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// Copyright © 2023 Niklas Siemer
//
// 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 algorithms for sampling
//! according to the binomial distribution.
use crate::{
error::MathError,
integer::Z,
integer_mod_q::{MatZq, Modulus},
rational::Q,
traits::{MatrixDimensions, MatrixSetEntry},
utils::sample::binomial::BinomialSampler,
};
use std::fmt::Display;
impl MatZq {
/// Outputs a [`MatZq`] instance with entries chosen according to the binomial
/// distribution parameterized by `n` and `p`.
///
/// Parameters:
/// - `num_rows`: specifies the number of rows the new matrix should have
/// - `num_cols`: specifies the number of columns the new matrix should have
/// - `modulus`: specifies the [`Modulus`] of the new [`MatZq`] instance
/// - `n`: specifies the number of trials
/// - `p`: specifies the probability of success
///
/// Returns a new [`MatZq`] instance with entries chosen
/// according to the binomial distribution or a [`MathError`]
/// if `n < 0`, `p ∉ (0,1)`, `n` does not fit into an [`i64`],
/// or the dimensions of the matrix were chosen too small.
///
/// # Examples
/// ```
/// use qfall_math::integer_mod_q::MatZq;
///
/// let sample = MatZq::sample_binomial(2, 2, 7, 2, 0.5).unwrap();
/// ```
///
/// # Errors and Failures
/// - Returns a [`MathError`] of type [`InvalidIntegerInput`](MathError::InvalidIntegerInput)
/// if `n < 0`.
/// - Returns a [`MathError`] of type [`InvalidInterval`](MathError::InvalidInterval)
/// if `p ∉ (0,1)`.
/// - Returns a [`MathError`] of type [`ConversionError`](MathError::ConversionError)
/// if `n` does not fit into an [`i64`].
///
/// # Panics ...
/// - if the provided number of rows and columns are not suited to create a matrix.
/// For further information see [`MatZq::new`].
/// - if `modulus` is smaller than `2`.
pub fn sample_binomial(
num_rows: impl TryInto<i64> + Display,
num_cols: impl TryInto<i64> + Display,
modulus: impl Into<Modulus>,
n: impl Into<Z>,
p: impl Into<Q>,
) -> Result<Self, MathError> {
Self::sample_binomial_with_offset(num_rows, num_cols, 0, modulus, n, p)
}
/// Outputs a [`MatZq`] instance with entries chosen according to the binomial
/// distribution parameterized by `n` and `p` with given `offset`.
///
/// Parameters:
/// - `num_rows`: specifies the number of rows the new matrix should have
/// - `num_cols`: specifies the number of columns the new matrix should have
/// - `offset`: specifies an offset applied to each sample
/// collected from the binomial distribution
/// - `modulus`: specifies the [`Modulus`] of the new [`MatZq`] instance
/// - `n`: specifies the number of trials
/// - `p`: specifies the probability of success
///
/// Returns a new [`MatZq`] instance with entries chosen
/// according to the binomial distribution or a [`MathError`]
/// if `n < 0`, `p ∉ (0,1)`, `n` does not fit into an [`i64`],
/// or the dimensions of the matrix were chosen too small.
///
/// # Examples
/// ```
/// use qfall_math::integer_mod_q::MatZq;
///
/// let sample = MatZq::sample_binomial_with_offset(2, 2, -1, 7, 2, 0.5).unwrap();
/// ```
///
/// # Errors and Failures
/// - Returns a [`MathError`] of type [`InvalidIntegerInput`](MathError::InvalidIntegerInput)
/// if `n < 0`.
/// - Returns a [`MathError`] of type [`InvalidInterval`](MathError::InvalidInterval)
/// if `p ∉ (0,1)`.
/// - Returns a [`MathError`] of type [`ConversionError`](MathError::ConversionError)
/// if `n` does not fit into an [`i64`].
///
/// # Panics ...
/// - if the provided number of rows and columns are not suited to create a matrix.
/// For further information see [`MatZq::new`].
