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Contents of /MITgcm_contrib/jscott/igsm/src/fft36.F

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Revision 1.1 - (show annotations) (download)
Fri Aug 11 19:35:30 2006 UTC (18 years, 11 months ago) by jscott
Branch: MAIN
CVS Tags: HEAD
atm2d package

1
2 #include "ctrparam.h"
3
4 ! ==========================================================
5 !
6 ! FFT36.F: FFT functions.
7 !
8 ! ----------------------------------------------------------
9 !
10 ! Revision History:
11 !
12 ! When Who What
13 ! ----- ---------- -------
14 ! 080200 Chien Wang repack based on CliChem3 & M24x11,
15 ! and add cpp.
16 !
17 ! ==========================================================
18
19 SUBROUTINE FRTR0 (KM) 1.
20 C**** INITIALIZATION ENTRY TO CALCULATE SIN VALUES AND CHECK THAT KM=36 2.
21 COMMON/FCOM/BYKM,BYKMH,BYKM2,SIN10,SIN20,SIN30,SIN40,SIN50,SIN60, 3.
22 * SIN70,SIN80 4.
23 CV REAL*8 TWOPI/6.283185307179586477/ 5.
24 c DOUBLE PRECISION TWOPI 6.
25 DATA TWOPI/6.283185307179586477/ 7.
26 IF(KM.NE.36) GO TO 220 8.
27 BYKM=1./KM 9.
28 BYKMH=2./KM 10.
29 BYKM2=1./(2.*KM) 11.
30 SIN10=DSIN(TWOPI/36.) 12.
31 SIN20=DSIN(TWOPI/18.) 13.
32 SIN30=1.D0/2. 14.
33 SIN40=DSIN(TWOPI/9.) 15.
34 SIN50=DCOS(TWOPI/9.) 16.
35 SIN60=DSQRT(3.D0)/2. 17.
36 SIN70=DCOS(TWOPI/18.) 18.
37 SIN80=DCOS(TWOPI/36.) 19.
38 CYDBL SIN10=DSIN(TWOPI/36.) 20.
39 CYDBL SIN20=DSIN(TWOPI/18.) 21.
40 CYDBL SIN30=1.D0/2. 22.
41 CYDBL SIN40=DSIN(TWOPI/9.) 23.
42 CYDBL SIN50=DCOS(TWOPI/9.) 24.
43 CYDBL SIN60=DSQRT(3.D0)/2. 25.
44 CYDBL SIN70=DCOS(TWOPI/18.) 26.
45 CYDBL SIN80=DCOS(TWOPI/36.) 27.
46 C SIN10=SIN(TWOPI/36.) 28.
47 C SIN20=SIN(TWOPI/18.) 29.
48 C SIN30=.5 30.
49 C SIN40=SIN(TWOPI/9.) 31.
50 C SIN50=COS(TWOPI/9.) 32.
51 C SIN60=SQRT(3.)/2. 33.
52 C SIN70=COS(TWOPI/18.) 34.
53 C SIN80=COS(TWOPI/36.) 35.
54 RETURN 36.
55 220 WRITE (6,901) KM 37.
56 STOP 38.
57 901 FORMAT ('0THIS FOURT SUBROUTINE NOT SUITED FOR KM = ',I8) 39.
58 END 40.
59 SUBROUTINE FRTR (F) 101.
60 C**** THIS SUBROUTINE PERFORMS A FOURIER ANALYSIS ON THE ONE DIMENSIONAL 102.
61 C**** ARRAY F WHICH MUST BE DIMENSIONED 36. IT RETURNS IN F THE ENERGY 103.
62 C**** ASSOCIATED WITH EACH WAVE NUMBER. UPON ENTERING THIS ROUTINE, 104.
63 C**** THE TOTAL ENERGY IS 105.
64 C**** .5*SUM(F(K)*F(K)) 106.
65 C**** WITH THE SUM BEING TAKEN OVER ALL K FROM 1 TO 36. UPON LEAVING 107.
66 C**** THIS ROUTINE, THE TOTAL ENERGY IS 108.
67 C**** SUM(F(N+1)) 109.
68 C**** WITH THE SUM BEING TAKEN OVER ALL WAVE NUMBERS FROM 0 TO 18. 110.
69 COMMON/FCOM/BYKM,BYKMH,BYKM2,SIN10,SIN20,SIN30,SIN40,SIN50,SIN60, 111.
70 * SIN70,SIN80 112.
