Struct rulinalg::matrix::Matrix

pub struct Matrix<T> { /* fields omitted */ }

The Matrix struct.

Can be instantiated with any type.

Methods

impl<T> Matrix<T> where T: Any + Float

fn qr_decomp(self) -> Result<(Matrix<T>, Matrix<T>), Error>

Compute the QR decomposition of the matrix.

Returns the tuple (Q,R).

Examples

use rulinalg::matrix::Matrix;

let m = matrix![1.0, 0.5, 0.5;
                0.5, 1.0, 0.5;
                0.5, 0.5, 1.0];

let (q, r) = m.qr_decomp().unwrap();

Failures

• Cannot compute the QR decomposition.

impl<T> Matrix<T> where T: Any + Float

fn cholesky(&self) -> Result<Matrix<T>, Error>

Cholesky decomposition

Returns the cholesky decomposition of a positive definite matrix.

Examples

use rulinalg::matrix::Matrix;

let m = matrix![1.0, 0.5, 0.5;
                0.5, 1.0, 0.5;
                0.5, 0.5, 1.0];

let l = m.cholesky();

Panics

• The matrix is not square.

Failures

• Matrix is not positive definite.

impl<T> Matrix<T> where T: Any + Float

fn bidiagonal_decomp(self) -> Result<(Matrix<T>, Matrix<T>, Matrix<T>), Error>

Converts matrix to bidiagonal form

Returns (B, U, V), where B is bidiagonal and self = U B V_T.

Note that if self has self.rows() > self.cols() the matrix will be transposed and then reduced - this will lead to a sub-diagonal instead of super-diagonal.

Failures

• The matrix cannot be reduced to bidiagonal form.

impl<T: Any + Float + Signed> Matrix<T>

fn svd(self) -> Result<(Matrix<T>, Matrix<T>, Matrix<T>), Error>

Singular Value Decomposition

Computes the SVD using the Golub-Reinsch algorithm.

Returns Σ, U, V, such that self = U Σ V^T. Σ is a diagonal matrix whose elements correspond to the non-negative singular values of the matrix. The singular values are ordered in non-increasing order. U and V have orthonormal columns, and each column represents the left and right singular vectors for the corresponding singular value in Σ, respectively.

If self has M rows and N columns, the dimensions of the returned matrices are as follows.

If M >= N:

• Σ: N x N
• U: M x N
• V: N x N

If M < N:

• Σ: M x M
• U: M x M
• V: N x M

Note: This version of the SVD is sometimes referred to as the 'economy SVD'.

Failures

This function may fail in some cases. The current decomposition whilst being efficient is fairly basic. Hopefully the algorithm can be made not to fail in the near future.

impl<T: Any + Float> Matrix<T>

fn upper_hessenberg(self) -> Result<Matrix<T>, Error>

Returns H, where H is the upper hessenberg form.

If the transformation matrix is also required, you should use upper_hess_decomp.

Examples

use rulinalg::matrix::Matrix;

let a = matrix![2., 0., 1., 1.;
                2., 0., 1., 2.;
                1., 2., 0., 0.;
                2., 0., 1., 1.];
let h = a.upper_hessenberg();

println!("{:}", h.expect("Could not get upper Hessenberg form."));

Panics

• The matrix is not square.

Failures

• The matrix cannot be reduced to upper hessenberg form.

fn upper_hess_decomp(self) -> Result<(Matrix<T>, Matrix<T>), Error>

Returns (U,H), where H is the upper hessenberg form and U is the unitary transform matrix.

Note: The current transform matrix seems broken...

Examples

use rulinalg::matrix::BaseMatrix;

let a = matrix![1., 2., 3.;
                4., 5., 6.;
                7., 8., 9.];

// u is the transform, h is the upper hessenberg form.
let (u, h) = a.clone().upper_hess_decomp().expect("This matrix should decompose!");

assert_matrix_eq!(h, u.transpose() * a * u, comp = abs, tol = 1e-12);

Panics

• The matrix is not square.

