slatec-bessel-cpp/fortran/zuni2.f

*DECK ZUNI2
      SUBROUTINE ZUNI2 (ZR, ZI, FNU, KODE, N, YR, YI, NZ, NLAST, FNUL,
     +   TOL, ELIM, ALIM)
C***BEGIN PROLOGUE  ZUNI2
C***SUBSIDIARY
C***PURPOSE  Subsidiary to ZBESI and ZBESK
C***LIBRARY   SLATEC
C***TYPE      ALL (CUNI2-A, ZUNI2-A)
C***AUTHOR  Amos, D. E., (SNL)
C***DESCRIPTION
C
C     ZUNI2 COMPUTES I(FNU,Z) IN THE RIGHT HALF PLANE BY MEANS OF
C     UNIFORM ASYMPTOTIC EXPANSION FOR J(FNU,ZN) WHERE ZN IS Z*I
C     OR -Z*I AND ZN IS IN THE RIGHT HALF PLANE ALSO.
C
C     FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC
C     EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET.
C     NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER
C     FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL.
C     Y(I)=CZERO FOR I=NLAST+1,N
C
C***SEE ALSO  ZBESI, ZBESK
C***ROUTINES CALLED  D1MACH, ZABS, ZAIRY, ZUCHK, ZUNHJ, ZUOIK
C***REVISION HISTORY  (YYMMDD)
C   830501  DATE WRITTEN
C   910415  Prologue converted to Version 4.0 format.  (BAB)
C***END PROLOGUE  ZUNI2
C     COMPLEX AI,ARG,ASUM,BSUM,CFN,CI,CID,CIP,CONE,CRSC,CSCL,CSR,CSS,
C    *CZERO,C1,C2,DAI,PHI,RZ,S1,S2,Y,Z,ZB,ZETA1,ZETA2,ZN
      DOUBLE PRECISION AARG, AIC, AII, AIR, ALIM, ANG, APHI, ARGI,
     * ARGR, ASCLE, ASUMI, ASUMR, BRY, BSUMI, BSUMR, CIDI, CIPI, CIPR,
     * CONER, CRSC, CSCL, CSRR, CSSR, C1R, C2I, C2M, C2R, DAII,
     * DAIR, ELIM, FN, FNU, FNUL, HPI, PHII, PHIR, RAST, RAZ, RS1, RZI,
     * RZR, STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR, ZBI, ZBR, ZEROI,
     * ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZI, ZNI, ZNR, ZR, CYR,
     * CYI, D1MACH, ZABS, CAR, SAR
      INTEGER I, IFLAG, IN, INU, J, K, KODE, N, NAI, ND, NDAI, NLAST,
     * NN, NUF, NW, NZ, IDUM
      DIMENSION BRY(3), YR(N), YI(N), CIPR(4), CIPI(4), CSSR(3),
     * CSRR(3), CYR(2), CYI(2)
      EXTERNAL ZABS
      DATA ZEROR,ZEROI,CONER / 0.0D0, 0.0D0, 1.0D0 /
      DATA CIPR(1),CIPI(1),CIPR(2),CIPI(2),CIPR(3),CIPI(3),CIPR(4),
     * CIPI(4)/ 1.0D0,0.0D0, 0.0D0,1.0D0, -1.0D0,0.0D0, 0.0D0,-1.0D0/
      DATA HPI, AIC  /
     1      1.57079632679489662D+00,     1.265512123484645396D+00/
C***FIRST EXECUTABLE STATEMENT  ZUNI2
      NZ = 0
      ND = N
      NLAST = 0
C-----------------------------------------------------------------------
C     COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG-
C     NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE,
C     EXP(ALIM)=EXP(ELIM)*TOL
C-----------------------------------------------------------------------
      CSCL = 1.0D0/TOL
      CRSC = TOL
      CSSR(1) = CSCL
      CSSR(2) = CONER
      CSSR(3) = CRSC
      CSRR(1) = CRSC
      CSRR(2) = CONER
      CSRR(3) = CSCL
      BRY(1) = 1.0D+3*D1MACH(1)/TOL
C-----------------------------------------------------------------------
C     ZN IS IN THE RIGHT HALF PLANE AFTER ROTATION BY CI OR -CI
C-----------------------------------------------------------------------
      ZNR = ZI
      ZNI = -ZR
      ZBR = ZR
      ZBI = ZI
      CIDI = -CONER
      INU = FNU