71 DIMENSION F(36) 113.
72 10 CC00=F(12)+F(24)+F(36) 114.
73 CC01=F(36)-(F(12)+F(24))*SIN30 115.
74 CC10=F(1)+F(13)+F(25) 116.
75 CC11=F(1)*SIN80-F(13)*SIN40-F(25)*SIN20 117.
76 CC20=F(2)+F(14)+F(26) 118.
77 CC21=F(2)*SIN70-F(14)*SIN50-F(26)*SIN10 119.
78 CC30=F(3)+F(15)+F(27) 120.
79 CC31=(F(3)-F(15))*SIN60 121.
80 CC40=F(4)+F(16)+F(28) 122.
81 CC41=F(4)*SIN50-F(16)*SIN70+F(28)*SIN10 123.
82 CC50=F(5)+F(17)+F(29) 124.
83 CC51=F(5)*SIN40-F(17)*SIN80+F(29)*SIN20 125.
84 CC60=F(6)+F(18)+F(30) 126.
85 CC61=(F(6)+F(30))*SIN30-F(18) 127.
86 CC70=F(7)+F(19)+F(31) 128.
87 CC71=F(7)*SIN20-F(19)*SIN80+F(31)*SIN40 129.
88 CC80=F(8)+F(20)+F(32) 130.
89 CC81=F(8)*SIN10-F(20)*SIN70+F(32)*SIN50 131.
90 CC90=F(9)+F(21)+F(33) 132.
91 CC91=(F(33)-F(21))*SIN60 133.
92 CCA0=F(10)+F(22)+F(34) 134.
93 CCA1=F(34)*SIN70-F(10)*SIN10-F(22)*SIN50 135.
94 CCB0=F(11)+F(23)+F(35) 136.
95 CCB1=F(35)*SIN80-F(11)*SIN20-F(23)*SIN40 137.
96 SC01=(F(12)-F(24))*SIN60 138.
97 SC11=F(1)*SIN10+F(13)*SIN50-F(25)*SIN70 139.
98 SC21=F(2)*SIN20+F(14)*SIN40-F(26)*SIN80 140.
99 SC31=(F(3)+F(15))*SIN30-F(27) 141.
100 SC41=F(4)*SIN40+F(16)*SIN20-F(28)*SIN80 142.
101 SC51=F(5)*SIN50+F(17)*SIN10-F(29)*SIN70 143.
102 SC61=(F(6)-F(30))*SIN60 144.
103 SC71=F(7)*SIN70-F(19)*SIN10-F(31)*SIN50 145.
104 SC81=F(8)*SIN80-F(20)*SIN20-F(32)*SIN40 146.
105 SC91=F(9)-(F(21)+F(33))*SIN30 147.
106 SCA1=F(10)*SIN80-F(22)*SIN40-F(34)*SIN20 148.
107 SCB1=F(11)*SIN70-F(23)*SIN50-F(35)*SIN10 149.
108 C**** CALCULATE EXPRESSIONS SUMMED BY INCREMENTS OF 4 150.
109 C400=CC00+CC40+CC80 151.
110 C401=CC01+CC41+CC81 152.
111 C403=CC00-(CC40+CC80)*SIN30 153.
112 C402=(CC01-(CC41+CC81)*SIN30)+((SC41-SC81)*SIN60) 154.
113 C404=(CC01-(CC41+CC81)*SIN30)-((SC41-SC81)*SIN60) 155.
114 C410=CC10+CC50+CC90 156.
115 C411=CC11+CC51+CC91 157.
116 C413=(CC10-CC50)*SIN60 158.
117 C412=((CC11-CC51)*SIN60)+((SC11+SC51)*SIN30-SC91) 159.
118 C414=((CC11-CC51)*SIN60)-((SC11+SC51)*SIN30-SC91) 160.
119 C420=CC20+CC60+CCA0 161.
120 C421=CC21+CC61+CCA1 162.
121 C423=(CC20+CCA0)*SIN30-CC60 163.
122 C422=((CC21+CCA1)*SIN30-CC61)+((SC21-SCA1)*SIN60) 164.
