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
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
|
*DECK ZUNK1
SUBROUTINE ZUNK1 (ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM,
+ ALIM)
C***BEGIN PROLOGUE ZUNK1
C***SUBSIDIARY
C***PURPOSE Subsidiary to ZBESK
C***LIBRARY SLATEC
C***TYPE ALL (CUNK1-A, ZUNK1-A)
C***AUTHOR Amos, D. E., (SNL)
C***DESCRIPTION
C
C ZUNK1 COMPUTES K(FNU,Z) AND ITS ANALYTIC CONTINUATION FROM THE
C RIGHT HALF PLANE TO THE LEFT HALF PLANE BY MEANS OF THE
C UNIFORM ASYMPTOTIC EXPANSION.
C MR INDICATES THE DIRECTION OF ROTATION FOR ANALYTIC CONTINUATION.
C NZ=-1 MEANS AN OVERFLOW WILL OCCUR
C
C***SEE ALSO ZBESK
C***ROUTINES CALLED D1MACH, ZABS, ZS1S2, ZUCHK, ZUNIK
C***REVISION HISTORY (YYMMDD)
C 830501 DATE WRITTEN
C 910415 Prologue converted to Version 4.0 format. (BAB)
C***END PROLOGUE ZUNK1
C COMPLEX CFN,CK,CONE,CRSC,CS,CSCL,CSGN,CSPN,CSR,CSS,CWRK,CY,CZERO,
C *C1,C2,PHI,PHID,RZ,SUM,SUMD,S1,S2,Y,Z,ZETA1,ZETA1D,ZETA2,ZETA2D,ZR
DOUBLE PRECISION ALIM, ANG, APHI, ASC, ASCLE, BRY, CKI, CKR,
* CONER, CRSC, CSCL, CSGNI, CSPNI, CSPNR, CSR, CSRR, CSSR,
* CWRKI, CWRKR, CYI, CYR, C1I, C1R, C2I, C2M, C2R, ELIM, FMR, FN,
* FNF, FNU, PHIDI, PHIDR, PHII, PHIR, PI, RAST, RAZR, RS1, RZI,
* RZR, SGN, STI, STR, SUMDI, SUMDR, SUMI, SUMR, S1I, S1R, S2I,
* S2R, TOL, YI, YR, ZEROI, ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R,
* ZET1DI, ZET1DR, ZET2DI, ZET2DR, ZI, ZR, ZRI, ZRR, D1MACH, ZABS
INTEGER I, IB, IFLAG, IFN, IL, INIT, INU, IUF, K, KDFLG, KFLAG,
* KK, KODE, MR, N, NW, NZ, INITD, IC, IPARD, J, M
DIMENSION BRY(3), INIT(2), YR(N), YI(N), SUMR(2), SUMI(2),
* ZETA1R(2), ZETA1I(2), ZETA2R(2), ZETA2I(2), CYR(2), CYI(2),
* CWRKR(16,3), CWRKI(16,3), CSSR(3), CSRR(3), PHIR(2), PHII(2)
EXTERNAL ZABS
DATA ZEROR,ZEROI,CONER / 0.0D0, 0.0D0, 1.0D0 /
DATA PI / 3.14159265358979324D0 /
C***FIRST EXECUTABLE STATEMENT ZUNK1
KDFLG = 1
NZ = 0
C-----------------------------------------------------------------------
C EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION GREATER THAN
C THE UNDERFLOW LIMIT
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
BRY(2) = 1.0D0/BRY(1)
BRY(3) = D1MACH(2)
ZRR = ZR
ZRI = ZI
IF (ZR.GE.0.0D0) GO TO 10
ZRR = -ZR
ZRI = -ZI
10 CONTINUE
J = 2
DO 70 I=1,N
C-----------------------------------------------------------------------
C J FLIP FLOPS BETWEEN 1 AND 2 IN J = 3 - J
C-----------------------------------------------------------------------
J = 3 - J
FN = FNU + (I-1)
INIT(J) = 0
CALL ZUNIK(ZRR, ZRI, FN, 2, 0, TOL, INIT(J), PHIR(J), PHII(J),
* ZETA1R(J), ZETA1I(J), ZETA2R(J), ZETA2I(J), SUMR(J), SUMI(J),
* CWRKR(1,J), CWRKI(1,J))
IF (KODE.EQ.1) GO TO 20
STR = ZRR + ZETA2R(J)
STI = ZRI + ZETA2I(J)
RAST = FN/ZABS(STR,STI)
STR = STR*RAST*RAST
STI = -STI*RAST*RAST
S1R = ZETA1R(J) - STR
S1I = ZETA1I(J) - STI
GO TO 30
20 CONTINUE
S1R = ZETA1R(J) - ZETA2R(J)
S1I = ZETA1I(J) - ZETA2I(J)
