1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
|
//
// random_histogram_example.c
//
// This example tests the random number generators for different
// distributions.
//
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#include <math.h>
#include <getopt.h>
#include "liquid.h"
#define OUTPUT_FILENAME "random_histogram_example.m"
// print usage/help message
void usage()
{
printf("random_histogram_example [options]\n");
printf(" -h : print usage\n");
printf(" -N : number of trials\n");
printf(" -n : number of histogram bins\n");
printf(" -d : distribution: {uniform, normal, exp, weib, gamma, nak, rice}\n");
printf(" -u : u UNIFORM: lower edge\n");
printf(" -v : v UNIFORM: upper edge\n");
printf(" -e : eta NORMAL: mean\n");
printf(" -s : sigma NORMAL: standard deviation\n");
printf(" -l : lambda EXPONENTIAL: decay factor\n");
printf(" -a : alpha WEIBULL: shape\n");
printf(" -b : beta WEIBULL: spread\n");
printf(" -g : gamma WEIBULL: threshold\n");
printf(" -A : alpha GAMMA: shape\n");
printf(" -B : beta GAMMA: spread\n");
printf(" -m : m NAKAGAMI: shape\n");
printf(" -o : omega NAKAGAMI: spread\n");
printf(" -K : K RICE-K: spread\n");
printf(" -O : omega RICE-K: spread\n");
}
int main(int argc, char*argv[])
{
srand(time(NULL));
unsigned long int num_trials = 100000; // number of trials
unsigned int num_bins = 30;
enum {
UNIFORM=0,
NORMAL,
EXPONENTIAL,
WEIBULL,
GAMMA,
NAKAGAMIM,
RICEK
} distribution=NORMAL;
// distribution parameters
float u = 0.0f; // UNIFORM: lower edge
float v = 1.0f; // UNIFORM: upper edge
float eta = 0.0f; // NORMAL: mean
float sigma = 1.0f; // NORMAL: standard deviation
float lambda = 3.0f; // EXPONENTIAL: decay factor
float alphaw = 1.0f; // WEIBULL: shape
float betaw = 1.0f; // WEIBULL: spread
float gammaw = 1.0f; // WEIBULL: threshold
float alphag = 4.5f; // GAMMA: shape
float betag = 1.0f; // GAMMA: spread
float m = 4.5f; // NAKAGAMI: shape factor
float omeganak = 1.0f; // NAKAGMAI: spread factor
float K = 4.0f; // RICE-K: K-factor (shape)
float omegarice = 1.0f; // RICE-K: spread factor
int dopt;
while ((dopt = getopt(argc,argv,"hN:n:d:u:v:e:s:l:a:b:g:A:B:m:o:K:O:")) != EOF) {
switch (dopt) {
case 'h':
usage();
return 0;
case 'N': num_trials = atoi(optarg); break;
case 'n': num_bins = atoi(optarg); break;
case 'd':
if (strcmp(optarg,"uniform")==0) distribution = UNIFORM;
else if (strcmp(optarg,"normal")==0) distribution = NORMAL;
else if (strcmp(optarg,"exp")==0) distribution = EXPONENTIAL;
else if (strcmp(optarg,"weib")==0) distribution = WEIBULL;
else if (strcmp(optarg,"gamma")==0) distribution = GAMMA;
else if (strcmp(optarg,"nak")==0) distribution = NAKAGAMIM;
else if (strcmp(optarg,"rice")==0) distribution = RICEK;
else {
fprintf(stderr,"error: %s, unknown/unsupported distribution '%s'\n", argv[0], optarg);
exit(1);
}
case 'u': u = atof(optarg); break;
case 'v': v = atof(optarg); break;
case 'e': eta = atof(optarg); break;
case 's': sigma = atof(optarg); break;
case 'l': lambda = atof(optarg); break;
case 'a': alphaw = atof(optarg); break;
case 'b': betaw = atof(optarg); break;
case 'g': gammaw = atof(optarg); break;
case 'A': alphag = atof(optarg); break;
case 'B': betag = atof(optarg); break;
case 'm': m = atof(optarg); break;
case 'o': omeganak = atof(optarg); break;
case 'K': K = atof(optarg); break;
case 'O': omegarice = atof(optarg); break;
default:
exit(1);
}
}
// validate input
if (num_bins == 0) {
fprintf(stderr,"error: %s, number of bins must be greater than zero\n", argv[0]);
exit(1);
} else if (num_trials == 0) {
fprintf(stderr,"error: %s, number of trials must be greater than zero\n", argv[0]);
exit(1);
}
float xmin = 0.0f;
float xmax = 1.0f;
unsigned long int i;
// make a guess at the histogram range so we don't need to
// store all the generated random variables in a giant array.
