// Copyright 2024 Marvin Beckmann
//
// This file is part of qFALL-math.
//
// qFALL-math is free software: you can redistribute it and/or modify it under
// the terms of the Mozilla Public License Version 2.0 as published by the
// Mozilla Foundation. See <https://mozilla.org/en-US/MPL/2.0/>.
//! This module contains sampling algorithms for Gaussian distributions over [`MatQ`].
use crate::{
error::MathError,
macros::seeded::seedable_function,
rational::{MatQ, Q},
traits::{MatrixDimensions, MatrixGetEntry, MatrixSetEntry},
utils::sample::uniform::SamplerRng,
};
use probability::{
prelude::{Gaussian, Sample},
source,
};
use rand::Rng;
use std::fmt::Display;
impl MatQ {
seedable_function!(
/// Chooses a [`MatQ`] instance according to the continuous Gaussian distribution.
/// Here, each entry is chosen according to the provided distribution.
///
/// Parameters:
/// - `center`: specifies the center for each entry of the matrix individually
/// - `sigma`: specifies the standard deviation
#[seeded]
/// - `seed`: specifies the 256-bit seed of the PRNG used for sampling
#[optionally_seeded]
/// - `seed`: specifies an optional 256-bit seed of the PRNG used for sampling.
#[optionally_seeded]
/// If `None` is provided, a fresh [`ThreadRng`](rand::rngs::ThreadRng) is used instead.
///
/// Returns new [`MatQ`] sample chosen according to the specified continuous Gaussian
/// distribution or a [`MathError`] if the specified parameters were not chosen
/// appropriately (`sigma > 0`).
///
/// # Examples
/// ```
/// use qfall_math::rational::MatQ;
///
#[unseeded]
/// let sample = MatQ::sample_gauss(&MatQ::new(5, 5), 1).unwrap();
#[seeded]
/// let sample = MatQ::sample_gauss_seeded(&MatQ::new(5, 5), 1, [42; 32]).unwrap();
/// ```
///
/// # Errors and Failures
/// - Returns a [`MathError`] of type [`NonPositive`](MathError::NonPositive)
/// if `sigma <= 0`.
pub(crate) fn sample_gauss(
center: &MatQ,
sigma: impl Into<f64>,
seed: Option<[u8; 32]>,
) -> Result<MatQ, MathError> {
// derives an independent seed for every call of a seedable function below,
// see the documentation of `seedable_function` in `src/macros/seeded.rs`
let mut rng = SamplerRng::new(seed);
let mut out = MatQ::new(center.get_num_rows(), center.get_num_columns());
let sigma = sigma.into();
for i in 0..out.get_num_rows() {
for j in 0..out.get_num_columns() {
let center_entry_ij = center.get_entry(i, j)?;
let sample = Q::sample_gauss_optionally_seeded(
center_entry_ij,
sigma,
rng.derive_seed(),
)?;
unsafe { out.set_entry_unchecked(i, j, sample) };
}
}
Ok(out)
}
);
seedable_function!(
/// Chooses a [`MatQ`] instance according to the continuous Gaussian distribution.
/// Here, each entry is chosen according to the provided distribution and each entry
/// is sampled with the same center.
///
/// Parameters:
/// - `num_rows`: specifies the number of rows of the sampled matrix
/// - `num_cols`: specifies the number of columns of the sampled matrix
/// - `center`: specifies the same center for each entry of the matrix
/// - `sigma`: specifies the standard deviation
#[seeded]
/// - `seed`: specifies the 256-bit seed of the PRNG used for sampling
#[optionally_seeded]
/// - `seed`: specifies an optional 256-bit seed of the PRNG used for sampling.
#[optionally_seeded]
/// If `None` is provided, a fresh [`ThreadRng`](rand::rngs::ThreadRng) is used instead.
///
/// Returns new [`MatQ`] sample chosen according to the specified continuous Gaussian
/// distribution or a [`MathError`] if the specified parameters were not chosen
/// appropriately (`sigma > 0`).
///
/// # Examples
/// ```
/// use qfall_math::rational::{Q, MatQ};
///
/// let center = Q::from((5,2));
///
#[unseeded]
/// let sample = MatQ::sample_gauss_same_center(5, 5, ¢er, 1).unwrap();
#[seeded]
/// let sample = MatQ::sample_gauss_same_center_seeded(5, 5, ¢er, 1, [42; 32]).unwrap();
/// ```
///
/// # Errors and Failures
/// - Returns a [`MathError`] of type [`NonPositive`](MathError::NonPositive)
/// if `sigma <= 0`.
