1 package org.opentrafficsim.core.dsol;
2
3 import java.util.Locale;
4
5 import nl.tudelft.simulation.jstats.distributions.DistContinuous;
6 import nl.tudelft.simulation.jstats.streams.MersenneTwister;
7 import nl.tudelft.simulation.jstats.streams.StreamInterface;
8
9
10
11
12
13
14
15
16
17
18
19
20
21 public class DistNormalTrunc extends DistContinuous
22 {
23
24 private static final long serialVersionUID = 1L;
25
26
27 private final double mu;
28
29
30 private final double sigma;
31
32
33 private final double min;
34
35
36 private final double max;
37
38
39 private final double cumulMin;
40
41
42 private final double cumulDiff;
43
44
45 private final double probDensFactor;
46
47
48
49
50
51
52
53
54 public DistNormalTrunc(final StreamInterface stream, final double min, final double max)
55 {
56 this(stream, 0.0, 1.0, min, max);
57 }
58
59
60
61
62
63
64
65
66
67 public DistNormalTrunc(final StreamInterface stream, final double mu, final double sigma, final double min,
68 final double max)
69 {
70 super(stream);
71 if (max < min)
72 {
73 throw new IllegalArgumentException("Error Normal Truncated - max < min");
74 }
75 this.mu = mu;
76 this.sigma = sigma;
77 this.min = min;
78 this.max = max;
79 this.cumulMin = getCumulativeProbabilityNotTruncated(min);
80 this.cumulDiff = getCumulativeProbabilityNotTruncated(max) - this.cumulMin;
81 this.probDensFactor = 1.0 / this.cumulDiff;
82 }
83
84
85 @Override
86 public double draw()
87 {
88 return getInverseCumulativeProbabilityNotTruncated(this.cumulMin + this.cumulDiff * this.stream.nextDouble());
89 }
90
91
92
93
94
95
96 public double getCumulativeProbability(final double x)
97 {
98 if (x < this.min)
99 {
100 return 0.0;
101 }
102 if (x > this.max)
103 {
104 return 1.0;
105 }
106 return (getCumulativeProbabilityNotTruncated(x) - this.cumulMin) * this.probDensFactor;
107 }
108
109
110
111
112
113
114 private double getCumulativeProbabilityNotTruncated(final double x)
115 {
116 double z = (x - this.mu) / this.sigma * 100;
117 double absZ = Math.abs(z);
118 int intZ = (int) absZ;
119 double f = 0.0;
120 if (intZ >= 1000)
121 {
122 intZ = 999;
123 f = 1.0;
124 }
125 else
126 {
127 f = absZ - intZ;
128 }
129 if (z >= 0)
130 {
131 return (1 - f) * CUMULATIVE_NORMAL_PROPABILITIES[intZ] + f * CUMULATIVE_NORMAL_PROPABILITIES[intZ + 1];
132 }
133 return 1 - ((1 - f) * CUMULATIVE_NORMAL_PROPABILITIES[intZ] + f * CUMULATIVE_NORMAL_PROPABILITIES[intZ + 1]);
134 }
135
136
137
138
139
140
141 public double getInverseCumulativeProbability(final double cumulativeProbability)
142 {
143 if (cumulativeProbability < 0 || cumulativeProbability > 1)
144 {
145 throw new IllegalArgumentException("1<cumulativeProbability<0 ?");
146 }
147
148
149
150
151
152
153 if (cumulativeProbability == 0.0)
154 {
155 return this.min;
156 }
157 if (cumulativeProbability == 1.0)
158 {
159 return this.max;
160 }
161 return getInverseCumulativeProbabilityNotTruncated(this.cumulMin + cumulativeProbability * this.cumulDiff);
162 }
163
164
165 @Override
166 public double probDensity(final double x)
167 {
168 if (x < this.min || x > this.max)
169 {
170 return 0.0;
171 }
172 return this.probDensFactor / (Math.sqrt(2 * Math.PI * Math.pow(this.sigma, 2)))
173 * Math.exp(-1 * Math.pow(x - this.mu, 2) / (2 * Math.pow(this.sigma, 2)));
174 }
175
176
177 @Override
178 public String toString()
179 {
180 return "NormalTrunc(" + this.mu + "," + this.sigma + "," + this.min + "," + this.max + ")";
181 }
182
183
184
185
186
187 public static void main(final String[] args)
