File: README.Debian

package info (click to toggle)
lapack 3.2.1-8
  • links: PTS, VCS
  • area: main
  • in suites: squeeze
  • size: 55,196 kB
  • ctags: 33,064
  • sloc: fortran: 448,214; perl: 8,226; makefile: 1,528; sh: 87; awk: 70
file content (1432 lines) | stat: -rw-r--r-- 52,725 bytes parent folder | download
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
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
reflapack3 for Debian
----------------------

The lapack code itself has not been modified from the lapack source
package, version 3.0.20000531a-25.  However the blas library, against
which lapack is linked, has had backwards binary incompatible
corrections applied.  Support for the old and new API in both source
and binary form are provided to aid in the transition.  This requires
a change in package name for the lapack packages.  Please see the
documentation for the refblas3 package for details on the
modifications to the cblas API.

=============================================================================
original lapack README.Debian
=============================================================================

lapack for Debian
----------------------

These libraries were built from the 20000531 Lapack release, as
amended by applying all of the unincorporated updates listed in the
release notes (e.g. files in the patch subdirectory of the lapack
directory at netlib.)  

The new build process runs the tester binaries after
building the libraries, and collects the results in the files
/usr/share/doc/lapack/test_results.  One can search for
any failures with 'grep -i fail /usr/share/doc/lapack/test_results'.

The failures in the ?GV and ?XV tester routines are known and
expected.  The following explanation can be found at
http://www.netlib.org/lapack/html/installation.hints:

    The only known testing failures are in condition number estimation
    routines in the generalized nonsymmetric eigenproblem testing.
    Specifically in sgd.out, dgd.out, cgd.out and zgd.out. The cause for
    the failures of some test cases is that the mathematical algorithm
    used for estimating the condition numbers could over- or
    under-estimate the true values in a certain factor in some rare cases.
    Further details can be found in LAPACK Working Note 87.

This version of lapack also introduces a few testing errors in the
single precision real symmetric and complex Hermitian eigenvalue
routines, at least on ix86 platforms.  Correspondence regarding this
issue with the lapack upstream authors follows at the end of this
file.  Suffice it to say that there is no known solution at present,
but that the errors should be confined to loss of at most 2-3 decimal
places of precision in the routine results.  For this reason, Debian
also supplies lapack libraries based on the earlier release in the
lapack99 package, which, though having errors of its own, does not
exhibit this particular failing.

=============================================================================

From: Camm Maguire <camm@enhanced.com>
Subject: Re: New Debian maintainer
To: Susan Blackford <susan@myri.com>
cc: camm@enhanced.com
Date: 15 Nov 2001 15:33:11 -0500
Received: from intech19.enhanced.com [192.168.2.19] (mail)
	by intech5.enhanced.com with esmtp (Exim 3.12 #1 (Debian))
	id 164TCL-0005qT-00; Thu, 15 Nov 2001 15:33:21 -0500
Received: from camm by intech19.enhanced.com with local (Exim 3.12 #1 (Debian))
	id 164TCB-0002gL-00; Thu, 15 Nov 2001 15:33:11 -0500
References: <E163L4N-0003Xf-00@intech19.enhanced.com> <01111312052804.00517@idefix>
In-Reply-To: Susan Blackford's message of "Tue, 13 Nov 2001 12:05:28 -0500"
Message-ID: <547ksrdbaw.fsf@intech19.enhanced.com>
X-Mailer: Gnus v5.7/Emacs 20.7
X-UIDL: 9358c79a10286a739f7134b4a7627355
Lines: 92
Xref: intech19.enhanced.com mail.camm:27060

Greetings, and thanks for your reply!

Susan Blackford <susan@myri.com> writes:

> Hi,
> 
> If the LIN timers (or any of the testers/timers) dies when loading,
> then you should reduce the size of NMAX in the=20
>    LAPACK/TESTING/LIN/*chkaa.f
>    LAPACK/TESTING/EIG/*chkee.f
>    LAPACK/TIMING/LIN/*timaa.f
>    LAPACK/TIMING/EIG/*timee.f
> 

Thanks for this.  I read a usenet post indicating that MAXVAL could be
reduced to 7 or 8 in the ?timaa.f, and this seems to work too.  Is
either solution acceptable?

Secondarily, I'm upgrading the package from the 1999 3.0 to the
latest, plus the unincorporated patches listed on the release note
pages.

With the old version, I just get the expected _gd.out errors on test,
but the new version has a few errors in the symmetric eigenroutine
single and complex precision as well (_sep.out):

1999:
=============================================================================
cgd.out: CGV drivers:      4 out of   1092 tests failed to pass the threshold
cgd.out:  9 = 1/ULP  if DIFEST <> 0 or DIFTRU > ULP*norm(A,B) when reordering fails
cgd.out: CGX drivers:      6 out of   1500 tests failed to pass the threshold
dgd.out:  9 = 1/ULP  if DIFEST <> 0 or DIFTRU > ULP*norm(A,B) when reordering fails
dgd.out: SGX drivers:      6 out of   1500 tests failed to pass the threshold
dgd.out: DXV drivers:    200 out of   5000 tests failed to pass the threshold
dtest.out: DLS drivers:   2250 out of  65268 tests failed to pass the threshold
sgd.out:  9 = 1/ULP  if DIFEST <> 0 or DIFTRU > ULP*norm(A,B) when reordering fails
sgd.out: SGX drivers:      8 out of   1500 tests failed to pass the threshold
sgd.out: SXV drivers:     37 out of   5000 tests failed to pass the threshold
zgd.out: ZGV drivers:      4 out of   1092 tests failed to pass the threshold
zgd.out:  9 = 1/ULP  if DIFEST <> 0 or DIFTRU > ULP*norm(A,B) when reordering fails
zgd.out: CGX drivers:      6 out of   1500 tests failed to pass the threshold
zgd.out: ZXV drivers:     24 out of   5000 tests failed to pass the threshold

latest:
=============================================================================
cgd.out: CGV drivers:      4 out of   1092 tests failed to pass the threshold
csep.out: CST:    1 out of  4662 tests failed to pass the threshold
csep.out: CST drivers:      1 out of  11664 tests failed to pass the threshold
csep.out: CST:    1 out of  4662 tests failed to pass the threshold
dgd.out: DXV drivers:    200 out of   5000 tests failed to pass the threshold
sgd.out: SXV drivers:     37 out of   5000 tests failed to pass the threshold
ssep.out: SST:    1 out of  4662 tests failed to pass the threshold
ssep.out: SST drivers:      1 out of  14256 tests failed to pass the threshold
zgd.out: ZGV drivers:      4 out of   1092 tests failed to pass the threshold
zgd.out: ZXV drivers:     24 out of   5000 tests failed to pass the threshold
=============================================================================

I am somewhat hesitant to introduce these new errors into the official
lib of the Debian distribution.  I've seen these errors reported in
the release_notes in similar setups to mine (g77 2.95, Linux, PIII).
The latest lib was compiled with the suggested flags in the Linux
make.inc in INSTALL (-funroll-all-loops -O3), whereas the older
version was compiled with (-funroll-all-loops -O3 -fomit-frame-pointer
-ff90).  I can't imagine that the omission of optimizing flags could
introduce new errors, but am willing to recompile with the old
settings if you think this would help.

Any advice appreciated!



