libcruft-util/test/rand/generator/normal.cpp

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#include "maths.hpp"
#include "rand/distribution/normal.hpp"
#include "tap.hpp"
#include <iostream>
#include <random>
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///////////////////////////////////////////////////////////////////////////////
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/// 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);
}
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///----------------------------------------------------------------------------
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/// 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;
}
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///////////////////////////////////////////////////////////////////////////////
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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 ();
}