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*DECK ZSERI
SUBROUTINE ZSERI (ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM,
+ ALIM)
C***BEGIN PROLOGUE ZSERI
C***SUBSIDIARY
C***PURPOSE Subsidiary to ZBESI and ZBESK
C***LIBRARY SLATEC
C***TYPE ALL (CSERI-A, ZSERI-A)
C***AUTHOR Amos, D. E., (SNL)
C***DESCRIPTION
C
C ZSERI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY
C MEANS OF THE POWER SERIES FOR LARGE ABS(Z) IN THE
C REGION ABS(Z).LE.2*SQRT(FNU+1). NZ=0 IS A NORMAL RETURN.
C NZ.GT.0 MEANS THAT THE LAST NZ COMPONENTS WERE SET TO ZERO
C DUE TO UNDERFLOW. NZ.LT.0 MEANS UNDERFLOW OCCURRED, BUT THE
C CONDITION ABS(Z).LE.2*SQRT(FNU+1) WAS VIOLATED AND THE
C COMPUTATION MUST BE COMPLETED IN ANOTHER ROUTINE WITH N=N-ABS(NZ).
C
C***SEE ALSO ZBESI, ZBESK
C***ROUTINES CALLED D1MACH, DGAMLN, ZABS, ZDIV, ZLOG, ZMLT, ZUCHK
C***REVISION HISTORY (YYMMDD)
C 830501 DATE WRITTEN
C 910415 Prologue converted to Version 4.0 format. (BAB)
C 930122 Added ZLOG to EXTERNAL statement. (RWC)
C***END PROLOGUE ZSERI
C COMPLEX AK1,CK,COEF,CONE,CRSC,CSCL,CZ,CZERO,HZ,RZ,S1,S2,Y,Z
DOUBLE PRECISION AA, ACZ, AK, AK1I, AK1R, ALIM, ARM, ASCLE, ATOL,
* AZ, CKI, CKR, COEFI, COEFR, CONEI, CONER, CRSCR, CZI, CZR, DFNU,
* ELIM, FNU, FNUP, HZI, HZR, RAZ, RS, RTR1, RZI, RZR, S, SS, STI,
* STR, S1I, S1R, S2I, S2R, TOL, YI, YR, WI, WR, ZEROI, ZEROR, ZI,
* ZR, DGAMLN, D1MACH, ZABS
INTEGER I, IB, IDUM, IFLAG, IL, K, KODE, L, M, N, NN, NZ, NW
DIMENSION YR(N), YI(N), WR(2), WI(2)
EXTERNAL ZABS, ZLOG
DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 /
C***FIRST EXECUTABLE STATEMENT ZSERI
NZ = 0
AZ = ZABS(ZR,ZI)
IF (AZ.EQ.0.0D0) GO TO 160
ARM = 1.0D+3*D1MACH(1)
RTR1 = SQRT(ARM)
CRSCR = 1.0D0
IFLAG = 0
IF (AZ.LT.ARM) GO TO 150
HZR = 0.5D0*ZR
HZI = 0.5D0*ZI
CZR = ZEROR
CZI = ZEROI
IF (AZ.LE.RTR1) GO TO 10
CALL ZMLT(HZR, HZI, HZR, HZI, CZR, CZI)
10 CONTINUE
ACZ = ZABS(CZR,CZI)
NN = N
CALL ZLOG(HZR, HZI, CKR, CKI, IDUM)
20 CONTINUE
DFNU = FNU + (NN-1)
FNUP = DFNU + 1.0D0
C-----------------------------------------------------------------------
C UNDERFLOW TEST
C-----------------------------------------------------------------------
AK1R = CKR*DFNU
AK1I = CKI*DFNU
AK = DGAMLN(FNUP,IDUM)
AK1R = AK1R - AK
IF (KODE.EQ.2) AK1R = AK1R - ZR
IF (AK1R.GT.(-ELIM)) GO TO 40
30 CONTINUE
NZ = NZ + 1
YR(NN) = ZEROR
YI(NN) = ZEROI
IF (ACZ.GT.DFNU) GO TO 190
NN = NN - 1
IF (NN.EQ.0) RETURN
GO TO 20
40 CONTINUE
IF (AK1R.GT.(-ALIM)) GO TO 50
IFLAG = 1
SS = 1.0D0/TOL
CRSCR = TOL
ASCLE = ARM*SS
50 CONTINUE
AA = EXP(AK1R)
IF (IFLAG.EQ.1) AA = AA*SS
