Fix missing import in finiterectlat-scatter.py
[qpms.git] / amos / zunhj.f
blobe56e43c391f5b29863c05dd81cff7d131cd196e5
1 SUBROUTINE ZUNHJ(ZR, ZI, FNU, IPMTR, TOL, PHIR, PHII, ARGR, ARGI,
2 * ZETA1R, ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
3 C***BEGIN PROLOGUE ZUNHJ
4 C***REFER TO ZBESI,ZBESK
6 C REFERENCES
7 C HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ AND I.A.
8 C STEGUN, AMS55, NATIONAL BUREAU OF STANDARDS, 1965, CHAPTER 9.
10 C ASYMPTOTICS AND SPECIAL FUNCTIONS BY F.W.J. OLVER, ACADEMIC
11 C PRESS, N.Y., 1974, PAGE 420
13 C ABSTRACT
14 C ZUNHJ COMPUTES PARAMETERS FOR BESSEL FUNCTIONS C(FNU,Z) =
15 C J(FNU,Z), Y(FNU,Z) OR H(I,FNU,Z) I=1,2 FOR LARGE ORDERS FNU
16 C BY MEANS OF THE UNIFORM ASYMPTOTIC EXPANSION
18 C C(FNU,Z)=C1*PHI*( ASUM*AIRY(ARG) + C2*BSUM*DAIRY(ARG) )
20 C FOR PROPER CHOICES OF C1, C2, AIRY AND DAIRY WHERE AIRY IS
21 C AN AIRY FUNCTION AND DAIRY IS ITS DERIVATIVE.
23 C (2/3)*FNU*ZETA**1.5 = ZETA1-ZETA2,
25 C ZETA1=0.5*FNU*CLOG((1+W)/(1-W)), ZETA2=FNU*W FOR SCALING
26 C PURPOSES IN AIRY FUNCTIONS FROM CAIRY OR CBIRY.
28 C MCONJ=SIGN OF AIMAG(Z), BUT IS AMBIGUOUS WHEN Z IS REAL AND
29 C MUST BE SPECIFIED. IPMTR=0 RETURNS ALL PARAMETERS. IPMTR=
30 C 1 COMPUTES ALL EXCEPT ASUM AND BSUM.
32 C***ROUTINES CALLED AZABS,ZDIV,AZLOG,AZSQRT,D1MACH
33 C***END PROLOGUE ZUNHJ
34 C COMPLEX ARG,ASUM,BSUM,CFNU,CONE,CR,CZERO,DR,P,PHI,PRZTH,PTFN,
35 C *RFN13,RTZTA,RZTH,SUMA,SUMB,TFN,T2,UP,W,W2,Z,ZA,ZB,ZC,ZETA,ZETA1,
36 C *ZETA2,ZTH
37 DOUBLE PRECISION ALFA, ANG, AP, AR, ARGI, ARGR, ASUMI, ASUMR,
38 * ATOL, AW2, AZTH, BETA, BR, BSUMI, BSUMR, BTOL, C, CONEI, CONER,
39 * CRI, CRR, DRI, DRR, EX1, EX2, FNU, FN13, FN23, GAMA, GPI, HPI,
40 * PHII, PHIR, PI, PP, PR, PRZTHI, PRZTHR, PTFNI, PTFNR, RAW, RAW2,
41 * RAZTH, RFNU, RFNU2, RFN13, RTZTI, RTZTR, RZTHI, RZTHR, STI, STR,
42 * SUMAI, SUMAR, SUMBI, SUMBR, TEST, TFNI, TFNR, THPI, TOL, TZAI,
43 * TZAR, T2I, T2R, UPI, UPR, WI, WR, W2I, W2R, ZAI, ZAR, ZBI, ZBR,
44 * ZCI, ZCR, ZEROI, ZEROR, ZETAI, ZETAR, ZETA1I, ZETA1R, ZETA2I,
45 * ZETA2R, ZI, ZR, ZTHI, ZTHR, AZABS, AC, D1MACH
46 INTEGER IAS, IBS, IPMTR, IS, J, JR, JU, K, KMAX, KP1, KS, L, LR,
47 * LRP1, L1, L2, M, IDUM
48 DIMENSION AR(14), BR(14), C(105), ALFA(180), BETA(210), GAMA(30),
49 * AP(30), PR(30), PI(30), UPR(14), UPI(14), CRR(14), CRI(14),
50 * DRR(14), DRI(14)
51 DATA AR(1), AR(2), AR(3), AR(4), AR(5), AR(6), AR(7), AR(8),
52 1 AR(9), AR(10), AR(11), AR(12), AR(13), AR(14)/
53 2 1.00000000000000000D+00, 1.04166666666666667D-01,
54 3 8.35503472222222222D-02, 1.28226574556327160D-01,
55 4 2.91849026464140464D-01, 8.81627267443757652D-01,
56 5 3.32140828186276754D+00, 1.49957629868625547D+01,
57 6 7.89230130115865181D+01, 4.74451538868264323D+02,
58 7 3.20749009089066193D+03, 2.40865496408740049D+04,
59 8 1.98923119169509794D+05, 1.79190200777534383D+06/
60 DATA BR(1), BR(2), BR(3), BR(4), BR(5), BR(6), BR(7), BR(8),
61 1 BR(9), BR(10), BR(11), BR(12), BR(13), BR(14)/
62 2 1.00000000000000000D+00, -1.45833333333333333D-01,
63 3 -9.87413194444444444D-02, -1.43312053915895062D-01,
64 4 -3.17227202678413548D-01, -9.42429147957120249D-01,
65 5 -3.51120304082635426D+00, -1.57272636203680451D+01,
66 6 -8.22814390971859444D+01, -4.92355370523670524D+02,
67 7 -3.31621856854797251D+03, -2.48276742452085896D+04,
68 8 -2.04526587315129788D+05, -1.83844491706820990D+06/
69 DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10),
70 1 C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18),
71 2 C(19), C(20), C(21), C(22), C(23), C(24)/
72 3 1.00000000000000000D+00, -2.08333333333333333D-01,
73 4 1.25000000000000000D-01, 3.34201388888888889D-01,
74 5 -4.01041666666666667D-01, 7.03125000000000000D-02,
75 6 -1.02581259645061728D+00, 1.84646267361111111D+00,
76 7 -8.91210937500000000D-01, 7.32421875000000000D-02,
77 8 4.66958442342624743D+00, -1.12070026162229938D+01,
78 9 8.78912353515625000D+00, -2.36408691406250000D+00,
79 A 1.12152099609375000D-01, -2.82120725582002449D+01,
