cloudy  trunk
atmdat_3body.cpp
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1 /* This file is part of Cloudy and is copyright (C)1978-2013 by Gary J. Ferland and
2  * others. For conditions of distribution and use see copyright notice in license.txt */
3 /*atmdat_3body derive three-body recombination coefficients */
4 /*da interpolate on three body recombination by Steve Cota */
5 #include "cddefines.h"
6 #include "ionbal.h"
7 #include "phycon.h"
8 #include "dense.h"
9 #include "trace.h"
10 #include "save.h"
11 #include "atmdat.h"
12 
13 #define MAXZ 28
14 
15 STATIC void blkdata1(void);
16 STATIC double da(double z, double temp, double eden);
17 
18 static double a2[63],
19  b2[63],
20  x2[63];
21 
22 static double a0[83],
23  x0[83];
24 static realnum b0[83],
25  b1[83];
26 
27 static double a1[83],
28  x1[83];
29 
30 static double tz[83],
31  zlog7[28],
32  zlog2[28];
33 
34 #define RC_INI(rs) (rs[_r].rc>1 ? DEC_RC_(rs) : (rs[_r].rc==1 ? INC_NDX_(rs) : rs[_r].ini ))
35 #define DEC_RC_(rs) (rs[_r].rc--,rs[_r].ini)
36 #define INC_NDX_(rs) (_r++,rs[_r-1].ini)
37 
38 /* this "mapping function" occurs below */
39 STATIC double xmap(double x[],
40  double y[],
41  double x0);
42 
43 /* inverse routine, also below */
44 STATIC double xinvrs(double y,
45  double a,
46  double b,
47  double u,
48  double v,
49  long int *ifail);
50 
51 /* =================================================================== */
52 void atmdat_3body(void)
53 {
54  long int i,
55  iup;
56 
57  DEBUG_ENTRY( "atmdat_3body()" );
58 
59 
60  if( ionbal.lgNoCota )
61  {
62  for( i=0; i < LIMELM; i++ )
63  {
64  ionbal.CotaRate[i] = 0.;
65  }
66  atmdat.nsbig = 0;
67  return;
68  }
69 
70  if( atmdat.nsbig == 0 )
71  {
72  /* steve cota only defined things up to 28 */
73  iup = MIN2(28,LIMELM);
74  }
75  else
76  {
77  iup = MIN3( LIMELM , atmdat.nsbig , 28 );
78  }
79 
80  for( i=0; i < iup; i++ )
81  {
82  ionbal.CotaRate[i] = (realnum)da((double)(i+1), MAX2(100.,phycon.te), dense.eden);
83  }
84 
85  atmdat.nsbig = 0;
86 
87  if( trace.lgTrace && trace.lgTrace3Bod )
88  {
89  fprintf( ioQQQ, " 3BOD rate:" );
90  for( i=1; i <= 14; i++ )
91  {
92  fprintf( ioQQQ, "%8.1e", ionbal.CotaRate[i-1] );
93  }
94  fprintf( ioQQQ, "\n" );
95  }
96 
97  if( save.lgioRecom )
98  {
99  /* option to save coefficients */
100  fprintf( save.ioRecom, " 3-body rec coef vs charge \n" );
101  for( i=0; i < iup; i++ )
102  {
103  fprintf( save.ioRecom, "%3ld%10.2e\n", i+1, ionbal.CotaRate[i] );
104  }
105  fprintf( save.ioRecom, "\n");
106  }
107  return;
108 }
109 
110 /* =================================================================== */
111 STATIC double da(double z, double temp, double eden)
112 {
113  /*lint -e736 loss of precision in assignment in translated data */
114  long int jfail,
115  nt,
116  nt0,
117  nt1,
118  nz;
119 
120  static bool lgCalled=false;
121  double a,
122  alogn,
123  alognc,
124  alogt,
125  b,
126  c,
127  d,
128  da_v,
129  expp,
130  u,
131  v,
132  x,
133  xnc,
134  y,
135  zlog;
136  double yya[3],
137  xx[3],
138  yyb[3],
139  yyx[3],
140  yyy[3];
141 
142  /* alogte is base 10 log of temperature and elec density*/
143  double alogte , alogne;
144 
145  DEBUG_ENTRY( "da()" );
146 
147  /* WRITTEN BY S. A. COTA, 2/87
148  * */
149 
150  /* MAXZ IS THE MAXIMUM EFFECTIVE NUCLEAR CHARGE ( = IONIC CHARGE + 1 )
151  * WHICH THE DIMENSION STATEMENTS ACCOMODATE.
152  *
153  * IT IS USED ONLY FOR THE ARRAY ZLOG7 ( = 7 * LOG ( Z ) )
154  * AND THE ARRAY ZLOG2 ( = 2 * LOG ( Z ) ) . THESE ARRAYS
155  * CONTAIN EASILY CALCULATED VALUES, WHICH HAVE BEEN STORED
156  * TO SAVE TIME IN EXECUTION.
157  *
158  * IF MAXZ IS EXCEEDED, THIS PROGRAM SIMPLY CALCULATES THE
159  * LOGS INSTEAD OF LOOKING THEM UP.
160  *
161  * */
162 
163  if( !lgCalled )
164  {
165  lgCalled = true;
166  blkdata1();
167  }
168 
169  /*begin sanity check */
170  ASSERT( zlog7[1] > 0. );
171 
172  nz = (long)(z + .1);
173  // The original routine has major discontinuities
174  // The use of eden_limited (here and at the end of the routine) is an attempt
175  // to smooth these problems and still get roughly the same behavior.
