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
// Random module
// Current state:
// - Autotests matching for rng functions
// - Distribution tests turned off for nakm, ricek, uniform
// - Some replacement may be possible from stdlib or other crates
// - Module orginization still WIP
pub mod exp;
pub mod gamma;
pub mod nakm;
pub mod normal;
pub mod ricek;
pub mod scramble;
pub mod uniform;
pub mod weib;
pub use exp::*;
pub use gamma::*;
pub use nakm::*;
pub use normal::*;
pub use ricek::*;
pub use uniform::*;
pub use weib::*;
#[cfg(test)]
mod tests {
use super::*;
use test_macro::autotest_annotate;
use approx::assert_relative_eq;
use crate::error::Result;
#[test]
#[autotest_annotate(autotest_random_config)]
fn test_random_config() {
// Exponential: lambda out of range
assert!(randexpf(-1.0).is_err());
assert!(randexpf_pdf(0.0, -1.0).is_err());
assert!(randexpf_cdf(0.0, -1.0).is_err());
// Exponential: pdf, cdf with valid input, but negative variable
assert_relative_eq!(randexpf_pdf(-2.0, 2.3).unwrap(), 0.0);
assert_relative_eq!(randexpf_cdf(-2.0, 2.3).unwrap(), 0.0);
// Gamma: parameters out of range (alpha)
assert!(randgammaf(-1.0, 1.0).is_err());
assert!(randgammaf_pdf(0.0, -1.0, 1.0).is_err());
assert!(randgammaf_cdf(0.0, -1.0, 1.0).is_err());
// Gamma: parameters out of range (beta)
assert!(randgammaf(1.0, -1.0).is_err());
assert!(randgammaf_pdf(0.0, 1.0, -1.0).is_err());
assert!(randgammaf_cdf(0.0, 1.0, -1.0).is_err());
// Gamma: delta function parameter out of range
// TODO not a public function, maybe test
// assert!(randgammaf_delta(-1.0).is_err());
// Gamma: pdf, cdf with valid input, but negative variable
assert_relative_eq!(randgammaf_pdf(-2.0, 1.2, 2.3).unwrap(), 0.0);
assert_relative_eq!(randgammaf_cdf(-2.0, 1.2, 2.3).unwrap(), 0.0);
// Nakagami-m: parameters out of range (m)
assert!(randnakmf(0.2, 1.0).is_err());
assert!(randnakmf_pdf(0.0, 0.2, 1.0).is_err());
assert!(randnakmf_cdf(0.0, 0.2, 1.0).is_err());
// Nakagami-m: parameters out of range (omega)
assert!(randnakmf(1.0, -1.0).is_err());
assert!(randnakmf_pdf(0.0, 1.0, -1.0).is_err());
assert!(randnakmf_cdf(0.0, 1.0, -1.0).is_err());
// Nakagami-m: pdf, cdf with valid input, but negative variable
assert_relative_eq!(randnakmf_pdf(-2.0, 1.2, 2.3).unwrap(), 0.0);
assert_relative_eq!(randnakmf_cdf(-2.0, 1.2, 2.3).unwrap(), 0.0);
}
// Helper functions for histogram operations
fn support_histogram_add(value: f32, bins: &mut [f32], num_bins: usize, vmin: f32, vmax: f32) -> usize {
if value < vmin || value > vmax {
return 0;
}
let vstep = (vmax - vmin) / num_bins as f32;
let mut indexf = (value - vmin) / vstep;
if indexf < 0.0 {
indexf = 0.0;
}
if indexf >= num_bins as f32 {
indexf = (num_bins - 1) as f32;
}
let index = indexf as usize;
bins[index] += 1.0;
index
}
fn support_histogram_normalize(bins: &mut [f32], num_bins: usize, num_trials: usize, vmin: f32, vmax: f32) -> f32 {
let vstep = (vmax - vmin) / num_bins as f32;
let area = num_trials as f32 * vstep;
for bin in bins.iter_mut() {
*bin /= area;
}
area
}
fn support_histogram_validate(bins: &[f32], pdf: impl Fn(f32) -> Result<f32>, cdf: impl Fn(f32) -> Result<f32>, num_bins: usize, num_trials: usize, vmin: f32, vmax: f32, tol: f32) {
const NUM_PDF_STEPS: usize = 20;
let mut bins_normalized = bins.to_vec();
support_histogram_normalize(&mut bins_normalized, num_bins, num_trials, vmin, vmax);
let vstep = (vmax - vmin) / num_bins as f32;
for i in 0..num_bins {
let mut pdf_avg = 0.0;
for j in 0..NUM_PDF_STEPS {
let x = vmin + (i as f32 + (j as f32 / NUM_PDF_STEPS as f32)) * vstep;
pdf_avg += pdf(x).unwrap() / NUM_PDF_STEPS as f32;
}
// println!("bin {:?}, range: {:?}, normalized: {:?}, pdf_avg: {:?}", i, (vmin + i as f32 * vstep, vmin + (i + 1) as f32 * vstep), bins_normalized[i], pdf_avg);
assert_relative_eq!(bins_normalized[i], pdf_avg, epsilon = tol * pdf_avg);
}
let mut accum = cdf(vmin).unwrap();
for i in 1..num_bins {
let right = vmin + i as f32 * vstep;
accum += bins_normalized[i-1] * vstep;
// println!("accum: {:?}, cdf(right): {:?}", accum, cdf(right).unwrap());
let cdf_val = cdf(right).unwrap();
assert_relative_eq!(accum, cdf_val, epsilon = tol * cdf_val);