123 C424=((CC21+CCA1)*SIN30-CC61)-((SC21-SCA1)*SIN60) 165.
124 C430=CC30+CC70+CCB0 166.
125 C431=CC31+CC71+CCB1 167.
126 C433=(CCB0-CC70)*SIN60 168.
127 C432=((CCB1-CC71)*SIN60)+(SC31-(SC71+SCB1)*SIN30) 169.
128 C434=((CCB1-CC71)*SIN60)-(SC31-(SC71+SCB1)*SIN30) 170.
129 S401=SC01+SC41+SC81 171.
130 S403=(CC40-CC80)*SIN60 172.
131 S402=((CC41-CC81)*SIN60)+((SC41+SC81)*SIN30-SC01) 173.
132 S404=((CC41-CC81)*SIN60)-((SC41+SC81)*SIN30-SC01) 174.
133 S411=SC11+SC51+SC91 175.
134 S413=(CC10+CC50)*SIN30-CC90 176.
135 S412=((CC11+CC51)*SIN30-CC91)+((SC51-SC11)*SIN60) 177.
136 S414=((CC11+CC51)*SIN30-CC91)-((SC51-SC11)*SIN60) 178.
137 S421=SC21+SC61+SCA1 179.
138 S423=(CC20-CCA0)*SIN60 180.
139 S422=((CC21-CCA1)*SIN60)+(SC61-(SC21+SCA1)*SIN30) 181.
140 S424=((CC21-CCA1)*SIN60)-(SC61-(SC21+SCA1)*SIN30) 182.
141 S431=SC31+SC71+SCB1 183.
142 S433=CC30-(CC70+CCB0)*SIN30 184.
143 S432=(CC31-(CC71+CCB1)*SIN30)+((SC71-SCB1)*SIN60) 185.
144 S434=(CC31-(CC71+CCB1)*SIN30)-((SC71-SCB1)*SIN60) 186.
145 C**** CALCULATE EXPRESSIONS SUMMED BY INCREMENTS OF 2 187.
146 C200=C400+C420 188.
147 C201=C401+C421 189.
148 C202=C402+C422 190.
149 C203=C403+C423 191.
150 C204=C404+C424 192.
151 C205=C404-C424 193.
152 C206=C403-C423 194.
153 C207=C402-C422 195.
154 C208=C401-C421 196.
155 C C209=C400-C420 197.
156 C210=C410+C430 198.
157 C211=C411+C431 199.
158 C212=C412+C432 200.
159 C213=C413+C433 201.
160 C214=C414+C434 202.
161 C215=S414-S434 203.
162 C216=S413-S433 204.
163 C217=S412-S432 205.
164 C218=S411-S431 206.
165 C C219=0 207.
166 C S200=0 208.
167 S201=S401+S421 209.
168 S202=S402+S422 210.
169 S203=S403+S423 211.
170 S204=S404+S424 212.
171 S205=S424-S404 213.
172 S206=S423-S403 214.
173 S207=S422-S402 215.
174 S208=S421-S401 216.
175 C S209=0 217.
176 C S210=0 218.
177 S211=S411+S431 219.
178 S212=S412+S432 220.
179 S213=S413+S433 221.
180 S214=S414+S434 222.
181 S215=C414-C434 223.
182 S216=C413-C433 224.
183 S217=C412-C432 225.
184 S218=C411-C431 226.
185 C S219=C410-C430 227.
186 C**** CALCULATE THE SQUARE OF THE MAGNITUDE OF G(1,N)+I*G(2,N) 228.
187 20 F(1)=(C200+C210)*(C200+C210)*BYKM2 229.