80 B 8.46362176746007346D+01, -9.18182415432400174D+01,
81 C 4.25349987453884549D+01, -7.36879435947963170D+00,
82 D 2.27108001708984375D-01, 2.12570130039217123D+02,
83 E -7.65252468141181642D+02, 1.05999045252799988D+03/
84 DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32),
85 1 C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40),
86 2 C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/
87 3 -6.99579627376132541D+02, 2.18190511744211590D+02,
88 4 -2.64914304869515555D+01, 5.72501420974731445D-01,
89 5 -1.91945766231840700D+03, 8.06172218173730938D+03,
90 6 -1.35865500064341374D+04, 1.16553933368645332D+04,
91 7 -5.30564697861340311D+03, 1.20090291321635246D+03,
92 8 -1.08090919788394656D+02, 1.72772750258445740D+00,
93 9 2.02042913309661486D+04, -9.69805983886375135D+04,
94 A 1.92547001232531532D+05, -2.03400177280415534D+05,
95 B 1.22200464983017460D+05, -4.11926549688975513D+04,
96 C 7.10951430248936372D+03, -4.93915304773088012D+02,
97 D 6.07404200127348304D+00, -2.42919187900551333D+05,
98 E 1.31176361466297720D+06, -2.99801591853810675D+06/
99 DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56),
100 1 C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64),
101 2 C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/
102 3 3.76327129765640400D+06, -2.81356322658653411D+06,
103 4 1.26836527332162478D+06, -3.31645172484563578D+05,
104 5 4.52187689813627263D+04, -2.49983048181120962D+03,
105 6 2.43805296995560639D+01, 3.28446985307203782D+06,
106 7 -1.97068191184322269D+07, 5.09526024926646422D+07,
107 8 -7.41051482115326577D+07, 6.63445122747290267D+07,
108 9 -3.75671766607633513D+07, 1.32887671664218183D+07,
109 A -2.78561812808645469D+06, 3.08186404612662398D+05,
110 B -1.38860897537170405D+04, 1.10017140269246738D+02,
111 C -4.93292536645099620D+07, 3.25573074185765749D+08,
112 D -9.39462359681578403D+08, 1.55359689957058006D+09,
113 E -1.62108055210833708D+09, 1.10684281682301447D+09/
114 DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80),
115 1 C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88),
116 2 C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/
117 3 -4.95889784275030309D+08, 1.42062907797533095D+08,
118 4 -2.44740627257387285D+07, 2.24376817792244943D+06,
119 5 -8.40054336030240853D+04, 5.51335896122020586D+02,
120 6 8.14789096118312115D+08, -5.86648149205184723D+09,
121 7 1.86882075092958249D+10, -3.46320433881587779D+10,
122 8 4.12801855797539740D+10, -3.30265997498007231D+10,
123 9 1.79542137311556001D+10, -6.56329379261928433D+09,
124 A 1.55927986487925751D+09, -2.25105661889415278D+08,
125 B 1.73951075539781645D+07, -5.49842327572288687D+05,
126 C 3.03809051092238427D+03, -1.46792612476956167D+10,
127 D 1.14498237732025810D+11, -3.99096175224466498D+11,
128 E 8.19218669548577329D+11, -1.09837515608122331D+12/
129 DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104),
130 1 C(105)/
131 2 1.00815810686538209D+12, -6.45364869245376503D+11,
132 3 2.87900649906150589D+11, -8.78670721780232657D+10,
133 4 1.76347306068349694D+10, -2.16716498322379509D+09,
134 5 1.43157876718888981D+08, -3.87183344257261262D+06,
135 6 1.82577554742931747D+04/
136 DATA ALFA(1), ALFA(2), ALFA(3), ALFA(4), ALFA(5), ALFA(6),
137 1 ALFA(7), ALFA(8), ALFA(9), ALFA(10), ALFA(11), ALFA(12),
138 2 ALFA(13), ALFA(14), ALFA(15), ALFA(16), ALFA(17), ALFA(18),
139 3 ALFA(19), ALFA(20), ALFA(21), ALFA(22)/
140 4 -4.44444444444444444D-03, -9.22077922077922078D-04,
141 5 -8.84892884892884893D-05, 1.65927687832449737D-04,
142 6 2.46691372741792910D-04, 2.65995589346254780D-04,
143 7 2.61824297061500945D-04, 2.48730437344655609D-04,
144 8 2.32721040083232098D-04, 2.16362485712365082D-04,
145 9 2.00738858762752355D-04, 1.86267636637545172D-04,
146 A 1.73060775917876493D-04, 1.61091705929015752D-04,
147 B 1.50274774160908134D-04, 1.40503497391269794D-04,
148 C 1.31668816545922806D-04, 1.23667445598253261D-04,
149 D 1.16405271474737902D-04, 1.09798298372713369D-04,
150 E 1.03772410422992823D-04, 9.82626078369363448D-05/