188 {
189 StreamInterface stream = new MersenneTwister();
190 double mu = 2.0;
191 double sigma = 3.0;
192 double min = -5.0;
193 double max = 4.0;
194 DistNormalTrunc dist = new DistNormalTrunc(stream, mu, sigma, min, max);
195
196 System.out.println("<< probability density >>");
197 double sum = 0.0;
198 double step = (max - min) / 96;
199 for (double x = min - 2 * step; x <= max + 2 * step; x += step)
200 {
201 double p = dist.probDensity(x);
202 System.out.println(String.format(Locale.GERMAN, "%.8f;%.8f", x, p));
203 sum += p * step;
204 }
205 System.out.println(String.format(Locale.GERMAN, "Approx. sum = %.8f", sum));
206 System.out.println("");
207
208 System.out.println("<< cumulative density >>");
209 for (double x = min - 2 * step; x <= max + 2 * step; x += step)
210 {
211 double c = dist.getCumulativeProbability(x);
212 System.out.println(String.format(Locale.GERMAN, "%.8f;%.8f", x, c));
213 }
214 System.out.println("");
215
216 System.out.println("<< inverse cumulative density >>");
217 for (double c = 0.0; c < 1.005; c += 0.01)
218 {
219 double x = dist.getInverseCumulativeProbability(Math.min(c, 1.0));
220 System.out.println(String.format(Locale.GERMAN, "%.8f;%.8f", c, x));
221 }
222 System.out.println("");
223
224 System.out.println("<< 10000 random numbers. >>");
225 for (int i = 1; i < 10000; i++)
226 {
227 System.out.println(String.format(Locale.GERMAN, "%,8f", dist.draw()));
228 }
229
230 }
231
232
233
234
235
236
237 private double getInverseCumulativeProbabilityNotTruncated(final double cumulativeProbability)
238 {
239 if (cumulativeProbability < 0 || cumulativeProbability > 1)
240 {
241 throw new IllegalArgumentException("1<cumulativeProbability<0 ?");
242 }
243 boolean located = false;
244 double prob = cumulativeProbability;
245 if (cumulativeProbability < 0.5)
246 {
247 prob = 1 - cumulativeProbability;
248 }
249 int i = 0;
250 double f = 0.0;
251 while (!located)
252 {
253 if (CUMULATIVE_NORMAL_PROPABILITIES[i] < prob && CUMULATIVE_NORMAL_PROPABILITIES[i + 1] >= prob)
254 {
255 located = true;
256 if (CUMULATIVE_NORMAL_PROPABILITIES[i] < CUMULATIVE_NORMAL_PROPABILITIES[i + 1])
257 {
258 f = (prob - CUMULATIVE_NORMAL_PROPABILITIES[i])
259 / (CUMULATIVE_NORMAL_PROPABILITIES[i + 1] - CUMULATIVE_NORMAL_PROPABILITIES[i]);
260 }
261 }
262 else
263 {
264 i++;
265 }
266 }
267 if (cumulativeProbability < 0.5)
268 {
269 return this.mu - ((f + i) / 100.0) * this.sigma;
270 }
271 return ((f + i) / 100.0) * this.sigma + this.mu;
272 }
273
274
275
276
277
278 public static final double[] CUMULATIVE_NORMAL_PROPABILITIES = { 0.5000000000000000, 0.5039873616189113, 0.5079763193203305,
279 0.5119644795160448, 0.5159514436524734, 0.5199368135347197, 0.5239201914458871, 0.5279011802661332,
280 0.5318793835914418, 0.5358544058520341, 0.5398258524303582, 0.5437933297786074, 0.5477564455357087,
281 0.5517148086437129, 0.5556680294635363, 0.5596157198900099, 0.5635574934661438, 0.567492965496589,
282 0.5714217531602216, 0.5753434756217956, 0.5792577541426178, 0.5831642121901748, 0.5870624755466856,
283 0.5909521724164968, 0.5948329335322977, 0.5987043922600851, 0.6025661847028365, 0.6064179498028396,
284 0.6102593294426336, 0.6140899685445192, 0.6179095151685767, 0.6217176206091617, 0.6255139394898266,
285 0.6292981298566381, 0.6330698532698229, 0.6368287748937326, 0.6405745635850643, 0.644306891979308,
286 0.6480254365753887, 0.6517298778184553, 0.6554199001807951, 0.6590951922408244, 0.6627554467601383,
