1*DECK ZUNIK
2      SUBROUTINE ZUNIK (ZRR, ZRI, FNU, IKFLG, IPMTR, TOL, INIT, PHIR,
3     +   PHII, ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI)
4C***BEGIN PROLOGUE  ZUNIK
5C***SUBSIDIARY
6C***PURPOSE  Subsidiary to ZBESI and ZBESK
7C***LIBRARY   SLATEC
8C***TYPE      ALL (CUNIK-A, ZUNIK-A)
9C***AUTHOR  Amos, D. E., (SNL)
10C***DESCRIPTION
11C
12C        ZUNIK COMPUTES PARAMETERS FOR THE UNIFORM ASYMPTOTIC
13C        EXPANSIONS OF THE I AND K FUNCTIONS ON IKFLG= 1 OR 2
14C        RESPECTIVELY BY
15C
16C        W(FNU,ZR) = PHI*EXP(ZETA)*SUM
17C
18C        WHERE       ZETA=-ZETA1 + ZETA2       OR
19C                          ZETA1 - ZETA2
20C
21C        THE FIRST CALL MUST HAVE INIT=0. SUBSEQUENT CALLS WITH THE
22C        SAME ZR AND FNU WILL RETURN THE I OR K FUNCTION ON IKFLG=
23C        1 OR 2 WITH NO CHANGE IN INIT. CWRK IS A COMPLEX WORK
24C        ARRAY. IPMTR=0 COMPUTES ALL PARAMETERS. IPMTR=1 COMPUTES PHI,
25C        ZETA1,ZETA2.
26C
27C***SEE ALSO  ZBESI, ZBESK
28C***ROUTINES CALLED  D1MACH, ZDIV, ZLOG, ZSQRT
29C***REVISION HISTORY  (YYMMDD)
30C   830501  DATE WRITTEN
31C   910415  Prologue converted to Version 4.0 format.  (BAB)
32C   930122  Added EXTERNAL statement with ZLOG and ZSQRT.  (RWC)
33C***END PROLOGUE  ZUNIK
34C     COMPLEX CFN,CON,CONE,CRFN,CWRK,CZERO,PHI,S,SR,SUM,T,T2,ZETA1,
35C    *ZETA2,ZN,ZR
36      DOUBLE PRECISION AC, C, CON, CONEI, CONER, CRFNI, CRFNR, CWRKI,
37     * CWRKR, FNU, PHII, PHIR, RFN, SI, SR, SRI, SRR, STI, STR, SUMI,
38     * SUMR, TEST, TI, TOL, TR, T2I, T2R, ZEROI, ZEROR, ZETA1I, ZETA1R,
39     * ZETA2I, ZETA2R, ZNI, ZNR, ZRI, ZRR, D1MACH
40      INTEGER I, IDUM, IKFLG, INIT, IPMTR, J, K, L
41      DIMENSION C(120), CWRKR(16), CWRKI(16), CON(2)
42      EXTERNAL ZLOG, ZSQRT
43      DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 /
44      DATA CON(1), CON(2)  /
45     1 3.98942280401432678D-01,  1.25331413731550025D+00 /
46      DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10),
47     1     C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18),
48     2     C(19), C(20), C(21), C(22), C(23), C(24)/
49     3     1.00000000000000000D+00,    -2.08333333333333333D-01,
50     4     1.25000000000000000D-01,     3.34201388888888889D-01,
51     5    -4.01041666666666667D-01,     7.03125000000000000D-02,
52     6    -1.02581259645061728D+00,     1.84646267361111111D+00,
53     7    -8.91210937500000000D-01,     7.32421875000000000D-02,
54     8     4.66958442342624743D+00,    -1.12070026162229938D+01,
55     9     8.78912353515625000D+00,    -2.36408691406250000D+00,
56     A     1.12152099609375000D-01,    -2.82120725582002449D+01,
57     B     8.46362176746007346D+01,    -9.18182415432400174D+01,
58     C     4.25349987453884549D+01,    -7.36879435947963170D+00,
59     D     2.27108001708984375D-01,     2.12570130039217123D+02,
60     E    -7.65252468141181642D+02,     1.05999045252799988D+03/
61      DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32),
62     1     C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40),
63     2     C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/
64     3    -6.99579627376132541D+02,     2.18190511744211590D+02,
65     4    -2.64914304869515555D+01,     5.72501420974731445D-01,
66     5    -1.91945766231840700D+03,     8.06172218173730938D+03,
67     6    -1.35865500064341374D+04,     1.16553933368645332D+04,
68     7    -5.30564697861340311D+03,     1.20090291321635246D+03,
