File: BB01AD.f

package info (click to toggle)
dynare 4.3.0-2
  • links: PTS, VCS
  • area: main
  • in suites: wheezy
  • size: 40,640 kB
  • sloc: fortran: 82,231; cpp: 72,734; ansic: 28,874; pascal: 13,241; sh: 4,300; objc: 3,281; yacc: 2,833; makefile: 1,288; lex: 1,162; python: 162; lisp: 54; xml: 8
file content (1286 lines) | stat: -rw-r--r-- 50,152 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
      SUBROUTINE BB01AD(DEF, NR, DPAR, IPAR, BPAR, CHPAR, VEC, N, M, P,
     1                  A, LDA, B, LDB, C, LDC, G, LDG, Q, LDQ, X, LDX,
     2                  DWORK, LDWORK, INFO)
C
C     SLICOT RELEASE 5.0.
C
C     Copyright (c) 2002-2009 NICONET e.V.
C
C     This program is free software: you can redistribute it and/or
C     modify it under the terms of the GNU General Public License as
C     published by the Free Software Foundation, either version 2 of
C     the License, or (at your option) any later version.
C
C     This program is distributed in the hope that it will be useful,
C     but WITHOUT ANY WARRANTY; without even the implied warranty of
C     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
C     GNU General Public License for more details.
C
C     You should have received a copy of the GNU General Public License
C     along with this program.  If not, see
C     <http://www.gnu.org/licenses/>.
C
C     PURPOSE
C
C     To generate the benchmark examples for the numerical solution of
C     continuous-time algebraic Riccati equations (CAREs) of the form
C
C       0 = Q + A'X + XA - XGX
C
C     corresponding to the Hamiltonian matrix
C
C            (  A   G  )
C        H = (       T ).
C            (  Q  -A  )
C
C     A,G,Q,X are real N-by-N matrices, Q and G are symmetric and may
C     be given in factored form
C
C                   -1 T                         T
C      (I)   G = B R  B  ,           (II)   Q = C W C .
C
C     Here, C is P-by-N, W P-by-P, B N-by-M, and R M-by-M, where W
C     and R are symmetric. In linear-quadratic optimal control problems,
C     usually W is positive semidefinite and R positive definite.  The
C     factorized form can be used if the CARE is solved using the
C     deflating subspaces of the extended Hamiltonian pencil
C
C                  (  A   0   B  )       (  I   0   0  )
C                  (       T     )       (             )
C        H - s K = (  Q   A   0  )  -  s (  0  -I   0  ) ,
C                  (       T     )       (             )
C                  (  0   B   R  )       (  0   0   0  )
C
C     where I and 0 denote the identity and zero matrix, respectively,
C     of appropriate dimensions.
C
C     NOTE: the formulation of the CARE and the related matrix (pencils)
C           used here does not include CAREs as they arise in robust
C           control (H_infinity optimization).
C
C     ARGUMENTS
C
C     Mode Parameters
C
C     DEF     CHARACTER
C             This parameter specifies if the default parameters are
C             to be used or not.
C             = 'N' or 'n' : The parameters given in the input vectors
C                            xPAR (x = 'D', 'I', 'B', 'CH') are used.
C             = 'D' or 'd' : The default parameters for the example
C                            are used.
C             This parameter is not meaningful if NR(1) = 1.
C
C     Input/Output Parameters
C
C     NR      (input) INTEGER array, dimension (2)
C             This array determines the example for which CAREX returns
C             data. NR(1) is the group of examples.
C             NR(1) = 1 : parameter-free problems of fixed size.
C             NR(1) = 2 : parameter-dependent problems of fixed size.
C             NR(1) = 3 : parameter-free problems of scalable size.
C             NR(1) = 4 : parameter-dependent problems of scalable size.
C             NR(2) is the number of the example in group NR(1).
C             Let NEXi be the number of examples in group i. Currently,
C             NEX1 = 6, NEX2 = 9, NEX3 = 2, NEX4 = 4.
C             1 <= NR(1) <= 4;
C             1 <= NR(2) <= NEXi , where i = NR(1).
C
C     DPAR    (input/output) DOUBLE PRECISION array, dimension (7)
C             Double precision parameter vector. For explanation of the
C             parameters see [1].
C             DPAR(1)           : defines the parameters
C                                 'delta' for NR(1) = 3,
C                                 'q' for NR(1).NR(2) = 4.1,
C                                 'a' for NR(1).NR(2) = 4.2, and
C                                 'mu' for NR(1).NR(2) = 4.3.
C             DPAR(2)           : defines parameters
C                                 'r' for NR(1).NR(2) = 4.1,
C                                 'b' for NR(1).NR(2) = 4.2, and
C                                 'delta' for NR(1).NR(2) = 4.3.
C             DPAR(3)           : defines parameters
C                                 'c' for NR(1).NR(2) = 4.2 and
C                                 'kappa' for NR(1).NR(2) = 4.3.
C             DPAR(j), j=4,5,6,7: These arguments are only used to
C                                 generate Example 4.2 and define in
C                                 consecutive order the intervals
C                                 ['beta_1', 'beta_2'],
C                                 ['gamma_1', 'gamma_2'].
C             NOTE that if DEF = 'D' or 'd', the values of DPAR entries
C             on input are ignored and, on output, they are overwritten
C             with the default parameters.
C
C     IPAR    (input/output) INTEGER array, dimension (3)
C             On input, IPAR(1) determines the actual state dimension,
C             i.e., the order of the matrix A as follows, where
C             NO = NR(1).NR(2).
C             NR(1) = 1 or 2.1-2.8: IPAR(1) is ignored.
C             NO = 2.9            : IPAR(1) = 1 generates the CARE for
C                                   optimal state feedback (default);
C                                   IPAR(1) = 2 generates the Kalman
C                                   filter CARE.
C             NO = 3.1            : IPAR(1) is the number of vehicles
C                                   (parameter 'l' in the description
C                                    in [1]).
C             NO = 3.2, 4.1 or 4.2: IPAR(1) is the order of the matrix
C                                   A.
C             NO = 4.3 or 4.4     : IPAR(1) determines the dimension of
C                                   the second-order system, i.e., the
C                                   order of the stiffness matrix for
C                                   Examples 4.3 and 4.4 (parameter 'l'
C                                   in the description in [1]).
C
C             The order of the output matrix A is N = 2*IPAR(1) for
C             Example 4.3 and N = 2*IPAR(1)-1 for Examples 3.1 and 4.4.
C             NOTE that IPAR(1) is overwritten for Examples 1.1-2.8. For
C             the other examples, IPAR(1) is overwritten if the default
C             parameters are to be used.
C             On output, IPAR(1) contains the order of the matrix A.
C
C             On input, IPAR(2) is the number of colums in the matrix B
C             in (I) (in control problems, the number of inputs of the
C             system). Currently, IPAR(2) is fixed or determined by
C             IPAR(1) for all examples and thus is not referenced on
C             input.
C             On output, IPAR(2) is the number of columns of the
C             matrix B from (I).
C             NOTE that currently IPAR(2) is overwritten and that
C             rank(G) <= IPAR(2).
C
C             On input, IPAR(3) is the number of rows in the matrix C
C             in (II) (in control problems, the number of outputs of the
C             system). Currently, IPAR(3) is fixed or determined by
C             IPAR(1) for all examples and thus is not referenced on
C             input.
C             On output, IPAR(3) contains the number of rows of the
C             matrix C in (II).
C             NOTE that currently IPAR(3) is overwritten and that
C             rank(Q) <= IPAR(3).
C
C     BPAR    (input) BOOLEAN array, dimension (6)
C             This array defines the form of the output of the examples
C             and the storage mode of the matrices G and Q.
C             BPAR(1) = .TRUE.  : G is returned.