151 DATA ALFA(23), ALFA(24), ALFA(25), ALFA(26), ALFA(27), ALFA(28),
152 1 ALFA(29), ALFA(30), ALFA(31), ALFA(32), ALFA(33), ALFA(34),
153 2 ALFA(35), ALFA(36), ALFA(37), ALFA(38), ALFA(39), ALFA(40),
154 3 ALFA(41), ALFA(42), ALFA(43), ALFA(44)/
155 4 9.32120517249503256D-05, 8.85710852478711718D-05,
156 5 8.42963105715700223D-05, 8.03497548407791151D-05,
157 6 7.66981345359207388D-05, 7.33122157481777809D-05,
158 7 7.01662625163141333D-05, 6.72375633790160292D-05,
159 8 6.93735541354588974D-04, 2.32241745182921654D-04,
160 9 -1.41986273556691197D-05, -1.16444931672048640D-04,
161 A -1.50803558053048762D-04, -1.55121924918096223D-04,
162 B -1.46809756646465549D-04, -1.33815503867491367D-04,
163 C -1.19744975684254051D-04, -1.06184319207974020D-04,
164 D -9.37699549891194492D-05, -8.26923045588193274D-05,
165 E -7.29374348155221211D-05, -6.44042357721016283D-05/
166 DATA ALFA(45), ALFA(46), ALFA(47), ALFA(48), ALFA(49), ALFA(50),
167 1 ALFA(51), ALFA(52), ALFA(53), ALFA(54), ALFA(55), ALFA(56),
168 2 ALFA(57), ALFA(58), ALFA(59), ALFA(60), ALFA(61), ALFA(62),
169 3 ALFA(63), ALFA(64), ALFA(65), ALFA(66)/
170 4 -5.69611566009369048D-05, -5.04731044303561628D-05,
171 5 -4.48134868008882786D-05, -3.98688727717598864D-05,
172 6 -3.55400532972042498D-05, -3.17414256609022480D-05,
173 7 -2.83996793904174811D-05, -2.54522720634870566D-05,
174 8 -2.28459297164724555D-05, -2.05352753106480604D-05,
175 9 -1.84816217627666085D-05, -1.66519330021393806D-05,
176 A -1.50179412980119482D-05, -1.35554031379040526D-05,
177 B -1.22434746473858131D-05, -1.10641884811308169D-05,
178 C -3.54211971457743841D-04, -1.56161263945159416D-04,
179 D 3.04465503594936410D-05, 1.30198655773242693D-04,
180 E 1.67471106699712269D-04, 1.70222587683592569D-04/
181 DATA ALFA(67), ALFA(68), ALFA(69), ALFA(70), ALFA(71), ALFA(72),
182 1 ALFA(73), ALFA(74), ALFA(75), ALFA(76), ALFA(77), ALFA(78),
183 2 ALFA(79), ALFA(80), ALFA(81), ALFA(82), ALFA(83), ALFA(84),
184 3 ALFA(85), ALFA(86), ALFA(87), ALFA(88)/
185 4 1.56501427608594704D-04, 1.36339170977445120D-04,
186 5 1.14886692029825128D-04, 9.45869093034688111D-05,
187 6 7.64498419250898258D-05, 6.07570334965197354D-05,
188 7 4.74394299290508799D-05, 3.62757512005344297D-05,
189 8 2.69939714979224901D-05, 1.93210938247939253D-05,
190 9 1.30056674793963203D-05, 7.82620866744496661D-06,
191 A 3.59257485819351583D-06, 1.44040049814251817D-07,
192 B -2.65396769697939116D-06, -4.91346867098485910D-06,
193 C -6.72739296091248287D-06, -8.17269379678657923D-06,
194 D -9.31304715093561232D-06, -1.02011418798016441D-05,
195 E -1.08805962510592880D-05, -1.13875481509603555D-05/
196 DATA ALFA(89), ALFA(90), ALFA(91), ALFA(92), ALFA(93), ALFA(94),
197 1 ALFA(95), ALFA(96), ALFA(97), ALFA(98), ALFA(99), ALFA(100),
198 2 ALFA(101), ALFA(102), ALFA(103), ALFA(104), ALFA(105),
199 3 ALFA(106), ALFA(107), ALFA(108), ALFA(109), ALFA(110)/
200 4 -1.17519675674556414D-05, -1.19987364870944141D-05,
201 5 3.78194199201772914D-04, 2.02471952761816167D-04,
202 6 -6.37938506318862408D-05, -2.38598230603005903D-04,
203 7 -3.10916256027361568D-04, -3.13680115247576316D-04,
204 8 -2.78950273791323387D-04, -2.28564082619141374D-04,
205 9 -1.75245280340846749D-04, -1.25544063060690348D-04,
206 A -8.22982872820208365D-05, -4.62860730588116458D-05,
207 B -1.72334302366962267D-05, 5.60690482304602267D-06,
208 C 2.31395443148286800D-05, 3.62642745856793957D-05,
209 D 4.58006124490188752D-05, 5.24595294959114050D-05,
210 E 5.68396208545815266D-05, 5.94349820393104052D-05/
211 DATA ALFA(111), ALFA(112), ALFA(113), ALFA(114), ALFA(115),
212 1 ALFA(116), ALFA(117), ALFA(118), ALFA(119), ALFA(120),
213 2 ALFA(121), ALFA(122), ALFA(123), ALFA(124), ALFA(125),
214 3 ALFA(126), ALFA(127), ALFA(128), ALFA(129), ALFA(130)/
215 4 6.06478527578421742D-05, 6.08023907788436497D-05,
216 5 6.01577894539460388D-05, 5.89199657344698500D-05,
217 6 5.72515823777593053D-05, 5.52804375585852577D-05,
218 7 5.31063773802880170D-05, 5.08069302012325706D-05,
