-
Notifications
You must be signed in to change notification settings - Fork 2
/
hogk.for
1173 lines (936 loc) · 24.3 KB
/
hogk.for
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
C %P%
LOGICAL FUNCTION OPENN(A,NX,N,LENGTH)
*** INITIALIZE NORMAL EQUATION MATRIX
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
CHARACTER*99 SCCSID
DIMENSION A(*),NX(*)
COMMON/DENNIS/NR,N1,N2,ISTATE
C SCCSID='$Id: hogk.for 81724 2014-12-22 16:17:53Z jarir.saleh $ 20$Date: 2007/11/20 15:23:51 $ NGS'
*** SET STATE TO UNREDUCED
ISTATE=0
NR=N
N1=N+1
N2=N1+N
*** ZERO THE MATRIX
IF(NX(N1).LE.LENGTH) THEN
OPENN=.TRUE.
DO 1 I=1,NX(N1)
1 A(I)=0.D0
ELSE
OPENN=.FALSE.
ENDIF
RETURN
END
LOGICAL FUNCTION GETA(II,JJ,VAL,A,NX)
*** RETURN ELEMENT OF MATRIX
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DIMENSION A(*),NX(*)
COMMON/DENNIS/N,N1,N2,ISTATE
*** CONVERT EXTERNAL NUMBERS TO INTERNAL
IF(II.LT.N1) THEN
I=NX(N2+II)
ELSE
I=N1
ENDIF
IF(JJ.LT.N1) THEN
J=NX(N2+JJ)
ELSE
J=N1
ENDIF
IF(I.LE.J) THEN
IF(J.EQ.N1) THEN
VAL=A(NX(N)+I)
GETA=.TRUE.
ELSEIF(I.EQ.N) THEN
VAL=A(NX(N))
GETA=.TRUE.
ELSE
INDEX=NX(I)-I+J
IF(INDEX.GE.NX(I+1)) THEN
VAL=0.D0
GETA=.FALSE.
ELSE
VAL=A(INDEX)
GETA=.TRUE.
ENDIF
ENDIF
ELSE
IF(J.EQ.N) THEN
VAL=A(NX(N))
GETA=.TRUE.
ELSEIF(I.EQ.N1) THEN
VAL=A(NX(N)+J)
GETA=.TRUE.
ELSE
INDEX=NX(J)-J+I
IF(INDEX.GE.NX(J+1)) THEN
VAL=0.D0
GETA=.FALSE.
ELSE
VAL=A(INDEX)
GETA=.TRUE.
ENDIF
ENDIF
ENDIF
RETURN
END
LOGICAL FUNCTION PUTA(II,JJ,VAL,A,NX)
*** STORE ELEMENT OF MATRIX
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DIMENSION A(*),NX(*)
COMMON/DENNIS/N,N1,N2,ISTATE
*** CONVERT EXTERNAL NUMBERS TO INTERNAL
IF(II.LT.N1) THEN
I=NX(N2+II)
ELSE
I=N1
ENDIF
IF(JJ.LT.N1) THEN
J=NX(N2+JJ)
ELSE
J=N1
ENDIF
IF(I.LE.J) THEN
IF(J.EQ.N1) THEN
A(NX(N)+I)=VAL
PUTA=.TRUE.
ELSEIF(I.EQ.N) THEN
A(NX(N))=VAL
PUTA=.TRUE.
ELSE
INDEX=NX(I)-I+J
IF(INDEX.GE.NX(I+1)) THEN
PUTA=.FALSE.
ELSE
A(INDEX)=VAL
PUTA=.TRUE.
ENDIF
ENDIF
ELSE
IF(J.EQ.N) THEN
A(NX(N))=VAL
PUTA=.TRUE.
ELSEIF(I.EQ.N1) THEN
A(NX(N)+J)=VAL
PUTA=.TRUE.
ELSE
INDEX=NX(J)-J+I
IF(INDEX.GE.NX(J+1)) THEN
PUTA=.FALSE.
ELSE
A(INDEX)=VAL
PUTA=.TRUE.
