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
|
C Copyright 1981-2007 ECMWF
C
C Licensed under the GNU Lesser General Public License which
C incorporates the terms and conditions of version 3 of the GNU
C General Public License.
C See LICENSE and gpl-3.0.txt for details.
C
LOGICAL FUNCTION JACOBIF(DATA,NM,W,ROTANG)
C
C---->
C**** JACOBIF
C
C Purpose
C -------
C
C Rotates spectral field by latitude (Fujitsu only).
C
C
C Interface
C ---------
C
C IRET = JACOBIF(DATA,NM,W,ROTANG)
C
C Input
C -----
C
C NM - Triangular truncation number of the field.
C DATA - Linear array of REAL*8s of size (NM+1)*(NM+2)
C holding the field.
C W - Work array of REAL*8s of size (NM+1)*(NM+2).
C ROTANG - Rotation angle (degrees, REAL*8)
C (degrees, negative => rotate counter-clockwise about the
C new Z-axis).
C
C
C Output
C ------
C
C DATA - The transformed field.
C
C Function returns .FALSE. if data cannot be transformed.
C
C
C Method
C ------
C
C See reference paper below.
C
C Coefficients are read into or are created in memory. A large
C amount of memory may be required; eg, for truncation NM:
C 8*(NM*(2*NM*NM + 9*NM +13)/3) bytes.
C
C Optionally, if the environment variable PP_SAVE_ROT is set, a
C file of coefficients can be created in the directory given by
C environment variable PP_ROT_DIR.
C
C The name of the file of rotation coefficients indicates the
C triangular truncation NM and the rotation angle ROTANG:
C
C $PP_ROT_DIR/rot_coefs_Tttt_nnnnnnnnn
C or $TMPDIR/rot_coefs_Tttt_nnnnnnnnn
C
C where:
C ttt = triangular truncation
C nnnnnnnnn = ROTANG*100000,
C or
C $PP_ROT_DIR/rot_coefs_Tttt_Mnnnnnnnn
C or $TMPDIR/rot_coefs_Tttt_Mnnnnnnnn
C
C where:
C ttt = triangular truncation
C nnnnnnnn = -ROTANG*100000 if ROTANG is negative.
C
C
C Externals
C ---------
C
C INTLOG - Logs messages.
C INTLOGR - Logs messages.
C GETENV - To get environment variable data.
C UNLINK - To remove a file.
C PPALLOW - Checks if the rotation coefficients can go into mrfs.
C
C
C Author
C ------
C
C J.D.Chambers ECMWF April 1999
C
C
C Reference.
C ----------
C
C "Spectral synthesis on rotated and regular grids"
C by P.Lynch and R.McGrath (Irish Meteorological Service).
C
C
C----<
C -----------------------------------------------------------------|
C
IMPLICIT NONE
C
#include "jparams.h"
#include "parim.h"
C
C Function arguments.
C
REAL*8 DATA, W
DIMENSION DATA(*), W(*)
INTEGER NM
REAL*8 ROTANG
C
C Parameters.
C
REAL*8 EPS
PARAMETER(EPS = 1.0E-10)
INTEGER JPNM_MAX, JPMAXMM, JPMEM20
PARAMETER( JPNM_MAX = 640 )
PARAMETER( JPMAXMM = 3 )
C `--> maximum number of memory slots
C used for rotation coefficients
PARAMETER( JPMEM20 = 20 )
C `--> offset in memory allocation table of
C first memory slot for rotation
C coefficients
C
C Local variables.