> > 3)  Is this also the place to submit patches/suggestions?
> 
> Yes, absolutely... :)
> 
> Susan
> 
> 
> --=20
> ---------------------------------------------
> Susan Blackford
> Member of Technical Staff
> Myricom, Inc.
> ---------------------------------------------
> 
> 

-- 
Camm Maguire			     			camm@enhanced.com
==========================================================================
"The earth is but one country, and mankind its citizens."  --  Baha'u'llah

=============================================================================

From: Edward Anderson <Anderson.Edward@epa.gov>
Subject: Re: New Debian maintainer
To: camm@enhanced.com
CC: Susan Blackford <susan@cs.utk.edu>
Date: Mon, 26 Nov 2001 09:51:48 -0500
Organization: Lockheed Martin (contractor to the U.S. EPA)
Received: from localhost [127.0.0.1] (root)
	by intech5.enhanced.com with esmtp (Exim 3.12 #1 (Debian))
	id 168N8I-0001aM-00; Mon, 26 Nov 2001 09:53:18 -0500
Received: from 204.213.252.11
	by localhost with POP3 (fetchmail-5.3.3)
	for camm@enhanced.com (multi-drop); Mon, 26 Nov 2001 09:53:18 -0500 (EST)
Received: from mail.eticomm.net [204.213.252.17] 
	by ux1.cyberenet.net with esmtp (Exim 1.61 #1)
	id 168N7M-0002gE-00; Mon, 26 Nov 2001 09:52:20 -0500
Received: from [134.67.64.25] (helo=nesc.epa.gov)
	by relay.eticomm.net with esmtp (Exim 3.33 #2)
	id 168N7M-000CuP-00
	for camm@enhanced.com; Mon, 26 Nov 2001 09:52:20 -0500
Received: from epa.gov (yew.nesc.epa.gov [134.67.64.48])
	by nesc.epa.gov (8.9.3+Sun/8.9.1) with ESMTP id JAA17204;
	Mon, 26 Nov 2001 09:51:49 -0500 (EST)
Sender: dle@nesc.epa.gov
Message-ID: <3C025704.86683917@epa.gov>
X-Mailer: Mozilla 4.75C-SGI [en] (X11; I; IRIX 6.5 IP32)
X-Accept-Language: en
MIME-Version: 1.0
References: <004701c17372$2a3580e0$2fee80ac@compaq>
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
X-UIDL: 11a1ca53c0909d8b833a35f7beea5f16
Lines: 167
Xref: intech19.enhanced.com mail.camm:27339

Camm:

I have my own version of LAPACK which incorporates some changes not yet
in the netlib version.  It's hard to say which if any of these might fix
the errors you are seeing.  But if you could send me the full text of
the output files containing tests that are failing, I may have a few
suggestions for you.

   --Ed Anderson

Ed Anderson wrote:
> 
> ----- Original Message -----
> From: Camm Maguire <camm@enhanced.com>
> To: <lapack@cs.utk.edu>
> Sent: Monday, November 19, 2001 5:05 PM
> Subject: [Camm Maguire <camm@enhanced.com>] Re: New Debian maintainer
> 
> > Susan--
> >
> > Resending this to the lapack address, as I haven't heard back
> > from my direct reply to you.  Any advice most appreciated!
> >
> > Take care,
> > --
> > Camm Maguire      camm@enhanced.com
> > ==========================================================================
> > "The earth is but one country, and mankind its citizens."  --  Baha'u'llah
> > ------- Start of forwarded message -------
> > To: Susan Blackford <susan@myri.com>
> > cc: camm@enhanced.com
> > Subject: Re: New Debian maintainer
> > References: <E163L4N-0003Xf-00@intech19.enhanced.com>
> <01111312052804.00517@idefix>
> > From: Camm Maguire <camm@enhanced.com>
> > Date: 15 Nov 2001 15:33:11 -0500
> > Message-ID: <547ksrdbaw.fsf@intech19.enhanced.com>
> >
> > Greetings, and thanks for your reply!
> >
> > Susan Blackford <susan@myri.com> writes:
> >
> > > Hi,
> > >
> > > If the LIN timers (or any of the testers/timers) dies when loading,
> > > then you should reduce the size of NMAX in the=20
> > >    LAPACK/TESTING/LIN/*chkaa.f
> > >    LAPACK/TESTING/EIG/*chkee.f
> > >    LAPACK/TIMING/LIN/*timaa.f
> > >    LAPACK/TIMING/EIG/*timee.f
> > >
> >
> > Thanks for this.  I read a usenet post indicating that MAXVAL could be
> > reduced to 7 or 8 in the ?timaa.f, and this seems to work too.  Is
> > either solution acceptable?
> >
> > Secondarily, I'm upgrading the package from the 1999 3.0 to the
> > latest, plus the unincorporated patches listed on the release note
> > pages.
> >
> > With the old version, I just get the expected _gd.out errors on test,
> > but the new version has a few errors in the symmetric eigenroutine
> > single and complex precision as well (_sep.out):
> >
> > 1999:
> >
> ============================================================================
> =
> > cgd.out: CGV drivers:      4 out of   1092 tests failed to pass the
> threshold
> > cgd.out:  9 = 1/ULP  if DIFEST <> 0 or DIFTRU > ULP*norm(A,B) when
> reordering fails
> > cgd.out: CGX drivers:      6 out of   1500 tests failed to pass the
> threshold
> > dgd.out:  9 = 1/ULP  if DIFEST <> 0 or DIFTRU > ULP*norm(A,B) when
> reordering fails
> > dgd.out: SGX drivers:      6 out of   1500 tests failed to pass the
> threshold
> > dgd.out: DXV drivers:    200 out of   5000 tests failed to pass the
> threshold
> > dtest.out: DLS drivers:   2250 out of  65268 tests failed to pass the
> threshold
> > sgd.out:  9 = 1/ULP  if DIFEST <> 0 or DIFTRU > ULP*norm(A,B) when
> reordering fails
> > sgd.out: SGX drivers:      8 out of   1500 tests failed to pass the
> threshold
> > sgd.out: SXV drivers:     37 out of   5000 tests failed to pass the
> threshold
> > zgd.out: ZGV drivers:      4 out of   1092 tests failed to pass the
> threshold
> > zgd.out:  9 = 1/ULP  if DIFEST <> 0 or DIFTRU > ULP*norm(A,B) when
> reordering fails
> > zgd.out: CGX drivers:      6 out of   1500 tests failed to pass the
> threshold
> > zgd.out: ZXV drivers:     24 out of   5000 tests failed to pass the
> threshold
> >
> > latest:
> >
> ============================================================================
> =
> > cgd.out: CGV drivers:      4 out of   1092 tests failed to pass the
> threshold
> > csep.out: CST:    1 out of  4662 tests failed to pass the threshold
> > csep.out: CST drivers:      1 out of  11664 tests failed to pass the
> threshold
> > csep.out: CST:    1 out of  4662 tests failed to pass the threshold
> > dgd.out: DXV drivers:    200 out of   5000 tests failed to pass the
> threshold
> > sgd.out: SXV drivers:     37 out of   5000 tests failed to pass the
> threshold
> > ssep.out: SST:    1 out of  4662 tests failed to pass the threshold
> > ssep.out: SST drivers:      1 out of  14256 tests failed to pass the
> threshold
> > zgd.out: ZGV drivers:      4 out of   1092 tests failed to pass the
> threshold
> > zgd.out: ZXV drivers:     24 out of   5000 tests failed to pass the
> threshold
> >
> ============================================================================
> =
> >
> > I am somewhat hesitant to introduce these new errors into the official
> > lib of the Debian distribution.  I've seen these errors reported in
> > the release_notes in similar setups to mine (g77 2.95, Linux, PIII).
> > The latest lib was compiled with the suggested flags in the Linux
> > make.inc in INSTALL (-funroll-all-loops -O3), whereas the older
> > version was compiled with (-funroll-all-loops -O3 -fomit-frame-pointer
> > -ff90).  I can't imagine that the omission of optimizing flags could
> > introduce new errors, but am willing to recompile with the old
> > settings if you think this would help.
> >
> > Any advice appreciated!
> >
> >
> >
> > > > 3)  Is this also the place to submit patches/suggestions?
> > >
> > > Yes, absolutely... :)
> > >
> > > Susan
> > >
> > >
> > > --=20
> > > ---------------------------------------------
> > > Susan Blackford
> > > Member of Technical Staff
> > > Myricom, Inc.
> > > ---------------------------------------------
> > >
> > >
> >
> > --
> > Camm Maguire      camm@enhanced.com
> > ==========================================================================
> > "The earth is but one country, and mankind its citizens."  --  Baha'u'llah
> >
> > ------- End of forwarded message -------