219 8 4.84418647620094842D-05, 4.60568581607475370D-05,
220 9 -6.91141397288294174D-04, -4.29976633058871912D-04,
221 A 1.83067735980039018D-04, 6.60088147542014144D-04,
222 B 8.75964969951185931D-04, 8.77335235958235514D-04,
223 C 7.49369585378990637D-04, 5.63832329756980918D-04,
224 D 3.68059319971443156D-04, 1.88464535514455599D-04/
225 DATA ALFA(131), ALFA(132), ALFA(133), ALFA(134), ALFA(135),
226 1 ALFA(136), ALFA(137), ALFA(138), ALFA(139), ALFA(140),
227 2 ALFA(141), ALFA(142), ALFA(143), ALFA(144), ALFA(145),
228 3 ALFA(146), ALFA(147), ALFA(148), ALFA(149), ALFA(150)/
229 4 3.70663057664904149D-05, -8.28520220232137023D-05,
230 5 -1.72751952869172998D-04, -2.36314873605872983D-04,
231 6 -2.77966150694906658D-04, -3.02079514155456919D-04,
232 7 -3.12594712643820127D-04, -3.12872558758067163D-04,
233 8 -3.05678038466324377D-04, -2.93226470614557331D-04,
234 9 -2.77255655582934777D-04, -2.59103928467031709D-04,
235 A -2.39784014396480342D-04, -2.20048260045422848D-04,
236 B -2.00443911094971498D-04, -1.81358692210970687D-04,
237 C -1.63057674478657464D-04, -1.45712672175205844D-04,
238 D -1.29425421983924587D-04, -1.14245691942445952D-04/
239 DATA ALFA(151), ALFA(152), ALFA(153), ALFA(154), ALFA(155),
240 1 ALFA(156), ALFA(157), ALFA(158), ALFA(159), ALFA(160),
241 2 ALFA(161), ALFA(162), ALFA(163), ALFA(164), ALFA(165),
242 3 ALFA(166), ALFA(167), ALFA(168), ALFA(169), ALFA(170)/
243 4 1.92821964248775885D-03, 1.35592576302022234D-03,
244 5 -7.17858090421302995D-04, -2.58084802575270346D-03,
245 6 -3.49271130826168475D-03, -3.46986299340960628D-03,
246 7 -2.82285233351310182D-03, -1.88103076404891354D-03,
247 8 -8.89531718383947600D-04, 3.87912102631035228D-06,
248 9 7.28688540119691412D-04, 1.26566373053457758D-03,
249 A 1.62518158372674427D-03, 1.83203153216373172D-03,
250 B 1.91588388990527909D-03, 1.90588846755546138D-03,
251 C 1.82798982421825727D-03, 1.70389506421121530D-03,
252 D 1.55097127171097686D-03, 1.38261421852276159D-03/
253 DATA ALFA(171), ALFA(172), ALFA(173), ALFA(174), ALFA(175),
254 1 ALFA(176), ALFA(177), ALFA(178), ALFA(179), ALFA(180)/
255 2 1.20881424230064774D-03, 1.03676532638344962D-03,
256 3 8.71437918068619115D-04, 7.16080155297701002D-04,
257 4 5.72637002558129372D-04, 4.42089819465802277D-04,
258 5 3.24724948503090564D-04, 2.20342042730246599D-04,
259 6 1.28412898401353882D-04, 4.82005924552095464D-05/
260 DATA BETA(1), BETA(2), BETA(3), BETA(4), BETA(5), BETA(6),
261 1 BETA(7), BETA(8), BETA(9), BETA(10), BETA(11), BETA(12),
262 2 BETA(13), BETA(14), BETA(15), BETA(16), BETA(17), BETA(18),
263 3 BETA(19), BETA(20), BETA(21), BETA(22)/
264 4 1.79988721413553309D-02, 5.59964911064388073D-03,
265 5 2.88501402231132779D-03, 1.80096606761053941D-03,
266 6 1.24753110589199202D-03, 9.22878876572938311D-04,
267 7 7.14430421727287357D-04, 5.71787281789704872D-04,
268 8 4.69431007606481533D-04, 3.93232835462916638D-04,
269 9 3.34818889318297664D-04, 2.88952148495751517D-04,
270 A 2.52211615549573284D-04, 2.22280580798883327D-04,
271 B 1.97541838033062524D-04, 1.76836855019718004D-04,
272 C 1.59316899661821081D-04, 1.44347930197333986D-04,
273 D 1.31448068119965379D-04, 1.20245444949302884D-04,
274 E 1.10449144504599392D-04, 1.01828770740567258D-04/
275 DATA BETA(23), BETA(24), BETA(25), BETA(26), BETA(27), BETA(28),
276 1 BETA(29), BETA(30), BETA(31), BETA(32), BETA(33), BETA(34),
277 2 BETA(35), BETA(36), BETA(37), BETA(38), BETA(39), BETA(40),
278 3 BETA(41), BETA(42), BETA(43), BETA(44)/
279 4 9.41998224204237509D-05, 8.74130545753834437D-05,
280 5 8.13466262162801467D-05, 7.59002269646219339D-05,
281 6 7.09906300634153481D-05, 6.65482874842468183D-05,
282 7 6.25146958969275078D-05, 5.88403394426251749D-05,
283 8 -1.49282953213429172D-03, -8.78204709546389328D-04,
284 9 -5.02916549572034614D-04, -2.94822138512746025D-04,
285 A -1.75463996970782828D-04, -1.04008550460816434D-04,
286 B -5.96141953046457895D-05, -3.12038929076098340D-05,
287 C -1.26089735980230047D-05, -2.42892608575730389D-07,
