Struct Matrix

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pub struct Matrix<F: Field> { /* private fields */ }

Implementations§

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impl<F: Field> Matrix<F>

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pub fn new(matrix: Vec<Vec<F>>) -> Matrix<F>

Creates a new matrix from a vector of vectors.

§Example

let a: Matrix<F> = Matrix::new(vec![
    vec![F::from(2), F::from(2)],
    vec![F::from(3), F::from(4)],
]);

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pub fn is_square(self) -> bool

Returns whether or not the matrix is square.

§Example

let is_square: bool = a.is_square();
assert!(is_square);

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pub fn determinant(self) -> F

Returns the determinant of the matrix.

§Example

let det: F = a.determinant();

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pub fn is_diagonal(self) -> bool

Returns whether or not the matrix is diagonal.

§Example

let is_diagonal: bool = a.is_diagonal();
assert!(is_diagonal);

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pub fn transpose(self) -> Matrix<F>

Returns the transpose of the matrix.

§Example

let b: Matrix<F> = a.transpose();

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pub fn adjoint(self) -> Matrix<F>

Returns the adjoint of the matrix.

§Example

let b: Matrix<F> = a.adjoint();

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pub fn inverse(self) -> Option<Matrix<F>>

Returns the inverse of the matrix.

§Example

let b: Matrix<F> = a.inverse();

§Panics

Panics if the matrix is not invertible.

§Notes

This function uses the LU decomposition to compute the inverse. The LU decomposition is computed using the Doolittle algorithm.

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pub fn is_identity(self) -> bool

Returns whether or not the matrix is the identity matrix.

§Example

let is_identity: bool = a.is_identity();
assert!(is_identity);

§Notes

This function returns false if the matrix is empty.

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pub fn ax_b_solve_for_x(self, b: Vec<F>) -> Vec<F>

Solves the system of linear equations Ax = b for x.

§Example

let x: Vec<F> = a.solve_for_x(b);

§Panics

Panics if the matrix is the determinant of the matrix is zero.

§Notes

This function uses the LU decomposition to solve the system of linear equations. The LU decomposition is computed using the Doolittle algorithm.

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pub fn lu_decomposition(&self) -> (Matrix<F>, Matrix<F>)

Returns the LU decomposition of the matrix.

§Example

let (l, u): (Matrix<F>, Matrix<F>) = a.lu_decomposition();

§Panics

Panics if the matrix is the determinant of the matrix is zero.

§Notes

This function uses the Doolittle algorithm to compute the LU decomposition. The Doolittle algorithm is a variant of the Gaussian elimination algorithm.

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pub fn scalar_mul(self, scalar: F) -> Matrix<F>

Multiplies the matrix by a scalar.

§Example

let c: Matrix<F> = a.scalar_mul(b);

§Notes

This function is equivalent to multiplying each element of the matrix by the scalar.

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pub fn mul_vec(self, vec: Vec<F>) -> Vec<F>

Multiplies the matrix by a vector.

§Example

let c: Vec<F> = a.mul_vec(b);

§Panics

Panics if the number of rows in the matrix is not equal to the number of elements in the vector.

§Notes

This function is equivalent to multiplying the matrix by a column vector.

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pub fn sum_of_matrix(self) -> F

Returns the sum of all the elements in the matrix.

§Example

let c: F = a.sum_of_matrix();

§Notes

This function is equivalent to summing all the elements in the matrix.

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pub fn set_element(&mut self, row: usize, column: usize, new_value: F)

Sets a specific element in the matrix.

§Example

type F = Field;
let a: Matrix<F> = Matrix::new(vec![
    vec![F::from(2), F::from(2)],
    vec![F::from(3), F::from(4)],
]);
a.set_element(0, 0, F::from(1));

§Panics

Panics if the row or column is out of bounds.

§Notes

This function is equivalent to setting the element in the matrix. With row being the position in the outer vector and column being the position in the inner vector. The first element in the outer vector is row 0 and the first element in the inner vector is column 0.

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pub fn get_element(&self, row: usize, column: usize) -> F

Gets a specific element in the matrix.

§Example

let a: Matrix<F> = Matrix::new(vec![
  vec![F::from(2), F::from(2)],
  vec![F::from(3), F::from(4)],
]);
let b: F = a.get_element(0, 0);
assert_eq!(b, F::from(2));

§Panics

Panics if the row or column is out of bounds.

§Notes

This function is equivalent to getting the element in the matrix. With row being the position in the outer vector and column being the position in the inner vector. The first element in the outer vector is row 0 and the first element in the inner vector is column 0.