----------------------------------------------------------------
Ed Anderson
Scientific Applications Consultant
Lockheed Martin Technology Services (contractor to the U.S. EPA)
Phone: 919-541-0299
mailto:Anderson.Edward@epa.gov

=============================================================================

From: Edward Anderson <Anderson.Edward@epa.gov>
Subject: Re: New Debian maintainer
To: Camm Maguire <camm@enhanced.com>
CC: Edward Anderson <Anderson.Edward@epamail.epa.gov>,
        Susan Blackford <susan@cs.utk.edu>
Date: Fri, 30 Nov 2001 10:30:36 -0500
Organization: Lockheed Martin (contractor to the U.S. EPA)
Received: from localhost [127.0.0.1] (root)
	by intech5.enhanced.com with esmtp (Exim 3.12 #1 (Debian))
	id 169peX-0001br-00; Fri, 30 Nov 2001 10:32:37 -0500
Received: from 204.213.252.11
	by localhost with POP3 (fetchmail-5.3.3)
	for camm@enhanced.com (multi-drop); Fri, 30 Nov 2001 10:32:37 -0500 (EST)
Received: from mail.eticomm.net [204.213.252.17] 
	by ux1.cyberenet.net with esmtp (Exim 1.61 #1)
	id 169pd6-0002EM-00; Fri, 30 Nov 2001 10:31:08 -0500
Received: from linden.nesc.epa.gov ([134.67.64.25] helo=nesc.epa.gov)
	by relay.eticomm.net with esmtp (Exim 3.33 #2)
	id 169pd5-0003vM-00
	for camm@enhanced.com; Fri, 30 Nov 2001 10:31:07 -0500
Received: from epa.gov (yew.nesc.epa.gov [134.67.64.48])
	by nesc.epa.gov (8.9.3+Sun/8.9.1) with ESMTP id KAA14465;
	Fri, 30 Nov 2001 10:30:36 -0500 (EST)
Sender: dle@nesc.epa.gov
Message-ID: <3C07A61C.57A40172@epa.gov>
X-Mailer: Mozilla 4.75C-SGI [en] (X11; I; IRIX 6.5 IP32)
X-Accept-Language: en
MIME-Version: 1.0
References: <004701c17372$2a3580e0$2fee80ac@compaq> <3C025704.86683917@epa.gov> <544rndhvce.fsf@intech19.enhanced.com>
Content-Type: multipart/mixed;
 boundary="------------6C386FC925298A0C59F101F0"
X-UIDL: 7119754484cd74abeaed169b5c841fe4
Lines: 770
Xref: intech19.enhanced.com mail.camm:27462

This is a multi-part message in MIME format.
--------------6C386FC925298A0C59F101F0
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit

Camm Maguire wrote:
> 
> Greetings!  Sorry to bother you again -- just wondering if you got my
> last reply regarding the netlib blas being used, and might have any
> suggestions for things I could try.
> 
> Take care, and thanks again,
> --
> Camm Maguire                                            camm@enhanced.com
> ==========================================================================
> "The earth is but one country, and mankind its citizens."  --  Baha'u'llah

Camm,

Sorry for the slow response.  I've looked at your failing tests, and the
test ratios are all relatively small.  This usually means a loss of
orthogonality or improper scaling that causes underflow, which most
often occurs in a situation where a sum of squares is required.  Besides
the obvious cases where you are taking a 2-norm of a vector or the
Frobenius norm of a matrix, it can also occur any time you divide by a
complex number.  LAPACK has auxiliary routines for doing a scaled
complex divide (CLADIV) and for taking the square root of a sum of
squares of two or three numbers (SLAPY2 and SLAPY3), but scaling errors
keep cropping up when new software is introduced, and even these
auxiliary routines aren't as safe as they should be.

The biggest offenders are the 2-norm routines SNRM2, SCNRM2, DNRM2, and
DZNRM2.  The original netlib routine had some difficult to follow code
(known as "Blue's algorithm"); unfortunately it was so hard to
understand that most vendors implemented their own version, and got the
scaling wrong.  A few years ago, the netlib version was replaced with
one based on LAPACK's SLASSQ, and they got the scaling wrong too.  You
can find some more description of these problems in my online technical
report, "Installing LAPACK 3 on CRAY machines",
http://www.cs.utk.edu/~eanderso/lapack3.html.  I am working on an
updated version more suitable to IEEE arithmetic machines with gradual
underflow, using the IBM SP at my site as a test bed.

To see if the 2-norms may be at fault, I will attach prototypes of my
latest xLASSQ versions and associated BLAS that I have tested on an IBM
SP.  I would like to hard code all the scaling constants in xLASSQ for
speed but compute them in this version.  If this doesn't help, then you
may need a larger set of changes, either from a future LAPACK release or
my IBM SP patch when it is ready.

   --Ed Anderson

----------------------------------------------------------------
Ed Anderson
Scientific Applications Consultant
Lockheed Martin Technology Services (contractor to the U.S. EPA)
Phone: 919-541-0299
mailto:Anderson.Edward@epa.gov
--------------6C386FC925298A0C59F101F0
Content-Type: text/plain; charset=us-ascii;
 name="tocamm"
Content-Transfer-Encoding: 7bit
Content-Disposition: inline;
 filename="tocamm"

      SUBROUTINE SLASSQ( N, X, INCX, SCL, SUMSQ )
!
!  -- LAPACK auxiliary routine (version 2.0) --
!     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
!     Courant Institute, Argonne National Lab, and Rice University
!     October 31, 1992
!     10-15-99:  New version based on LAWN 126 (eca)
!     08-31-01:  Use smaller constants for 32-bit IEEE (eca)
!     09-25-01:  Don't scale by < SAFMIN or more than SAFMAX (eca)
!
!     .. Scalar Arguments ..
      INTEGER            INCX, N
      REAL               SCL, SUMSQ
!     ..
!     .. Array Arguments ..
      REAL               X( * )
!     ..
!
!  Purpose
!  =======
!
!  SLASSQ  returns the values  scl  and  smsq  such that
!
!     ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
!
!  where  x( i ) = X( 1 + ( i - 1 )*INCX ). The value of  sumsq  is
!  assumed to be non-negative and  scl  returns the value
!
!     scl = max( scale, abs( x( i ) ) ).
!
!  scale and sumsq must be supplied in SCL and SUMSQ and
!  scl and smsq are overwritten on SCL and SUMSQ respectively.
!
!  Arguments
!  =========
!
!  N       (input) INTEGER
!          The number of elements to be used from the vector X.
!
!  X       (input) REAL array, dimension (N)
!          The vector for which a scaled sum of squares is computed.
!             x( i )  = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
!
!  INCX    (input) INTEGER
!          The increment between successive values of the vector X.
!          INCX > 0.
!
!  SCL     (input/output) REAL
!          On entry, the value  scale  in the equation above.
!          On exit, SCL is overwritten with  scl , the scaling factor
!          for the sum of squares.
!
!  SUMSQ   (input/output) REAL
!          On entry, the value  sumsq  in the equation above.
!          On exit, SUMSQ is overwritten with  smsq , the basic sum of
!          squares from which  scl  has been factored out.
!
! =====================================================================
!
      REAL ONE, ZERO
      PARAMETER ( ONE = 1.0E0, ZERO = 0.0E0 )
      INTEGER I, IX, IX2
      REAL CUTHI, CUTLO, HITEST, SAFMAX, SAFMIN, SMAX, SQMAX
      INTRINSIC ABS, EPSILON, MAX, REAL, TINY
      DATA CUTLO / 1.0E-15 /
      DATA CUTHI / 1.0E+19 /

