amos/zuni2.f

   1       SUBROUTINE ZUNI2(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NLAST, FNUL,
   2      * TOL, ELIM, ALIM)
   3 C***BEGIN PROLOGUE  ZUNI2
   4 C***REFER TO  ZBESI,ZBESK
   5 C
   6 C     ZUNI2 COMPUTES I(FNU,Z) IN THE RIGHT HALF PLANE BY MEANS OF
   7 C     UNIFORM ASYMPTOTIC EXPANSION FOR J(FNU,ZN) WHERE ZN IS Z*I
   8 C     OR -Z*I AND ZN IS IN THE RIGHT HALF PLANE ALSO.
   9 C
  10 C     FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC
  11 C     EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET.
  12 C     NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER
  13 C     FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL.
  14 C     Y(I)=CZERO FOR I=NLAST+1,N
  15 C
  16 C***ROUTINES CALLED  ZAIRY,ZUCHK,ZUNHJ,ZUOIK,D1MACH,AZABS
  17 C***END PROLOGUE  ZUNI2
  18 C     COMPLEX AI,ARG,ASUM,BSUM,CFN,CI,CID,CIP,CONE,CRSC,CSCL,CSR,CSS,
  19 C    *CZERO,C1,C2,DAI,PHI,RZ,S1,S2,Y,Z,ZB,ZETA1,ZETA2,ZN
  20       DOUBLE PRECISION AARG, AIC, AII, AIR, ALIM, ANG, APHI, ARGI,
  21      * ARGR, ASCLE, ASUMI, ASUMR, BRY, BSUMI, BSUMR, CIDI, CIPI, CIPR,
  22      * CONER, CRSC, CSCL, CSRR, CSSR, C1R, C2I, C2M, C2R, DAII,
  23      * DAIR, ELIM, FN, FNU, FNUL, HPI, PHII, PHIR, RAST, RAZ, RS1, RZI,
  24      * RZR, STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR, ZBI, ZBR, ZEROI,
  25      * ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZI, ZNI, ZNR, ZR, CYR,
  26      * CYI, D1MACH, AZABS, CAR, SAR
  27       INTEGER I, IFLAG, IN, INU, J, K, KODE, N, NAI, ND, NDAI, NLAST,
  28      * NN, NUF, NW, NZ, IDUM
  29       DIMENSION BRY(3), YR(N), YI(N), CIPR(4), CIPI(4), CSSR(3),
  30      * CSRR(3), CYR(2), CYI(2)
  31       DATA ZEROR,ZEROI,CONER / 0.0D0, 0.0D0, 1.0D0 /
  32       DATA CIPR(1),CIPI(1),CIPR(2),CIPI(2),CIPR(3),CIPI(3),CIPR(4),
  33      * CIPI(4)/ 1.0D0,0.0D0, 0.0D0,1.0D0, -1.0D0,0.0D0, 0.0D0,-1.0D0/
  34       DATA HPI, AIC  /
  35      1      1.57079632679489662D+00,     1.265512123484645396D+00/
  36 C
  37       NZ = 0
  38       ND = N
  39       NLAST = 0
  40 C-----------------------------------------------------------------------
  41 C     COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG-
  42 C     NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE,
  43 C     EXP(ALIM)=EXP(ELIM)*TOL
  44 C-----------------------------------------------------------------------
  45       CSCL = 1.0D0/TOL
  46       CRSC = TOL
  47       CSSR(1) = CSCL
  48       CSSR(2) = CONER
  49       CSSR(3) = CRSC
  50       CSRR(1) = CRSC
  51       CSRR(2) = CONER
  52       CSRR(3) = CSCL
  53       BRY(1) = 1.0D+3*D1MACH(1)/TOL
  54 C-----------------------------------------------------------------------
  55 C     ZN IS IN THE RIGHT HALF PLANE AFTER ROTATION BY CI OR -CI
  56 C-----------------------------------------------------------------------
  57       ZNR = ZI
  58       ZNI = -ZR
  59       ZBR = ZR
  60       ZBI = ZI
  61       CIDI = -CONER
  62       INU = INT(SNGL(FNU))
  63       ANG = HPI*(FNU-DBLE(FLOAT(INU)))
  64       C2R = DCOS(ANG)
  65       C2I = DSIN(ANG)
  66       CAR = C2R
  67       SAR = C2I
  68       IN = INU + N - 1
  69       IN = MOD(IN,4) + 1
  70       STR = C2R*CIPR(IN) - C2I*CIPI(IN)
  71       C2I = C2R*CIPI(IN) + C2I*CIPR(IN)
  72       C2R = STR
  73       IF (ZI.GT.0.0D0) GO TO 10
  74       ZNR = -ZNR
  75       ZBI = -ZBI