ENDIF
ENDIF
ENDIF
RETURN
END
LOGICAL FUNCTION ADDOBS(C,IC,LEN,OBS,WT,A,NX)
*** ACCUMULATE OBSERVATIONS INTO NORMALS
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
LOGICAL IN
DIMENSION C(LEN),IC(LEN)
DIMENSION A(*),NX(*)
COMMON/DENNIS/N,N1,N2,ISTATE
*** LOOP OVER COEFFICIENTS
A(NX(N1))=A(NX(N1))+OBS*WT*OBS
DO 2 I=1,LEN
II=NX(N2+IC(I))
CIWT=C(I)*WT
A(NX(N)+II)=A(NX(N)+II)+CIWT*OBS
DO 2 J=I,LEN
JJ=NX(N2+IC(J))
*** CHECK IF COEFFICIENTS WITHIN PROFILE
IF(.NOT.IN(II,JJ,NX,INDEX)) THEN
ADDOBS=.FALSE.
RETURN
ENDIF
*** ACCUMULATE
2 A(INDEX)=A(INDEX)+CIWT*C(J)
*** ACCUMULATION SUCCESSFUL
ADDOBS=.TRUE.
RETURN
END
LOGICAL FUNCTION ADDCOR(C,IC,OBS,SIGOBS,LUNK,LOBS,A,NX,IFLAG)
*** ACCUMULATE CORRELATED OBSERVATIONS INTO NORMALS
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
LOGICAL IN
DIMENSION C(*),IC(LUNK),SIGOBS(LOBS,LOBS),OBS(LOBS)
DIMENSION A(*),NX(*)
COMMON/DENNIS/N,N1,N2,ISTATE
DATA TOL/1.D-10/
*** CHOLESKY FACTOR WEIGHT MATRIX
DO 1 I=1,LOBS
I1=I-1
IF(I1.GT.0) THEN
DO 2 K=1,I1
2 SIGOBS(I,I)=SIGOBS(I,I)-SIGOBS(K,I)*SIGOBS(K,I)
ENDIF
*** SINGULARITY TEST
IF(SIGOBS(I,I).LT.TOL) THEN
ADDCOR=.FALSE.
IFLAG=1
RETURN
ENDIF
*** RESUME CHOLESKY FACTOR
SIGOBS(I,I)=DSQRT(SIGOBS(I,I))
IF(I+1.LE.LOBS) THEN
DO 6 J=I+1,LOBS
IF(I1.GT.0) THEN
DO 4 K=1,I1
4 SIGOBS(I,J)=SIGOBS(I,J)-SIGOBS(K,I)*SIGOBS(K,J)
ENDIF
SIGOBS(I,J)=SIGOBS(I,J)/SIGOBS(I,I)
6 SIGOBS(J,I)=SIGOBS(I,J)
ENDIF
1 CONTINUE
*** TRANSFORM OBSERVATIONS
CALL CHSOLV(SIGOBS,OBS,LOBS)
*** TRANSFORM COEFFICIENTS
DO 3 I=1,LUNK
J=(I-1)*LOBS+1
3 CALL CHSOLV(SIGOBS,C(J),LOBS)
*** ACCUMULATE TRANSFORMED OBSERVATIONS -- UNIT WEIGHT
DO 100 K=1,LOBS
*** LOOP OVER COEFFICIENTS
A(NX(N1))=A(NX(N1))+OBS(K)*OBS(K)
DO 5 I=1,LUNK
II=NX(N2+IC(I))
CI=C((I-1)*LOBS+K)
A(NX(N)+II)=A(NX(N)+II)+CI*OBS(K)
DO 5 J=I,LUNK
JJ=NX(N2+IC(J))
*** CHECK IF COEFFICIENTS WITHIN PROFILE
IF(.NOT.IN(II,JJ,NX,INDEX)) THEN
ADDCOR=.FALSE.
IFLAG=2
RETURN
ENDIF
*** ACCUMULATE
5 A(INDEX)=A(INDEX)+CI*C((J-1)*LOBS+K)
100 CONTINUE
*** ACCUMULATION SUCCESSFUL
ADDCOR=.TRUE.