69     8    -1.08090919788394656D+02,     1.72772750258445740D+00,
70     9     2.02042913309661486D+04,    -9.69805983886375135D+04,
71     A     1.92547001232531532D+05,    -2.03400177280415534D+05,
72     B     1.22200464983017460D+05,    -4.11926549688975513D+04,
73     C     7.10951430248936372D+03,    -4.93915304773088012D+02,
74     D     6.07404200127348304D+00,    -2.42919187900551333D+05,
75     E     1.31176361466297720D+06,    -2.99801591853810675D+06/
76      DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56),
77     1     C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64),
78     2     C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/
79     3     3.76327129765640400D+06,    -2.81356322658653411D+06,
80     4     1.26836527332162478D+06,    -3.31645172484563578D+05,
81     5     4.52187689813627263D+04,    -2.49983048181120962D+03,
82     6     2.43805296995560639D+01,     3.28446985307203782D+06,
83     7    -1.97068191184322269D+07,     5.09526024926646422D+07,
84     8    -7.41051482115326577D+07,     6.63445122747290267D+07,
85     9    -3.75671766607633513D+07,     1.32887671664218183D+07,
86     A    -2.78561812808645469D+06,     3.08186404612662398D+05,
87     B    -1.38860897537170405D+04,     1.10017140269246738D+02,
88     C    -4.93292536645099620D+07,     3.25573074185765749D+08,
89     D    -9.39462359681578403D+08,     1.55359689957058006D+09,
90     E    -1.62108055210833708D+09,     1.10684281682301447D+09/
91      DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80),
92     1     C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88),
93     2     C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/
94     3    -4.95889784275030309D+08,     1.42062907797533095D+08,
95     4    -2.44740627257387285D+07,     2.24376817792244943D+06,
96     5    -8.40054336030240853D+04,     5.51335896122020586D+02,
97     6     8.14789096118312115D+08,    -5.86648149205184723D+09,
98     7     1.86882075092958249D+10,    -3.46320433881587779D+10,
99     8     4.12801855797539740D+10,    -3.30265997498007231D+10,
100     9     1.79542137311556001D+10,    -6.56329379261928433D+09,
101     A     1.55927986487925751D+09,    -2.25105661889415278D+08,
102     B     1.73951075539781645D+07,    -5.49842327572288687D+05,
103     C     3.03809051092238427D+03,    -1.46792612476956167D+10,
104     D     1.14498237732025810D+11,    -3.99096175224466498D+11,
105     E     8.19218669548577329D+11,    -1.09837515608122331D+12/
106      DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104),
107     1     C(105), C(106), C(107), C(108), C(109), C(110), C(111),
108     2     C(112), C(113), C(114), C(115), C(116), C(117), C(118)/
109     3     1.00815810686538209D+12,    -6.45364869245376503D+11,
110     4     2.87900649906150589D+11,    -8.78670721780232657D+10,
111     5     1.76347306068349694D+10,    -2.16716498322379509D+09,
112     6     1.43157876718888981D+08,    -3.87183344257261262D+06,
113     7     1.82577554742931747D+04,     2.86464035717679043D+11,
114     8    -2.40629790002850396D+12,     9.10934118523989896D+12,
115     9    -2.05168994109344374D+13,     3.05651255199353206D+13,
116     A    -3.16670885847851584D+13,     2.33483640445818409D+13,
117     B    -1.23204913055982872D+13,     4.61272578084913197D+12,
118     C    -1.19655288019618160D+12,     2.05914503232410016D+11,
