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EvtGen  2.0.0
Monte Carlo generator of particle decays, in particular the weak decays of heavy flavour particles such as B mesons.
EvtVubAC.cpp
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20 
21 #include "EvtGenModels/EvtVubAC.hh"
22 
23 #include "EvtGenBase/EvtGenKine.hh"
24 #include "EvtGenBase/EvtPDL.hh"
26 #include "EvtGenBase/EvtPatches.hh"
27 #include "EvtGenBase/EvtRandom.hh"
28 #include "EvtGenBase/EvtReport.hh"
30 
32 
33 #include <stdlib.h>
34 #include <string>
35 
36 using std::cout;
37 using std::endl;
38 
39 std::string EvtVubAC::getName()
40 {
41  return "VUB_AC";
42 }
43 
45 {
46  return new EvtVubAC;
47 }
48 
50 {
51  // get parameters (declared in the header file)
52 
53  // B Meson mass
54  mB = 5.2792;
55 
56  // Perturbative quantities
57  CF = 4.0 / 3.0;
58  CA = 3.0;
59  double nf = 3.0;
60 
61  //Constants
62  alphaSmZ = getArg( 0 );
63  c = 0.04;
64  q = 0.01;
65  k = 0.02;
66 
67  beta0 = ( 11.0 / 3.0 * CA - 2.0 / 3.0 * nf ) / ( 4 * M_PI );
68  alphaSmB = 0.22 * alphaSmZ / 0.1189;
69 
70  gvars.push_back( 0.0 ); // 0
71  gvars.push_back( 0.0 ); // 1
72  gvars.push_back( 0.0 ); // 2
73  gvars.push_back( alphaSmB ); // 3
74  gvars.push_back( alphaSmZ ); // 4
75  gvars.push_back( mB ); // 5
76  gvars.push_back( beta0 ); // 6
77  gvars.push_back( c ); // 7
78  gvars.push_back( q ); // 8
79  gvars.push_back( k ); // 9
80 
81  // check that there are 3 daughters and 1 argument
82  checkNDaug( 3 );
83  checkNArg( 1 );
84 }
85 
87 {
88  noProbMax();
89 }
90 
92 {
93  int j;
94 
95  EvtParticle *xuhad, *lepton, *neutrino;
96  EvtVector4R p4;
97  double u, w, xb, Pp, Pm, pdf, ml, PX( 0.0 ), EX( 0.0 ), sh( 0.0 ), El( 0.0 );
98 
99  Bmeson->initializePhaseSpace( getNDaug(), getDaugs() );
100 
101  xuhad = Bmeson->getDaug( 0 );
102  lepton = Bmeson->getDaug( 1 );
103  neutrino = Bmeson->getDaug( 2 );
104 
105  ml = lepton->mass();
106 
107  bool tryit = true;
108  while ( tryit ) {
109  double mpi = 0.14;
110  u = EvtRandom::Flat( 0.0, 1.0 );
111  w = EvtRandom::Flat( 0.0, 2.0 );
112  xb = EvtRandom::Flat( 0.0, 1.0 );
113 
114  EX = w * mB / 2.0;
115  PX = EX * ( 1.0 - u ) / ( u + 1.0 );
116  El = ( 1.0 - xb ) * mB / 2.0;
117  Pp = ( EX - PX );
118  Pm = ( EX + PX );
119  sh = Pm * Pp;
120 
121  if ( ( ( w * u ) / ( 1.0 + u ) < xb ) && ( xb < w / ( 1.0 + u ) ) &&
122  ( max( 0, w - 1.0 ) < u ) && ( sh > 4.0 * mpi * mpi ) &&
123  ( El > ml ) ) {
124  pdf = rate( u, w, xb );
125  double testRan = EvtRandom::Flat( 0.0, 24.2 );
126  if ( pdf >= testRan )
127  tryit = false;
128  }
129  }
130 
131  // o.k. we have the three kinemtic variables
132  // now calculate a flat cos Theta_H [-1,1] distribution of the
133  // hadron flight direction w.r.t the B flight direction
134  // because the B is a scalar and should decay isotropic.
135  // Then chose a flat Phi_H [0,2Pi] w.r.t the B flight direction
136  // and and a flat Phi_L [0,2Pi] in the W restframe w.r.t the
137  // W flight direction.
138 
139  double ctH = EvtRandom::Flat( -1, 1 );
140  double phH = EvtRandom::Flat( 0, 2 * M_PI );
141  double phL = EvtRandom::Flat( 0, 2 * M_PI );
142 
143  // now compute the four vectors in the B Meson restframe
144 
145  double ptmp, sttmp;
146  // calculate the hadron 4 vector in the B Meson restframe
147 
148  sttmp = sqrt( 1 - ctH * ctH );
149  ptmp = sqrt( EX * EX - sh );
150  double pHB[4] = {EX, ptmp * sttmp * cos( phH ), ptmp * sttmp * sin( phH ),
151  ptmp * ctH};
152  p4.set( pHB[0], pHB[1], pHB[2], pHB[3] );
153  xuhad->init( getDaug( 0 ), p4 );
154 
155  // calculate the W 4 vector in the B Meson restrframe
156 
157  double apWB = ptmp;
158  double pWB[4] = {mB - EX, -pHB[1], -pHB[2], -pHB[3]};
159 
160  // first go in the W restframe and calculate the lepton and
161  // the neutrino in the W frame
162 
163  double mW2 = mB * mB + sh - 2 * mB * EX;
164  double beta = ptmp / pWB[0];
165  double gamma = pWB[0] / sqrt( mW2 );
166 
167  double pLW[4];
168 
169  ptmp = ( mW2 - ml * ml ) / 2 / sqrt( mW2 );
170  pLW[0] = sqrt( ml * ml + ptmp * ptmp );
171 
172  double ctL = ( El - gamma * pLW[0] ) / beta / gamma / ptmp;
173  if ( ctL < -1 )
174  ctL = -1;
175  if ( ctL > 1 )
176  ctL = 1;
177  sttmp = sqrt( 1 - ctL * ctL );
178 
179  // eX' = eZ x eW
180  double xW[3] = {-pWB[2], pWB[1], 0};
181  // eZ' = eW
182  double zW[3] = {pWB[1] / apWB, pWB[2] / apWB, pWB[3] / apWB};
183 
184  double lx = sqrt( xW[0] * xW[0] + xW[1] * xW[1] );
185  for ( j = 0; j < 2; j++ )
186  xW[j] /= lx;
187 
188  // eY' = eZ' x eX'
189  double yW[3] = {-pWB[1] * pWB[3], -pWB[2] * pWB[3],
190  pWB[1] * pWB[1] + pWB[2] * pWB[2]};
191  double ly = sqrt( yW[0] * yW[0] + yW[1] * yW[1] + yW[2] * yW[2] );
192  for ( j = 0; j < 3; j++ )
193  yW[j] /= ly;
194 
195  // p_lep = |p_lep| * ( sin(Theta) * cos(Phi) * eX'
196  // + sin(Theta) * sin(Phi) * eY'
197  // + cos(Theta) * eZ')
198  for ( j = 0; j < 3; j++ )
199  pLW[j + 1] = sttmp * cos( phL ) * ptmp * xW[j] +
200  sttmp * sin( phL ) * ptmp * yW[j] + ctL * ptmp * zW[j];
201 
202  double apLW = ptmp;
203 
204  // boost them back in the B Meson restframe
205 
206  double appLB = beta * gamma * pLW[0] + gamma * ctL * apLW;
207 
208  ptmp = sqrt( El * El - ml * ml );
209  double ctLL = appLB / ptmp;
210 
211  if ( ctLL > 1 )
212  ctLL = 1;
213  if ( ctLL < -1 )
214  ctLL = -1;
215 
216  double pLB[4] = {El, 0, 0, 0};
217  double pNB[4] = {pWB[0] - El, 0, 0, 0};
218 
219  for ( j = 1; j < 4; j++ ) {
220  pLB[j] = pLW[j] + ( ctLL * ptmp - ctL * apLW ) / apWB * pWB[j];
221  pNB[j] = pWB[j] - pLB[j];
222  }
223 
224  p4.set( pLB[0], pLB[1], pLB[2], pLB[3] );
225  lepton->init( getDaug( 1 ), p4 );
226 
227  p4.set( pNB[0], pNB[1], pNB[2], pNB[3] );
228  neutrino->init( getDaug( 2 ), p4 );
229 
230  return;
231 }
232 
233 double EvtVubAC::rate( double u, double w, double xb )
234 {
235  std::vector<double> vars( 11 );
236  vars[0] = u;
237  vars[1] = w;
238  vars[2] = xb;
239  double dGam = Coeff( u, w, xb ) * Sigma( wreg( w / ( 1 + u ) ), ularge( u ) ) +
240  d( u, w, xb );
241 
242  return dGam;
243 }
244 
245 double EvtVubAC::PolyLog( double v, double z )
246 {
247  if ( z >= 1 )
248  cout << "Error in EvtVubAC: 2nd argument to PolyLog is >= 1." << endl;
249 
250  double sum = 0.0;
251  for ( int k = 1; k < 101; k++ ) {
252  sum = sum + pow( z, k ) / pow( k, v );
253  }
254  return sum;
255 }
256 
257 double EvtVubAC::max( double ub, double lb )
258 {
259  if ( ub > lb )
260  return ub;
261  else
262  return lb;
263 }
264 
265 double EvtVubAC::wreg( double w )
266 {
267  std::vector<double> vars( 11 );
268  vars[1] = w;
269  for ( int j = 3; j < 11; j++ ) {
270  vars[j] = gvars[j];
271  }
272  double K = ( 1 + c ) / ( 1 + c + pow( c, 2 ) );
273  return K * ( c + pow( w, 2 ) / ( w + c ) );
274 }
275 
276 double EvtVubAC::ureg( double u )
277 {
278  std::vector<double> vars( 11 );
279  vars[0] = u;
280  for ( int j = 3; j < 11; j++ ) {
281  vars[j] = gvars[j];
282  }
283  return q + u * u / ( u + q );
284 }
285 
286 double EvtVubAC::ularge( double u )
287 {
288  std::vector<double> vars( 11 );
289  vars[0] = u;
290  for ( int j = 3; j < 11; j++ ) {
291  vars[j] = gvars[j];
292  }
293  return u - k * u * u;
294 }
295 
296 double EvtVubAC::alphaS( double Q )
297 {
298  std::vector<double> vars( 11 );
299  for ( int j = 3; j < 11; j++ ) {
300  vars[j] = gvars[j];
301  }
302 
303  double a = 1.0 / ( log( Q * Q / FindRoot( alphaSmZ ) ) );
304  double b = FindRoot( alphaSmZ ) / ( FindRoot( alphaSmZ ) - Q * Q );
305  double ans = 1.0 / beta0 * ( a + b );
306 
307  return ans;
308 }
309 
310 double EvtVubAC::Coeff( double u, double w, double xb )
311 {
312  std::vector<double> vars( 11 );
313  vars[0] = u;