///
/// # Panics ...
/// - if the number of rows or columns is negative, `0`, or does not fit into an [`i64`].
pub(crate) fn sample_gauss_same_center(
num_rows: impl TryInto<i64> + Display,
num_cols: impl TryInto<i64> + Display,
center: impl Into<Q>,
sigma: impl Into<f64>,
seed: Option<[u8; 32]>,
) -> Result<MatQ, MathError> {
let mut out = MatQ::new(num_rows, num_cols);
let (center, sigma) = (center.into(), sigma.into());
if sigma <= 0.0 {
return Err(MathError::NonPositive(format!(
"The sigma has to be positive and not zero, but the provided value is {sigma}."
)));
}
let mut rng = SamplerRng::new(seed);
let mut source = source::default(rng.next_u64());
// Instead of sampling with a center of c, we sample with center 0 and add the
// center later. These are equivalent and this way we can sample in larger ranges
let sampler = Gaussian::new(0.0, sigma);
for i in 0..out.get_num_rows() {
for j in 0..out.get_num_columns() {
let mut sample = Q::from(sampler.sample(&mut source));
sample += ¢er;
unsafe { out.set_entry_unchecked(i, j, sample) };
}
}
Ok(out)
}
);
}
#[cfg(test)]
mod test_sample_gauss {
use crate::utils::sample::test_seed;
use crate::{rational::MatQ, traits::MatrixDimensions};
/// Ensure that an error is returned if `sigma` is not positive
#[test]
fn non_positive_sigma() {
for seeded in [false, true] {
let center = MatQ::new(5, 5);
for sigma in [0, -1] {
assert!(
MatQ::sample_gauss_optionally_seeded(¢er, sigma, seeded.then(test_seed))
.is_err()
)
}
}
}
/// Ensure that the samples are of correct dimension
#[test]
fn correct_dimension() {
for seeded in [false, true] {
for (x, y) in [(5, 5), (1, 10), (10, 1)] {
let center = MatQ::new(x, y);
let sample =
MatQ::sample_gauss_optionally_seeded(¢er, 1, seeded.then(test_seed))
.unwrap();
assert_eq!(center.get_num_rows(), sample.get_num_rows());
assert_eq!(center.get_num_columns(), sample.get_num_columns());
}
}
}
/// Checks whether the same seed results in the same sample.
#[test]
fn same_seed_same_sample() {
use crate::rational::MatQ;
let sample_0 = MatQ::sample_gauss_seeded(&MatQ::new(5, 5), 1, [42; 32]).unwrap();
let sample_1 = MatQ::sample_gauss_seeded(&MatQ::new(5, 5), 1, [42; 32]).unwrap();
assert_eq!(sample_0, sample_1);
}
/// Checks whether the seeded variant outputs the known sample for a fixed seed.
#[test]
fn known_answer() {
use crate::rational::MatQ;
let sample = MatQ::sample_gauss_seeded(&MatQ::new(5, 5), 1, [42; 32]).unwrap();
assert_eq!(
"[[-4945271350741753/2251799813685248, 1117106275816641/2251799813685248, 4434555541986695/4503599627370496, -6539644456987479/4503599627370496, -4677571318743725/9007199254740992],[3908611230479557/4503599627370496, 5573654194347613/9007199254740992, 5403302998575453/9007199254740992, 2430733040590187/9007199254740992, 1031578748721027/4503599627370496],[-4883384444105643/9007199254740992, -3764944878914815/2251799813685248, -7161261431757703/2251799813685248, -5092217727994081/9007199254740992, -2353868661553283/4503599627370496],[4063319294552583/9007199254740992, 2715651668966247/2251799813685248, -7464330407867217/9007199254740992, -8311230105715239/72057594037927936, -4329275745410667/2251799813685248],[-3100112952240901/18014398509481984, 3412362636860941/576460752303423488, -4689787695738317/4503599627370496, 3370477389923299/2251799813685248, 1145812122695171/4503599627370496]]",
sample.to_string()
);
}
/// Checks whether the unseeded and the seeded function are available.