}
}
#[test]
#[autotest_annotate(autotest_distribution_randnf)]
fn test_distribution_randnf() {
let num_trials = 10000000;
let eta = 0.0;
let sig = 1.0;
let tol = 0.1;
let num_bins = 31;
let mut bins = vec![0.0; num_bins];
let vmin = -3.0;
let vmax = 3.0;
// compute histogram
for _ in 0..num_trials {
let v = randnf() * sig + eta;
support_histogram_add(v, &mut bins, num_bins, vmin, vmax);
}
let pdf = |v| randnf_pdf(v, eta, sig);
let cdf = |v| randnf_cdf(v, eta, sig);
// validate distributions
support_histogram_validate(&bins, pdf, cdf, num_bins, num_trials, vmin, vmax, tol);
}
#[test]
fn test_distribution_randexpf() {
let num_trials = 10000000;
let lambda = 1.3;
let tol = 0.1;
let num_bins = 21;
let mut bins = vec![0.0; num_bins];
let vmin = -1.0;
let vmax = 6.0;
// compute histogram
for _ in 0..num_trials {
let v = randexpf(lambda).unwrap();
support_histogram_add(v, &mut bins, num_bins, vmin, vmax);
}
let pdf = |v| randexpf_pdf(v, lambda);
let cdf = |v| randexpf_cdf(v, lambda);
// validate distributions
support_histogram_validate(&bins, pdf, cdf, num_bins, num_trials, vmin, vmax, tol);
}
#[test]
fn test_distribution_randgammaf() {
let num_trials = 1000000;
let alpha = 2.5;
let beta = 1.0;
let tol = 0.1;
let num_bins = 21;
let mut bins = vec![0.0; num_bins];
let vmin = -1.0;
let vmax = 9.0;
// compute histogram
for _ in 0..num_trials {
let v = randgammaf(alpha, beta).unwrap();
support_histogram_add(v, &mut bins, num_bins, vmin, vmax);
}
let pdf = |v| randgammaf_pdf(v, alpha, beta);
let cdf = |v| randgammaf_cdf(v, alpha, beta);
// validate distributions
support_histogram_validate(&bins, pdf, cdf, num_bins, num_trials, vmin, vmax, tol);
}
// #[test]
// fn test_distribution_randnakmf() {
// let num_trials = 10000000;
// let m = 2.0;
// let omega = 1.0;
// let tol = 0.1;
// let num_bins = 28;
// let mut bins = vec![0.0; num_bins];
// let vmin = -1.0;
// let vmax = 2.5;
// // compute histogram
// for _ in 0..num_trials {
// let v = randnakmf(m, omega).unwrap();
// support_histogram_add(v, &mut bins, num_bins, vmin, vmax);
// }
// let pdf = |v| randnakmf_pdf(v, m, omega);
// let cdf = |v| randnakmf_cdf(v, m, omega);
// // validate distributions
// support_histogram_validate(&bins, pdf, cdf, num_bins, num_trials, vmin, vmax, tol);
// }
// #[test]
// fn test_distribution_randricekf() {
// let num_trials = 5000000;
// let k = 2.0;
// let sigma = 1.0;
// let tol = 0.1;
// let num_bins = 24;
// let mut bins = vec![0.0; num_bins];
// let vmin = -1.0;
// let vmax = 5.0;
// // compute histogram
// for _ in 0..num_trials {
// let v = randricekf(k, sigma).unwrap();
// support_histogram_add(v, &mut bins, num_bins, vmin, vmax);
// }
// let pdf = |v| randricekf_pdf(v, k, sigma);
// let cdf = |v| randricekf_cdf(v, k, sigma);
// // validate distributions
// support_histogram_validate(&bins, pdf, cdf, num_bins, num_trials, vmin, vmax, tol);
// }
// #[test]
// fn test_distribution_randweibf() {
// let num_trials = 1000000;
// let alpha = 1.0;
// let beta = 2.0;
// let gamma = 6.0;
// let tol = 0.1;
// let num_bins = 21;
// let mut bins = vec![0.0; num_bins];
// let vmin = -1.0;
// let vmax = 9.0;
// // compute histogram
// for _ in 0..num_trials {
// let v = randweibf(alpha, beta, gamma).unwrap();
// support_histogram_add(v, &mut bins, num_bins, vmin, vmax);
// }
// let pdf = |v| randweibf_pdf(v, alpha, beta, gamma);
// let cdf = |v| randweibf_cdf(v, alpha, beta, gamma);
// // validate distributions
// support_histogram_validate(&bins, pdf, cdf, num_bins, num_trials, vmin, vmax, tol);
// }
// #[test]
// fn test_distribution_randuf() {
// let num_trials = 248000;
// let a = 10.0;
// let b = 25.0;
// let tol = 0.05;
// let num_bins = 59;
// let mut bins = vec![0.0; num_bins];
// let vmin = 5.0;
// let vmax = 35.0;
// // compute histogram
// for _ in 0..num_trials {
// let v = randuf(a, b).unwrap();
// support_histogram_add(v, &mut bins, num_bins, vmin, vmax);
// }
// let pdf = |v| randuf_pdf(v, a, b);
// let cdf = |v| randuf_cdf(v, a, b);
// // validate distributions
// support_histogram_validate(&bins, pdf, cdf, num_bins, num_trials, vmin, vmax, tol);
// }
}