triangle_matrix

Upper and lower triangle matrix indexing operations. Provides indexing operations for one dimensional collections using Index<usize>. Requires implementing Triangle for any Index<usize> type, and optionally TriangleMut for any IndexMut<usize> type. Usage requires delegation to the collection, and the axis length, n.

use crate::triangle_matrix::{Triangle, TriangleMut};

// A vector represented as a triangle matrix.
struct TriVec(usize, Vec<usize>);

impl Triangle for TriVec {
    type Inner = Vec<usize>;

    fn n(&self) -> usize {
        self.0
    }

    fn inner(&self) -> &Self::Inner {
        &self.1
    }
}

impl TriangleMut for TriVec {
    fn inner_mut(&mut self) -> &mut Self::Inner {
        &mut self.1
    }
}

Triangle matrix types

For all types, the indices i and j refer to rows and columns respectively. The indices of a diagonal element (i == j) are out of bounds for all types.

Simple Upper Triangle (SimpleUpperTri, SimpleUpperTriMut)

Indexing operations for an upper triangle matrix with no diagonal elements. Allows getting the element or one dimensional index for any i and j indices where i < j. Does not allow indexing into rows or columns outside of the triangle.

use crate::triangle_matrix::SimpleUpperTri;

let n = 5;
let m = TriVec(n, Vec::from_iter(0..tri_num(n - 1)));

// Get the elements of rows 0..4.
assert_eq!(m.get_row(0).cloned().collect::<Vec<_>>(), [   0, 1, 2, 3]);
assert_eq!(m.get_row(1).cloned().collect::<Vec<_>>(), [      4, 5, 6]);
assert_eq!(m.get_row(2).cloned().collect::<Vec<_>>(), [         7, 8]);
assert_eq!(m.get_row(3).cloned().collect::<Vec<_>>(), [            9]);

assert_eq!(m.get_col_indices(2).collect::<Vec<_>>(), [1, 4]);
assert_eq!(m.get_col_indices(4).collect::<Vec<_>>(), [3, 6, 8, 9]);

assert_eq!(*m.get_element(0, 3), 2);
assert_eq!(*m.get_element(1, 3), 5);
assert_eq!(*m.get_element(2, 3), 7);

Symmetric Upper Triangle (SymmetricUpperTri, SymmetricUpperTriMut)

Indexing operations for a symmetric upper triangle matrix with no diagonal elements. Allows getting the element or one dimensional index for any i and j indices where any pair of (i, j) indices is equal to the pair, (j, i). Does not allow indexing into rows or columns outside of the triangle.

use crate::triangle_matrix::SymmetricUpperTri;

let n = 5;
let m = TriVec(n, Vec::from_iter(0..tri_num(n - 1)));

// Get the elements of rows 0..5.
assert_eq!(m.get_row(0).cloned().collect::<Vec<_>>(), [   0, 1, 2, 3]);
assert_eq!(m.get_row(1).cloned().collect::<Vec<_>>(), [0,    4, 5, 6]);
assert_eq!(m.get_row(2).cloned().collect::<Vec<_>>(), [1, 4,    7, 8]);
assert_eq!(m.get_row(3).cloned().collect::<Vec<_>>(), [2, 5, 7,    9]);
assert_eq!(m.get_row(4).cloned().collect::<Vec<_>>(), [3, 6, 8, 9   ]);

assert_eq!(m.get_col_indices(2).collect::<Vec<_>>(), [1, 4,     7, 8]);
assert_eq!(m.get_col_indices(4).collect::<Vec<_>>(), [3, 6, 8, 9    ]);

assert_eq!(*m.get_element(0, 3), 2);
assert_eq!(*m.get_element(3, 1), 5);
assert_eq!(*m.get_element(3, 2), 7);

Simple Lower Triangle (SimpleLowerTri, SimpleLowerTriMut)

Indexing operations for a lower triangle matrix with no diagonal elements. Allows getting the element or one dimensional index for any i and j indices where j < i. Does not allow indexing into rows or columns outside of the triangle.

use crate::triangle_matrix::SimpleLowerTri;

let n = 5;
let m = TriVec(n, Vec::from_iter(0..tri_num(n - 1)));

// Get the elements of rows 1..4.
assert_eq!(m.get_row(1).cloned().collect::<Vec<_>>(), [0            ]);
assert_eq!(m.get_row(2).cloned().collect::<Vec<_>>(), [1, 2         ]);
assert_eq!(m.get_row(3).cloned().collect::<Vec<_>>(), [3, 4, 5      ]);
assert_eq!(m.get_row(4).cloned().collect::<Vec<_>>(), [6, 7, 8, 9   ]);

assert_eq!(m.get_col_indices(1).collect::<Vec<_>>(), [2, 4, 7]);
assert_eq!(m.get_col_indices(3).collect::<Vec<_>>(), [9]);

assert_eq!(*m.get_element(2, 1), 2);
assert_eq!(*m.get_element(3, 1), 4);
assert_eq!(*m.get_element(4, 1), 7);

Symmetric Lower Triangle (SymmetricLowerTri, SymmetricLowerTriMut)

Indexing operations for a symmetric lower triangle matrix with no diagonal elements. Allows getting the element or one dimensional index for any i and j indices where any pair of (i, j) indices is equal to the pair, (j, i). Does not allow indexing into rows or columns outside of the triangle.

use crate::triangle_matrix::SymmetricLowerTri;

let n = 5;
let m = TriVec(n, Vec::from_iter(0..tri_num(n - 1)));

// Get the elements of rows 0..5.
assert_eq!(m.get_row(0).cloned().collect::<Vec<_>>(), [   0, 1, 3, 6]);
assert_eq!(m.get_row(1).cloned().collect::<Vec<_>>(), [0,    2, 4, 7]);
assert_eq!(m.get_row(2).cloned().collect::<Vec<_>>(), [1, 2,    5, 8]);
assert_eq!(m.get_row(3).cloned().collect::<Vec<_>>(), [3, 4, 5,    9]);
assert_eq!(m.get_row(4).cloned().collect::<Vec<_>>(), [6, 7, 8, 9   ]);

assert_eq!(m.get_col_indices(2).collect::<Vec<_>>(), [1, 2,     5, 8]);
assert_eq!(m.get_col_indices(4).collect::<Vec<_>>(), [6, 7, 8, 9    ]);

assert_eq!(*m.get_element(0, 3), 3);
assert_eq!(*m.get_element(3, 1), 4);
assert_eq!(*m.get_element(3, 2), 5);