qfall_math/rational/mat_q/

properties.rs

// Copyright © 2023 Phil Milewski, 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 includes functionality about properties of [`MatQ`] instances.

use super::MatQ;
use crate::traits::{MatrixDimensions, MatrixGetEntry};
use flint_sys::fmpq_mat::{fmpq_mat_is_one, fmpq_mat_is_square, fmpq_mat_is_zero};

impl MatQ {
    /// Checks if a [`MatQ`] is the identity matrix.
    ///
    /// Returns `true` if every diagonal entry of the upper square matrix is `1`
    /// and all other entries are `0`.
    ///
    /// # Examples
    /// ```
    /// use qfall_math::rational::MatQ;
    ///
    /// let value = MatQ::identity(2, 2);
    /// assert!(value.is_identity());
    /// ```
    ///
    /// ```
    /// use qfall_math::rational::MatQ;
    /// use std::str::FromStr;
    ///
    /// let value = MatQ::from_str("[[1, 0],[0, 1],[0, 0]]").unwrap();
    /// assert!(value.is_identity());
    /// ```
    pub fn is_identity(&self) -> bool {
        1 == unsafe { fmpq_mat_is_one(&self.matrix) }
    }

    /// Checks if a [`MatQ`] is a square matrix.
    ///
    /// Returns `true` if the number of rows and columns is identical.
    ///
    /// # Examples
    /// ```
    /// use qfall_math::rational::MatQ;
    /// use std::str::FromStr;
    ///
    /// let value = MatQ::from_str("[[4/7, 0],[5/8, 1/9]]").unwrap();
    /// assert!(value.is_square());
    /// ```
    pub fn is_square(&self) -> bool {
        1 == unsafe { fmpq_mat_is_square(&self.matrix) }
    }

    /// Checks if every entry of a [`MatQ`] is `0`.
    ///
    /// Returns `true` if every entry is `0`.
    ///
    /// # Examples
    /// ```
    /// use qfall_math::rational::MatQ;
    /// use std::str::FromStr;
    ///
    /// let value = MatQ::from_str("[[0, 0],[0, 0]]").unwrap();
    /// assert!(value.is_zero());
    /// ```
    pub fn is_zero(&self) -> bool {
        1 == unsafe { fmpq_mat_is_zero(&self.matrix) }
    }

    /// Checks if a [`MatQ`] is symmetric.
    ///
    /// Returns `true` if we have `a_ij == a_ji` for all i,j.
    ///
    /// # Examples
    /// ```
    /// use qfall_math::rational::MatQ;
    ///
    /// let value = MatQ::identity(2,2);
    /// assert!(value.is_symmetric());
    /// ```
    pub fn is_symmetric(&self) -> bool {
        if !self.is_square() {
            return false;
        }
        for row in 0..self.get_num_rows() {
            for column in 0..row {
                if unsafe {
                    self.get_entry_unchecked(row, column) != self.get_entry_unchecked(column, row)
                } {
                    return false;
                }
            }
        }
        true
    }
}

#[cfg(test)]
mod test_is_identity {
    use super::MatQ;
    use std::str::FromStr;

    /// Ensure that is_identity returns `true` for identity matrices.
    #[test]
    fn identity_detection() {
        let ident = MatQ::identity(2, 2);

        assert!(ident.is_identity());
    }

    /// Ensure that is_identity returns `false` for non-identity matrices.
    #[test]
    fn identity_rejection() {
        let small = MatQ::from_str("[[0, 0],[2/81, 0]]").unwrap();
        let large = MatQ::from_str(&format!("[[1, 0],[0, {}]]", (u128::MAX - 1) / 2 + 2)).unwrap();

        assert!(!small.is_identity());
        assert!(!large.is_identity());
    }
}

#[cfg(test)]
mod test_is_zero {
    use super::MatQ;
    use std::str::FromStr;

    /// Ensure that is_zero returns `true` for all zero matrices.
    #[test]
    fn zero_detection() {
        let zero = MatQ::from_str("[[0, 0],[0, 0]]").unwrap();

        assert!(zero.is_zero());
    }

    /// Ensure that is_zero returns `false` for non-zero matrices.
    #[test]
    fn zero_rejection() {
        let small = MatQ::from_str("[[0, 7/8],[2, 0]]").unwrap();
        let large = MatQ::from_str(&format!("[[0, 0],[{}, 0]]", (u128::MAX - 1) / 2 + 1)).unwrap();

        assert!(!small.is_zero());
        assert!(!large.is_zero());
    }
}

#[cfg(test)]
mod test_is_square {
    use super::MatQ;
    use std::str::FromStr;

    /// Ensure that is_square returns `true` for square matrices.
    #[test]
    fn square_detection() {
        let mat_2x2 = MatQ::from_str("[[0, 4/9],[0, 0]]").unwrap();
        let mat_3x3 = MatQ::from_str("[[0, 6/123, 4/7],[0, 0, 1/213],[4/341, 6/83, 1]]").unwrap();

        assert!(mat_2x2.is_square());
        assert!(mat_3x3.is_square());
    }

    /// Ensure that is_square returns `false` for non-square matrices.
    #[test]
    fn sqaure_rejection() {
        let mat_2x3 = MatQ::from_str("[[0, 5/6, 4],[2/7, 0, 1]]").unwrap();
        let mat_3x2 = MatQ::from_str("[[9, 0],[127/71, 0],[0, 0]]").unwrap();

        assert!(!mat_2x3.is_square());
        assert!(!mat_3x2.is_square());
    }
}

#[cfg(test)]
mod test_is_symmetric {
    use super::MatQ;
    use std::str::FromStr;

    /// Ensure that is_symmetric returns `false` for non-symmetric matrices.
    #[test]
    fn symmetric_rejection() {
        let mat_2x3 = MatQ::from_str("[[0, 5/6, 4],[2/7, 0, 1]]").unwrap();
        let mat_2x2 = MatQ::from_str("[[9, 0],[127/71, 0]]").unwrap();

        assert!(!mat_2x3.is_symmetric());
        assert!(!mat_2x2.is_symmetric());
    }

    /// Ensure that is_symmetric returns `true` for symmetric matrices.
    #[test]
    fn symmetric_detection() {
        let mat_2x2 = MatQ::from_str(&format!(
            "[[{}, 1/{}],[1/{}, {}]]",
            u64::MIN,
            u64::MAX,
            u64::MAX,
            i64::MAX
        ))
        .unwrap();

        assert!(mat_2x2.is_symmetric());
    }
}