amos/zunik.f

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