  76       CIDI = -CIDI
  77       C2I = -C2I
  78    10 CONTINUE
  79 C-----------------------------------------------------------------------
  80 C     CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER
  81 C-----------------------------------------------------------------------
  82       FN = DMAX1(FNU,1.0D0)
  83       CALL ZUNHJ(ZNR, ZNI, FN, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R,
  84      * ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
  85       IF (KODE.EQ.1) GO TO 20
  86       STR = ZBR + ZETA2R
  87       STI = ZBI + ZETA2I
  88       RAST = FN/AZABS(STR,STI)
  89       STR = STR*RAST*RAST
  90       STI = -STI*RAST*RAST
  91       S1R = -ZETA1R + STR
  92       S1I = -ZETA1I + STI
  93       GO TO 30
  94    20 CONTINUE
  95       S1R = -ZETA1R + ZETA2R
  96       S1I = -ZETA1I + ZETA2I
  97    30 CONTINUE
  98       RS1 = S1R
  99       IF (DABS(RS1).GT.ELIM) GO TO 150
 100    40 CONTINUE
 101       NN = MIN0(2,ND)
 102       DO 90 I=1,NN
 103         FN = FNU + DBLE(FLOAT(ND-I))
 104         CALL ZUNHJ(ZNR, ZNI, FN, 0, TOL, PHIR, PHII, ARGR, ARGI,
 105      *   ZETA1R, ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI)
 106         IF (KODE.EQ.1) GO TO 50
 107         STR = ZBR + ZETA2R
 108         STI = ZBI + ZETA2I
 109         RAST = FN/AZABS(STR,STI)
 110         STR = STR*RAST*RAST
 111         STI = -STI*RAST*RAST
 112         S1R = -ZETA1R + STR
 113         S1I = -ZETA1I + STI + DABS(ZI)
 114         GO TO 60
 115    50   CONTINUE
 116         S1R = -ZETA1R + ZETA2R
 117         S1I = -ZETA1I + ZETA2I
 118    60   CONTINUE
 119 C-----------------------------------------------------------------------
 120 C     TEST FOR UNDERFLOW AND OVERFLOW
 121 C-----------------------------------------------------------------------
 122         RS1 = S1R
 123         IF (DABS(RS1).GT.ELIM) GO TO 120
 124         IF (I.EQ.1) IFLAG = 2
 125         IF (DABS(RS1).LT.ALIM) GO TO 70
 126 C-----------------------------------------------------------------------
 127 C     REFINE  TEST AND SCALE
 128 C-----------------------------------------------------------------------
 129 C-----------------------------------------------------------------------
 130         APHI = AZABS(PHIR,PHII)
 131         AARG = AZABS(ARGR,ARGI)
 132         RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC
 133         IF (DABS(RS1).GT.ELIM) GO TO 120
 134         IF (I.EQ.1) IFLAG = 1
 135         IF (RS1.LT.0.0D0) GO TO 70
 136         IF (I.EQ.1) IFLAG = 3
 137    70   CONTINUE
 138 C-----------------------------------------------------------------------
 139 C     SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
 140 C     EXPONENT EXTREMES
 141 C-----------------------------------------------------------------------
 142         CALL ZAIRY(ARGR, ARGI, 0, 2, AIR, AII, NAI, IDUM)
 143         CALL ZAIRY(ARGR, ARGI, 1, 2, DAIR, DAII, NDAI, IDUM)
 144         STR = DAIR*BSUMR - DAII*BSUMI
 145         STI = DAIR*BSUMI + DAII*BSUMR
 146         STR = STR + (AIR*ASUMR-AII*ASUMI)
 147         STI = STI + (AIR*ASUMI+AII*ASUMR)
 148         S2R = PHIR*STR - PHII*STI
 149         S2I = PHIR*STI + PHII*STR
 150         STR = DEXP(S1R)*CSSR(IFLAG)
 151         S1R = STR*DCOS(S1I)
 152         S1I = STR*DSIN(S1I)
 153         STR = S2R*S1R - S2I*S1I
 154         S2I = S2R*S1I + S2I*S1R
 155         S2R = STR
