1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
|
SUBROUTINE ZUNI2(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NLAST, FNUL,
* TOL, ELIM, ALIM)
C***BEGIN PROLOGUE ZUNI2
C***REFER TO ZBESI,ZBESK
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***ROUTINES CALLED ZAIRY,ZUCHK,ZUNHJ,ZUOIK,D1MACH,AZABS
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, AZABS, 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)
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
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 = INT(SNGL(FNU))
ANG = HPI*(FNU-DBLE(FLOAT(INU)))
C2R = DCOS(ANG)
C2I = DSIN(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 = DMAX1(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/AZABS(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 (DABS(RS1).GT.ELIM) GO TO 150
40 CONTINUE
NN = MIN0(2,ND)
DO 90 I=1,NN
FN = FNU + DBLE(FLOAT(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/AZABS(STR,STI)
STR = STR*RAST*RAST
STI = -STI*RAST*RAST
S1R = -ZETA1R + STR
S1I = -ZETA1I + STI + DABS(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 (DABS(RS1).GT.ELIM) GO TO 120
IF (I.EQ.1) IFLAG = 2
IF (DABS(RS1).LT.ALIM) GO TO 70
C-----------------------------------------------------------------------
C REFINE TEST AND SCALE
C-----------------------------------------------------------------------
C-----------------------------------------------------------------------
APHI = AZABS(PHIR,PHII)
AARG = AZABS(ARGR,ARGI)
RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC
IF (DABS(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 = DEXP(S1R)*CSSR(IFLAG)
S1R = STR*DCOS(S1I)
S1I = STR*DSIN(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/AZABS(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 = DBLE(FLOAT(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 = DABS(C2R)
STI = DABS(C2I)
C2M = DMAX1(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 + DBLE(FLOAT(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
|