#[test]
fn availability() {
use crate::rational::MatQ;
// explicitly checks the existence of the unseeded and the seeded function
let _ = MatQ::sample_gauss(&MatQ::new(5, 5), 1);
let _ = MatQ::sample_gauss_seeded(&MatQ::new(5, 5), 1, test_seed());
}
}
#[cfg(test)]
mod test_sample_gauss_same_center {
use crate::utils::sample::test_seed;
use crate::{rational::MatQ, traits::MatrixDimensions};
/// Ensure that an error is returned if `sigma` is not positive
#[test]
fn non_positive_sigma() {
for seeded in [false, true] {
for sigma in [0, -1] {
assert!(
MatQ::sample_gauss_same_center_optionally_seeded(
5,
5,
0,
sigma,
seeded.then(test_seed)
)
.is_err()
)
}
}
}
/// Ensure that the samples are of correct dimension
#[test]
fn correct_dimension() {
for seeded in [false, true] {
for (x, y) in [(5, 5), (1, 10), (10, 1)] {
let sample = MatQ::sample_gauss_same_center_optionally_seeded(
x,
y,
0,
1,
seeded.then(test_seed),
)
.unwrap();
assert_eq!(x, sample.get_num_rows());
assert_eq!(y, sample.get_num_columns());
}
}
}
/// Ensure that a negative number of rows causes a panic
#[test]
fn negative_number_rows() {
for seeded in [false, true] {
let result = std::panic::catch_unwind(|| {
let _ = MatQ::sample_gauss_same_center_optionally_seeded(
-1,
1,
0,
1,
seeded.then(test_seed),
)
.unwrap();
});
assert!(result.is_err());
}
}
/// Ensure that a negative number of columns causes a panic
#[test]
fn negative_number_columns() {
for seeded in [false, true] {
let result = std::panic::catch_unwind(|| {
let _ = MatQ::sample_gauss_same_center_optionally_seeded(
1,
-1,
0,
1,
seeded.then(test_seed),
)
.unwrap();
});
assert!(result.is_err());
}
}
/// Checks whether the same seed results in the same sample.
#[test]
fn same_seed_same_sample() {
use crate::rational::{MatQ, Q};
let center = Q::from((5, 2));
let sample_0 = MatQ::sample_gauss_same_center_seeded(5, 5, ¢er, 1, [42; 32]).unwrap();
let sample_1 = MatQ::sample_gauss_same_center_seeded(5, 5, ¢er, 1, [42; 32]).unwrap();
assert_eq!(sample_0, sample_1);
}
/// Checks whether the seeded variant outputs the known sample for a fixed seed.
#[test]
fn known_answer() {
use crate::rational::{MatQ, Q};
let center = Q::from((5, 2));
let sample = MatQ::sample_gauss_same_center_seeded(5, 5, ¢er, 1, [42; 32]).unwrap();
assert_eq!(
"[[8525870560382491/2251799813685248, 17119947174636167/4503599627370496, 1259641011116081/1125899906842624, 39499623190823409/18014398509481984, 3385362557569009/4503599627370496],[3938234223310835/2251799813685248, 17542906212059721/4503599627370496, 16597635972078743/4503599627370496, 8266208908835155/2251799813685248, 39314002964552041/18014398509481984],[881046098121435/562949953421312, 29287177467398541/9007199254740992, 2413886157177875/562949953421312, 981581273026087/281474976710656, 43488189713909861/18014398509481984],[6127343065657779/4503599627370496, 30937068457746009/9007199254740992, 27849268867401663/9007199254740992, 2727502571816845/2251799813685248, 27040028183639271/9007199254740992],[13289162739536831/4503599627370496, 87685859291908515/36028797018963968, 93185871850127433/36028797018963968, 2111809547791415/1125899906842624, 4077230155367515/2251799813685248]]",
sample.to_string()
);
}
/// Checks whether the unseeded and the seeded function are available.
#[test]
fn availability() {
use crate::rational::{MatQ, Q};
let center = Q::from((5, 2));
// explicitly checks the existence of the unseeded and the seeded function
let _ = MatQ::sample_gauss_same_center(5, 5, ¢er, 1);
let _ = MatQ::sample_gauss_same_center_seeded(5, 5, ¢er, 1, test_seed());
}
}