C             BPAR(1) = .FALSE. : G is returned in factored form, i.e.,
C                                 B and R from (I) are returned.
C             BPAR(2) = .TRUE.  : The matrix returned in array G (i.e.,
C                                 G if BPAR(1) = .TRUE. and R if
C                                 BPAR(1) = .FALSE.) is stored as full
C                                 matrix.
C             BPAR(2) = .FALSE. : The matrix returned in array G is
C                                 provided in packed storage mode.
C             BPAR(3) = .TRUE.  : If BPAR(2) = .FALSE., the matrix
C                                 returned in array G is stored in upper
C                                 packed mode, i.e., the upper triangle
C                                 of a symmetric n-by-n matrix is stored
C                                 by columns, e.g., the matrix entry
C                                 G(i,j) is stored in the array entry
C                                 G(i+j*(j-1)/2) for i <= j.
C                                 Otherwise, this entry is ignored.
C             BPAR(3) = .FALSE. : If BPAR(2) = .FALSE., the matrix
C                                 returned in array G is stored in lower
C                                 packed mode, i.e., the lower triangle
C                                 of a symmetric n-by-n matrix is stored
C                                 by columns, e.g., the matrix entry
C                                 G(i,j) is stored in the array entry
C                                 G(i+(2*n-j)*(j-1)/2) for j <= i.
C                                 Otherwise, this entry is ignored.
C             BPAR(4) = .TRUE.  : Q is returned.
C             BPAR(4) = .FALSE. : Q is returned in factored form, i.e.,
C                                 C and W from (II) are returned.
C             BPAR(5) = .TRUE.  : The matrix returned in array Q (i.e.,
C                                 Q if BPAR(4) = .TRUE. and W if
C                                 BPAR(4) = .FALSE.) is stored as full
C                                 matrix.
C             BPAR(5) = .FALSE. : The matrix returned in array Q is
C                                 provided in packed storage mode.
C             BPAR(6) = .TRUE.  : If BPAR(5) = .FALSE., the matrix
C                                 returned in array Q is stored in upper
C                                 packed mode (see above).
C                                 Otherwise, this entry is ignored.
C             BPAR(6) = .FALSE. : If BPAR(5) = .FALSE., the matrix
C                                 returned in array Q is stored in lower
C                                 packed mode (see above).
C                                 Otherwise, this entry is ignored.
C             NOTE that there are no default values for BPAR.  If all
C             entries are declared to be .TRUE., then matrices G and Q
C             are returned in conventional storage mode, i.e., as
C             N-by-N arrays where the array element Z(I,J) contains the
C             matrix entry Z_{i,j}.
C
C     CHPAR   (input/output) CHARACTER*255
C             On input, this is the name of a data file supplied by the
C             user.
C             In the current version, only Example 4.4 allows a
C             user-defined data file. This file must contain
C             consecutively DOUBLE PRECISION vectors mu, delta, gamma,
C             and kappa. The length of these vectors is determined by
C             the input value for IPAR(1).
C             If on entry, IPAR(1) = L, then mu and delta must each
C             contain L DOUBLE PRECISION values, and gamma and kappa
C             must each contain L-1 DOUBLE PRECISION values.
C             On output, this string contains short information about
C             the chosen example.
C
C     VEC     (output) LOGICAL array, dimension (9)
C             Flag vector which displays the availability of the output
C             data:
C             VEC(j), j=1,2,3, refer to N, M, and P, respectively, and
C             are always .TRUE.
C             VEC(4) refers to A and is always .TRUE.
C             VEC(5) is .TRUE. if BPAR(1) = .FALSE., i.e., the factors B
C             and R from (I) are returned.
C             VEC(6) is .TRUE. if BPAR(4) = .FALSE., i.e., the factors C
C             and W from (II) are returned.
C             VEC(7) refers to G and is always .TRUE.
C             VEC(8) refers to Q and is always .TRUE.
C             VEC(9) refers to X and is .TRUE. if the exact solution
C             matrix is available.
C             NOTE that VEC(i) = .FALSE. for i = 1 to 9 if on exit
C             INFO .NE. 0.
C
C     N       (output) INTEGER
C             The order of the matrices A, X, G if BPAR(1) = .TRUE., and
C             Q if BPAR(4) = .TRUE.
C
C     M       (output) INTEGER
C             The number of columns in the matrix B (or the dimension of
C             the control input space of the underlying dynamical
C             system).
C
C     P       (output) INTEGER
C             The number of rows in the matrix C (or the dimension of
C             the output space of the underlying dynamical system).
C
C     A       (output) DOUBLE PRECISION array, dimension (LDA,N)
C             The leading N-by-N part of this array contains the
C             coefficient matrix A of the CARE.
C
C     LDA     INTEGER
C             The leading dimension of array A.  LDA >= N.
C
C     B       (output) DOUBLE PRECISION array, dimension (LDB,M)
C             If (BPAR(1) = .FALSE.), then the leading N-by-M part of
C             this array contains the matrix B of the factored form (I)
C             of G. Otherwise, B is used as workspace.
C
C     LDB     INTEGER
C             The leading dimension of array B.  LDB >= N.
C
C     C       (output) DOUBLE PRECISION array, dimension (LDC,N)
C             If (BPAR(4) = .FALSE.), then the leading P-by-N part of
C             this array contains the matrix C of the factored form (II)
C             of Q. Otherwise, C is used as workspace.
C
C     LDC     INTEGER
C             The leading dimension of array C.
C             LDC >= P, where P is the number of rows of the matrix C,
C             i.e., the output value of IPAR(3). (For all examples,
C             P <= N, where N equals the output value of the argument
C             IPAR(1), i.e., LDC >= LDA is always safe.)
C
C     G       (output) DOUBLE PRECISION array, dimension (NG)
C             If (BPAR(2) = .TRUE.)  then NG = LDG*N.
C             If (BPAR(2) = .FALSE.) then NG = N*(N+1)/2.
C             If (BPAR(1) = .TRUE.), then array G contains the
C             coefficient matrix G of the CARE.
C             If (BPAR(1) = .FALSE.), then array G contains the 'control
C             weighting matrix' R of G's factored form as in (I). (For
C             all examples, M <= N.) The symmetric matrix contained in
C             array G is stored according to BPAR(2) and BPAR(3).
C
C     LDG     INTEGER
C             If conventional storage mode is used for G, i.e.,
C             BPAR(2) = .TRUE., then G is stored like a 2-dimensional
C             array with leading dimension LDG. If packed symmetric
C             storage mode is used, then LDG is not referenced.
C             LDG >= N if BPAR(2) = .TRUE..
C
C     Q       (output) DOUBLE PRECISION array, dimension (NQ)
C             If (BPAR(5) = .TRUE.)  then NQ = LDQ*N.
C             If (BPAR(5) = .FALSE.) then NQ = N*(N+1)/2.
C             If (BPAR(4) = .TRUE.), then array Q contains the
C             coefficient matrix Q of the CARE.
C             If (BPAR(4) = .FALSE.), then array Q contains the 'output
C             weighting matrix' W of Q's factored form as in (II).
C             The symmetric matrix contained in array Q is stored
C             according to BPAR(5) and BPAR(6).
C
C     LDQ     INTEGER
C             If conventional storage mode is used for Q, i.e.,
C             BPAR(5) = .TRUE., then Q is stored like a 2-dimensional
C             array with leading dimension LDQ. If packed symmetric
C             storage mode is used, then LDQ is not referenced.
C             LDQ >= N if BPAR(5) = .TRUE..
C
C     X       (output) DOUBLE PRECISION array, dimension (LDX,IPAR(1))
C             If an exact solution is available (NR = 1.1, 1.2, 2.1,
C             2.3-2.6, 3.2), then the leading N-by-N part of this array
C             contains the solution matrix X in conventional storage
C             mode. Otherwise, X is not referenced.