IFLAG=0
RETURN
END
SUBROUTINE CHSOLV(A,X,LENG)
*** SOLVE AY=X FOR Y AND STORE RESULT IN X (GIVEN CHOLESKY FACTOR, A)
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DIMENSION A(LENG,LENG),X(LENG)
*** SUBSTITUTION
DO 5 I=1,LENG
I1=I-1
TEMP=0.D0
IF(I1.GT.0) THEN
DO 6 K=1,I1
6 TEMP=TEMP+A(K,I)*X(K)
ENDIF
5 X(I)=(X(I)-TEMP)/A(I,I)
RETURN
END
LOGICAL FUNCTION SOLVE(A,NX,TOL,ISING,GSING,LSING)
*** FACTOR AND SOLVE A LINEAR SYSTEM
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
LOGICAL IN
DIMENSION ISING(*),GSING(*)
DIMENSION A(*),NX(*)
COMMON/DENNIS/N,N1,N2,ISTATE
DATA BIG,TINY/1.D30,1.D-30/
NM1=N-1
LSING=0
IF(ISTATE.EQ.0) THEN
ISTATE=1
SOLVE=.TRUE.
*** CHOLESKY FACTOR
DO 1 I=N,1,-1
IDIAG=NX(I)
DIAG=A(IDIAG)
IF(I.NE.N) THEN
ITOP=NX(I+1)-1
ILEN=ITOP-IDIAG
IF(ILEN.GT.0) THEN
ICOL=ILEN+I
DO 2 J=I-1,1,-1
JDIAG=NX(J)
JTOP=NX(J+1)-1
JLEN=JTOP-JDIAG
JCOL=JLEN+J
IF(JCOL.GT.I) THEN
JI=JDIAG-J+I
IF(ICOL.LT.JCOL) THEN
NP=ILEN
IP=ITOP-NP+1
JP=JTOP-(JCOL-ICOL)-NP+1
ELSE
NP=JLEN+J-I
JP=JTOP-NP+1
IP=ITOP-(ICOL-JCOL)-NP+1
ENDIF
CALL INNERP(A(IP),A(JP),NP,PROD)
A(JI)=A(JI)-PROD
ENDIF
2 CONTINUE
ENDIF
IA=IDIAG+1
IB=NX(I+1)-1
DO 4 JI=IA,IB
4 A(IDIAG)=A(IDIAG)-A(JI)*A(JI)
ENDIF
*** SINGULARITY TEST
IF(DIAG.LE.0.D0) THEN
GOOGE=0.D0
ELSE
GOOGE=A(IDIAG)/DIAG
ENDIF
IF(GOOGE.LT.TOL) THEN
LSING=LSING+1
ISING(LSING)=NX(N1+I)
IF(GOOGE.LE.0.D0) THEN
GSING(LSING)=0.D0
ELSE
GSING(LSING)=GOOGE
ENDIF
SOLVE=.FALSE.
A(IDIAG)=BIG
ENDIF
*** RESUME CHOLESKY FACTOR
DIAG=DSQRT(A(IDIAG))
A(IDIAG)=DIAG
RDIAG=1.D0/DIAG
DO 5 J=1,I-1
JI=NX(J)-J+I
IF(JI.LT.NX(J+1)) THEN
TEMP=A(JI)*RDIAG
IF(DABS(TEMP).LT.TINY) THEN
A(JI)=0.D0
ELSE
A(JI)=TEMP
ENDIF
ENDIF
5 CONTINUE
1 CONTINUE
*** COMPLETE CHOLESKY FACTOR
*** FORWARD SUBSTITUTION
NM1=N-1
A(NX(N1)+N)=A(NX(N)+N)/A(NX(N))
DO 7 I=NM1,1,-1
TEMP=0.D0
IA=NX(I)+1
IB=NX(I+1)-1
K=I
DO 8 IK=IA,IB
K=K+1
TEMP=TEMP+A(IK)*A(NX(N1)+K)
8 CONTINUE
7 A(NX(N1)+I)=(A(NX(N)+I)-TEMP)/A(NX(I))
*** BASEMENT WINDOW
TEMP=A(NX(N1))
DO 10 I=1,N
Y=A(NX(N1)+I)
10 TEMP=TEMP-Y*Y
A(NX(N1))=TEMP
*** BACKWARD SOLUTION
DO 9 I=1,N
I1=I-1
TEMP=0.D0
DO 6 K=1,I1
KI=NX(K)-K+I
IF(KI.LT.NX(K+1)) TEMP=TEMP+A(KI)*A(NX(N)+K)
6 CONTINUE
9 A(NX(N)+I)=(A(NX(N1)+I)-TEMP)/A(NX(I))
ELSE
SOLVE=.FALSE.
