slatec-bessel-cpp/fortran/zuoik.f

*DECK ZUOIK
      SUBROUTINE ZUOIK (ZR, ZI, FNU, KODE, IKFLG, N, YR, YI, NUF, TOL,
     +   ELIM, ALIM)
C***BEGIN PROLOGUE  ZUOIK
C***SUBSIDIARY
C***PURPOSE  Subsidiary to ZBESH, ZBESI and ZBESK
C***LIBRARY   SLATEC
C***TYPE      ALL (CUOIK-A, ZUOIK-A)
C***AUTHOR  Amos, D. E., (SNL)
C***DESCRIPTION
C
C     ZUOIK COMPUTES THE LEADING TERMS OF THE UNIFORM ASYMPTOTIC
C     EXPANSIONS FOR THE I AND K FUNCTIONS AND COMPARES THEM
C     (IN LOGARITHMIC FORM) TO ALIM AND ELIM FOR OVER AND UNDERFLOW
C     WHERE ALIM.LT.ELIM. IF THE MAGNITUDE, BASED ON THE LEADING
C     EXPONENTIAL, IS LESS THAN ALIM OR GREATER THAN -ALIM, THEN
C     THE RESULT IS ON SCALE. IF NOT, THEN A REFINED TEST USING OTHER
C     MULTIPLIERS (IN LOGARITHMIC FORM) IS MADE BASED ON ELIM. HERE
C     EXP(-ELIM)=SMALLEST MACHINE NUMBER*1.0E+3 AND EXP(-ALIM)=
C     EXP(-ELIM)/TOL
C
C     IKFLG=1 MEANS THE I SEQUENCE IS TESTED
C          =2 MEANS THE K SEQUENCE IS TESTED
C     NUF = 0 MEANS THE LAST MEMBER OF THE SEQUENCE IS ON SCALE
C         =-1 MEANS AN OVERFLOW WOULD OCCUR
C     IKFLG=1 AND NUF.GT.0 MEANS THE LAST NUF Y VALUES WERE SET TO ZERO
C             THE FIRST N-NUF VALUES MUST BE SET BY ANOTHER ROUTINE
C     IKFLG=2 AND NUF.EQ.N MEANS ALL Y VALUES WERE SET TO ZERO
C     IKFLG=2 AND 0.LT.NUF.LT.N NOT CONSIDERED. Y MUST BE SET BY
C             ANOTHER ROUTINE
C
C***SEE ALSO  ZBESH, ZBESI, ZBESK
C***ROUTINES CALLED  D1MACH, ZABS, ZLOG, ZUCHK, ZUNHJ, ZUNIK
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  ZUOIK
C     COMPLEX ARG,ASUM,BSUM,CWRK,CZ,CZERO,PHI,SUM,Y,Z,ZB,ZETA1,ZETA2,ZN,
C    *ZR
      DOUBLE PRECISION AARG, AIC, ALIM, APHI, ARGI, ARGR, ASUMI, ASUMR,
     * ASCLE, AX, AY, BSUMI, BSUMR, CWRKI, CWRKR, CZI, CZR, ELIM, FNN,
     * FNU, GNN, GNU, PHII, PHIR, RCZ, STR, STI, SUMI, SUMR, TOL, YI,
     * YR, ZBI, ZBR, ZEROI, ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZI,
     * ZNI, ZNR, ZR, ZRI, ZRR, D1MACH, ZABS
      INTEGER I, IDUM, IFORM, IKFLG, INIT, KODE, N, NN, NUF, NW
      DIMENSION YR(N), YI(N), CWRKR(16), CWRKI(16)
      EXTERNAL ZABS, ZLOG
      DATA ZEROR,ZEROI / 0.0D0, 0.0D0 /
      DATA AIC / 1.265512123484645396D+00 /
C***FIRST EXECUTABLE STATEMENT  ZUOIK
      NUF = 0
      NN = N
      ZRR = ZR
      ZRI = ZI
      IF (ZR.GE.0.0D0) GO TO 10
      ZRR = -ZR
      ZRI = -ZI
   10 CONTINUE
      ZBR = ZRR
      ZBI = ZRI
      AX = ABS(ZR)*1.7321D0
      AY = ABS(ZI)
      IFORM = 1
      IF (AY.GT.AX) IFORM = 2
      GNU = MAX(FNU,1.0D0)
      IF (IKFLG.EQ.1) GO TO 20
      FNN = NN
      GNN = FNU + FNN - 1.0D0
      GNU = MAX(GNN,FNN)
   20 CONTINUE
C-----------------------------------------------------------------------
C     ONLY THE MAGNITUDE OF ARG AND PHI ARE NEEDED ALONG WITH THE
C     REAL PARTS OF ZETA1, ZETA2 AND ZB. NO ATTEMPT IS MADE TO GET
C     THE SIGN OF THE IMAGINARY PART CORRECT.