176  double eden_limited = MIN2( eden, 1e5 );
177  alogne = log10(eden_limited);
178  alogte = log10(temp);
179  if( nz > MAXZ )
180  {
181  zlog = log10(z);
182  alogt = alogte - 2.*zlog;
183  alogn = alogne - 7.*zlog;
184  }
185  else
186  {
187  alogt = alogte - zlog2[nz-1];
188  alogn = alogne - zlog7[nz-1];
189  }
190 
191  /* CHECK IF PARAMETERS ARE WITHIN BOUNDS. IF NOT, INCREMENT
192  * APPROPRIATE ERROR COUNTER AND SET TO BOUNDARY IF
193  * NECESSARY:
194  *
195  * DEFINITION OF ERROR COUNTERS:
196  *
197  * ILT : LOW T
198  * ILTLN : LOW T , LOW N
199  * ILTHN : LOW T , HIGH N
200  * IHTHN : HIGH T , HIGH N
201  * */
202  if( alogt < 0. )
203  {
204  ionbal.ilt += 1;
205  alogt = 0.;
206  }
207 
208  if( alogt <= 2.1760913 )
209  {
210  if( alogn < (3.5*alogt - 8.) )
211  {
212  ionbal.iltln += 1;
213  }
214  else if( alogn > (3.5*alogt - 2.) )
215  {
216  ionbal.ilthn += 1;
217  alogn = 3.5*alogt - 2.;
218  }
219 
220  }
221  else if( alogt <= 2.4771213 )
222  {
223  if( alogn > 9. )
224  {
225  ASSERT( 0 );
226  ionbal.ilthn += 1;
227  alogn = 9.;
228  }
229 
230  }
231  else if( alogt <= 5.1139434 )
232  {
233  if( alogn > 13. )
234  {
235  ASSERT( 0 );
236  ionbal.ihthn += 1;
237  alogn = 13.;
238  }
239 
240  }
241 
242  // limit used temperature to 10^5 K and
243  // extrapolate with T^-2 at end of routine (to avoid discontinuous behavior).
244  double alogt_limited = MIN2( alogt, 5.0 );
245  double alogt_save = alogt;
246  alogt = alogt_limited;
247 
248  /* LOCATE POSITION IN ARRAYS */
249  if( alogt <= 2. )
250  {
251  nt = (long)(9.9657843*alogt + 1.);
252  }
253  else
254  {
255  nt = (long)(19.931568*alogt - 19.);
256  }
257  nt = MIN2(83,nt);
258  nt = MAX2(1,nt);
259 
260  /* CENTER UP SINCE ARRAY VALUES ARE ROUNDED */
261  if( fabs(alogt-tz[nt-1]) >= fabs(alogt-tz[MIN2(83,nt+1)-1]) )
262  {
263  nt = MIN2(83,nt+1);
264  }
265  else if( fabs(alogt-tz[nt-1]) > fabs(alogt-tz[MAX2(1,nt-1)-1]) )
266  {
267  nt = MAX2(1,nt-1);
268  }
269 
270  /* CHECK IF INTERPOLATION IS NEEDED AND PROCEED IF NOT.*/
271  if( fabs(alogt-tz[nt-1]) < 0.00001 )
272  {
273  if( z != 1.0 )
274  {
275  c = a1[nt-1];
276  d = b1[nt-1];
277  u = x1[nt-1];
278  v = 8.90;
279  }
280  else
281  {
282  nt = MAX2(21,nt);
283  nt = MIN2(83,nt);
284  c = a2[nt-(21)];
285  d = b2[nt-(21)];
286  u = x2[nt-(21)];
287  v = 9.40;
288  }
289 
290  xnc = xinvrs(alogn,c,d,u,v,&jfail);
291  if( xnc <= 0. || jfail != 0 )
292  {
293  ionbal.ifail = 1;
294  jfail = 1;
295  da_v = 0.;
296  return( da_v );
297  }
298  alognc = log10(xnc);
299 
300  a = a0[nt-1];
301  b = b0[nt-1];
302  x = -2.45;
303  y = x0[nt-1];
304  nt0 = nt - 1;
305 
306  /* IF INTERPOLATION WAS REQUIRED,
307  * CHECK THAT NT IS NOT ON THE EDGE OF A DISCONTINUITY,
308  * EITHER AT END OF ARRAYS OR WITHIN THEM,
309  * WHERE VALUES CHANGE ABRUPTLY.
310  * */
311  }
312  else
313  {
314  if( (nt <= 21) && (z == 1.0) )
315  {
316  nt = 22;
317  }
318  else if( nt <= 1 )
319  {
320  nt = 2;
321  }
322  else if( nt >= 83 )
323  {
324  nt = 82;
325  }
326  else if( nt == 24 )
327  {
328  if( alogt <= 2.1760913 )
329  {
330  nt = 23;
331  }
332  else
333  {
334  nt = 25;
335  }
336  }
337  else if( nt == 30 )
338  {
339  if( alogt <= 2.4771213 )
340  {
341  nt = 29;
342  }
343  else
344  {
345  nt = 31;
346  }
347  }
348 
349  nt0 = nt - 1;
350  nt1 = nt + 1;
351  xx[0] = tz[nt0-1];
352  xx[1] = tz[nt-1];
353  xx[2] = tz[nt1-1];
354 
355  if( z != 1.0 )
356  {
357  if( nt0 == 24 )
358  {
359  yya[0] = 17.2880135;
360  yyb[0] = 6.93410742e03;
361  yyx[0] = -3.75;
362  }
363  else if( nt0 == 30 )
364  {
365  yya[0] = 17.4317989;
366  yyb[0] = 1.36653821e03;
367  yyx[0] = -3.40;
368  }
369  else
370  {
371  yya[0] = a1[nt0-1];
372  yyb[0] = b1[nt0-1];
373  yyx[0] = x1[nt0-1];
374  }
375 
376  yya[1] = a1[nt-1];
377  yya[2] = a1[nt1-1];
378  c = xmap(xx,yya,alogt);
379  yyb[1] = b1[nt-1];
380  yyb[2] = b1[nt1-1];
381  d = xmap(xx,yyb,alogt);
382  yyx[1] = x1[nt-1];
383  yyx[2] = x1[nt1-1];
384  u = xmap(xx,yyx,alogt);
385  v = 8.90;
386 
387  }
388  else
389  {
390  if( nt0 == 24 )
391  {
392  yya[0] = 20.1895161;
393  yyb[0] = 2.25774918e01;