      IF( N.LE.0 ) RETURN
      HITEST = CUTHI / REAL( N+1 )
!eca  SAFMIN = SLAMCH( 'Safe minimum' ) / SLAMCH( 'Epsilon' )
      SAFMIN = TINY( ONE ) / EPSILON( ONE )
      SAFMAX = ONE / SAFMIN
      IF( SUMSQ.EQ.ZERO ) SCL = ONE

      IF( INCX.EQ.1 ) THEN
!
!        Pass through once to find the maximum value in X.
!
         SMAX = ZERO
         DO I = 1, N
            SMAX = MAX( SMAX, ABS(X(I)) )
         END DO
         SQMAX = MAX( SCL*SQRT( SUMSQ ), SMAX )
!
         IF( SCL.EQ.ONE .AND. SQMAX.GT.CUTLO .AND. SQMAX.LT.HITEST )
     &      THEN
!
!           If SCL = ONE and SQMAX is greater than CUTLO and less than
!           HITEST, no scaling should be needed.
!
            DO I = 1, N
               SUMSQ = SUMSQ + X(I)**2
            END DO
         ELSE IF( SMAX.GT.ZERO ) THEN
!
!           Scale by SQMAX if SCL = ONE, otherwise scale by
!           max( SQMAX, SCL ).
!
            SQMAX = MIN( MAX( SQMAX, SAFMIN ), SAFMAX )
            IF( SCL.EQ.ONE .OR. SCL.LT.SQMAX ) THEN
               SUMSQ = ( SUMSQ*( SCL / SQMAX ) )*( SCL / SQMAX )
               SCL = SQMAX
            END IF
!
!           Add the sum of squares of values of X scaled by SCL.
!
            DO I = 1, N
               SUMSQ = SUMSQ + ( X(I) / SCL )**2
            END DO
         END IF
      ELSE
!
!        Pass through once to find the maximum value in X.
!
         SMAX = ZERO
         IX = 1
         IF( INCX.LT.0 ) IX = 1 - (N-1)*INCX
         DO I = 1, N
            SMAX = MAX( SMAX, ABS(X(IX)) )
            IX = IX + INCX
         END DO
         SQMAX = MAX( SCL*SQRT( SUMSQ ), SMAX )
!
         IF( SCL.EQ.ONE .AND. SQMAX.GT.CUTLO .AND. SQMAX.LT.HITEST )
     &      THEN
!
!           If SCL = ONE and SQMAX is greater than CUTLO and less than
!           HITEST, no scaling should be needed.
!
            IX = 1
            IF( INCX.LT.0 ) IX = 1 - (N-1)*INCX
            DO I = 1, N
               SUMSQ = SUMSQ + X(IX)**2
               IX = IX + INCX
            END DO
         ELSE IF( SMAX.GT.ZERO ) THEN
!
!           Scale by SQMAX if SCL = ONE, otherwise scale by
!           max( SQMAX, SCL ).
!
            SQMAX = MIN( MAX( SQMAX, SAFMIN ), SAFMAX )
            IF( SCL.EQ.ONE .OR. SCL.LT.SQMAX ) THEN
               SUMSQ = ( SUMSQ*( SCL / SQMAX ) )*( SCL / SQMAX )
               SCL = SQMAX
            END IF
!
!           Add the sum of squares of values of X scaled by SCL.
!
            IX = 1
            IF( INCX.LT.0 ) IX = 1 - (N-1)*INCX
            DO I = 1, N
               SUMSQ = SUMSQ + ( X(IX) / SCL )**2
               IX = IX + INCX
            END DO
         END IF
      END IF
      RETURN
      END
      SUBROUTINE CLASSQ( N, X, INCX, SCL, SUMSQ )
!
!  -- LAPACK auxiliary routine (version 2.0) --
!     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
!     Courant Institute, Argonne National Lab, and Rice University
!     October 31, 1992
!     10-15-99:  New version based on LAWN 126 (eca)
!     08-31-01:  Use smaller constants for 32-bit IEEE (eca)
!     09-25-01:  Don't scale by < SAFMIN or more than SAFMAX (eca)
!
!     .. Scalar Arguments ..
      INTEGER            INCX, N
      REAL               SCL, SUMSQ
!     ..
!     .. Array Arguments ..
      COMPLEX            X( * )
!     ..
!
!  Purpose
!  =======
!
!  CLASSQ returns the values scl and ssq such that
!
!     ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
!
!  where x( i ) = abs( X( 1 + ( i - 1 )*INCX ) ). The value of sumsq is
!  assumed to be non-negative and scl returns the value
!
!     scl = max( scale, abs( real( x( i ) ) ), abs( aimag( x( i ) ) ) ),
!            i
!
!  scale and sumsq must be supplied in SCL and SUMSQ respectively.
!  SCL and SUMSQ are overwritten by scl and ssq respectively.
!
!  Arguments
!  =========
!
!  N       (input) INTEGER
!          The number of elements to be used from the vector X.
!
!  X       (input) COMPLEX array, dimension (N)
!          The vector x as described above.
!             x( i )  = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
!
!  INCX    (input) INTEGER
!          The increment between successive values of the vector X.
!          INCX > 0.
!
!  SCL     (input/output) REAL
!          On entry, the value  scale  in the equation above.
!          On exit, SCALE is overwritten with the value  scl .
!
!  SUMSQ   (input/output) REAL
!          On entry, the value  sumsq  in the equation above.
!          On exit, SUMSQ is overwritten with the value  ssq .
!
! =====================================================================
!
      REAL ONE, ZERO
      PARAMETER ( ONE = 1.0E0, ZERO = 0.0E0 )
      INTEGER I, IX, IX2
      REAL CUTHI, CUTLO, HITEST, SAFMAX, SAFMIN, SMAX, SQMAX
      INTRINSIC ABS, EPSILON, MAX, REAL, TINY
      DATA CUTLO / 1.0E-15 /
      DATA CUTHI / 1.0E+19 /

      IF( N.LE.0 ) RETURN
      HITEST = CUTHI / REAL( 2*N+1 )
!eca  SAFMIN = SLAMCH( 'Safe minimum' ) / SLAMCH( 'Epsilon' )
      SAFMIN = TINY( ONE ) / EPSILON( ONE )
      SAFMAX = ONE / SAFMIN
      IF( SUMSQ.EQ.ZERO ) SCL = ONE