C
LOGICAL LFOR, LALLOW
INTEGER I, ISKIP, J, N, MM, K, IEND
INTEGER NN, M, NDEX, IMEMORY
C
REAL*4 SROTANG
REAL*8 SIMAG, S, TEMP, DROTANG
REAL*8 RAD, TANB, SINB, COSB, Q, RNKN, BNKN, SQNN
REAL*8 SQNN1, SQ2N, PKN, PK1N, RNKN1, SREAL ,RNK0, RNK1
REAL*8 INDEXR(JPNM_MAX), INDEXI(JPNM_MAX)
REAL*8 MINUS1(JPNM_MAX)
REAL*8 FACTOR(JPNM_MAX)
REAL*8 WISQR(JPNM_MAX)
REAL*8 WIB(JPNM_MAX)
REAL*8 WIR(JPNM_MAX)
REAL*8 WIDAT(2*JPNM_MAX)
C
CHARACTER*256 FILENAME
CHARACTER*40 COEFILE
DATA COEFILE/'rot_coefs_Tnnn_nnnnnnnnn'/
C
INTEGER IUNIT, IRET, ILAT, OLDLAT(3), OLDTRUN(3), IOFFSET
INTEGER IFSIZE, ICNDEX
INTEGER LOOP, NMP1TM, MAXMEM
LOGICAL LINMEM, LEXIST
C
INTEGER CURRENT, OLDEST
DATA OLDEST/1/, MAXMEM/JPMAXMM/
SAVE OLDEST, MAXMEM
C
DATA OLDLAT/3*9999999/, OLDTRUN/3*0/
DATA LINMEM/.FALSE./, LEXIST/.FALSE./
SAVE IUNIT, ILAT, OLDLAT, OLDTRUN, COEFILE, LINMEM, LEXIST
C
#ifdef POINTER_64
Cjdc INTEGER*8 ICOEFF
#endif
REAL*8 ACOEFF
DIMENSION ACOEFF(1)
POINTER ( ICOEFF, ACOEFF )
C
C Externals
C
INTEGER JCHMOD, UNLINK
LOGICAL PPALLOW
EXTERNAL JCHMOD, UNLINK, PPALLOW
C
C Statement function
C
REAL*8 A, B
LOGICAL ABSCHK
ABSCHK(A,B) = (ABS(A-B) .LT. EPS*(ABS(A) + ABS(B)))
C
C W array: 1 -> (NM+1)*(NM+2) for PMN/SQRT(2*N+1) values.
C
C RNKM values in WIR (for M>0),
C in WIB (M<0).
C Array of temporary SQRT values in WISQR, and
C temporary transformed data in WIDAT
C
C -----------------------------------------------------------------|
C* Section 1. Initialise
C -----------------------------------------------------------------|
C
100 CONTINUE
C
JACOBIF = .FALSE.
C
LALLOW = PPALLOW(NM,ROTANG)
C
CALL INTLOG(JP_DEBUG,'JACOBIF: truncation = ', NM)
SROTANG = SNGL(ROTANG)
CALL INTLOGR(JP_DEBUG,'JACOBIF: rotation angle = ', SROTANG)
C
C Exit immediately if rotation angle is zero.
C
IF (ABS(ROTANG).LT.EPS) THEN
CALL INTLOG(JP_DEBUG,'JACOBIF: No rotation necessary',JPQUIET)
JACOBIF = .TRUE.
GOTO 999
ENDIF
C
C Change to radians.
C
RAD = 180.0/PPI
DROTANG = ROTANG/RAD
TANB = TAN(DROTANG/(2.0))
SINB = SIN(DROTANG)
COSB = COS(DROTANG)
Q = SQRT(2.0)/2.0
C
ICNDEX = 0
C
C -----------------------------------------------------------------|
C* Section 2. Generate PMN/SQRT(2*N+1) values in W.
C -----------------------------------------------------------------|
C
200 CONTINUE
C
W(1) = 1.0
W(2) = COSB
C
ISKIP = NM + 1
!OCL SCALAR
DO I = 1,ISKIP
W(1+ISKIP*I) = W(1+ISKIP*I-ISKIP)*SINB*
X SQRT(DBLE(2*I-1)/DBLE(2*I))
W(1+ISKIP*I+1) = COSB*DSQRT(DBLE(2*I+1))*W(1+ISKIP*I)
ENDDO
C
!OCL SCALAR
DO I = 2,ISKIP-1
C
!OCL VECTOR
DO J = 0,ISKIP-I+1
FACTOR(J) = 1.0/DSQRT(DBLE((I+2*J)*I))
ENDDO
C
DO J = 0,ISKIP-I+1
W(I+J*ISKIP+1) = COSB*DBLE(2*I+2*J-1)
X *FACTOR(J)*W(I+J*ISKIP)
X - DSQRT(DBLE((I-1)*(I+2*J-1)))
X *FACTOR(J)*W(I+J*ISKIP-1)
ENDDO
C
ENDDO
C
MINUS1(1) = -1
!OCL SCALAR
DO I = 2, JPNM_MAX
MINUS1(I) = -MINUS1(I-1)
ENDDO
C
C -----------------------------------------------------------------|
C* Section 3. Pick up the rotation coefficients RNKM.
