1
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3
4
5
6
7
8
9
10
11 package org.lcsim.math.distribution;
12
13
14 import static java.lang.Math.log;
15 import java.util.Random;
16
17
18
19
20 public class RandLandau
21 {
22 private Random _ran = new Random();
23 private double _sigma;
24 private double _mean;
25
26
27 public RandLandau()
28 {
29 _mean = 0.;
30 _sigma = 1.0;
31 }
32
33 public RandLandau(double mean, double sigma)
34 {
35 _mean = mean;
36 _sigma = sigma;
37 }
38
39
40 public double shoot()
41 {
42 return _mean+_sigma*transform(_ran.nextDouble());
43 }
44
45 private double transform(double r)
46 {
47
48 double u = r * TABLE_MULTIPLIER;
49 int index = (int) u;
50 double du = u - index;
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69 if ( index >= 70 && index <= 800 )
70 {
71
72 double f0 = inverseLandau [index];
73 double f1 = inverseLandau [index+1];
74 return f0 + du * (f1 - f0);
75
76 }
77 else if ( index >= 7 && index <= 980 )
78 {
79
80 double f_1 = inverseLandau [index-1];
81 double f0 = inverseLandau [index];
82 double f1 = inverseLandau [index+1];
83 double f2 = inverseLandau [index+2];
84
85 return f0 + du * (f1 - f0 - .25*(1-du)* (f2 -f1 - f0 + f_1) );
86
87 }
88 else if ( index < 7 )
89 {
90
91 final double n0 = 0.99858950;
92 final double n1 = 34.5213058; final double d1 = 34.1760202;
93 final double n2 = 17.0854528; final double d2 = 4.01244582;
94
95 double logr = log(r);
96 double x = 1/logr;
97 double x2 = x*x;
98
99 double pade = (n0 + n1*x + n2*x2) / (1.0 + d1*x + d2*x2);
100
101 return ( - log( -.91893853 - logr ) -1 ) * pade;
102
103 }
104 else if ( index <= 999 )
105 {
106
107 final double n0 = 1.00060006;
108 final double n1 = 263.991156; final double d1 = 257.368075;
109 final double n2 = 4373.20068; final double d2 = 3414.48018;
110
111 double x = 1-r;
112 double x2 = x*x;
113
114 return (n0 + n1*x + n2*x2) / (x * (1.0 + d1*x + d2*x2));
115
116 }
117 else
118 {
119
120 final double n0 = 1.00001538;
121 final double n1 = 6075.14119; final double d1 = 6065.11919;
122 final double n2 = 734266.409; final double d2 = 694021.044;
123
124 double x = 1-r;
125 double x2 = x*x;
126
127 return (n0 + n1*x + n2*x2) / (x * (1.0 + d1*x + d2*x2));
128
129 }
130
131 }
132
133
134
135
136
137
138
139
140
141
142 static final float TABLE_INTERVAL = .001f;
143 static final int TABLE_END = 982;
144 static final float TABLE_MULTIPLIER = 1.0f/TABLE_INTERVAL;
145
146
147
148
149
150
151
152
153
154
155
156 static final float[] inverseLandau = {
157
158 0.0f,
159 0.0f, 0.0f, 0.0f, 0.0f, 0.0f,
160 -2.244733f, -2.204365f, -2.168163f, -2.135219f, -2.104898f,
161 -2.076740f, -2.050397f, -2.025605f, -2.002150f, -1.979866f,
162 -1.958612f, -1.938275f, -1.918760f, -1.899984f, -1.881879f,
163 -1.864385f, -1.847451f, -1.831030f, -1.815083f, -1.799574f,
164 -1.784473f, -1.769751f, -1.755383f, -1.741346f, -1.727620f,
165 -1.714187f, -1.701029f, -1.688130f, -1.675477f, -1.663057f,
166 -1.650858f, -1.638868f, -1.627078f, -1.615477f, -1.604058f,
167 -1.592811f, -1.581729f, -1.570806f, -1.560034f, -1.549407f,
168 -1.538919f, -1.528565f, -1.518339f, -1.508237f, -1.498254f,
169 -1.488386f, -1.478628f, -1.468976f, -1.459428f, -1.449979f,