C
C     LDX     INTEGER
C             The leading dimension of array X.  LDX >= 1, and
C             LDX >= N if NR = 1.1, 1.2, 2.1, 2.3-2.6, 3.2.
C
C     Workspace
C
C     DWORK   DOUBLE PRECISION array, dimension (LDWORK)
C
C     LDWORK  INTEGER
C             The length of the array DWORK.
C             LDWORK >= N*MAX(4,N).
C
C     Error Indicator
C
C     INFO    INTEGER
C             = 0 : successful exit;
C             < 0 : if INFO = -i, the i-th argument had an illegal
C                   value;
C             = 1 : data file could not be opened or had wrong format;
C             = 2 : division by zero;
C             = 3 : G can not be computed as in (I) due to a singular R
C                   matrix.
C
C     REFERENCES
C
C     [1] Abels, J. and Benner, P.
C         CAREX - A Collection of Benchmark Examples for Continuous-Time
C         Algebraic Riccati Equations (Version 2.0).
C         SLICOT Working Note 1999-14, November 1999. Available from
C         http://www.win.tue.nl/niconet/NIC2/reports.html.
C
C     This is an updated and extended version of
C
C     [2] Benner, P., Laub, A.J., and Mehrmann, V.
C         A Collection of Benchmark Examples for the Numerical Solution
C         of Algebraic Riccati Equations I: Continuous-Time Case.
C         Technical Report SPC 95_22, Fak. f. Mathematik,
C         TU Chemnitz-Zwickau (Germany), October 1995.
C
C     NUMERICAL ASPECTS
C
C     If the original data as taken from the literature is given via
C     matrices G and Q, but factored forms are requested as output, then
C     these factors are obtained from Cholesky or LDL' decompositions of
C     G and Q, i.e., the output data will be corrupted by roundoff
C     errors.
C
C     FURTHER COMMENTS
C
C     Some benchmark examples read data from the data files provided
C     with the collection.
C
C     CONTRIBUTOR
C
C     Peter Benner (Universitaet Bremen), November 15, 1999.
C
C     For questions concerning the collection or for the submission of
C     test examples, please send e-mail to benner@math.uni-bremen.de.
C
C     REVISIONS
C
C     1999, December 23 (V. Sima).
C
C     KEYWORDS
C
C     Algebraic Riccati equation, Hamiltonian matrix.
C
C     ******************************************************************
C
C     .. Parameters ..
C     . # of examples available , # of examples with fixed size. .
      INTEGER          NEX1, NEX2, NEX3, NEX4, NMAX
      PARAMETER        ( NMAX = 9, NEX1 = 6, NEX2 = 9, NEX3 = 2,
     1                   NEX4 = 4 )
      DOUBLE PRECISION ZERO, ONE, TWO, THREE, FOUR, PI
      PARAMETER        ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0,
     1                   THREE = 3.0D0, FOUR = 4.0D0,
     2                   PI = .3141592653589793D1 )
C
C     .. Scalar Arguments ..
      INTEGER          INFO, LDA, LDB, LDC, LDG, LDQ, LDWORK, LDX, M, N,
     $                 P
      CHARACTER        DEF
C
C     .. Array Arguments ..
      INTEGER          IPAR(3), NR(2)
      DOUBLE PRECISION A(LDA,*), B(LDB,*), C(LDC,*), DPAR(*), DWORK(*),
     1                 G(*), Q(*), X(LDX,*)
      CHARACTER        CHPAR*255
      LOGICAL          BPAR(6), VEC(9)
C
C     .. Local Scalars ..
      INTEGER          GDIMM, I, IOS, ISYMM, J, K, L, MSYMM, NSYMM, POS,
     1                 PSYMM, QDIMM
      DOUBLE PRECISION APPIND, B1, B2, C1, C2, SUM, TEMP, TTEMP
C
C     ..Local Arrays ..
      INTEGER          MDEF(2,NMAX), NDEF(4,NMAX), NEX(4), PDEF(2,NMAX)
      DOUBLE PRECISION PARDEF(4,NMAX)
      CHARACTER        IDENT*4
      CHARACTER*255    NOTES(4,NMAX)
C
C     .. External Functions ..
C     . BLAS .
      DOUBLE PRECISION DDOT
      EXTERNAL         DDOT
C     . LAPACK .
      LOGICAL          LSAME
      DOUBLE PRECISION DLAPY2
      EXTERNAL         LSAME, DLAPY2
C
C     .. External Subroutines ..
C     . BLAS .
      EXTERNAL         DCOPY, DGEMV, DSCAL, DSPMV, DSPR, DSYMM, DSYRK
C     . LAPACK .
      EXTERNAL         DLASET, DPPTRF, DPPTRI, DPTTRF, DPTTRS, XERBLA
C     . SLICOT .
      EXTERNAL         MA02DD, MA02ED
C
C     .. Intrinsic Functions ..
      INTRINSIC        COS, MAX, MIN, MOD, SQRT
C
C     .. Data Statements ..
C     . default values for dimensions .
      DATA (NEX(I), I = 1, 4) /NEX1, NEX2, NEX3, NEX4/
      DATA (NDEF(1,I), I = 1, NEX1) /2, 2, 4, 8, 9, 30/
      DATA (NDEF(2,I), I = 1, NEX2) /2, 2, 2, 2, 2, 3, 4, 4, 55/
      DATA (NDEF(3,I), I = 1, NEX3) /20, 64/
      DATA (NDEF(4,I), I = 1, NEX4) /21, 100, 30, 211/
      DATA (MDEF(1,I), I = 1, NEX1) /1, 1, 2, 2, 3, 3/
      DATA (MDEF(2,I), I = 1, NEX2) /1, 2, 1, 2, 1, 3, 1, 1, 2/
      DATA (PDEF(1,I), I = 1, NEX1) /2, 2, 4, 8, 9, 5/
      DATA (PDEF(2,I), I = 1, NEX2) /1, 1, 2, 2, 2, 3, 2, 1, 10/
C     . default values for parameters .
      DATA (PARDEF(1,I), I = 1, NEX1) /ZERO, ZERO, ZERO, ZERO, ZERO,
     1                                 ZERO/
      DATA (PARDEF(2,I), I = 1, NEX2) /.1D-5, .1D-7, .1D7, .1D-6, ZERO,
     1                                 .1D7, .1D-5, .1D-5, .1D1/
      DATA (PARDEF(3,I), I = 1, NEX3) /ZERO, ZERO/
      DATA (PARDEF(4,I), I = 1, NEX4) /ONE, .1D-1, FOUR, ZERO/
C     . comments on examples .
      DATA (NOTES(1,I), I = 1, NEX1) /
     1'Laub 1979, Ex.1', 'Laub 1979, Ex.2: uncontrollable-unobservable d
     2ata', 'Beale/Shafai 1989: model of L-1011 aircraft', 'Bhattacharyy
     3a et al. 1983: binary distillation column', 'Patnaik et al. 1980:
     4tubular ammonia reactor', 'Davison/Gesing 1978: J-100 jet engine'/
      DATA (NOTES(2,I), I = 1, NEX2) /
     1'Arnold/Laub 1984, Ex.1: (A,B) unstabilizable as EPS -> 0', 'Arnol
     2d/Laub 1984, Ex.3: control weighting matrix singular as EPS -> 0',
     3'Kenney/Laub/Wette 1989, Ex.2: ARE ill conditioned for EPS -> oo',
     4'Bai/Qian 1994: ill-conditioned Hamiltonian for EPS -> 0', 'Laub 1
     5992: H-infinity problem, eigenvalues  +/- EPS +/- i', 'Petkov et a
     6l. 1987: increasingly badly scaled Hamiltonian as EPS -> oo', 'Cho
     7w/Kokotovic 1976: magnetic tape control system', 'Arnold/Laub 1984
     8, Ex.2: poor sep. of closed-loop spectrum as EPS -> 0', 'IFAC Benc
     9hmark Problem #90-06: LQG design for modified Boing B-767 at flutt
     1er condition'/
      DATA (NOTES(3,I), I = 1, NEX3) /
     1'Laub 1979, Ex.4: string of high speed vehicles', 'Laub 1979, Ex.5
     2: circulant matrices'/
      DATA (NOTES(4,I), I = 1, NEX4) /
     1'Laub 1979, Ex.6: ill-conditioned Riccati equation', 'Rosen/Wang 1
     2992: lq control of 1-dimensional heat flow','Hench et al. 1995: co
     3upled springs, dashpots and masses','Lang/Penzl 1994: rotating axl
     4e' /
C
C     .. Executable Statements ..
