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SUBROUTINE ZBUNI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NUI, NLAST,
* FNUL, TOL, ELIM, ALIM)
C***BEGIN PROLOGUE ZBUNI
C***REFER TO ZBESI,ZBESK
C
C ZBUNI COMPUTES THE I BESSEL FUNCTION FOR LARGE CABS(Z).GT.
C FNUL AND FNU+N-1.LT.FNUL. THE ORDER IS INCREASED FROM
C FNU+N-1 GREATER THAN FNUL BY ADDING NUI AND COMPUTING
C ACCORDING TO THE UNIFORM ASYMPTOTIC EXPANSION FOR I(FNU,Z)
C ON IFORM=1 AND THE EXPANSION FOR J(FNU,Z) ON IFORM=2
C
C***ROUTINES CALLED ZUNI1,ZUNI2,AZABS,D1MACH
C***END PROLOGUE ZBUNI
C COMPLEX CSCL,CSCR,CY,RZ,ST,S1,S2,Y,Z
DOUBLE PRECISION ALIM, AX, AY, CSCLR, CSCRR, CYI, CYR, DFNU,
* ELIM, FNU, FNUI, FNUL, GNU, RAZ, RZI, RZR, STI, STR, S1I, S1R,
* S2I, S2R, TOL, YI, YR, ZI, ZR, AZABS, ASCLE, BRY, C1R, C1I, C1M,
* D1MACH
INTEGER I, IFLAG, IFORM, K, KODE, N, NL, NLAST, NUI, NW, NZ
DIMENSION YR(N), YI(N), CYR(2), CYI(2), BRY(3)
NZ = 0
AX = DABS(ZR)*1.7321D0
AY = DABS(ZI)
IFORM = 1
IF (AY.GT.AX) IFORM = 2
IF (NUI.EQ.0) GO TO 60
FNUI = DBLE(FLOAT(NUI))
DFNU = FNU + DBLE(FLOAT(N-1))
GNU = DFNU + FNUI
IF (IFORM.EQ.2) GO TO 10
C-----------------------------------------------------------------------
C ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN
C -PI/3.LE.ARG(Z).LE.PI/3
C-----------------------------------------------------------------------
CALL ZUNI1(ZR, ZI, GNU, KODE, 2, CYR, CYI, NW, NLAST, FNUL, TOL,
* ELIM, ALIM)
GO TO 20
10 CONTINUE
C-----------------------------------------------------------------------
C ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU
C APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I
C AND HPI=PI/2
C-----------------------------------------------------------------------
CALL ZUNI2(ZR, ZI, GNU, KODE, 2, CYR, CYI, NW, NLAST, FNUL, TOL,
* ELIM, ALIM)
20 CONTINUE
IF (NW.LT.0) GO TO 50
IF (NW.NE.0) GO TO 90
STR = AZABS(CYR(1),CYI(1))
C----------------------------------------------------------------------
C SCALE BACKWARD RECURRENCE, BRY(3) IS DEFINED BUT NEVER USED
C----------------------------------------------------------------------
BRY(1)=1.0D+3*D1MACH(1)/TOL
BRY(2) = 1.0D0/BRY(1)
BRY(3) = BRY(2)
IFLAG = 2
ASCLE = BRY(2)
CSCLR = 1.0D0
IF (STR.GT.BRY(1)) GO TO 21
IFLAG = 1
ASCLE = BRY(1)
CSCLR = 1.0D0/TOL
GO TO 25
21 CONTINUE
IF (STR.LT.BRY(2)) GO TO 25
IFLAG = 3
ASCLE=BRY(3)
CSCLR = TOL
25 CONTINUE
CSCRR = 1.0D0/CSCLR
S1R = CYR(2)*CSCLR
S1I = CYI(2)*CSCLR
S2R = CYR(1)*CSCLR
S2I = CYI(1)*CSCLR
RAZ = 1.0D0/AZABS(ZR,ZI)
STR = ZR*RAZ
STI = -ZI*RAZ
RZR = (STR+STR)*RAZ
RZI = (STI+STI)*RAZ
DO 30 I=1,NUI
STR = S2R
STI = S2I
S2R = (DFNU+FNUI)*(RZR*STR-RZI*STI) + S1R
S2I = (DFNU+FNUI)*(RZR*STI+RZI*STR) + S1I
S1R = STR
S1I = STI
FNUI = FNUI - 1.0D0
IF (IFLAG.GE.3) GO TO 30
STR = S2R*CSCRR
STI = S2I*CSCRR
C1R = DABS(STR)
C1I = DABS(STI)
C1M = DMAX1(C1R,C1I)
IF (C1M.LE.ASCLE) GO TO 30
IFLAG = IFLAG+1
ASCLE = BRY(IFLAG)
S1R = S1R*CSCRR
S1I = S1I*CSCRR
S2R = STR
S2I = STI
CSCLR = CSCLR*TOL
CSCRR = 1.0D0/CSCLR
S1R = S1R*CSCLR
S1I = S1I*CSCLR
S2R = S2R*CSCLR
S2I = S2I*CSCLR
30 CONTINUE
YR(N) = S2R*CSCRR
YI(N) = S2I*CSCRR
IF (N.EQ.1) RETURN
NL = N - 1
FNUI = DBLE(FLOAT(NL))
K = NL
DO 40 I=1,NL
STR = S2R
STI = S2I
S2R = (FNU+FNUI)*(RZR*STR-RZI*STI) + S1R
S2I = (FNU+FNUI)*(RZR*STI+RZI*STR) + S1I
S1R = STR
S1I = STI
STR = S2R*CSCRR
STI = S2I*CSCRR
YR(K) = STR
YI(K) = STI
FNUI = FNUI - 1.0D0
K = K - 1
IF (IFLAG.GE.3) GO TO 40
C1R = DABS(STR)
C1I = DABS(STI)
C1M = DMAX1(C1R,C1I)
IF (C1M.LE.ASCLE) GO TO 40
IFLAG = IFLAG+1
ASCLE = BRY(IFLAG)
S1R = S1R*CSCRR
S1I = S1I*CSCRR
S2R = STR
S2I = STI
CSCLR = CSCLR*TOL
CSCRR = 1.0D0/CSCLR
S1R = S1R*CSCLR
S1I = S1I*CSCLR
S2R = S2R*CSCLR
S2I = S2I*CSCLR
40 CONTINUE
RETURN
50 CONTINUE
NZ = -1
IF(NW.EQ.(-2)) NZ=-2
RETURN
60 CONTINUE
IF (IFORM.EQ.2) GO TO 70
C-----------------------------------------------------------------------
C ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN
C -PI/3.LE.ARG(Z).LE.PI/3
C-----------------------------------------------------------------------
CALL ZUNI1(ZR, ZI, FNU, KODE, N, YR, YI, NW, NLAST, FNUL, TOL,
* ELIM, ALIM)
GO TO 80
70 CONTINUE
C-----------------------------------------------------------------------
C ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU
C APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I
C AND HPI=PI/2
C-----------------------------------------------------------------------
CALL ZUNI2(ZR, ZI, FNU, KODE, N, YR, YI, NW, NLAST, FNUL, TOL,
* ELIM, ALIM)
80 CONTINUE
IF (NW.LT.0) GO TO 50
NZ = NW
RETURN
90 CONTINUE
NLAST = N
RETURN
END
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