287 0.6664003607585898, 0.6700296355873492, 0.6736429769999337, 0.6772400952211824, 0.6808207050141283,
288 0.684384525744776, 0.6879312814447339, 0.6914607008716991, 0.6949725175677556, 0.6984664699154933,
289 0.7019423011919023, 0.7053997596200493, 0.7088385984185037, 0.7122585758485337, 0.7156594552589977,
290 0.719041005128991, 0.722402999108207, 0.7257452160549791, 0.7290674400720636, 0.7323694605400943,
291 0.7356510721487322, 0.73891207492553, 0.7421522742624731, 0.7453714809402076, 0.7485695111499924,
292 0.7517461865133215, 0.754901334099275, 0.7580347864395746, 0.761146381541351, 0.764235962897659, 0.7673033794957203,
293 0.7703484858229172, 0.7733711418705582, 0.7763712131354236, 0.779348570619097, 0.7823030908251122,
294 0.7852346557539338, 0.7881431528957866, 0.79102847522134, 0.7938905211703059, 0.7967291946379159,
295 0.7995444049593787, 0.8023360668922485, 0.8051041005968205, 0.8078484316145099, 0.810568990844285,
296 0.8132657145171739, 0.8159385441688476, 0.8185874266103501, 0.8212123138969823, 0.8238131632953734,
297 0.8263899372487721, 0.8289426033406134, 0.831471134256341, 0.8339755077435994, 0.8364557065707554,
298 0.8389117184838284, 0.8413435361618438, 0.8437511571706939, 0.8461345839154543, 0.8484938235912971,
299 0.8508288881329673, 0.8531397941628848, 0.8554265629379223, 0.8576892202948876, 0.8599277965947512,
300 0.8621423266656558, 0.8643328497447642, 0.866499409418988, 0.8686420535645871, 0.8707608342857796,
301 0.872855807852312, 0.8749270346360735, 0.8769745790467864, 0.8789985094668413, 0.8809988981852741,
302 0.8829758213309686, 0.8849293588050865, 0.886859594212814, 0.8887666147944305, 0.8906505113557653,
303 0.8925113781980463, 0.8943493130472426, 0.8961644169828942, 0.8979567943664809, 0.8997265527693831,
304 0.9014738029004713, 0.9031986585333613, 0.9049012364333603, 0.9065816562841962, 0.9082400406144879,
305 0.9098765147240866, 0.9114912066102397, 0.9130842468937037, 0.9146557687447538, 0.9162059078092082,
306 0.9177348021344403, 0.9192425920954638, 0.9207294203210978, 0.9221954316202577, 0.9236407729084056,
307 0.9250655931341809, 0.9264700432062887, 0.9278542759206125, 0.9292184458876369, 0.9305627094602053,
308 0.9318872246616042, 0.9331921511140636, 0.9344776499676445, 0.9357438838296055, 0.9369910166942079,
309 0.9382192138730403, 0.9394286419258764, 0.940619468592069, 0.941791862722541, 0.9429459942123697, 0.944082033934012,
310 0.9452001536711674, 0.9463005260533299, 0.9473833244910284, 0.9484487231117875, 0.94949689669682,
311 0.9505280206184922, 0.9515422707785594, 0.9525398235471815, 0.9535208557027719, 0.9544855443726583,
312 0.9554340669746081, 0.9563666011591815, 0.9572833247529947, 0.9581844157028426, 0.9590700520207252,
313 0.9599404117298032, 0.9607956728112474, 0.9616360131520566, 0.9624616104937792, 0.9632726423822178,
314 0.9640692861180821, 0.9648517187086078, 0.9656201168201517, 0.9663746567317699, 0.9671155142897785,
315 0.9678428648633103, 0.9685568833008597, 0.9692577438878406, 0.9699456203051116, 0.9706206855885555,
316 0.971283112089614, 0.9719330714368619, 0.9725707344985791, 0.9731962713463076, 0.973809851219447,
317 0.9744116424908279, 0.9750018126333039, 0.9755805281873245, 0.9761479547295168, 0.9767042568422514,
318 0.9772495980842009, 0.9777841409618732, 0.9783080469021415, 0.9788214762257182, 0.979324588121612,
319 0.9798175406225412, 0.9803004905813041, 0.9807735936480722, 0.981237004248657, 0.9816908755636616,
320 0.9821353595085873, 0.9825706067148376, 0.9829967665116119, 0.9834139869087157, 0.9838224145802272,