288 D 8.05996165414273571D-06, 1.36507009262147391D-05,
289 E 1.73964125472926261D-05, 1.98672978842133780D-05/
290 DATA BETA(45), BETA(46), BETA(47), BETA(48), BETA(49), BETA(50),
291 1 BETA(51), BETA(52), BETA(53), BETA(54), BETA(55), BETA(56),
292 2 BETA(57), BETA(58), BETA(59), BETA(60), BETA(61), BETA(62),
293 3 BETA(63), BETA(64), BETA(65), BETA(66)/
294 4 2.14463263790822639D-05, 2.23954659232456514D-05,
295 5 2.28967783814712629D-05, 2.30785389811177817D-05,
296 6 2.30321976080909144D-05, 2.28236073720348722D-05,
297 7 2.25005881105292418D-05, 2.20981015361991429D-05,
298 8 2.16418427448103905D-05, 2.11507649256220843D-05,
299 9 2.06388749782170737D-05, 2.01165241997081666D-05,
300 A 1.95913450141179244D-05, 1.90689367910436740D-05,
301 B 1.85533719641636667D-05, 1.80475722259674218D-05,
302 C 5.52213076721292790D-04, 4.47932581552384646D-04,
303 D 2.79520653992020589D-04, 1.52468156198446602D-04,
304 E 6.93271105657043598D-05, 1.76258683069991397D-05/
305 DATA BETA(67), BETA(68), BETA(69), BETA(70), BETA(71), BETA(72),
306 1 BETA(73), BETA(74), BETA(75), BETA(76), BETA(77), BETA(78),
307 2 BETA(79), BETA(80), BETA(81), BETA(82), BETA(83), BETA(84),
308 3 BETA(85), BETA(86), BETA(87), BETA(88)/
309 4 -1.35744996343269136D-05, -3.17972413350427135D-05,
310 5 -4.18861861696693365D-05, -4.69004889379141029D-05,
311 6 -4.87665447413787352D-05, -4.87010031186735069D-05,
312 7 -4.74755620890086638D-05, -4.55813058138628452D-05,
313 8 -4.33309644511266036D-05, -4.09230193157750364D-05,
314 9 -3.84822638603221274D-05, -3.60857167535410501D-05,
315 A -3.37793306123367417D-05, -3.15888560772109621D-05,
316 B -2.95269561750807315D-05, -2.75978914828335759D-05,
317 C -2.58006174666883713D-05, -2.41308356761280200D-05,
318 D -2.25823509518346033D-05, -2.11479656768912971D-05,
319 E -1.98200638885294927D-05, -1.85909870801065077D-05/
320 DATA BETA(89), BETA(90), BETA(91), BETA(92), BETA(93), BETA(94),
321 1 BETA(95), BETA(96), BETA(97), BETA(98), BETA(99), BETA(100),
322 2 BETA(101), BETA(102), BETA(103), BETA(104), BETA(105),
323 3 BETA(106), BETA(107), BETA(108), BETA(109), BETA(110)/
324 4 -1.74532699844210224D-05, -1.63997823854497997D-05,
325 5 -4.74617796559959808D-04, -4.77864567147321487D-04,
326 6 -3.20390228067037603D-04, -1.61105016119962282D-04,
327 7 -4.25778101285435204D-05, 3.44571294294967503D-05,
328 8 7.97092684075674924D-05, 1.03138236708272200D-04,
329 9 1.12466775262204158D-04, 1.13103642108481389D-04,
330 A 1.08651634848774268D-04, 1.01437951597661973D-04,
331 B 9.29298396593363896D-05, 8.40293133016089978D-05,
332 C 7.52727991349134062D-05, 6.69632521975730872D-05,
333 D 5.92564547323194704D-05, 5.22169308826975567D-05,
334 E 4.58539485165360646D-05, 4.01445513891486808D-05/
335 DATA BETA(111), BETA(112), BETA(113), BETA(114), BETA(115),
336 1 BETA(116), BETA(117), BETA(118), BETA(119), BETA(120),
337 2 BETA(121), BETA(122), BETA(123), BETA(124), BETA(125),
338 3 BETA(126), BETA(127), BETA(128), BETA(129), BETA(130)/
339 4 3.50481730031328081D-05, 3.05157995034346659D-05,
340 5 2.64956119950516039D-05, 2.29363633690998152D-05,
341 6 1.97893056664021636D-05, 1.70091984636412623D-05,
342 7 1.45547428261524004D-05, 1.23886640995878413D-05,
343 8 1.04775876076583236D-05, 8.79179954978479373D-06,
344 9 7.36465810572578444D-04, 8.72790805146193976D-04,
345 A 6.22614862573135066D-04, 2.85998154194304147D-04,
346 B 3.84737672879366102D-06, -1.87906003636971558D-04,
347 C -2.97603646594554535D-04, -3.45998126832656348D-04,
348 D -3.53382470916037712D-04, -3.35715635775048757D-04/
349 DATA BETA(131), BETA(132), BETA(133), BETA(134), BETA(135),
350 1 BETA(136), BETA(137), BETA(138), BETA(139), BETA(140),
351 2 BETA(141), BETA(142), BETA(143), BETA(144), BETA(145),
352 3 BETA(146), BETA(147), BETA(148), BETA(149), BETA(150)/
353 4 -3.04321124789039809D-04, -2.66722723047612821D-04,
354 5 -2.27654214122819527D-04, -1.89922611854562356D-04,
355 6 -1.55058918599093870D-04, -1.23778240761873630D-04,