394  yyx[0] = -1.66;
395  }
396  else if( nt0 == 30 )
397  {
398  yya[0] = 19.8647804;
399  yyb[0] = 6.70408707e02;
400  yyx[0] = -2.12;
401  }
402  else
403  {
404  yya[0] = a2[nt0-(21)];
405  yyb[0] = b2[nt0-(21)];
406  yyx[0] = x2[nt0-(21)];
407  }
408 
409  yya[1] = a2[nt-(21)];
410  yya[2] = a2[nt1-(21)];
411  c = xmap(xx,yya,alogt);
412  yyb[1] = b2[nt-(21)];
413  yyb[2] = b2[nt1-(21)];
414  d = xmap(xx,yyb,alogt);
415  yyx[1] = x2[nt-(21)];
416  yyx[2] = x2[nt1-(21)];
417  u = xmap(xx,yyx,alogt);
418  v = 9.40;
419  }
420 
421  xnc = xinvrs(alogn,c,d,u,v,&jfail);
422  if( xnc <= 0. || jfail != 0 )
423  {
424  ionbal.ifail = 1;
425  jfail = 1;
426  da_v = 0.;
427  return( da_v );
428  }
429  alognc = log10(xnc);
430 
431  if( nt0 == 24 )
432  {
433  yya[0] = -8.04963875;
434  yyb[0] = 1.07205127e03;
435  yyy[0] = 2.05;
436  }
437  else if( nt0 == 30 )
438  {
439  yya[0] = -8.54721069;
440  yyb[0] = 4.70450195e02;
441  yyy[0] = 2.05;
442  }
443  else
444  {
445  yya[0] = a0[nt0-1];
446  yyb[0] = b0[nt0-1];
447  yyy[0] = x0[nt0-1];
448  }
449 
450  yya[1] = a0[nt-1];
451  yya[2] = a0[nt1-1];
452  a = xmap(xx,yya,alogt);
453  yyb[1] = b0[nt-1];
454  yyb[2] = b0[nt1-1];
455  b = xmap(xx,yyb,alogt);
456  x = -2.45;
457  yyy[1] = x0[nt-1];
458  yyy[2] = x0[nt1-1];
459  y = xmap(xx,yyy,alogt);
460  }
461 
462  expp = a - y*alognc + b*pow(xnc,x);
463  if( expp < 37 )
464  {
465  da_v = z*pow(10.,expp);
466  }
467  else
468  {
469  da_v = 0.;
470  }
471  ionbal.ifail += jfail;
472 
473  da_v *= pow( eden/eden_limited, 0.25 );
474  da_v *= pow( 10., 2.*(alogt_limited-alogt_save) );
475 
476  return( da_v );
477 }
478 
479 /****************************************************************************** */
480 STATIC void blkdata1(void)
481 {
482  /*block data with Steve Cota's 3-body recombination coefficients */
483 
484  /* data for function da.
485  *
486  * S. A. COTA, 2/1987
487  * */
488 
489  long int _i,
490  _r;
491  realnum *const ba0 = (realnum*)b0;
492  realnum *const ba1 = (realnum*)b1;
493  realnum *const bb0 = (realnum*)((char*)(b0 + 79));
494  realnum *const bb1 = (realnum*)((char*)(b1 + 79));
495 
496  /* to fix all the conversion errors, change realnum ini to double ini,
497  * but chech that results still ok */
498  { static struct{ long rc; double ini; } _rs0[] = {
499  {1, 0.00000e00},
500  {1, 2.10721e00},
501  {1, 3.33985e00},
502  {1, 4.21442e00},
503  {1, 4.89279e00},
504  {1, 5.44706e00},
505  {1, 5.91569e00},
506  {1, 6.32163e00},
507  {1, 6.67970e00},
508  {1, 7.00000e00},
509  {1, 7.28975e00},
510  {1, 7.55427e00},
511  {1, 7.79760e00},
512  {1, 8.02290e00},
513  {1, 8.23264e00},
514  {1, 8.42884e00},
515  {1, 8.61314e00},
516  {1, 8.78691e00},
517  {1, 8.95128e00},
518  {1, 9.10721e00},
519  {1, 9.25554e00},
520  {1, 9.39696e00},
521  {1, 9.53209e00},
522  {1, 9.66148e00},
523  {1, 9.78558e00},
524  {1, 9.90481e00},
525  {1, 10.01954e00},
526  {1, 10.13010e00},
527  {0L, 0}
528  };
529  for(_i=_r=0L; _i < 28; _i++)
530  zlog7[_i] = RC_INI(_rs0); }
531  { static struct{ long rc; double ini; } _rs1[] = {
532  {1, 0.00000e00},
533  {1, 6.02060e-01},
534  {1, 9.54243e-01},
535  {1, 1.20412e00},
536  {1, 1.39794e00},
537  {1, 1.55630e00},
538  {1, 1.69020e00},
539  {1, 1.80618e00},
540  {1, 1.90849e00},
541  {1, 2.00000e00},
542  {1, 2.08279e00},
543  {1, 2.15836e00},
544  {1, 2.22789e00},
545  {1, 2.29226e00},
546  {1, 2.35218e00},
547  {1, 2.40824e00},
548  {1, 2.46090e00},
549  {1, 2.51055e00},
550  {1, 2.55751e00},
551  {1, 2.60206e00},
552  {1, 2.64444e00},
553  {1, 2.68485e00},
554  {1, 2.72346e00},
555  {1, 2.76042e00},
556  {1, 2.79588e00},
557  {1, 2.82995e00},
558  {1, 2.86272e00},
559  {1, 2.89431e00},
560  {0L, 0}
561  };
562  for(_i=_r=0L; _i < 28; _i++)
563  zlog2[_i] = RC_INI(_rs1); }
564  { static struct{ long rc; double ini; } _rs2[] = {
565  {1, 0.},
566  {1, 0.09691},
567  {1, 0.17609},
568  {1, 0.30103},
569  {1, 0.39794},
570  {1, 0.47712},
571  {1, 0.60206},
572  {1, 0.69897},
573  {1, 0.77815},
574  {1, 0.90309},
575  {1, 1.00000},
576  {1, 1.07918},
577  {1, 1.20412},
578  {1, 1.30103},
579  {1, 1.39794},
580  {1, 1.47712},
581  {1, 1.60206},