188 F(2)=((C201+C211)*(C201+C211)+(S201+S211)*(S201+S211))*BYKM 230.
189 F(3)=((C202+C212)*(C202+C212)+(S202+S212)*(S202+S212))*BYKM 231.
190 F(4)=((C203+C213)*(C203+C213)+(S203+S213)*(S203+S213))*BYKM 232.
191 F(5)=((C204+C214)*(C204+C214)+(S204+S214)*(S204+S214))*BYKM 233.
192 F(6)=((C205+C215)*(C205+C215)+(S205+S215)*(S205+S215))*BYKM 234.
193 F(7)=((C206+C216)*(C206+C216)+(S206+S216)*(S206+S216))*BYKM 235.
194 F(8)=((C207+C217)*(C207+C217)+(S207+S217)*(S207+S217))*BYKM 236.
195 F(9)=((C208+C218)*(C208+C218)+(S208+S218)*(S208+S218))*BYKM 237.
196 F(10)=((C400-C420)*(C400-C420)+(C410-C430)*(C410-C430))*BYKM 238.
197 F(11)=((C208-C218)*(C208-C218)+(S218-S208)*(S218-S208))*BYKM 239.
198 F(12)=((C207-C217)*(C207-C217)+(S217-S207)*(S217-S207))*BYKM 240.
199 F(13)=((C206-C216)*(C206-C216)+(S216-S206)*(S216-S206))*BYKM 241.
200 F(14)=((C205-C215)*(C205-C215)+(S215-S205)*(S215-S205))*BYKM 242.
201 F(15)=((C204-C214)*(C204-C214)+(S214-S204)*(S214-S204))*BYKM 243.
202 F(16)=((C203-C213)*(C203-C213)+(S213-S203)*(S213-S203))*BYKM 244.
203 F(17)=((C202-C212)*(C202-C212)+(S212-S202)*(S212-S202))*BYKM 245.
204 F(18)=((C201-C211)*(C201-C211)+(S211-S201)*(S211-S201))*BYKM 246.
205 F(19)=(C200-C210)*(C200-C210)*BYKM2 247.
206 RETURN 248.
207 END 249.
208 SUBROUTINE GETAN (F,G) 301.
209 C**** GETAN RETRIEVES THE FOURIER COEFFICIENTS CONTAINED IN AN 302.
210 C**** ARRAY G DIMENSIONED 2 BY 19 AND DEFINED BY 303.
211 C**** G(1,N+1)+I*G(2,N+1)=SUM(F(K)*EXP(-2*PI*I*N*K/KM))/KMH 304.
212 C**** WITH THE SUM TAKEN OVER ALL K FROM 1 TO KM. KMH = KM FOR N = 0 305.
213 C**** OR 18, OTHERWISE KMH = KM/2. THE INTERNAL NOTATION CPQN MEANS 306.
214 C**** CPQN = SUM(F(K)*COS(2*PI*N*K/KM)) 307.
215 C**** WITH THE SUM BEING TAKEN OVER ALL K FROM 1 TO KM WHICH ARE EQUAL 308.
216 C**** TO Q MODULO(P). SPQN IS THE SAME BUT WITH COS REPLACED BY SIN. 309.
217 C**** THE NOTATION A=10, B=11, ETC. IS USED FOR P, Q AND N. 310.
218 COMMON/FCOM/BYKM,BYKMH,BYKM2,SIN10,SIN20,SIN30,SIN40,SIN50,SIN60, 311.
219 * SIN70,SIN80 312.
220 DIMENSION F(36),G(2,19) 313.
221 C**** CALCULATE EXPRESSIONS SUMMED BY INCREMENTS OF 12 314.
222 10 CC00=F(12)+F(24)+F(36) 315.