      IF( INCX.EQ.1 ) THEN
!
!        Pass through once to find the maximum value in X.
!
         SMAX = ZERO
         DO I = 1, N
            SMAX = MAX( SMAX, ABS(REAL(X(I))), ABS(AIMAG(X(I))) )
         END DO
         SQMAX = MAX( SCL*SQRT( SUMSQ ), SMAX )
!
         IF( SCL.EQ.ONE .AND. SQMAX.GT.CUTLO .AND. SQMAX.LT.HITEST )
     &      THEN
!
!           If SCL = ONE and SQMAX is greater than CUTLO and less than
!           HITEST, no scaling should be needed.
!
            DO I = 1, N
               SUMSQ = SUMSQ + REAL(X(I))**2 + AIMAG(X(I))**2
            END DO
         ELSE IF( SMAX.GT.ZERO ) THEN
!
!           Scale by SQMAX if SCL = ONE, otherwise scale by
!           max( SQMAX, SCL ).
!
            SQMAX = MIN( MAX( SQMAX, SAFMIN ), SAFMAX )
            IF( SCL.EQ.ONE .OR. SCL.LT.SQMAX ) THEN
               SUMSQ = ( SUMSQ*( SCL / SQMAX ) )*( SCL / SQMAX )
               SCL = SQMAX
            END IF
!
!           Add the sum of squares of values of X scaled by SCL.
!
            DO I = 1, N
               SUMSQ = SUMSQ + ( REAL(X(I)) / SCL )**2 +
     &                 ( AIMAG(X(I)) / SCL )**2
            END DO
         END IF
      ELSE
!
!        Pass through once to find the maximum value in X.
!
         SMAX = ZERO
         IX = 1
         IF( INCX.LT.0 ) IX = 1 - (N-1)*INCX
         DO I = 1, N
            SMAX = MAX( SMAX, ABS(REAL(X(IX))), ABS(AIMAG(X(IX))) )
            IX = IX + INCX
         END DO
         SQMAX = MAX( SCL*SQRT( SUMSQ ), SMAX )
!
         IF( SCL.EQ.ONE .AND. SQMAX.GT.CUTLO .AND. SQMAX.LT.HITEST )
     &      THEN
!
!           If SCL = ONE and SQMAX is greater than CUTLO and less than
!           HITEST, no scaling should be needed.
!
            IX = 1
            IF( INCX.LT.0 ) IX = 1 - (N-1)*INCX
            DO I = 1, N
               SUMSQ = SUMSQ + REAL(X(IX))**2 + AIMAG(X(IX))**2
               IX = IX + INCX
            END DO
         ELSE IF( SMAX.GT.ZERO ) THEN
!
!           Scale by SQMAX if SCL = ONE, otherwise scale by
!           max( SQMAX, SCL ).
!
            SQMAX = MIN( MAX( SQMAX, SAFMIN ), SAFMAX )
            IF( SCL.EQ.ONE .OR. SCL.LT.SQMAX ) THEN
               SUMSQ = ( SUMSQ*( SCL / SQMAX ) )*( SCL / SQMAX )
               SCL = SQMAX
            END IF
!
!           Add the sum of squares of values of X scaled by SCL.
!
            IX = 1
            IF( INCX.LT.0 ) IX = 1 - (N-1)*INCX
            DO I = 1, N
               SUMSQ = SUMSQ + ( REAL(X(IX)) / SCL )**2 +
     &                 ( AIMAG(X(IX)) / SCL )**2
               IX = IX + INCX
            END DO
         END IF
      END IF
      RETURN
      END
      SUBROUTINE DLASSQ( N, X, INCX, SCL, SUMSQ )
!
!  -- LAPACK auxiliary routine (version 2.0) --
!     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
!     Courant Institute, Argonne National Lab, and Rice University
!     October 31, 1992
!     10-15-99:  New version based on LAWN 126 (eca)
!     09-25-01:  Don't scale by < SAFMIN or more than SAFMAX (eca)
!
!     .. Scalar Arguments ..
      INTEGER            INCX, N
      DOUBLE PRECISION   SCL, SUMSQ
!     ..
!     .. Array Arguments ..
      DOUBLE PRECISION   X( * )
!     ..
!
!  Purpose
!  =======
!
!  DLASSQ  returns the values  scl  and  smsq  such that
!
!     ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
!
!  where  x( i ) = X( 1 + ( i - 1 )*INCX ). The value of  sumsq  is
!  assumed to be non-negative and  scl  returns the value
!
!     scl = max( scale, abs( x( i ) ) ).
!
!  scale and sumsq must be supplied in SCL and SUMSQ and
!  scl and smsq are overwritten on SCL and SUMSQ respectively.
!
!  Arguments
!  =========
!
!  N       (input) INTEGER
!          The number of elements to be used from the vector X.
!
!  X       (input) DOUBLE PRECISION array, dimension (N)
!          The vector for which a scaled sum of squares is computed.
!             x( i )  = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
!
!  INCX    (input) INTEGER
!          The increment between successive values of the vector X.
!          INCX > 0.
!
!  SCL     (input/output) DOUBLE PRECISION
!          On entry, the value  scale  in the equation above.
!          On exit, SCL is overwritten with  scl , the scaling factor
!          for the sum of squares.
!
!  SUMSQ   (input/output) DOUBLE PRECISION
!          On entry, the value  sumsq  in the equation above.
!          On exit, SUMSQ is overwritten with  smsq , the basic sum of
!          squares from which  scl  has been factored out.
!
! =====================================================================
!
      DOUBLE PRECISION ONE, ZERO
      PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 )
      INTEGER I, IX, IX2
      DOUBLE PRECISION CUTHI, CUTLO, HITEST, SAFMAX, SAFMIN, SMAX, SQMAX
      INTRINSIC ABS, MAX, DBLE, EPSILON, SQRT, TINY
      DATA CUTLO / 1.00104154759155046D-146 /
      DATA CUTHI / 9.48075190810917589D+153 /

      IF( N.LE.0 ) RETURN
      HITEST = CUTHI / DBLE( N+1 )
!eca  SAFMIN = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Epsilon' )
      SAFMIN = TINY( ONE ) / EPSILON( ONE )
      SAFMAX = ONE / SAFMIN
      IF( SUMSQ.EQ.ZERO ) SCL = ONE