C
      INFO = 0
      DO 5 I = 1, 9
        VEC(I) = .FALSE.
    5 CONTINUE
C
      IF ((NR(1) .NE. 1) .AND. (.NOT. (LSAME(DEF,'N')
     1    .OR. LSAME(DEF,'D')))) THEN
        INFO = -1
      ELSE IF ((NR(1) .LT. 1) .OR. (NR(2) .LT. 1) .OR.
     1  (NR(1) .GT. 4) .OR. (NR(2) .GT. NEX(NR(1)))) THEN
        INFO = -2
      ELSE IF (NR(1) .GT. 2) THEN
        IF (.NOT. LSAME(DEF,'N')) IPAR(1) = NDEF(NR(1),NR(2))
        IF (NR(1) .EQ. 3) THEN
          IF (NR(2) .EQ. 1) THEN
            IPAR(2) = IPAR(1)
            IPAR(3) = IPAR(1) - 1
            IPAR(1) = 2*IPAR(1) - 1
          ELSE IF (NR(2) .EQ. 2) THEN
            IPAR(2) = IPAR(1)
            IPAR(3) = IPAR(1)
          ELSE
            IPAR(2) = 1
            IPAR(3) = 1
          END IF
        ELSE IF (NR(1) .EQ. 4) THEN
          IF (NR(2) .EQ. 3) THEN
            L = IPAR(1)
            IPAR(2) = 2
            IPAR(3) = 2*L
            IPAR(1) = 2*L
          ELSE IF (NR(2) .EQ. 4) THEN
            L = IPAR(1)
            IPAR(2) = L
            IPAR(3) = L
            IPAR(1) = 2*L-1
          ELSE
            IPAR(2) = 1
            IPAR(3) = 1
          END IF
        END IF
      ELSE IF ((NR(1) .EQ. 2) .AND. (NR(2) .EQ. 9) .AND.
     1         (IPAR(1) . EQ. 2)) THEN
        IPAR(1) = NDEF(NR(1),NR(2))
        IPAR(2) = MDEF(NR(1),NR(2))
        IPAR(3) = 3
      ELSE
        IPAR(1) = NDEF(NR(1),NR(2))
        IPAR(2) = MDEF(NR(1),NR(2))
        IPAR(3) = PDEF(NR(1),NR(2))
      END IF
      IF (INFO .NE. 0)  GOTO 7
C
      IF (IPAR(1) .LT. 1) THEN
        INFO = -4
      ELSE IF (IPAR(1) .GT. LDA) THEN
        INFO = -12
      ELSE IF (IPAR(1) .GT. LDB) THEN
        INFO = -14
      ELSE IF (IPAR(3) .GT. LDC) THEN
        INFO = -16
      ELSE IF (BPAR(2) .AND. (IPAR(1).GT. LDG)) THEN
        INFO = -18
      ELSE IF (BPAR(5) .AND. (IPAR(1).GT. LDQ)) THEN
        INFO = -20
      ELSE IF (LDX.LT.1) THEN
        INFO = -22
      ELSE IF ((NR(1) .EQ. 1) .AND.
     $        ((NR(2) .EQ. 1) .OR. (NR(2) .EQ.2))) THEN
        IF (IPAR(1) .GT. LDX) INFO = -22
      ELSE IF ((NR(1) .EQ. 2) .AND. (NR(2) .EQ. 1)) THEN
        IF (IPAR(1) .GT. LDX) INFO = -22
      ELSE IF ((NR(1) .EQ. 2) .AND. ((NR(2) .GE. 3) .AND.
     1         (NR(2) .LE. 6))) THEN
        IF (IPAR(1) .GT. LDX) INFO = -22
      ELSE IF ((NR(1) .EQ. 3) .AND. (NR(2) .EQ. 2)) THEN
        IF (IPAR(1) .GT. LDX) INFO = -22
      ELSE IF (LDWORK .LT. N*(MAX(4,N))) THEN
        INFO = -24
      END IF
C
    7 CONTINUE
      IF (INFO .NE. 0)  THEN
        CALL XERBLA( 'BB01AD', -INFO )
        RETURN
      END IF
C
      NSYMM = (IPAR(1)*(IPAR(1)+1))/2
      MSYMM = (IPAR(2)*(IPAR(2)+1))/2
      PSYMM = (IPAR(3)*(IPAR(3)+1))/2
      IF (.NOT. LSAME(DEF,'N')) DPAR(1) = PARDEF(NR(1),NR(2))
C
      CALL DLASET('A', IPAR(1), IPAR(1), ZERO, ZERO, A, LDA)
      CALL DLASET('A', IPAR(1), IPAR(2), ZERO, ZERO, B, LDB)
      CALL DLASET('A', IPAR(3), IPAR(1), ZERO, ZERO, C, LDC)
      CALL DLASET('L', MSYMM, 1, ZERO, ZERO, G, 1)
      CALL DLASET('L', PSYMM, 1, ZERO, ZERO, Q, 1)
C
      IF (NR(1) .EQ. 1) THEN
        IF (NR(2) .EQ. 1) THEN
          A(1,2) = ONE
          B(2,1) = ONE
          Q(1)   = ONE
          Q(3)   = TWO
          IDENT  = '0101'
          CALL DLASET('A', IPAR(1), IPAR(1), ONE, TWO, X, LDX)
C
        ELSE IF (NR(2) .EQ. 2) THEN
          A(1,1) = FOUR
          A(2,1) = -.45D1
          A(1,2) = THREE
          A(2,2) = -.35D1
          CALL DLASET('A', IPAR(1), IPAR(2), -ONE, ONE, B, LDB)
          Q(1)  = 9.0D0
          Q(2)  = 6.0D0
          Q(3)  = FOUR
          IDENT = '0101'
          TEMP  = ONE + SQRT(TWO)
          CALL DLASET('A', IPAR(1), IPAR(1), 6.0D0*TEMP, FOUR*TEMP, X,
     1                LDX)
          X(1,1) = 9.0D0*TEMP
C
        ELSE IF ((NR(2) .GE. 3) .AND. (NR(2) .LE. 6)) THEN
          WRITE (CHPAR(1:11), '(A,I1,A,I1,A)') 'BB01', NR(1), '0',
     1                                          NR(2) , '.dat'
          IF ((NR(2) .EQ. 3) .OR. (NR(2) .EQ. 4)) THEN
            IDENT = '0101'
          ELSE IF (NR(2) .EQ. 5) THEN
            IDENT = '0111'
          ELSE IF (NR(2) .EQ. 6) THEN
            IDENT = '0011'
          END IF
          OPEN(1, IOSTAT = IOS, STATUS = 'OLD', FILE = CHPAR(1:11))
          IF (IOS .NE. 0) THEN
            INFO = 1
          ELSE IF (NR(2) .LE. 6) THEN
            DO 10  I = 1, IPAR(1)
              READ (1, FMT = *, IOSTAT = IOS)
     1                                 (A(I,J), J = 1, IPAR(1))
              IF (IOS .NE. 0) INFO = 1
   10       CONTINUE
            DO 20  I = 1, IPAR(1)
              READ (1, FMT = *, IOSTAT = IOS)
     1                                 (B(I,J), J = 1, IPAR(2))
              IF (IOS .NE. 0) INFO = 1
   20       CONTINUE
            IF (NR(2) .LE. 4) THEN
              DO 30  I = 1, IPAR(1)
                POS = (I-1)*IPAR(1)
                READ (1, FMT = *, IOSTAT = IOS) (DWORK(POS+J),
     1                                          J = 1,IPAR(1))
   30         CONTINUE