if (distribution == UNIFORM) {
xmin = u - 0.08*(v-u); // lower edge less 8% range
xmax = v + 0.08*(v-u); // upper edge plus 8% range
} else if (distribution == NORMAL) {
xmin = eta - 4.0f*sigma;
xmax = eta + 4.0f*sigma;
} else if (distribution == EXPONENTIAL) {
xmin = 0.0f;
xmax = 7.0f / lambda;
} else if (distribution == WEIBULL) {
xmin = gammaw;
xmax = gammaw + betaw*powf( -logf(1e-3f), 1.0f/alphaw );
} else if (distribution == GAMMA) {
xmin = 0.0f;
xmax = 6.5 * betag + 2.0*alphag;
} else if (distribution == NAKAGAMIM) {
xmin = 0.0f;
xmax = 1.5f*( powf(omeganak, 0.8f) + 1.0f/m );
} else if (distribution == RICEK) {
xmin = 0.0f;
xmax = 3.0f*logf(omegarice+1.0f) + 1.5f/(K+1.0f);
} else {
fprintf(stderr, "error: %s, unknown/unsupported distribution\n", argv[0]);
exit(1);
}
//
//float xspan = xmax - xmin;
float bin_width = (xmax - xmin) / (num_bins);
// initialize histogram
unsigned int hist[num_bins];
for (i=0; i<num_bins; i++)
hist[i] = 0;
// generate random variables
float x = 0.0f;
float m1 = 0.0f; // first moment
float m2 = 0.0f; // second moment
for (i=0; i<num_trials; i++) {
switch (distribution) {
case UNIFORM: x = randuf(u,v); break;
case NORMAL: x = sigma*randnf() + eta; break;
case EXPONENTIAL: x = randexpf(lambda); break;
case WEIBULL: x = randweibf(alphaw,betaw,gammaw); break;
case GAMMA: x = randgammaf(alphag,betag); break;
case NAKAGAMIM: x = randnakmf(m,omeganak); break;
case RICEK: x = randricekf(K,omegarice); break;
default:
fprintf(stderr,"error: %s, unknown/unsupported distribution\n", argv[0]);
exit(1);
}
// compute bin index
unsigned int index;
float ihat = num_bins * (x - xmin) / (xmax - xmin);
if (ihat < 0.0f)
index = 0;
else
index = (unsigned int)ihat;
if (index >= num_bins)
index = num_bins-1;
hist[index]++;
// update statistics
m1 += x; // first moment
m2 += x*x; // second moment
}
//
m1 /= (float)num_trials;
m2 /= (float)num_trials;
// compute expected distribution
unsigned int num_steps = 100;
float xstep = (xmax - xmin) / (num_steps - 1);
float f[num_steps];
float F[num_steps];
for (i=0; i<num_steps; i++) {
x = xmin + i*xstep;
switch (distribution) {
case UNIFORM:
f[i] = randuf_pdf(x,u,v);
F[i] = randuf_cdf(x,u,v);
break;
case NORMAL:
f[i] = randnf_pdf(x,eta,sigma);
F[i] = randnf_cdf(x,eta,sigma);
break;
case EXPONENTIAL:
f[i] = randexpf_pdf(x,lambda);
F[i] = randexpf_cdf(x,lambda);
break;
case WEIBULL:
f[i] = randweibf_pdf(x,alphaw,betaw,gammaw);
F[i] = randweibf_cdf(x,alphaw,betaw,gammaw);
break;
case GAMMA:
f[i] = randgammaf_pdf(x,alphag,betag);
F[i] = randgammaf_cdf(x,alphag,betag);
break;
case NAKAGAMIM:
f[i] = randnakmf_pdf(x,m,omeganak);
F[i] = randnakmf_cdf(x,m,omeganak);
break;
case RICEK:
f[i] = randricekf_pdf(x,K,omegarice);
F[i] = randricekf_cdf(x,K,omegarice);
break;
default:
fprintf(stderr,"error: %s, unknown/unsupported distribution\n", argv[0]);
exit(1);
}
}
// print results to screen
// find max(hist)
unsigned int hist_max = 0;
for (i=0; i<num_bins; i++)
hist_max = hist[i] > hist_max ? hist[i] : hist_max;
printf("%8s : %6s [%6s]\n", "x", "count", "prob.");
for (i=0; i<num_bins; i++) {
