4
               Z( J4-3 ) = D + Z( J4 )
               IF( D.LT.ZERO ) THEN
                  RETURN
               ELSE
                  Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) )
                  D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU
               END IF
               DMIN = MIN( DMIN, D )
               EMIN = MIN( EMIN, Z( J4-1 ) )
   40       CONTINUE
         END IF
*
*        Unroll last two steps.
*
         DNM2 = D
         DMIN2 = DMIN
         J4 = 4*( N0-2 ) - PP
         J4P2 = J4 + 2*PP - 1
         Z( J4-2 ) = DNM2 + Z( J4P2 )
         IF( DNM2.LT.ZERO ) THEN
            RETURN
         ELSE
            Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
            DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
         END IF
         DMIN = MIN( DMIN, DNM1 )
*
         DMIN1 = DMIN
         J4 = J4 + 4
         J4P2 = J4 + 2*PP - 1
         Z( J4-2 ) = DNM1 + Z( J4P2 )
         IF( DNM1.LT.ZERO ) THEN
            RETURN
         ELSE
            Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
            DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
         END IF
         DMIN = MIN( DMIN, DN )
*
      END IF
      ELSE
*     This is the version that sets d's to zero if they are small enough
         J4 = 4*I0 + PP - 3
         EMIN = Z( J4+4 )
         D = Z( J4 ) - TAU
         DMIN = D
         DMIN1 = -Z( J4 )
         IF( IEEE ) THEN
*
*     Code for IEEE arithmetic.
*
            IF( PP.EQ.0 ) THEN
               DO 50 J4 = 4*I0, 4*( N0-3 ), 4
                  Z( J4-2 ) = D + Z( J4-1 )
                  TEMP = Z( J4+1 ) / Z( J4-2 )
                  D = D*TEMP - TAU
                  IF( D.LT.DTHRESH ) D = ZERO
                  DMIN = MIN( DMIN, D )
                  Z( J4 ) = Z( J4-1 )*TEMP
                  EMIN = MIN( Z( J4 ), EMIN )
 50            CONTINUE
            ELSE
               DO 60 J4 = 4*I0, 4*( N0-3 ), 4
                  Z( J4-3 ) = D + Z( J4 )
                  TEMP = Z( J4+2 ) / Z( J4-3 )
                  D = D*TEMP - TAU
                  IF( D.LT.DTHRESH ) D = ZERO
                  DMIN = MIN( DMIN, D )
                  Z( J4-1 ) = Z( J4 )*TEMP
                  EMIN = MIN( Z( J4-1 ), EMIN )
 60            CONTINUE
            END IF
*
*     Unroll last two steps.
*
            DNM2 = D
            DMIN2 = DMIN
            J4 = 4*( N0-2 ) - PP
            J4P2 = J4 + 2*PP - 1
            Z( J4-2 ) = DNM2 + Z( J4P2 )
            Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
            DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
            DMIN = MIN( DMIN, DNM1 )
*
            DMIN1 = DMIN
            J4 = J4 + 4
            J4P2 = J4 + 2*PP - 1
            Z( J4-2 ) = DNM1 + Z( J4P2 )
            Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
            DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
            DMIN = MIN( DMIN, DN )
*
         ELSE
*
*     Code for non IEEE arithmetic.
*
            IF( PP.EQ.0 ) THEN
               DO 70 J4 = 4*I0, 4*( N0-3 ), 4
                  Z( J4-2 ) = D + Z( J4-1 )
                  IF( D.LT.ZERO ) THEN
                     RETURN
                  ELSE
                     Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) )
                     D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU
                  END IF
                  IF( D.LT.DTHRESH) D = ZERO
                  DMIN = MIN( DMIN, D )
                  EMIN = MIN( EMIN, Z( J4 ) )
 70            CONTINUE
            ELSE
               DO 80 J4 = 4*I0, 4*( N0-3 ), 4
                  Z( J4-3 ) = D + Z( J4 )
                  IF( D.LT.ZERO ) THEN
                     RETURN
                  ELSE
                     Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) )
                     D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU
                  END IF
                  IF( D.LT.DTHRESH) D = ZERO
                  DMIN = MIN( DMIN, D )
                  EMIN = MIN( EMIN, Z( J4-1 ) )
 80            CONTINUE
            END IF
*
*     Unroll last two steps.
*
            DNM2 = D
            DMIN2 = DMIN
            J4 = 4*( N0-2 ) - PP
            J4P2 = J4 + 2*PP - 1
            Z( J4-2 ) = DNM2 + Z( J4P2 )
            IF( DNM2.LT.ZERO ) THEN
               RETURN
            ELSE
               Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
               DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU
            END IF
            DMIN = MIN( DMIN, DNM1 )
*
            DMIN1 = DMIN
            J4 = J4 + 4
            J4P2 = J4 + 2*PP - 1
            Z( J4-2 ) = DNM1 + Z( J4P2 )
            IF( DNM1.LT.ZERO ) THEN
               RETURN
            ELSE
               Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) )
               DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU
            END IF
            DMIN = MIN( DMIN, DN )
*
         END IF
      END IF
*
      Z( J4+2 ) = DN
      Z( 4*N0-PP ) = EMIN
      RETURN
*
*     End of DLASQ5
*
      END