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zacon.f

*DECK ZACON
      SUBROUTINE ZACON (ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, FNUL,
     +   TOL, ELIM, ALIM)
C***BEGIN PROLOGUE  ZACON
C***SUBSIDIARY
C***PURPOSE  Subsidiary to ZBESH and ZBESK
C***LIBRARY   SLATEC
C***TYPE      ALL (CACON-A, ZACON-A)
C***AUTHOR  Amos, D. E., (SNL)
C***DESCRIPTION
C
C     ZACON 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
C
C***SEE ALSO  ZBESH, ZBESK
C***ROUTINES CALLED  D1MACH, ZABS, ZBINU, ZBKNU, ZMLT, ZS1S2
C***REVISION HISTORY  (YYMMDD)
C   830501  DATE WRITTEN
C   910415  Prologue converted to Version 4.0 format.  (BAB)
C***END PROLOGUE  ZACON
C     COMPLEX CK,CONE,CSCL,CSCR,CSGN,CSPN,CY,CZERO,C1,C2,RZ,SC1,SC2,ST,
C    *S1,S2,Y,Z,ZN
      DOUBLE PRECISION ALIM, ARG, ASCLE, AS2, AZN, BRY, BSCLE, CKI,
     * CKR, CONER, CPN, CSCL, CSCR, CSGNI, CSGNR, CSPNI, CSPNR,
     * CSR, CSRR, CSSR, CYI, CYR, C1I, C1M, C1R, C2I, C2R, ELIM, FMR,
     * FN, FNU, FNUL, PI, PTI, PTR, RAZN, RL, RZI, RZR, SC1I, SC1R,
     * SC2I, SC2R, SGN, SPN, STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR,
     * YY, ZEROR, ZI, ZNI, ZNR, ZR, D1MACH, ZABS
      INTEGER I, INU, IUF, KFLAG, KODE, MR, N, NN, NW, NZ
      DIMENSION YR(N), YI(N), CYR(2), CYI(2), CSSR(3), CSRR(3), BRY(3)
      EXTERNAL ZABS
      DATA PI / 3.14159265358979324D0 /
      DATA ZEROR,CONER / 0.0D0,1.0D0 /
C***FIRST EXECUTABLE STATEMENT  ZACON
      NZ = 0
      ZNR = -ZR
      ZNI = -ZI
      NN = N
      CALL ZBINU(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, RL, FNUL, TOL,
     * ELIM, ALIM)
      IF (NW.LT.0) GO TO 90
C-----------------------------------------------------------------------
C     ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION
C-----------------------------------------------------------------------
      NN = MIN(2,N)
      CALL ZBKNU(ZNR, ZNI, FNU, KODE, NN, CYR, CYI, NW, TOL, ELIM, ALIM)
      IF (NW.NE.0) GO TO 90
      S1R = CYR(1)
      S1I = CYI(1)
      FMR = MR
      SGN = -DSIGN(PI,FMR)
      CSGNR = ZEROR
      CSGNI = SGN
      IF (KODE.EQ.1) GO TO 10
      YY = -ZNI
      CPN = COS(YY)
      SPN = SIN(YY)
      CALL ZMLT(CSGNR, CSGNI, CPN, SPN, CSGNR, CSGNI)
   10 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
      CPN = COS(ARG)
      SPN = SIN(ARG)
      CSPNR = CPN
      CSPNI = SPN
      IF (MOD(INU,2).EQ.0) GO TO 20
      CSPNR = -CSPNR
      CSPNI = -CSPNI
   20 CONTINUE
      IUF = 0
      C1R = S1R
      C1I = S1I
      C2R = YR(1)
      C2I = YI(1)
      ASCLE = 1.0D+3*D1MACH(1)/TOL
      IF (KODE.EQ.1) GO TO 30
      CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF)
      NZ = NZ + NW
      SC1R = C1R
      SC1I = C1I
   30 CONTINUE
      CALL ZMLT(CSPNR, CSPNI, C1R, C1I, STR, STI)
      CALL ZMLT(CSGNR, CSGNI, C2R, C2I, PTR, PTI)
      YR(1) = STR + PTR
      YI(1) = STI + PTI
      IF (N.EQ.1) RETURN
      CSPNR = -CSPNR
      CSPNI = -CSPNI
      S2R = CYR(2)
      S2I = CYI(2)
      C1R = S2R
      C1I = S2I