170 -1.440626f, -1.431365f, -1.422195f, -1.413111f, -1.404112f,
171 -1.395194f, -1.386356f, -1.377594f, -1.368906f, -1.360291f,
172 -1.351746f, -1.343269f, -1.334859f, -1.326512f, -1.318229f,
173 -1.310006f, -1.301843f, -1.293737f, -1.285688f, -1.277693f,
174 -1.269752f, -1.261863f, -1.254024f, -1.246235f, -1.238494f,
175 -1.230800f, -1.223153f, -1.215550f, -1.207990f, -1.200474f,
176 -1.192999f, -1.185566f, -1.178172f, -1.170817f, -1.163500f,
177 -1.156220f, -1.148977f, -1.141770f, -1.134598f, -1.127459f,
178 -1.120354f, -1.113282f, -1.106242f, -1.099233f, -1.092255f,
179
180 -1.085306f, -1.078388f, -1.071498f, -1.064636f, -1.057802f,
181 -1.050996f, -1.044215f, -1.037461f, -1.030733f, -1.024029f,
182 -1.017350f, -1.010695f, -1.004064f, -.997456f, -.990871f,
183 -.984308f, -.977767f, -.971247f, -.964749f, -.958271f,
184 -.951813f, -.945375f, -.938957f, -.932558f, -.926178f,
185 -.919816f, -.913472f, -.907146f, -.900838f, -.894547f,
186 -.888272f, -.882014f, -.875773f, -.869547f, -.863337f,
187 -.857142f, -.850963f, -.844798f, -.838648f, -.832512f,
188 -.826390f, -.820282f, -.814187f, -.808106f, -.802038f,
189 -.795982f, -.789940f, -.783909f, -.777891f, -.771884f,
190 -.765889f, -.759906f, -.753934f, -.747973f, -.742023f,
191 -.736084f, -.730155f, -.724237f, -.718328f, -.712429f,
192 -.706541f, -.700661f, -.694791f, -.688931f, -.683079f,
193 -.677236f, -.671402f, -.665576f, -.659759f, -.653950f,
194 -.648149f, -.642356f, -.636570f, -.630793f, -.625022f,
195 -.619259f, -.613503f, -.607754f, -.602012f, -.596276f,
196 -.590548f, -.584825f, -.579109f, -.573399f, -.567695f,
197 -.561997f, -.556305f, -.550618f, -.544937f, -.539262f,
198 -.533592f, -.527926f, -.522266f, -.516611f, -.510961f,
199 -.505315f, -.499674f, -.494037f, -.488405f, -.482777f,
200
201 -.477153f, -.471533f, -.465917f, -.460305f, -.454697f,
202 -.449092f, -.443491f, -.437893f, -.432299f, -.426707f,
203 -.421119f, -.415534f, -.409951f, -.404372f, -.398795f,
204 -.393221f, -.387649f, -.382080f, -.376513f, -.370949f,
205 -.365387f, -.359826f, -.354268f, -.348712f, -.343157f,
206 -.337604f, -.332053f, -.326503f, -.320955f, -.315408f,
207 -.309863f, -.304318f, -.298775f, -.293233f, -.287692f,
208 -.282152f, -.276613f, -.271074f, -.265536f, -.259999f,
209 -.254462f, -.248926f, -.243389f, -.237854f, -.232318f,
210 -.226783f, -.221247f, -.215712f, -.210176f, -.204641f,
211 -.199105f, -.193568f, -.188032f, -.182495f, -.176957f,
212 -.171419f, -.165880f, -.160341f, -.154800f, -.149259f,
213 -.143717f, -.138173f, -.132629f, -.127083f, -.121537f,
214 -.115989f, -.110439f, -.104889f, -.099336f, -.093782f,
215 -.088227f, -.082670f, -.077111f, -.071550f, -.065987f,
216 -.060423f, -.054856f, -.049288f, -.043717f, -.038144f,
217 -.032569f, -.026991f, -.021411f, -.015828f, -.010243f,
218 -.004656f, .000934f, .006527f, .012123f, .017722f,
219 .023323f, .028928f, .034535f, .040146f, .045759f,
220 .051376f, .056997f, .062620f, .068247f, .073877f,
221
222 .079511f, .085149f, .090790f, .096435f, .102083f,
223 .107736f, .113392f, .119052f, .124716f, .130385f,
224 .136057f, .141734f, .147414f, .153100f, .158789f,
225 .164483f, .170181f, .175884f, .181592f, .187304f,
