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LandauDistribution.cpp
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1 // This file is part of the Acts project.
2 //
3 // Copyright (C) 2018 CERN for the benefit of the Acts project
4 //
5 // This Source Code Form is subject to the terms of the Mozilla Public
6 // License, v. 2.0. If a copy of the MPL was not distributed with this
7 // file, You can obtain one at http://mozilla.org/MPL/2.0/.
8 
9 #include "ActsFatras/Utilities/LandauDistribution.hpp"
10 
11 #include <cmath>
12 
13 double ActsFatras::LandauDistribution::quantile(double z) {
14  // LANDAU quantile : algorithm from CERNLIB G110 ranlan
15  // Converted by Rene Brun from CERNLIB routine ranlan(G110),
16  // Moved and adapted to QuantFuncMathCore by B. List 29.4.2010
17 
18  static const double f[982] = {
19  0, 0, 0, 0, 0, -2.244733,
20  -2.204365, -2.168163, -2.135219, -2.104898, -2.076740, -2.050397,
21  -2.025605, -2.002150, -1.979866, -1.958612, -1.938275, -1.918760,
22  -1.899984, -1.881879, -1.864385, -1.847451, -1.831030, -1.815083,
23  -1.799574, -1.784473, -1.769751, -1.755383, -1.741346, -1.727620,
24  -1.714187, -1.701029, -1.688130, -1.675477, -1.663057, -1.650858,
25  -1.638868, -1.627078, -1.615477, -1.604058, -1.592811, -1.581729,
26  -1.570806, -1.560034, -1.549407, -1.538919, -1.528565, -1.518339,
27  -1.508237, -1.498254, -1.488386, -1.478628, -1.468976, -1.459428,
28  -1.449979, -1.440626, -1.431365, -1.422195, -1.413111, -1.404112,
29  -1.395194, -1.386356, -1.377594, -1.368906, -1.360291, -1.351746,
30  -1.343269, -1.334859, -1.326512, -1.318229, -1.310006, -1.301843,
31  -1.293737, -1.285688, -1.277693, -1.269752, -1.261863, -1.254024,
32  -1.246235, -1.238494, -1.230800, -1.223153, -1.215550, -1.207990,
33  -1.200474, -1.192999, -1.185566, -1.178172, -1.170817, -1.163500,
34  -1.156220, -1.148977, -1.141770, -1.134598, -1.127459, -1.120354,
35  -1.113282, -1.106242, -1.099233, -1.092255, -1.085306, -1.078388,
36  -1.071498, -1.064636, -1.057802, -1.050996, -1.044215, -1.037461,
37  -1.030733, -1.024029, -1.017350, -1.010695, -1.004064, -.997456,
38  -.990871, -.984308, -.977767, -.971247, -.964749, -.958271,
39  -.951813, -.945375, -.938957, -.932558, -.926178, -.919816,
40  -.913472, -.907146, -.900838, -.894547, -.888272, -.882014,
41  -.875773, -.869547, -.863337, -.857142, -.850963, -.844798,
42  -.838648, -.832512, -.826390, -.820282, -.814187, -.808106,
43  -.802038, -.795982, -.789940, -.783909, -.777891, -.771884,
44  -.765889, -.759906, -.753934, -.747973, -.742023, -.736084,
45  -.730155, -.724237, -.718328, -.712429, -.706541, -.700661,
46  -.694791, -.688931, -.683079, -.677236, -.671402, -.665576,
47  -.659759, -.653950, -.648149, -.642356, -.636570, -.630793,
48  -.625022, -.619259, -.613503, -.607754, -.602012, -.596276,
49  -.590548, -.584825, -.579109, -.573399, -.567695, -.561997,
50  -.556305, -.550618, -.544937, -.539262, -.533592, -.527926,
51  -.522266, -.516611, -.510961, -.505315, -.499674, -.494037,
52  -.488405, -.482777, -.477153, -.471533, -.465917, -.460305,
53  -.454697, -.449092, -.443491, -.437893, -.432299, -.426707,