      ANG = HPI*(FNU-INU)
      C2R = COS(ANG)
      C2I = SIN(ANG)
      CAR = C2R
      SAR = C2I
      IN = INU + N - 1
      IN = MOD(IN,4) + 1
      STR = C2R*CIPR(IN) - C2I*CIPI(IN)
      C2I = C2R*CIPI(IN) + C2I*CIPR(IN)
      C2R = STR
      IF (ZI.GT.0.0D0) GO TO 10
      ZNR = -ZNR
      ZBI = -ZBI
      CIDI = -CIDI
      C2I = -C2I
   10 CONTINUE
C-----------------------------------------------------------------------
C     CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER
C-----------------------------------------------------------------------
      FN = MAX(FNU,1.0D0)
      CALL ZUNHJ(ZNR, ZNI, FN, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R,
     * ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
      IF (KODE.EQ.1) GO TO 20
      STR = ZBR + ZETA2R
      STI = ZBI + ZETA2I
      RAST = FN/ZABS(STR,STI)
      STR = STR*RAST*RAST
      STI = -STI*RAST*RAST
      S1R = -ZETA1R + STR
      S1I = -ZETA1I + STI
      GO TO 30
   20 CONTINUE
      S1R = -ZETA1R + ZETA2R
      S1I = -ZETA1I + ZETA2I
   30 CONTINUE
      RS1 = S1R
      IF (ABS(RS1).GT.ELIM) GO TO 150
   40 CONTINUE
      NN = MIN(2,ND)
      DO 90 I=1,NN
        FN = FNU + (ND-I)
        CALL ZUNHJ(ZNR, ZNI, FN, 0, TOL, PHIR, PHII, ARGR, ARGI,
     *   ZETA1R, ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
        IF (KODE.EQ.1) GO TO 50
        STR = ZBR + ZETA2R
        STI = ZBI + ZETA2I
        RAST = FN/ZABS(STR,STI)
        STR = STR*RAST*RAST
        STI = -STI*RAST*RAST
        S1R = -ZETA1R + STR
        S1I = -ZETA1I + STI + ABS(ZI)
        GO TO 60
   50   CONTINUE
        S1R = -ZETA1R + ZETA2R
        S1I = -ZETA1I + ZETA2I
   60   CONTINUE
C-----------------------------------------------------------------------
C     TEST FOR UNDERFLOW AND OVERFLOW
C-----------------------------------------------------------------------
        RS1 = S1R
        IF (ABS(RS1).GT.ELIM) GO TO 120
        IF (I.EQ.1) IFLAG = 2
        IF (ABS(RS1).LT.ALIM) GO TO 70
C-----------------------------------------------------------------------
C     REFINE  TEST AND SCALE
C-----------------------------------------------------------------------
C-----------------------------------------------------------------------
        APHI = ZABS(PHIR,PHII)
        AARG = ZABS(ARGR,ARGI)
        RS1 = RS1 + LOG(APHI) - 0.25D0*LOG(AARG) - AIC
        IF (ABS(RS1).GT.ELIM) GO TO 120
        IF (I.EQ.1) IFLAG = 1
        IF (RS1.LT.0.0D0) GO TO 70
        IF (I.EQ.1) IFLAG = 3
   70   CONTINUE
C-----------------------------------------------------------------------
C     SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
C     EXPONENT EXTREMES
C-----------------------------------------------------------------------
        CALL ZAIRY(ARGR, ARGI, 0, 2, AIR, AII, NAI, IDUM)
        CALL ZAIRY(ARGR, ARGI, 1, 2, DAIR, DAII, NDAI, IDUM)
        STR = DAIR*BSUMR - DAII*BSUMI
        STI = DAIR*BSUMI + DAII*BSUMR
        STR = STR + (AIR*ASUMR-AII*ASUMI)
        STI = STI + (AIR*ASUMI+AII*ASUMR)
        S2R = PHIR*STR - PHII*STI
