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
|
*DECK DJAIRY
SUBROUTINE DJAIRY (X, RX, C, AI, DAI)
C***BEGIN PROLOGUE DJAIRY
C***SUBSIDIARY
C***PURPOSE Subsidiary to DBESJ and DBESY
C***LIBRARY SLATEC
C***TYPE DOUBLE PRECISION (JAIRY-S, DJAIRY-D)
C***AUTHOR Amos, D. E., (SNLA)
C Daniel, S. L., (SNLA)
C Weston, M. K., (SNLA)
C***DESCRIPTION
C
C DJAIRY computes the Airy function AI(X)
C and its derivative DAI(X) for DASYJY
C
C INPUT
C
C X - Argument, computed by DASYJY, X unrestricted
C RX - RX=SQRT(ABS(X)), computed by DASYJY
C C - C=2.*(ABS(X)**1.5)/3., computed by DASYJY
C
C OUTPUT
C
C AI - Value of function AI(X)
C DAI - Value of the derivative DAI(X)
C
C***SEE ALSO DBESJ, DBESY
C***ROUTINES CALLED (NONE)
C***REVISION HISTORY (YYMMDD)
C 750101 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 891009 Removed unreferenced variable. (WRB)
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900328 Added TYPE section. (WRB)
C 910408 Updated the AUTHOR section. (WRB)
C***END PROLOGUE DJAIRY
C
INTEGER I, J, M1, M1D, M2, M2D, M3, M3D, M4, M4D, N1, N1D, N2,
1 N2D, N3, N3D, N4, N4D
DOUBLE PRECISION A,AI,AJN,AJP,AK1,AK2,AK3,B,C,CCV,CON2,
1 CON3, CON4, CON5, CV, DA, DAI, DAJN, DAJP, DAK1, DAK2, DAK3,
2 DB, EC, E1, E2, FPI12, F1, F2, RTRX, RX, SCV, T, TEMP1, TEMP2,
3 TT, X
DIMENSION AJP(19), AJN(19), A(15), B(15)
DIMENSION AK1(14), AK2(23), AK3(14)
DIMENSION DAJP(19), DAJN(19), DA(15), DB(15)
DIMENSION DAK1(14), DAK2(24), DAK3(14)
SAVE N1, N2, N3, N4, M1, M2, M3, M4, FPI12, CON2, CON3,
1 CON4, CON5, AK1, AK2, AK3, AJP, AJN, A, B,
2 N1D, N2D, N3D, N4D, M1D, M2D, M3D, M4D, DAK1, DAK2, DAK3,
3 DAJP, DAJN, DA, DB
DATA N1,N2,N3,N4/14,23,19,15/
DATA M1,M2,M3,M4/12,21,17,13/
DATA FPI12,CON2,CON3,CON4,CON5/
1 1.30899693899575D+00, 5.03154716196777D+00, 3.80004589867293D-01,
2 8.33333333333333D-01, 8.66025403784439D-01/
DATA AK1(1), AK1(2), AK1(3), AK1(4), AK1(5), AK1(6), AK1(7),
1 AK1(8), AK1(9), AK1(10),AK1(11),AK1(12),AK1(13),
2 AK1(14) / 2.20423090987793D-01,-1.25290242787700D-01,
3 1.03881163359194D-02, 8.22844152006343D-04,-2.34614345891226D-04,
4 1.63824280172116D-05, 3.06902589573189D-07,-1.29621999359332D-07,
5 8.22908158823668D-09, 1.53963968623298D-11,-3.39165465615682D-11,
6 2.03253257423626D-12,-1.10679546097884D-14,-5.16169497785080D-15/
DATA AK2(1), AK2(2), AK2(3), AK2(4), AK2(5), AK2(6), AK2(7),
