lin_algebra 0.3.0

A linear algebra package to compute image, kernel and rank of linear applications.
Documentation 
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pub mod matrix;
pub mod gf2_matrix;
pub use gf2_matrix::GF2Matrix;

#[cfg(test)]
mod tests {
    use crate::matrix::MatrixTrait;

    use super::*;

    #[test]
    fn instantiate_matrix() {
        let mat = GF2Matrix::new(vec![vec![1,0], vec![1,1]]);
        let el = mat.elements;
        assert_eq!(el, vec![vec![1,0], vec![1,1]]);
    }

    #[test]
    fn  echelon_form_matrix() {
        let mat = GF2Matrix::new(vec![vec![1,0], vec![1,1]]);
        let (ech_form, _) = mat.echelon_form();     
        assert_eq!(ech_form.elements, vec![vec![1,0], vec![0,1]]);
        let mat = GF2Matrix::new(vec![vec![1,0,0,0], vec![0,1,0,1], vec![0,1,0,1]]);
        let (ech_form, _) = mat.echelon_form();     
        assert_eq!(ech_form.elements, vec![vec![1,0,0,0], vec![0,1,0,1], vec![0,0,0,0]]);
   
    }

    #[test]
    fn echelon_form_ops() {
        let mat = GF2Matrix::new(vec![vec![1,0], vec![1,1]]);
        let (_, ops) = mat.echelon_form();
        assert_eq!(ops, vec![(1,0)])
    }

    #[test]
    fn ncols_nrows(){
        let mat = GF2Matrix::new(vec![vec![1,0,1], vec![1,1,0]]);
        assert_eq!(mat.nrows(), 2);
        assert_eq!(mat.ncols(), 3)
    }

    #[test]
    fn get_pivot(){
        assert_eq!(GF2Matrix::get_pivot(&vec![1,0,0,1]).unwrap(), 0);
        assert_eq!(GF2Matrix::get_pivot(&vec![0,1,1,0]).unwrap(), 1);
        assert_eq!(GF2Matrix::get_pivot(&vec![0,0,1,1]).unwrap(), 2);
        assert_eq!(GF2Matrix::get_pivot(&vec![0,0,0,1]).unwrap(), 3);
        assert!(GF2Matrix::get_pivot(&vec![0,0,0,0]).is_none());
    }

    #[test]
    fn is_reduced_echelon(){
        assert_eq!(GF2Matrix::new(vec![vec![1,0,0,0], vec![1,1,0,1]]).is_reduced_echelon(), false);
        assert_eq!(GF2Matrix::new(vec![vec![1,0,0,0], vec![1,1,0,1]]).is_reduced_echelon(), false);
        assert_eq!(GF2Matrix::new(vec![vec![1,1,0,1], vec![0,1,0,1]]).is_reduced_echelon(), false);
        assert_eq!(GF2Matrix::new(vec![vec![1,0,0,1], vec![0,1,0,1]]).is_reduced_echelon(), true);
        assert_eq!(GF2Matrix::new(vec![vec![1,0,0,0], vec![1,1,0,1], vec![0,0,1,1]]).is_reduced_echelon(), false);
        assert_eq!(GF2Matrix::new(vec![vec![1,0,0,0], vec![0,1,0,0], vec![0,0,1,1]]).is_reduced_echelon(), true);
        assert_eq!(GF2Matrix::new(vec![vec![1,0,0,0], vec![0,1,0,1], vec![0,1,0,1]]).is_reduced_echelon(), false);
        assert_eq!(GF2Matrix::new(vec![vec![1,0,0,0], vec![0,0,0,0], vec![0,1,0,1]]).is_reduced_echelon(), false);

    }

    #[test]
    fn is_reduced_echelon_zero_row(){
        assert_eq!(GF2Matrix::new(vec![vec![0,0,0,0], vec![1,0,0,0], vec![0,1,0,1]]).is_reduced_echelon(), false);
        assert_eq!(GF2Matrix::new(vec![vec![1,0,0,0], vec![0,0,0,0], vec![0,1,0,1]]).is_reduced_echelon(), false);
        assert_eq!(GF2Matrix::new(vec![vec![1,0,1,0], vec![0,0,0,0]]).is_reduced_echelon(), true);