ENDIF
RETURN
END
SUBROUTINE INNERP(X,Y,N,PROD)
*** COMPUTE INNER PRODUCT
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DIMENSION X(*),Y(*)
PROD=0.D0
DO 1 I=1,N
1 PROD=PROD+X(I)*Y(I)
RETURN
END
LOGICAL FUNCTION RESOLV(A,NX)
*** SOLVE THE FACTORED NORMAL EQUATIONS FOR A NEW R.H. SIDE
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
LOGICAL IN
DIMENSION A(*),NX(*)
COMMON/DENNIS/N,N1,N2,ISTATE
IF(ISTATE.NE.1) THEN
RESOLV=.FALSE.
ELSE
*** FORWARD SUBSTITUTION
RESOLV=.TRUE.
NM1=N-1
A(NX(N1)+N)=A(NX(N)+N)/A(NX(N))
DO 7 I=NM1,1,-1
TEMP=0.D0
IA=NX(I)+1
IB=NX(I+1)-1
K=I
DO 8 IK=IA,IB
K=K+1
TEMP=TEMP+A(IK)*A(NX(N1)+K)
8 CONTINUE
7 A(NX(N1)+I)=(A(NX(N)+I)-TEMP)/A(NX(I))
*** BASEMENT WINDOW
TEMP=A(NX(N1))
DO 10 I=1,N
Y=A(NX(N1)+I)
10 TEMP=TEMP-Y*Y
A(NX(N1))=TEMP
*** BACKWARD SOLUTION
DO 9 I=1,N
I1=I-1
TEMP=0.D0
DO 6 K=1,I1
KI=NX(K)-K+I
IF(KI.LT.NX(K+1)) TEMP=TEMP+A(KI)*A(NX(N)+K)
6 CONTINUE
9 A(NX(N)+I)=(A(NX(N1)+I)-TEMP)/A(NX(I))
ENDIF
RETURN
END
LOGICAL FUNCTION INVERT(A,NX)
*** INVERT THE CHOLESKY FACTOR
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
LOGICAL IN
DIMENSION A(*),NX(*)
COMMON/DENNIS/N,N1,N2,ISTATE
NM1=N-1
IF(ISTATE.NE.1) THEN
INVERT=.FALSE.
ELSE
ISTATE=2
INVERT=.TRUE.