1 AK2(8), AK2(9), AK2(10),AK2(11),AK2(12),AK2(13),AK2(14),
2 AK2(15),AK2(16),AK2(17),AK2(18),AK2(19),AK2(20),AK2(21),
3 AK2(22),AK2(23) / 2.74366150869598D-01, 5.39790969736903D-03,
4-1.57339220621190D-03, 4.27427528248750D-04,-1.12124917399925D-04,
5 2.88763171318904D-05,-7.36804225370554D-06, 1.87290209741024D-06,
6-4.75892793962291D-07, 1.21130416955909D-07,-3.09245374270614D-08,
7 7.92454705282654D-09,-2.03902447167914D-09, 5.26863056595742D-10,
8-1.36704767639569D-10, 3.56141039013708D-11,-9.31388296548430D-12,
9 2.44464450473635D-12,-6.43840261990955D-13, 1.70106030559349D-13,
1-4.50760104503281D-14, 1.19774799164811D-14,-3.19077040865066D-15/
DATA AK3(1), AK3(2), AK3(3), AK3(4), AK3(5), AK3(6), AK3(7),
1 AK3(8), AK3(9), AK3(10),AK3(11),AK3(12),AK3(13),
2 AK3(14) / 2.80271447340791D-01,-1.78127042844379D-03,
3 4.03422579628999D-05,-1.63249965269003D-06, 9.21181482476768D-08,
4-6.52294330229155D-09, 5.47138404576546D-10,-5.24408251800260D-11,
5 5.60477904117209D-12,-6.56375244639313D-13, 8.31285761966247D-14,
6-1.12705134691063D-14, 1.62267976598129D-15,-2.46480324312426D-16/
DATA AJP(1), AJP(2), AJP(3), AJP(4), AJP(5), AJP(6), AJP(7),
1 AJP(8), AJP(9), AJP(10),AJP(11),AJP(12),AJP(13),AJP(14),
2 AJP(15),AJP(16),AJP(17),AJP(18),
3 AJP(19) / 7.78952966437581D-02,-1.84356363456801D-01,
4 3.01412605216174D-02, 3.05342724277608D-02,-4.95424702513079D-03,
5-1.72749552563952D-03, 2.43137637839190D-04, 5.04564777517082D-05,
6-6.16316582695208D-06,-9.03986745510768D-07, 9.70243778355884D-08,
7 1.09639453305205D-08,-1.04716330588766D-09,-9.60359441344646D-11,
8 8.25358789454134D-12, 6.36123439018768D-13,-4.96629614116015D-14,
9-3.29810288929615D-15, 2.35798252031104D-16/
DATA AJN(1), AJN(2), AJN(3), AJN(4), AJN(5), AJN(6), AJN(7),
1 AJN(8), AJN(9), AJN(10),AJN(11),AJN(12),AJN(13),AJN(14),
2 AJN(15),AJN(16),AJN(17),AJN(18),
3 AJN(19) / 3.80497887617242D-02,-2.45319541845546D-01,
4 1.65820623702696D-01, 7.49330045818789D-02,-2.63476288106641D-02,
5-5.92535597304981D-03, 1.44744409589804D-03, 2.18311831322215D-04,
6-4.10662077680304D-05,-4.66874994171766D-06, 7.15218807277160D-07,
7 6.52964770854633D-08,-8.44284027565946D-09,-6.44186158976978D-10,
8 7.20802286505285D-11, 4.72465431717846D-12,-4.66022632547045D-13,
9-2.67762710389189D-14, 2.36161316570019D-15/
DATA A(1), A(2), A(3), A(4), A(5), A(6), A(7),
1 A(8), A(9), A(10), A(11), A(12), A(13), A(14),