COEFR = AA*COS(AK1I)
COEFI = AA*SIN(AK1I)
ATOL = TOL*ACZ/FNUP
IL = MIN(2,NN)
DO 90 I=1,IL
DFNU = FNU + (NN-I)
FNUP = DFNU + 1.0D0
S1R = CONER
S1I = CONEI
IF (ACZ.LT.TOL*FNUP) GO TO 70
AK1R = CONER
AK1I = CONEI
AK = FNUP + 2.0D0
S = FNUP
AA = 2.0D0
60 CONTINUE
RS = 1.0D0/S
STR = AK1R*CZR - AK1I*CZI
STI = AK1R*CZI + AK1I*CZR
AK1R = STR*RS
AK1I = STI*RS
S1R = S1R + AK1R
S1I = S1I + AK1I
S = S + AK
AK = AK + 2.0D0
AA = AA*ACZ*RS
IF (AA.GT.ATOL) GO TO 60
70 CONTINUE
S2R = S1R*COEFR - S1I*COEFI
S2I = S1R*COEFI + S1I*COEFR
WR(I) = S2R
WI(I) = S2I
IF (IFLAG.EQ.0) GO TO 80
CALL ZUCHK(S2R, S2I, NW, ASCLE, TOL)
IF (NW.NE.0) GO TO 30
80 CONTINUE
M = NN - I + 1
YR(M) = S2R*CRSCR
YI(M) = S2I*CRSCR
IF (I.EQ.IL) GO TO 90
CALL ZDIV(COEFR, COEFI, HZR, HZI, STR, STI)
COEFR = STR*DFNU
COEFI = STI*DFNU
90 CONTINUE
IF (NN.LE.2) RETURN
K = NN - 2
AK = K
RAZ = 1.0D0/AZ
STR = ZR*RAZ
STI = -ZI*RAZ
RZR = (STR+STR)*RAZ
RZI = (STI+STI)*RAZ
IF (IFLAG.EQ.1) GO TO 120
IB = 3
100 CONTINUE
DO 110 I=IB,NN
YR(K) = (AK+FNU)*(RZR*YR(K+1)-RZI*YI(K+1)) + YR(K+2)
YI(K) = (AK+FNU)*(RZR*YI(K+1)+RZI*YR(K+1)) + YI(K+2)
AK = AK - 1.0D0
K = K - 1
110 CONTINUE
RETURN
C-----------------------------------------------------------------------
C RECUR BACKWARD WITH SCALED VALUES
C-----------------------------------------------------------------------
120 CONTINUE
C-----------------------------------------------------------------------
C EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION ABOVE THE
C UNDERFLOW LIMIT = ASCLE = D1MACH(1)*SS*1.0D+3
C-----------------------------------------------------------------------
S1R = WR(1)
S1I = WI(1)
S2R = WR(2)
S2I = WI(2)
DO 130 L=3,NN
CKR = S2R
CKI = S2I
S2R = S1R + (AK+FNU)*(RZR*CKR-RZI*CKI)
S2I = S1I + (AK+FNU)*(RZR*CKI+RZI*CKR)
S1R = CKR
S1I = CKI
CKR = S2R*CRSCR
CKI = S2I*CRSCR
YR(K) = CKR
YI(K) = CKI
AK = AK - 1.0D0
K = K - 1
IF (ZABS(CKR,CKI).GT.ASCLE) GO TO 140
130 CONTINUE
RETURN
140 CONTINUE
IB = L + 1
IF (IB.GT.NN) RETURN
GO TO 100
150 CONTINUE
NZ = N
IF (FNU.EQ.0.0D0) NZ = NZ - 1
160 CONTINUE
YR(1) = ZEROR
YI(1) = ZEROI
IF (FNU.NE.0.0D0) GO TO 170
YR(1) = CONER
YI(1) = CONEI
170 CONTINUE
IF (N.EQ.1) RETURN
DO 180 I=2,N
YR(I) = ZEROR
YI(I) = ZEROI
180 CONTINUE
RETURN
C-----------------------------------------------------------------------
C RETURN WITH NZ.LT.0 IF ABS(Z*Z/4).GT.FNU+N-NZ-1 COMPLETE
C THE CALCULATION IN CBINU WITH N=N-ABS(NZ)
C-----------------------------------------------------------------------
190 CONTINUE
NZ = -NZ
RETURN
END
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