314  vars[1] = w;
315  vars[2] = xb;
316 
317  for ( int j = 3; j < 11; j++ ) {
318  vars[j] = gvars[j];
319  }
320 
321  double coeff = Coeff0( w, xb ) +
322  alphaS( mB * wreg( w / ( 1 + u ) ) ) * Coeff1( w, xb );
323  return coeff;
324 }
325 
326 double EvtVubAC::Coeff0( double w, double xb )
327 {
328  std::vector<double> vars( 11 );
329  vars[1] = w;
330  vars[2] = xb;
331  for ( int j = 3; j < 11; j++ ) {
332  vars[j] = gvars[j];
333  }
334  return 12.0 * ( 1 + xb - w ) * ( w - xb );
335 }
336 
337 double EvtVubAC::Coeff1( double w, double xb )
338 {
339  std::vector<double> vars( 11 );
340  vars[1] = w;
341  vars[2] = xb;
342  for ( int j = 3; j < 11; j++ ) {
343  vars[j] = gvars[j];
344  }
345  double a = 1 + xb - w;
346  double b = -PolyLog( 2, 1 - w ) - 3.0 / 2.0 * log( wreg( w ) ) -
347  1.0 / 2.0 * w * f( w ) - 35.0 / 8.0 + ( M_PI * M_PI ) / 6.0;
348  double c = 1.0 / 2.0 * xb * f( wreg( w ) );
349 
350  double ans = 12.0 * CF / M_PI * ( w - xb ) * ( ( a * b ) + c );
351 
352  return ans;
353 }
354 
355 double EvtVubAC::d( double u, double w, double xb )
356 {
357  std::vector<double> vars( 11 );
358  vars[0] = u;
359  vars[1] = w;
360  vars[2] = xb;
361  for ( int j = 3; j < 11; j++ ) {
362  vars[j] = gvars[j];
363  }
364 
365  return alphaS( mB * wreg( w / ( 1.0 + u ) ) ) * CF / M_PI * d1( u, w, xb );
366 }
367 
368 double EvtVubAC::d1( double u, double w, double xb )
369 {
370  std::vector<double> vars( 11 );
371  vars[0] = u;
372  vars[1] = w;
373  vars[2] = xb;
374  for ( int j = 3; j < 11; j++ ) {
375  vars[j] = gvars[j];
376  }
377 
378  double a = 3 * pow( w, 4 ) * ( 24 + 3 * w - 8 * xb ) /
379  ( 4 * pow( 1 + u, 5 ) );
380  double b = 9 * pow( w, 4 ) * ( 24 + 3 * w - 8 * xb ) /
381  ( 8 * pow( 1 + u, 4 ) );
382  double c = 9 * ( -12 + w ) * pow( -2 + w, 2 ) * pow( w - 2 * xb, 2 ) /
383  ( 16 * pow( 1 - u, 3 ) );
384  double cc = 9 * ( -12 + w ) * pow( -2 + w, 2 ) * pow( w - 2 * xb, 2 ) /
385  ( 32 * pow( 1 - u, 2 ) );
386  double d = 3 * pow( w, 2 ) *
387  ( 32 - 47 * w - 8 * w * w + 16 * xb + 20 * w * xb + w * w * xb +
388  8 * xb * xb - 3 * w * xb * xb ) /
389  ( 8 * pow( 1 + u, 2 ) );
390  double e = 1 / ( 8 * pow( 1 + u, 3 ) ) *
391  ( 3 * w * w *
392  ( -64 + 94 * w + 40 * w * w + 3 * pow( w, 3 ) - 32 * xb -
393  40 * xb * w - 10 * w * w * xb - 16 * xb * xb +
394  6 * w * xb * xb ) );
395  double f = 1 / ( 64 * ( 1 + u ) ) *
396  ( 3 * ( 640 * w - 368 * w * w - 200 * w * w * w -
397  16 * pow( w, 4 ) + 3 * pow( w, 5 ) - 384 * xb +
398  320 * w * xb + 528 * w * w * xb + 112 * pow( w, 3 ) * xb -
399  16 * pow( w, 4 ) * xb - 256 * xb * xb -
400  48 * w * xb * xb - 224 * pow( w, 2 ) * pow( xb, 2 ) +
401  24 * pow( w, 3 ) * pow( xb, 2 ) ) );
402  double g = 1 / ( 64 * ( 1 - u ) ) *
403  ( 3 * ( -256 * w + 528 * w * w - 200 * pow( w, 3 ) -
404  16 * pow( w, 4 ) + 3 * pow( w, 5 ) + 512 * xb -
405  1472 * w * xb + 528 * pow( w, 2 ) * xb +
406  112 * pow( w, 3 ) * xb - 16 * pow( w, 4 ) * xb +
407  640 * xb * xb - 48 * w * xb * xb -
408  224 * pow( w, 2 ) * pow( xb, 2 ) +
409  24 * pow( w, 3 ) * pow( xb, 2 ) ) );
410  double h = 9 * pow( w, 5 ) * log( ureg( u ) ) / ( 4 * pow( 1 + u, 6 ) );
411  double i = 9 * pow( w, 5 ) * log( ureg( u ) ) / ( 2 * pow( 1 + u, 5 ) );
412  double ii = 9 * ( -12 + w ) * pow( -2 + w, 2 ) * pow( w - 2 * xb, 2 ) *
413  log( ureg( u ) ) / ( 16 * pow( 1 - u, 4 ) );
414  double j = 9 * ( -12 + w ) * pow( -2 + w, 2 ) * pow( w - 2 * xb, 2 ) *
415  log( ureg( u ) ) / ( 16 * pow( 1 - u, 3 ) );
416  double k = ( 3 * pow( w, 3 ) *
417  ( -10 + 16 * w + pow( w, 2 ) + 8 * xb - 2 * w * xb -
418  2 * pow( xb, 2 ) ) *
419  log( ureg( u ) ) ) /
420  ( 8 * pow( 1 + u, 3 ) );
421  double l = ( 3 * pow( w, 3 ) *
422  ( -10 + 16 * w + 7 * pow( w, 2 ) + 8 * xb - 2 * w * xb -
423  2 * pow( xb, 2 ) ) *
424  log( ureg( u ) ) ) /
425  ( 8 * pow( 1 + u, 4 ) );
426  double m = 1 / ( 64 * pow( 1 + u, 2 ) ) *
427  ( 3 * w *
428  ( -144 * w + 208 * pow( w, 2 ) + 16 * pow( w, 3 ) +
429  pow( w, 4 ) - 64 * xb - 80 * w * xb - 16 * pow( w, 2 ) * xb -
430  8 * pow( w, 3 ) * xb + 48 * xb * xb - 96 * w * xb * xb +
431  16 * pow( w, 2 ) * pow( xb, 2 ) ) *
432  log( ureg( u ) ) );
433  double n = 1 / ( 64 * pow( 1 - u, 2 ) ) *
434  ( 3 *
435  ( -256 * w + 624 * pow( w, 2 ) - 304 * pow( w, 3 ) +
436  16 * pow( w, 4 ) + pow( w, 5 ) + 512 * xb - 1856 * w * xb +
437  944 * pow( w, 2 ) * xb - 16 * pow( w, 3 ) * xb -
438  8 * pow( w, 4 ) * xb + 1024 * xb * xb - 464 * w * xb * xb -
439  96 * pow( w, 2 ) * pow( xb, 2 ) +
440  16 * pow( w, 3 ) * pow( xb, 2 ) ) *
441  log( ureg( u ) ) );
442 
443  double rem = -a + b - c + cc - d - e + f + g - h + i - ii + j + k - l - m + n;
444 
445  return rem;
446 }
447 
448 double EvtVubAC::f( double w )
449 {
450  std::vector<double> vars( 11 );
451  vars[1] = w;
452  for ( int j = 3; j < 11; j++ ) {
453  vars[j] = gvars[j];
454  }
455  if ( w != 1 )
456  return log( w ) / ( 1 - w );
457  else
458  return -1;
459 }
460 
461 double EvtVubAC::Lambda2( double x, const double alphaSmZ )
462 {
463  std::vector<double> vars( 11 );
464  for ( int j = 3; j < 11; j++ ) {
465  vars[j] = gvars[j];
466  }
467  double alphaSmB = 0.22 * alphaSmZ / 0.1189;
468  double func = ( 1 / beta0 ) *
469  ( 1 / log( mB * mB / x ) + x / ( x - mB * mB ) ) -
470  alphaSmB;
471  return func;
472 }
473 
474 double EvtVubAC::FindRoot( const double alphaSmZ )
475 {
476  std::vector<double> vars( 11 );
477  for ( int j = 3; j < 11; j++ ) {
478  vars[j] = gvars[j];
479  }
480  double root;
481  const double precision = 1e-8;
482  Bisect( 0.0, 1.0, precision, root, alphaSmZ );
483  return root;
484 }
485 
486 int EvtVubAC::Bisect( double x1, double x2, double precision, double& root,
487  const double alphaSmZ )
488 {
489  std::vector<double> vars( 11 );
490 
491  for ( int j = 3; j < 11; j++ ) {
492  vars[j] = gvars[j];
493  }
494 
495  if ( Lambda2( x1, alphaSmZ ) * Lambda2( x2, alphaSmZ ) > 0 ) {
496  root = 0;
497  return 0;
498 
499  } else {
500  double x = 0.5 * ( x1 + x2 );
501 
502  if ( fabs( Lambda2( x, alphaSmZ ) ) < precision ) {
503  root = x;
504  return 1;
505  } else {
506  if ( Lambda2( x1, alphaSmZ ) * Lambda2( x, alphaSmZ ) < 0 ) {
507  return Bisect( x1, x, precision, root, alphaSmZ );
508 
509  } else {
510  return Bisect( x, x2, precision, root, alphaSmZ );
511  }
512  }
513  }
514 }
515 
516 //Bi-Linear interpolation function for sigma()
517 
518 double EvtVubAC::Sigma( double x1, double x2 )
519 {
520  double ans;
521  int j = 0;
522  int k = 0;
523  int JMAX = 20;
524  int KMAX = 6282;
525 
526  if ( ( x1 < 0.04 ) | ( x1 > 1.0 ) | ( x2 > 0.9981306360766614 ) ) {
527  cout << "Input variables are not in range" << endl;
528  return 0;
529  }
530 
531  else {
532  double sigma[6283][21] = {
533  {1.4165575231667025e-6, 2.367068423885654e-6, 3.010516455581869e-6,
534  3.5037825936986625e-6, 3.929518324374288e-6, 4.306057170491293e-6,
535  4.670305737607004e-6, 5.03601978363166e-6, 5.38081382734055e-6,
536  5.706111094422232e-6, 6.01592741932564e-6, 6.312683745642994e-6,
537  6.599149887344445e-6, 6.876589598409881e-6, 7.146140172115845e-6,
538  7.408228896739411e-6, 7.66381903520912e-6, 7.914216132923142e-6,
539  8.158375083092094e-6, 8.387923687779773e-6, 8.609047991600152e-6},
540  {1.4242950283096505e-6, 2.3821813865451333e-6,
541  3.0321094979724177e-6, 3.531463105585163e-6,
542  3.963281819193405e-6, 4.345928764350666e-6,
543  4.716578534159503e-6, 5.0891092458471885e-6,
544  5.440882358124266e-6, 5.773300334146699e-6,
545  6.090393611799158e-6, 6.394582544259559e-6,
546  6.6886559040585555e-6, 6.973876196346317e-6,
547  7.251379536127028e-6, 7.521582534359883e-6,
548  7.78545760383978e-6, 8.044322886507219e-6,
549  8.297093782815202e-6, 8.535252273580483e-6,