321 0.9842221948490532, 0.9846134716723274, 0.9849963876276845, 0.9853710839003452, 0.985737700271045,
322 0.9860963751047681, 0.9864472453402844, 0.9867904464804915, 0.9871261125835228, 0.9874543762546124,
323 0.9877753686387415, 0.9880892194139929, 0.988396056785651, 0.9886960074810209, 0.9889891967449299,
324 0.9892757483359246, 0.989555784523144, 0.9898294260838525, 0.9900967923016145, 0.9903580009651043,
325 0.9906131683675308, 0.9908624093066779, 0.9911058370855164, 0.9913435635134026, 0.991575698907852,
326 0.9918023520968361, 0.9920236304216317, 0.9922396397401824, 0.9924504844309792, 0.9926562673974049,
327 0.992857090072596, 0.9930530524247368, 0.9932442529628207, 0.9934307887428471, 0.9936127553744406,
328 0.993790247027868, 0.9939633564414762, 0.9941321749294971, 0.9942967923902228, 0.9944572973145361,
329 0.9946137767947988, 0.9947663165340496, 0.9949150008555357, 0.9950599127125389, 0.9952011336985047,
330 0.9953387440574476, 0.9954728226946147, 0.9956034471874149, 0.9957306937965966, 0.9958546374776436,
331 0.9959753518924065, 0.9960929094209239, 0.9962073811734615, 0.9963188370027265, 0.9964273455162624,
332 0.9965329740889989, 0.9966357888759699, 0.9967358548251734, 0.9968332356905508, 0.9969279940451093,
333 0.9970201912941401, 0.9971098876885598, 0.9971971423383441, 0.9972820132260181, 0.9973645572202651,
334 0.9974448300895796, 0.9975228865159886, 0.9975987801088081, 0.9976725634184758, 0.9977442879503817,
335 0.9978140041787443, 0.9978817615605097, 0.9979476085492539, 0.9980115926090906, 0.9980737602285842,
336 0.9981341569346482, 0.9981928273064313, 0.9982498149891729, 0.998305162708049, 0.9983589122819604,
337 0.9984111046372987, 0.9984617798216666, 0.9985109770175317, 0.9985587345558365, 0.9986050899295523,
338 0.9986500798071501, 0.9986937400460181, 0.9987361057057903, 0.9987772110616016, 0.9988170896172607,
339 0.9988557741183267, 0.9988932965651068, 0.9989296882255506, 0.9989649796480435, 0.9989992006741035,
340 0.9990323804509681, 0.9990645474440748, 0.999095729449436, 0.999125953605889, 0.9991552464072354,
341 0.9991836337142654, 0.9992111407666507, 0.9992377921947238, 0.9992636120311323, 0.9992886237223589,
342 0.9993128501401143, 0.9993363135925993, 0.9993590358356453, 0.999381038083711, 0.9994023410207445,
343 0.9994229648109153, 0.9994429291092068, 0.9994622530718738, 0.9994809553667513, 0.9994990541834521,
344 0.9995165672433891, 0.9995335118096818, 0.9995499046969138, 0.999565762280761, 0.9995811005074615,
345 0.9995959349031589, 0.9996102805830935, 0.9996241522606701, 0.9996375642563711, 0.9996505305065254,
346 0.9996630645719558, 0.9996751796464766, 0.9996868885652497, 0.9996982038129988, 0.9997091375321072,
347 0.999719701530551, 0.9997299072897112, 0.9997397659720517, 0.9997492884286557, 0.9997584852066235,
348 0.9997673665563579, 0.9997759424386968, 0.9997842225319191, 0.9997922162386252, 0.9997999326924907,
349 0.999807380764881, 0.999814569071358, 0.9998215059780381, 0.9998281996078514, 0.9998346578466425,
350 0.9998408883492018, 0.9998468985451213, 0.9998526956445724, 0.999858286643944, 0.9998636783313704,
351 0.9998688772921471, 0.9998738899140359, 0.9998787223924446, 0.9998833807355126, 0.9998878707690767,
352 0.9998921981415287, 0.9998963683285831, 0.9999003866379228, 0.9999042582137387, 0.99990798804119, 0.999911580950741,
353 0.9999150416224173, 0.9999183745899578, 0.9999215842448586, 0.9999246748403525, 0.9999276504952729,
354 0.9999305151978185, 0.9999332728092672, 0.9999359270675735, 0.9999384815908634, 0.9999409398808894,
