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