550  8.76506526572483e-6},
551  {1.432085473265309e-6, 2.397426211753438e-6, 3.053927960769999e-6,
552  3.559478172452427e-6, 3.997507657500483e-6, 4.386409405362107e-6,
553  4.763630567689123e-6, 5.143175144213434e-6, 5.5021483329791995e-6,
554  5.841932217571044e-6, 6.166572855026258e-6, 6.478490721190443e-6,
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1800  5.225014086978904, 6.0758682765262355, 6.722927882282562,
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1900  6.900537969841293, 6.6670194867703225, 6.385584651185518,
1901  6.076203680266441, 5.754955186790059, 5.4323401559950275,
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1910  {0.039253224644958354, 0.4216918566099683, 1.2962857064287256,
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1912  5.728775345215761, 6.381996974910275, 6.800018095268266,
1913  7.013878420293094, 7.061658590847507, 6.979017622040983,
1914  6.799576137454789, 6.5514200703503, 6.259130770132801,
1915  5.942409543233798, 5.61693892869674, 5.292520965825961,
1916  4.978786945105033, 4.677101163873526, 4.391888825287451},
1917  {0.04077987480934057, 0.43320972072788017, 1.3222341985260395,
1918  2.5142242890945563, 3.753967869232759, 4.863510253444616,
1919  5.752060279637619, 6.391788817504034, 6.795368848092567,
1920  6.995320933807391, 7.030513192666088, 6.9370020238831716,
1921  6.748588534247812, 6.493446763510754, 6.196053798008725,
1922  5.8759623808091, 5.548643376117382, 5.223542185310412,
1923  4.9100329837909715, 4.609246199213923, 4.325430994758629},
1924  {0.042349446031273226, 0.4448980078261362, 1.3483230348260442,
1925  2.5504224681235197, 3.7923060641979256, 4.896526691519418,
1926  5.7744087324550435, 6.400562333879243, 6.789732172580457,
1927  6.975890624362948, 6.998657708651327, 6.89447089854233,
1928  6.697299176025943, 6.435390945602655, 6.1331055905672045,
1929  5.8098385223316, 5.480839757803095, 5.15519425365674,
1930  4.842019466207997, 4.542217526801885, 4.259863792746115},
1931  {0.043962593737414984, 0.45675586403926893, 1.374546187584878,
1932  2.5865102666195665, 3.8302047105320725, 4.928808342782569,
1933  5.795827243334658, 6.408332034035241, 6.783129077963393,
1934  6.9556123132976255, 6.966118636439548, 6.851451188128601,
1935  6.645734169829962, 6.3772764886179685, 6.070306626699644,
1936  5.74405436403496, 5.413539648503557, 5.08748392733819,
1937  4.774748744275349, 4.476013497142189, 4.195182022836065},
1938  {0.045619969612673554, 0.46878237596551614, 1.4008976182997506,
1939  2.6224786409007375, 3.867656779610982, 4.960354164720785,
1940  5.816322670251149, 6.4151125773415405, 6.775580488905903,
1941  6.9345104834459015, 6.9329219848875, 6.807969226494273,
1942  6.593918898467005, 6.319126448055782, 6.007676524293082,
1943  5.67862543029024, 5.346753791149829, 5.020417225376567,
1944  4.708222543833211, 4.410631951538835, 4.131380097455584},
1945  {0.047322221323267064, 0.4809765716332258, 1.4273712813914883,
1946  2.6583187161302146, 3.9046555689347797, 4.991163490980296,
1947  5.835902173813256, 6.420918755815558, 6.767107229738198,
1948  6.912609273117812, 6.8990932765654716, 6.764050745359405,
1949  6.541878030635248, 6.260963078623769, 5.945234062836881,
1950  5.613566399177464, 5.280492128044891, 4.953999462169973,
1951  4.642441996761009, 4.346070252499544, 4.068452065912379},
1952  {0.049069992243398725, 0.4933374214913434, 1.453961127799496,
1953  2.694021788227673, 3.9411946979148182, 5.021236020488868,
1954  5.854573201948896, 6.425765478015377, 6.7577300094185695,
1955  6.889932471104576, 6.864657550609598, 6.719720880580658,
1956  6.489635531191951, 6.202807850001469, 5.882997205802685,
1957  5.548891127768376, 5.214763831372232, 4.888235279284942,
1958  4.57740767189552, 4.282325312864321, 4.006391641120212},
1959  {0.05086392118569389, 0.5058638394224481, 1.4806611084883983,
1960  2.7295793255700573, 3.977268103515626, 5.050571806654799,
1961  5.872343474951109, 6.429667753536115, 6.747469407242464,
1962  6.866503512636994, 6.829639365886358, 6.675004178550525,
1963  6.437214671553454, 6.144681462646525, 5.820983122733515,
1964  5.4846126771128745, 5.149577333007127, 4.823128676225444,
1965  4.513119604778914, 4.219393623698797, 3.9451922250581535},
1966  {0.05270464213554132, 0.5185546837768145, 1.5074651778657508,
1967  2.7649829704882594, 4.012870035763752, 5.079171246652693,
1968  5.889220970885719, 6.432640678097981, 6.736345859315083,
1969  6.842345476223345, 6.794062804427463, 6.629924602715763,
1970  6.384638040215857, 6.086603863625555, 5.75920821098723,
1971  5.420743336919725, 5.084940353618001, 4.75868304019308,
1972  4.449577326267232, 4.157271280992391, 3.8848469330104725},
1973  {0.05459278398947413, 0.5314087584260283, 1.534367297110375,
1974  2.8002245405661967, 4.047995053134942, 5.107035070805235,
1975  5.905213911361108, 6.434699419213606, 6.7243796458033955,
1976  6.817481081295079, 6.75795147509841, 6.584505540205469,
1977  6.33192755338529, 6.028594262451968, 5.6976881170906655,
1978  5.35729464992062, 5.020859931047979, 4.6949011748543805,
1979  4.386779890030246, 4.095954011200663, 3.825348616632993},
1980  {0.05652897029771912, 0.5444248138346939, 1.561361437410992,
1981  2.8352960297487226, 4.08263801783062, 5.134164332069422,
1982  5.920330747659726, 6.435859202421109, 6.711590878980682,
1983  6.791932686590659, 6.721328517468195, 6.5387698085603425,
1984  6.279104465706789, 5.97067114691349, 5.63643775767209,
1985  5.294277435905313, 4.95734244796933, 4.631785328132372,
1986  4.324725898973767, 4.0354371956705135, 3.766689885890514},
1987  {0.05851381901103543, 0.5576015481488104, 1.5884415831149612,
1988  2.870189609264795, 4.116794090954187, 5.160560395635053,
1989  5.934580147230489, 6.436135298067739, 6.697999492073319,
1990  6.765722289210488, 6.684216605851956, 6.492739662555623,
1991  6.226189381080847, 5.912852298872875, 5.575471339950696,
1992  5.2317018154146675, 4.894393658805963, 4.569337219040835,
1993  4.263413530615524, 3.9757158939860413, 3.7088631299088175},
1994  {0.060547942231959084, 0.5709376082994315, 1.6156017347870597,
1995  2.9048976283722863, 4.150458727597306, 5.186224928642731,
1996  5.947970980540662, 6.435543008626884, 6.68362522891523,
1997  6.738871524278971, 6.6466379535018865, 6.44643680111113,
1998  6.173202263556863, 5.855154810025841, 5.514802381772059,
1999  5.169577233077891, 4.832018715921563, 4.5075580635804915,
2000  4.202840561445689, 3.9167848662722182, 3.6518605367836363},
2001  {0.06263194597056108, 0.5844315911202399, 1.64283591217836,
2002  2.9394126149307533, 4.1836276718458665, 5.211159890027962,
2003  5.960512308285344, 6.434097656528524, 6.668487634410721,
2004  6.71140166515303, 6.608614316925095, 6.399882374282311,
2005  6.120162448292796, 5.79759509760098, 5.454443731187338,
2006  5.107912480579994, 4.770222195073085, 4.446448599717246,
2007  4.14300439030289, 3.858638594492589, 3.595674112387761},
2008  {0.06476642990482158, 0.5980820444777124, 1.6701381571053409,
2009  2.973727275808426, 4.216296951714913, 5.235367520497384,
2010  5.972213368952196, 6.431814572480693, 6.652606045801417,
2011  6.683333624119918, 6.570167000310007, 6.3530969903267245,
2012  6.067088652570363, 5.740188919986926, 5.3944075855812805,
2013  5.046715719245568, 4.709008120131308, 4.386009111463106,
2014  4.08390206079622, 3.8012713027764966, 3.540295698216319},
2015  {0.06695198714571599, 0.611887468412579, 1.697502536239513,
2016  3.007834497129609, 4.248462874021444, 5.258850332642619,
2017  5.983083566738642, 6.428709084257314, 6.635999584728111,
2018  6.6546879535308845, 6.531316860045587, 6.306100722840804,
2019  6.013998986855336, 5.682951392272927, 5.334705510359913,