582  {1, 1.69897},
583  {1, 1.77815},
584  {1, 1.90309},
585  {1, 2.00000},
586  {1, 2.06070},
587  {1, 2.09691},
588  {1, 2.17609},
589  {1, 2.20412},
590  {1, 2.24304},
591  {1, 2.30103},
592  {1, 2.35218},
593  {1, 2.39794},
594  {1, 2.47712},
595  {1, 2.51188},
596  {1, 2.54407},
597  {1, 2.60206},
598  {1, 2.65321},
599  {1, 2.69897},
600  {1, 2.75967},
601  {1, 2.81291},
602  {1, 2.86034},
603  {1, 2.91645},
604  {1, 2.95424},
605  {1, 3.00000},
606  {1, 3.07918},
607  {1, 3.11394},
608  {1, 3.17609},
609  {1, 3.20412},
610  {1, 3.25527},
611  {1, 3.30103},
612  {1, 3.36173},
613  {1, 3.39794},
614  {1, 3.46240},
615  {1, 3.51188},
616  {1, 3.56820},
617  {1, 3.60206},
618  {1, 3.66276},
619  {1, 3.72016},
620  {1, 3.76343},
621  {1, 3.81291},
622  {1, 3.86034},
623  {1, 3.90309},
624  {1, 3.95424},
625  {1, 4.02119},
626  {1, 4.06070},
627  {1, 4.11394},
628  {1, 4.16137},
629  {1, 4.20412},
630  {1, 4.25527},
631  {1, 4.31175},
632  {1, 4.36173},
633  {1, 4.41497},
634  {1, 4.46240},
635  {1, 4.51521},
636  {1, 4.56526},
637  {1, 4.61542},
638  {1, 4.66605},
639  {1, 4.71600},
640  {1, 4.76343},
641  {1, 4.81624},
642  {1, 4.86629},
643  {1, 4.91645},
644  {1, 4.96614},
645  {1, 5.02119},
646  {1, 5.06726},
647  {1, 5.11394},
648  {0L, 0 }
649  };
650  for(_i=_r=0L; _i < 83; _i++)
651  tz[_i] = RC_INI(_rs2); }
652  { static struct{ long rc; double ini; } _rs3[] = {
653  {1, -4.31396484},
654  {1, -4.56640625},
655  {1, -4.74560547},
656  {1, -4.98535156},
657  {1, -5.15373850},
658  {1, -5.28123093},
659  {1, -5.48215008},
660  {1, -5.63811255},
661  {1, -5.76573515},
662  {1, -5.96755028},
663  {1, -6.12449837},
664  {1, -6.25304174},
665  {1, -6.45615673},
666  {1, -6.61384058},
667  {1, -6.77161551},
668  {1, -6.90069818},
669  {1, -7.10470295},
670  {1, -7.26322412},
671  {1, -7.39289951},
672  {1, -7.59792519},
673  {1, -7.75725508},
674  {1, -7.85722494},
675  {1, -7.91697407},
676  {1, -8.04758644},
677  {1, -8.09447479},
678  {1, -8.15859795},
679  {1, -8.25424385},
680  {1, -8.33880615},
681  {1, -8.41452408},
682  {1, -8.54581165},
683  {1, -8.60400581},
684  {1, -8.65751839},
685  {1, -8.75414848},
686  {1, -8.83946800},
687  {1, -8.91589737},
688  {1, -9.01741695},
689  {1, -9.10663033},
690  {1, -9.18621922},
691  {1, -9.28059292},
692  {1, -9.34430218},
693  {1, -9.42154408},
694  {1, -9.55562973},
695  {1, -9.61459446},
696  {1, -9.72023010},
697  {1, -9.76802444},
698  {1, -9.85540199},
699  {1, -9.93374062},
700  {1, -10.03800774},
701  {1, -10.10044670},
702  {1, -10.21178055},
703  {1, -10.29757786},
704  {1, -10.39561272},
705  {1, -10.45469666},
706  {1, -10.56102180},
707  {1, -10.66205502},
708  {1, -10.73780537},
709  {1, -10.82557774},
710  {1, -10.91007328},
711  {1, -10.98659325},
712  {1, -11.07857418},
713  {1, -11.19975281},
714  {1, -11.27170753},
715  {1, -11.36930943},
716  {1, -11.45675945},
717  {1, -11.53620148},
718  {1, -11.63198853},
719  {1, -11.73875237},
720  {1, -11.83400822},
721  {1, -11.93677044},
722  {1, -12.02933311},
723  {1, -12.13374519},
724  {1, -12.23410702},
725  {1, -12.33664989},
726  {1, -12.44163322},
727  {1, -12.54730415},
728  {1, -12.64975739},
729  {1, -12.76682186},
730  {1, -12.88185978},
731  {1, -13.00052643},
732  {1, -13.12289810},
733  {1, -13.26689529},
734  {1, -13.39390945},
735  {1, -30.00000000},
736  {0L, 0 }
737  };
738  for(_i=_r=0L; _i < 83; _i++)
739  a0[_i] = RC_INI(_rs3); }
740  { static struct{ long rc; double ini; } _rs4[] = {
741  {1, 4.53776000e05},
742  {1, 3.48304000e05},
743  {1, 2.80224000e05},
744  {1, 1.98128000e05},
745  {1, 1.51219797e05},
746  {1, 1.21113266e05},
747  {1, 8.52812109e04},
748  {1, 6.49598125e04},
749  {1, 5.20075781e04},
750  {1, 3.66190977e04},
751  {1, 2.79060723e04},
752  {1, 2.23634102e04},
753  {1, 1.57683135e04},
754  {1, 1.20284307e04},
755  {1, 9.17755273e03},
756  {1, 7.36044873e03},
757  {1, 5.19871680e03},
758  {1, 3.97240796e03},
759  {1, 3.18934326e03},
760  {1, 2.25737622e03},
761  {1, 1.72767114e03},
762  {1, 1.46202722e03},
763  {1, 1.32456628e03},
764  {1, 1.06499792e03},
765  {1, 9.92735291e02},
766  {1, 8.91604858e02},
767  {1, 7.59411560e02},