C -----------------------------------------------------------------|
C
300 CONTINUE
C
C Change the interpolation coefficents if the input latitude is
C not the same as the one used the last time through.
C
ILAT = NINT(ROTANG*100000)
C
DO LOOP = 1, MAXMEM
IF( ILAT.EQ.OLDLAT(LOOP).AND.(OLDTRUN(LOOP).EQ.NM) ) THEN
C
C Set flags to show the rotation coefficients are in memory
C
LINMEM = .TRUE.
LEXIST = .TRUE.
CURRENT = LOOP + JPMEM20 - 1
CALL INTLOG(JP_DEBUG,
X 'JACOBIF: Existing memory slot re-used = ', CURRENT)
CALL JMEMHAN( CURRENT, ICOEFF, IMEMORY, 1, IRET)
IF( IRET.NE.0 ) THEN
CALL INTLOG(JP_FATAL,
X 'JACOBIF: Failed to pick up existing memory pool',CURRENT)
JACOBIF = .FALSE.
GOTO 999
ENDIF
GOTO 310
ENDIF
ENDDO
C
LINMEM = .FALSE.
LEXIST = .FALSE.
CURRENT = OLDEST + JPMEM20 - 1
OLDLAT(OLDEST) = ILAT
OLDTRUN(OLDEST) = NM
OLDEST = OLDEST + 1
IF( OLDEST.GT.MAXMEM ) OLDEST = 1
CALL INTLOG(JP_DEBUG,
X 'JACOBIF: Different memory slot selected = ', CURRENT)
C
310 CONTINUE
C
IF( .NOT. LINMEM ) THEN
C
C Calculate the coefficients file size (coefficients are REAL*8)
C
IFSIZE = 8*(NM*(2*NM*NM + 9*NM +13)/3)
C
C Allocate memory for the REAL*8 coefficients
C
#ifdef REAL_8
IMEMORY = (NM*(2*NM*NM + 9*NM +13)/3)
#else
IMEMORY = 2*(NM*(2*NM*NM + 9*NM +13)/3)
#endif
C
320 CONTINUE
C
CALL JMEMHAN( CURRENT, ICOEFF, IMEMORY, 1, IRET)
IF( IRET.NE.0 ) THEN
C
C If memory allocation fails, reduce the number of slots in the
C memory pool. Exit if the pool is already down to one slot.
C
IF( MAXMEM.LT.2 ) THEN
CALL INTLOG(JP_FATAL,
X 'JACOBIF: memory allocation error',ICOEFF)
JACOBIF = .FALSE.
GOTO 999
ENDIF
MAXMEM = MAXMEM - 1
CALL INTLOG(JP_DEBUG,
X 'JACOBIF: Reduce number of memory slots to ', MAXMEM)
LINMEM = .FALSE.
LEXIST = .FALSE.
OLDEST = 1
OLDLAT(OLDEST) = ILAT
OLDTRUN(OLDEST) = NM
CURRENT = OLDEST + JPMEM20 - 1
OLDEST = OLDEST + 1
IF( OLDEST.GT.MAXMEM ) OLDEST = 1
CALL INTLOG(JP_DEBUG,
X 'JACOBIF: Different memory slot selected = ', CURRENT)
GOTO 320
ENDIF
ICNDEX = 0
C
C If the file already exists, read it into memory.
