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.

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);