1      SUBROUTINE ZACAI(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, TOL,
2     * ELIM, ALIM)
3C***BEGIN PROLOGUE  ZACAI
4C***REFER TO  ZAIRY
5C
6C     ZACAI APPLIES THE ANALYTIC CONTINUATION FORMULA
7C
8C         K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN)
9C                 MP=PI*MR*CMPLX(0.0,1.0)
10C
11C     TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT
12C     HALF Z PLANE FOR USE WITH ZAIRY WHERE FNU=1/3 OR 2/3 AND N=1.
13C     ZACAI IS THE SAME AS ZACON WITH THE PARTS FOR LARGER ORDERS AND
14C     RECURRENCE REMOVED. A RECURSIVE CALL TO ZACON CAN RESULT IF ZACON
15C     IS CALLED FROM ZAIRY.
16C
17C***ROUTINES CALLED  ZASYI,ZBKNU,ZMLRI,ZSERI,ZS1S2,D1MACH,AZABS
18C***END PROLOGUE  ZACAI
19C     COMPLEX CSGN,CSPN,C1,C2,Y,Z,ZN,CY
20      DOUBLE PRECISION ALIM, ARG, ASCLE, AZ, CSGNR, CSGNI, CSPNR,
21     * CSPNI, C1R, C1I, C2R, C2I, CYR, CYI, DFNU, ELIM, FMR, FNU, PI,
22     * RL, SGN, TOL, YY, YR, YI, ZR, ZI, ZNR, ZNI, D1MACH, AZABS
23      INTEGER INU, IUF, KODE, MR, N, NN, NW, NZ
24      DIMENSION YR(N), YI(N), CYR(2), CYI(2)
25      DATA PI / 3.14159265358979324D0 /
26      NZ = 0
27      ZNR = -ZR
28      ZNI = -ZI
29      AZ = AZABS(ZR,ZI)
30      NN = N
31      DFNU = FNU + DBLE(FLOAT(N-1))
32      IF (AZ.LE.2.0D0) GO TO 10
33      IF (AZ*AZ*0.25D0.GT.DFNU+1.0D0) GO TO 20
34   10 CONTINUE
35C-----------------------------------------------------------------------
36C     POWER SERIES FOR THE I FUNCTION
37C-----------------------------------------------------------------------
38      CALL ZSERI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL, ELIM, ALIM)
39      GO TO 40
40   20 CONTINUE
41      IF (AZ.LT.RL) GO TO 30
42C-----------------------------------------------------------------------
43C     ASYMPTOTIC EXPANSION FOR LARGE Z FOR THE I FUNCTION
44C-----------------------------------------------------------------------
45      CALL ZASYI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, RL, TOL, ELIM,
46     * ALIM)
47      IF (NW.LT.0) GO TO 80
48      GO TO 40
49   30 CONTINUE
50C-----------------------------------------------------------------------
51C     MILLER ALGORITHM NORMALIZED BY THE SERIES FOR THE I FUNCTION
52C-----------------------------------------------------------------------
53      CALL ZMLRI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL)
54      IF(NW.LT.0) GO TO 80
55   40 CONTINUE
56C-----------------------------------------------------------------------
57C     ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION
58C-----------------------------------------------------------------------
59      CALL ZBKNU(ZNR, ZNI, FNU, KODE, 1, CYR, CYI, NW, TOL, ELIM, ALIM)
60      IF (NW.NE.0) GO TO 80
61      FMR = DBLE(FLOAT(MR))
62      SGN = -DSIGN(PI,FMR)
63      CSGNR = 0.0D0
64      CSGNI = SGN
65      IF (KODE.EQ.1) GO TO 50
66      YY = -ZNI
67      CSGNR = -CSGNI*DSIN(YY)
68      CSGNI = CSGNI*DCOS(YY)
69   50 CONTINUE
70C-----------------------------------------------------------------------
71C     CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE
72C     WHEN FNU IS LARGE
73C-----------------------------------------------------------------------
74      INU = INT(SNGL(FNU))
75      ARG = (FNU-DBLE(FLOAT(INU)))*SGN
76      CSPNR = DCOS(ARG)
77      CSPNI = DSIN(ARG)
78      IF (MOD(INU,2).EQ.0) GO TO 60
79      CSPNR = -CSPNR
80      CSPNI = -CSPNI
81   60 CONTINUE
82      C1R = CYR(1)
83      C1I = CYI(1)
84      C2R = YR(1)
85      C2I = YI(1)
86      IF (KODE.EQ.1) GO TO 70
87      IUF = 0
88      ASCLE = 1.0D+3*D1MACH(1)/TOL
89      CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF)
90      NZ = NZ + NW
91   70 CONTINUE
92      YR(1) = CSPNR*C1R - CSPNI*C1I + CSGNR*C2R - CSGNI*C2I
93      YI(1) = CSPNR*C1I + CSPNI*C1R + CSGNR*C2I + CSGNI*C2R
94      RETURN
95   80 CONTINUE
96      NZ = -1
97      IF(NW.EQ.(-2)) NZ=-2
98      RETURN
99      END
100