slatec-bessel-cpp/fortran/zmlri.f

*DECK ZMLRI
      SUBROUTINE ZMLRI (ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL)
C***BEGIN PROLOGUE  ZMLRI
C***SUBSIDIARY
C***PURPOSE  Subsidiary to ZBESI and ZBESK
C***LIBRARY   SLATEC
C***TYPE      ALL (CMLRI-A, ZMLRI-A)
C***AUTHOR  Amos, D. E., (SNL)
C***DESCRIPTION
C
C     ZMLRI COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY THE
C     MILLER ALGORITHM NORMALIZED BY A NEUMANN SERIES.
C
C***SEE ALSO  ZBESI, ZBESK
C***ROUTINES CALLED  D1MACH, DGAMLN, ZABS, ZEXP, ZLOG, ZMLT
C***REVISION HISTORY  (YYMMDD)
C   830501  DATE WRITTEN
C   910415  Prologue converted to Version 4.0 format.  (BAB)
C   930122  Added ZEXP and ZLOG to EXTERNAL statement.  (RWC)
C***END PROLOGUE  ZMLRI
C     COMPLEX CK,CNORM,CONE,CTWO,CZERO,PT,P1,P2,RZ,SUM,Y,Z
      DOUBLE PRECISION ACK, AK, AP, AT, AZ, BK, CKI, CKR, CNORMI,
     * CNORMR, CONEI, CONER, FKAP, FKK, FLAM, FNF, FNU, PTI, PTR, P1I,
     * P1R, P2I, P2R, RAZ, RHO, RHO2, RZI, RZR, SCLE, STI, STR, SUMI,
     * SUMR, TFNF, TOL, TST, YI, YR, ZEROI, ZEROR, ZI, ZR, DGAMLN,
     * D1MACH, ZABS
      INTEGER I, IAZ, IDUM, IFNU, INU, ITIME, K, KK, KM, KODE, M, N, NZ
      DIMENSION YR(N), YI(N)
      EXTERNAL ZABS, ZEXP, ZLOG
      DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 /
C***FIRST EXECUTABLE STATEMENT  ZMLRI
      SCLE = D1MACH(1)/TOL
      NZ=0
      AZ = ZABS(ZR,ZI)
      IAZ = AZ
      IFNU = FNU
      INU = IFNU + N - 1
      AT = IAZ + 1.0D0
      RAZ = 1.0D0/AZ
      STR = ZR*RAZ
      STI = -ZI*RAZ
      CKR = STR*AT*RAZ
      CKI = STI*AT*RAZ
      RZR = (STR+STR)*RAZ
      RZI = (STI+STI)*RAZ
      P1R = ZEROR
      P1I = ZEROI
      P2R = CONER
      P2I = CONEI
      ACK = (AT+1.0D0)*RAZ
      RHO = ACK + SQRT(ACK*ACK-1.0D0)
      RHO2 = RHO*RHO
      TST = (RHO2+RHO2)/((RHO2-1.0D0)*(RHO-1.0D0))
      TST = TST/TOL
C-----------------------------------------------------------------------
C     COMPUTE RELATIVE TRUNCATION ERROR INDEX FOR SERIES
C-----------------------------------------------------------------------
      AK = AT
      DO 10 I=1,80
        PTR = P2R
        PTI = P2I
        P2R = P1R - (CKR*PTR-CKI*PTI)
        P2I = P1I - (CKI*PTR+CKR*PTI)
        P1R = PTR
        P1I = PTI
        CKR = CKR + RZR
        CKI = CKI + RZI
        AP = ZABS(P2R,P2I)
        IF (AP.GT.TST*AK*AK) GO TO 20
        AK = AK + 1.0D0
   10 CONTINUE
      GO TO 110
   20 CONTINUE
      I = I + 1
      K = 0
      IF (INU.LT.IAZ) GO TO 40
C-----------------------------------------------------------------------
C     COMPUTE RELATIVE TRUNCATION ERROR FOR RATIOS
C-----------------------------------------------------------------------
      P1R = ZEROR
      P1I = ZEROI
      P2R = CONER
      P2I = CONEI
      AT = INU + 1.0D0
      STR = ZR*RAZ
      STI = -ZI*RAZ
      CKR = STR*AT*RAZ
      CKI = STI*AT*RAZ
      ACK = AT*RAZ
      TST = SQRT(ACK/TOL)
      ITIME = 1
      DO 30 K=1,80
        PTR = P2R
        PTI = P2I
        P2R = P1R - (CKR*PTR-CKI*PTI)
        P2I = P1I - (CKR*PTI+CKI*PTR)
        P1R = PTR
        P1I = PTI
        CKR = CKR + RZR
        CKI = CKI + RZI
        AP = ZABS(P2R,P2I)
        IF (AP.LT.TST) GO TO 30
        IF (ITIME.EQ.2) GO TO 40
        ACK = ZABS(CKR,CKI)