C For 'standard' rotations try PP_ROT_DIR, otherwise TMPDIR.
C
IF( LALLOW ) THEN
CALL GETENV('PP_ROT_DIR',FILENAME)
ELSE
CALL GETENV('TMPDIR',FILENAME)
ENDIF
IOFFSET = INDEX(FILENAME,' ')
IF( IOFFSET.EQ.1) THEN
CALL INTLOG(JP_WARN,
X 'JACOBIF: Unable to open rotation coefficents.',JPQUIET)
C
ELSE
C
CALL INTLOG(JP_DEBUG,
X 'JACOBIF: Existing coefficients sought in:',JPQUIET)
CALL INTLOG(JP_DEBUG,
X 'JACOBIF: '// FILENAME(1:IOFFSET-1),JPQUIET)
C
WRITE(COEFILE(12:14),'(I3.3)') NM
IF( ILAT.GE.0) THEN
WRITE(COEFILE(16:),'(I9.9)') ILAT
ELSE
COEFILE(16:) = 'M'
WRITE(COEFILE(17:),'(I8.8)') -ILAT
ENDIF
FILENAME = FILENAME(1:IOFFSET-1) // '/' // COEFILE
IOFFSET = INDEX(FILENAME,' ') - 1
C
CALL PBOPEN(IUNIT,FILENAME(1:IOFFSET),'r',IRET)
IF( IRET.EQ.0 ) THEN
C
C Let user know that a existing file has been opened
C
CALL INTLOG(JP_DEBUG,
X 'JACOBIF: Existing coefficients found in file:',JPQUIET)
CALL INTLOG(JP_DEBUG,'JACOBIF: '// COEFILE, JPQUIET)
C
C Read coefficients into memory
C
CALL PBREAD(IUNIT,ACOEFF,IFSIZE,IRET)
IF( IRET.NE.IFSIZE ) THEN
CALL INTLOG(JP_WARN,'JACOBIF: PBREAD failed.',JPQUIET)
ELSE
C
C Set flags to show the rotation coefficients are in memory
C and exist.
C
LINMEM = .TRUE.
LEXIST = .TRUE.
ENDIF
C
CALL PBCLOSE(IUNIT,IRET)
ENDIF
C
ENDIF
C
ENDIF
C
C -----------------------------------------------------------------|
C* Section 4. Generate the rotation coefficients RNKM.
C -----------------------------------------------------------------|
C
400 CONTINUE
C
C
C Generate the rotation coefficients RNKM (K = M dashed in note)
C and store in W. For K = 0 special case.
C
C PMN = W(M*(NM+1) + (N-M+1))
C
!OCL VECTOR
DO 630 N = 1,NM
RNKN = (0.5*(1.0 + COSB))**N
BNKN = (0.5*(1.0 - COSB))**N
SQNN = DSQRT(DBLE((N+1)*N))
SQNN1 = SQNN*SINB
SQ2N = DSQRT(2.0/DBLE(N))/SINB
C
C Save SQRTS.
C
!OCL VECTOR
DO MM = 0,N
WISQR(MM+1) = DSQRT(DBLE((N+MM)*(N-MM+1)))*SINB
ENDDO
C
NN = 1
C
C Generate RNKM, M = 0 to N.
C
!OCL SCALAR
DO 590 K = N,0,-1
C
C If the coefficients are not (yet) in memory, they have to
C be calculated.
C
IF( .NOT. LINMEM ) THEN
C
PKN = W(K*(NM+1) + (N-K+1))
IF (K.EQ.0) GOTO 500
C
C For K > 0, go forward from zero.
C
PK1N = W((K-1)*(NM+1) + (N-(K-1)+1))
C
C Flip sign if necessary.
C
IF (MOD(K,2).NE.0)THEN
PKN = -PKN
ELSE
PK1N = -PK1N
ENDIF
C
C Work using forward recurrence as long as coefficient
C calculated passes checks.
C
LFOR = .TRUE.