      IF( INCX.EQ.1 ) THEN
!
!        Pass through once to find the maximum value in X.
!
         SMAX = ZERO
         DO I = 1, N
            SMAX = MAX( SMAX, ABS(X(I)) )
         END DO
         SQMAX = MAX( SCL*SQRT( SUMSQ ), SMAX )
!
         IF( SCL.EQ.ONE .AND. SQMAX.GT.CUTLO .AND. SQMAX.LT.HITEST )
     &      THEN
!
!           If SCL = ONE and SQMAX is greater than CUTLO and less than
!           HITEST, no scaling should be needed.
!
            DO I = 1, N
               SUMSQ = SUMSQ + X(I)**2
            END DO
         ELSE IF( SMAX.GT.ZERO ) THEN
!
!           Scale by SQMAX if SCL = ONE, otherwise scale by
!           max( SQMAX, SCL ).
!
            SQMAX = MIN( MAX( SQMAX, SAFMIN ), SAFMAX )
            IF( SCL.EQ.ONE .OR. SCL.LT.SQMAX ) THEN
               SUMSQ = ( SUMSQ*( SCL / SQMAX ) )*( SCL / SQMAX )
               SCL = SQMAX
            END IF
!
!           Add the sum of squares of values of X scaled by SCL.
!
            DO I = 1, N
               SUMSQ = SUMSQ + ( X(I) / SCL )**2
            END DO
         END IF
      ELSE
!
!        Pass through once to find the maximum value in X.
!
         SMAX = ZERO
         IX = 1
         IF( INCX.LT.0 ) IX = 1 - (N-1)*INCX
         DO I = 1, N
            SMAX = MAX( SMAX, ABS(X(IX)) )
            IX = IX + INCX
         END DO
         SQMAX = MAX( SCL*SQRT( SUMSQ ), SMAX )
!
         IF( SCL.EQ.ONE .AND. SQMAX.GT.CUTLO .AND. SQMAX.LT.HITEST )
     &      THEN
!
!           If SCL = ONE and SQMAX is greater than CUTLO and less than
!           HITEST, no scaling should be needed.
!
            IX = 1
            IF( INCX.LT.0 ) IX = 1 - (N-1)*INCX
            DO I = 1, N
               SUMSQ = SUMSQ + X(IX)**2
               IX = IX + INCX
            END DO
         ELSE IF( SMAX.GT.ZERO ) THEN
!
!           Scale by SQMAX if SCL = ONE, otherwise scale by
!           max( SQMAX, SCL ).
!
            SQMAX = MIN( MAX( SQMAX, SAFMIN ), SAFMAX )
            IF( SCL.EQ.ONE .OR. SCL.LT.SQMAX ) THEN
               SUMSQ = ( SUMSQ*( SCL / SQMAX ) )*( SCL / SQMAX )
               SCL = SQMAX
            END IF
!
!           Add the sum of squares of values of X scaled by SCL.
!
            IX = 1
            IF( INCX.LT.0 ) IX = 1 - (N-1)*INCX
            DO I = 1, N
               SUMSQ = SUMSQ + ( X(IX) / SCL )**2
               IX = IX + INCX
            END DO
         END IF
      END IF
      RETURN
      END
      SUBROUTINE ZLASSQ( N, X, INCX, SCL, SUMSQ )
!
!  -- LAPACK auxiliary routine (version 2.0) --
!     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
!     Courant Institute, Argonne National Lab, and Rice University
!     October 31, 1992
!     10-15-99:  New version based on LAWN 126 (eca)
!     09-25-01:  Don't scale by < SAFMIN or more than SAFMAX (eca)
!
!     .. Scalar Arguments ..
      INTEGER            INCX, N
      DOUBLE PRECISION   SCL, SUMSQ
!     ..
!     .. Array Arguments ..
      COMPLEX*16         X( * )
!     ..
!
!  Purpose
!  =======
!
!  ZLASSQ returns the values scl and ssq such that
!
!     ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
!
!  where x( i ) = abs( X( 1 + ( i - 1 )*INCX ) ). The value of sumsq is
!  assumed to be non-negative and scl returns the value
!
!     scl = max( scale, abs( real( x( i ) ) ), abs( aimag( x( i ) ) ) ),
!            i
!
!  scale and sumsq must be supplied in SCL and SUMSQ respectively.
!  SCL and SUMSQ are overwritten by scl and ssq respectively.
!
!  Arguments
!  =========
!
!  N       (input) INTEGER
!          The number of elements to be used from the vector X.
!
!  X       (input) COMPLEX*16 array, dimension (N)
!          The vector x as described above.
!             x( i )  = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n.
!
!  INCX    (input) INTEGER
!          The increment between successive values of the vector X.
!          INCX > 0.
!
!  SCL     (input/output) DOUBLE PRECSION
!          On entry, the value  scale  in the equation above.
!          On exit, SCALE is overwritten with the value  scl .
!
!  SUMSQ   (input/output) DOUBLE PRECSION
!          On entry, the value  sumsq  in the equation above.
!          On exit, SUMSQ is overwritten with the value  ssq .
!
! =====================================================================
!
      DOUBLE PRECISION ONE, ZERO
      PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 )
      INTEGER I, IX, IX2
      DOUBLE PRECISION CUTHI, CUTLO, HITEST, SAFMAX, SAFMIN, SMAX, SQMAX
      INTRINSIC ABS, MAX, DBLE, EPSILON, SQRT, TINY
      DATA CUTLO / 1.00104154759155046D-146 /
      DATA CUTHI / 9.48075190810917589D+153 /

      IF( N.LE.0 ) RETURN
      HITEST = CUTHI / DBLE( 2*N+1 )
!eca  SAFMIN = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Epsilon' )
      SAFMIN = TINY( ONE ) / EPSILON( ONE )
      SAFMAX = ONE / SAFMIN
      IF( SUMSQ.EQ.ZERO ) SCL = ONE

      IF( INCX.EQ.1 ) THEN
!
!        Pass through once to find the maximum value in X.
!
         SMAX = ZERO
         DO I = 1, N
            SMAX = MAX( SMAX, ABS(DBLE(X(I))), ABS(DIMAG(X(I))) )
         END DO
         SQMAX = MAX( SCL*SQRT( SUMSQ ), SMAX )
!
         IF( SCL.EQ.ONE .AND. SQMAX.GT.CUTLO .AND. SQMAX.LT.HITEST )
     &      THEN
!
!           If SCL = ONE and SQMAX is greater than CUTLO and less than
!           HITEST, no scaling should be needed.
!
            DO I = 1, N
               SUMSQ = SUMSQ + DBLE(X(I))**2 + DIMAG(X(I))**2
            END DO
         ELSE IF( SMAX.GT.ZERO ) THEN
!
!           Scale by SQMAX if SCL = ONE, otherwise scale by
!           max( SQMAX, SCL ).
!
            SQMAX = MIN( MAX( SQMAX, SAFMIN ), SAFMAX )
            IF( SCL.EQ.ONE .OR. SCL.LT.SQMAX ) THEN
               SUMSQ = ( SUMSQ*( SCL / SQMAX ) )*( SCL / SQMAX )
               SCL = SQMAX
            END IF
!
!           Add the sum of squares of values of X scaled by SCL.
!
            DO I = 1, N
               SUMSQ = SUMSQ + ( DBLE(X(I)) / SCL )**2 +
     &                 ( DIMAG(X(I)) / SCL )**2
            END DO
         END IF
      ELSE
!
!        Pass through once to find the maximum value in X.
!
         SMAX = ZERO
         IX = 1
         IF( INCX.LT.0 ) IX = 1 - (N-1)*INCX
         DO I = 1, N
            SMAX = MAX( SMAX, ABS(DBLE(X(IX))), ABS(DIMAG(X(IX))) )
            IX = IX + INCX
         END DO
         SQMAX = MAX( SCL*SQRT( SUMSQ ), SMAX )
!
         IF( SCL.EQ.ONE .AND. SQMAX.GT.CUTLO .AND. SQMAX.LT.HITEST )
     &      THEN
!
!           If SCL = ONE and SQMAX is greater than CUTLO and less than
!           HITEST, no scaling should be needed.
!
            IX = 1
            IF( INCX.LT.0 ) IX = 1 - (N-1)*INCX
            DO I = 1, N
               SUMSQ = SUMSQ + DBLE(X(IX))**2 + DIMAG(X(IX))**2
               IX = IX + INCX
            END DO
         ELSE IF( SMAX.GT.ZERO ) THEN
!
!           Scale by SQMAX if SCL = ONE, otherwise scale by
!           max( SQMAX, SCL ).
!
            SQMAX = MIN( MAX( SQMAX, SAFMIN ), SAFMAX )
            IF( SCL.EQ.ONE .OR. SCL.LT.SQMAX ) THEN
               SUMSQ = ( SUMSQ*( SCL / SQMAX ) )*( SCL / SQMAX )
               SCL = SQMAX
            END IF
!
!           Add the sum of squares of values of X scaled by SCL.
!
            IX = 1
            IF( INCX.LT.0 ) IX = 1 - (N-1)*INCX
            DO I = 1, N
               SUMSQ = SUMSQ + ( DBLE(X(IX)) / SCL )**2 +
     &                 ( DIMAG(X(IX)) / SCL )**2
               IX = IX + INCX
            END DO
         END IF
      END IF
      RETURN
      END
      real function SNRM2( n, x, incx ) 
!
!  -- Level 1 BLAS --
!     E. Anderson, NESC
!     November 17, 1999
!
      integer n, incx
      real x(*)
      real scl, sumsq
      external SLASSQ
      intrinsic SQRT
      scl = 1.0
      sumsq = 0.0
      call SLASSQ( n, x, incx, scl, sumsq )
      SNRM2 = scl*SQRT( sumsq )
      return
      end
      real function SCNRM2( n, x, incx ) 
!
!  -- Level 1 BLAS --
!     E. Anderson, NESC
!     November 17, 1999
!
      integer n, incx
      complex x(*)
      real scl, sumsq
      external CLASSQ
      intrinsic SQRT
      scl = 1.0
      sumsq = 0.0
      call CLASSQ( n, x, incx, scl, sumsq )
      SCNRM2 = scl*SQRT( sumsq )
      return
      end
      double precision function DNRM2( n, x, incx ) 
!
!  -- Level 1 BLAS --
!     E. Anderson, NESC
!     November 17, 1999
!
      integer n, incx
      double precision x(*)
      double precision scl, sumsq
      external DLASSQ
      intrinsic DSQRT
      scl = 1.0D0
      sumsq = 0.0D0
      call DLASSQ( n, x, incx, scl, sumsq )
      DNRM2 = scl*DSQRT( sumsq )
      return
      end
      double precision function DZNRM2( n, x, incx ) 
!
!  -- Level 1 BLAS --
!     E. Anderson, NESC
!     November 17, 1999
!
      integer n, incx
      complex*16 x(*)
      double precision scl, sumsq
      external ZLASSQ
      intrinsic DSQRT
      scl = 1.0D0
      sumsq = 0.0D0
      call ZLASSQ( n, x, incx, scl, sumsq )
      DZNRM2 = scl*DSQRT( sumsq )
      return
      end