2020  4.9859945022253855, 4.6483799870721665, 4.3262394520809035,
2021  4.025530282803402, 3.744676976810417, 3.4857169883091315},
2022  {0.06918920400710293, 0.6258463162913142, 1.7249231438079267,
2023  3.041727344368626, 4.280122019203648, 5.281611101196769,
2024  5.993132459818464, 6.424796505926529, 6.618687150073537,
2025  6.6254848473210615, 6.492084309319945, 6.258913117961971,
2026  5.960910965892599, 5.625897001689877, 5.275348457212951,
2027  4.925755796273053, 4.588340787244133, 4.267139066434238,
2028  3.967885453074765, 3.688849382327259, 3.431929545287855},
2029  {0.07147865978049701, 0.6399569959664279, 1.75239410420499,
2030  3.0753990622963174, 4.31127123609463, 5.303652853437991,
2031  6.00236974895422, 6.4200921274932465, 6.600687411567497,
2032  6.595744142869482, 6.452489322786872, 6.211553201631308,
2033  5.907841519825706, 5.569039622940798, 5.216346781968632,
2034  4.866006003099554, 4.528893029918499, 4.2087070125041794,
2035  3.9109636749721366, 3.6337820827265253, 3.3789248155444764},
2036  {0.07382092651480383, 0.6542178709443647, 1.77990957451617,
2037  3.108843074785062, 4.341907636658476, 5.324978859744205,
2038  6.010805266451732, 6.414611204930757, 6.5820188041317635,
2039  6.565485323157125, 6.412551441290742, 6.164039486912266,
2040  5.854807005330969, 5.512392533413519, 5.157710262060147,
2041  4.806750980294896, 4.470038764130777, 4.150941982094501,
2042  3.8547607773712667, 3.579468455857517, 3.3266941436166144},
2043  {0.07621656880108911, 0.6686272615598414, 1.8074637469541854,
2044  3.1420529844781697, 4.372028590696003, 5.3455926243025,
2045  6.018448965452553, 6.408368950578277, 6.562699522938508,
2046  6.534727519184274, 6.372289776641609, 6.116389981360781,
2047  5.8018232167561905, 5.4559684282737475, 5.099448113623171,
2048  4.747996061806887, 4.411779599822664, 4.0938423207471315,
2049  3.7992723327556845, 3.5259017099968566, 3.275228785783917},
2050  {0.07866614356244701, 0.6831834461555035, 1.835050851208396,
2051  3.1750225723293806, 4.401631720527301, 5.36549787597638,
2052  6.025310909560001, 6.401380523884519, 6.542747519152913,
2053  6.503489512612065, 6.331723016433746, 6.0686221944423435,
2054  5.748905397254423, 5.39977943544289, 5.04156900824342,
2055  4.689746077968565, 4.354116728295001, 4.037406046889575,
2056  3.7444936745293553, 3.4730748990507903, 3.224519922918739},
2057  {0.08117019984902749, 0.6978846622657947, 1.8626651567081633,
2058  3.2077457970181538, 4.430714895657728, 5.384698559333623,
2059  6.031401262794204, 6.393661022481091, 6.522180496328084,
2060  6.471789738596458, 6.290869428901917, 6.020753144991493,
2061  5.696068249903351, 5.343837130469415, 4.98408108937196,
2062  4.632005375066987, 4.2970509419831675, 3.981630870236072,
2063  3.690419913574813, 3.420980937011917, 3.1745586726231894},
2064  {0.08372927863827745, 0.7127291078039861, 1.8903009748010358,
2065  3.2402167942462667, 4.459276227433797, 5.403198825837098,
2066  6.036730279871356, 6.3852254735739455, 6.501015907418445,
2067  6.439646288786031, 6.2497468678107255, 5.972799368709243,
2068  5.643325948801126, 5.2881525513038055, 4.926991988424419,
2069  4.574777834447458, 4.2405826535670705, 3.9265142094641083,
2070  3.637045954082821, 3.369612611699173, 3.1253361006835547},
2071  {0.08634391264044353, 0.7277149422513318, 1.9179526608466424,
2072  3.272429875921174, 4.487314063694965, 5.421003025200567,
2073  6.041308296802111, 6.37608882564528, 6.479270952376199,
2074  6.407076914457952, 6.208372777372985, 5.924776925693847,
2075  5.590692150129773, 5.232736212984186, 4.870308840578141,
2076  4.518066891148632, 4.18471191442856, 3.8720532091878397,
2077  3.584366508678952, 3.3189625978090516, 3.076843231871998},
2078  {0.08901462610938064, 0.7428402878473563, 1.945614616227284,
2079  3.3043795292314355, 4.514826983427118, 5.438115696911135,
2080  6.045145721804062, 6.366265940462617, 6.456962576294651,
2081  6.374099029769386, 6.166764197193968, 5.87670140800039,
2082  5.538180003177536, 5.177598122233386, 4.8140383002794005,
2083  4.461875552065208, 4.129438432469703, 3.8182447562498685,
2084  3.532376112871844, 3.2690234693052616, 3.0290710601244544},
2085  {0.09174193465870402, 0.7581032307803157, 1.973281290276223,
2086  3.3360604156194453, 4.541813791423164, 5.454541561919714,
2087  6.048253026522858, 6.355771585395449, 6.434107468061605,
2088  6.340729715104119, 6.124937767238649, 5.82858794722451,
2089  5.485802161311833, 5.122747791959566, 4.75818655647058,
2090  4.406206413636228, 4.074761589305743, 3.7650854953525297,
2091  3.481069138847232, 3.219787711173219, 2.9820105581225427},
2092  {0.09452634508331753, 0.7735018223768984, 2.0009471821247455,
2093  3.3674673696565174, 4.5682735129559, 5.470285514500519,
2094  6.050640737556642, 6.344620426043088, 6.410722059486019,
2095  6.306985720496625, 6.082909732819696, 5.780451222105673,
2096  5.433570792894819, 5.0681942556435216, 4.702759347545167,
2097  4.351061679058249, 4.02068045684693, 3.712571844049676,
2098  3.4304398086312373, 3.1712477305649416, 2.9356526863063537},
2099  {0.09736835518634665, 0.7890340802902706, 2.028606842469114,
2100  3.3985953978253334, 4.594205388468027, 5.485352614280378,
2101  6.052319428278129, 6.332827019179821, 6.386822524861423,
2102  6.27288346911806, 6.040695949604174, 5.732305466145254,
2103  5.381497592133825, 5.013946081587824, 4.64776197603661,
2104  4.296443175023767, 3.9671938132837243, 3.660700007119589,
2105  3.380482206645738, 3.123395867359166, 2.8899884013439783},
2106  {0.10026845361149887, 0.8046979896856085, 2.0562548752585674,
2107  3.4294396772145843, 4.61960886828391, 5.499748078438363,
2108  6.053299710948794, 6.320405806025268, 6.362424780930351,
2109  6.238439060810614, 5.998311888637243, 5.684164475234771,
2110  5.32959378985931, 4.960011386996928, 4.593199323045262,
2111  4.24235236798641, 3.9143001584900547, 3.6094659903393587,
2112  3.331190291678077, 3.0762244041607163, 2.8450086640826715},
2113  {0.10322711968086967, 0.8204915044222755, 2.083885939305551,
2114  3.4599955541305354, 4.644483607347368, 5.51347727407592,
2115  6.053592229119332, 6.307371105848769, 6.337544487214818,
2116  6.203668275658592, 5.955772641381262, 5.63604161528951,
2117  5.2778701642232555, 4.906397851854106, 4.539075862406158,
2118  4.188790379955402, 3.861997728859381, 3.5588656136805987,
2119  3.282557908286678, 3.029725575762362, 2.8007044470056215},
2120  {0.10624482323820844, 0.8364125482318537, 2.111494749819436,
2121  3.490258542630142, 4.668829459989649, 5.526545710757597,
2122  6.053207650310687, 6.293737109917064, 6.312197046679244,
2123  6.1685865775861695, 5.913092924768929, 5.587949829882882,
2124  5.226337051311307, 4.853112732560479, 4.485395674599112,
2125  4.135758003822767, 3.810284511588488, 3.508894523946063,
2126  3.2345787976636036, 2.9838915780916904, 2.757066741217388},
2127  {0.10932202449765273, 0.8524590158912543, 2.139076079864953,
2128  3.5202243229801695, 4.692646474731342, 5.538959033222043,
2129  6.052156658969761, 6.279517875794057, 6.286397606693472,
2130  6.133209117973328, 5.870287086269055, 5.539901647876762,
2131  5.175004355662264, 4.800162875303066, 4.432162460401533,
2132  4.083255718227581, 3.759158258423849, 3.4595482068661827,
2133  3.18724660797444, 2.938714576664748, 2.714086562980149},
2134  {0.1124591738979366, 0.8686287743901758, 2.1666247617466734,
2135  3.5498887400467196, 4.7159348891218515, 5.550723014262958,
2136  6.050449949693943, 6.26472732200066, 6.260161060265141,
2137  6.097550739282788, 5.82736910896375, 5.4919091910431685,
2138  5.123881560688925, 4.747554729122626, 4.379379554283478,
2139  4.031283701962358, 3.708616498885406, 3.4108219986741384,
2140  3.1405549041953367, 2.894186714567466, 2.6717549598221084},