768  {1, 6.59120056e02},
769  {1, 5.80688965e02},
770  {1, 4.66602264e02},
771  {1, 4.27612854e02},
772  {1, 3.91531494e02},
773  {1, 3.34516968e02},
774  {1, 2.91021820e02},
775  {1, 2.56853912e02},
776  {1, 2.17598007e02},
777  {1, 1.88145462e02},
778  {1, 1.65329865e02},
779  {1, 1.41960342e02},
780  {1, 1.28181686e02},
781  {1, 1.13336761e02},
782  {1, 9.17785034e01},
783  {1, 8.36242981e01},
784  {1, 7.08843536e01},
785  {1, 6.58346100e01},
786  {1, 5.75790634e01},
787  {1, 5.11293755e01},
788  {1, 4.37563019e01},
789  {1, 3.99226875e01},
790  {1, 3.39562836e01},
791  {1, 3.00413170e01},
792  {1, 2.61871891e01},
793  {1, 2.41310368e01},
794  {1, 2.08853607e01},
795  {1, 1.82632275e01},
796  {1, 1.60007000e01},
797  {1, 1.42617064e01},
798  {1, 1.27951088e01},
799  {1, 1.16221066e01},
800  {1, 1.03779335e01},
801  {1, 8.97864914e00},
802  {1, 8.25593281e00},
803  {1, 7.39339924e00},
804  {1, 6.70784378e00},
805  {1, 6.16084862e00},
806  {1, 5.57818031e00},
807  {1, 5.01341105e00},
808  {1, 4.55679178e00},
809  {1, 4.13692093e00},
810  {1, 3.80004382e00},
811  {1, 3.46328306e00},
812  {1, 3.17340493e00},
813  {1, 2.93525696e00},
814  {1, 2.69083858e00},
815  {1, 2.46588683e00},
816  {1, 2.26083040e00},
817  {1, 2.04337358e00},
818  {1, 1.89027369e00},
819  {1, 1.69208312e00},
820  {0L, 0 }
821  };
822  for(_i=_r=0L; _i < 79; _i++)
823  ba0[_i] = (realnum)RC_INI(_rs4); }
824  { static struct{ long rc; double ini; } _rs5[] = {
825  {1, 1.48992336e00},
826  {1, 1.32466662e00},
827  {1, 1.10697949e00},
828  {1, 9.29813862e-01},
829  {0L, 0 }
830  };
831  for(_i=_r=0L; _i < 4; _i++)
832  bb0[_i] = (realnum)RC_INI(_rs5); }
833  { static struct{ long rc; double ini; } _rs6[] = {
834  {1, 2.12597656},
835  {1, 2.08984375},
836  {1, 2.06958008},
837  {1, 2.05444336},
838  {1, 2.05},
839  {1, 2.05},
840  {1, 2.05},
841  {1, 2.05},
842  {1, 2.05},
843  {1, 2.05},
844  {1, 2.05},
845  {1, 2.05},
846  {1, 2.05},
847  {1, 2.05},
848  {1, 2.05},
849  {1, 2.05},
850  {1, 2.05},
851  {1, 2.05},
852  {1, 2.05},
853  {1, 2.05},
854  {1, 2.05},
855  {1, 2.05},
856  {1, 2.05},
857  {1, 2.05},
858  {1, 2.05},
859  {1, 2.05},
860  {1, 2.05},
861  {1, 2.05},
862  {1, 2.05},
863  {1, 2.05},
864  {1, 2.05},
865  {1, 2.05},
866  {1, 2.05},
867  {1, 2.05},
868  {1, 2.05},
869  {1, 2.05},
870  {1, 2.05},
871  {1, 2.05},
872  {1, 2.05},
873  {1, 2.05},
874  {1, 2.05},
875  {1, 2.05},
876  {1, 2.05},
877  {1, 2.05},
878  {1, 2.05},
879  {1, 2.05},
880  {1, 2.05},
881  {1, 2.05},
882  {1, 2.05},
883  {1, 2.05},
884  {1, 2.05},
885  {1, 2.05},
886  {1, 2.05},
887  {1, 2.05},
888  {1, 2.05},
889  {1, 2.05},
890  {1, 2.05},
891  {1, 2.05},
892  {1, 2.05},
893  {1, 2.05},
894  {1, 2.05},
895  {1, 2.05},
896  {1, 2.05},
897  {1, 2.05},
898  {1, 2.05},
899  {1, 2.05},
900  {1, 2.05},
901  {1, 2.05},
902  {1, 2.05},
903  {1, 2.05},
904  {1, 2.05},
905  {1, 2.05},
906  {1, 2.05},
907  {1, 2.05},
908  {1, 2.05},
909  {1, 2.05},
910  {1, 2.05},
911  {1, 2.05},
912  {1, 2.05},
913  {1, 2.05},
914  {1, 2.05},
915  {1, 2.05},
916  {1, 2.05},
917  {0L, 0 }
918  };
919  for(_i=_r=0L; _i < 83; _i++)
920  x0[_i] = RC_INI(_rs6); }
921 
922  { static struct{ long rc; double ini; } _rs7[] = {
923  {1, 16.23337936},
924  {1, 16.27946854},
925  {1, 16.31696320},
926  {1, 16.37597656},
927  {1, 16.42210960},
928  {1, 16.45996284},
929  {1, 16.51994896},
930  {1, 16.56644440},
931  {1, 16.60460854},
932  {1, 16.66510773},
933  {1, 16.71198654},
934  {1, 16.75038719},
935  {1, 16.81106949},
936  {1, 16.85778809},
937  {1, 16.90416527},
938  {1, 16.94209099},
939  {1, 17.00195694},
940  {1, 17.04838943},
941  {1, 17.08633804},
942  {1, 17.14627838},
943  {1, 17.19270515},
944  {1, 17.22186279},
945  {1, 17.23933601},
946  {1, 17.27728271},
947  {1, 17.30161858},
948  {1, 17.32085800},
949  {1, 17.34928894},
950  {1, 17.37349129},
951  {1, 17.39528084},
952  {1, 17.43282318},
953  {1, 17.44827652},
954  {1, 17.46357536},
955  {1, 17.49082375},
956  {1, 17.51517677},
957  {1, 17.53697205},
958  {1, 17.56587219},
959  {1, 17.59125519},
960  {1, 17.61410332},
961  {1, 17.64081383},
962  {1, 17.65900803},
963  {1, 17.68086433},
