*DECK ZACAI SUBROUTINE ZACAI (ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, TOL, + ELIM, ALIM) C***BEGIN PROLOGUE ZACAI C***SUBSIDIARY C***PURPOSE Subsidiary to ZAIRY C***LIBRARY SLATEC C***TYPE ALL (CACAI-A, ZACAI-A) C***AUTHOR Amos, D. E., (SNL) C***DESCRIPTION C C ZACAI APPLIES THE ANALYTIC CONTINUATION FORMULA C C K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN) C MP=PI*MR*CMPLX(0.0,1.0) C C TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT C HALF Z PLANE FOR USE WITH ZAIRY WHERE FNU=1/3 OR 2/3 AND N=1. C ZACAI IS THE SAME AS ZACON WITH THE PARTS FOR LARGER ORDERS AND C RECURRENCE REMOVED. A RECURSIVE CALL TO ZACON CAN RESULT IF ZACON C IS CALLED FROM ZAIRY. C C***SEE ALSO ZAIRY C***ROUTINES CALLED D1MACH, ZABS, ZASYI, ZBKNU, ZMLRI, ZS1S2, ZSERI C***REVISION HISTORY (YYMMDD) C 830501 DATE WRITTEN C 910415 Prologue converted to Version 4.0 format. (BAB) C***END PROLOGUE ZACAI C COMPLEX CSGN,CSPN,C1,C2,Y,Z,ZN,CY DOUBLE PRECISION ALIM, ARG, ASCLE, AZ, CSGNR, CSGNI, CSPNR, * CSPNI, C1R, C1I, C2R, C2I, CYR, CYI, DFNU, ELIM, FMR, FNU, PI, * RL, SGN, TOL, YY, YR, YI, ZR, ZI, ZNR, ZNI, D1MACH, ZABS INTEGER INU, IUF, KODE, MR, N, NN, NW, NZ DIMENSION YR(N), YI(N), CYR(2), CYI(2) EXTERNAL ZABS DATA PI / 3.14159265358979324D0 / C***FIRST EXECUTABLE STATEMENT ZACAI NZ = 0 ZNR = -ZR ZNI = -ZI AZ = ZABS(ZR,ZI) NN = N DFNU = FNU + (N-1) IF (AZ.LE.2.0D0) GO TO 10 IF (AZ*AZ*0.25D0.GT.DFNU+1.0D0) GO TO 20 10 CONTINUE C----------------------------------------------------------------------- C POWER SERIES FOR THE I FUNCTION C----------------------------------------------------------------------- CALL ZSERI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL, ELIM, ALIM) GO TO 40 20 CONTINUE IF (AZ.LT.RL) GO TO 30 C----------------------------------------------------------------------- C ASYMPTOTIC EXPANSION FOR LARGE Z FOR THE I FUNCTION C----------------------------------------------------------------------- CALL ZASYI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, RL, TOL, ELIM, * ALIM) IF (NW.LT.0) GO TO 80 GO TO 40 30 CONTINUE C----------------------------------------------------------------------- C MILLER ALGORITHM NORMALIZED BY THE SERIES FOR THE I FUNCTION C----------------------------------------------------------------------- CALL ZMLRI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL) IF(NW.LT.0) GO TO 80 40 CONTINUE C----------------------------------------------------------------------- C ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION C----------------------------------------------------------------------- CALL ZBKNU(ZNR, ZNI, FNU, KODE, 1, CYR, CYI, NW, TOL, ELIM, ALIM) IF (NW.NE.0) GO TO 80 FMR = MR SGN = -DSIGN(PI,FMR) CSGNR = 0.0D0 CSGNI = SGN IF (KODE.EQ.1) GO TO 50 YY = -ZNI CSGNR = -CSGNI*SIN(YY) CSGNI = CSGNI*COS(YY) 50 CONTINUE C----------------------------------------------------------------------- C CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE C WHEN FNU IS LARGE C----------------------------------------------------------------------- INU = FNU ARG = (FNU-INU)*SGN CSPNR = COS(ARG) CSPNI = SIN(ARG) IF (MOD(INU,2).EQ.0) GO TO 60 CSPNR = -CSPNR CSPNI = -CSPNI 60 CONTINUE C1R = CYR(1) C1I = CYI(1) C2R = YR(1) C2I = YI(1) IF (KODE.EQ.1) GO TO 70 IUF = 0 ASCLE = 1.0D+3*D1MACH(1)/TOL CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF) NZ = NZ + NW 70 CONTINUE YR(1) = CSPNR*C1R - CSPNI*C1I + CSGNR*C2R - CSGNI*C2I YI(1) = CSPNR*C1I + CSPNI*C1R + CSGNR*C2I + CSGNI*C2R RETURN 80 CONTINUE NZ = -1 IF(NW.EQ.(-2)) NZ=-2 RETURN END