356 7 -9.62926147717644187D-05, -7.25178327714425337D-05,
357 8 -5.22070028895633801D-05, -3.50347750511900522D-05,
358 9 -2.06489761035551757D-05, -8.70106096849767054D-06,
359 A 1.13698686675100290D-06, 9.16426474122778849D-06,
360 B 1.56477785428872620D-05, 2.08223629482466847D-05,
361 C 2.48923381004595156D-05, 2.80340509574146325D-05,
362 D 3.03987774629861915D-05, 3.21156731406700616D-05/
363 DATA BETA(151), BETA(152), BETA(153), BETA(154), BETA(155),
364 1 BETA(156), BETA(157), BETA(158), BETA(159), BETA(160),
365 2 BETA(161), BETA(162), BETA(163), BETA(164), BETA(165),
366 3 BETA(166), BETA(167), BETA(168), BETA(169), BETA(170)/
367 4 -1.80182191963885708D-03, -2.43402962938042533D-03,
368 5 -1.83422663549856802D-03, -7.62204596354009765D-04,
369 6 2.39079475256927218D-04, 9.49266117176881141D-04,
370 7 1.34467449701540359D-03, 1.48457495259449178D-03,
371 8 1.44732339830617591D-03, 1.30268261285657186D-03,
372 9 1.10351597375642682D-03, 8.86047440419791759D-04,
373 A 6.73073208165665473D-04, 4.77603872856582378D-04,
374 B 3.05991926358789362D-04, 1.60315694594721630D-04,
375 C 4.00749555270613286D-05, -5.66607461635251611D-05,
376 D -1.32506186772982638D-04, -1.90296187989614057D-04/
377 DATA BETA(171), BETA(172), BETA(173), BETA(174), BETA(175),
378 1 BETA(176), BETA(177), BETA(178), BETA(179), BETA(180),
379 2 BETA(181), BETA(182), BETA(183), BETA(184), BETA(185),
380 3 BETA(186), BETA(187), BETA(188), BETA(189), BETA(190)/
381 4 -2.32811450376937408D-04, -2.62628811464668841D-04,
382 5 -2.82050469867598672D-04, -2.93081563192861167D-04,
383 6 -2.97435962176316616D-04, -2.96557334239348078D-04,
384 7 -2.91647363312090861D-04, -2.83696203837734166D-04,
385 8 -2.73512317095673346D-04, -2.61750155806768580D-04,
386 9 6.38585891212050914D-03, 9.62374215806377941D-03,
387 A 7.61878061207001043D-03, 2.83219055545628054D-03,
388 B -2.09841352012720090D-03, -5.73826764216626498D-03,
389 C -7.70804244495414620D-03, -8.21011692264844401D-03,
390 D -7.65824520346905413D-03, -6.47209729391045177D-03/
391 DATA BETA(191), BETA(192), BETA(193), BETA(194), BETA(195),
392 1 BETA(196), BETA(197), BETA(198), BETA(199), BETA(200),
393 2 BETA(201), BETA(202), BETA(203), BETA(204), BETA(205),
394 3 BETA(206), BETA(207), BETA(208), BETA(209), BETA(210)/
395 4 -4.99132412004966473D-03, -3.45612289713133280D-03,
396 5 -2.01785580014170775D-03, -7.59430686781961401D-04,
397 6 2.84173631523859138D-04, 1.10891667586337403D-03,
398 7 1.72901493872728771D-03, 2.16812590802684701D-03,
399 8 2.45357710494539735D-03, 2.61281821058334862D-03,
400 9 2.67141039656276912D-03, 2.65203073395980430D-03,
401 A 2.57411652877287315D-03, 2.45389126236094427D-03,
402 B 2.30460058071795494D-03, 2.13684837686712662D-03,
403 C 1.95896528478870911D-03, 1.77737008679454412D-03,
404 D 1.59690280765839059D-03, 1.42111975664438546D-03/
405 DATA GAMA(1), GAMA(2), GAMA(3), GAMA(4), GAMA(5), GAMA(6),
406 1 GAMA(7), GAMA(8), GAMA(9), GAMA(10), GAMA(11), GAMA(12),
407 2 GAMA(13), GAMA(14), GAMA(15), GAMA(16), GAMA(17), GAMA(18),
408 3 GAMA(19), GAMA(20), GAMA(21), GAMA(22)/
409 4 6.29960524947436582D-01, 2.51984209978974633D-01,
410 5 1.54790300415655846D-01, 1.10713062416159013D-01,
411 6 8.57309395527394825D-02, 6.97161316958684292D-02,
412 7 5.86085671893713576D-02, 5.04698873536310685D-02,
413 8 4.42600580689154809D-02, 3.93720661543509966D-02,
414 9 3.54283195924455368D-02, 3.21818857502098231D-02,
415 A 2.94646240791157679D-02, 2.71581677112934479D-02,
416 B 2.51768272973861779D-02, 2.34570755306078891D-02,
417 C 2.19508390134907203D-02, 2.06210828235646240D-02,
418 D 1.94388240897880846D-02, 1.83810633800683158D-02,
419 E 1.74293213231963172D-02, 1.65685837786612353D-02/
420 DATA GAMA(23), GAMA(24), GAMA(25), GAMA(26), GAMA(27), GAMA(28),
421 1 GAMA(29), GAMA(30)/
422 2 1.57865285987918445D-02, 1.50729501494095594D-02,
423 3 1.44193250839954639D-02, 1.38184805735341786D-02,
424 4 1.32643378994276568D-02, 1.27517121970498651D-02,
425 5 1.22761545318762767D-02, 1.18338262398482403D-02/