223 CC01=F(36)-(F(12)+F(24))*SIN30 316.
224 CC10=F(1)+F(13)+F(25) 317.
225 CC11=F(1)*SIN80-F(13)*SIN40-F(25)*SIN20 318.
226 CC20=F(2)+F(14)+F(26) 319.
227 CC21=F(2)*SIN70-F(14)*SIN50-F(26)*SIN10 320.
228 CC30=F(3)+F(15)+F(27) 321.
229 CC31=(F(3)-F(15))*SIN60 322.
230 CC40=F(4)+F(16)+F(28) 323.
231 CC41=F(4)*SIN50-F(16)*SIN70+F(28)*SIN10 324.
232 CC50=F(5)+F(17)+F(29) 325.
233 CC51=F(5)*SIN40-F(17)*SIN80+F(29)*SIN20 326.
234 CC60=F(6)+F(18)+F(30) 327.
235 CC61=(F(6)+F(30))*SIN30-F(18) 328.
236 CC70=F(7)+F(19)+F(31) 329.
237 CC71=F(7)*SIN20-F(19)*SIN80+F(31)*SIN40 330.
238 CC80=F(8)+F(20)+F(32) 331.
239 CC81=F(8)*SIN10-F(20)*SIN70+F(32)*SIN50 332.
240 CC90=F(9)+F(21)+F(33) 333.
241 CC91=(F(33)-F(21))*SIN60 334.
242 CCA0=F(10)+F(22)+F(34) 335.
243 CCA1=F(34)*SIN70-F(10)*SIN10-F(22)*SIN50 336.
244 CCB0=F(11)+F(23)+F(35) 337.
245 CCB1=F(35)*SIN80-F(11)*SIN20-F(23)*SIN40 338.
246 SC01=(F(12)-F(24))*SIN60 339.
247 SC11=F(1)*SIN10+F(13)*SIN50-F(25)*SIN70 340.
248 SC21=F(2)*SIN20+F(14)*SIN40-F(26)*SIN80 341.
249 SC31=(F(3)+F(15))*SIN30-F(27) 342.
250 SC41=F(4)*SIN40+F(16)*SIN20-F(28)*SIN80 343.
251 SC51=F(5)*SIN50+F(17)*SIN10-F(29)*SIN70 344.
252 SC61=(F(6)-F(30))*SIN60 345.
253 SC71=F(7)*SIN70-F(19)*SIN10-F(31)*SIN50 346.
254 SC81=F(8)*SIN80-F(20)*SIN20-F(32)*SIN40 347.
255 SC91=F(9)-(F(21)+F(33))*SIN30 348.
256 SCA1=F(10)*SIN80-F(22)*SIN40-F(34)*SIN20 349.
257 SCB1=F(11)*SIN70-F(23)*SIN50-F(35)*SIN10 350.
258 C**** CALCULATE EXPRESSIONS SUMMED BY INCREMENTS OF 4 351.
259 C400=CC00+CC40+CC80 352.
260 C401=CC01+CC41+CC81 353.
261 C403=CC00-(CC40+CC80)*SIN30 354.
262 C402=(CC01-(CC41+CC81)*SIN30)+((SC41-SC81)*SIN60) 355.
263 C404=(CC01-(CC41+CC81)*SIN30)-((SC41-SC81)*SIN60) 356.
264 C410=CC10+CC50+CC90 357.
265 C411=CC11+CC51+CC91 358.
266 C413=(CC10-CC50)*SIN60 359.
267 C412=((CC11-CC51)*SIN60)+((SC11+SC51)*SIN30-SC91) 360.
268 C414=((CC11-CC51)*SIN60)-((SC11+SC51)*SIN30-SC91) 361.
269 C420=CC20+CC60+CCA0 362.
270 C421=CC21+CC61+CCA1 363.
271 C423=(CC20+CCA0)*SIN30-CC60 364.
272 C422=((CC21+CCA1)*SIN30-CC61)+((SC21-SCA1)*SIN60) 365.
273 C424=((CC21+CCA1)*SIN30-CC61)-((SC21-SCA1)*SIN60) 366.
274 C430=CC30+CC70+CCB0 367.
275 C431=CC31+CC71+CCB1 368.
276 C433=(CCB0-CC70)*SIN60 369.
277 C432=((CCB1-CC71)*SIN60)+(SC31-(SC71+SCB1)*SIN30) 370.
278 C434=((CCB1-CC71)*SIN60)-(SC31-(SC71+SCB1)*SIN30) 371.
279 S401=SC01+SC41+SC81 372.
280 S403=(CC40-CC80)*SIN60 373.
281 S402=((CC41-CC81)*SIN60)+((SC41+SC81)*SIN30-SC01) 374.
282 S404=((CC41-CC81)*SIN60)-((SC41+SC81)*SIN30-SC01) 375.
283 S411=SC11+SC51+SC91 376.
284 S413=(CC10+CC50)*SIN30-CC90 377.
285 S412=((CC11+CC51)*SIN30-CC91)+((SC51-SC11)*SIN60) 378.
286 S414=((CC11+CC51)*SIN30-CC91)-((SC51-SC11)*SIN60) 379.
287 S421=SC21+SC61+SCA1 380.
288 S423=(CC20-CCA0)*SIN60 381.