226 .193021f, .198743f, .204469f, .210201f, .215937f,
227 .221678f, .227425f, .233177f, .238933f, .244696f,
228 .250463f, .256236f, .262014f, .267798f, .273587f,
229 .279382f, .285183f, .290989f, .296801f, .302619f,
230 .308443f, .314273f, .320109f, .325951f, .331799f,
231 .337654f, .343515f, .349382f, .355255f, .361135f,
232 .367022f, .372915f, .378815f, .384721f, .390634f,
233 .396554f, .402481f, .408415f, .414356f, .420304f,
234 .426260f, .432222f, .438192f, .444169f, .450153f,
235 .456145f, .462144f, .468151f, .474166f, .480188f,
236 .486218f, .492256f, .498302f, .504356f, .510418f,
237 .516488f, .522566f, .528653f, .534747f, .540850f,
238 .546962f, .553082f, .559210f, .565347f, .571493f,
239 .577648f, .583811f, .589983f, .596164f, .602355f,
240 .608554f, .614762f, .620980f, .627207f, .633444f,
241 .639689f, .645945f, .652210f, .658484f, .664768f,
242
243 .671062f, .677366f, .683680f, .690004f, .696338f,
244 .702682f, .709036f, .715400f, .721775f, .728160f,
245 .734556f, .740963f, .747379f, .753807f, .760246f,
246 .766695f, .773155f, .779627f, .786109f, .792603f,
247 .799107f, .805624f, .812151f, .818690f, .825241f,
248 .831803f, .838377f, .844962f, .851560f, .858170f,
249 .864791f, .871425f, .878071f, .884729f, .891399f,
250 .898082f, .904778f, .911486f, .918206f, .924940f,
251 .931686f, .938446f, .945218f, .952003f, .958802f,
252 .965614f, .972439f, .979278f, .986130f, .992996f,
253 .999875f, 1.006769f, 1.013676f, 1.020597f, 1.027533f,
254 1.034482f, 1.041446f, 1.048424f, 1.055417f, 1.062424f,
255 1.069446f, 1.076482f, 1.083534f, 1.090600f, 1.097681f,
256 1.104778f, 1.111889f, 1.119016f, 1.126159f, 1.133316f,
257 1.140490f, 1.147679f, 1.154884f, 1.162105f, 1.169342f,
258 1.176595f, 1.183864f, 1.191149f, 1.198451f, 1.205770f,
259 1.213105f, 1.220457f, 1.227826f, 1.235211f, 1.242614f,
260 1.250034f, 1.257471f, 1.264926f, 1.272398f, 1.279888f,
261 1.287395f, 1.294921f, 1.302464f, 1.310026f, 1.317605f,
262 1.325203f, 1.332819f, 1.340454f, 1.348108f, 1.355780f,
263
264 1.363472f, 1.371182f, 1.378912f, 1.386660f, 1.394429f,
265 1.402216f, 1.410024f, 1.417851f, 1.425698f, 1.433565f,
266 1.441453f, 1.449360f, 1.457288f, 1.465237f, 1.473206f,
267 1.481196f, 1.489208f, 1.497240f, 1.505293f, 1.513368f,
268 1.521465f, 1.529583f, 1.537723f, 1.545885f, 1.554068f,
269 1.562275f, 1.570503f, 1.578754f, 1.587028f, 1.595325f,
270 1.603644f, 1.611987f, 1.620353f, 1.628743f, 1.637156f,
271 1.645593f, 1.654053f, 1.662538f, 1.671047f, 1.679581f,
272 1.688139f, 1.696721f, 1.705329f, 1.713961f, 1.722619f,
273 1.731303f, 1.740011f, 1.748746f, 1.757506f, 1.766293f,
274 1.775106f, 1.783945f, 1.792810f, 1.801703f, 1.810623f,
275 1.819569f, 1.828543f, 1.837545f, 1.846574f, 1.855631f,
276 1.864717f, 1.873830f, 1.882972f, 1.892143f, 1.901343f,
277 1.910572f, 1.919830f, 1.929117f, 1.938434f, 1.947781f,
278 1.957158f, 1.966566f, 1.976004f, 1.985473f, 1.994972f,
279 2.004503f, 2.014065f, 2.023659f, 2.033285f, 2.042943f,
280 2.052633f, 2.062355f, 2.072110f, 2.081899f, 2.091720f,
281 2.101575f, 2.111464f, 2.121386f, 2.131343f, 2.141334f,
282 2.151360f, 2.161421f, 2.171517f, 2.181648f, 2.191815f,
283 2.202018f, 2.212257f, 2.222533f, 2.232845f, 2.243195f,
284
