Struct Matrix

pub struct Matrix<T, const M: usize, const N: usize> {
    pub store: [[T; N]; M],
}

A generic matrix type with M rows and N columns.

Examples

use mini_matrix::Matrix;

let matrix = Matrix::<f64, 2, 2>::from([[1.0, 2.0], [3.0, 4.0]]);
assert_eq!(matrix.size(), (2, 2));

Fields

store: [[T; N]; M]

The underlying storage for the matrix elements.

Implementations

impl<T, const M: usize, const N: usize> Matrix<T, M, N>

where T: Copy + Default,

pub fn from(data: [[T; N]; M]) -> Self

Creates a new Matrix from the given 2D array.

Examples

use mini_matrix::Matrix;

let matrix = Matrix::<i32, 2, 3>::from([[1, 2, 3], [4, 5, 6]]);

pub const fn size(&self) -> (usize, usize)

Returns the dimensions of the matrix as a tuple (rows, columns).

Examples

use mini_matrix::Matrix;

let matrix = Matrix::<f64, 3, 4>::zero();
assert_eq!(matrix.size(), (3, 4));

pub fn zero() -> Self

Creates a new Matrix with all elements set to the default value of type T.

Examples

use mini_matrix::Matrix;

let matrix = Matrix::<f64, 2, 2>::zero();
assert_eq!(matrix.store, [[0.0, 0.0], [0.0, 0.0]]);

pub fn from_vecs(vecs: Vec<Vec<T>>) -> Self

impl<T, const M: usize, const N: usize> Matrix<T, M, N>

where T: AddAssign + SubAssign + MulAssign + Copy + Default,

pub fn add(&mut self, other: &Self)

Adds another matrix to this matrix in-place.

Examples

use mini_matrix::Matrix;

let mut a = Matrix::<i32, 2, 2>::from([[1, 2], [3, 4]]);
let b = Matrix::<i32, 2, 2>::from([[5, 6], [7, 8]]);
a.add(&b);
assert_eq!(a.store, [[6, 8], [10, 12]]);

pub fn sub(&mut self, other: &Self)

Subtracts another matrix from this matrix in-place.

Examples

use mini_matrix::Matrix;

let mut a = Matrix::<i32, 2, 2>::from([[5, 6], [7, 8]]);
let b = Matrix::<i32, 2, 2>::from([[1, 2], [3, 4]]);
a.sub(&b);
assert_eq!(a.store, [[4, 4], [4, 4]]);

pub fn scl(&mut self, scalar: T)

Multiplies this matrix by a scalar value in-place.

Examples

use mini_matrix::Matrix;

let mut a = Matrix::<i32, 2, 2>::from([[1, 2], [3, 4]]);
a.scl(2);
assert_eq!(a.store, [[2, 4], [6, 8]]);

impl<T, const M: usize, const N: usize> Matrix<T, M, N>

where T: Num + Copy + AddAssign + Default,

pub fn mul_vec(&mut self, vec: &Vector<T, N>) -> Vector<T, N>

Multiplies the matrix by a vector.

Arguments

• vec - The vector to multiply with the matrix.

Returns

The resulting vector of the multiplication.

pub fn mul_mat(&mut self, mat: &Matrix<T, M, N>) -> Matrix<T, M, N>

Multiplies the matrix by another matrix.

Arguments

• mat - The matrix to multiply with.

Returns

The resulting matrix of the multiplication.

impl<T, const M: usize, const N: usize> Matrix<T, M, N>

where T: Num + Copy + AddAssign + Default,

pub fn trace(&self) -> T

Calculates the trace of the matrix.

The trace is defined as the sum of the elements on the main diagonal.

Panics

Panics if the matrix is not square (i.e., if M != N).

Examples

use mini_matrix::Matrix;

let mut a = Matrix::<i32, 3, 3>::from([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
assert_eq!(a.trace(), 15);

impl<T, const M: usize, const N: usize> Matrix<T, M, N>

where T: Copy + Default,

pub fn transpose(&mut self) -> Matrix<T, N, M>

Computes the transpose of the matrix.

Examples

use mini_matrix::Matrix;

let mut a = Matrix::<i32, 2, 3>::from([[1, 2, 3], [4, 5, 6]]);
let b = a.transpose();
assert_eq!(b.store, [[1, 4], [2, 5], [3, 6]]);

impl<T, const M: usize, const N: usize> Matrix<T, M, N>

where T: Copy + Default + Num,

pub fn identity() -> Matrix<T, M, N>

Creates an identity matrix.