2 A(15) / 4.90275424742791D-01, 1.57647277946204D-03,
3-9.66195963140306D-05, 1.35916080268815D-07, 2.98157342654859D-07,
4-1.86824767559979D-08,-1.03685737667141D-09, 3.28660818434328D-10,
5-2.57091410632780D-11,-2.32357655300677D-12, 9.57523279048255D-13,
6-1.20340828049719D-13,-2.90907716770715D-15, 4.55656454580149D-15,
7-9.99003874810259D-16/
DATA B(1), B(2), B(3), B(4), B(5), B(6), B(7),
1 B(8), B(9), B(10), B(11), B(12), B(13), B(14),
2 B(15) / 2.78593552803079D-01,-3.52915691882584D-03,
3-2.31149677384994D-05, 4.71317842263560D-06,-1.12415907931333D-07,
4-2.00100301184339D-08, 2.60948075302193D-09,-3.55098136101216D-11,
5-3.50849978423875D-11, 5.83007187954202D-12,-2.04644828753326D-13,
6-1.10529179476742D-13, 2.87724778038775D-14,-2.88205111009939D-15,
7-3.32656311696166D-16/
DATA N1D,N2D,N3D,N4D/14,24,19,15/
DATA M1D,M2D,M3D,M4D/12,22,17,13/
DATA DAK1(1), DAK1(2), DAK1(3), DAK1(4), DAK1(5), DAK1(6),
1 DAK1(7), DAK1(8), DAK1(9), DAK1(10),DAK1(11),DAK1(12),
2 DAK1(13),DAK1(14)/ 2.04567842307887D-01,-6.61322739905664D-02,
3-8.49845800989287D-03, 3.12183491556289D-03,-2.70016489829432D-04,
4-6.35636298679387D-06, 3.02397712409509D-06,-2.18311195330088D-07,
5-5.36194289332826D-10, 1.13098035622310D-09,-7.43023834629073D-11,
6 4.28804170826891D-13, 2.23810925754539D-13,-1.39140135641182D-14/
DATA DAK2(1), DAK2(2), DAK2(3), DAK2(4), DAK2(5), DAK2(6),
1 DAK2(7), DAK2(8), DAK2(9), DAK2(10),DAK2(11),DAK2(12),
2 DAK2(13),DAK2(14),DAK2(15),DAK2(16),DAK2(17),DAK2(18),
3 DAK2(19),DAK2(20),DAK2(21),DAK2(22),DAK2(23),
4 DAK2(24) / 2.93332343883230D-01,-8.06196784743112D-03,
5 2.42540172333140D-03,-6.82297548850235D-04, 1.85786427751181D-04,
6-4.97457447684059D-05, 1.32090681239497D-05,-3.49528240444943D-06,
7 9.24362451078835D-07,-2.44732671521867D-07, 6.49307837648910D-08,
8-1.72717621501538D-08, 4.60725763604656D-09,-1.23249055291550D-09,
9 3.30620409488102D-10,-8.89252099772401D-11, 2.39773319878298D-11,
1-6.48013921153450D-12, 1.75510132023731D-12,-4.76303829833637D-13,
2 1.29498241100810D-13,-3.52679622210430D-14, 9.62005151585923D-15,
3-2.62786914342292D-15/
DATA DAK3(1), DAK3(2), DAK3(3), DAK3(4), DAK3(5), DAK3(6),
1 DAK3(7), DAK3(8), DAK3(9), DAK3(10),DAK3(11),DAK3(12),
2 DAK3(13),DAK3(14)/ 2.84675828811349D-01, 2.53073072619080D-03,
3-4.83481130337976D-05, 1.84907283946343D-06,-1.01418491178576D-07,