30 CONTINUE
RS1 = S1R
C-----------------------------------------------------------------------
C TEST FOR UNDERFLOW AND OVERFLOW
C-----------------------------------------------------------------------
IF (ABS(RS1).GT.ELIM) GO TO 60
IF (KDFLG.EQ.1) KFLAG = 2
IF (ABS(RS1).LT.ALIM) GO TO 40
C-----------------------------------------------------------------------
C REFINE TEST AND SCALE
C-----------------------------------------------------------------------
APHI = ZABS(PHIR(J),PHII(J))
RS1 = RS1 + LOG(APHI)
IF (ABS(RS1).GT.ELIM) GO TO 60
IF (KDFLG.EQ.1) KFLAG = 1
IF (RS1.LT.0.0D0) GO TO 40
IF (KDFLG.EQ.1) KFLAG = 3
40 CONTINUE
C-----------------------------------------------------------------------
C SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR
C EXPONENT EXTREMES
C-----------------------------------------------------------------------
S2R = PHIR(J)*SUMR(J) - PHII(J)*SUMI(J)
S2I = PHIR(J)*SUMI(J) + PHII(J)*SUMR(J)
STR = EXP(S1R)*CSSR(KFLAG)
S1R = STR*COS(S1I)
S1I = STR*SIN(S1I)
STR = S2R*S1R - S2I*S1I
S2I = S1R*S2I + S2R*S1I
S2R = STR
IF (KFLAG.NE.1) GO TO 50
CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
IF (NW.NE.0) GO TO 60
50 CONTINUE
CYR(KDFLG) = S2R
CYI(KDFLG) = S2I
YR(I) = S2R*CSRR(KFLAG)
YI(I) = S2I*CSRR(KFLAG)
IF (KDFLG.EQ.2) GO TO 75
KDFLG = 2
GO TO 70
60 CONTINUE
IF (RS1.GT.0.0D0) GO TO 300
C-----------------------------------------------------------------------
C FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
C-----------------------------------------------------------------------
IF (ZR.LT.0.0D0) GO TO 300
KDFLG = 1
YR(I)=ZEROR
YI(I)=ZEROI
NZ=NZ+1
IF (I.EQ.1) GO TO 70
IF ((YR(I-1).EQ.ZEROR).AND.(YI(I-1).EQ.ZEROI)) GO TO 70
YR(I-1)=ZEROR
YI(I-1)=ZEROI
NZ=NZ+1
70 CONTINUE
I = N
75 CONTINUE
RAZR = 1.0D0/ZABS(ZRR,ZRI)
STR = ZRR*RAZR
STI = -ZRI*RAZR
RZR = (STR+STR)*RAZR
RZI = (STI+STI)*RAZR
CKR = FN*RZR
CKI = FN*RZI
IB = I + 1
IF (N.LT.IB) GO TO 160
C-----------------------------------------------------------------------
C TEST LAST MEMBER FOR UNDERFLOW AND OVERFLOW. SET SEQUENCE TO ZERO
C ON UNDERFLOW.
C-----------------------------------------------------------------------
FN = FNU + (N-1)
IPARD = 1
IF (MR.NE.0) IPARD = 0
INITD = 0
CALL ZUNIK(ZRR, ZRI, FN, 2, IPARD, TOL, INITD, PHIDR, PHIDI,
* ZET1DR, ZET1DI, ZET2DR, ZET2DI, SUMDR, SUMDI, CWRKR(1,3),
* CWRKI(1,3))
IF (KODE.EQ.1) GO TO 80
STR = ZRR + ZET2DR
STI = ZRI + ZET2DI
RAST = FN/ZABS(STR,STI)
STR = STR*RAST*RAST
STI = -STI*RAST*RAST
S1R = ZET1DR - STR
S1I = ZET1DI - STI
GO TO 90
80 CONTINUE
S1R = ZET1DR - ZET2DR
S1I = ZET1DI - ZET2DI
90 CONTINUE
RS1 = S1R
IF (ABS(RS1).GT.ELIM) GO TO 95
IF (ABS(RS1).LT.ALIM) GO TO 100
C-----------------------------------------------------------------------
C REFINE ESTIMATE AND TEST
C-----------------------------------------------------------------------
APHI = ZABS(PHIDR,PHIDI)
RS1 = RS1+LOG(APHI)