2141  {0.11565671196207221, 0.884919664092193, 2.194135688320806,
2142  3.5792478016193527, 4.738695124619751, 5.561843547779255,
2143  6.048098220718518, 6.249379223041294, 6.233502047512186,
2144  6.0616259786919215, 5.784352616635645, 5.443984181672592,
2145  5.072977738994525, 4.695294358657028, 4.327049937543897,
2146  3.9798418479273376, 3.6586565529824555, 3.3627110971775664,
2147  3.0944971774663905, 2.8503001199851803, 2.6300630162384597},
2148  {0.11891506916250343, 0.9013294998888128, 2.2216038142357024,
2149  3.608297676673992, 4.76092778151724, 5.572326641993759,
2150  6.0451121676610935, 6.233487204802026, 6.20643495734819,
2151  6.025449071724742, 5.741250878863972, 5.396137950164487,
2152  5.0223015625795195, 4.643387456541809, 4.27517625118653,
2153  3.928929776639147, 3.6092755434362838, 3.3152105723445904,
2154  3.0490668539801056, 2.8070469132998728, 2.589001859004644},
2155  {0.12223466579172167, 0.9178560723458382, 2.2490241571023795,
2156  3.6370346935785385, 4.7826336339115105, 5.582178412839358,
2157  6.041502477516915, 6.217064740323239, 6.178973929354797,
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3715  3.5468112078894336, 2.843869240599594, 2.1641508323701895,
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3722  3.532380725778225, 2.8271209454717954, 2.147477711307109,
3723  1.5815520311889448, 1.148515251798417, 0.8282265183993175,
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3729  3.517942755923944, 2.810413766734847, 2.1308827329162505,
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3736  3.5034982080399586, 2.7937481806777376, 2.1143659761220355,
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3744  2.777124653715712, 2.09792751059981,
3745  1.5369056396609948, 1.110222384375051,
3746  0.7961057928030011, 0.5676896738027304,
3747  0.40422231781708784, 0.28610876493641263,
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3756  1.5222163094950127, 1.0976565893495114,
3757  0.7855862375192154, 0.5589395476908525,
3758  0.39698153508847306, 0.27999975688258744,
3759  0.19120886851007654, 0.12300494808470566,
3760  0.0701850460766525, 0.029112500137097937,
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3765  3.4601339901842247, 2.7440055941282697, 2.0652856867779934,
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3778  {2.1831318574600918, 3.9590440018298776, 4.015031759799817,
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3793  3.402275769924349, 2.6782916395633865, 2.0009436102840654,
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3799  {2.2162697307367227, 3.965614983340294, 3.9885536877423555,
3800  3.387809732205138, 2.6619747825291706, 1.9850543905933378,
3801  1.4360792018356232, 1.0243020168470562, 0.7243833744417006,
3802  0.5081650851180088, 0.35504715638136686, 0.24464775539072356,
3803  0.1610220011593722, 0.09699596117691166, 0.04758743939487511,
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3805  -0.06653339781761874, -0.08434858854058397, -0.09864577417421144},
3806  {2.2272657255597004, 3.9675976712115397, 3.9796010904797106,
3807  3.3733447008424116, 2.645703375173945, 1.9692437053324476,
3808  1.422052652890411, 1.0124104396873939, 0.7144950519931503,
3809  0.4999834864387081, 0.34830275430928564, 0.23896646727512005,
3810  0.1561749142144998, 0.09282287315569498, 0.043963884914745004,
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3812  -0.06889210479922894, -0.0864830995838494, -0.10056867495426378},
3813  {2.238236018238643, 3.9694773735450712, 3.970586892347149,
3814  3.358881452806888, 2.629477800472527, 1.9535115478925167,
3815  1.4081192601297832, 1.0006126784483538, 0.7046939643400014,
3816  0.49188018663120453, 0.34162628569324566, 0.23334363036944528,
3817  0.15137884254420061, 0.08869458062898472, 0.040379830340900674,
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3819  -0.0712255441360671, -0.08859324468263288, -0.10246889392364932},
3820  {2.2491801820847357, 3.97125459580969,
3821  3.9615120939168658, 3.34442075221015,
3822  2.6132984326906032, 1.9378579039336132,
3823  1.3942786311793274, 0.988908110972709,
3824  0.6949793891848107, 0.4838544749959396,
3825  0.3350170292948691, 0.22777860462943222,
3826  0.14663321238603388, 0.08461056721564109,
3827  0.03683481129511424, -0.0001184389241269991,
3828  -0.028968586226948125, -0.052847674551829545,
3829  -0.07353394232886096, -0.09067928029294096,
3830  -0.10434669960483549},
3831  {2.260097794232453, 3.9729298466646705,
3832  3.9523776884955923, 3.3299633503939665,
3833  2.597165637489898, 1.9222827515281342,
3834  1.3805303704567515, 0.9772961163315106,
3835  0.6853506086323786, 0.47590564687242276,
3836  0.32847427149898134, 0.2222707574194415,
3837  0.1419374568998057, 0.08057032299641476,
3838  0.033328369393311345, -0.003189754391162458,
3839  -0.031691809264306495, -0.05534200356208578,
3840  -0.07581752433427932, -0.09274146120654711,
3841  -0.10620235782751475},
3842  {2.270988435647397, 3.9745036378585836,
3843  3.94318466211742, 3.315509986023383,
3844  2.5810797720316443, 1.9067860613026766,
3845  1.3668740793046037, 0.9657760749004533,
3846  0.6758069092091288, 0.46803300350798416,
3847  0.3219973062570495, 0.21681946342869887,
3848  0.1372910160820166, 0.07657334442925719,
3849  0.029860052163105104, -0.006227288542632083,
3850  -0.034386219126404584, -0.05781141238269601,
3851  -0.07807651366090321, -0.0947800405364525,
3852  -0.10803613172609772},
3853  {2.2818516911335025, 3.975976484129323, 3.933933993538006,
3854  3.3010613851834822, 2.5650411850783397, 1.8913677965783724,
3855  1.3533093561203715, 0.9543473684339058, 0.6663475818808814,
3856  0.4602358519299789, 0.31558543502978814, 0.21142410458822095,
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4009  3.7280106348303605, 2.9998993106559024,
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4021  2.2247596541962666, 1.5718497565793812,
4022  1.077209870339872, 0.7247939206196266,
4023  0.4782103406646192, 0.3064615372753437,
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4060  1.0201462442834095, 0.6780862940439335, 0.44037099846485345,
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4065  {2.573340073032941, 3.9783976543650543, 3.6552575234543867,
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4073  2.8869629560474914, 2.121776269231244, 1.4779569172814624,
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4081  0.9868665548620473, 0.650964061298635, 0.41846833704811953,
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4086  {2.6029431548198323, 3.9744829943201503, 3.623575870252233,
4087  2.8589334646184796, 2.092838837292584, 1.4518043460397256,
4088  0.9759304274666948, 0.6420703782743222, 0.41129747062137917,
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4315  {2.8872015129420734, 3.892842127880991, 3.283730715782515,
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4322  {2.8956703847304763, 3.889062990030208, 3.2725102949464193,
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4466  {3.0551738950525764, 3.800452338162716, 3.0467681541269296,
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4507  -0.20457284018029612, -0.20721927777569524, -0.20859080406414104},
4508  {3.099260999628191, 3.769404687041558,
4509  2.9788867295753376, 2.09402268308299,
4510  1.3502662668777548, 0.8144746973329057,
4511  0.4607534565181698, 0.2341378217744183,
4512  0.08866326879251771, -0.0025416630221352515,
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4517  -0.20538590798026546, -0.20793545752326859,
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4526  {3.11356208871936, 3.758636534157666, 2.9562762332613484,