426 DATA EX1, EX2, HPI, GPI, THPI /
427 1 3.33333333333333333D-01, 6.66666666666666667D-01,
428 2 1.57079632679489662D+00, 3.14159265358979324D+00,
429 3 4.71238898038468986D+00/
430 DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 /
432 RFNU = 1.0D0/FNU
433 C-----------------------------------------------------------------------
434 C OVERFLOW TEST (Z/FNU TOO SMALL)
435 C-----------------------------------------------------------------------
436 TEST = D1MACH(1)*1.0D+3
437 AC = FNU*TEST
438 IF (DABS(ZR).GT.AC .OR. DABS(ZI).GT.AC) GO TO 15
439 ZETA1R = 2.0D0*DABS(DLOG(TEST))+FNU
440 ZETA1I = 0.0D0
441 ZETA2R = FNU
442 ZETA2I = 0.0D0
443 PHIR = 1.0D0
444 PHII = 0.0D0
445 ARGR = 1.0D0
446 ARGI = 0.0D0
447 RETURN
448 15 CONTINUE
449 ZBR = ZR*RFNU
450 ZBI = ZI*RFNU
451 RFNU2 = RFNU*RFNU
452 C-----------------------------------------------------------------------
453 C COMPUTE IN THE FOURTH QUADRANT
454 C-----------------------------------------------------------------------
455 FN13 = FNU**EX1
456 FN23 = FN13*FN13
457 RFN13 = 1.0D0/FN13
458 W2R = CONER - ZBR*ZBR + ZBI*ZBI
459 W2I = CONEI - ZBR*ZBI - ZBR*ZBI
460 AW2 = AZABS(W2R,W2I)
461 IF (AW2.GT.0.25D0) GO TO 130
462 C-----------------------------------------------------------------------
463 C POWER SERIES FOR CABS(W2).LE.0.25D0
464 C-----------------------------------------------------------------------
465 K = 1
466 PR(1) = CONER
467 PI(1) = CONEI
468 SUMAR = GAMA(1)
469 SUMAI = ZEROI
470 AP(1) = 1.0D0
471 IF (AW2.LT.TOL) GO TO 20
472 DO 10 K=2,30
473 PR(K) = PR(K-1)*W2R - PI(K-1)*W2I
474 PI(K) = PR(K-1)*W2I + PI(K-1)*W2R
475 SUMAR = SUMAR + PR(K)*GAMA(K)
476 SUMAI = SUMAI + PI(K)*GAMA(K)
477 AP(K) = AP(K-1)*AW2
478 IF (AP(K).LT.TOL) GO TO 20
479 10 CONTINUE
480 K = 30
481 20 CONTINUE
482 KMAX = K
483 ZETAR = W2R*SUMAR - W2I*SUMAI
484 ZETAI = W2R*SUMAI + W2I*SUMAR
485 ARGR = ZETAR*FN23
486 ARGI = ZETAI*FN23
487 CALL AZSQRT(SUMAR, SUMAI, ZAR, ZAI)
488 CALL AZSQRT(W2R, W2I, STR, STI)
489 ZETA2R = STR*FNU
490 ZETA2I = STI*FNU
491 STR = CONER + EX2*(ZETAR*ZAR-ZETAI*ZAI)
492 STI = CONEI + EX2*(ZETAR*ZAI+ZETAI*ZAR)
493 ZETA1R = STR*ZETA2R - STI*ZETA2I
494 ZETA1I = STR*ZETA2I + STI*ZETA2R
495 ZAR = ZAR + ZAR
496 ZAI = ZAI + ZAI
497 CALL AZSQRT(ZAR, ZAI, STR, STI)
498 PHIR = STR*RFN13
499 PHII = STI*RFN13
500 IF (IPMTR.EQ.1) GO TO 120
501 C-----------------------------------------------------------------------
502 C SUM SERIES FOR ASUM AND BSUM
503 C-----------------------------------------------------------------------
504 SUMBR = ZEROR
505 SUMBI = ZEROI
506 DO 30 K=1,KMAX
507 SUMBR = SUMBR + PR(K)*BETA(K)
508 SUMBI = SUMBI + PI(K)*BETA(K)
509 30 CONTINUE
510 ASUMR = ZEROR
511 ASUMI = ZEROI
512 BSUMR = SUMBR
513 BSUMI = SUMBI
514 L1 = 0
515 L2 = 30
516 BTOL = TOL*(DABS(BSUMR)+DABS(BSUMI))
517 ATOL = TOL
518 PP = 1.0D0
519 IAS = 0
520 IBS = 0
521 IF (RFNU2.LT.TOL) GO TO 110
522 DO 100 IS=2,7
523 ATOL = ATOL/RFNU2
524 PP = PP*RFNU2
525 IF (IAS.EQ.1) GO TO 60
526 SUMAR = ZEROR
527 SUMAI = ZEROI
528 DO 40 K=1,KMAX
529 M = L1 + K
530 SUMAR = SUMAR + PR(K)*ALFA(M)
531 SUMAI = SUMAI + PI(K)*ALFA(M)
532 IF (AP(K).LT.ATOL) GO TO 50
533 40 CONTINUE
534 50 CONTINUE
535 ASUMR = ASUMR + SUMAR*PP
536 ASUMI = ASUMI + SUMAI*PP
537 IF (PP.LT.TOL) IAS = 1
538 60 CONTINUE
539 IF (IBS.EQ.1) GO TO 90
540 SUMBR = ZEROR
541 SUMBI = ZEROI
542 DO 70 K=1,KMAX
543 M = L2 + K
544 SUMBR = SUMBR + PR(K)*BETA(M)
545 SUMBI = SUMBI + PI(K)*BETA(M)
546 IF (AP(K).LT.ATOL) GO TO 80
547 70 CONTINUE
548 80 CONTINUE
549 BSUMR = BSUMR + SUMBR*PP
550 BSUMI = BSUMI + SUMBI*PP
551 IF (PP.LT.BTOL) IBS = 1
552 90 CONTINUE
553 IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 110
554 L1 = L1 + 30
555 L2 = L2 + 30
556 100 CONTINUE
557 110 CONTINUE
558 ASUMR = ASUMR + CONER
559 PP = RFNU*RFN13
560 BSUMR = BSUMR*PP
561 BSUMI = BSUMI*PP
562 120 CONTINUE
563 RETURN
564 C-----------------------------------------------------------------------
565 C CABS(W2).GT.0.25D0