54  -.421119, -.415534, -.409951, -.404372, -.398795, -.393221,
55  -.387649, -.382080, -.376513, -.370949, -.365387, -.359826,
56  -.354268, -.348712, -.343157, -.337604, -.332053, -.326503,
57  -.320955, -.315408, -.309863, -.304318, -.298775, -.293233,
58  -.287692, -.282152, -.276613, -.271074, -.265536, -.259999,
59  -.254462, -.248926, -.243389, -.237854, -.232318, -.226783,
60  -.221247, -.215712, -.210176, -.204641, -.199105, -.193568,
61  -.188032, -.182495, -.176957, -.171419, -.165880, -.160341,
62  -.154800, -.149259, -.143717, -.138173, -.132629, -.127083,
63  -.121537, -.115989, -.110439, -.104889, -.099336, -.093782,
64  -.088227, -.082670, -.077111, -.071550, -.065987, -.060423,
65  -.054856, -.049288, -.043717, -.038144, -.032569, -.026991,
66  -.021411, -.015828, -.010243, -.004656, .000934, .006527,
67  .012123, .017722, .023323, .028928, .034535, .040146,
68  .045759, .051376, .056997, .062620, .068247, .073877,
69  .079511, .085149, .090790, .096435, .102083, .107736,
70  .113392, .119052, .124716, .130385, .136057, .141734,
71  .147414, .153100, .158789, .164483, .170181, .175884,
72  .181592, .187304, .193021, .198743, .204469, .210201,
73  .215937, .221678, .227425, .233177, .238933, .244696,
74  .250463, .256236, .262014, .267798, .273587, .279382,
75  .285183, .290989, .296801, .302619, .308443, .314273,
76  .320109, .325951, .331799, .337654, .343515, .349382,
77  .355255, .361135, .367022, .372915, .378815, .384721,
78  .390634, .396554, .402481, .408415, .414356, .420304,
79  .426260, .432222, .438192, .444169, .450153, .456145,
80  .462144, .468151, .474166, .480188, .486218, .492256,
81  .498302, .504356, .510418, .516488, .522566, .528653,
82  .534747, .540850, .546962, .553082, .559210, .565347,
83  .571493, .577648, .583811, .589983, .596164, .602355,
84  .608554, .614762, .620980, .627207, .633444, .639689,
85  .645945, .652210, .658484, .664768, .671062, .677366,
86  .683680, .690004, .696338, .702682, .709036, .715400,
87  .721775, .728160, .734556, .740963, .747379, .753807,
88  .760246, .766695, .773155, .779627, .786109, .792603,
89  .799107, .805624, .812151, .818690, .825241, .831803,
90  .838377, .844962, .851560, .858170, .864791, .871425,
91  .878071, .884729, .891399, .898082, .904778, .911486,
92  .918206, .924940, .931686, .938446, .945218, .952003,
93  .958802, .965614, .972439, .979278, .986130, .992996,
94  .999875, 1.006769, 1.013676, 1.020597, 1.027533, 1.034482,
95  1.041446, 1.048424, 1.055417, 1.062424, 1.069446, 1.076482,
96  1.083534, 1.090600, 1.097681, 1.104778, 1.111889, 1.119016,
97  1.126159, 1.133316, 1.140490, 1.147679, 1.154884, 1.162105,
98  1.169342, 1.176595, 1.183864, 1.191149, 1.198451, 1.205770,
99  1.213105, 1.220457, 1.227826, 1.235211, 1.242614, 1.250034,
100  1.257471, 1.264926, 1.272398, 1.279888, 1.287395, 1.294921,
101  1.302464, 1.310026, 1.317605, 1.325203, 1.332819, 1.340454,
102  1.348108, 1.355780, 1.363472, 1.371182, 1.378912, 1.386660,
103  1.394429, 1.402216, 1.410024, 1.417851, 1.425698, 1.433565,
104  1.441453, 1.449360, 1.457288, 1.465237, 1.473206, 1.481196,