C
RNK0 = PKN
RNK1 = (-DBLE(K)*TANB*PKN + (WISQR(K+1)/SINB)*PK1N)/SQNN
C
C Recurrence starts at 2 for M = 0
C
WIR(1) = RNK0
WIR(2) = RNK1
C
!OCL SCALAR
DO MM = 1,N-1
WIR(MM+2) = (2.0*WIR(MM+1)*(DBLE(MM)*COSB-DBLE(K))
X - WISQR(MM+1)*WIR(MM)) /WISQR(MM+2)
C
C Apply check to generated coefficient to see if its
C absolute value is greater than 1. If so, have to
C switch to using backwards recurrences.
C
IF (ABS(WIR(MM+2)).GT.1.0)THEN
LFOR = .FALSE.
IEND = MM + 3
GOTO 435
ENDIF
ENDDO
C
C If forward recurrence appears OK so far,
C test last element RNKN by comparing with WIR(N+1).
C
IEND = N + 2
IF (ABSCHK(RNKN,WIR(N+1))) GOTO 445
C
C If test failed, try generating coefficients using
C backwards recurrences.
C
435 CONTINUE
C
C Work backwards from the top.
C Specify N; K is already set from the loop above.
C Stop at M = 1 (NOT 0).
C
RNKN1 = RNKN*SQ2N*(DBLE(N)*COSB-DBLE(K))
WIR(N+1) = RNKN
C
C Check whether difference is within prescribed tolerance.
C
IF (LFOR .AND. ABSCHK(RNKN1,WIR(N))) GO TO 445
WIR(N) = RNKN1
C
C For M = 0:
C
!OCL SCALAR
DO MM = N-1,1,-1
S = (2.0*WIR(MM+1)*(DBLE(MM)*COSB-DBLE(K))
X - (WISQR(MM+2)*WIR(MM+2))) / WISQR(MM+1)
C
C Accept these if forward recursion failed before
C reaching this point.
C
IF (MM+1.LT.IEND)THEN
IF (ABSCHK(S,WIR(MM))) GOTO 445
ENDIF
WIR(MM) = S
C
C If absolute value is greater than 1, give up gracefully
C
IF (ABS(S).GT.1.0) GOTO 920
C
ENDDO
C
GOTO 920
C
445 CONTINUE
C
C Now RNKM for M = 0,-N
C
C RNKM M = -1,-N
C
C Forward recurrence starts at 1 for M = 0, 2 for -1 etc.
C
LFOR = .TRUE.
C
WIB(1) = RNK0
WIB(2) = -RNK1-RNK0*DBLE(2*K)/(SQNN1)
C
!OCL SCALAR
DO MM = 1,(N-1)
WIB(MM+2) = (2.0*WIB(MM+1)*(DBLE(-MM)*COSB-DBLE(K))
X - WISQR(MM+1)*SINB*WIB(MM)) /WISQR(MM+2)
C
C Apply check to generated coefficient to see if its
C absolute value is greater than 1. If so, have to
C switch to using backwards recurrences.
C
IF (ABS(WIB(MM+2)).GT.1.0)THEN
LFOR = .FALSE.
IEND = MM + 3
GOTO 455
ENDIF
ENDDO
C
C If forward recurrence appears OK so far,
C test last element BNKN by comparing with WIB(N+1).
C
IEND = N + 1
IF (ABSCHK(BNKN,WIB(N+1))) GOTO 500
C
C If test failed, try generating coefficients using backwards
C recurrences.
C
455 CONTINUE
C
C Get R values.
C First RNKN, then next highest RNKN1.
C
RNKN1 = -BNKN*SQ2N*(DBLE(N)*COSB + DBLE(K))
C
C Work backwards from the top.
C Specify N; K is already set from the loop above.
C
C Stop at M = 1 (NOT 0).
C
WIB(N+1) = BNKN
IF (LFOR .AND. ABSCHK(RNKN1,WIB(N))) GOTO 500
WIB(N) = RNKN1
C
!OCL SCALAR
DO MM = N-1,1,-1
S = (2.0*WIB(MM+1)*(DBLE(-MM)*COSB-DBLE(K))
X - (WISQR(MM+2)*WIB(MM+2))) / WISQR(MM+1)
C
C Accept backwards generated coefficients if forward
C recursion failed before reaching this point.
