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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 super::MatZ;
use crate::traits::{MatrixDimensions, Tensor};
use flint_sys::fmpz_mat::fmpz_mat_kronecker_product;
impl Tensor for MatZ {
/// 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::integer::MatZ;
/// use qfall_math::traits::Tensor;
/// use std::str::FromStr;
///
/// let mat_1 = MatZ::from_str("[[1, 1],[2, 2]]").unwrap();
/// let mat_2 = MatZ::from_str("[[1, 2],[3, 4]]").unwrap();
///
/// let mat_ab = mat_1.tensor_product(&mat_2);
/// let mat_ba = mat_2.tensor_product(&mat_1);
///
/// let res_ab = "[[1, 2, 1, 2],[3, 4, 3, 4],[2, 4, 2, 4],[6, 8, 6, 8]]";
/// let res_ba = "[[1, 1, 2, 2],[2, 2, 4, 4],[3, 3, 4, 4],[6, 6, 8, 8]]";
/// assert_eq!(mat_ab, MatZ::from_str(res_ab).unwrap());
/// assert_eq!(mat_ba, MatZ::from_str(res_ba).unwrap());
/// ```
fn tensor_product(&self, other: &Self) -> Self {
let mut out = MatZ::new(
self.get_num_rows() * other.get_num_rows(),
self.get_num_columns() * other.get_num_columns(),
);
unsafe { fmpz_mat_kronecker_product(&mut out.matrix, &self.matrix, &other.matrix) };
out
}
}
#[cfg(test)]
mod test_tensor {
use crate::{
integer::MatZ,
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 = MatZ::new(17, 13);
let mat_2 = MatZ::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 = MatZ::identity(2, 2);
let mat_1 =
MatZ::from_str(&format!("[[1, {}, 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 = MatZ::from_str(&format!(
"[[1, {}, 1, 0, 0, 0],[0, {}, -1, 0, 0, 0],[0, 0, 0, 1, {}, 1],[0, 0, 0, 0, {}, -1]]",
u64::MAX,
i64::MIN,
u64::MAX,
i64::MIN
))
.unwrap();
let cmp_mat_3 = MatZ::from_str(&format!(
"[[1, 0, {}, 0, 1, 0],[0, 1, 0, {}, 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 = MatZ::from_str("[[1],[-1]]").unwrap();
let mat_1 =
MatZ::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 = MatZ::from_str(&format!(
"[[1, {}, 1],[0, {}, -1],[-1, -{}, -1],[0, -{}, 1]]",
u64::MAX,
i64::MAX,
u64::MAX,
i64::MAX
))
.unwrap();
let cmp_mat_3 = MatZ::from_str(&format!(
"[[1, {}, 1],[-1, -{}, -1],[0, {}, -1],[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 = MatZ::from_str("[[2],[1]]").unwrap();
let vec_2 =
MatZ::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 = MatZ::from_str(&format!(
"[[{}],[{}],[{}],[{}]]",
u64::MAX - 1,
i64::MIN,
(u64::MAX - 1) / 2,
i64::MIN / 2
))
.unwrap();
let cmp_vec_4 = MatZ::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);
}
}