IF (ABS(RS1).LT.ELIM) GO TO 100
95 CONTINUE
IF (ABS(RS1).GT.0.0D0) GO TO 300
C-----------------------------------------------------------------------
C FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW
C-----------------------------------------------------------------------
IF (ZR.LT.0.0D0) GO TO 300
NZ = N
DO 96 I=1,N
YR(I) = ZEROR
YI(I) = ZEROI
96 CONTINUE
RETURN
C-----------------------------------------------------------------------
C FORWARD RECUR FOR REMAINDER OF THE SEQUENCE
C-----------------------------------------------------------------------
100 CONTINUE
S1R = CYR(1)
S1I = CYI(1)
S2R = CYR(2)
S2I = CYI(2)
C1R = CSRR(KFLAG)
ASCLE = BRY(KFLAG)
DO 120 I=IB,N
C2R = S2R
C2I = S2I
S2R = CKR*C2R - CKI*C2I + S1R
S2I = CKR*C2I + CKI*C2R + S1I
S1R = C2R
S1I = C2I
CKR = CKR + RZR
CKI = CKI + RZI
C2R = S2R*C1R
C2I = S2I*C1R
YR(I) = C2R
YI(I) = C2I
IF (KFLAG.GE.3) GO TO 120
STR = ABS(C2R)
STI = ABS(C2I)
C2M = MAX(STR,STI)
IF (C2M.LE.ASCLE) GO TO 120
KFLAG = KFLAG + 1
ASCLE = BRY(KFLAG)
S1R = S1R*C1R
S1I = S1I*C1R
S2R = C2R
S2I = C2I
S1R = S1R*CSSR(KFLAG)
S1I = S1I*CSSR(KFLAG)
S2R = S2R*CSSR(KFLAG)
S2I = S2I*CSSR(KFLAG)
C1R = CSRR(KFLAG)
120 CONTINUE
160 CONTINUE
IF (MR.EQ.0) RETURN
C-----------------------------------------------------------------------
C ANALYTIC CONTINUATION FOR RE(Z).LT.0.0D0
C-----------------------------------------------------------------------
NZ = 0
FMR = MR
SGN = -DSIGN(PI,FMR)
C-----------------------------------------------------------------------
C CSPN AND CSGN ARE COEFF OF K AND I FUNCTIONS RESP.
C-----------------------------------------------------------------------
CSGNI = SGN
INU = FNU
FNF = FNU - INU
IFN = INU + N - 1
ANG = FNF*SGN
CSPNR = COS(ANG)
CSPNI = SIN(ANG)
IF (MOD(IFN,2).EQ.0) GO TO 170
CSPNR = -CSPNR
CSPNI = -CSPNI
170 CONTINUE
ASC = BRY(1)
IUF = 0
KK = N
KDFLG = 1
IB = IB - 1
IC = IB - 1
DO 270 K=1,N
FN = FNU + (KK-1)
C-----------------------------------------------------------------------
C LOGIC TO SORT OUT CASES WHOSE PARAMETERS WERE SET FOR THE K
C FUNCTION ABOVE
C-----------------------------------------------------------------------
M=3
IF (N.GT.2) GO TO 175
172 CONTINUE
INITD = INIT(J)
PHIDR = PHIR(J)
PHIDI = PHII(J)
ZET1DR = ZETA1R(J)
ZET1DI = ZETA1I(J)
ZET2DR = ZETA2R(J)
ZET2DI = ZETA2I(J)
SUMDR = SUMR(J)
SUMDI = SUMI(J)
M = J
J = 3 - J
GO TO 180
175 CONTINUE
IF ((KK.EQ.N).AND.(IB.LT.N)) GO TO 180
IF ((KK.EQ.IB).OR.(KK.EQ.IC)) GO TO 172
INITD = 0
180 CONTINUE
CALL ZUNIK(ZRR, ZRI, FN, 1, 0, TOL, INITD, PHIDR, PHIDI,
* ZET1DR, ZET1DI, ZET2DR, ZET2DI, SUMDR, SUMDI,
* CWRKR(1,M), CWRKI(1,M))
IF (KODE.EQ.1) GO TO 200
STR = ZRR + ZET2DR
STI = ZRI + ZET2DI
RAST = FN/ZABS(STR,STI)
STR = STR*RAST*RAST
STI = -STI*RAST*RAST
S1R = -ZET1DR + STR
S1I = -ZET1DI + STI
GO TO 210
200 CONTINUE
S1R = -ZET1DR + ZET2DR
S1I = -ZET1DI + ZET2DI
210 CONTINUE
C-----------------------------------------------------------------------