/// - if `modulus` is smaller than `2`.
pub fn sample_binomial_with_offset(
num_rows: impl TryInto<i64> + Display,
num_cols: impl TryInto<i64> + Display,
offset: impl Into<Z>,
modulus: impl Into<Modulus>,
n: impl Into<Z>,
p: impl Into<Q>,
) -> Result<Self, MathError> {
let offset: Z = offset.into();
let mut bin_sampler = BinomialSampler::init(n, p)?;
let mut matrix = MatZq::new(num_rows, num_cols, modulus);
for row in 0..matrix.get_num_rows() {
for col in 0..matrix.get_num_columns() {
let mut sample = bin_sampler.sample();
sample += &offset;
unsafe { matrix.set_entry_unchecked(row, col, sample) };
}
}
Ok(matrix)
}
}
#[cfg(test)]
mod test_sample_binomial {
use super::{MatZq, Q, Z};
use crate::traits::{MatrixDimensions, MatrixGetEntry};
// As all major tests regarding an appropriate binomial distribution,
// whether the correct interval is kept, and if the errors are thrown correctly,
// are performed in the `utils` module, we omit these tests here.
/// Checks whether the boundaries of the interval are kept.
#[test]
fn boundaries_kept() {
for _ in 0..8 {
let matrix = MatZq::sample_binomial(1, 1, 7, 2, 0.5).unwrap();
let sample: Z = matrix.get_entry(0, 0).unwrap();
assert!(Z::ZERO <= sample || sample <= 2);
}
}
/// Checks whether matrices with at least one dimension chosen smaller than `1`
/// or too big for an [`i64`] results in an error.
#[should_panic]
#[test]
fn false_size() {
let _ = MatZq::sample_binomial(0, 3, 7, 1, 0.5);
}
/// Checks whether `sample_binomial` is available for all types
/// implementing [`Into<Z>`], i.e. u8, u16, u32, u64, i8, ...
/// and [`Into<Q>`], i.e. u8, u16, i8, i16, f32, f64, ...
/// and [`Into<Modulus>`], i.e. u8, u16, u32, u64, i8, ...
#[test]
fn availability() {
let _ = MatZq::sample_binomial(1, 1, 7u8, 1u16, 7u8);
let _ = MatZq::sample_binomial(1, 1, 7u16, 1u32, 7u16);
let _ = MatZq::sample_binomial(1, 1, 7u32, 1u64, 7u32);
let _ = MatZq::sample_binomial(1, 1, 7u64, 1i8, 7u64);
let _ = MatZq::sample_binomial(1, 1, 7i8, 1i16, 7i8);
let _ = MatZq::sample_binomial(1, 1, 7i16, 1i32, 7i16);
let _ = MatZq::sample_binomial(1, 1, 7i32, 1i64, 7i32);
let _ = MatZq::sample_binomial(1, 1, 7i64, Z::ONE, 7i64);
let _ = MatZq::sample_binomial(1, 1, 7, 1u8, 0.5f32);
let _ = MatZq::sample_binomial(1, 1, 7, 1u8, 0.5f64);
let _ = MatZq::sample_binomial(1, 1, 7, 1, Q::from((1, 2)));
}
/// Checks whether the size of uniformly random sampled matrices
/// fits the specified dimensions.
#[test]
fn matrix_size() {
let mat_0 = MatZq::sample_binomial(3, 3, 7, 1, 0.5).unwrap();
let mat_1 = MatZq::sample_binomial(4, 1, 7, 1, 0.5).unwrap();
let mat_2 = MatZq::sample_binomial(1, 5, 7, 1, 0.5).unwrap();
let mat_3 = MatZq::sample_binomial(15, 20, 7, 1, 0.5).unwrap();
assert_eq!(3, mat_0.get_num_rows());
assert_eq!(3, mat_0.get_num_columns());
assert_eq!(4, mat_1.get_num_rows());
assert_eq!(1, mat_1.get_num_columns());
assert_eq!(1, mat_2.get_num_rows());
assert_eq!(5, mat_2.get_num_columns());
assert_eq!(15, mat_3.get_num_rows());
assert_eq!(20, mat_3.get_num_columns());
}
}
#[cfg(test)]
mod test_sample_binomial_with_offset {
use super::{MatZq, Q, Z};
use crate::traits::{MatrixDimensions, MatrixGetEntry};
// As all major tests regarding an appropriate binomial distribution,
// whether the correct interval is kept, and if the errors are thrown correctly,
// are performed in the `utils` module, we omit these tests here.