C
IF ( (MM.LT.IEND ) .AND. ABSCHK(S,WIB(MM)) ) GOTO 500
WIB(MM) = S
C
C If absolute value is greater than 1, give up.
C
IF (ABS(S).GT.1.0) GOTO 910
C
ENDDO
C
C End of backwards recurrences reached with no agreed
C coefficients, give up.
C
GOTO 910
C
C -----------------------------------------------------------------|
C* Section 5. Got RNKM. Now transform spectral data.
C -----------------------------------------------------------------|
C
500 CONTINUE
C
C Put coefficients in allocated memory
C
!OCL VECTOR
DO LOOP = 1, N+1
ACOEFF(ICNDEX +LOOP) = WIR(LOOP)
ACOEFF(ICNDEX+N+1+LOOP) = WIB(LOOP)
ENDDO
C
ENDIF
C
C Coefficients are in memory
C
PKN = W(K*(NM+1) + (N-K+1))
PK1N = W((K-1)*(NM+1) + (N-(K-1)+1))
C
C Flip sign if necessary.
C
IF (MOD(K,2).NE.0)THEN
PKN = -PKN
ELSE
PK1N = -PK1N
ENDIF
C
!OCL VECTOR
DO LOOP = 1, N+1
WIR(LOOP) = ACOEFF(ICNDEX +LOOP)
WIB(LOOP) = ACOEFF(ICNDEX+N+1+LOOP)
ENDDO
ICNDEX = ICNDEX + 2*(N+1)
C
C
C Special case when K=0.
C
IF( K.EQ.0) THEN
C
SREAL = DATA(2*(N+1)-1)*PKN
SIMAG = 0.0
!OCL VECTOR
DO M = 1,N
SREAL = SREAL
X + 2.0*DATA(2*((NM+1)*M-((M-1)*M)/2+1+N-M)-1)
X * W((NM+1)*M+(N-M+1))
ENDDO
C
NDEX = 1+N
WIDAT(NN) = SREAL
WIDAT(NN+1) = SIMAG
NN = NN + 2
C
ELSE
C
SREAL = DATA(2*(N+1)-1)*PKN
SIMAG = 0.0
!OCL VECTOR
DO M = 1,N
INDEXR(M) = 2*((NM+1)*M-((M-1)*M)/2+1+N-M)-1
ENDDO
!OCL VECTOR
DO M = 1,N
INDEXI(M) = INDEXR(M) + 1
ENDDO
C
!OCL VECTOR
DO M = 1,N
SREAL = SREAL +
X DATA(INDEXR(M))
X * (WIR(M+1)+WIB(M+1)*MINUS1(M))
SIMAG = SIMAG -
X DATA(INDEXI(M))
X * (-WIR(M+1)+WIB(M+1)*MINUS1(M))
ENDDO
C
NDEX = (NM+1)*K - ((K-1)*K)/2+1+N-K
WIDAT(NN) = SREAL
WIDAT(NN+1) = SIMAG
NN = NN + 2
ENDIF
C
C Update RNKN at both ends of the forward and backward
C recurrences.
C
TEMP = DSQRT(DBLE(N+K)/DBLE(N-K+1))
RNKN = RNKN*TEMP*SINB/(1+COSB)
BNKN = -BNKN*TEMP*(1+COSB)/SINB
C
C End of inner loop.
C
590 CONTINUE
C
C -----------------------------------------------------------------|
C* Section 6. Now place the values of the rotated spectral
C coefficients in DATA.
C -----------------------------------------------------------------|
C
600 CONTINUE
C
NN = 1
!OCL VECTOR
DO K = N,0,-1
NDEX = (NM+1)*K - ((K-1)*K)/2+1+N-K
DATA(2*NDEX-1) = WIDAT(NN)
DATA(2*NDEX) = WIDAT(NN+1)
NN = NN + 2
C
ENDDO
C
C End of outer loop.