--------------6C386FC925298A0C59F101F0--

=============================================================================

From: Edward Anderson <Anderson.Edward@epa.gov>
Subject: Re: New Debian maintainer
To: Camm Maguire <camm@enhanced.com>
Date: Mon, 03 Dec 2001 08:42:42 -0500
Organization: Lockheed Martin (contractor to the U.S. EPA)
Received: from localhost [127.0.0.1] (root)
	by intech5.enhanced.com with esmtp (Exim 3.12 #1 (Debian))
	id 16AtPH-0000Jg-00; Mon, 03 Dec 2001 08:45:15 -0500
Received: from 204.213.252.11
	by localhost with POP3 (fetchmail-5.3.3)
	for camm@enhanced.com (multi-drop); Mon, 03 Dec 2001 08:45:15 -0500 (EST)
Received: from mail.eticomm.net [204.213.252.17] 
	by ux1.cyberenet.net with esmtp (Exim 1.61 #1)
	id 16AtNS-0005d8-00; Mon, 3 Dec 2001 08:43:22 -0500
Received: from linden.nesc.epa.gov ([134.67.64.25] helo=nesc.epa.gov)
	by relay.eticomm.net with esmtp (Exim 3.33 #2)
	id 16AtNR-0002PS-00
	for camm@enhanced.com; Mon, 03 Dec 2001 08:43:21 -0500
Received: from epa.gov (yew.nesc.epa.gov [134.67.64.48])
	by nesc.epa.gov (8.9.3+Sun/8.9.1) with ESMTP id IAA01538
	for <camm@enhanced.com>; Mon, 3 Dec 2001 08:42:42 -0500 (EST)
Sender: dle@nesc.epa.gov
Message-ID: <3C0B8152.6CDAF8BD@epa.gov>
X-Mailer: Mozilla 4.75C-SGI [en] (X11; I; IRIX 6.5 IP32)
X-Accept-Language: en
MIME-Version: 1.0
References: <004701c17372$2a3580e0$2fee80ac@compaq> <3C025704.86683917@epa.gov>
	 <544rndhvce.fsf@intech19.enhanced.com> <3C07A61C.57A40172@epa.gov> <547ks7kft4.fsf@intech19.enhanced.com>
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
X-UIDL: b458a850136eaa1c731faa8144f7d567
Lines: 57
Xref: intech19.enhanced.com mail.camm:27531

Camm:

If you only have a Fortran 77 compiler then you won't be able to use the
Fortran 90 intrinsic functions EPSILON and TINY.  You will need to use
the calls to SLAMCH/DLAMCH which appear in the comments of the code I
sent, and remove the declarations of EPSILON and TINY from the INTRINSIC
line.

Should you decide to use these versions, you would want to put the
LAPACK auxiliary routines xLASSQ in LAPACK/SRC and the BLAS routines
xNRM2 in LAPACK/BLAS/SRC.

   --Ed

Camm Maguire wrote:
> 
> Sorry to bother you again -- one other item.  I'm having a bit of
> trouble compiling the lassq with g77:
> 
> f77 -pipe -c -O6 -fomit-frame-pointer  -fPIC classq.f
> classq.f: In subroutine `classq':
> classq.f:63: warning:
>          INTRINSIC ABS, EPSILON, MAX, REAL, TINY
>                         ^
> Reference to unimplemented intrinsic `EPSILON' at (^) (assumed EXTERNAL)
> classq.f:63:
>          INTRINSIC ABS, EPSILON, MAX, REAL, TINY
>                         ^
> Invalid declaration of or reference to symbol `epsilon' at (^) [initially seen at (^)]
> classq.f:63: warning:
>          INTRINSIC ABS, EPSILON, MAX, REAL, TINY
>                                             ^
> Reference to unimplemented intrinsic `TINY' at (^) (assumed EXTERNAL)
> classq.f:63:
>          INTRINSIC ABS, EPSILON, MAX, REAL, TINY
>                                             ^
> Invalid declaration of or reference to symbol `tiny' at (^) [initially seen at (^)]
> make: *** [classq.o] Error 1
> 
> Have I merely put these files in the wrong place?  Or does your
> fortran compiler define more intrinsics than g77?  Can I hardcode
> these values from the lapack lamch output?
> 
> Take care,
> --
> Camm Maguire                                            camm@enhanced.com
> ==========================================================================
> "The earth is but one country, and mankind its citizens."  --  Baha'u'llah

----------------------------------------------------------------
Ed Anderson
Scientific Applications Consultant
Lockheed Martin Technology Services (contractor to the U.S. EPA)
Phone: 919-541-0299
mailto:Anderson.Edward@epa.gov