285 2.253582f, 2.264006f, 2.274468f, 2.284968f, 2.295507f,
286 2.306084f, 2.316701f, 2.327356f, 2.338051f, 2.348786f,
287 2.359562f, 2.370377f, 2.381234f, 2.392131f, 2.403070f,
288 2.414051f, 2.425073f, 2.436138f, 2.447246f, 2.458397f,
289 2.469591f, 2.480828f, 2.492110f, 2.503436f, 2.514807f,
290 2.526222f, 2.537684f, 2.549190f, 2.560743f, 2.572343f,
291 2.583989f, 2.595682f, 2.607423f, 2.619212f, 2.631050f,
292 2.642936f, 2.654871f, 2.666855f, 2.678890f, 2.690975f,
293 2.703110f, 2.715297f, 2.727535f, 2.739825f, 2.752168f,
294 2.764563f, 2.777012f, 2.789514f, 2.802070f, 2.814681f,
295 2.827347f, 2.840069f, 2.852846f, 2.865680f, 2.878570f,
296 2.891518f, 2.904524f, 2.917588f, 2.930712f, 2.943894f,
297 2.957136f, 2.970439f, 2.983802f, 2.997227f, 3.010714f,
298 3.024263f, 3.037875f, 3.051551f, 3.065290f, 3.079095f,
299 3.092965f, 3.106900f, 3.120902f, 3.134971f, 3.149107f,
300 3.163312f, 3.177585f, 3.191928f, 3.206340f, 3.220824f,
301 3.235378f, 3.250005f, 3.264704f, 3.279477f, 3.294323f,
302 3.309244f, 3.324240f, 3.339312f, 3.354461f, 3.369687f,
303 3.384992f, 3.400375f, 3.415838f, 3.431381f, 3.447005f,
304 3.462711f, 3.478500f, 3.494372f, 3.510328f, 3.526370f,
305
306 3.542497f, 3.558711f, 3.575012f, 3.591402f, 3.607881f,
307 3.624450f, 3.641111f, 3.657863f, 3.674708f, 3.691646f,
308 3.708680f, 3.725809f, 3.743034f, 3.760357f, 3.777779f,
309 3.795300f, 3.812921f, 3.830645f, 3.848470f, 3.866400f,
310 3.884434f, 3.902574f, 3.920821f, 3.939176f, 3.957640f,
311 3.976215f, 3.994901f, 4.013699f, 4.032612f, 4.051639f,
312 4.070783f, 4.090045f, 4.109425f, 4.128925f, 4.148547f,
313 4.168292f, 4.188160f, 4.208154f, 4.228275f, 4.248524f,
314 4.268903f, 4.289413f, 4.310056f, 4.330832f, 4.351745f,
315 4.372794f, 4.393982f, 4.415310f, 4.436781f, 4.458395f,
316 4.480154f, 4.502060f, 4.524114f, 4.546319f, 4.568676f,
317 4.591187f, 4.613854f, 4.636678f, 4.659662f, 4.682807f,
318 4.706116f, 4.729590f, 4.753231f, 4.777041f, 4.801024f,
319 4.825179f, 4.849511f, 4.874020f, 4.898710f, 4.923582f,
320 4.948639f, 4.973883f, 4.999316f, 5.024942f, 5.050761f,
321 5.076778f, 5.102993f, 5.129411f, 5.156034f, 5.182864f,
322 5.209903f, 5.237156f, 5.264625f, 5.292312f, 5.320220f,
323 5.348354f, 5.376714f, 5.405306f, 5.434131f, 5.463193f,
324 5.492496f, 5.522042f, 5.551836f, 5.581880f, 5.612178f,
325 5.642734f, 5.673552f, 5.704634f, 5.735986f, 5.767610f,
326
327 5.799512f, 5.831694f, 5.864161f, 5.896918f, 5.929968f,
328 5.963316f, 5.996967f, 6.030925f, 6.065194f, 6.099780f,
329 6.134687f, 6.169921f, 6.205486f, 6.241387f, 6.277630f,
330 6.314220f, 6.351163f, 6.388465f, 6.426130f, 6.464166f,
331 6.502578f, 6.541371f, 6.580553f, 6.620130f, 6.660109f,
332 6.700495f, 6.741297f, 6.782520f, 6.824173f, 6.866262f,
333 6.908795f, 6.951780f, 6.995225f, 7.039137f, 7.083525f,
334 7.128398f, 7.173764f, 7.219632f, 7.266011f, 7.312910f,
335 7.360339f, 7.408308f, 7.456827f, 7.505905f, 7.555554f,
336 7.605785f, 7.656608f, 7.708035f, 7.760077f, 7.812747f,
337 7.866057f, 7.920019f, 7.974647f, 8.029953f, 8.085952f,
338 8.142657f, 8.200083f, 8.258245f, 8.317158f, 8.376837f,
339 8.437300f, 8.498562f, 8.560641f, 8.623554f, 8.687319f,
340 8.751955f, 8.817481f, 8.883916f, 8.951282f, 9.019600f,