        S2I = PHIR*STI + PHII*STR
        STR = EXP(S1R)*CSSR(IFLAG)
        S1R = STR*COS(S1I)
        S1I = STR*SIN(S1I)
        STR = S2R*S1R - S2I*S1I
        S2I = S2R*S1I + S2I*S1R
        S2R = STR
        IF (IFLAG.NE.1) GO TO 80
        CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
        IF (NW.NE.0) GO TO 120
   80   CONTINUE
        IF (ZI.LE.0.0D0) S2I = -S2I
        STR = S2R*C2R - S2I*C2I
        S2I = S2R*C2I + S2I*C2R
        S2R = STR
        CYR(I) = S2R
        CYI(I) = S2I
        J = ND - I + 1
        YR(J) = S2R*CSRR(IFLAG)
        YI(J) = S2I*CSRR(IFLAG)
        STR = -C2I*CIDI
        C2I = C2R*CIDI
        C2R = STR
   90 CONTINUE
      IF (ND.LE.2) GO TO 110
      RAZ = 1.0D0/ZABS(ZR,ZI)
      STR = ZR*RAZ
      STI = -ZI*RAZ
      RZR = (STR+STR)*RAZ
      RZI = (STI+STI)*RAZ
      BRY(2) = 1.0D0/BRY(1)
      BRY(3) = D1MACH(2)
      S1R = CYR(1)
      S1I = CYI(1)
      S2R = CYR(2)
      S2I = CYI(2)
      C1R = CSRR(IFLAG)
      ASCLE = BRY(IFLAG)
      K = ND - 2
      FN = K
      DO 100 I=3,ND
        C2R = S2R
        C2I = S2I
        S2R = S1R + (FNU+FN)*(RZR*C2R-RZI*C2I)
        S2I = S1I + (FNU+FN)*(RZR*C2I+RZI*C2R)
        S1R = C2R
        S1I = C2I
        C2R = S2R*C1R
        C2I = S2I*C1R
        YR(K) = C2R
        YI(K) = C2I
        K = K - 1
        FN = FN - 1.0D0
        IF (IFLAG.GE.3) GO TO 100
        STR = ABS(C2R)
        STI = ABS(C2I)
        C2M = MAX(STR,STI)
        IF (C2M.LE.ASCLE) GO TO 100
        IFLAG = IFLAG + 1
        ASCLE = BRY(IFLAG)
        S1R = S1R*C1R
        S1I = S1I*C1R
        S2R = C2R
        S2I = C2I
        S1R = S1R*CSSR(IFLAG)
        S1I = S1I*CSSR(IFLAG)
        S2R = S2R*CSSR(IFLAG)
        S2I = S2I*CSSR(IFLAG)
        C1R = CSRR(IFLAG)
  100 CONTINUE
  110 CONTINUE
      RETURN
  120 CONTINUE
      IF (RS1.GT.0.0D0) GO TO 140
C-----------------------------------------------------------------------
C     SET UNDERFLOW AND UPDATE PARAMETERS
C-----------------------------------------------------------------------
      YR(ND) = ZEROR
      YI(ND) = ZEROI
      NZ = NZ + 1
      ND = ND - 1
      IF (ND.EQ.0) GO TO 110
      CALL ZUOIK(ZR, ZI, FNU, KODE, 1, ND, YR, YI, NUF, TOL, ELIM, ALIM)
      IF (NUF.LT.0) GO TO 140
      ND = ND - NUF
      NZ = NZ + NUF
      IF (ND.EQ.0) GO TO 110
      FN = FNU + (ND-1)
      IF (FN.LT.FNUL) GO TO 130
C      FN = CIDI
C      J = NUF + 1
C      K = MOD(J,4) + 1
C      S1R = CIPR(K)
C      S1I = CIPI(K)
C      IF (FN.LT.0.0D0) S1I = -S1I
C      STR = C2R*S1R - C2I*S1I
C      C2I = C2R*S1I + C2I*S1R
C      C2R = STR
      IN = INU + ND - 1
      IN = MOD(IN,4) + 1
      C2R = CAR*CIPR(IN) - SAR*CIPI(IN)
      C2I = CAR*CIPI(IN) + SAR*CIPR(IN)
      IF (ZI.LE.0.0D0) C2I = -C2I
      GO TO 40
  130 CONTINUE
      NLAST = ND
      RETURN
  140 CONTINUE
      NZ = -1
      RETURN
  150 CONTINUE
      IF (RS1.GT.0.0D0) GO TO 140
      NZ = N
      DO 160 I=1,N
        YR(I) = ZEROR
        YI(I) = ZEROI
  160 CONTINUE
      RETURN
      END