=============================================================================

From: Edward Anderson <Anderson.Edward@epa.gov>
Subject: Re: New Debian maintainer
To: Camm Maguire <camm@enhanced.com>
Date: Tue, 04 Dec 2001 09:00:44 -0500
Organization: Lockheed Martin (contractor to the U.S. EPA)
Received: from localhost [127.0.0.1] (root)
	by intech5.enhanced.com with esmtp (Exim 3.12 #1 (Debian))
	id 16BGBM-0000Ti-00; Tue, 04 Dec 2001 09:04:24 -0500
Received: from 204.213.252.11
	by localhost with POP3 (fetchmail-5.3.3)
	for camm@enhanced.com (multi-drop); Tue, 04 Dec 2001 09:04:24 -0500 (EST)
Received: from mail.eticomm.net [204.213.252.17] 
	by ux1.cyberenet.net with esmtp (Exim 1.61 #1)
	id 16BG8K-0001XT-00; Tue, 4 Dec 2001 09:01:16 -0500
Received: from linden.nesc.epa.gov ([134.67.64.25] helo=nesc.epa.gov)
	by relay.eticomm.net with esmtp (Exim 3.33 #2)
	id 16BG8K-000FX3-00
	for camm@enhanced.com; Tue, 04 Dec 2001 09:01:16 -0500
Received: from epa.gov (yew.nesc.epa.gov [134.67.64.48])
	by nesc.epa.gov (8.9.3+Sun/8.9.1) with ESMTP id JAA07649
	for <camm@enhanced.com>; Tue, 4 Dec 2001 09:00:44 -0500 (EST)
Sender: dle@nesc.epa.gov
Message-ID: <3C0CD70C.EA958B8C@epa.gov>
X-Mailer: Mozilla 4.75C-SGI [en] (X11; I; IRIX 6.5 IP32)
X-Accept-Language: en
MIME-Version: 1.0
References: <004701c17372$2a3580e0$2fee80ac@compaq> <3C025704.86683917@epa.gov>
	 <544rndhvce.fsf@intech19.enhanced.com> <3C07A61C.57A40172@epa.gov>
	 <547ks7kft4.fsf@intech19.enhanced.com> <3C0B8152.6CDAF8BD@epa.gov> <54oflgyq59.fsf@intech19.enhanced.com>
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
X-UIDL: adfa4279f91ebf2369b8aaef02ca151f
Lines: 23
Xref: intech19.enhanced.com mail.camm:27561

Camm,

There's some danger in continuing in this vein because you'll end up
with your own version of LAPACK that differs from every other one out
there.  But that's probably not so unusual for a software installation.

You may be able to fix some bad test ratios in the symmetric eigenvalue
driver routines by adjusting the value of "FUDGE" in sstebz/dstebz.  As
the name implies, this was a "fudge factor" and it is adjustable.  I
increased it from 2.0 to 2.1 for the CRAY T3E, but I heard from someone
else (can't find the mail now) that they had set it even higher, like
2.5.  Give it a whirl and see what happens.

   --Ed

----------------------------------------------------------------
Ed Anderson
Scientific Applications Consultant
Lockheed Martin Technology Services (contractor to the U.S. EPA)
Phone: 919-541-0299
mailto:Anderson.Edward@epa.gov


=============================================================================
From: Edward Anderson <Anderson.Edward@epa.gov>
Subject: Re: New Debian maintainer
To: Camm Maguire <camm@enhanced.com>
CC: Susan Blackford <susan@cs.utk.edu>
Date: Wed, 05 Dec 2001 16:27:32 -0500
Organization: Lockheed Martin (contractor to the U.S. EPA)
Received: from localhost [127.0.0.1] (root)
	by intech5.enhanced.com with esmtp (Exim 3.12 #1 (Debian))
	id 16Bjcx-0002Uh-00; Wed, 05 Dec 2001 16:30:51 -0500
Received: from 204.213.252.11
	by localhost with POP3 (fetchmail-5.3.3)
	for camm@enhanced.com (multi-drop); Wed, 05 Dec 2001 16:30:51 -0500 (EST)
Received: from mail.eticomm.net [204.213.252.17] 
	by ux1.cyberenet.net with esmtp (Exim 1.61 #1)
	id 16BjaG-0005He-00; Wed, 5 Dec 2001 16:28:04 -0500
Received: from linden.nesc.epa.gov ([134.67.64.25] helo=nesc.epa.gov)
	by relay.eticomm.net with esmtp (Exim 3.33 #2)
	id 16BjaF-000IIY-00
	for camm@enhanced.com; Wed, 05 Dec 2001 16:28:03 -0500
Received: from epa.gov (yew.nesc.epa.gov [134.67.64.48])
	by nesc.epa.gov (8.9.3+Sun/8.9.1) with ESMTP id QAA18500;
	Wed, 5 Dec 2001 16:27:32 -0500 (EST)
Sender: dle@nesc.epa.gov
Message-ID: <3C0E9144.3035D152@epa.gov>
X-Mailer: Mozilla 4.75C-SGI [en] (X11; I; IRIX 6.5 IP32)
X-Accept-Language: en
MIME-Version: 1.0
References: <004701c17372$2a3580e0$2fee80ac@compaq> <3C025704.86683917@epa.gov>
	 <544rndhvce.fsf@intech19.enhanced.com> <3C07A61C.57A40172@epa.gov>
	 <547ks7kft4.fsf@intech19.enhanced.com> <3C0B8152.6CDAF8BD@epa.gov>
	 <54oflgyq59.fsf@intech19.enhanced.com> <3C0CD70C.EA958B8C@epa.gov> <54vgflms1a.fsf@intech19.enhanced.com>
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
X-UIDL: 7c86af4c1b5cd2c960fef3c9e2448126
Lines: 68
Xref: intech19.enhanced.com mail.camm:27607

Camm Maguire wrote:
> 
> Greetings, and thank you again for the suggestion.  I saw the
> adjustment to 2.1, but changing it a bit all the way up to 3.5 made no
> difference at all in the test results.  I don't know what this means.
> 
> I'd also like to ask you about the significance of the errors, and
> which set is 'preferable'.  Are routine errors worse than driver
> errors?  Why did the complex driver errors get so much larger in
> magnitude with your blas changes? (everything else seems to have
> decreased.)  What effect in practice will the magnitudes of the errors
> seen in both sets have on typical library use?  And lastly, is it known
> how these errors got introduced into the code in the last year? (1999
> 3.0 doesn't have them.)
> 

Camm:

With a few exceptions, all the mathematics of LAPACK is contained in the
computational routines.  If you get a failure in a driver routine when
all the computational routines passed their tests, it is usually because
one path through the driver routines didn't agree with another path
through the driver routines, and the writer of the test code thought
that they should.  I regard all the errors as equal in importance, but
many of the eigensystem tests are not very well documented.

There are a lot of calculations in LAPACK that are sensitive to the
scaling and even the order of operations.  Also, the LAPACK test code
deliberately generates some numerically sensitive test problems to
exercise parts of the code.  Sometimes a change in the scaling will make
a particular test ratio disappear, while creating a bad test ratio
somewhere else.  It's hard to say which method is "better" without more
analysis.  I've managed to get all except the xgd tests to pass on a
CRAY PVP, CRAY MPP, and IBM SP, but my set of changes is rather large
and not limited to numerical accuracy (some are to improve performance).

In my experience, test ratios under 1000 or so are usually not that
serious.  Most of the test ratios are scaled so that an order of
magnitude is a lost decimal place of accuracy, and the thresholds are
set to about 50.  So, if your test ratio were 1000, you would have lost
about 3 places of accuracy -- a lot in single precision, but probably in
the noise in double precision.  If you were concerned about the accuracy
of a particular solution in the context of an application, LAPACK has
error bounds and condition number information built into the "expert"
driver routines that may offer some guidance about what to expect.

Your best bet as the installer of LAPACK would be to document the
failures you currently see, ask that they be posted in the LAPACK
release notes, and wait for something better to come along.  It will
also give you a baseline for comparison if and when there is a new
LAPACK release.  Just by looking at the error messages that were
generated, you've already done more than some library developers I know!

I'll put you on my list of people to notify when my (totally unsupported
and unauthorized) patch for the IBM SP is available.  It's been useful
for me to see that some set of users still needs Fortran 77
compatibility.

   --Ed

----------------------------------------------------------------
Ed Anderson
Scientific Applications Consultant
Lockheed Martin Technology Services (contractor to the U.S. EPA)
Phone: 919-541-0299
mailto:Anderson.Edward@epa.gov


=============================================================================

 -- Camm Maguire <camm@enhanced.com>, Tue, 29 Jan 2002 11:42:34 -0500