C TEST FOR UNDERFLOW AND OVERFLOW
C-----------------------------------------------------------------------
RS1 = S1R
IF (ABS(RS1).GT.ELIM) GO TO 260
IF (KDFLG.EQ.1) IFLAG = 2
IF (ABS(RS1).LT.ALIM) GO TO 220
C-----------------------------------------------------------------------
C REFINE TEST AND SCALE
C-----------------------------------------------------------------------
APHI = ZABS(PHIDR,PHIDI)
RS1 = RS1 + LOG(APHI)
IF (ABS(RS1).GT.ELIM) GO TO 260
IF (KDFLG.EQ.1) IFLAG = 1
IF (RS1.LT.0.0D0) GO TO 220
IF (KDFLG.EQ.1) IFLAG = 3
220 CONTINUE
STR = PHIDR*SUMDR - PHIDI*SUMDI
STI = PHIDR*SUMDI + PHIDI*SUMDR
S2R = -CSGNI*STI
S2I = CSGNI*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 230
CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL)
IF (NW.EQ.0) GO TO 230
S2R = ZEROR
S2I = ZEROI
230 CONTINUE
CYR(KDFLG) = S2R
CYI(KDFLG) = S2I
C2R = S2R
C2I = S2I
S2R = S2R*CSRR(IFLAG)
S2I = S2I*CSRR(IFLAG)
C-----------------------------------------------------------------------
C ADD I AND K FUNCTIONS, K SEQUENCE IN Y(I), I=1,N
C-----------------------------------------------------------------------
S1R = YR(KK)
S1I = YI(KK)
IF (KODE.EQ.1) GO TO 250
CALL ZS1S2(ZRR, ZRI, S1R, S1I, S2R, S2I, NW, ASC, ALIM, IUF)
NZ = NZ + NW
250 CONTINUE
YR(KK) = S1R*CSPNR - S1I*CSPNI + S2R
YI(KK) = CSPNR*S1I + CSPNI*S1R + S2I
KK = KK - 1
CSPNR = -CSPNR
CSPNI = -CSPNI
IF (C2R.NE.0.0D0 .OR. C2I.NE.0.0D0) GO TO 255
KDFLG = 1
GO TO 270
255 CONTINUE
IF (KDFLG.EQ.2) GO TO 275
KDFLG = 2
GO TO 270
260 CONTINUE
IF (RS1.GT.0.0D0) GO TO 300
S2R = ZEROR
S2I = ZEROI
GO TO 230
270 CONTINUE
K = N
275 CONTINUE
IL = N - K
IF (IL.EQ.0) RETURN
C-----------------------------------------------------------------------
C RECUR BACKWARD FOR REMAINDER OF I SEQUENCE AND ADD IN THE
C K FUNCTIONS, SCALING THE I SEQUENCE DURING RECURRENCE TO KEEP
C INTERMEDIATE ARITHMETIC ON SCALE NEAR EXPONENT EXTREMES.
C-----------------------------------------------------------------------
S1R = CYR(1)
S1I = CYI(1)
S2R = CYR(2)
S2I = CYI(2)
CSR = CSRR(IFLAG)
ASCLE = BRY(IFLAG)
FN = INU+IL
DO 290 I=1,IL
C2R = S2R
C2I = S2I
S2R = S1R + (FN+FNF)*(RZR*C2R-RZI*C2I)
S2I = S1I + (FN+FNF)*(RZR*C2I+RZI*C2R)
S1R = C2R
S1I = C2I
FN = FN - 1.0D0
C2R = S2R*CSR
C2I = S2I*CSR
CKR = C2R
CKI = C2I
C1R = YR(KK)
C1I = YI(KK)
IF (KODE.EQ.1) GO TO 280
CALL ZS1S2(ZRR, ZRI, C1R, C1I, C2R, C2I, NW, ASC, ALIM, IUF)
NZ = NZ + NW
280 CONTINUE
YR(KK) = C1R*CSPNR - C1I*CSPNI + C2R
YI(KK) = C1R*CSPNI + C1I*CSPNR + C2I
KK = KK - 1
CSPNR = -CSPNR
CSPNI = -CSPNI
IF (IFLAG.GE.3) GO TO 290
C2R = ABS(CKR)
C2I = ABS(CKI)
C2M = MAX(C2R,C2I)
IF (C2M.LE.ASCLE) GO TO 290
IFLAG = IFLAG + 1
ASCLE = BRY(IFLAG)
S1R = S1R*CSR
S1I = S1I*CSR
S2R = CKR
S2I = CKI
S1R = S1R*CSSR(IFLAG)
S1I = S1I*CSSR(IFLAG)
S2R = S2R*CSSR(IFLAG)
S2I = S2I*CSSR(IFLAG)
CSR = CSRR(IFLAG)
290 CONTINUE
RETURN
300 CONTINUE
NZ = -1
RETURN
END
|