printf("%8.2f : %6u [%6.4f]", xmin + i*bin_width, hist[i], (float)hist[i] / (float)num_trials);
unsigned int k;
unsigned int n = round(60 * (float)hist[i] / (float)hist_max);
for (k=0; k<n; k++)
printf("#");
printf("\n");
}
// print distribution info, statistics
printf("statistics:\n");
switch (distribution) {
case UNIFORM:
printf(" distribution : %s\n", "uniform");
printf(" u : %f\n", u);
printf(" v : %f\n", v);
break;
case NORMAL:
printf(" distribution : %s\n", "normal (Gauss)");
printf(" eta : %f\n", eta);
printf(" sigma : %f\n", sigma);
break;
case EXPONENTIAL:
printf(" distribution : %s\n", "exponential");
printf(" lambda : %f\n", lambda);
break;
case WEIBULL:
printf(" distribution : %s\n", "Weibull");
printf(" alpha : %f\n", alphaw);
printf(" beta : %f\n", betaw);
printf(" gamma : %f\n", gammaw);
break;
case GAMMA:
printf(" distribution : %s\n", "gamma");
printf(" alpha : %f\n", alphag);
printf(" beta : %f\n", betag);
break;
case NAKAGAMIM:
printf(" distribution : %s\n", "Nakagami-m");
printf(" m : %f\n", m);
printf(" omega : %f\n", omeganak);
break;
case RICEK:
printf(" distribution : %s\n", "Rice-K");
printf(" K : %f\n", K);
printf(" omega : %f\n", omegarice);
break;
default:
fprintf(stderr,"error: %s, unknown/unsupported distribution\n", argv[0]);
exit(1);
}
printf("\n");
printf(" samples : %8lu\n", num_trials);
printf(" first moment, E( x } : %8.3f\n", m1);
printf(" second moment, E{x^2} : %8.3f\n", m2);
printf(" variance : %8.3f\n", m2 - m1*m1);
printf(" standard deviation : %8.3f\n", sqrtf(m2 - m1*m1));
//
// export results
//
FILE * fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"%% %s : auto-generated file\n\n", OUTPUT_FILENAME);
fprintf(fid,"clear all;\n");
fprintf(fid,"close all;\n");
fprintf(fid,"xmin = %12.4e;\n", xmin);
fprintf(fid,"xmax = %12.4e;\n", xmax);
fprintf(fid,"num_bins = %u;\n", num_bins);
fprintf(fid,"xspan = xmax - xmin;\n");
float F_hat = 0.0f;
for (i=0; i<num_bins; i++) {
x = xmin + ((float)i + 0.5f)*bin_width;
float h = (float)(hist[i]) / (num_trials * bin_width);
fprintf(fid,"xh(%3lu) = %12.4e; h(%3lu) = %12.4e;\n", i+1, x, i+1, h);
x = xmin + ((float)i + 1.0f)*bin_width;
F_hat += h;
fprintf(fid,"xH(%3lu) = %12.4e; H(%3lu) = %12.4e;\n", i+1, x, i+1, F_hat);
}
fprintf(fid,"H = H/H(end);\n");
for (i=0; i<num_steps; i++) {
x = xmin + i*xstep;
fprintf(fid,"xf(%3lu) = %12.4e; f(%3lu) = %12.4e; F(%3lu) = %12.4e;\n", i+1, x, i+1, f[i], i+1, F[i]);
}
// plot results
fprintf(fid,"figure;\n");
fprintf(fid,"plot(xh,h,'x', xf,f,'-');\n");
fprintf(fid,"xlabel('x');\n");
fprintf(fid,"ylabel('f_x(x)');\n");
fprintf(fid,"axis([(xmin-0.1*xspan) (xmax+0.1*xspan) 0 1.1*max([h f])]);\n");
fprintf(fid,"legend('histogram','true PDF',1);\n");
// plot results
fprintf(fid,"figure;\n");
fprintf(fid,"plot(xH,H,'x', xf,F,'-');\n");
fprintf(fid,"xlabel('x');\n");
fprintf(fid,"ylabel('f_x(x)');\n");
//fprintf(fid,"axis([(xmin-0.1*xspan) (xmax+0.1*xspan) 0 1]);\n");
fprintf(fid,"legend('histogram','true CDF',0);\n");
fclose(fid);
printf("results written to %s.\n",OUTPUT_FILENAME);
printf("done.\n");
return 0;
}
|