341 9.088889f, 9.159174f, 9.230477f, 9.302822f, 9.376233f,
342 9.450735f, 9.526355f, 9.603118f, 9.681054f, 9.760191f,
343 9.840558f, 9.922186f, 10.005107f, 10.089353f, 10.174959f,
344 10.261958f, 10.350389f, 10.440287f, 10.531693f, 10.624646f,
345 10.719188f, 10.815362f, 10.913214f, 11.012789f, 11.114137f,
346 11.217307f, 11.322352f, 11.429325f, 11.538283f, 11.649285f,
347
348 11.762390f, 11.877664f, 11.995170f, 12.114979f, 12.237161f,
349 12.361791f, 12.488946f, 12.618708f, 12.751161f, 12.886394f,
350 13.024498f, 13.165570f, 13.309711f, 13.457026f, 13.607625f,
351 13.761625f, 13.919145f, 14.080314f, 14.245263f, 14.414134f,
352 14.587072f, 14.764233f, 14.945778f, 15.131877f, 15.322712f,
353 15.518470f, 15.719353f, 15.925570f, 16.137345f, 16.354912f,
354 16.578520f, 16.808433f, 17.044929f, 17.288305f, 17.538873f,
355 17.796967f, 18.062943f, 18.337176f, 18.620068f, 18.912049f,
356 19.213574f, 19.525133f, 19.847249f, 20.180480f, 20.525429f,
357 20.882738f, 21.253102f, 21.637266f, 22.036036f, 22.450278f,
358 22.880933f, 23.329017f, 23.795634f, 24.281981f, 24.789364f,
359 25.319207f, 25.873062f, 26.452634f, 27.059789f, 27.696581f,
360 28.365274f, 29.068370f, 29.808638f, 30.589157f, 31.413354f,
361 32.285060f, 33.208568f, 34.188705f, 35.230920f, 36.341388f,
362 37.527131f, 38.796172f, 40.157721f, 41.622399f, 43.202525f,
363 44.912465f, 46.769077f, 48.792279f, 51.005773f, 53.437996f,
364 56.123356f, 59.103894f,
365
366 };
367
368
369
370
371 static final double[] f = {
372 0 , 0 , 0 ,0 ,0 ,-2.244733,
373 -2.204365,-2.168163,-2.135219,-2.104898,-2.076740,-2.050397,
374 -2.025605,-2.002150,-1.979866,-1.958612,-1.938275,-1.918760,
375 -1.899984,-1.881879,-1.864385,-1.847451,-1.831030,-1.815083,
376 -1.799574,-1.784473,-1.769751,-1.755383,-1.741346,-1.727620,
377 -1.714187,-1.701029,-1.688130,-1.675477,-1.663057,-1.650858,
378 -1.638868,-1.627078,-1.615477,-1.604058,-1.592811,-1.581729,
379 -1.570806,-1.560034,-1.549407,-1.538919,-1.528565,-1.518339,
380 -1.508237,-1.498254,-1.488386,-1.478628,-1.468976,-1.459428,
381 -1.449979,-1.440626,-1.431365,-1.422195,-1.413111,-1.404112,
382 -1.395194,-1.386356,-1.377594,-1.368906,-1.360291,-1.351746,
383 -1.343269,-1.334859,-1.326512,-1.318229,-1.310006,-1.301843,
384 -1.293737,-1.285688,-1.277693,-1.269752,-1.261863,-1.254024,
385 -1.246235,-1.238494,-1.230800,-1.223153,-1.215550,-1.207990,
386 -1.200474,-1.192999,-1.185566,-1.178172,-1.170817,-1.163500,
387 -1.156220,-1.148977,-1.141770,-1.134598,-1.127459,-1.120354,
388 -1.113282,-1.106242,-1.099233,-1.092255,
389 -1.085306,-1.078388,-1.071498,-1.064636,-1.057802,-1.050996,
390 -1.044215,-1.037461,-1.030733,-1.024029,-1.017350,-1.010695,
391 -1.004064, -.997456, -.990871, -.984308, -.977767, -.971247,
392 -.964749, -.958271, -.951813, -.945375, -.938957, -.932558,
393 -.926178, -.919816, -.913472, -.907146, -.900838, -.894547,
394 -.888272, -.882014, -.875773, -.869547, -.863337, -.857142,
395 -.850963, -.844798, -.838648, -.832512, -.826390, -.820282,
396 -.814187, -.808106, -.802038, -.795982, -.789940, -.783909,
397 -.777891, -.771884, -.765889, -.759906, -.753934, -.747973,
398 -.742023, -.736084, -.730155, -.724237, -.718328, -.712429,