/// Checks whether the boundaries of the interval are kept.
#[test]
fn boundaries_kept() {
for _ in 0..8 {
let matrix = MatZq::sample_binomial_with_offset(1, 1, -1, 7, 2, 0.5).unwrap();
let sample: Z = matrix.get_entry(0, 0).unwrap();
assert!(Z::MINUS_ONE <= sample || sample <= Z::ONE);
}
}
/// Checks whether matrices with at least one dimension chosen smaller than `1`
/// or too big for an [`i64`] results in an error.
#[should_panic]
#[test]
fn false_size() {
let _ = MatZq::sample_binomial_with_offset(0, 3, 0, 7, 1, 0.5);
}
/// Checks whether `sample_binomial_with_offset` is available for all types
/// implementing [`Into<Z>`], i.e. u8, u16, u32, u64, i8, ...
/// and [`Into<Q>`], i.e. u8, u16, i8, i16, f32, f64, ...
/// and [`Into<Modulus>`], i.e. u8, u16, u32, u64, i8, ...
#[test]
fn availability() {
let _ = MatZq::sample_binomial_with_offset(1, 1, 0u8, 7u8, 1u16, 7u8);
let _ = MatZq::sample_binomial_with_offset(1, 1, 0u16, 7u16, 1u32, 7u16);
let _ = MatZq::sample_binomial_with_offset(1, 1, 0u32, 7u32, 1u64, 7u32);
let _ = MatZq::sample_binomial_with_offset(1, 1, 0u64, 7u64, 1i8, 7u64);
let _ = MatZq::sample_binomial_with_offset(1, 1, 0i8, 7i8, 1i16, 7i8);
let _ = MatZq::sample_binomial_with_offset(1, 1, 0i16, 7i16, 1i32, 7i16);
let _ = MatZq::sample_binomial_with_offset(1, 1, 0i64, 7i32, 1i64, 7i32);
let _ = MatZq::sample_binomial_with_offset(1, 1, 0, 7i64, Z::ONE, 7i64);
let _ = MatZq::sample_binomial_with_offset(1, 1, 0, 7, 1u8, 0.5f32);
let _ = MatZq::sample_binomial_with_offset(1, 1, 0, 7, 1u8, 0.5f64);
let _ = MatZq::sample_binomial_with_offset(1, 1, 0, 7, 1, Q::from((1, 2)));
}
/// Checks whether the size of uniformly random sampled matrices
/// fits the specified dimensions.
#[test]
fn matrix_size() {
let mat_0 = MatZq::sample_binomial_with_offset(3, 3, 0, 7, 1, 0.5).unwrap();
let mat_1 = MatZq::sample_binomial_with_offset(4, 1, 0, 7, 1, 0.5).unwrap();
let mat_2 = MatZq::sample_binomial_with_offset(1, 5, 0, 7, 1, 0.5).unwrap();
let mat_3 = MatZq::sample_binomial_with_offset(15, 20, 0, 7, 1, 0.5).unwrap();
assert_eq!(3, mat_0.get_num_rows());
assert_eq!(3, mat_0.get_num_columns());
assert_eq!(4, mat_1.get_num_rows());
assert_eq!(1, mat_1.get_num_columns());
assert_eq!(1, mat_2.get_num_rows());
assert_eq!(5, mat_2.get_num_columns());
assert_eq!(15, mat_3.get_num_rows());
assert_eq!(20, mat_3.get_num_columns());
}
}