*** PUT CHOLESKY RECIPROCALS ON DIAGONAL
DO 1 I=1,N
1 A(NX(I))=1.D0/A(NX(I))
*** COMPUTE GAUSSIAN FACTOR FROM CHOLESKY FACTOR
DO 2 I=N,2,-1
DIAG=A(NX(I))
DO 7 J=1,I
JI=NX(J)-J+I
IF(JI.LT.NX(J+1)) A(JI)=DIAG*A(JI)
7 CONTINUE
2 CONTINUE
A(1)=A(1)*A(1)
*** PROCEED BY COLUMNS--TOP TO BOTTOM
DO 6 I=2,N
*** SAVE I-TH COL IN SCRATCH SPACE
DO 3 J=1,I-1
JI=NX(J)-J+I
IF(JI.LT.NX(J+1)) A(NX(N1)+J)=-A(JI)
3 CONTINUE
*** GET INVERSE OF OFF DIAGONAL ELEMENTS OF I-TH COL
DO 5 J=1,I-1
JI=NX(J)-J+I
IF(JI.LT.NX(J+1)) THEN
A(JI)=0.D0
DO 4 K=1,I-1
KI=NX(K)-K+I
IF(KI.LT.NX(K+1)) THEN
YK=A(NX(N1)+K)
IF(K.LT.J) THEN
KJ=NX(K)-K+J
IF(KJ.LT.NX(K+1)) A(JI)=A(JI)+YK*A(KJ)
ELSE
JK=NX(J)-J+K
IF(JK.LT.NX(J+1)) A(JI)=A(JI)+YK*A(JK)
ENDIF
ENDIF
4 CONTINUE
ENDIF
5 CONTINUE
*** GET INVERSE OF DIAGONAL AT I-TH COL
DO 8 J=1,I-1
JI=NX(J)-J+I
IF(JI.LT.NX(J+1)) THEN
A(NX(I))=A(NX(I))+A(JI)*A(NX(N1)+J)
ENDIF
8 CONTINUE
6 CONTINUE
ENDIF
RETURN
END
LOGICAL FUNCTION PROP(C,IC,LEN,VAR,A,NX,IFLAG)
*** COMPUTE VARIANCE BY LINEAR ERROR PROPAGATION
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
LOGICAL IN
DIMENSION C(LEN),IC(LEN)
DIMENSION A(*),NX(*)
COMMON/DENNIS/N,N1,N2,ISTATE
*** VERIFY PARAMETER COVARIANCE AVAILABLE
IF(ISTATE.NE.2) THEN
IFLAG=1
PROP=.FALSE.
ELSE
VAR=0.D0
DO 20 I=1,LEN
II=NX(N2+IC(I))
VAR=VAR+C(I)*C(I)*A(NX(II))
I1=I+1
IF(I1.LE.LEN) THEN
C2=C(I)+C(I)
DO 10 J=I1,LEN
JJ=NX(N2+IC(J))
IF(.NOT.IN(II,JJ,NX,INDEX)) THEN
IFLAG=2
PROP=.FALSE.
RETURN
ENDIF
10 VAR=VAR+C2*C(J)*A(INDEX)
ENDIF
20 CONTINUE
IFLAG=0
PROP=.TRUE.
ENDIF
RETURN
END
LOGICAL FUNCTION PROPCV(C1,IC1,LEN1,C2,IC2,LEN2,COV,A,NX,IFLAG)
*** COMPUTE COVARIANCE BY LINEAR ERROR PROPAGATION
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
LOGICAL GETA
DIMENSION C1(LEN1),IC1(LEN1)
DIMENSION C2(LEN2),IC2(LEN2)
DIMENSION A(*),NX(*)
COMMON/DENNIS/N,N1,N2,ISTATE
*** VERIFY PARAMETER COVARIANCES AVAILABLE
IF(ISTATE.NE.2) THEN
IFLAG=1
PROPCV=.FALSE.
ELSE
COV=0.D0
DO 20 I=1,LEN1
CI=C1(I)
II=IC1(I)
DO 10 J=1,LEN2
JJ=IC2(J)
IF(.NOT.GETA(II,JJ,SIG,A,NX)) THEN
IFLAG=2
PROPCV=.FALSE.
RETURN
ENDIF
10 COV=COV+CI*C2(J)*SIG
20 CONTINUE
IFLAG=0
PROPCV=.TRUE.
ENDIF
RETURN
END
LOGICAL FUNCTION CORR(A,NX)
*** COMPUTE CORRELATION MATRIX FROM COVARIANCE
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
LOGICAL IN
DIMENSION A(*),NX(*)
COMMON/DENNIS/N,N1,N2,ISTATE
NM1=N-1
IF(ISTATE.NE.2) THEN
CORR=.FALSE.
ELSE
ISTATE=3
CORR=.TRUE.