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4533  {3.1206382258213337, 3.753176197774397, 2.9449759248775136,
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4535  0.4396922936980317, 0.21794151731919334, 0.07612368817004692,
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4540  {3.1276646439304683, 3.7476656938277526, 2.9336794323654627,
4541  2.0452543059599857, 1.3059139339861128, 0.7784362046603172,
4542  0.43277780208341443, 0.21263290767588028, 0.07201852843142183,
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4547  {3.1346412611114083, 3.742105524211426, 2.9223871417625773,
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4553  -0.20931272468632472, -0.2113938749092126, -0.21231560565884863},
4554  {3.141567998275769, 3.7364961888748773, 2.9110994343658776,
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4722  {3.2926881157003174, 3.5883867060814203, 2.6424811201051397,
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4729  {3.298350078948171, 3.5817047277562137, 2.6314187806637137,
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4736  {3.303961041522798, 3.5749858545553113, 2.620369390867936,
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4743  {3.309520993845907, 3.5682305290770535, 2.609333217373698,
4744  1.7088872629191578, 1.0096196087591816, 0.5435226364210625,
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4750  {3.3150299286399765, 3.5614391916701384, 2.598310523068831,
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4752  0.24810980091978696, 0.07250485227593279, -0.03537651429427718,
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4754  -0.1861451514164747, -0.19914714432795094, -0.20997351086342345,
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4757  {3.3204878409088154, 3.5546122804281404, 2.5873015671058863,
4758  1.6868263298918278, 0.9907728656459424, 0.5289257267522739,
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4764  {3.325894727918111, 3.5477502311843145, 2.5763066049347074,
4765  1.6758515475838973, 0.9814239131819803, 0.5217003597242187,
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4771  {3.331250589176019, 3.5408534775067197, 2.5653258883348333,
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5419  {3.6116349771828897, 2.808764940259659, 1.639610409935627,
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5552  {3.6205933508162724, 2.646027406863743, 1.4730947726450918,
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5615  {3.6195910540100282, 2.5688538982958207, 1.3973128137046724,
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5621  -0.26217433951653774, -0.25761292440478323, -0.2532604557048784},
5622  {3.6192784130276032, 2.5602852951662953, 1.389014479347425,
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5629  {3.618926052363648, 2.5517186280348776, 1.3807404316795389,
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5636  {3.6185341191757754, 2.5431540801530836, 1.3724906441920433,
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5860  {3.585994717075427, 2.2712222460372553, 1.1211233056049794,
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44849  {-24.81663261691574, -28.25699765110039, -28.05050407772069,
44850  -27.219065528566716, -26.387840182724176, -25.602369372965768,
44851  -25.026117854227778, -24.607201372040436, -24.192095354024787,
44852  -23.814748412463814, -23.468907394679263, -23.131494365865365,
44853  -22.816469694429543, -22.526449625904206, -22.257762749912217,
44854  -22.007946082449052, -21.774487921444234, -21.555453195178416,
44855  -21.349664952256717, -21.128836586896796, -20.908550107094925},
44856  {-24.88672988206963, -28.336404305009637, -28.129166676750174,
44857  -27.294910618278664, -26.46107214744552, -25.673153977957554,
44858  -25.09535050415434, -24.67483894585166, -24.258425071486272,
44859  -23.880216964054853, -23.53322395379655, -23.194702105713077,
44860  -22.878729653835762, -22.587862102489453, -22.31838402309222,
44861  -22.06783805345185, -21.833690583822317, -21.614017086976673,
44862  -21.407634040690027, -21.1861402001814, -20.965219124918804},
44863  {-24.95702726318268, -28.41603374108672, -28.208046173589537,
44864  -27.370962059532758, -26.53450110432459, -25.74412687594304,
44865  -25.16476929106284, -24.74265667324653, -24.324929237249307,
44866  -23.945858225924894, -23.597706217726227, -23.258072621247265,
44867  -22.94115044485079, -22.649432538542897, -22.379161227901932,
44868  -22.12788341025589, -21.893044561729766, -21.672730688005686,
44869  -21.465751135896426, -21.24358945764834, -21.022028209641576}};
44870 
44871  double wreg[] = {0.04,
44872  0.088,
44873  0.136,
44874  0.18400000000000002,
44875  0.232,
44876  0.27999999999999997,
44877  0.328,
44878  0.376,
44879  0.424,
44880  0.472,
44881  0.52,
44882  0.5680000000000001,
44883  0.6160000000000001,
44884  0.664,
44885  0.7120000000000001,
44886  0.76,
44887  0.808,
44888  0.8560000000000001,
44889  0.904,
44890  0.9520000000000001,
44891  1.0};
44892 
44893  double ularge[] = {0.,
44894  0.000999525142261537,
44895  0.0019980512340131984,
44896  0.002995579273830762,
44897  0.0039921102592925806,
44898  0.00498764518697925,
44899  0.00598218505247583,
44900  0.006975730850371842,
44901  0.007968283574262824,
44902  0.008959844216751223,
44903  0.009950413769447386,
44904  0.010939993222970568,
44905  0.011928583566949591,
44906  0.012916185790024404,
44907  0.013902800879846744,
44908  0.014888429823081029,
44909  0.015873073605405685,
44910  0.016856733211513708,
44911  0.01783940962511399,
44912  0.018821103828932206,
44913  0.019801816804711603,
44914  0.020781549533214427,
44915  0.02176030299422238,
44916  0.022738078166538056,
44917  0.0237148760279855,
44918  0.024690697555411423,
44919  0.025665543724686435,
44920  0.026639415510705367,
44921  0.02761231388738883,
44922  0.028584239827683988,
44923  0.029555194303565346,
44924  0.03052517828603607,
44925  0.03149419274512877,
44926  0.03246223864990638,
44927  0.033429316968463296,
44928  0.03439542866792622,
44929  0.035360574714455306,
44930  0.036324756073245035,
44931  0.03728797370852488,
44932  0.03825022858356075,
44933  0.03921152166065589,
44934  0.0401718539011513,
44935  0.04113122626542742,
44936  0.04208963971290469,
44937  0.043047095202044416,
44938  0.04400359369035023,
44939  0.044959136134368416,
44940  0.04591372348968936,
44941  0.046867356710948216,
44942  0.04782003675182578,
44943  0.04877176456505006,
44944  0.04972254110239649,
44945  0.05067236731468905,
44946  0.05162124415180169,
44947  0.052569172562658695,
44948  0.053516153495236085,
44949  0.05446218789656199,
44950  0.05540727671271839,
44951  0.056351420888841375,
44952  0.057294621369122334,
44953  0.05823687909680919,
44954  0.059178195014206625,
44955  0.060118570062677845,
44956  0.061058005182645037,
44957  0.061996501313590135,
44958  0.06293405939405661,
44959  0.06387068036164922,
44960  0.06480636515303595,
44961  0.0657411147039485,
44962  0.06667492994918323,
44963  0.067607811822602,
44964  0.06853976125713368,
44965  0.06947077918477418,
44966  0.07040086653658806,
44967  0.07133002424270929,
44968  0.07225825323234214,
44969  0.07318555443376207,
44970  0.07411192877431683,
44971  0.07503737718042691,
44972  0.07596190057758734,
44973  0.07688549989036764,
44974  0.07780817604241341,
44975  0.07872992995644712,
44976  0.07965076255426873,
44977  0.08057067475675705,
44978  0.08148966748387021,
44979  0.08240774165464715,
44980  0.0833248981872079,
44981  0.08424113799875499,
44982  0.08515646200557414,
44983  0.08607087112303513,
44984  0.0869843662655928,
44985  0.0878969483467883,
44986  0.08880861827924913,
44987  0.08971937697469112,
44988  0.09062922534391848,
44989  0.09153816429682515,