4 7.05925634457153D-09,-5.85325291400382D-10, 5.56357688831339D-11,
5-5.90889094779500D-12, 6.88574353784436D-13,-8.68588256452194D-14,
6 1.17374762617213D-14,-1.68523146510923D-15, 2.55374773097056D-16/
DATA DAJP(1), DAJP(2), DAJP(3), DAJP(4), DAJP(5), DAJP(6),
1 DAJP(7), DAJP(8), DAJP(9), DAJP(10),DAJP(11),DAJP(12),
2 DAJP(13),DAJP(14),DAJP(15),DAJP(16),DAJP(17),DAJP(18),
3 DAJP(19) / 6.53219131311457D-02,-1.20262933688823D-01,
4 9.78010236263823D-03, 1.67948429230505D-02,-1.97146140182132D-03,
5-8.45560295098867D-04, 9.42889620701976D-05, 2.25827860945475D-05,
6-2.29067870915987D-06,-3.76343991136919D-07, 3.45663933559565D-08,
7 4.29611332003007D-09,-3.58673691214989D-10,-3.57245881361895D-11,
8 2.72696091066336D-12, 2.26120653095771D-13,-1.58763205238303D-14,
9-1.12604374485125D-15, 7.31327529515367D-17/
DATA DAJN(1), DAJN(2), DAJN(3), DAJN(4), DAJN(5), DAJN(6),
1 DAJN(7), DAJN(8), DAJN(9), DAJN(10),DAJN(11),DAJN(12),
2 DAJN(13),DAJN(14),DAJN(15),DAJN(16),DAJN(17),DAJN(18),
3 DAJN(19) / 1.08594539632967D-02, 8.53313194857091D-02,
4-3.15277068113058D-01,-8.78420725294257D-02, 5.53251906976048D-02,
5 9.41674060503241D-03,-3.32187026018996D-03,-4.11157343156826D-04,
6 1.01297326891346D-04, 9.87633682208396D-06,-1.87312969812393D-06,
7-1.50798500131468D-07, 2.32687669525394D-08, 1.59599917419225D-09,
8-2.07665922668385D-10,-1.24103350500302D-11, 1.39631765331043D-12,
9 7.39400971155740D-14,-7.32887475627500D-15/
DATA DA(1), DA(2), DA(3), DA(4), DA(5), DA(6), DA(7),
1 DA(8), DA(9), DA(10), DA(11), DA(12), DA(13), DA(14),
2 DA(15) / 4.91627321104601D-01, 3.11164930427489D-03,
3 8.23140762854081D-05,-4.61769776172142D-06,-6.13158880534626D-08,
4 2.87295804656520D-08,-1.81959715372117D-09,-1.44752826642035D-10,
5 4.53724043420422D-11,-3.99655065847223D-12,-3.24089119830323D-13,
6 1.62098952568741D-13,-2.40765247974057D-14, 1.69384811284491D-16,
7 8.17900786477396D-16/
DATA DB(1), DB(2), DB(3), DB(4), DB(5), DB(6), DB(7),
1 DB(8), DB(9), DB(10), DB(11), DB(12), DB(13), DB(14),
2 DB(15) /-2.77571356944231D-01, 4.44212833419920D-03,
3-8.42328522190089D-05,-2.58040318418710D-06, 3.42389720217621D-07,
4-6.24286894709776D-09,-2.36377836844577D-09, 3.16991042656673D-10,
5-4.40995691658191D-12,-5.18674221093575D-12, 9.64874015137022D-13,
6-4.90190576608710D-14,-1.77253430678112D-14, 5.55950610442662D-15,
7-7.11793337579530D-16/
C***FIRST EXECUTABLE STATEMENT DJAIRY