        FLAM = ACK + SQRT(ACK*ACK-1.0D0)
        FKAP = AP/ZABS(P1R,P1I)
        RHO = MIN(FLAM,FKAP)
        TST = TST*SQRT(RHO/(RHO*RHO-1.0D0))
        ITIME = 2
   30 CONTINUE
      GO TO 110
   40 CONTINUE
C-----------------------------------------------------------------------
C     BACKWARD RECURRENCE AND SUM NORMALIZING RELATION
C-----------------------------------------------------------------------
      K = K + 1
      KK = MAX(I+IAZ,K+INU)
      FKK = KK
      P1R = ZEROR
      P1I = ZEROI
C-----------------------------------------------------------------------
C     SCALE P2 AND SUM BY SCLE
C-----------------------------------------------------------------------
      P2R = SCLE
      P2I = ZEROI
      FNF = FNU - IFNU
      TFNF = FNF + FNF
      BK = DGAMLN(FKK+TFNF+1.0D0,IDUM) - DGAMLN(FKK+1.0D0,IDUM) -
     * DGAMLN(TFNF+1.0D0,IDUM)
      BK = EXP(BK)
      SUMR = ZEROR
      SUMI = ZEROI
      KM = KK - INU
      DO 50 I=1,KM
        PTR = P2R
        PTI = P2I
        P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI)
        P2I = P1I + (FKK+FNF)*(RZI*PTR+RZR*PTI)
        P1R = PTR
        P1I = PTI
        AK = 1.0D0 - TFNF/(FKK+TFNF)
        ACK = BK*AK
        SUMR = SUMR + (ACK+BK)*P1R
        SUMI = SUMI + (ACK+BK)*P1I
        BK = ACK
        FKK = FKK - 1.0D0
   50 CONTINUE
      YR(N) = P2R
      YI(N) = P2I
      IF (N.EQ.1) GO TO 70
      DO 60 I=2,N
        PTR = P2R
        PTI = P2I
        P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI)
        P2I = P1I + (FKK+FNF)*(RZI*PTR+RZR*PTI)
        P1R = PTR
        P1I = PTI
        AK = 1.0D0 - TFNF/(FKK+TFNF)
        ACK = BK*AK
        SUMR = SUMR + (ACK+BK)*P1R
        SUMI = SUMI + (ACK+BK)*P1I
        BK = ACK
        FKK = FKK - 1.0D0
        M = N - I + 1
        YR(M) = P2R
        YI(M) = P2I
   60 CONTINUE
   70 CONTINUE
      IF (IFNU.LE.0) GO TO 90
      DO 80 I=1,IFNU
        PTR = P2R
        PTI = P2I
        P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI)
        P2I = P1I + (FKK+FNF)*(RZR*PTI+RZI*PTR)
        P1R = PTR
        P1I = PTI
        AK = 1.0D0 - TFNF/(FKK+TFNF)
        ACK = BK*AK
        SUMR = SUMR + (ACK+BK)*P1R
        SUMI = SUMI + (ACK+BK)*P1I
        BK = ACK
        FKK = FKK - 1.0D0
   80 CONTINUE
   90 CONTINUE
      PTR = ZR
      PTI = ZI
      IF (KODE.EQ.2) PTR = ZEROR
      CALL ZLOG(RZR, RZI, STR, STI, IDUM)
      P1R = -FNF*STR + PTR
      P1I = -FNF*STI + PTI
      AP = DGAMLN(1.0D0+FNF,IDUM)
      PTR = P1R - AP
      PTI = P1I
C-----------------------------------------------------------------------
C     THE DIVISION CEXP(PT)/(SUM+P2) IS ALTERED TO AVOID OVERFLOW
C     IN THE DENOMINATOR BY SQUARING LARGE QUANTITIES
C-----------------------------------------------------------------------
      P2R = P2R + SUMR
      P2I = P2I + SUMI
      AP = ZABS(P2R,P2I)
      P1R = 1.0D0/AP
      CALL ZEXP(PTR, PTI, STR, STI)
      CKR = STR*P1R
      CKI = STI*P1R
      PTR = P2R*P1R
      PTI = -P2I*P1R
      CALL ZMLT(CKR, CKI, PTR, PTI, CNORMR, CNORMI)
      DO 100 I=1,N
        STR = YR(I)*CNORMR - YI(I)*CNORMI
        YI(I) = YR(I)*CNORMI + YI(I)*CNORMR
        YR(I) = STR
  100 CONTINUE
      RETURN
  110 CONTINUE
      NZ=-2
      RETURN
      END