              IF (IOS .NE. 0) THEN
                INFO = 1
              ELSE
                CALL MA02DD('Pack', 'Lower', IPAR(1), DWORK, IPAR(1), Q)
              END IF
            ELSE IF (NR(2) .EQ. 6) THEN
              DO 35  I = 1, IPAR(3)
                READ (1, FMT = *, IOSTAT = IOS)
     1                                   (C(I,J), J = 1, IPAR(1))
                IF (IOS .NE. 0) INFO = 1
   35         CONTINUE
            END IF
            CLOSE(1)
          END IF
        END IF
C
      ELSE IF (NR(1) .EQ. 2) THEN
        IF (NR(2) .EQ. 1) THEN
          A(1,1) =  ONE
          A(2,2) = -TWO
          B(1,1) = DPAR(1)
          CALL DLASET('U', IPAR(3), IPAR(1), ONE, ONE, C, LDC)
          IDENT  = '0011'
          IF (DPAR(1) .NE. ZERO) THEN
            TEMP   = DLAPY2(ONE, DPAR(1))
            X(1,1) = (ONE + TEMP)/DPAR(1)/DPAR(1)
            X(2,1) = ONE/(TWO + TEMP)
            X(1,2) = X(2,1)
            TTEMP  = DPAR(1)*X(1,2)
            TEMP   = (ONE - TTEMP) * (ONE + TTEMP)
            X(2,2) = TEMP / FOUR
          ELSE
            INFO = 2
          END IF
C
        ELSE IF (NR(2) .EQ. 2) THEN
          A(1,1) = -.1D0
          A(2,2) = -.2D-1
          B(1,1) =  .1D0
          B(2,1) =  .1D-2
          B(2,2) =  .1D-1
          CALL DLASET('L', MSYMM, 1, ONE, ONE, G, MSYMM)
          G(1)   = G(1) + DPAR(1)
          C(1,1) = .1D2
          C(1,2) = .1D3
          IDENT  = '0010'
C
        ELSE IF (NR(2) .EQ. 3) THEN
          A(1,2) = DPAR(1)
          B(2,1) = ONE
          IDENT  = '0111'
          IF (DPAR(1) .NE. ZERO) THEN
            TEMP   = SQRT(ONE + TWO*DPAR(1))
            CALL DLASET('A', IPAR(1), IPAR(1), ONE, TEMP, X, LDX)
            X(1,1) = X(1,1)/DPAR(1)
          ELSE
            INFO = 2
          END IF
C
        ELSE IF (NR(2) .EQ. 4) THEN
          TEMP = DPAR(1) + ONE
          CALL DLASET('A', IPAR(1), IPAR(1), ONE, TEMP, A, LDA)
          Q(1) = DPAR(1)**2
          Q(3) = Q(1)
          IDENT = '1101'
          X(1,1) = TWO*TEMP + SQRT(TWO)*(SQRT(TEMP**2 + ONE) + DPAR(1))
          X(1,1) = X(1,1)/TWO
          X(2,2) = X(1,1)
          TTEMP  = X(1,1) - TEMP
          IF (TTEMP .NE. ZERO) THEN
             X(2,1) = X(1,1) / TTEMP
             X(1,2) = X(2,1)
          ELSE
             INFO = 2
          END IF
C
        ELSE IF (NR(2) .EQ. 5) THEN
          A(1,1) = THREE - DPAR(1)
          A(2,1) = FOUR
          A(1,2) = ONE
          A(2,2) = TWO - DPAR(1)
          CALL DLASET('L', IPAR(1), IPAR(2), ONE, ONE, B, LDB)
          Q(1)   = FOUR*DPAR(1) - 11.0D0
          Q(2)   = TWO*DPAR(1)  - 5.0D0
          Q(3)   = TWO*DPAR(1)  - TWO
          IDENT  = '0101'
          CALL DLASET('A', IPAR(1), IPAR(1), ONE, ONE, X, LDX)
          X(1,1) = TWO
C
        ELSE IF (NR(2) .EQ. 6) THEN
          IF (DPAR(1) .NE. ZERO) THEN
            A(1,1) = DPAR(1)
            A(2,2) = DPAR(1)*TWO
            A(3,3) = DPAR(1)*THREE
C     .. set C = V ..
            TEMP   = TWO/THREE
            CALL DLASET('A', IPAR(3), IPAR(1), -TEMP, ONE - TEMP,
     1                  C, LDC)
            CALL DSYMM('L', 'L', IPAR(1), IPAR(1), ONE, C, LDC, A, LDA,
     1                 ZERO, DWORK, IPAR(1))
            CALL DSYMM('R', 'L', IPAR(1), IPAR(1), ONE, C, LDC, DWORK,
     1                 IPAR(1), ZERO, A, LDA)
C     .. G = R ! ..
            G(1) = DPAR(1)
            G(4) = DPAR(1)
            G(6) = DPAR(1)
            Q(1) = ONE/DPAR(1)
            Q(4) = ONE
            Q(6) = DPAR(1)
            IDENT = '1000'
            CALL DLASET('A', IPAR(1), IPAR(1), ZERO, ZERO, X, LDX)
            TEMP   = DPAR(1)**2
            X(1,1) = TEMP + SQRT(TEMP**2 + ONE)
            X(2,2) = TEMP*TWO + SQRT(FOUR*TEMP**2 + DPAR(1))
            X(3,3) = TEMP*THREE + DPAR(1)*SQRT(9.0D0*TEMP + ONE)
            CALL DSYMM('L', 'L', IPAR(1), IPAR(1), ONE, C, LDC, X, LDX,
     1                  ZERO, DWORK, IPAR(1))
            CALL DSYMM('R', 'L', IPAR(1), IPAR(1), ONE, C, LDC, DWORK,
     1                 IPAR(1), ZERO, X, LDX)
          ELSE
            INFO = 2
          END IF
C
        ELSE IF (NR(2) .EQ. 7) THEN
          IF (DPAR(1) .NE. ZERO) THEN
            A(1,2) =  .400D0
            A(2,3) =  .345D0
            A(3,2) = -.524D0/DPAR(1)
            A(3,3) = -.465D0/DPAR(1)
            A(3,4) =  .262D0/DPAR(1)
            A(4,4) = -ONE/DPAR(1)
            B(4,1) =  ONE/DPAR(1)
            C(1,1) =  ONE
            C(2,3) =  ONE
            IDENT  = '0011'
          ELSE
            INFO = 2
          END IF
C
        ELSE IF (NR(2) .EQ. 8) THEN
          A(1,1) = -DPAR(1)
          A(2,1) = -ONE
          A(1,2) =  ONE
          A(2,2) = -DPAR(1)
          A(3,3) =  DPAR(1)
          A(4,3) = -ONE
          A(3,4) =  ONE
          A(4,4) =  DPAR(1)
          CALL DLASET('L', IPAR(1), IPAR(2), ONE, ONE, B, LDB)
          CALL DLASET('U', IPAR(3), IPAR(1), ONE, ONE, C, LDC)
          IDENT = '0011'
C
        ELSE IF (NR(2) .EQ. 9) THEN
          IF (IPAR(3) .EQ. 10) THEN
C     .. read LQR CARE ...