44990  0.09244619474239557,
44991  0.09335331758870569,
44992  0.09425953374292384,
44993  0.09516484411131154,
44994  0.09606924959922447,
44995  0.09697275111111336,
44996  0.09787534955052513,
44997  0.09877704582010327,
44998  0.09967784082158937,
44999  0.10057773545582349,
45000  0.1014767306227452,
45001  0.10237482722139479,
45002  0.10327202614991393,
45003  0.10416832830554645,
45004  0.10506373458463925,
45005  0.10595824588264358,
45006  0.10685186309411554,
45007  0.10774458711271706,
45008  0.10863641883121689,
45009  0.10952735914149136,
45010  0.11041740893452556,
45011  0.1113065691004137,
45012  0.11219484052836048,
45013  0.113082224106682,
45014  0.11396872072280606,
45015  0.11485433126327382,
45016  0.11573905661374018,
45017  0.1166228976589746,
45018  0.11750585528286273,
45019  0.11838793036840611,
45020  0.11926912379772414,
45021  0.12014943645205434,
45022  0.1210288692117536,
45023  0.12190742295629853,
45024  0.12278509856428699,
45025  0.12366189691343843,
45026  0.12453781888059534,
45027  0.12541286534172336,
45028  0.1262870371719128,
45029  0.12716033524537929,
45030  0.12803276043546474,
45031  0.12890431361463794,
45032  0.12977499565449568,
45033  0.1306448074257638,
45034  0.13151374979829733,
45035  0.13238182364108242,
45036  0.1332490298222363,
45037  0.13411536920900857,
45038  0.1349808426677821,
45039  0.13584545106407353,
45040  0.13670919526253478,
45041  0.1375720761269531,
45042  0.13843409452025268,
45043  0.13929525130449505,
45044  0.1401555473408801,
45045  0.14101498348974706,
45046  0.141873560610575,
45047  0.14273127956198417,
45048  0.14358814120173635,
45049  0.1444441463867362,
45050  0.1452992959730317,
45051  0.14615359081581536,
45052  0.14700703176942476,
45053  0.1478596196873435,
45054  0.14871135542220237,
45055  0.14956223982577965,
45056  0.15041227374900246,
45057  0.15126145804194713,
45058  0.1521097935538407,
45059  0.15295728113306095,
45060  0.15380392162713807,
45061  0.1546497158827549,
45062  0.15549466474574802,
45063  0.15633876906110877,
45064  0.15718202967298356,
45065  0.15802444742467525,
45066  0.15886602315864384,
45067  0.15970675771650733,
45068  0.16054665193904216,
45069  0.16138570666618468,
45070  0.1622239227370318,
45071  0.1630613009898414,
45072  0.16389784226203374,
45073  0.16473354739019208,
45074  0.1655684172100632,
45075  0.16640245255655883,
45076  0.1672356542637562,
45077  0.16806802316489855,
45078  0.1688995600923966,
45079  0.1697302658778289,
45080  0.17056014135194286,
45081  0.17138918734465547,
45082  0.1722174046850543,
45083  0.17304479420139818,
45084  0.17387135672111798,
45085  0.1746970930708177,
45086  0.17552200407627494,
45087  0.1763460905624421,
45088  0.17716935335344708,
45089  0.17799179327259362,
45090  0.17881341114236304,
45091  0.1796342077844143,
45092  0.18045418401958513,
45093  0.1812733406678928,
45094  0.18209167854853503,
45095  0.18290919847989073,
45096  0.18372590127952082,
45097  0.18454178776416885,
45098  0.18535685874976227,
45099  0.18617111505141282,
45100  0.18698455748341758,
45101  0.18779718685925983,
45102  0.18860900399160963,
45103  0.18942000969232464,
45104  0.19023020477245134,
45105  0.19103959004222526,
45106  0.19184816631107227,
45107  0.1926559343876092,
45108  0.19346289507964443,
45109  0.1942690491941792,
45110  0.19507439753740796,
45111  0.19587894091471936,
45112  0.19668268013069712,
45113  0.19748561598912073,
45114  0.1982877492929661,
45115  0.1990890808444069,
45116  0.19988961144481487,
45117  0.2006893418947604,
45118  0.20148827299401428,
45119  0.20228640554154742,
45120  0.20308374033553256,
45121  0.2038802781733442,
45122  0.20467601985156025,
45123  0.20547096616596217,
45124  0.20626511791153612,
45125  0.2070584758824735,
45126  0.2078510408721722,
45127  0.20864281367323678,
45128  0.20943379507747983,
45129  0.21022398587592217,
45130  0.21101338685879434,
45131  0.21180199881553674,
45132  0.21258982253480097,
45133  0.21337685880445012,
45134  0.21416310841155983,
45135  0.21494857214241914,
45136  0.21573325078253125,
45137  0.2165171451166138,
45138  0.2173002559286007,
45139  0.2180825840016417,
45140  0.21886413011810424,
45141  0.21964489505957363,
45142  0.22042487960685375,
45143  0.22120408453996832,
45144  0.2219825106381612,
45145  0.22276015867989762,
45146  0.22353702944286447,
45147  0.22431312370397138,
45148  0.22508844223935165,
45149  0.22586298582436248,
45150  0.2266367552335864,
45151  0.2274097512408314,
45152  0.22818197461913237,
45153  0.2289534261407512,
45154  0.22972410657717812,
45155  0.23049401669913228,
45156  0.23126315727656221,
45157  0.2320315290786471,
45158  0.23279913287379717,
45159  0.23356596942965469,
45160  0.23433203951309467,
45161  0.2350973438902254,
45162  0.2358618833263898,
45163  0.23662565858616547,
45164  0.23738867043336598,
45165  0.2381509196310414,
45166  0.23891240694147908,
45167  0.23967313312620442,
45168  0.24043309894598175,
45169  0.2411923051608149,
45170  0.24195075252994824,
45171  0.24270844181186702,
45172  0.24346537376429855,
45173  0.24422154914421257,
45174  0.24497696870782248,
45175  0.24573163321058555,
45176  0.24648554340720408,
45177  0.24723870005162618,
45178  0.24799110389704615,
45179  0.24874275569590532,
45180  0.2494936561998935,
45181  0.25024380615994857,
45182  0.250993206326258,
45183  0.2517418574482596,
45184  0.2524897602746421,
45185  0.2532369155533455,
45186  0.25398332403156276,
45187  0.2547289864557396,
45188  0.25547390357157584,
45189  0.25621807612402603,
45190  0.25696150485729974,
45191  0.25770419051486304,
45192  0.2584461338394388,
45193  0.25918733557300766,
45194  0.2599277964568082,
45195  0.2606675172313385,
45196  0.26140649863635645,
45197  0.2621447414108805,
45198  0.26288224629319024,
45199  0.26361901402082755,
45200  0.26435504533059706,
45201  0.2650903409585671,
45202  0.2658249016400699,
45203  0.26655872810970294,
45204  0.26729182110132965,
45205  0.2680241813480796,
45206  0.2687558095823497,
45207  0.26948670653580487,
45208  0.27021687293937857,
45209  0.2709463095232739,
45210  0.27167501701696406,
45211  0.27240299614919283,
45212  0.2731302476479759,
45213  0.27385677224060123,
45214  0.2745825706536297,
45215  0.27530764361289617,
45216  0.2760319918435099,
45217  0.2767556160698553,
45218  0.277478517015593,
45219  0.27820069540366,
45220  0.278922151956271,
45221  0.2796428873949186,
45222  0.2803629024403743,
45223  0.2810821978126893,
45224  0.281800774231195,
45225  0.2825186324145037,
45226  0.2832357730805096,
45227  0.2839521969463893,
45228  0.2846679047286026,
45229  0.285382897142893,
45230  0.2860971749042889,
45231  0.2868107387271036,
45232  0.2875235893249368,
45233  0.2882357274106748,
45234  0.2889471536964914,
45235  0.28965786889384837,
45236  0.2903678737134967,
45237  0.2910771688654765,
45238  0.29178575505911875,
45239  0.292493633003045,
45240  0.29320080340516863,
45241  0.2939072669726954,
45242  0.29461302441212445,
45243  0.29531807642924834,
45244  0.29602242372915455,
45245  0.2967260670162256,
45246  0.2974290069941401,
45247  0.2981312443658731,
45248  0.29883277983369727,
45249  0.2995336140991832,
45250  0.30023374786320023,
45251  0.3009331818259171,
45252  0.3016319166868029,
45253  0.3023299531446274,
45254  0.30302729189746225,
45255  0.3037239336426808,
45256  0.30441987907696,
45257  0.3051151288962799,
45258  0.3058096837959252,
45259  0.3065035444704858,
45260  0.30719671161385675,
45261  0.3078891859192402,
45262  0.30858096807914515,
45263  0.3092720587853881,
45264  0.3099624587290948,
45265  0.31065216860069933,
45266  0.31134118908994646,
45267  0.3120295208858911,
45268  0.31271716467689936,
45269  0.31340412115064964,