964  {1, 17.71843529},
965  {1, 17.73512840},
966  {1, 17.76512146},
967  {1, 17.77873421},
968  {1, 17.80340767},
969  {1, 17.82530022},
970  {1, 17.85470963},
971  {1, 17.87210464},
972  {1, 17.90334511},
973  {1, 17.92751503},
974  {1, 17.95458603},
975  {1, 17.97117233},
976  {1, 18.00062943},
977  {1, 18.02842712},
978  {1, 18.04934502},
979  {1, 18.07340050},
980  {1, 18.09639168},
981  {1, 18.11732864},
982  {1, 18.14218903},
983  {1, 18.17465591},
984  {1, 18.19370079},
985  {1, 18.21962166},
986  {1, 18.24237251},
987  {1, 18.26305962},
988  {1, 18.28767967},
989  {1, 18.31531525},
990  {1, 18.33900452},
991  {1, 18.36478043},
992  {1, 18.38741112},
993  {1, 18.41271973},
994  {1, 18.43644333},
995  {1, 18.46075630},
996  {1, 18.48509216},
997  {1, 18.50897980},
998  {1, 18.53143501},
999  {1, 18.55570030},
1000  {1, 18.58008003},
1001  {1, 18.60348320},
1002  {1, 18.62536430},
1003  {1, 18.65199852},
1004  {1, 18.67623520},
1005  {1, 18.70072174},
1006  {0L, 0 }
1007  };
1008  for(_i=_r=0L; _i < 83; _i++)
1009  a1[_i] = RC_INI(_rs7); }
1010  { static struct{ long rc; double ini; } _rs8[] = {
1011  {1, 1.09462866e10},
1012  {1, 9.32986675e09},
1013  {1, 6.15947008e09},
1014  {1, 1.54486170e09},
1015  {1, 1.00812454e09},
1016  {1, 7.00559552e08},
1017  {1, 6.25999232e08},
1018  {1, 3.50779968e08},
1019  {1, 3.11956288e08},
1020  {1, 3.74866016e08},
1021  {1, 2.47019424e08},
1022  {1, 1.73169776e08},
1023  {1, 1.01753168e08},
1024  {1, 6.81861920e07},
1025  {1, 4.61764000e07},
1026  {1, 3.31671360e07},
1027  {1, 2.03160540e07},
1028  {1, 1.40249480e07},
1029  {1, 1.02577860e07},
1030  {1, 3.53822650e06},
1031  {1, 1.32563388e06},
1032  {1, 9.14284688e05},
1033  {1, 1.25230388e06},
1034  {1, 3.17865156e05},
1035  {1, 4.76750244e03},
1036  {1, 4.81107031e03},
1037  {1, 4.88406152e03},
1038  {1, 4.80611279e03},
1039  {1, 4.78843652e03},
1040  {1, 4.65988477e03},
1041  {1, 1.26723059e03},
1042  {1, 1.20825342e03},
1043  {1, 8.66052612e02},
1044  {1, 7.76661316e02},
1045  {1, 7.05279358e02},
1046  {1, 6.21722656e02},
1047  {1, 5.46207581e02},
1048  {1, 4.96247742e02},
1049  {1, 4.26340118e02},
1050  {1, 3.96090424e02},
1051  {1, 3.48429657e02},
1052  {1, 2.37949142e02},
1053  {1, 2.14678406e02},
1054  {1, 1.81019180e02},
1055  {1, 1.68923676e02},
1056  {1, 1.45979385e02},
1057  {1, 1.25311127e02},
1058  {1, 1.05205528e02},
1059  {1, 9.39378357e01},
1060  {1, 7.75339966e01},
1061  {1, 6.68987427e01},
1062  {1, 5.53580055e01},
1063  {1, 5.00100212e01},
1064  {1, 4.14198608e01},
1065  {1, 3.46289063e01},
1066  {1, 3.00775223e01},
1067  {1, 2.60294399e01},
1068  {1, 2.26602840e01},
1069  {1, 2.02123032e01},
1070  {1, 1.76353855e01},
1071  {1, 1.47198439e01},
1072  {1, 1.33078461e01},
1073  {1, 1.17181997e01},
1074  {1, 1.04125805e01},
1075  {1, 9.45785904e00},
1076  {1, 8.42799950e00},
1077  {1, 7.62769842e00},
1078  {1, 6.85484743e00},
1079  {1, 6.25903368e00},
1080  {1, 5.75135279e00},
1081  {1, 5.28468180e00},
1082  {1, 4.87669659e00},
1083  {1, 4.57353973e00},
1084  {1, 4.30108690e00},
1085  {1, 4.05412245e00},
1086  {1, 3.83283114e00},
1087  {1, 3.57902861e00},
1088  {1, 3.43705726e00},
1089  {1, 3.26563096e00},
1090  {0L, 0 }
1091  };
1092  for(_i=_r=0L; _i < 79; _i++)
1093  ba1[_i] = (realnum)RC_INI(_rs8); }
1094  { static struct{ long rc; double ini; } _rs9[] = {
1095  {1, 3.07498097e00},
1096  {1, 2.96334076e00},
1097  {1, 2.92890000e00},
1098  {1, 2.89550042e00},
1099  {0L, 0 }
1100  };
1101  for(_i=_r=0L; _i < 4; _i++)
1102  bb1[_i] = (realnum)RC_INI(_rs9); }
1103  { static struct{ long rc; double ini; } _rs10[] = {
1104  {1, -5.46},
1105  {1, -5.51},
1106  {1, -5.49},
1107  {1, -5.30},
1108  {1, -5.29},
1109  {1, -5.28},
1110  {1, -5.37},
1111  {1, -5.33},
1112  {1, -5.38},
1113  {1, -5.55},
1114  {1, -5.55},
1115  {1, -5.55},
1116  {1, -5.55},
1117  {1, -5.55},
1118  {1, -5.55},
1119  {1, -5.55},
1120  {1, -5.55},
1121  {1, -5.55},
1122  {1, -5.55},
1123  {1, -5.38},
1124  {1, -5.19},
1125  {1, -5.14},
1126  {1, -5.27},
1127  {1, -4.93},
1128  {1, -3.64},
1129  {1, -3.68},
1130  {1, -3.74},
1131  {1, -3.78},
1132  {1, -3.82},
1133  {1, -3.88},
1134  {1, -3.40},
