69 lines
2.0 KiB
C++
69 lines
2.0 KiB
C++
|
#include "maths.hpp"
|
||
|
|
#include "rand/distribution/normal.hpp"
|
||
|
|
#include "tap.hpp"
|
||
|
|
|
||
|
|
#include <iostream>
|
||
|
|
#include <random>
|
||
|
|
|
||
|
|
|
||
|
|
/// Probability density function for a normal distribution with specified
|
||
|
|
/// mean and stddev at point `x`.
|
||
|
|
static
|
||
|
|
float pdf (float x, float mean, float stddev)
|
||
|
|
{
|
||
|
|
float const power = cruft::pow2 ((x - mean) / stddev) / -2;
|
||
|
|
float const scale = 1.f / (stddev * std::sqrt (2.f * cruft::pi<float>));
|
||
|
|
return scale * std::exp (power);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
/// Calculate the maximum difference between a histogram and a PDF for a
|
||
|
|
/// normal distribution with a number of buckets.
|
||
|
|
static
|
||
|
|
float max_histogram_error (int buckets)
|
||
|
|
{
|
||
|
|
// These constants weren't rigorously selected. Eyeballing the generated
|
||
|
|
// values suggested they had some level of precision and didn't explode
|
||
|
|
// the test's runtime.
|
||
|
|
int const BUCKETS = buckets;
|
||
|
|
int const ITERATIONS = BUCKETS * 10'000;
|
||
|
|
float const MEAN = BUCKETS / 2.f;
|
||
|
|
float const STDDEV = BUCKETS * .15f;
|
||
|
|
|
||
|
|
// Use _our_ normal distribution, not the stdlib one.
|
||
|
|
cruft::rand::distribution::normal<float> g (MEAN, STDDEV);
|
||
|
|
// We use a stdlib generator with reasonable quality just so we're not
|
||
|
|
// testing both our generator and our distributions simultaneously.
|
||
|
|
std::mt19937_64 rand;
|
||
|
|
|
||
|
|
std::vector<int> counts (BUCKETS, 0);
|
||
|
|
for (int i = 0; i < ITERATIONS; ++i) {
|
||
|
|
auto const val = g (rand);
|
||
|
|
if (val >= BUCKETS || val < 0)
|
||
|
|
continue;
|
||
|
|
counts[int (val)]++;
|
||
|
|
}
|
||
|
|
|
||
|
|
float max_diff = 0.f;
|
||
|
|
for (int i = 0; i < BUCKETS; ++i) {
|
||
|
|
float expected = pdf (i, MEAN, STDDEV);
|
||
|
|
float actual = counts[i] / float (ITERATIONS);
|
||
|
|
float diff = std::abs (expected - actual);
|
||
|
|
|
||
|
|
max_diff = std::max (max_diff, diff);
|
||
|
|
}
|
||
|
|
|
||
|
|
return max_diff;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
int main (void)
|
||
|
|
{
|
||
|
|
cruft::TAP::logger tap;
|
||
|
|
tap.expect_lt (
|
||
|
|
max_histogram_error (500),
|
||
|
|
1.e-4f,
|
||
|
|
"normal distribution histogram maximum relative error"
|
||
|
|
);
|
||
|
|
return tap.status ();
|
||
|
|
}
|