45270  0.3140903909941327,
45271  0.31477597489365294,
45272  0.3154608735348283,
45273  0.3161450876025921,
45274  0.3168286177811924,
45275  0.3175114647541937,
45276  0.31819362920447714,
45277  0.31887511181424144,
45278  0.3195559132650032,
45279  0.32023603423759806,
45280  0.3209154754121809,
45281  0.32159423746822724,
45282  0.32227232108453296,
45283  0.32294972693921553,
45284  0.3236264557097148,
45285  0.3243025080727936,
45286  0.3249778847045379,
45287  0.3256525862803583,
45288  0.32632661347499015,
45289  0.32699996696249445,
45290  0.32767264741625823,
45291  0.32834465550899594,
45292  0.329015991912749,
45293  0.3296866572988876,
45294  0.33035665233811085,
45295  0.33102597770044706,
45296  0.33169463405525534,
45297  0.33236262207122547,
45298  0.33302994241637884,
45299  0.3336965957580693,
45300  0.3343625827629836,
45301  0.3350279040971421,
45302  0.33569256042589946,
45303  0.33635655241394513,
45304  0.33701988072530453,
45305  0.33768254602333925,
45306  0.3383445489707475,
45307  0.3390058902295656,
45308  0.3396665704611681,
45309  0.340326590326268,
45310  0.3409859504849183,
45311  0.34164465159651225,
45312  0.3423026943197839,
45313  0.3429600793128089,
45314  0.34361680723300536,
45315  0.34427287873713386,
45316  0.3449282944812989,
45317  0.3455830551209491,
45318  0.3462371613108777,
45319  0.3468906137052238,
45320  0.3475434129574725,
45321  0.34819555972045557,
45322  0.3488470546463528,
45323  0.34949789838669143,
45324  0.35014809159234794,
45325  0.350797634913548,
45326  0.3514465289998677,
45327  0.3520947745002333,
45328  0.3527423720629229,
45329  0.35338932233556664,
45330  0.35403562596514704,
45331  0.3546812835980001,
45332  0.3553262958798159,
45333  0.355970663455639,
45334  0.35661438696986913,
45335  0.35725746706626205,
45336  0.3578999043879303,
45337  0.35854169957734305,
45338  0.35918285327632793,
45339  0.3598233661260706,
45340  0.36046323876711595,
45341  0.3611024718393687,
45342  0.3617410659820941,
45343  0.362379021833918,
45344  0.36301634003282846,
45345  0.3636530212161755,
45346  0.3642890660206721,
45347  0.364924475082395,
45348  0.36555924903678516,
45349  0.36619338851864824,
45350  0.3668268941621554,
45351  0.36745976660084423,
45352  0.36809200646761864,
45353  0.3687236143947503,
45354  0.3693545910138788,
45355  0.3699849369560123,
45356  0.3706146528515283,
45357  0.3712437393301742,
45358  0.3718721970210681,
45359  0.3725000265526991,
45360  0.3731272285529281,
45361  0.3737538036489887,
45362  0.3743797524674871,
45363  0.3750050756344038,
45364  0.3756297737750931,
45365  0.3762538475142845,
45366  0.3768772974760829,
45367  0.3775001242839695,
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51115  0.9980150380898906,
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51117  0.9980190041454845,
51118  0.9980209842006479,
51119  0.9980229622766963,
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51129  0.9980426346200809,
51130  0.9980445910559907,
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51133  0.9980504486384952,
51134  0.9980523972640972,
51135  0.9980543439419989,
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51143  0.9980698474812071,
51144  0.998071776717178,
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51147  0.9980775528628794,
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51149  0.9980813940107539,
51150  0.9980833117056783,
51151  0.9980852274838183,
51152  0.99808714134709,
51153  0.9980890532974072,
51154  0.9980909633366819,
51155  0.9980928714668245,
51156  0.9980947776897429,
51157  0.9980966820073436,
51158  0.9980985844215309,
51159  0.9981004849342074,
51160  0.9981023835472739,
51161  0.9981042802626288,
51162  0.9981061750821689,
51163  0.9981080680077893,
51164  0.998109959041383,
51165  0.998111848184841,
51166  0.9981137354400527,
51167  0.9981156208089054,
51168  0.9981175042932844,
51169  0.9981193858950734,
51170  0.9981212656161542,
51171  0.9981231434584065,
51172  0.9981250194237082,
51173  0.9981268935139355,
51174  0.9981287657309624,
51175  0.9981306360766614};
51176 
51177  //Find the correct [j][k] element for a given x1 and x2
51178 
51179  if ( x1 == wreg[JMAX] ) {
51180  j = JMAX;
51181  } else {
51182  for ( int y = 0; y <= JMAX; y++ ) {
51183  if ( ( wreg[y] <= x1 ) && ( x1 < wreg[y + 1] ) ) {
51184  j = y;
51185  break;
51186  }
51187  }
51188  }
51189  if ( x2 > ularge[KMAX - 1] ) {
51190  k = KMAX;
51191  } else {
51192  for ( int z = 0; z <= KMAX; z++ ) {
51193  if ( ( ularge[z] <= x2 ) && ( x2 < ularge[z + 1] ) ) {
51194  k = z;
51195  break;
51196  }
51197  }
51198  }
51199 
51200  //Calculate sigma() using Bi-Linear interpolaion
51201 
51202  double y0, y1, y2, y3;
51203  double t, u;
51204 
51205  if ( k == KMAX ) {
51206  ans = sigma[k][j];
51207  }
51208 
51209  else {
51210  y0 = sigma[k][j];
51211  y1 = sigma[k][j + 1];
51212  y2 = sigma[k + 1][j + 1];
51213  y3 = sigma[k + 1][j];
51214 
51215  t = ( x1 - wreg[j] ) / ( wreg[j + 1] - wreg[j] );
51216  u = ( x2 - ularge[k] ) / ( ularge[k + 1] - ularge[k] );
51217 
51218  ans = ( 1 - t ) * ( 1 - u ) * y0 + t * ( 1 - u ) * y1 + t * u * y2 +
51219  ( 1 - t ) * u * y3;
51220  }
51221  }
51222  return ans;
51223 }
void decay(EvtParticle *Bmeson) override
Definition: EvtVubAC.cpp:91
double CF
Definition: EvtVubAC.hh:54
double k
Definition: EvtVubAC.hh:52
double d1(double u, double w, double xb)
Definition: EvtVubAC.cpp:368
double ureg(double u)
Definition: EvtVubAC.cpp:276
double FindRoot(const double alphaSmZ)
Definition: EvtVubAC.cpp:474
void initProbMax() override
Definition: EvtVubAC.cpp:86
double max(double ub, double lb)
Definition: EvtVubAC.cpp:257
double PolyLog(double v, double z)
Definition: EvtVubAC.cpp:245
double getArg(unsigned int j)
double q
Definition: EvtVubAC.hh:51
virtual void init(EvtId part_n, const EvtVector4R &p4)=0
double mB
Definition: EvtVubAC.hh:46
double Lambda2(double x, double alphaSmZ)
Definition: EvtVubAC.cpp:461
std::vector< double > gvars
Definition: EvtVubAC.hh:59
double alphaS(double Q)
Definition: EvtVubAC.cpp:296
double f(double w)
Definition: EvtVubAC.cpp:448
double alphaSmB
Definition: EvtVubAC.hh:49
void set(int i, double d)
Definition: EvtVector4R.hh:167
EvtId * getDaugs()
Definition: EvtDecayBase.hh:66
double Sigma(double x1, double x2)
Definition: EvtVubAC.cpp:518
EvtDecayBase * clone() override
Definition: EvtVubAC.cpp:44
double CA
Definition: EvtVubAC.hh:55
void init() override
Definition: EvtVubAC.cpp:49
double Coeff(double u, double w, double xb)
Definition: EvtVubAC.cpp:310
double initializePhaseSpace(unsigned int numdaughter, EvtId *daughters, bool forceResetMasses=false, double poleSize=-1., int whichTwo1=0, int whichTwo2=1)
void checkNDaug(int d1, int d2=-1)
static double Flat()
Definition: EvtRandom.cpp:72
void checkNArg(int a1, int a2=-1, int a3=-1, int a4=-1)
double ularge(double u)
Definition: EvtVubAC.cpp:286
std::string getName() override
Definition: EvtVubAC.cpp:39
double mass() const
double Coeff0(double w, double xb)
Definition: EvtVubAC.cpp:326
int getNDaug() const
Definition: EvtDecayBase.hh:65
double rate(double u, double w, double xb)
Definition: EvtVubAC.cpp:233
double wreg(double w)
Definition: EvtVubAC.cpp:265
EvtParticle * getDaug(int i)
Definition: EvtParticle.cpp:91
double Coeff1(double w, double xb)
Definition: EvtVubAC.cpp:337
double c
Definition: EvtVubAC.hh:50
double beta0
Definition: EvtVubAC.hh:57
double d(double u, double w, double xb)
Definition: EvtVubAC.cpp:355
double alphaSmZ
Definition: EvtVubAC.hh:48
int Bisect(double x1, double x2, double precision, double &root, const double alphaSmZ)
Definition: EvtVubAC.cpp:486
EvtId getDaug(int i) const
Definition: EvtDecayBase.hh:67