 156         IF (IFLAG.NE.1) GO TO 80
 157         CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
 158         IF (NW.NE.0) GO TO 120
 159    80   CONTINUE
 160         IF (ZI.LE.0.0D0) S2I = -S2I
 161         STR = S2R*C2R - S2I*C2I
 162         S2I = S2R*C2I + S2I*C2R
 163         S2R = STR
 164         CYR(I) = S2R
 165         CYI(I) = S2I
 166         J = ND - I + 1
 167         YR(J) = S2R*CSRR(IFLAG)
 168         YI(J) = S2I*CSRR(IFLAG)
 169         STR = -C2I*CIDI
 170         C2I = C2R*CIDI
 171         C2R = STR
 172    90 CONTINUE
 173       IF (ND.LE.2) GO TO 110
 174       RAZ = 1.0D0/AZABS(ZR,ZI)
 175       STR = ZR*RAZ
 176       STI = -ZI*RAZ
 177       RZR = (STR+STR)*RAZ
 178       RZI = (STI+STI)*RAZ
 179       BRY(2) = 1.0D0/BRY(1)
 180       BRY(3) = D1MACH(2)
 181       S1R = CYR(1)
 182       S1I = CYI(1)
 183       S2R = CYR(2)
 184       S2I = CYI(2)
 185       C1R = CSRR(IFLAG)
 186       ASCLE = BRY(IFLAG)
 187       K = ND - 2
 188       FN = DBLE(FLOAT(K))
 189       DO 100 I=3,ND
 190         C2R = S2R
 191         C2I = S2I
 192         S2R = S1R + (FNU+FN)*(RZR*C2R-RZI*C2I)
 193         S2I = S1I + (FNU+FN)*(RZR*C2I+RZI*C2R)
 194         S1R = C2R
 195         S1I = C2I
 196         C2R = S2R*C1R
 197         C2I = S2I*C1R
 198         YR(K) = C2R
 199         YI(K) = C2I
 200         K = K - 1
 201         FN = FN - 1.0D0
 202         IF (IFLAG.GE.3) GO TO 100
 203         STR = DABS(C2R)
 204         STI = DABS(C2I)
 205         C2M = DMAX1(STR,STI)
 206         IF (C2M.LE.ASCLE) GO TO 100
 207         IFLAG = IFLAG + 1
 208         ASCLE = BRY(IFLAG)
 209         S1R = S1R*C1R
 210         S1I = S1I*C1R
 211         S2R = C2R
 212         S2I = C2I
 213         S1R = S1R*CSSR(IFLAG)
 214         S1I = S1I*CSSR(IFLAG)
 215         S2R = S2R*CSSR(IFLAG)
 216         S2I = S2I*CSSR(IFLAG)
 217         C1R = CSRR(IFLAG)
 218   100 CONTINUE
 219   110 CONTINUE
 220       RETURN
 221   120 CONTINUE
 222       IF (RS1.GT.0.0D0) GO TO 140
 223 C-----------------------------------------------------------------------
 224 C     SET UNDERFLOW AND UPDATE PARAMETERS
 225 C-----------------------------------------------------------------------
 226       YR(ND) = ZEROR
 227       YI(ND) = ZEROI
 228       NZ = NZ + 1
 229       ND = ND - 1
 230       IF (ND.EQ.0) GO TO 110
 231       CALL ZUOIK(ZR, ZI, FNU, KODE, 1, ND, YR, YI, NUF, TOL, ELIM, ALIM)
 232       IF (NUF.LT.0) GO TO 140
 233       ND = ND - NUF
 234       NZ = NZ + NUF
 235       IF (ND.EQ.0) GO TO 110
 236       FN = FNU + DBLE(FLOAT(ND-1))
 237       IF (FN.LT.FNUL) GO TO 130
 238 C      FN = CIDI
 239 C      J = NUF + 1
 240 C      K = MOD(J,4) + 1
 241 C      S1R = CIPR(K)
 242 C      S1I = CIPI(K)
 243 C      IF (FN.LT.0.0D0) S1I = -S1I
 244 C      STR = C2R*S1R - C2I*S1I
 245 C      C2I = C2R*S1I + C2I*S1R
 246 C      C2R = STR
 247       IN = INU + ND - 1
 248       IN = MOD(IN,4) + 1
 249       C2R = CAR*CIPR(IN) - SAR*CIPI(IN)
 250       C2I = CAR*CIPI(IN) + SAR*CIPR(IN)
 251       IF (ZI.LE.0.0D0) C2I = -C2I
 252       GO TO 40
 253   130 CONTINUE
 254       NLAST = ND
 255       RETURN
 256   140 CONTINUE
 257       NZ = -1
 258       RETURN
 259   150 CONTINUE
 260       IF (RS1.GT.0.0D0) GO TO 140
 261       NZ = N
 262       DO 160 I=1,N
 263         YR(I) = ZEROR
 264         YI(I) = ZEROI
 265   160 CONTINUE
 266       RETURN
 267       END