105  1.489208, 1.497240, 1.505293, 1.513368, 1.521465, 1.529583,
106  1.537723, 1.545885, 1.554068, 1.562275, 1.570503, 1.578754,
107  1.587028, 1.595325, 1.603644, 1.611987, 1.620353, 1.628743,
108  1.637156, 1.645593, 1.654053, 1.662538, 1.671047, 1.679581,
109  1.688139, 1.696721, 1.705329, 1.713961, 1.722619, 1.731303,
110  1.740011, 1.748746, 1.757506, 1.766293, 1.775106, 1.783945,
111  1.792810, 1.801703, 1.810623, 1.819569, 1.828543, 1.837545,
112  1.846574, 1.855631, 1.864717, 1.873830, 1.882972, 1.892143,
113  1.901343, 1.910572, 1.919830, 1.929117, 1.938434, 1.947781,
114  1.957158, 1.966566, 1.976004, 1.985473, 1.994972, 2.004503,
115  2.014065, 2.023659, 2.033285, 2.042943, 2.052633, 2.062355,
116  2.072110, 2.081899, 2.091720, 2.101575, 2.111464, 2.121386,
117  2.131343, 2.141334, 2.151360, 2.161421, 2.171517, 2.181648,
118  2.191815, 2.202018, 2.212257, 2.222533, 2.232845, 2.243195,
119  2.253582, 2.264006, 2.274468, 2.284968, 2.295507, 2.306084,
120  2.316701, 2.327356, 2.338051, 2.348786, 2.359562, 2.370377,
121  2.381234, 2.392131, 2.403070, 2.414051, 2.425073, 2.436138,
122  2.447246, 2.458397, 2.469591, 2.480828, 2.492110, 2.503436,
123  2.514807, 2.526222, 2.537684, 2.549190, 2.560743, 2.572343,
124  2.583989, 2.595682, 2.607423, 2.619212, 2.631050, 2.642936,
125  2.654871, 2.666855, 2.678890, 2.690975, 2.703110, 2.715297,
126  2.727535, 2.739825, 2.752168, 2.764563, 2.777012, 2.789514,
127  2.802070, 2.814681, 2.827347, 2.840069, 2.852846, 2.865680,
128  2.878570, 2.891518, 2.904524, 2.917588, 2.930712, 2.943894,
129  2.957136, 2.970439, 2.983802, 2.997227, 3.010714, 3.024263,
130  3.037875, 3.051551, 3.065290, 3.079095, 3.092965, 3.106900,
131  3.120902, 3.134971, 3.149107, 3.163312, 3.177585, 3.191928,
132  3.206340, 3.220824, 3.235378, 3.250005, 3.264704, 3.279477,
133  3.294323, 3.309244, 3.324240, 3.339312, 3.354461, 3.369687,
134  3.384992, 3.400375, 3.415838, 3.431381, 3.447005, 3.462711,
135  3.478500, 3.494372, 3.510328, 3.526370, 3.542497, 3.558711,
136  3.575012, 3.591402, 3.607881, 3.624450, 3.641111, 3.657863,
137  3.674708, 3.691646, 3.708680, 3.725809, 3.743034, 3.760357,
138  3.777779, 3.795300, 3.812921, 3.830645, 3.848470, 3.866400,
139  3.884434, 3.902574, 3.920821, 3.939176, 3.957640, 3.976215,
140  3.994901, 4.013699, 4.032612, 4.051639, 4.070783, 4.090045,
141  4.109425, 4.128925, 4.148547, 4.168292, 4.188160, 4.208154,
142  4.228275, 4.248524, 4.268903, 4.289413, 4.310056, 4.330832,
143  4.351745, 4.372794, 4.393982, 4.415310, 4.436781, 4.458395,
144  4.480154, 4.502060, 4.524114, 4.546319, 4.568676, 4.591187,
145  4.613854, 4.636678, 4.659662, 4.682807, 4.706116, 4.729590,
146  4.753231, 4.777041, 4.801024, 4.825179, 4.849511, 4.874020,
147  4.898710, 4.923582, 4.948639, 4.973883, 4.999316, 5.024942,
148  5.050761, 5.076778, 5.102993, 5.129411, 5.156034, 5.182864,
149  5.209903, 5.237156, 5.264625, 5.292312, 5.320220, 5.348354,
150  5.376714, 5.405306, 5.434131, 5.463193, 5.492496, 5.522042,
151  5.551836, 5.581880, 5.612178, 5.642734, 5.673552, 5.704634,
152  5.735986, 5.767610, 5.799512, 5.831694, 5.864161, 5.896918,