1135  {1, -3.41},
1136  {1, -3.32},
1137  {1, -3.32},
1138  {1, -3.32},
1139  {1, -3.32},
1140  {1, -3.31},
1141  {1, -3.31},
1142  {1, -3.29},
1143  {1, -3.29},
1144  {1, -3.27},
1145  {1, -3.16},
1146  {1, -3.14},
1147  {1, -3.11},
1148  {1, -3.10},
1149  {1, -3.07},
1150  {1, -3.03},
1151  {1, -2.99},
1152  {1, -2.96},
1153  {1, -2.91},
1154  {1, -2.87},
1155  {1, -2.81},
1156  {1, -2.78},
1157  {1, -2.72},
1158  {1, -2.66},
1159  {1, -2.61},
1160  {1, -2.56},
1161  {1, -2.51},
1162  {1, -2.47},
1163  {1, -2.42},
1164  {1, -2.35},
1165  {1, -2.31},
1166  {1, -2.26},
1167  {1, -2.21},
1168  {1, -2.17},
1169  {1, -2.12},
1170  {1, -2.08},
1171  {1, -2.03},
1172  {1, -1.99},
1173  {1, -1.95},
1174  {1, -1.91},
1175  {1, -1.87},
1176  {1, -1.84},
1177  {1, -1.81},
1178  {1, -1.78},
1179  {1, -1.75},
1180  {1, -1.71},
1181  {1, -1.69},
1182  {1, -1.66},
1183  {1, -1.62},
1184  {1, -1.60},
1185  {1, -1.60},
1186  {1, -1.60},
1187  {0L, 0 }
1188  };
1189  for(_i=_r=0L; _i < 83; _i++)
1190  x1[_i] = RC_INI(_rs10); }
1191  { static struct{ long rc; double ini; } _rs11[] = {
1192  {1, 20.30049515},
1193  {1, 20.28500366},
1194  {1, 20.25300407},
1195  {1, 20.16626740},
1196  {1, 20.15743256},
1197  {1, 20.11256981},
1198  {1, 20.04818344},
1199  {1, 19.99261856},
1200  {1, 19.94472885},
1201  {1, 19.86478043},
1202  {1, 19.83321571},
1203  {1, 19.80185127},
1204  {1, 19.74884224},
1205  {1, 19.70136070},
1206  {1, 19.65981102},
1207  {1, 19.60598755},
1208  {1, 19.56017494},
1209  {1, 19.52042389},
1210  {1, 19.47429657},
1211  {1, 19.44413757},
1212  {1, 19.40796280},
1213  {1, 19.34819984},
1214  {1, 19.32203293},
1215  {1, 19.27634430},
1216  {1, 19.25627136},
1217  {1, 19.22009087},
1218  {1, 19.18853378},
1219  {1, 19.14809799},
1220  {1, 19.12456703},
1221  {1, 19.08409119},
1222  {1, 19.05431557},
1223  {1, 19.02083015},
1224  {1, 19.00176430},
1225  {1, 18.96817970},
1226  {1, 18.93762589},
1227  {1, 18.91706085},
1228  {1, 18.89299583},
1229  {1, 18.87085915},
1230  {1, 18.85210609},
1231  {1, 18.83035851},
1232  {1, 18.80403900},
1233  {1, 18.78901100},
1234  {1, 18.77099228},
1235  {1, 18.75540161},
1236  {1, 18.74287033},
1237  {1, 18.72928810},
1238  {1, 18.71601868},
1239  {1, 18.70474434},
1240  {1, 18.69515800},
1241  {1, 18.68782425},
1242  {1, 18.68120766},
1243  {1, 18.67630005},
1244  {1, 18.67357445},
1245  {1, 18.67129898},
1246  {1, 18.67042351},
1247  {1, 18.67090988},
1248  {1, 18.67313004},
1249  {1, 18.67636490},
1250  {1, 18.68120003},
1251  {1, 18.68803024},
1252  {1, 18.69487381},
1253  {1, 18.70458412},
1254  {1, 18.71205139},
1255  {0L, 0 }
1256  };
1257  for(_i=_r=0L; _i < 63; _i++)
1258  a2[_i] = RC_INI(_rs11); }
1259  { static struct{ long rc; double ini; } _rs12[] = {
1260  {1, 1.01078403e00},
1261  {1, 1.97956896e00},
1262  {1, 3.14605665e00},
1263  {1, 6.46874905e00},
1264  {1, 3.16406364e01},
1265  {1, 3.74927673e01},
1266  {1, 4.75353088e01},
1267  {1, 5.27809143e01},
1268  {1, 5.86515846e01},
1269  {1, 6.70408707e01},
1270  {1, 1.14904137e02},
1271  {1, 1.03133133e02},
1272  {1, 1.26508728e02},
1273  {1, 1.03827606e02},
1274  {1, 8.79508896e01},
1275  {1, 7.18328934e01},
1276  {1, 6.19807892e01},
1277  {1, 5.51255455e01},
1278  {1, 4.87156143e01},
1279  {1, 4.58579826e01},
1280  {1, 4.19952011e01},
1281  {1, 4.08252220e01},
1282  {1, 3.78243637e01},
1283  {1, 3.34573860e01},
1284  {1, 3.19036102e01},
1285  {1, 2.92026005e01},
1286  {1, 2.74482193e01},
1287  {1, 2.54643936e01},
1288  {1, 2.46636391e01},
1289  {1, 2.33054180e01},
1290  {1, 2.23069897e01},
1291  {1, 2.12891216e01},
1292  {1, 2.06667900e01},
1293  {1, 1.96430798e01},
1294  {1, 1.87381802e01},
1295  {1, 1.76523514e01},
1296  {1, 1.69235287e01},
1297  {1, 1.62647285e01},
1298  {1, 1.56806908e01},
1299  {1, 1.50346069e01},
1300  {1, 1.42240467e01},
1301  {1, 1.37954988e01},
1302  {1, 1.31949224e01},
1303  {1, 1.27211905e01},
1304  {1, 1.22885675e01},
1305  {1, 1.17868662e01},
1306  {1, 1.12577572e01},
1307  {1, 1.08565578e01},
1308  {1, 1.04121590e01},
1309  {1, 1.00410652e01},
1310  {1, 9.64534473e00},
1311  {1, 9.29232121e00},
1312  {1, 8.92519569e00},
1313  {1, 8.60898972e00},
