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// Copyright © 2023 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 the implementation of the `tensor` product.
use flint_sys::fmpq_mat::fmpq_mat_kronecker_product;
use super::MatQ;
use crate::traits::{MatrixDimensions, Tensor};
impl Tensor for MatQ {
/// Computes the tensor product of `self` with `other`.
///
/// Parameters:
/// - `other`: the value with which the tensor product is computed.
///
/// Returns the tensor product of `self` with `other`.
///
/// # Examples
/// ```
/// use qfall_math::rational::MatQ;
/// use qfall_math::traits::Tensor;
/// use std::str::FromStr;
///
/// let mat_1 = MatQ::from_str("[[1, 1],[2/3, 2/3]]").unwrap();
/// let mat_2 = MatQ::from_str("[[1, 2],[3, 4]]").unwrap();
///
/// let mat_12 = mat_1.tensor_product(&mat_2);
/// let mat_21 = mat_2.tensor_product(&mat_1);
///
/// let res_12 = "[[1, 2, 1, 2],[3, 4, 3, 4],[2/3, 4/3, 2/3, 4/3],[2, 8/3, 2, 8/3]]";
/// let res_21 = "[[1, 1, 2, 2],[2/3, 2/3, 4/3, 4/3],[3, 3, 4, 4],[2, 2, 8/3, 8/3]]";
/// assert_eq!(mat_12, MatQ::from_str(res_12).unwrap());
/// assert_eq!(mat_21, MatQ::from_str(res_21).unwrap());
/// ```
fn tensor_product(&self, other: &Self) -> Self {
let mut out = MatQ::new(
self.get_num_rows() * other.get_num_rows(),
self.get_num_columns() * other.get_num_columns(),
);
unsafe { fmpq_mat_kronecker_product(&mut out.matrix, &self.matrix, &other.matrix) };
out
}
}
#[cfg(test)]
mod test_tensor {
use crate::{
rational::MatQ,
traits::{MatrixDimensions, Tensor},
};
use std::str::FromStr;
/// Ensure that the dimensions of the tensor product are taken over correctly.
#[test]
fn dimensions_fit() {
let mat_1 = MatQ::new(17, 13);
let mat_2 = MatQ::new(3, 4);
let mat_3 = mat_1.tensor_product(&mat_2);
assert_eq!(51, mat_3.get_num_rows());
assert_eq!(52, mat_3.get_num_columns());
}
/// Ensure that the tensor works correctly with identity.
#[test]
fn identity() {
let identity = MatQ::identity(2, 2);
let mat_1 =
MatQ::from_str(&format!("[[1, 2/{}, 1],[0, {}, -1]]", u64::MAX, i64::MIN)).unwrap();
let mat_2 = identity.tensor_product(&mat_1);
let mat_3 = mat_1.tensor_product(&identity);
let cmp_mat_2 = MatQ::from_str(&format!(
"[[1, 2/{}, 1, 0, 0, 0],[0, {}, -1, 0, 0, 0],[0, 0, 0, 1, 2/{}, 1],[0, 0, 0, 0, {}, -1]]",
u64::MAX,
i64::MIN,
u64::MAX,
i64::MIN
))
.unwrap();
let cmp_mat_3 = MatQ::from_str(&format!(
"[[1, 0, 2/{}, 0, 1, 0],[0, 1, 0, 2/{}, 0, 1],[0, 0, {}, 0, -1, 0],[0, 0, 0, {}, 0, -1]]",
u64::MAX,
u64::MAX,
i64::MIN,
i64::MIN
))
.unwrap();
assert_eq!(cmp_mat_2, mat_2);
assert_eq!(cmp_mat_3, mat_3);
}
/// Ensure the tensor product works where one is a vector and the other is a matrix.
#[test]
fn vector_matrix() {
let vector = MatQ::from_str("[[1/3],[-1]]").unwrap();
let mat_1 =
MatQ::from_str(&format!("[[1, {}, 1],[0, {}, -1]]", u64::MAX, i64::MAX)).unwrap();
let mat_2 = vector.tensor_product(&mat_1);
let mat_3 = mat_1.tensor_product(&vector);
let cmp_mat_2 = MatQ::from_str(&format!(
"[[1/3, {}/3, 1/3],[0, {}/3, -1/3],[-1, -{}, -1],[0, -{}, 1]]",
u64::MAX,
i64::MAX,
u64::MAX,
i64::MAX
))
.unwrap();
let cmp_mat_3 = MatQ::from_str(&format!(
"[[1/3, {}/3, 1/3],[-1, -{}, -1],[0, {}/3, -1/3],[0, -{}, 1]]",
u64::MAX,
u64::MAX,
i64::MAX,
i64::MAX
))
.unwrap();
assert_eq!(cmp_mat_2, mat_2);
assert_eq!(cmp_mat_3, mat_3);
}
/// Ensure that the tensor product works correctly with two vectors.
#[test]
fn vector_vector() {
let vec_1 = MatQ::from_str("[[2],[1]]").unwrap();
let vec_2 =
MatQ::from_str(&format!("[[{}],[{}]]", (u64::MAX - 1) / 2, i64::MIN / 2)).unwrap();
let vec_3 = vec_1.tensor_product(&vec_2);
let vec_4 = vec_2.tensor_product(&vec_1);
let cmp_vec_3 = MatQ::from_str(&format!(
"[[{}],[{}],[{}],[{}]]",
u64::MAX - 1,
i64::MIN,
(u64::MAX - 1) / 2,
i64::MIN / 2
))
.unwrap();
let cmp_vec_4 = MatQ::from_str(&format!(
"[[{}],[{}],[{}],[{}]]",
u64::MAX - 1,
(u64::MAX - 1) / 2,
i64::MIN,
i64::MIN / 2
))
.unwrap();
assert_eq!(cmp_vec_3, vec_3);
assert_eq!(cmp_vec_4, vec_4);
}
}