153  5.929968, 5.963316, 5.996967, 6.030925, 6.065194, 6.099780,
154  6.134687, 6.169921, 6.205486, 6.241387, 6.277630, 6.314220,
155  6.351163, 6.388465, 6.426130, 6.464166, 6.502578, 6.541371,
156  6.580553, 6.620130, 6.660109, 6.700495, 6.741297, 6.782520,
157  6.824173, 6.866262, 6.908795, 6.951780, 6.995225, 7.039137,
158  7.083525, 7.128398, 7.173764, 7.219632, 7.266011, 7.312910,
159  7.360339, 7.408308, 7.456827, 7.505905, 7.555554, 7.605785,
160  7.656608, 7.708035, 7.760077, 7.812747, 7.866057, 7.920019,
161  7.974647, 8.029953, 8.085952, 8.142657, 8.200083, 8.258245,
162  8.317158, 8.376837, 8.437300, 8.498562, 8.560641, 8.623554,
163  8.687319, 8.751955, 8.817481, 8.883916, 8.951282, 9.019600,
164  9.088889, 9.159174, 9.230477, 9.302822, 9.376233, 9.450735,
165  9.526355, 9.603118, 9.681054, 9.760191, 9.840558, 9.922186,
166  10.005107, 10.089353, 10.174959, 10.261958, 10.350389, 10.440287,
167  10.531693, 10.624646, 10.719188, 10.815362, 10.913214, 11.012789,
168  11.114137, 11.217307, 11.322352, 11.429325, 11.538283, 11.649285,
169  11.762390, 11.877664, 11.995170, 12.114979, 12.237161, 12.361791,
170  12.488946, 12.618708, 12.751161, 12.886394, 13.024498, 13.165570,
171  13.309711, 13.457026, 13.607625, 13.761625, 13.919145, 14.080314,
172  14.245263, 14.414134, 14.587072, 14.764233, 14.945778, 15.131877,
173  15.322712, 15.518470, 15.719353, 15.925570, 16.137345, 16.354912,
174  16.578520, 16.808433, 17.044929, 17.288305, 17.538873, 17.796967,
175  18.062943, 18.337176, 18.620068, 18.912049, 19.213574, 19.525133,
176  19.847249, 20.180480, 20.525429, 20.882738, 21.253102, 21.637266,
177  22.036036, 22.450278, 22.880933, 23.329017, 23.795634, 24.281981,
178  24.789364, 25.319207, 25.873062, 26.452634, 27.059789, 27.696581,
179  28.365274, 29.068370, 29.808638, 30.589157, 31.413354, 32.285060,
180  33.208568, 34.188705, 35.230920, 36.341388, 37.527131, 38.796172,
181  40.157721, 41.622399, 43.202525, 44.912465, 46.769077, 48.792279,
182  51.005773, 53.437996, 56.123356, 59.103894};
183 
184  if (z <= 0) {
185  return -std::numeric_limits<double>::infinity();
186  }
187  if (z >= 1) {
188  return std::numeric_limits<double>::infinity();
189  }
190 
191  double ranlan = 0, u = 0, v = 0;
192  u = 1000 * z;
193  int i = int(u);
194  u -= i;
195  if (i >= 70 && i < 800) {
196  ranlan = f[i - 1] + u * (f[i] - f[i - 1]);
197  } else if (i >= 7 && i <= 980) {
198  ranlan = f[i - 1] +
199  u * (f[i] - f[i - 1] -
200  0.25 * (1 - u) * (f[i + 1] - f[i] - f[i - 1] + f[i - 2]));
201  } else if (i < 7) {
202  v = std::log(z);
203  u = 1 / v;
204  ranlan = ((0.99858950 + (3.45213058E1 + 1.70854528E1 * u) * u) /
205  (1 + (3.41760202E1 + 4.01244582 * u) * u)) *
206  (-std::log(-0.91893853 - v) - 1);
207  } else {
208  u = 1 - z;
209  v = u * u;
210  if (z <= 0.999) {
211  ranlan = (1.00060006 + 2.63991156E2 * u + 4.37320068E3 * v) /
212  ((1 + 2.57368075E2 * u + 3.41448018E3 * v) * u);
213  } else {
214  ranlan = (1.00001538 + 6.07514119E3 * u + 7.34266409E5 * v) /
215  ((1 + 6.06511919E3 * u + 6.94021044E5 * v) * u);
216  }
217  }
218  return ranlan;
219 }