            WRITE (CHPAR(1:12), '(A,I1,A,I1,A)') 'BB01', NR(1), '0',
     1                                           NR(2), '1.dat'
            OPEN(1, IOSTAT = IOS, STATUS = 'OLD', FILE = CHPAR(1:12))
            IF (IOS .NE. 0) THEN
              INFO = 1
            ELSE
              DO 36 I = 1, 27, 2
                READ (1, FMT = *, IOSTAT = IOS)
     1               ((A(I+J,I+K), K = 0, 1), J = 0, 1)
                IF (IOS .NE. 0) INFO = 1
   36         CONTINUE
              DO 37 I = 30, 44, 2
                READ (1, FMT = *, IOSTAT = IOS)
     1               ((A(I+J,I+K), K = 0, 1), J = 0, 1)
                IF (IOS .NE. 0) INFO = 1
   37         CONTINUE
              DO 38 I = 1, IPAR(1)
                READ (1, FMT = *, IOSTAT = IOS)
     1               (A(I,J), J = 46, IPAR(1))
                IF (IOS .NE. 0) INFO = 1
   38         CONTINUE
              A(29,29) = -.5301D1
              B(48,1) = .8D06
              B(51,2) = .8D06
              G(1) = .3647D03
              G(3) = .1459D02
              DO 39 I = 1,6
                READ (1, FMT = *, IOSTAT = IOS)
     1               (C(I,J), J = 1,45)
                IF (IOS .NE. 0) INFO = 1
   39         CONTINUE
              C(7,47)  = ONE
              C(8,46)  = ONE
              C(9,50)  = ONE
              C(10,49) = ONE
              Q(11) = .376D-13
              Q(20) = .120D-12
              Q(41) = .245D-11
            END IF
          ELSE
C     .. read Kalman filter CARE ..
            WRITE (CHPAR(1:12), '(A,I1,A,I1,A)') 'BB01', NR(1), '0',
     1                                           NR(2), '2.dat'
            OPEN(1, IOSTAT = IOS, STATUS = 'OLD', FILE = CHPAR(1:12))
            IF (IOS .NE. 0) THEN
              INFO = 1
            ELSE
              DO 40 I = 1, 27, 2
                READ (1, FMT = *, IOSTAT = IOS)
     1               ((A(I+K,I+J), K = 0, 1), J = 0, 1)
                IF (IOS .NE. 0) INFO = 1
   40         CONTINUE
              DO 41 I = 30, 44, 2
                READ (1, FMT = *, IOSTAT = IOS)
     1               ((A(I+K,I+J), K = 0, 1), J = 0, 1)
                IF (IOS .NE. 0) INFO = 1
   41         CONTINUE
              DO 42 I = 1, IPAR(1)
                READ (1, FMT = *, IOSTAT = IOS)
     1               (A(J,I), J = 46, IPAR(1))
                IF (IOS .NE. 0) INFO = 1
   42         CONTINUE
              A(29,29) = -.5301D1
              DO 43 J = 1, IPAR(2)
                READ (1, FMT = *, IOSTAT = IOS)
     1                                 (B(I,J), I = 1, IPAR(1))
                IF (IOS .NE. 0) INFO = 1
   43         CONTINUE
              G(1) = .685D-5
              G(3) = .373D3
              C(1,52) = .3713
              C(1,53) = .1245D1
              C(2,48) = .8D6
              C(2,54) = ONE
              C(3,51) = .8D6
              C(3,55) = ONE
              Q(1) = .28224D5
              Q(4) = .2742D-4
              Q(6) = .6854D-3
            END IF
          END IF
          CLOSE(1)
          IDENT = '0000'
        END IF
C
      ELSE IF (NR(1) .EQ. 3) THEN
        IF (NR(2) .EQ. 1) THEN
          DO 45  I = 1, IPAR(1)
            IF (MOD(I,2) .EQ. 1) THEN
              A(I,I)       = -ONE
              B(I,(I+1)/2) =  ONE
            ELSE
              A(I,I-1) =  ONE
              A(I,I+1) = -ONE
              C(I/2,I) =  ONE
            END IF
   45     CONTINUE
          ISYMM = 1
          DO 50  I = IPAR(3), 1, -1
            Q(ISYMM) = 10.0D0
            ISYMM    = ISYMM + I
   50     CONTINUE
          IDENT = '0001'
C
        ELSE IF (NR(2) .EQ. 2) THEN
          DO 60  I = 1, IPAR(1)
            A(I,I) = -TWO
            IF (I .LT. IPAR(1)) THEN
              A(I,I+1) = ONE
              A(I+1,I) = ONE
            END IF
   60	    CONTINUE
          A(1,IPAR(1)) = ONE
          A(IPAR(1),1) = ONE
          IDENT = '1111'
          TEMP = TWO * PI / DBLE(IPAR(1))
          DO 70  I = 1, IPAR(1)
            DWORK(I)   = COS(TEMP*DBLE(I-1))
            DWORK(IPAR(1)+I) = -TWO + TWO*DWORK(I) +
     1                 SQRT(5.0D0 + FOUR*DWORK(I)*(DWORK(I) - TWO))
   70     CONTINUE
          DO 90  J = 1, IPAR(1)
            DO 80  I = 1, IPAR(1)
               DWORK(2*IPAR(1)+I) = COS(TEMP*DBLE(I-1)*DBLE(J-1))
   80       CONTINUE
            X(J,1) = DDOT(IPAR(1), DWORK(IPAR(1)+1), 1,
     1                    DWORK(2*IPAR(1)+1), 1)/DBLE(IPAR(1))
   90     CONTINUE
C         .. set up circulant solution matrix ..
          DO 100  I = 2, IPAR(1)
            CALL DCOPY(IPAR(1)-I+1, X(1,1),   1, X(I,I), 1)
            CALL DCOPY(I-1, X(IPAR(1)-I+2,1), 1, X(1,I), 1)
  100     CONTINUE
        END IF
C
      ELSE IF (NR(1) .EQ. 4) THEN
        IF (NR(2) .EQ. 1) THEN
C       .. set up remaining parameter ..
          IF (.NOT. LSAME(DEF,'N')) THEN
            DPAR(1) = ONE
            DPAR(2) = ONE
          END IF
          CALL DLASET('A', IPAR(1)-1, IPAR(1)-1, ZERO, ONE, A(1,2), LDA)
          B(IPAR(1),1) = ONE
          C(1,1) = ONE
          Q(1)   = DPAR(1)
          G(1)   = DPAR(2)
          IDENT  = '0000'
C
        ELSE IF (NR(2) .EQ. 2) THEN
C         .. set up remaining parameters ..
          APPIND = DBLE(IPAR(1) + 1)
          IF (.NOT. LSAME(DEF,'N')) THEN
            DPAR(1) = PARDEF(NR(1), NR(2))
            DPAR(2) = ONE
            DPAR(3) = ONE
            DPAR(4) = .2D0
            DPAR(5) = .3D0
            DPAR(6) = .2D0
            DPAR(7) = .3D0
          END IF
C         .. set up stiffness matrix ..
          TEMP = -DPAR(1)*APPIND
          CALL DLASET('A', IPAR(1), IPAR(1), ZERO, TWO*TEMP, A, LDA)
          DO 110  I = 1, IPAR(1) - 1
            A(I+1,I) = -TEMP
            A(I,I+1) = -TEMP
  110     CONTINUE
C         .. set up Gramian, stored by diagonals ..
          TEMP = ONE/(6.0D0*APPIND)
          CALL DLASET('L', IPAR(1), 1, FOUR*TEMP, FOUR*TEMP, DWORK,
     1                IPAR(1))
          CALL DLASET('L', IPAR(1)-1, 1, TEMP, TEMP, DWORK(IPAR(1)+1),
     1                IPAR(1))
          CALL DPTTRF(IPAR(1), DWORK(1), DWORK(IPAR(1)+1), INFO)
C         .. A = (inverse of Gramian) * (stiffness matrix) ..