355 0.9999433053263691, 0.9999455812062524, 0.9999477706929066, 0.999949876855225, 0.9999519026616563,
356 0.9999538509831598, 0.9999557245960793, 0.9999575261849584, 0.9999592583452697, 0.9999609235860767,
357 0.9999625243326383, 0.9999640629289291, 0.9999655416401065, 0.9999669626549059, 0.9999683280879766,
358 0.9999696399821539, 0.9999709003106689, 0.9999721109793053, 0.9999732738284871, 0.9999743906353185,
359 0.9999754631155693, 0.9999764929255975, 0.9999774816642223, 0.9999784308745513, 0.9999793420457469,
360 0.9999802166147403, 0.9999810559679307, 0.9999818614427762, 0.9999826343293992, 0.9999833758721115,
361 0.9999840872709006, 0.999984769682885, 0.9999854242237042, 0.9999860519689024, 0.9999866539552403,
362 0.9999872311819792, 0.9999877846121323, 0.9999883151736708, 0.9999888237607027, 0.9999893112346047,
363 0.999989778425137, 0.9999902261314975, 0.9999906551233723, 0.9999910661419341, 0.9999914599008299,
364 0.9999918370871163, 0.999992198362175, 0.9999925443626037, 0.9999928757010765, 0.999993192967172,
365 0.9999934967281847, 0.9999937875299059, 0.9999940658973759, 0.9999943323356203, 0.9999945873303567,
366 0.9999948313486832, 0.9999950648397335, 0.9999952882353275, 0.9999955019505884, 0.9999957063845496,
367 0.9999959019207282, 0.9999960889276895, 0.9999962677595902, 0.9999964387567071, 0.9999966022459394,
368 0.9999967585412978, 0.9999969079443901, 0.9999970507448684, 0.9999971872208745, 0.9999973176394685,
369 0.9999974422570479, 0.9999975613197305, 0.9999976750637555, 0.9999977837158475, 0.9999978874935767,
370 0.9999979866057059, 0.9999980812525245, 0.9999981716261707, 0.9999982579109443, 0.9999983402836066,
371 0.9999984189136624, 0.999998493963655, 0.9999985655894209, 0.9999986339403611, 0.9999986991596813,
372 0.9999987613846415, 0.9999988207467845, 0.9999988773721528, 0.9999989313815221, 0.999998982890599,
373 0.9999990320102132, 0.9999990788465284, 0.9999991235012167, 0.9999991660716405, 0.9999992066510266,
374 0.99999924532863, 0.9999992821898891, 0.9999993173165908, 0.9999993507870083, 0.999999382676051, 0.9999994130553951,
375 0.9999994419936197, 0.9999994695563318, 0.999999495806289, 0.9999995208035128, 0.9999995446054075,
376 0.9999995672668669, 0.9999995888403767, 0.9999996093761104, 0.9999996289220386, 0.9999996475240089,
377 0.999999665225837, 0.9999996820693978, 0.9999996980947014, 0.9999997133399728, 0.9999997278417341,
378 0.9999997416348584, 0.9999997547526686, 0.9999997672269785, 0.999999779088168, 0.9999997903652507,
379 0.9999998010859101, 0.9999998112765858, 0.9999998209625084, 0.9999998301677586, 0.999999838915313,
380 0.9999998472271051, 0.9999998551240461, 0.9999998626260925, 0.9999998697522797, 0.9999998765207626,
381 0.999999882948852, 0.9999998890530569, 0.9999998948491172, 0.9999999003520337, 0.9999999055761172,
382 0.9999999105349969, 0.9999999152416649, 0.9999999197085024, 0.9999999239473055, 0.9999999279693159,
383 0.9999999317852374, 0.9999999354052702, 0.9999999388391236, 0.9999999420960494, 0.9999999451848542,
384 0.9999999481139239, 0.9999999508912378, 0.999999953524401, 0.999999956020643, 0.999999958386847, 0.9999999606295614,
385 0.9999999627550202, 0.999999964769152, 0.9999999666775974, 0.9999999684857224, 0.9999999701986259,
386 0.9999999718211613, 0.9999999733579436, 0.9999999748133596, 0.9999999761915778, 0.9999999774965675,
387 0.9999999787320892, 0.9999999799017258, 0.9999999810088808, 0.9999999820567871, 0.9999999830485156,
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478
479 }