Mercurial > octave-nkf
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[project @ 2005-11-17 05:47:13 by jwe]
| author | jwe |
|---|---|
| date | Thu, 17 Nov 2005 05:47:13 +0000 |
| parents | 8b0cb8f79fdc |
| children |
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SUBROUTINE ZUNIK(ZRR, ZRI, FNU, IKFLG, IPMTR, TOL, INIT, PHIR, * PHII, ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) C***BEGIN PROLOGUE ZUNIK C***REFER TO ZBESI,ZBESK C C ZUNIK COMPUTES PARAMETERS FOR THE UNIFORM ASYMPTOTIC C EXPANSIONS OF THE I AND K FUNCTIONS ON IKFLG= 1 OR 2 C RESPECTIVELY BY C C W(FNU,ZR) = PHI*EXP(ZETA)*SUM C C WHERE ZETA=-ZETA1 + ZETA2 OR C ZETA1 - ZETA2 C C THE FIRST CALL MUST HAVE INIT=0. SUBSEQUENT CALLS WITH THE C SAME ZR AND FNU WILL RETURN THE I OR K FUNCTION ON IKFLG= C 1 OR 2 WITH NO CHANGE IN INIT. CWRK IS A COMPLEX WORK C ARRAY. IPMTR=0 COMPUTES ALL PARAMETERS. IPMTR=1 COMPUTES PHI, C ZETA1,ZETA2. C C***ROUTINES CALLED ZDIV,XZLOG,XZSQRT,D1MACH C***END PROLOGUE ZUNIK C COMPLEX CFN,CON,CONE,CRFN,CWRK,CZERO,PHI,S,SR,SUM,T,T2,ZETA1, C *ZETA2,ZN,ZR DOUBLE PRECISION AC, C, CON, CONEI, CONER, CRFNI, CRFNR, CWRKI, * CWRKR, FNU, PHII, PHIR, RFN, SI, SR, SRI, SRR, STI, STR, SUMI, * SUMR, TEST, TI, TOL, TR, T2I, T2R, ZEROI, ZEROR, ZETA1I, ZETA1R, * ZETA2I, ZETA2R, ZNI, ZNR, ZRI, ZRR, D1MACH INTEGER I, IDUM, IKFLG, INIT, IPMTR, J, K, L DIMENSION C(120), CWRKR(16), CWRKI(16), CON(2) DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / DATA CON(1), CON(2) / 1 3.98942280401432678D-01, 1.25331413731550025D+00 / DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10), 1 C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18), 2 C(19), C(20), C(21), C(22), C(23), C(24)/ 3 1.00000000000000000D+00, -2.08333333333333333D-01, 4 1.25000000000000000D-01, 3.34201388888888889D-01, 5 -4.01041666666666667D-01, 7.03125000000000000D-02, 6 -1.02581259645061728D+00, 1.84646267361111111D+00, 7 -8.91210937500000000D-01, 7.32421875000000000D-02, 8 4.66958442342624743D+00, -1.12070026162229938D+01, 9 8.78912353515625000D+00, -2.36408691406250000D+00, A 1.12152099609375000D-01, -2.82120725582002449D+01, B 8.46362176746007346D+01, -9.18182415432400174D+01, C 4.25349987453884549D+01, -7.36879435947963170D+00, D 2.27108001708984375D-01, 2.12570130039217123D+02, E -7.65252468141181642D+02, 1.05999045252799988D+03/ DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32), 1 C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40), 2 C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/ 3 -6.99579627376132541D+02, 2.18190511744211590D+02, 4 -2.64914304869515555D+01, 5.72501420974731445D-01, 5 -1.91945766231840700D+03, 8.06172218173730938D+03, 6 -1.35865500064341374D+04, 1.16553933368645332D+04, 7 -5.30564697861340311D+03, 1.20090291321635246D+03, 8 -1.08090919788394656D+02, 1.72772750258445740D+00, 9 2.02042913309661486D+04, -9.69805983886375135D+04, A 1.92547001232531532D+05, -2.03400177280415534D+05, B 1.22200464983017460D+05, -4.11926549688975513D+04, C 7.10951430248936372D+03, -4.93915304773088012D+02, D 6.07404200127348304D+00, -2.42919187900551333D+05, E 1.31176361466297720D+06, -2.99801591853810675D+06/ DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56), 1 C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64), 2 C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/ 3 3.76327129765640400D+06, -2.81356322658653411D+06, 4 1.26836527332162478D+06, -3.31645172484563578D+05, 5 4.52187689813627263D+04, -2.49983048181120962D+03, 6 2.43805296995560639D+01, 3.28446985307203782D+06, 7 -1.97068191184322269D+07, 5.09526024926646422D+07, 8 -7.41051482115326577D+07, 6.63445122747290267D+07, 9 -3.75671766607633513D+07, 1.32887671664218183D+07, A -2.78561812808645469D+06, 3.08186404612662398D+05, B -1.38860897537170405D+04, 1.10017140269246738D+02, C -4.93292536645099620D+07, 3.25573074185765749D+08, D -9.39462359681578403D+08, 1.55359689957058006D+09, E -1.62108055210833708D+09, 1.10684281682301447D+09/ DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80), 1 C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88), 2 C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/ 3 -4.95889784275030309D+08, 1.42062907797533095D+08, 4 -2.44740627257387285D+07, 2.24376817792244943D+06, 5 -8.40054336030240853D+04, 5.51335896122020586D+02, 6 8.14789096118312115D+08, -5.86648149205184723D+09, 7 1.86882075092958249D+10, -3.46320433881587779D+10, 8 4.12801855797539740D+10, -3.30265997498007231D+10, 9 1.79542137311556001D+10, -6.56329379261928433D+09, A 1.55927986487925751D+09, -2.25105661889415278D+08, B 1.73951075539781645D+07, -5.49842327572288687D+05, C 3.03809051092238427D+03, -1.46792612476956167D+10, D 1.14498237732025810D+11, -3.99096175224466498D+11, E 8.19218669548577329D+11, -1.09837515608122331D+12/ DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104), 1 C(105), C(106), C(107), C(108), C(109), C(110), C(111), 2 C(112), C(113), C(114), C(115), C(116), C(117), C(118)/ 3 1.00815810686538209D+12, -6.45364869245376503D+11, 4 2.87900649906150589D+11, -8.78670721780232657D+10, 5 1.76347306068349694D+10, -2.16716498322379509D+09, 6 1.43157876718888981D+08, -3.87183344257261262D+06, 7 1.82577554742931747D+04, 2.86464035717679043D+11, 8 -2.40629790002850396D+12, 9.10934118523989896D+12, 9 -2.05168994109344374D+13, 3.05651255199353206D+13, A -3.16670885847851584D+13, 2.33483640445818409D+13, B -1.23204913055982872D+13, 4.61272578084913197D+12, C -1.19655288019618160D+12, 2.05914503232410016D+11, D -2.18229277575292237D+10, 1.24700929351271032D+09/ DATA C(119), C(120)/ 1 -2.91883881222208134D+07, 1.18838426256783253D+05/ C IF (INIT.NE.0) GO TO 40 C----------------------------------------------------------------------- C INITIALIZE ALL VARIABLES C----------------------------------------------------------------------- RFN = 1.0D0/FNU C----------------------------------------------------------------------- C OVERFLOW TEST (ZR/FNU TOO SMALL) C----------------------------------------------------------------------- TEST = D1MACH(1)*1.0D+3 AC = FNU*TEST IF (DABS(ZRR).GT.AC .OR. DABS(ZRI).GT.AC) GO TO 15 ZETA1R = 2.0D0*DABS(DLOG(TEST))+FNU ZETA1I = 0.0D0 ZETA2R = FNU ZETA2I = 0.0D0 PHIR = 1.0D0 PHII = 0.0D0 RETURN 15 CONTINUE TR = ZRR*RFN TI = ZRI*RFN SR = CONER + (TR*TR-TI*TI) SI = CONEI + (TR*TI+TI*TR) CALL XZSQRT(SR, SI, SRR, SRI) STR = CONER + SRR STI = CONEI + SRI CALL ZDIV(STR, STI, TR, TI, ZNR, ZNI) CALL XZLOG(ZNR, ZNI, STR, STI, IDUM) ZETA1R = FNU*STR ZETA1I = FNU*STI ZETA2R = FNU*SRR ZETA2I = FNU*SRI CALL ZDIV(CONER, CONEI, SRR, SRI, TR, TI) SRR = TR*RFN SRI = TI*RFN CALL XZSQRT(SRR, SRI, CWRKR(16), CWRKI(16)) PHIR = CWRKR(16)*CON(IKFLG) PHII = CWRKI(16)*CON(IKFLG) IF (IPMTR.NE.0) RETURN CALL ZDIV(CONER, CONEI, SR, SI, T2R, T2I) CWRKR(1) = CONER CWRKI(1) = CONEI CRFNR = CONER CRFNI = CONEI AC = 1.0D0 L = 1 DO 20 K=2,15 SR = ZEROR SI = ZEROI DO 10 J=1,K L = L + 1 STR = SR*T2R - SI*T2I + C(L) SI = SR*T2I + SI*T2R SR = STR 10 CONTINUE STR = CRFNR*SRR - CRFNI*SRI CRFNI = CRFNR*SRI + CRFNI*SRR CRFNR = STR CWRKR(K) = CRFNR*SR - CRFNI*SI CWRKI(K) = CRFNR*SI + CRFNI*SR AC = AC*RFN TEST = DABS(CWRKR(K)) + DABS(CWRKI(K)) IF (AC.LT.TOL .AND. TEST.LT.TOL) GO TO 30 20 CONTINUE K = 15 30 CONTINUE INIT = K 40 CONTINUE IF (IKFLG.EQ.2) GO TO 60 C----------------------------------------------------------------------- C COMPUTE SUM FOR THE I FUNCTION C----------------------------------------------------------------------- SR = ZEROR SI = ZEROI DO 50 I=1,INIT SR = SR + CWRKR(I) SI = SI + CWRKI(I) 50 CONTINUE SUMR = SR SUMI = SI PHIR = CWRKR(16)*CON(1) PHII = CWRKI(16)*CON(1) RETURN 60 CONTINUE C----------------------------------------------------------------------- C COMPUTE SUM FOR THE K FUNCTION C----------------------------------------------------------------------- SR = ZEROR SI = ZEROI TR = CONER DO 70 I=1,INIT SR = SR + TR*CWRKR(I) SI = SI + TR*CWRKI(I) TR = -TR 70 CONTINUE SUMR = SR SUMI = SI PHIR = CWRKR(16)*CON(2) PHII = CWRKI(16)*CON(2) RETURN END