    }

    #[test]
    fn rank(){
        assert_eq!(GF2Matrix::new(vec![vec![1,0,0,0], vec![0,1,0,1]]).rank(), 2);
        assert_eq!(GF2Matrix::new(vec![vec![1,0,0,0], vec![1,0,0,0]]).rank(), 1);
    }

    #[test]
    fn image(){
        let mat_1 = GF2Matrix::new(vec![vec![1,0,0,0], vec![0,1,0,1]]);
        assert_eq!(mat_1.image(), mat_1.elements);
        let mat_2 = GF2Matrix::new(vec![vec![1,0,0,0], vec![0,1,0,1], vec![0,1,0,1]]);
        assert_eq!(mat_2.image(), mat_1.elements);
        let mat = GF2Matrix::new(vec![vec![1,0,0,0], vec![0,0,0,0]]);
        assert_eq!(mat.image(), vec![vec![1,0,0,0]]);
    
    }

    #[test]
    fn kernel(){
        let mat = GF2Matrix::new(vec![vec![1,0,0,0], vec![0,1,0,1]]);
        assert_eq!(mat.kernel(), vec![vec![0,0,1,0], vec![0,1,0,1]]);
        let mat = GF2Matrix::new(vec![vec![1,0,0,0], vec![0,0,0,0], vec![0,1,0,1]]);
        assert_eq!(mat.kernel(), vec![vec![0,0,1,0], vec![0,1,0,1]])
    }

    #[test]
    fn test_solve_matrix_system(){
        let left_elements = vec![
            vec![1,0,0],
            vec![0,1,1],
            vec![1,0,1]
        ];

        let right_elements = vec![
            vec![0,0,1],
            vec![0,1,1],
            vec![1,1,1]
        ];

        let m = GF2Matrix::new(left_elements);
        let rm = GF2Matrix::new(right_elements);
        let r = m.solve_matrix_system(&rm);
        assert_eq!(r.elements, vec![vec![0,1,1], vec![0,0,1], vec![1,1,0]]);
    }

    #[test]
    fn test_solve_matrix_system_linear_dependence(){
        let left_elements = vec![
            vec![1,0,0],
            vec![0,1,1],
            vec![1,0,1],
            vec![1,1,1]
        ];

        let right_elements = vec![
            vec![0,0,1],
            vec![0,1,1],
            vec![1,1,1],
            vec![1,1,0],
        ];

        let m = GF2Matrix::new(left_elements);
        let rm = GF2Matrix::new(right_elements);
        let r = m.solve_matrix_system(&rm);
        assert_eq!(r.elements, vec![vec![0,1,1], vec![0,0,1], vec![1,1,0]]);
    }

    #[test]
    #[should_panic(expected = "Matrix must have full rank")]
    fn test_solve_matrix_system_no_full_rank(){
        let left_elements = vec![
            vec![1,0,0],
            vec![0,1,1]
        ];

        let right_elements = vec![
            vec![0,0,1],
            vec![0,1,1],
            vec![1,1,1]
        ];

        let m = GF2Matrix::new(left_elements);
        let rm = GF2Matrix::new(right_elements);
        m.solve_matrix_system(&rm);
    }

    #[test]
    fn test_solve(){
        let left_elements = vec![
            vec![1,0,0],
            vec![0,1,1],
            vec![1,0,1]
        ];

        let b = vec![0,0,1];

        let m = GF2Matrix::new(left_elements);
        let r = m.solve(&b);
        assert_eq!(r, vec![0,1,1]);
    }

    #[test]
    #[should_panic(expected = "Matrix must have full rank")]
    fn test_solve_no_full_rank(){
        let left_elements = vec![
            vec![1,0,0],
            vec![0,1,1]
        ];

        let b = vec![0,0,1];

        let m = GF2Matrix::new(left_elements);
        m.solve(&b);
    }

}