C-----------------------------------------------------------------------
      IF (IFORM.EQ.2) GO TO 30
      INIT = 0
      CALL ZUNIK(ZRR, ZRI, GNU, IKFLG, 1, TOL, INIT, PHIR, PHII,
     * ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI)
      CZR = -ZETA1R + ZETA2R
      CZI = -ZETA1I + ZETA2I
      GO TO 50
   30 CONTINUE
      ZNR = ZRI
      ZNI = -ZRR
      IF (ZI.GT.0.0D0) GO TO 40
      ZNR = -ZNR
   40 CONTINUE
      CALL ZUNHJ(ZNR, ZNI, GNU, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R,
     * ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
      CZR = -ZETA1R + ZETA2R
      CZI = -ZETA1I + ZETA2I
      AARG = ZABS(ARGR,ARGI)
   50 CONTINUE
      IF (KODE.EQ.1) GO TO 60
      CZR = CZR - ZBR
      CZI = CZI - ZBI
   60 CONTINUE
      IF (IKFLG.EQ.1) GO TO 70
      CZR = -CZR
      CZI = -CZI
   70 CONTINUE
      APHI = ZABS(PHIR,PHII)
      RCZ = CZR
C-----------------------------------------------------------------------
C     OVERFLOW TEST
C-----------------------------------------------------------------------
      IF (RCZ.GT.ELIM) GO TO 210
      IF (RCZ.LT.ALIM) GO TO 80
      RCZ = RCZ + LOG(APHI)
      IF (IFORM.EQ.2) RCZ = RCZ - 0.25D0*LOG(AARG) - AIC
      IF (RCZ.GT.ELIM) GO TO 210
      GO TO 130
   80 CONTINUE
C-----------------------------------------------------------------------
C     UNDERFLOW TEST
C-----------------------------------------------------------------------
      IF (RCZ.LT.(-ELIM)) GO TO 90
      IF (RCZ.GT.(-ALIM)) GO TO 130
      RCZ = RCZ + LOG(APHI)
      IF (IFORM.EQ.2) RCZ = RCZ - 0.25D0*LOG(AARG) - AIC
      IF (RCZ.GT.(-ELIM)) GO TO 110
   90 CONTINUE
      DO 100 I=1,NN
        YR(I) = ZEROR
        YI(I) = ZEROI
  100 CONTINUE
      NUF = NN
      RETURN
  110 CONTINUE
      ASCLE = 1.0D+3*D1MACH(1)/TOL
      CALL ZLOG(PHIR, PHII, STR, STI, IDUM)
      CZR = CZR + STR
      CZI = CZI + STI
      IF (IFORM.EQ.1) GO TO 120
      CALL ZLOG(ARGR, ARGI, STR, STI, IDUM)
      CZR = CZR - 0.25D0*STR - AIC
      CZI = CZI - 0.25D0*STI
  120 CONTINUE
      AX = EXP(RCZ)/TOL
      AY = CZI
      CZR = AX*COS(AY)
      CZI = AX*SIN(AY)
      CALL ZUCHK(CZR, CZI, NW, ASCLE, TOL)
      IF (NW.NE.0) GO TO 90
  130 CONTINUE
      IF (IKFLG.EQ.2) RETURN
      IF (N.EQ.1) RETURN
C-----------------------------------------------------------------------
C     SET UNDERFLOWS ON I SEQUENCE
C-----------------------------------------------------------------------
  140 CONTINUE
      GNU = FNU + (NN-1)
      IF (IFORM.EQ.2) GO TO 150
      INIT = 0
      CALL ZUNIK(ZRR, ZRI, GNU, IKFLG, 1, TOL, INIT, PHIR, PHII,
     * ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI)
      CZR = -ZETA1R + ZETA2R
      CZI = -ZETA1I + ZETA2I
      GO TO 160
  150 CONTINUE
      CALL ZUNHJ(ZNR, ZNI, GNU, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R,
     * ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
      CZR = -ZETA1R + ZETA2R
      CZI = -ZETA1I + ZETA2I
      AARG = ZABS(ARGR,ARGI)
  160 CONTINUE
      IF (KODE.EQ.1) GO TO 170
      CZR = CZR - ZBR
      CZI = CZI - ZBI
  170 CONTINUE
      APHI = ZABS(PHIR,PHII)
      RCZ = CZR
      IF (RCZ.LT.(-ELIM)) GO TO 180
      IF (RCZ.GT.(-ALIM)) RETURN
      RCZ = RCZ + LOG(APHI)
      IF (IFORM.EQ.2) RCZ = RCZ - 0.25D0*LOG(AARG) - AIC
      IF (RCZ.GT.(-ELIM)) GO TO 190
  180 CONTINUE
      YR(NN) = ZEROR
      YI(NN) = ZEROI
      NN = NN - 1
      NUF = NUF + 1
      IF (NN.EQ.0) RETURN
      GO TO 140
  190 CONTINUE
      ASCLE = 1.0D+3*D1MACH(1)/TOL
      CALL ZLOG(PHIR, PHII, STR, STI, IDUM)
      CZR = CZR + STR
      CZI = CZI + STI
      IF (IFORM.EQ.1) GO TO 200
      CALL ZLOG(ARGR, ARGI, STR, STI, IDUM)
      CZR = CZR - 0.25D0*STR - AIC
      CZI = CZI - 0.25D0*STI
  200 CONTINUE
      AX = EXP(RCZ)/TOL
      AY = CZI
      CZR = AX*COS(AY)
      CZI = AX*SIN(AY)
      CALL ZUCHK(CZR, CZI, NW, ASCLE, TOL)
      IF (NW.NE.0) GO TO 180
      RETURN
  210 CONTINUE
      NUF = -1
      RETURN
      END