C
630 CONTINUE
C
C -----------------------------------------------------------------|
C* Section 9. Return.
C -----------------------------------------------------------------|
C
900 CONTINUE
C
LINMEM = .TRUE.
C
IF( .NOT. LEXIST ) THEN
C
C If the environment variable PP_SAVE_ROT is set, save the
C rotation coefficients in a file.
C 'Standard' rotations go into PP_ROT_DIR, others into TMPDIR.
C
LEXIST = .TRUE.
CALL GETENV('PP_SAVE_ROT',FILENAME)
IOFFSET = INDEX(FILENAME,' ')
IF( IOFFSET.GT.1 ) THEN
IF( LALLOW ) THEN
CALL GETENV('PP_ROT_DIR',FILENAME)
ELSE
CALL GETENV('TMPDIR',FILENAME)
ENDIF
IOFFSET = INDEX(FILENAME,' ')
IF( IOFFSET.EQ.1) THEN
CALL INTLOG(JP_WARN,
X 'JACOBIF: Unable to save rotation coefficents.',JPQUIET)
C
ELSE
C
C Let user know that a new file is being created.
C
CALL INTLOG(JP_DEBUG,
X 'JACOBIF: Creating new coefficients in directory',JPQUIET)
CALL INTLOG(JP_DEBUG,
X 'JACOBIF: '// FILENAME(1:IOFFSET-1),JPQUIET)
C
WRITE(COEFILE(12:14),'(I3.3)') NM
IF( ILAT.GE.0) THEN
WRITE(COEFILE(16:),'(I9.9)') ILAT
ELSE
COEFILE(16:) = 'M'
WRITE(COEFILE(17:),'(I8.8)') -ILAT
ENDIF
FILENAME = FILENAME(1:IOFFSET-1) // '/' // COEFILE
IOFFSET = INDEX(FILENAME,' ')
C
CALL PBOPEN(IUNIT,FILENAME(1:IOFFSET-1),'w',IRET)
IF( IRET.NE.0 ) THEN
CALL INTLOG(JP_WARN,
X 'JACOBIF: PBOPEN for write failed',JPQUIET)
GOTO 995
ENDIF
C
CALL INTLOG(JP_DEBUG,
X 'JACOBIF: New coefficients filename:',JPQUIET)
CALL INTLOG(JP_DEBUG,'JACOBIF: '// COEFILE, JPQUIET)
C
C Change access mode to 'read only' for all users.
C
IRET = JCHMOD(FILENAME(1:IOFFSET-1),'0444')
IF( IRET.NE.0 )
X CALL INTLOG(JP_WARN,'JACOBIF: JCHMOD error.',IRET)
C
C Write coefficients to file
C
CALL PBWRITE(IUNIT,ACOEFF,IFSIZE,IRET)
IF( IRET.NE.IFSIZE ) THEN
CALL INTLOG(JP_FATAL,'JACOBIF: PBWRITE failed.',JPQUIET)
IRET = UNLINK(FILENAME(1:IOFFSET-1))
IF( IRET.NE.0 )
X CALL INTLOG(JP_FATAL,'JACOBIF: UNLINK failed',JPQUIET)
CALL PBCLOSE(IUNIT,IRET)
JACOBIF = .FALSE.
GOTO 999
ENDIF
CALL PBCLOSE(IUNIT,IRET)
LINMEM = .TRUE.
ENDIF
ENDIF
ENDIF
C
995 CONTINUE
C
JACOBIF = .TRUE.
C
999 CONTINUE
RETURN
C
C Failure to converge with M < 0.
C
910 CONTINUE
CALL INTLOG(JP_FATAL,'JACOBIF: Fail to converge M < 0', JPQUIET)
JACOBIF = .FALSE.
GOTO 999
C
C Failure to converge with M > 0.
C
920 CONTINUE
CALL INTLOG(JP_FATAL,'JACOBIF: Fail to converge M > 0', JPQUIET)
JACOBIF = .FALSE.
GOTO 999
END
|