      C2R = YR(2)
      C2I = YI(2)
      IF (KODE.EQ.1) GO TO 40
      CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF)
      NZ = NZ + NW
      SC2R = C1R
      SC2I = C1I
   40 CONTINUE
      CALL ZMLT(CSPNR, CSPNI, C1R, C1I, STR, STI)
      CALL ZMLT(CSGNR, CSGNI, C2R, C2I, PTR, PTI)
      YR(2) = STR + PTR
      YI(2) = STI + PTI
      IF (N.EQ.2) RETURN
      CSPNR = -CSPNR
      CSPNI = -CSPNI
      AZN = ZABS(ZNR,ZNI)
      RAZN = 1.0D0/AZN
      STR = ZNR*RAZN
      STI = -ZNI*RAZN
      RZR = (STR+STR)*RAZN
      RZI = (STI+STI)*RAZN
      FN = FNU + 1.0D0
      CKR = FN*RZR
      CKI = FN*RZI
C-----------------------------------------------------------------------
C     SCALE NEAR EXPONENT EXTREMES DURING RECURRENCE ON K FUNCTIONS
C-----------------------------------------------------------------------
      CSCL = 1.0D0/TOL
      CSCR = TOL
      CSSR(1) = CSCL
      CSSR(2) = CONER
      CSSR(3) = CSCR
      CSRR(1) = CSCR
      CSRR(2) = CONER
      CSRR(3) = CSCL
      BRY(1) = ASCLE
      BRY(2) = 1.0D0/ASCLE
      BRY(3) = D1MACH(2)
      AS2 = ZABS(S2R,S2I)
      KFLAG = 2
      IF (AS2.GT.BRY(1)) GO TO 50
      KFLAG = 1
      GO TO 60
   50 CONTINUE
      IF (AS2.LT.BRY(2)) GO TO 60
      KFLAG = 3
   60 CONTINUE
      BSCLE = BRY(KFLAG)
      S1R = S1R*CSSR(KFLAG)
      S1I = S1I*CSSR(KFLAG)
      S2R = S2R*CSSR(KFLAG)
      S2I = S2I*CSSR(KFLAG)
      CSR = CSRR(KFLAG)
      DO 80 I=3,N
        STR = S2R
        STI = S2I
        S2R = CKR*STR - CKI*STI + S1R
        S2I = CKR*STI + CKI*STR + S1I
        S1R = STR
        S1I = STI
        C1R = S2R*CSR
        C1I = S2I*CSR
        STR = C1R
        STI = C1I
        C2R = YR(I)
        C2I = YI(I)
        IF (KODE.EQ.1) GO TO 70
        IF (IUF.LT.0) GO TO 70
        CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF)
        NZ = NZ + NW
        SC1R = SC2R
        SC1I = SC2I
        SC2R = C1R
        SC2I = C1I
        IF (IUF.NE.3) GO TO 70
        IUF = -4
        S1R = SC1R*CSSR(KFLAG)
        S1I = SC1I*CSSR(KFLAG)
        S2R = SC2R*CSSR(KFLAG)
        S2I = SC2I*CSSR(KFLAG)
        STR = SC2R
        STI = SC2I
   70   CONTINUE
        PTR = CSPNR*C1R - CSPNI*C1I
        PTI = CSPNR*C1I + CSPNI*C1R
        YR(I) = PTR + CSGNR*C2R - CSGNI*C2I
        YI(I) = PTI + CSGNR*C2I + CSGNI*C2R
        CKR = CKR + RZR
        CKI = CKI + RZI
        CSPNR = -CSPNR
        CSPNI = -CSPNI
        IF (KFLAG.GE.3) GO TO 80
        PTR = ABS(C1R)
        PTI = ABS(C1I)
        C1M = MAX(PTR,PTI)
        IF (C1M.LE.BSCLE) GO TO 80
        KFLAG = KFLAG + 1
        BSCLE = BRY(KFLAG)
        S1R = S1R*CSR
        S1I = S1I*CSR
        S2R = STR
        S2I = STI
        S1R = S1R*CSSR(KFLAG)
        S1I = S1I*CSSR(KFLAG)
        S2R = S2R*CSSR(KFLAG)
        S2I = S2I*CSSR(KFLAG)
        CSR = CSRR(KFLAG)
   80 CONTINUE
      RETURN
   90 CONTINUE
      NZ = -1
      IF(NW.EQ.(-2)) NZ=-2
      RETURN
      END

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