399 -.706541, -.700661, -.694791, -.688931, -.683079, -.677236,
400 -.671402, -.665576, -.659759, -.653950, -.648149, -.642356,
401 -.636570, -.630793, -.625022, -.619259, -.613503, -.607754,
402 -.602012, -.596276, -.590548, -.584825, -.579109, -.573399,
403 -.567695, -.561997, -.556305, -.550618, -.544937, -.539262,
404 -.533592, -.527926, -.522266, -.516611, -.510961, -.505315,
405 -.499674, -.494037, -.488405, -.482777,
406 -.477153, -.471533, -.465917, -.460305, -.454697, -.449092,
407 -.443491, -.437893, -.432299, -.426707, -.421119, -.415534,
408 -.409951, -.404372, -.398795, -.393221, -.387649, -.382080,
409 -.376513, -.370949, -.365387, -.359826, -.354268, -.348712,
410 -.343157, -.337604, -.332053, -.326503, -.320955, -.315408,
411 -.309863, -.304318, -.298775, -.293233, -.287692, -.282152,
412 -.276613, -.271074, -.265536, -.259999, -.254462, -.248926,
413 -.243389, -.237854, -.232318, -.226783, -.221247, -.215712,
414 -.210176, -.204641, -.199105, -.193568, -.188032, -.182495,
415 -.176957, -.171419, -.165880, -.160341, -.154800, -.149259,
416 -.143717, -.138173, -.132629, -.127083, -.121537, -.115989,
417 -.110439, -.104889, -.099336, -.093782, -.088227, -.082670,
418 -.077111, -.071550, -.065987, -.060423, -.054856, -.049288,
419 -.043717, -.038144, -.032569, -.026991, -.021411, -.015828,
420 -.010243, -.004656, .000934, .006527, .012123, .017722,
421 .023323, .028928, .034535, .040146, .045759, .051376,
422 .056997, .062620, .068247, .073877,
423 .079511, .085149, .090790, .096435, .102083, .107736,
424 .113392, .119052, .124716, .130385, .136057, .141734,
425 .147414, .153100, .158789, .164483, .170181, .175884,
426 .181592, .187304, .193021, .198743, .204469, .210201,
427 .215937, .221678, .227425, .233177, .238933, .244696,
428 .250463, .256236, .262014, .267798, .273587, .279382,
429 .285183, .290989, .296801, .302619, .308443, .314273,
430 .320109, .325951, .331799, .337654, .343515, .349382,
431 .355255, .361135, .367022, .372915, .378815, .384721,
432 .390634, .396554, .402481, .408415, .414356, .420304,
433 .426260, .432222, .438192, .444169, .450153, .456145,
434 .462144, .468151, .474166, .480188, .486218, .492256,
435 .498302, .504356, .510418, .516488, .522566, .528653,
436 .534747, .540850, .546962, .553082, .559210, .565347,
437 .571493, .577648, .583811, .589983, .596164, .602355,
438 .608554, .614762, .620980, .627207, .633444, .639689,
439 .645945, .652210, .658484, .664768,
440 .671062, .677366, .683680, .690004, .696338, .702682,
441 .709036, .715400, .721775, .728160, .734556, .740963,
442 .747379, .753807, .760246, .766695, .773155, .779627,
443 .786109, .792603, .799107, .805624, .812151, .818690,
444 .825241, .831803, .838377, .844962, .851560, .858170,
445 .864791, .871425, .878071, .884729, .891399, .898082,
446 .904778, .911486, .918206, .924940, .931686, .938446,
447 .945218, .952003, .958802, .965614, .972439, .979278,
448 .986130, .992996, .999875, 1.006769, 1.013676, 1.020597,
449 1.027533, 1.034482, 1.041446, 1.048424, 1.055417, 1.062424,
450 1.069446, 1.076482, 1.083534, 1.090600, 1.097681, 1.104778,
451 1.111889, 1.119016, 1.126159, 1.133316, 1.140490, 1.147679,