566 C-----------------------------------------------------------------------
567 130 CONTINUE
568 CALL AZSQRT(W2R, W2I, WR, WI)
569 IF (WR.LT.0.0D0) WR = 0.0D0
570 IF (WI.LT.0.0D0) WI = 0.0D0
571 STR = CONER + WR
572 STI = WI
573 CALL ZDIV(STR, STI, ZBR, ZBI, ZAR, ZAI)
574 CALL AZLOG(ZAR, ZAI, ZCR, ZCI, IDUM)
575 IF (ZCI.LT.0.0D0) ZCI = 0.0D0
576 IF (ZCI.GT.HPI) ZCI = HPI
577 IF (ZCR.LT.0.0D0) ZCR = 0.0D0
578 ZTHR = (ZCR-WR)*1.5D0
579 ZTHI = (ZCI-WI)*1.5D0
580 ZETA1R = ZCR*FNU
581 ZETA1I = ZCI*FNU
582 ZETA2R = WR*FNU
583 ZETA2I = WI*FNU
584 AZTH = AZABS(ZTHR,ZTHI)
585 ANG = THPI
586 IF (ZTHR.GE.0.0D0 .AND. ZTHI.LT.0.0D0) GO TO 140
587 ANG = HPI
588 IF (ZTHR.EQ.0.0D0) GO TO 140
589 ANG = DATAN(ZTHI/ZTHR)
590 IF (ZTHR.LT.0.0D0) ANG = ANG + GPI
591 140 CONTINUE
592 PP = AZTH**EX2
593 ANG = ANG*EX2
594 ZETAR = PP*DCOS(ANG)
595 ZETAI = PP*DSIN(ANG)
596 IF (ZETAI.LT.0.0D0) ZETAI = 0.0D0
597 ARGR = ZETAR*FN23
598 ARGI = ZETAI*FN23
599 CALL ZDIV(ZTHR, ZTHI, ZETAR, ZETAI, RTZTR, RTZTI)
600 CALL ZDIV(RTZTR, RTZTI, WR, WI, ZAR, ZAI)
601 TZAR = ZAR + ZAR
602 TZAI = ZAI + ZAI
603 CALL AZSQRT(TZAR, TZAI, STR, STI)
604 PHIR = STR*RFN13
605 PHII = STI*RFN13
606 IF (IPMTR.EQ.1) GO TO 120
607 RAW = 1.0D0/DSQRT(AW2)
608 STR = WR*RAW
609 STI = -WI*RAW
610 TFNR = STR*RFNU*RAW
611 TFNI = STI*RFNU*RAW
612 RAZTH = 1.0D0/AZTH
613 STR = ZTHR*RAZTH
614 STI = -ZTHI*RAZTH
615 RZTHR = STR*RAZTH*RFNU
616 RZTHI = STI*RAZTH*RFNU
617 ZCR = RZTHR*AR(2)
618 ZCI = RZTHI*AR(2)
619 RAW2 = 1.0D0/AW2
620 STR = W2R*RAW2
621 STI = -W2I*RAW2
622 T2R = STR*RAW2
623 T2I = STI*RAW2
624 STR = T2R*C(2) + C(3)
625 STI = T2I*C(2)
626 UPR(2) = STR*TFNR - STI*TFNI
627 UPI(2) = STR*TFNI + STI*TFNR
628 BSUMR = UPR(2) + ZCR
629 BSUMI = UPI(2) + ZCI
630 ASUMR = ZEROR
631 ASUMI = ZEROI
632 IF (RFNU.LT.TOL) GO TO 220
633 PRZTHR = RZTHR
634 PRZTHI = RZTHI
635 PTFNR = TFNR
636 PTFNI = TFNI
637 UPR(1) = CONER
638 UPI(1) = CONEI
639 PP = 1.0D0
640 BTOL = TOL*(DABS(BSUMR)+DABS(BSUMI))
641 KS = 0
642 KP1 = 2
643 L = 3
644 IAS = 0
645 IBS = 0
646 DO 210 LR=2,12,2
647 LRP1 = LR + 1
648 C-----------------------------------------------------------------------
649 C COMPUTE TWO ADDITIONAL CR, DR, AND UP FOR TWO MORE TERMS IN
650 C NEXT SUMA AND SUMB
651 C-----------------------------------------------------------------------
652 DO 160 K=LR,LRP1
653 KS = KS + 1
654 KP1 = KP1 + 1
655 L = L + 1
656 ZAR = C(L)
657 ZAI = ZEROI
658 DO 150 J=2,KP1
659 L = L + 1
660 STR = ZAR*T2R - T2I*ZAI + C(L)
661 ZAI = ZAR*T2I + ZAI*T2R
662 ZAR = STR
663 150 CONTINUE
664 STR = PTFNR*TFNR - PTFNI*TFNI
665 PTFNI = PTFNR*TFNI + PTFNI*TFNR
666 PTFNR = STR
667 UPR(KP1) = PTFNR*ZAR - PTFNI*ZAI
668 UPI(KP1) = PTFNI*ZAR + PTFNR*ZAI
669 CRR(KS) = PRZTHR*BR(KS+1)
670 CRI(KS) = PRZTHI*BR(KS+1)
671 STR = PRZTHR*RZTHR - PRZTHI*RZTHI
672 PRZTHI = PRZTHR*RZTHI + PRZTHI*RZTHR
673 PRZTHR = STR
674 DRR(KS) = PRZTHR*AR(KS+2)
675 DRI(KS) = PRZTHI*AR(KS+2)
676 160 CONTINUE
677 PP = PP*RFNU2
678 IF (IAS.EQ.1) GO TO 180
679 SUMAR = UPR(LRP1)
680 SUMAI = UPI(LRP1)
681 JU = LRP1
682 DO 170 JR=1,LR
683 JU = JU - 1
684 SUMAR = SUMAR + CRR(JR)*UPR(JU) - CRI(JR)*UPI(JU)
685 SUMAI = SUMAI + CRR(JR)*UPI(JU) + CRI(JR)*UPR(JU)
686 170 CONTINUE
687 ASUMR = ASUMR + SUMAR
688 ASUMI = ASUMI + SUMAI
689 TEST = DABS(SUMAR) + DABS(SUMAI)
690 IF (PP.LT.TOL .AND. TEST.LT.TOL) IAS = 1
691 180 CONTINUE
692 IF (IBS.EQ.1) GO TO 200
693 SUMBR = UPR(LR+2) + UPR(LRP1)*ZCR - UPI(LRP1)*ZCI
694 SUMBI = UPI(LR+2) + UPR(LRP1)*ZCI + UPI(LRP1)*ZCR
695 JU = LRP1
696 DO 190 JR=1,LR
697 JU = JU - 1
698 SUMBR = SUMBR + DRR(JR)*UPR(JU) - DRI(JR)*UPI(JU)
699 SUMBI = SUMBI + DRR(JR)*UPI(JU) + DRI(JR)*UPR(JU)
700 190 CONTINUE
701 BSUMR = BSUMR + SUMBR
702 BSUMI = BSUMI + SUMBI
703 TEST = DABS(SUMBR) + DABS(SUMBI)
704 IF (PP.LT.BTOL .AND. TEST.LT.BTOL) IBS = 1
705 200 CONTINUE
706 IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 220
707 210 CONTINUE
708 220 CONTINUE
709 ASUMR = ASUMR + CONER
710 STR = -BSUMR*RFN13
711 STI = -BSUMI*RFN13
712 CALL ZDIV(STR, STI, RTZTR, RTZTI, BSUMR, BSUMI)
713 GO TO 120