iron_shapes/
matrix2d.rs

1// Copyright (c) 2018-2020 Thomas Kramer.
2// SPDX-FileCopyrightText: 2018-2022 Thomas Kramer
3//
4// SPDX-License-Identifier: AGPL-3.0-or-later
5
6//! Data structures and functions for 2x2 matrices.
7
8use crate::CoordinateType;
9
10use crate::vector::Vector;
11
12/// A 2x2 matrix of the form:
13/// ```txt
14/// [[ m11, m12 ],
15///  [ m21, m22 ]]
16/// ```
17#[derive(Clone, Hash, PartialEq, Eq, Debug)]
18#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
19pub struct Matrix2d<T: CoordinateType> {
20    /// m11
21    pub(crate) m11: T,
22    /// m12
23    pub(crate) m12: T,
24    /// m21
25    pub(crate) m21: T,
26    /// m22
27    pub(crate) m22: T,
28}
29
30impl<T> Matrix2d<T>
31where
32    T: CoordinateType,
33{
34    /// Create a new 2x2 matrix with entries of the form:
35    /// ```txt
36    /// [[ m11, m12 ],
37    ///  [ m21, m22 ]]
38    /// ```
39    pub fn new(m11: T, m12: T, m21: T, m22: T) -> Self {
40        Matrix2d { m11, m12, m21, m22 }
41    }
42
43    /// Return the identity matrix.
44    pub fn identity() -> Self {
45        Self::new(T::one(), T::zero(), T::zero(), T::one())
46    }
47
48    /// Compute product of the matrix with a scalar.
49    pub fn mul_scalar(&self, rhs: T) -> Self {
50        Matrix2d::new(
51            self.m11 * rhs,
52            self.m12 * rhs,
53            self.m21 * rhs,
54            self.m22 * rhs,
55        )
56    }
57
58    /// Compute matrix-column-vector multiplication.
59    /// The vector is interpreted as column vector.
60    pub fn mul_column_vector(&self, rhs: Vector<T>) -> Vector<T> {
61        Vector::new(
62            rhs.x * self.m11 + rhs.y * self.m12,
63            rhs.x * self.m21 + rhs.y * self.m22,
64        )
65    }
66
67    /// Matrix-matrix multiplication.
68    pub fn mul_matrix(&self, rhs: &Self) -> Self {
69        let a = self;
70        let b = rhs;
71        let c11 = a.m11 * b.m11 + a.m12 * b.m21;
72        let c12 = a.m11 * b.m12 + a.m12 * b.m22;
73        let c21 = a.m21 * b.m11 + a.m22 * b.m21;
74        let c22 = a.m21 * b.m12 + a.m22 * b.m22;
75        Self::new(c11, c12, c21, c22)
76    }
77
78    /// Compute the transpose of the matrix.
79    pub fn transpose(&self) -> Self {
80        Self::new(self.m11, self.m21, self.m12, self.m22)
81    }
82
83    /// Compute the determinant of this matrix.
84    pub fn determinant(&self) -> T {
85        self.m11 * self.m22 - self.m12 * self.m21
86    }
87
88    /// Test if this matrix is the identity matrix.
89    pub fn is_identity(&self) -> bool {
90        self == &Self::identity()
91    }
92
93    /// Test if this matrix is unitary.
94    pub fn is_unitary(&self) -> bool {
95        self.mul_matrix(&self.transpose()).is_identity()
96    }
97
98    /// Compute the inverse matrix.
99    /// `None` will be returned if the determinant is zero and the matrix
100    /// is not invertible.
101    pub fn try_inverse(&self) -> Option<Self> {
102        // Compute determinant.
103        let det = self.determinant();
104        if !det.is_zero() {
105            let z = T::zero();
106            Some(Self::new(
107                self.m22 / det,
108                z - self.m12 / det,
109                z - self.m21 / det,
110                self.m11 / det,
111            ))
112        } else {
113            None
114        }
115    }
116}
117
118impl<T: CoordinateType> Default for Matrix2d<T> {
119    fn default() -> Self {
120        Self::identity()
121    }
122}
123
124#[test]
125fn test_matrix_multiplication() {
126    let a = Matrix2d::new(1.0, 2.0, 3.0, 4.0);
127    let b = Matrix2d::new(5.0, 6.0, 7.0, 8.0);
128    let id = Matrix2d::identity();
129    assert_eq!(id.mul_matrix(&id), id);
130    assert_eq!(b.mul_matrix(&id), b);
131    assert_eq!(id.mul_matrix(&b), b);
132    assert_eq!(
133        a.mul_matrix(&b),
134        Matrix2d::new(19.0, 22.0, 15.0 + 28.0, 18.0 + 32.0)
135    );
136}
137
138#[test]
139fn test_inverse() {
140    let m = Matrix2d::new(2.0, 1.0, 4.0, 8.0);
141    let i = m.try_inverse().unwrap();
142    assert_eq!(m.mul_matrix(&i), Matrix2d::identity());
143    assert_eq!(i.mul_matrix(&m), Matrix2d::identity());
144}
iron_shapes/matrix2d.rs

iron_shapes/
matrix2d.rs