452 1.154884, 1.162105, 1.169342, 1.176595, 1.183864, 1.191149,
453 1.198451, 1.205770, 1.213105, 1.220457, 1.227826, 1.235211,
454 1.242614, 1.250034, 1.257471, 1.264926, 1.272398, 1.279888,
455 1.287395, 1.294921, 1.302464, 1.310026, 1.317605, 1.325203,
456 1.332819, 1.340454, 1.348108, 1.355780,
457 1.363472, 1.371182, 1.378912, 1.386660, 1.394429, 1.402216,
458 1.410024, 1.417851, 1.425698, 1.433565, 1.441453, 1.449360,
459 1.457288, 1.465237, 1.473206, 1.481196, 1.489208, 1.497240,
460 1.505293, 1.513368, 1.521465, 1.529583, 1.537723, 1.545885,
461 1.554068, 1.562275, 1.570503, 1.578754, 1.587028, 1.595325,
462 1.603644, 1.611987, 1.620353, 1.628743, 1.637156, 1.645593,
463 1.654053, 1.662538, 1.671047, 1.679581, 1.688139, 1.696721,
464 1.705329, 1.713961, 1.722619, 1.731303, 1.740011, 1.748746,
465 1.757506, 1.766293, 1.775106, 1.783945, 1.792810, 1.801703,
466 1.810623, 1.819569, 1.828543, 1.837545, 1.846574, 1.855631,
467 1.864717, 1.873830, 1.882972, 1.892143, 1.901343, 1.910572,
468 1.919830, 1.929117, 1.938434, 1.947781, 1.957158, 1.966566,
469 1.976004, 1.985473, 1.994972, 2.004503, 2.014065, 2.023659,
470 2.033285, 2.042943, 2.052633, 2.062355, 2.072110, 2.081899,
471 2.091720, 2.101575, 2.111464, 2.121386, 2.131343, 2.141334,
472 2.151360, 2.161421, 2.171517, 2.181648, 2.191815, 2.202018,
473 2.212257, 2.222533, 2.232845, 2.243195,
474 2.253582, 2.264006, 2.274468, 2.284968, 2.295507, 2.306084,
475 2.316701, 2.327356, 2.338051, 2.348786, 2.359562, 2.370377,
476 2.381234, 2.392131, 2.403070, 2.414051, 2.425073, 2.436138,
477 2.447246, 2.458397, 2.469591, 2.480828, 2.492110, 2.503436,
478 2.514807, 2.526222, 2.537684, 2.549190, 2.560743, 2.572343,
479 2.583989, 2.595682, 2.607423, 2.619212, 2.631050, 2.642936,
480 2.654871, 2.666855, 2.678890, 2.690975, 2.703110, 2.715297,
481 2.727535, 2.739825, 2.752168, 2.764563, 2.777012, 2.789514,
482 2.802070, 2.814681, 2.827347, 2.840069, 2.852846, 2.865680,
483 2.878570, 2.891518, 2.904524, 2.917588, 2.930712, 2.943894,
484 2.957136, 2.970439, 2.983802, 2.997227, 3.010714, 3.024263,
485 3.037875, 3.051551, 3.065290, 3.079095, 3.092965, 3.106900,
486 3.120902, 3.134971, 3.149107, 3.163312, 3.177585, 3.191928,
487 3.206340, 3.220824, 3.235378, 3.250005, 3.264704, 3.279477,
488 3.294323, 3.309244, 3.324240, 3.339312, 3.354461, 3.369687,
489 3.384992, 3.400375, 3.415838, 3.431381, 3.447005, 3.462711,
490 3.478500, 3.494372, 3.510328, 3.526370,
491 3.542497, 3.558711, 3.575012, 3.591402, 3.607881, 3.624450,
492 3.641111, 3.657863, 3.674708, 3.691646, 3.708680, 3.725809,
493 3.743034, 3.760357, 3.777779, 3.795300, 3.812921, 3.830645,
494 3.848470, 3.866400, 3.884434, 3.902574, 3.920821, 3.939176,
495 3.957640, 3.976215, 3.994901, 4.013699, 4.032612, 4.051639,
496 4.070783, 4.090045, 4.109425, 4.128925, 4.148547, 4.168292,
497 4.188160, 4.208154, 4.228275, 4.248524, 4.268903, 4.289413,
498 4.310056, 4.330832, 4.351745, 4.372794, 4.393982, 4.415310,
499 4.436781, 4.458395, 4.480154, 4.502060, 4.524114, 4.546319,
500 4.568676, 4.591187, 4.613854, 4.636678, 4.659662, 4.682807,
501 4.706116, 4.729590, 4.753231, 4.777041, 4.801024, 4.825179,
502 4.849511, 4.874020, 4.898710, 4.923582, 4.948639, 4.973883,