289 S422=((CC21-CCA1)*SIN60)+(SC61-(SC21+SCA1)*SIN30) 382.
290 S424=((CC21-CCA1)*SIN60)-(SC61-(SC21+SCA1)*SIN30) 383.
291 S431=SC31+SC71+SCB1 384.
292 S433=CC30-(CC70+CCB0)*SIN30 385.
293 S432=(CC31-(CC71+CCB1)*SIN30)+((SC71-SCB1)*SIN60) 386.
294 S434=(CC31-(CC71+CCB1)*SIN30)-((SC71-SCB1)*SIN60) 387.
295 C**** CALCULATE EXPRESSIONS SUMMED BY INCREMENTS OF 2 388.
296 C200=C400+C420 389.
297 C201=C401+C421 390.
298 C202=C402+C422 391.
299 C203=C403+C423 392.
300 C204=C404+C424 393.
301 C205=C404-C424 394.
302 C206=C403-C423 395.
303 C207=C402-C422 396.
304 C208=C401-C421 397.
305 C C209=C400-C420 398.
306 C210=C410+C430 399.
307 C211=C411+C431 400.
308 C212=C412+C432 401.
309 C213=C413+C433 402.
310 C214=C414+C434 403.
311 C215=S414-S434 404.
312 C216=S413-S433 405.
313 C217=S412-S432 406.
314 C218=S411-S431 407.
315 C C219=0 408.
316 C S200=0 409.
317 S201=S401+S421 410.
318 S202=S402+S422 411.
319 S203=S403+S423 412.
320 S204=S404+S424 413.
321 S205=S424-S404 414.
322 S206=S423-S403 415.
323 S207=S422-S402 416.
324 S208=S421-S401 417.
325 C S209=0 418.
326 C S210=0 419.
327 S211=S411+S431 420.
328 S212=S412+S432 421.
329 S213=S413+S433 422.
330 S214=S414+S434 423.
331 S215=C414-C434 424.
332 S216=C413-C433 425.
333 S217=C412-C432 426.
334 S218=C411-C431 427.
335 C S219=C410-C430 428.
336 C**** CALCULATE FINAL COEFFICIENTS OF FOURIER EXPANSION 429.
337 G(1,1)=(C200+C210)*BYKM 430.
338 G(1,2)=(C201+C211)*BYKMH 431.
339 G(1,3)=(C202+C212)*BYKMH 432.
340 G(1,4)=(C203+C213)*BYKMH 433.
341 G(1,5)=(C204+C214)*BYKMH 434.
342 G(1,6)=(C205+C215)*BYKMH 435.
343 G(1,7)=(C206+C216)*BYKMH 436.
344 G(1,8)=(C207+C217)*BYKMH 437.
345 G(1,9)=(C208+C218)*BYKMH 438.
346 G(1,10)=(C400-C420)*BYKMH 439.
347 G(1,11)=(C208-C218)*BYKMH 440.
348 G(1,12)=(C207-C217)*BYKMH 441.
349 G(1,13)=(C206-C216)*BYKMH 442.
350 G(1,14)=(C205-C215)*BYKMH 443.
351 G(1,15)=(C204-C214)*BYKMH 444.
352 G(1,16)=(C203-C213)*BYKMH 445.
353 G(1,17)=(C202-C212)*BYKMH 446.
354 G(1,18)=(C201-C211)*BYKMH 447.
355 G(1,19)=(C200-C210)*BYKM 448.
356 G(2,1)=0. 449.
357 G(2,2)=(S201+S211)*BYKMH 450.
358 G(2,3)=(S202+S212)*BYKMH 451.
359 G(2,4)=(S203+S213)*BYKMH 452.
360 G(2,5)=(S204+S214)*BYKMH 453.
361 G(2,6)=(S205+S215)*BYKMH 454.
362 G(2,7)=(S206+S216)*BYKMH 455.
363 G(2,8)=(S207+S217)*BYKMH 456.
364 G(2,9)=(S208+S218)*BYKMH 457.
365 G(2,10)=(C410-C430)*BYKMH 458.
366 G(2,11)=(S218-S208)*BYKMH 459.
367 G(2,12)=(S217-S207)*BYKMH 460.
368 G(2,13)=(S216-S206)*BYKMH 461.
369 G(2,14)=(S215-S205)*BYKMH 462.
370 G(2,15)=(S214-S204)*BYKMH 463.
371 G(2,16)=(S213-S203)*BYKMH 464.
372 G(2,17)=(S212-S202)*BYKMH 465.
373 G(2,18)=(S211-S201)*BYKMH 466.
374 G(2,19)=0. 467.
375 RETURN 468.
376 END 469.

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