IF (X.LT.0.0D0) GO TO 90
IF (C.GT.5.0D0) GO TO 60
IF (X.GT.1.20D0) GO TO 30
T = (X+X-1.2D0)*CON4
TT = T + T
J = N1
F1 = AK1(J)
F2 = 0.0D0
DO 10 I=1,M1
J = J - 1
TEMP1 = F1
F1 = TT*F1 - F2 + AK1(J)
F2 = TEMP1
10 CONTINUE
AI = T*F1 - F2 + AK1(1)
C
J = N1D
F1 = DAK1(J)
F2 = 0.0D0
DO 20 I=1,M1D
J = J - 1
TEMP1 = F1
F1 = TT*F1 - F2 + DAK1(J)
F2 = TEMP1
20 CONTINUE
DAI = -(T*F1-F2+DAK1(1))
RETURN
C
30 CONTINUE
T = (X+X-CON2)*CON3
TT = T + T
J = N2
F1 = AK2(J)
F2 = 0.0D0
DO 40 I=1,M2
J = J - 1
TEMP1 = F1
F1 = TT*F1 - F2 + AK2(J)
F2 = TEMP1
40 CONTINUE
RTRX = SQRT(RX)
EC = EXP(-C)
AI = EC*(T*F1-F2+AK2(1))/RTRX
J = N2D
F1 = DAK2(J)
F2 = 0.0D0
DO 50 I=1,M2D
J = J - 1
TEMP1 = F1
F1 = TT*F1 - F2 + DAK2(J)
F2 = TEMP1
50 CONTINUE
DAI = -EC*(T*F1-F2+DAK2(1))*RTRX
RETURN
C
60 CONTINUE
T = 10.0D0/C - 1.0D0
TT = T + T
J = N1
F1 = AK3(J)
F2 = 0.0D0
DO 70 I=1,M1
J = J - 1
TEMP1 = F1
F1 = TT*F1 - F2 + AK3(J)
F2 = TEMP1
70 CONTINUE
RTRX = SQRT(RX)
EC = EXP(-C)
AI = EC*(T*F1-F2+AK3(1))/RTRX
J = N1D
F1 = DAK3(J)
F2 = 0.0D0
DO 80 I=1,M1D
J = J - 1
TEMP1 = F1
F1 = TT*F1 - F2 + DAK3(J)
F2 = TEMP1
80 CONTINUE
DAI = -RTRX*EC*(T*F1-F2+DAK3(1))
RETURN
C
90 CONTINUE
IF (C.GT.5.0D0) GO TO 120
T = 0.4D0*C - 1.0D0
TT = T + T
J = N3
F1 = AJP(J)
E1 = AJN(J)
F2 = 0.0D0
E2 = 0.0D0
DO 100 I=1,M3
J = J - 1
TEMP1 = F1
TEMP2 = E1
F1 = TT*F1 - F2 + AJP(J)
E1 = TT*E1 - E2 + AJN(J)
F2 = TEMP1
E2 = TEMP2
100 CONTINUE
AI = (T*E1-E2+AJN(1)) - X*(T*F1-F2+AJP(1))
J = N3D
F1 = DAJP(J)
E1 = DAJN(J)
F2 = 0.0D0
E2 = 0.0D0
DO 110 I=1,M3D
J = J - 1
TEMP1 = F1
TEMP2 = E1
F1 = TT*F1 - F2 + DAJP(J)
E1 = TT*E1 - E2 + DAJN(J)
F2 = TEMP1
E2 = TEMP2
110 CONTINUE
DAI = X*X*(T*F1-F2+DAJP(1)) + (T*E1-E2+DAJN(1))
RETURN
C
120 CONTINUE
T = 10.0D0/C - 1.0D0
TT = T + T
J = N4
F1 = A(J)
E1 = B(J)
F2 = 0.0D0
E2 = 0.0D0
DO 130 I=1,M4
J = J - 1
TEMP1 = F1
TEMP2 = E1
F1 = TT*F1 - F2 + A(J)
E1 = TT*E1 - E2 + B(J)
F2 = TEMP1
E2 = TEMP2
130 CONTINUE
TEMP1 = T*F1 - F2 + A(1)
TEMP2 = T*E1 - E2 + B(1)
RTRX = SQRT(RX)
CV = C - FPI12
CCV = COS(CV)
SCV = SIN(CV)
AI = (TEMP1*CCV-TEMP2*SCV)/RTRX
J = N4D
F1 = DA(J)
E1 = DB(J)
F2 = 0.0D0
E2 = 0.0D0
DO 140 I=1,M4D
J = J - 1
TEMP1 = F1
TEMP2 = E1
F1 = TT*F1 - F2 + DA(J)
E1 = TT*E1 - E2 + DB(J)
F2 = TEMP1
E2 = TEMP2
140 CONTINUE
TEMP1 = T*F1 - F2 + DA(1)
TEMP2 = T*E1 - E2 + DB(1)
E1 = CCV*CON5 + 0.5D0*SCV
E2 = SCV*CON5 - 0.5D0*CCV
DAI = (TEMP1*E1-TEMP2*E2)*RTRX
RETURN
END
|