503 4.999316, 5.024942, 5.050761, 5.076778, 5.102993, 5.129411,
504 5.156034, 5.182864, 5.209903, 5.237156, 5.264625, 5.292312,
505 5.320220, 5.348354, 5.376714, 5.405306, 5.434131, 5.463193,
506 5.492496, 5.522042, 5.551836, 5.581880, 5.612178, 5.642734,
507 5.673552, 5.704634, 5.735986, 5.767610,
508 5.799512, 5.831694, 5.864161, 5.896918, 5.929968, 5.963316,
509 5.996967, 6.030925, 6.065194, 6.099780, 6.134687, 6.169921,
510 6.205486, 6.241387, 6.277630, 6.314220, 6.351163, 6.388465,
511 6.426130, 6.464166, 6.502578, 6.541371, 6.580553, 6.620130,
512 6.660109, 6.700495, 6.741297, 6.782520, 6.824173, 6.866262,
513 6.908795, 6.951780, 6.995225, 7.039137, 7.083525, 7.128398,
514 7.173764, 7.219632, 7.266011, 7.312910, 7.360339, 7.408308,
515 7.456827, 7.505905, 7.555554, 7.605785, 7.656608, 7.708035,
516 7.760077, 7.812747, 7.866057, 7.920019, 7.974647, 8.029953,
517 8.085952, 8.142657, 8.200083, 8.258245, 8.317158, 8.376837,
518 8.437300, 8.498562, 8.560641, 8.623554, 8.687319, 8.751955,
519 8.817481, 8.883916, 8.951282, 9.019600, 9.088889, 9.159174,
520 9.230477, 9.302822, 9.376233, 9.450735, 9.526355, 9.603118,
521 9.681054, 9.760191, 9.840558, 9.922186,10.005107,10.089353,
522 10.174959,10.261958,10.350389,10.440287,10.531693,10.624646,
523 10.719188,10.815362,10.913214,11.012789,11.114137,11.217307,
524 11.322352,11.429325,11.538283,11.649285,
525 11.762390,11.877664,11.995170,12.114979,12.237161,12.361791,
526 12.488946,12.618708,12.751161,12.886394,13.024498,13.165570,
527 13.309711,13.457026,13.607625,13.761625,13.919145,14.080314,
528 14.245263,14.414134,14.587072,14.764233,14.945778,15.131877,
529 15.322712,15.518470,15.719353,15.925570,16.137345,16.354912,
530 16.578520,16.808433,17.044929,17.288305,17.538873,17.796967,
531 18.062943,18.337176,18.620068,18.912049,19.213574,19.525133,
532 19.847249,20.180480,20.525429,20.882738,21.253102,21.637266,
533 22.036036,22.450278,22.880933,23.329017,23.795634,24.281981,
534 24.789364,25.319207,25.873062,26.452634,27.059789,27.696581,
535 28.365274,29.068370,29.808638,30.589157,31.413354,32.285060,
536 33.208568,34.188705,35.230920,36.341388,37.527131,38.796172,
537 40.157721,41.622399,43.202525,44.912465,46.769077,48.792279,
538 51.005773,53.437996,56.123356,59.103894 };
539
540 public double nextLandau()
541 {
542 if (_sigma <= 0) return 0;
543 double ranlan, x, u, v;
544 x = _ran.nextDouble();
545 u = 1000.*x;
546 int i = (int) u;
547 u -= i;
548 if (i >= 70 && i < 800)
549 {
550 ranlan = f[i-1] + u*(f[i] - f[i-1]);
551 }
552 else if (i >= 7 && i <= 980)
553 {
554 ranlan = f[i-1] + u*(f[i]-f[i-1]-0.25*(1-u)*(f[i+1]-f[i]-f[i-1]+f[i-2]));
555 }
556 else if (i < 7)
557 {
558 v = log(x);
559 u = 1/v;
560 ranlan = ((0.99858950+(3.45213058E1+1.70854528E1*u)*u)/
561 (1 +(3.41760202E1+4.01244582 *u)*u))*
562 (log(-0.91893853-v)-1);
563 }
564 else
565 {
566 u = 1-x;
567 v = u*u;
568 if (x <= 0.999)
569 {
570 ranlan = (1.00060006+2.63991156E2*u+4.37320068E3*v)/
571 ((1 +2.57368075E2*u+3.41448018E3*v)*u);
572 }
573 else
574 {
575 ranlan = (1.00001538+6.07514119E3*u+7.34266409E5*v)/
576 ((1 +6.06511919E3*u+6.94021044E5*v)*u);
577 }
578 }
579 return _mean + _sigma*ranlan;
580 }
581
582 }