*** CONVERT VARIANCES TO STANDARD DEVIATIONS
DO 1 I=1,N
1 A(NX(I))=DSQRT(A(NX(I)))
*** DIVIDE EACH OFF-DIAGONAL ROW ELEMENT BY DIAGONAL
DO 5 I=1,NM1
RDIAG=1.D0/A(NX(I))
IA=NX(I)+1
IB=NX(I+1)-1
IF(IA.LE.IB) THEN
DO 2 IJ=IA,IB
2 A(IJ)=A(IJ)*RDIAG
ENDIF
5 CONTINUE
*** DIVIDE EACH OFF-DIAGONAL COLUMN ELEMENT BY DIAGONAL
DO 3 J=N,2,-1
RDIAG=1.D0/A(NX(J))
DO 3 I=1,J-1
IF(IN(I,J,NX,IJ)) A(IJ)=A(IJ)*RDIAG
3 CONTINUE
*** PLACE ONE'S ALONG DIAGONAL
DO 4 I=1,N
4 A(NX(I))=1.D0
ENDIF
RETURN
END
LOGICAL FUNCTION IN(I,J,NX,INDEX)
*** RETURN ELEMENT INDEX OF MATRIX PROFILE
*** CAUTION: I AND J ARE INTERNAL NUMBERS !!
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DIMENSION NX(*)
COMMON/DENNIS/N,N1,N2,ISTATE
IF(I.LE.J) THEN
IF(J.EQ.N1) THEN
INDEX=NX(N)+I
IN=.TRUE.
ELSEIF(I.EQ.N) THEN
INDEX=NX(N)
IN=.TRUE.
ELSE
INDEX=NX(I)-I+J
IF(INDEX.GE.NX(I+1)) THEN
IN=.FALSE.
ELSE
IN=.TRUE.
ENDIF
ENDIF
ELSE
IF(J.EQ.N) THEN
INDEX=NX(N)
IN=.TRUE.
ELSEIF(I.EQ.N1) THEN
INDEX=NX(N)+J
IN=.TRUE.
ELSE
INDEX=NX(J)-J+I
IF(INDEX.GE.NX(J+1)) THEN
IN=.FALSE.
ELSE
IN=.TRUE.
ENDIF
ENDIF
ENDIF
RETURN
END
subroutine openg(n,nx,nxleng)
*** initialize linked neighbor list
dimension nx(*)
common/kathy/nr,n1,n2,iemx,ifree
*** compute indicies
nr=n
n1=n+1
n2=n1+n
*** compute maximum number of edges
*** insure iemx (2*edges) is even
iemx=((nxleng-n-n-1)/6)*2
do 1 i=1,n
1 nx(i)=-i
ifree=1
return
end
logical function addcon(ic,len,nx)
*** add observation equation connections to neighbor list
logical addg
dimension ic(*),nx(*)
common/kathy/n,n1,n2,iemx,ifree
if(len.le.1) then
c write(*,2) len
2 format('len error in addcon',i5)
stop
endif
l1=len-1
*** loop over all connections
do 1 i=1,l1
do 1 j=i+1,len
if(.not.addg(ic(i),ic(j),nx(1),nx(n1),nx(n1+iemx))) then
addcon=.false.
return
endif
1 continue
addcon=.true.
return
end
logical function addg(i,j,ihead,nbr,link)
*** add a connection
dimension ihead(*),nbr(*),link(*)
logical conect
common/kathy/n,n1,n2,iemx,ifree
addg=.true.
*** add connection if it does not exist
if(.not.conect(i,j,ipoint,ihead,nbr,link)) then
if(ipoint.eq.0) then
ihead(i)=ifree
else
if(link(ipoint).ne.-i) then
c write(*,1) i,j,ipoint,link(ipoint)
1 format(4i5,' -- graph subroutine link error')
stop
else
link(ipoint)=ifree
endif
endif
nbr(ifree)=j
link(ifree)=-i
ifree=ifree+1
if(ifree.gt.iemx) then
addg=.false.
return
endif
endif
*** add connection in other direction
if(.not.conect(j,i,ipoint,ihead,nbr,link)) then
if(ipoint.eq.0) then
ihead(j)=ifree
else
if(link(ipoint).ne.-j) then
c write(*,1) i,j,ipoint,link(ipoint)
stop
else
link(ipoint)=ifree
endif
endif
nbr(ifree)=i
link(ifree)=-j
ifree=ifree+1
if(ifree.gt.iemx) then
addg=.false.