1314  {1, 8.31234550e00},
1315  {1, 8.04089737e00},
1316  {1, 7.74343491e00},
1317  {1, 7.48133039e00},
1318  {1, 7.21957016e00},
1319  {1, 6.94726801e00},
1320  {1, 6.71931219e00},
1321  {1, 6.45107985e00},
1322  {1, 6.28593779e00},
1323  {0L, 0 }
1324  };
1325  for(_i=_r=0L; _i < 63; _i++)
1326  b2[_i] = RC_INI(_rs12); }
1327  { static struct{ long rc; double ini; } _rs13[] = {
1328  {1, -0.43},
1329  {1, -0.75},
1330  {1, -0.93},
1331  {1, -1.20},
1332  {1, -1.78},
1333  {1, -1.85},
1334  {1, -1.95},
1335  {1, -2.00},
1336  {1, -2.05},
1337  {1, -2.12},
1338  {1, -2.34},
1339  {1, -2.31},
1340  {1, -2.42},
1341  {1, -2.36},
1342  {1, -2.31},
1343  {1, -2.25},
1344  {1, -2.21},
1345  {1, -2.18},
1346  {1, -2.15},
1347  {1, -2.14},
1348  {1, -2.12},
1349  {1, -2.14},
1350  {1, -2.12},
1351  {1, -2.09},
1352  {1, -2.08},
1353  {1, -2.06},
1354  {1, -2.05},
1355  {1, -2.04},
1356  {1, -2.04},
1357  {1, -2.04},
1358  {1, -2.04},
1359  {1, -2.04},
1360  {1, -2.04},
1361  {1, -2.04},
1362  {1, -2.04},
1363  {1, -2.04},
1364  {1, -2.04},
1365  {1, -2.04},
1366  {1, -2.04},
1367  {1, -2.04},
1368  {1, -2.04},
1369  {1, -2.04},
1370  {1, -2.04},
1371  {1, -2.04},
1372  {1, -2.04},
1373  {1, -2.04},
1374  {1, -2.04},
1375  {1, -2.04},
1376  {1, -2.04},
1377  {1, -2.04},
1378  {1, -2.04},
1379  {1, -2.04},
1380  {1, -2.04},
1381  {1, -2.04},
1382  {1, -2.04},
1383  {1, -2.04},
1384  {1, -2.04},
1385  {1, -2.04},
1386  {1, -2.04},
1387  {1, -2.04},
1388  {1, -2.04},
1389  {1, -2.04},
1390  {1, -2.04},
1391  {0L, 0 }
1392  };
1393  for(_i=_r=0L; _i < 63; _i++)
1394  x2[_i] = RC_INI(_rs13); }
1395  /*lint +e736 loss of precision in assignment in translated data */
1396 
1397  DEBUG_ENTRY( "blkdata0()" );
1398 }
1399 
1400 /* =================================================================== */
1401 /*xmap mapping function for Cota's 3-body recombination */
1402 STATIC double xmap(double x[],
1403  double y[],
1404  double xmapx0)
1405 {
1406  double a,
1407  b,
1408  c,
1409  xmapx1,
1410  x12m,
1411  x13m,
1412  xmapx2,
1413  x3,
1414  xmap_v,
1415  yinit,
1416  y13m;
1417 
1418  DEBUG_ENTRY( "xmap()" );
1419 
1420  /* PARABOLIC INTERPOLATION.
1421  * */
1422 
1423  yinit = y[0];
1424  xmapx1 = x[0];
1425  xmapx2 = x[1];
1426  x3 = x[2];
1427  x13m = xmapx1 - x3;
1428  x12m = xmapx1 - xmapx2;
1429  y13m = yinit - y[2];
1430  x3 = (xmapx1 + x3)*x13m;
1431  xmapx2 = (xmapx1 + xmapx2)*x12m;
1432  b = ((yinit - y[1])*x3 - y13m*xmapx2)/(x12m*x3 - x13m*xmapx2);
1433  a = (y13m - x13m*b)/x3;
1434  c = yinit - a*xmapx1*xmapx1 - b*xmapx1;
1435 
1436  xmap_v = a*xmapx0*xmapx0 + b*xmapx0 + c;
1437 
1438  return( xmap_v );
1439 }
1440 
1441 /* =================================================================== */
1442 /*xinvrs do inverse function for Cota's three-body recombination */
1443 STATIC double xinvrs(double y,
1444  double a,
1445  double b,
1446  double u,
1447  double v,
1448  long int *ifail)
1449 {
1450  long int i;
1451  double bxu,
1452  dfx,
1453  fx,
1454  fxdfx,
1455  x,
1456  xinvrs_v,
1457  xlog,
1458  xx;
1459  static long itmax = 10;
1460 
1461  DEBUG_ENTRY( "xinvrs()" );
1462 
1463  /* inverts equation of the form :
1464  *
1465  * Y = A + B * X ** U - V * LOG ( X )
1466  * */
1467  *ifail = 0;
1468  xlog = (a - y)/v;
1469  x = pow(10.,xlog);
1470  xx = 0.;
1471 
1472  for( i=0; i < itmax; i++ )
1473  {
1474  bxu = b*pow(x,u);
1475  fx = y - a - bxu + v*xlog;
1476  dfx = v*.4342945 - bxu*u;
1477 
1478  if( dfx != 0. )
1479  {
1480  fxdfx = fabs(fx/dfx);
1481  fxdfx = MIN2(0.2,fxdfx);
1482  xx = x*(1. - sign(fxdfx,fx/dfx));
1483  }
1484  else
1485  {
1486  /* >>chng 96 feb 02 this added in case dfx ever 0
1487  * suggested by Peter van Hoof */
1488  xx = x*(1. - sign(0.2,fx));
1489  }
1490 
1491  if( (fabs(xx-x)/x) < 1.e-4 )
1492  {
1493  xinvrs_v = xx;
1494  return( xinvrs_v );
1495  }
1496  else
1497  {
1498  x = xx;
1499  if( x < 1e-30 )
1500  {
1501  xinvrs_v = 100.;
1502  *ifail = 1;
1503  return( xinvrs_v );
1504  }
1505  xlog = log10(x);
1506  }
1507  }
1508  xinvrs_v = xx;
1509  *ifail = 1;
1510  return( xinvrs_v );
1511 }
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