          CALL DPTTRS(IPAR(1), IPAR(1), DWORK(1), DWORK(IPAR(1)+1),
     1                A, LDA, INFO)
C         .. compute B, C ..
          DO 120  I = 1, IPAR(1)
            B1 = MAX(DBLE(I-1)/APPIND, DPAR(4))
            B2 = MIN(DBLE(I+1)/APPIND, DPAR(5))
            C1 = MAX(DBLE(I-1)/APPIND, DPAR(6))
            C2 = MIN(DBLE(I+1)/APPIND, DPAR(7))
            IF (B1 .GE. B2) THEN
              B(I,1) = ZERO
            ELSE
              B(I,1) = B2 - B1
              TEMP   = MIN(B2, DBLE(I)/APPIND)
              IF (B1 .LT. TEMP) THEN
                B(I,1) = B(I,1) + APPIND*(TEMP**2 - B1**2)/TWO
                B(I,1) = B(I,1) + DBLE(I)*(B1 - TEMP)
              END IF
              TEMP = MAX(B1, DBLE(I)/APPIND)
              IF (TEMP .LT. B2) THEN
                B(I,1) = B(I,1) - APPIND*(B2**2 - TEMP**2)/TWO
                B(I,1) = B(I,1) - DBLE(I)*(TEMP - B2)
              END IF
            END IF
            IF (C1 .GE. C2) THEN
              C(1,I) = ZERO
            ELSE
              C(1,I) = C2 - C1
              TEMP   = MIN(C2, DBLE(I)/APPIND)
              IF (C1 .LT. TEMP) THEN
                C(1,I) = C(1,I) + APPIND*(TEMP**2 - C1**2)/TWO
                C(1,I) = C(1,I) + DBLE(I)*(C1 - TEMP)
              END IF
              TEMP = MAX(C1, DBLE(I)/APPIND)
              IF (TEMP .LT. C2) THEN
                C(1,I) = C(1,I) - APPIND*(C2**2 - TEMP**2)/TWO
                C(1,I) = C(1,I) - DBLE(I)*(TEMP - C2)
              END IF
            END IF
  120     CONTINUE
          CALL DSCAL(IPAR(1), DPAR(2), B(1,1), 1)
          CALL DSCAL(IPAR(1), DPAR(3), C(1,1), LDC)
          CALL DPTTRS(IPAR(1), 1, DWORK(1), DWORK(IPAR(1)+1), B, LDB,
     1                INFO)
          IDENT = '0011'
C
        ELSE IF (NR(2) .EQ. 3) THEN
C         .. set up remaining parameters ..
          IF (.NOT. LSAME(DEF,'N')) THEN
            DPAR(1) = PARDEF(NR(1),NR(2))
            DPAR(2) = FOUR
            DPAR(3) = ONE
          END IF
          IF (DPAR(1) . NE. 0) THEN
            CALL DLASET('A', L, L, ZERO, ONE, A(1,L+1), LDA)
            TEMP  = DPAR(3) / DPAR(1)
            A(L+1,1) = -TEMP
            A(L+1,2) =  TEMP
            A(IPAR(1),L-1) =  TEMP
            A(IPAR(1),L)   = -TEMP
            TTEMP = TWO*TEMP
            DO 130  I = 2, L-1
              A(L+I,I)   = -TTEMP
              A(L+I,I+1) =  TEMP
              A(L+I,I-1) =  TEMP
  130       CONTINUE
            CALL DLASET('A', L, L, ZERO, -DPAR(2)/DPAR(1), A(L+1,L+1),
     1                  LDA)
            B(L+1,1) =  ONE / DPAR(1)
            B(IPAR(1),IPAR(2)) = -ONE / DPAR(1)
            IDENT = '0111'
          ELSE
            INFO = 2
          END IF
C
        ELSE IF (NR(2) .EQ. 4) THEN
          IF (.NOT. LSAME(DEF,'N')) WRITE (CHPAR(1:11), '(A,I1,A,I1,A)')
     1                               'BB01', NR(1), '0', NR(2), '.dat'
          OPEN(1, IOSTAT = IOS, STATUS = 'OLD', FILE = CHPAR(1:11))
          IF (IOS .NE. 0) THEN
            INFO = 1
          ELSE
            READ (1, FMT = *, IOSTAT = IOS) (DWORK(I), I = 1, 4*L-2)
            IF (IOS .NE. 0)  INFO = 1
          END IF
          CLOSE(1)
          IF (INFO .EQ. 0) THEN
            CALL DLASET('A', L-1, L-1, ZERO, ONE, A(L+1,2), LDA)
            POS    = 2*L + 1
            A(1,2) = - DWORK(POS) / DWORK(1)
            DO 140  I = 2, L
              TEMP  = DWORK(POS) / DWORK(I-1)
              TTEMP = DWORK(POS) / DWORK(I)
              IF (I .GT. 2)  A(I-1,I) = TEMP
              A(I,I) = -(TEMP + TTEMP)
              IF (I .LT. L)  A(I+1,I) = TTEMP
              POS = POS + 1
  140       CONTINUE
            POS    = L
            TEMP   = DWORK(POS+1) / DWORK(1)
            A(1,1) = -TEMP
            DO 160  I = 2, L
              TTEMP  = TEMP
              TEMP   = DWORK(POS+I) / DWORK(I)
              SUM    = TTEMP - TEMP
              A(I,1) = -SUM
              A(I,I) = A(I,I) - TEMP
              DO 150  J = 2, I-2
                A(I,J) = SUM
  150         CONTINUE
              IF (I .GT. 2)  A(I,I-1) = A(I,I-1) + SUM
  160       CONTINUE
            POS      = 3*L
            A(1,L+1) = -DWORK(3*L)/DWORK(1)
            DO 170  I = 2, L
              TEMP  = DWORK(POS) / DWORK(I-1)
              TTEMP = DWORK(POS) / DWORK(I)
              IF (I .GT. 2)  A(I-1,L+I-1) = TEMP
              A(I,L+I-1) = -(TEMP + TTEMP)
              IF (I .LT. L)  A(I+1,L+I-1) = TTEMP
              POS = POS + 1
  170       CONTINUE
            B(1,1) = ONE/DWORK(1)
            DO 180  I = 1, L
              TEMP = ONE/DWORK(I)
              IF (I .GT. 1)  B(I,I)   = -TEMP
              IF (I .LT. L)  B(I+1,I) =  TEMP
  180       CONTINUE
            C(1,1) = ONE
            Q(1)   = ONE
            POS    = 2*L - 1
            ISYMM  = L + 1
            DO 190  I = 2, L
              TEMP       = DWORK(POS+I)
              TTEMP      = DWORK(POS+L+I-1)
              C(I,I)     = TEMP
              C(I,L+I-1) = TTEMP
              Q(ISYMM)   = ONE / (TEMP*TEMP + TTEMP*TTEMP)
              ISYMM      = ISYMM + L - I + 1
  190       CONTINUE
            IDENT = '0001'
          END IF
        END IF
      END IF
C
      IF (INFO .NE. 0)  GOTO 2001
C     .. set up data in required format ..
C
      IF (BPAR(1)) THEN
C     .. G is to be returned in product form ..
        GDIMM = IPAR(1)
        IF (IDENT(4:4) .EQ. '0') THEN
C       .. invert R using Cholesky factorization, store in G ..
          CALL DPPTRF('L', IPAR(2), G, INFO)
          IF (INFO .EQ. 0) THEN
            CALL DPPTRI('L', IPAR(2), G, INFO)
            IF (IDENT(1:1) .EQ. '0') THEN
C         .. B is not identity matrix ..