return
endif
endif
return
end
logical function conect(i,j,ipntx,ihead,nbr,link)
*** is connection in the graph?
*** if not, find pointer to end of linked list
dimension ihead(*),nbr(*),link(*)
ipntx=0
ipoint=ihead(i)
1 if(ipoint.lt.0) then
conect=.false.
return
else
if(nbr(ipoint).eq.j) then
conect=.true.
return
endif
ipntx=ipoint
ipoint=link(ipoint)
go to 1
endif
return
end
subroutine reordr(nx)
*** reorder unknowns into king order
*** for minimum profile, row storage, upper triangle
dimension nx(*)
common/kathy/n,n1,n2,iemx,ifree
*** produce adjacency structure from linked list
call trnslt(nx(1),nx(n1),nx(n1+iemx),nx(n1+3*iemx),nx(n1+2*iemx))
*** produce king order
call gking(n,nx(n1+3*iemx),nx(n1+2*iemx),nx(n2+1),nx(n1+1),
* nx(3*n+2))
*** reverse order (for row profile)
do 776 i=1,n
776 nx(n2+1-i)=nx(n2+i)
*** invert order
do 777 i=1,n
j=nx(n1+i)
777 nx(n2+j)=i
*** produce profile
call profil(nx(1),nx(n1+3*iemx),nx(n1+2*iemx))
return
end
subroutine trnslt(ihead,nbr,link,nbrpnt,nbrlst)
*** translate linked neighbor list into adjacency structure
dimension ihead(*),nbr(*),link(*),nbrpnt(*),nbrlst(*)
common/kathy/n,n1,n2,iemx,ifree
ifree=1
do 100 i=1,n
ipoint=ihead(i)
nbrpnt(i)=ifree
1 if(ipoint.gt.0) then
nbrlst(ifree)=nbr(ipoint)
ipoint=link(ipoint)
ifree=ifree+1
go to 1
endif
100 continue
nbrpnt(n1)=ifree
return
end
subroutine profil(nx,nbrpnt,nbrlst)
*** find variable column profile from adjacency structure
dimension nx(*),nbrpnt(*),nbrlst(*)
common/kathy/n,n1,n2,iemx,ifree
*** store row widths in nx(2 thru n1)
do 20 ir=1,n
i=nx(n2+ir)
lbegin=nbrpnt(ir)
lend=nbrpnt(ir+1)-1
lrow=0
if(lbegin.le.lend) then
do 10 ipt=lbegin,lend
jc=nbrlst(ipt)
j=nx(n2+jc)
if(j.gt.i) then
len=j-i
if(len.gt.lrow) lrow=len
endif
10 continue
endif
20 nx(i+1)=lrow+1
*** convert row widths to profile
nx(1)=1
do 30 i=2,n
30 nx(i)=nx(i)+nx(i-1)
nx(n1)=nx(n)+n1
return
end
subroutine gking(neqns,nbrpnt,nbrlst,neword,mask,levptr)
*** find king ordering for a general graph
*** for each component, ordering is found by subroutine king
dimension nbrlst(*),mask(*),neword(*),levptr(*),nbrpnt(*)
*** initialize component mask
do 100 i=1,neqns
100 mask(i)=1
num=1
*** loop over all equations
do 200 i=1,neqns
if(mask(i).eq.0) go to 200
iroot=i
*** find pseudo-peripheral node
call fnroot(iroot,nbrpnt,nbrlst,mask,nlvl,levptr,neword(num))
*** number component in king order
call king(iroot,nbrpnt,nbrlst,mask,neword(num),lcomp,levptr)
num=num+lcomp
if(num.gt.neqns) return
200 continue
return
end
subroutine fnroot(iroot,nbrpnt,nbrlst,mask,nlvl,levptr,ls)
*** find pseudo-peripheral node
dimension nbrlst(*),ls(*),mask(*),levptr(*),nbrpnt(*)