Examples

use mini_matrix::Matrix;

let a = Matrix::<i32, 3, 3>::identity();
assert_eq!(a.store, [[1, 0, 0], [0, 1, 0], [0, 0, 1]]);

impl<T, const M: usize, const N: usize> Matrix<T, M, N>

where T: Copy + Default + Mul<Output = T> + PartialEq + Num + Div<Output = T> + Sub<Output = T>,

pub fn row_echelon(&self) -> Matrix<T, M, N>

Converts a given matrix to its Reduced Row-Echelon Form (RREF).

Row-echelon form is a specific form of a matrix that is particularly useful for solving systems of linear equations and for understanding the properties of the matrix. To explain it simply and in detail, let’s go through what row-echelon form is, how to achieve it, and an example to illustrate the process.

Row-Echelon Form

A matrix is in row-echelon form if it satisfies the following conditions:

1. Leading Entry: The leading entry (first non-zero number from the left) in each row is 1. This is called the pivot.
2. Zeros Below: The pivot in each row is to the right of the pivot in the row above, and all entries below a pivot are zeros.
3. Rows of Zeros: Any rows consisting entirely of zeros are at the bottom of the matrix.

Reduced Row-Echelon Form

A matrix is in reduced row-echelon form (RREF) if it additionally satisfies:

4. Leading Entries: Each leading 1 is the only non-zero entry in its column.

Achieving Row-Echelon Form

To convert a matrix into row-echelon form, we use a process called Gaussian elimination. This involves performing row operations:

1. Row swapping: Swapping the positions of two rows.
2. Row multiplication: Multiplying all entries of a row by a non-zero scalar.
3. Row addition: Adding or subtracting the multiples of one row to another row.

Let’s consider an example with a 3 x 3 matrix:

A = [ [1, 2, 3], [4, 5, 6], [7, 8, 9] ]

Step-by-Step Process

1. Starting Matrix:

   [ [1, 2, 3], [4, 5, 6], [7, 8, 9] ]

2. Make the Pivot of Row 1 (already 1):

   The first leading entry is already 1.

3. Eliminate Below Pivot in Column 1:

   Subtract 4 times the first row from the second row:

 R2 = R2 - 4R1
 [
   [1, 2, 3],
   [0, -3, -6],
   [7, 8, 9]
 ]

Subtract 7 times the first row from the third row:

  R3 = R3 - 7R1
  [
    [1, 2, 3],
    [0, -3, -6],
    [0, -6, -12]
  ]

4. Make the Pivot of Row 2:

   Divide the second row by -3 to make the pivot 1:

   R2 = (1 / -3) * R2
   [
     [1, 2, 3],
     [0, 1, 2],
     [0, -6, -12]
   ]

5. **Eliminate Below Pivot in Column 2**:

   Add 6 times the second row to the third row:
```markdown
   R3 = R3 + 6R2
   [
     [1, 2, 3],
     [0, 1, 2],
     [0, 0, 0]
   ]

Now, the matrix is in row-echelon form.

Examples

use mini_matrix::Matrix;

let a = Matrix::<f64, 3, 4>::from([
    [1.0, 2.0, 3.0, 4.0],
    [5.0, 6.0, 7.0, 8.0],
    [9.0, 10.0, 11.0, 12.0]
]);
let b = a.row_echelon();
// Check the result (approximate due to floating-point arithmetic)

impl<T, const M: usize, const N: usize> Matrix<T, M, N>

where T: Copy + Default + Mul + Num + Neg<Output = T> + AddAssign + Debug,

pub fn determinant(&self) -> T

Computes the determinant of the matrix.

Determinant in General

The determinant is a scalar value that can be computed from the elements of a square matrix. It provides important properties about the matrix and the linear transformation it represents. In general, the determinant represents the scaling factor of the volume when the matrix is used as a linear transformation. It can be positive, negative, or zero, each with different implications:

• (\det(A) = 0):

  • The matrix A is singular and does not have an inverse.
  • The columns (or rows) of A are linearly dependent.
  • The transformation collapses the space into a lower-dimensional subspace.
  • Geometrically, it indicates that the volume of the transformed space is 0.

• (\det(A) > 0):

  • The matrix A is non-singular and has an inverse.
  • The transformation preserves the orientation of the space.
  • Geometrically, it indicates a positive scaling factor of the volume.

• (\det(A) < 0):

  • The matrix A is non-singular and has an inverse.
  • The transformation reverses the orientation of the space.
  • Geometrically, it indicates a negative scaling factor of the volume.

Example

Consider a 2 x 2 matrix:

A = [
  [1, 2],
  [3, 4]
]

The determinant is:

det(A) = 1 * 4 - 2 * 3 = 4 - 6 = -2

This indicates that the transformation represented by A scales areas by a factor of 2 and reverses their orientation.

Panics

Panics if the matrix size is larger than 4 x 4.

Returns

The determinant of the matrix.

Examples

use mini_matrix::Matrix;

let a = Matrix::<i32, 3, 3>::from([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
assert_eq!(a.determinant(), 0);

impl<T, const M: usize, const N: usize> Matrix<T, M, N>

where T: Copy + Default + Mul + Num + Neg<Output = T> + AddAssign + Debug + Float,

pub fn inverse(&self) -> Result<Self, &'static str>

Calculates the inverse of the matrix.

This method supports matrices up to 3x3 in size.

Returns

Returns Ok(Matrix) if the inverse exists, or an Err with a descriptive message if not.

Examples

use mini_matrix::Matrix;

let a = Matrix::<f64, 2, 2>::from([[1.0, 2.0], [3.0, 4.0]]);
let inv = a.inverse().unwrap();
// Check the result (approximate due to floating-point arithmetic)

impl<T, const M: usize, const N: usize> Matrix<T, M, N>

where T: Copy + Default + Mul + Num + Neg<Output = T> + AddAssign + PartialEq,

pub fn rank(&self) -> usize

Calculates the rank of the matrix.

The rank is determined by computing the row echelon form and counting non-zero rows.

Examples

use mini_matrix::Matrix;

let a = Matrix::<i32, 3, 3>::from([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
assert_eq!(a.rank(), 2);

impl<T, const M: usize, const N: usize> Matrix<T, M, N>

where T: Copy + Default + Mul + Num + Neg<Output = T> + AddAssign + PartialEq,

pub fn cofactor2x2(&self, row: usize, col: usize) -> Matrix<T, 2, 2>

pub fn cofactor1x1(&self, row: usize, col: usize) -> Matrix<T, 1, 1>

Trait Implementations

impl<T, const M: usize, const N: usize> Add for Matrix<T, M, N>

where T: AddAssign + Copy + Num,

fn add(self, rhs: Self) -> Self::Output

Adds two matrices element-wise.

Examples

use mini_matrix::Matrix;

let a = Matrix::<i32, 2, 2>::from([[1, 2], [3, 4]]);
let b = Matrix::<i32, 2, 2>::from([[5, 6], [7, 8]]);
let c = a + b;
assert_eq!(c.store, [[6, 8], [10, 12]]);

type Output = Matrix<T, M, N>

The resulting type after applying the + operator.

impl<T: Clone, const M: usize, const N: usize> Clone for Matrix<T, M, N>

fn clone(&self) -> Matrix<T, M, N>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Debug, const M: usize, const N: usize> Debug for Matrix<T, M, N>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T, const M: usize, const N: usize> Deref for Matrix<T, M, N>

fn deref(&self) -> &Self::Target

Dereferences the matrix, allowing it to be treated as a slice.

Note

This implementation is currently unfinished.

Examples

use mini_matrix::Matrix;

let matrix = Matrix::<i32, 2, 2>::from([[1, 2], [3, 4]]);