119     D    -2.18229277575292237D+10,     1.24700929351271032D+09/
120      DATA C(119), C(120)/
121     1    -2.91883881222208134D+07,     1.18838426256783253D+05/
122C***FIRST EXECUTABLE STATEMENT  ZUNIK
123      IF (INIT.NE.0) GO TO 40
124C-----------------------------------------------------------------------
125C     INITIALIZE ALL VARIABLES
126C-----------------------------------------------------------------------
127      RFN = 1.0D0/FNU
128C-----------------------------------------------------------------------
129C     OVERFLOW TEST (ZR/FNU TOO SMALL)
130C-----------------------------------------------------------------------
131      TEST = D1MACH(1)*1.0D+3
132      AC = FNU*TEST
133      IF (ABS(ZRR).GT.AC .OR. ABS(ZRI).GT.AC) GO TO 15
134      ZETA1R = 2.0D0*ABS(LOG(TEST))+FNU
135      ZETA1I = 0.0D0
136      ZETA2R = FNU
137      ZETA2I = 0.0D0
138      PHIR = 1.0D0
139      PHII = 0.0D0
140      RETURN
141   15 CONTINUE
142      TR = ZRR*RFN
143      TI = ZRI*RFN
144      SR = CONER + (TR*TR-TI*TI)
145      SI = CONEI + (TR*TI+TI*TR)
146      CALL ZSQRT(SR, SI, SRR, SRI)
147      STR = CONER + SRR
148      STI = CONEI + SRI
149      CALL ZDIV(STR, STI, TR, TI, ZNR, ZNI)
150      CALL ZLOG(ZNR, ZNI, STR, STI, IDUM)
151      ZETA1R = FNU*STR
152      ZETA1I = FNU*STI
153      ZETA2R = FNU*SRR
154      ZETA2I = FNU*SRI
155      CALL ZDIV(CONER, CONEI, SRR, SRI, TR, TI)
156      SRR = TR*RFN
157      SRI = TI*RFN
158      CALL ZSQRT(SRR, SRI, CWRKR(16), CWRKI(16))
159      PHIR = CWRKR(16)*CON(IKFLG)
160      PHII = CWRKI(16)*CON(IKFLG)
161      IF (IPMTR.NE.0) RETURN
162      CALL ZDIV(CONER, CONEI, SR, SI, T2R, T2I)
163      CWRKR(1) = CONER
164      CWRKI(1) = CONEI
165      CRFNR = CONER
166      CRFNI = CONEI
167      AC = 1.0D0
168      L = 1
169      DO 20 K=2,15
170        SR = ZEROR
171        SI = ZEROI
172        DO 10 J=1,K
173          L = L + 1
174          STR = SR*T2R - SI*T2I + C(L)
175          SI = SR*T2I + SI*T2R
176          SR = STR
177   10   CONTINUE
178        STR = CRFNR*SRR - CRFNI*SRI
179        CRFNI = CRFNR*SRI + CRFNI*SRR
180        CRFNR = STR
181        CWRKR(K) = CRFNR*SR - CRFNI*SI
182        CWRKI(K) = CRFNR*SI + CRFNI*SR
183        AC = AC*RFN
184        TEST = ABS(CWRKR(K)) + ABS(CWRKI(K))
185        IF (AC.LT.TOL .AND. TEST.LT.TOL) GO TO 30
186   20 CONTINUE
187      K = 15
188   30 CONTINUE
189      INIT = K
190   40 CONTINUE
191      IF (IKFLG.EQ.2) GO TO 60
192C-----------------------------------------------------------------------
193C     COMPUTE SUM FOR THE I FUNCTION
194C-----------------------------------------------------------------------
195      SR = ZEROR
196      SI = ZEROI
197      DO 50 I=1,INIT
198        SR = SR + CWRKR(I)
199        SI = SI + CWRKI(I)
200   50 CONTINUE
201      SUMR = SR
202      SUMI = SI
203      PHIR = CWRKR(16)*CON(1)
204      PHII = CWRKI(16)*CON(1)
205      RETURN
206   60 CONTINUE
207C-----------------------------------------------------------------------
208C     COMPUTE SUM FOR THE K FUNCTION
209C-----------------------------------------------------------------------
210      SR = ZEROR
211      SI = ZEROI
212      TR = CONER
213      DO 70 I=1,INIT
214        SR = SR + TR*CWRKR(I)
215        SI = SI + TR*CWRKI(I)
216        TR = -TR
217   70 CONTINUE
218      SUMR = SR
219      SUMI = SI
220      PHIR = CWRKR(16)*CON(2)
221      PHII = CWRKI(16)*CON(2)
222      RETURN
223      END
224