              DO 200  I = 1, IPAR(1)
                CALL DSPMV('L', IPAR(2), ONE, G, B(I,1), LDB, ZERO,
     1                     DWORK((I-1)*IPAR(1)+1), 1)
  200         CONTINUE
              CALL DGEMV('T', IPAR(2), IPAR(1), ONE, DWORK, IPAR(1),
     1                   B(1,1), LDB, ZERO, G, 1)
              ISYMM = IPAR(1) + 1
              DO 210  I = 2, IPAR(1)
                CALL DGEMV('T', IPAR(2), IPAR(1), ONE, DWORK, IPAR(1),
     1                     B(I,1), LDB, ZERO, B(1,1), LDB)
                CALL DCOPY(IPAR(1) - I + 1, B(1,I), LDB, G(ISYMM), 1)
                ISYMM = ISYMM + (IPAR(1) - I + 1)
  210         CONTINUE
            END IF
          ELSE
            IF (INFO .GT. 0) THEN
              INFO = 3
              GOTO 2001
            END IF
          END IF
        ELSE
C       .. R = identity ..
          IF (IDENT(1:1) .EQ. '0') THEN
C         .. B is not identity matrix ..
            IF (IPAR(2) .EQ. 1) THEN
              CALL DLASET('L', NSYMM, 1, ZERO, ZERO, G, 1)
              CALL DSPR('L', IPAR(1), ONE, B, 1, G)
            ELSE
              CALL DSYRK('L', 'N', IPAR(1), IPAR(2), ONE,
     1                    B, LDB, ZERO, DWORK, IPAR(1))
              CALL MA02DD('Pack', 'Lower', IPAR(1), DWORK, IPAR(1), G)
            END IF
          ELSE
C         .. B = R = identity ..
            ISYMM = 1
            DO 220  I = IPAR(1), 1, -1
              G(ISYMM) = ONE
              ISYMM = ISYMM + I
  220       CONTINUE
          END IF
        END IF
      ELSE
        GDIMM = IPAR(2)
        IF (IDENT(1:1) .EQ. '1')
     1    CALL DLASET('A', IPAR(1), IPAR(2), ZERO, ONE, B, LDB)
        IF (IDENT(4:4) .EQ. '1') THEN
          ISYMM = 1
          DO 230  I = IPAR(2), 1, -1
            G(ISYMM) = ONE
            ISYMM = ISYMM + I
  230     CONTINUE
        END IF
      END IF
C
      IF (BPAR(4)) THEN
C     .. Q is to be returned in product form ..
        QDIMM = IPAR(1)
        IF (IDENT(3:3) .EQ. '0') THEN
          IF (IDENT(2:2) .EQ. '0') THEN
C         .. C is not identity matrix ..
            DO 240  I = 1, IPAR(1)
              CALL DSPMV('L', IPAR(3), ONE, Q, C(1,I), 1, ZERO,
     1                   DWORK((I-1)*IPAR(1)+1), 1)
  240       CONTINUE
C         .. use Q(1:IPAR(1)) as workspace and compute the first column
C            of Q in the end ..
            ISYMM = IPAR(1) + 1
            DO 250  I = 2, IPAR(1)
              CALL DGEMV('T', IPAR(3), IPAR(1), ONE, DWORK, IPAR(1),
     1                   C(1,I), 1, ZERO, Q(1), 1)
              CALL DCOPY(IPAR(1) - I + 1, Q(I), 1, Q(ISYMM), 1)
              ISYMM = ISYMM + (IPAR(1) - I + 1)
  250       CONTINUE
            CALL DGEMV('T', IPAR(3), IPAR(1), ONE, DWORK, IPAR(1),
     1                 C(1,1), 1, ZERO, Q, 1)
          END IF
        ELSE
C       .. Q = identity ..
          IF (IDENT(2:2) .EQ. '0') THEN
C         .. C is not identity matrix ..
            IF (IPAR(3) .EQ. 1) THEN
              CALL DLASET('L', NSYMM, 1, ZERO, ZERO, Q, 1)
              CALL DSPR('L', IPAR(1), ONE, C, LDC, Q)
            ELSE
              CALL DSYRK('L', 'T', IPAR(1), IPAR(3), ONE, C, LDC,
     1                   ZERO, DWORK, IPAR(1))
              CALL MA02DD('Pack', 'Lower', IPAR(1), DWORK, IPAR(1), Q)
            END IF
          ELSE
C         .. C = Q = identity ..
            ISYMM = 1
            DO 260  I = IPAR(1), 1, -1
              Q(ISYMM) = ONE
              ISYMM    = ISYMM + I
  260       CONTINUE
          END IF
        END IF
      ELSE
        QDIMM = IPAR(3)
        IF (IDENT(2:2) .EQ. '1')
     1    CALL DLASET('A', IPAR(3), IPAR(1), ZERO, ONE, C, LDC)
        IF (IDENT(3:3) .EQ. '1') THEN
          ISYMM = 1
          DO 270  I = IPAR(3), 1, -1
            Q(ISYMM) = ONE
            ISYMM    = ISYMM + I
  270     CONTINUE
        END IF
      END IF
C
C     .. unpack symmetric matrices if desired ..
      IF (BPAR(2)) THEN
        ISYMM = (GDIMM * (GDIMM + 1)) / 2
        CALL DCOPY(ISYMM, G, 1, DWORK, 1)
        CALL MA02DD('Unpack', 'Lower', GDIMM, G, LDG, DWORK)
        CALL MA02ED('Lower', GDIMM, G, LDG)
      ELSE IF (BPAR(3)) THEN
        CALL MA02DD('Unpack', 'Lower', GDIMM, DWORK, GDIMM, G)
        CALL MA02ED('Lower', GDIMM, DWORK, GDIMM)
        CALL MA02DD('Pack', 'Upper', GDIMM, DWORK, GDIMM, G)
      END IF
      IF (BPAR(5)) THEN
        ISYMM = (QDIMM * (QDIMM + 1)) / 2
        CALL DCOPY(ISYMM, Q, 1, DWORK, 1)
        CALL MA02DD('Unpack', 'Lower', QDIMM, Q, LDQ, DWORK)
        CALL MA02ED('Lower', QDIMM, Q, LDQ)
      ELSE IF (BPAR(6)) THEN
        CALL MA02DD('Unpack', 'Lower', QDIMM, DWORK, QDIMM, Q)
        CALL MA02ED('Lower', QDIMM, DWORK, QDIMM)
        CALL MA02DD('Pack', 'Upper', QDIMM, DWORK, QDIMM, Q)
      END IF
C
C     ...set VEC...
      VEC(1) = .TRUE.
      VEC(2) = .TRUE.
      VEC(3) = .TRUE.
      VEC(4) = .TRUE.
      VEC(5) = .NOT. BPAR(1)
      VEC(6) = .NOT. BPAR(4)
      VEC(7) = .TRUE.
      VEC(8) = .TRUE.
      IF (NR(1) .EQ. 1) THEN
        IF ((NR(2) .EQ. 1) .OR. (NR(2) .EQ. 2)) VEC(9) = .TRUE.
      ELSE IF (NR(1) .EQ. 2) THEN
        IF ((NR(2) .EQ. 1) .OR. ((NR(2) .GE. 3) .AND. (NR(2) .LE. 6)))
     1     VEC(9) = .TRUE.
      ELSE IF (NR(1) .EQ. 3) THEN
        IF (NR(2) .EQ. 2) VEC(9) = .TRUE.
      END IF
      CHPAR  = NOTES(NR(1),NR(2))
      N = IPAR(1)
      M = IPAR(2)
      P = IPAR(3)
 2001 CONTINUE
      RETURN
C *** Last line of BB01AD ***
      END