// Usage example will be available once implementation is complete

type Target = [[T; N]; M]

The resulting type after dereferencing.

impl<T, const M: usize, const N: usize> DerefMut for Matrix<T, M, N>

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the matrix, allowing it to be treated as a mutable slice.

Note

This implementation is currently unfinished.

Examples

use mini_matrix::Matrix;

let mut matrix = Matrix::<i32, 2, 2>::from([[1, 2], [3, 4]]);
// Usage example will be available once implementation is complete

impl<T, const M: usize, const N: usize> Display for Matrix<T, M, N>

where T: AddAssign + SubAssign + MulAssign + Copy + Display,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the matrix for display.

Each row of the matrix is displayed on a new line, with elements separated by commas. Elements are formatted with one decimal place precision.

Examples

use mini_matrix::Matrix;

let a = Matrix::<f32, 2, 2>::from([[1.0, 2.5], [3.7, 4.2]]);
println!("{}", a);
// Output:
// // [1.0, 2.5]
// // [3.7, 4.2]

impl<T, const M: usize, const N: usize> Index<(usize, usize)> for Matrix<T, M, N>

fn index(&self, index: (usize, usize)) -> &Self::Output

Immutably indexes into the matrix, allowing read access to its elements.

Arguments

• index - A tuple (row, column) specifying the element to access.

Examples

use mini_matrix::Matrix;

let matrix = Matrix::<i32, 2, 2>::from([[1, 2], [3, 4]]);
assert_eq!(matrix[(1, 0)], 3);

type Output = T

The returned type after indexing.

impl<T, const M: usize, const N: usize> IndexMut<(usize, usize)> for Matrix<T, M, N>

fn index_mut(&mut self, index: (usize, usize)) -> &mut T

Mutably indexes into the matrix, allowing modification of its elements.

Arguments

• index - A tuple (row, column) specifying the element to access.

Examples

use mini_matrix::Matrix;

let mut matrix = Matrix::<i32, 2, 2>::from([[1, 2], [3, 4]]);
matrix[(0, 1)] = 5;
assert_eq!(matrix.store, [[1, 5], [3, 4]]);

impl<T, const M: usize, const N: usize> Mul<Matrix<T, N, N>> for Matrix<T, M, N>

where T: MulAssign + AddAssign + Copy + Num + Default,

fn mul(self, rhs: Matrix<T, N, N>) -> Self::Output

Multiplies two matrices.

Examples

use mini_matrix::Matrix;

let a = Matrix::<i32, 2, 2>::from([[1, 2], [3, 4]]);
let b = Matrix::<i32, 2, 2>::from([[5, 6], [7, 8]]);
let c = a * b;
assert_eq!(c.store, [[17, 23], [39, 53]]);

type Output = Matrix<T, M, N>

The resulting type after applying the * operator.

impl<T, const M: usize, const N: usize> Mul<T> for Matrix<T, M, N>

where T: MulAssign + Copy + Num,

fn mul(self, rhs: T) -> Self::Output

Multiplies a matrix by a scalar value.

Examples

use mini_matrix::Matrix;

let a = Matrix::<i32, 2, 2>::from([[1, 2], [3, 4]]);
let b = a * 2;
assert_eq!(b.store, [[2, 4], [6, 8]]);

type Output = Matrix<T, M, N>

The resulting type after applying the * operator.

impl<T, const M: usize, const N: usize> Mul<Vector<T, N>> for Matrix<T, M, N>

where T: MulAssign + AddAssign + Copy + Num + Default,

fn mul(self, rhs: Vector<T, N>) -> Self::Output

Multiplies a matrix by a vector.

Examples

use mini_matrix::{Matrix, Vector};

let a = Matrix::<i32, 2, 2>::from([[1, 2], [3, 4]]);
let v = Vector::<i32, 2>::from([5, 6]);
let result = a * v;
assert_eq!(result.store, [17, 39]);

type Output = Vector<T, M>

The resulting type after applying the * operator.

impl<T, const M: usize, const N: usize> Neg for Matrix<T, M, N>

where T: Neg<Output = T> + Copy,

fn neg(self) -> Self::Output

Negates all elements of the matrix.

Examples

use mini_matrix::Matrix;

let a = Matrix::<i32, 2, 2>::from([[1, -2], [-3, 4]]);
let b = -a;
assert_eq!(b.store, [[-1, 2], [3, -4]]);

type Output = Matrix<T, M, N>

The resulting type after applying the - operator.

impl<T: PartialEq, const M: usize, const N: usize> PartialEq for Matrix<T, M, N>

fn eq(&self, other: &Matrix<T, M, N>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<T, const M: usize, const N: usize> Sub for Matrix<T, M, N>

where T: SubAssign + Copy + Num,

fn sub(self, rhs: Self) -> Self::Output

Subtracts one matrix from another element-wise.

Examples

use mini_matrix::Matrix;

let a = Matrix::<i32, 2, 2>::from([[5, 6], [7, 8]]);
let b = Matrix::<i32, 2, 2>::from([[1, 2], [3, 4]]);
let c = a - b;
assert_eq!(c.store, [[4, 4], [4, 4]]);

type Output = Matrix<T, M, N>

The resulting type after applying the - operator.

impl<T: Copy, const M: usize, const N: usize> Copy for Matrix<T, M, N>

impl<T, const M: usize, const N: usize> StructuralPartialEq for Matrix<T, M, N>