Failures

• The matrix cannot be reduced to upper hessenberg form.

impl<T> Matrix<T> where T: Any + Float

fn lup_decomp(self) -> Result<(Matrix<T>, Matrix<T>, Matrix<T>), Error>

Deprecated

Computes L, U, and P for LUP decomposition.

Returns L,U, and P respectively.

This function is deprecated. Please see PartialPivLu for a replacement.

Examples

use rulinalg::matrix::Matrix;

let a = matrix![1.0, 2.0, 0.0;
                0.0, 3.0, 4.0;
                5.0, 1.0, 2.0];

let (l, u, p) = a.lup_decomp().expect("This matrix should decompose!");

Panics

• Matrix is not square.

Failures

• Matrix cannot be LUP decomposed.

impl<T: Any + Float + Signed> Matrix<T>

fn eigenvalues(self) -> Result<Vec<T>, Error>

Eigenvalues of a square matrix.

Returns a Vec of eigenvalues.

Examples

use rulinalg::matrix::Matrix;

let a = Matrix::new(4,4, (1..17).map(|v| v as f64).collect::<Vec<f64>>());
let e = a.eigenvalues().expect("We should be able to compute these eigenvalues!");
println!("{:?}", e);

Panics

• The matrix is not square.

Failures

• Eigenvalues cannot be computed.

fn eigendecomp(self) -> Result<(Vec<T>, Matrix<T>), Error>

Eigendecomposition of a square matrix.

Returns a Vec of eigenvalues, and a matrix with eigenvectors as the columns.

The eigenvectors are only gauranteed to be correct if the matrix is real-symmetric.

Examples

use rulinalg::matrix::Matrix;

let a = matrix![3., 2., 4.;
                2., 0., 2.;
                4., 2., 3.];

let (e, m) = a.eigendecomp().expect("We should be able to compute this eigendecomp!");
println!("{:?}", e);
println!("{:?}", m.data());

Panics

• The matrix is not square.

Failures

• The eigen decomposition can not be computed.

impl<T> Matrix<T>

fn new<U: Into<Vec<T>>>(rows: usize, cols: usize, data: U) -> Matrix<T>

Constructor for Matrix struct.

Requires both the row and column dimensions.

Examples

use rulinalg::matrix::{Matrix, BaseMatrix};

let mat = Matrix::new(2,2, vec![1.0, 2.0, 3.0, 4.0]);

assert_eq!(mat.rows(), 2);
assert_eq!(mat.cols(), 2);

Panics

• The input data does not match the given dimensions.

fn from_fn<F>(rows: usize, cols: usize, f: F) -> Matrix<T> where F: FnMut(usize, usize) -> T

Constructor for Matrix struct that takes a function f and constructs a new matrix such that A_ij = f(i, j), where i is the row index and j the column index.

Requires both the row and column dimensions as well as a generating function.

Examples

use rulinalg::matrix::{Matrix, BaseMatrix};

// Let's assume you have an array of "things" for
// which you want to generate a distance matrix:
let things: [i32; 3] = [1, 2, 3];
let distances: Matrix<f64> = Matrix::from_fn(things.len(), things.len(), |col, row| {
    (things[col] - things[row]).abs().into()
});

assert_eq!(distances.rows(), 3);
assert_eq!(distances.cols(), 3);
assert_eq!(distances.data(), &vec![
    0.0, 1.0, 2.0,
    1.0, 0.0, 1.0,
    2.0, 1.0, 0.0,
]);

fn data(&self) -> &Vec<T>

Returns a non-mutable reference to the underlying data.

fn mut_data(&mut self) -> &mut [T]

Returns a mutable slice of the underlying data.

fn into_vec(self) -> Vec<T>

Consumes the Matrix and returns the Vec of data.

impl<T: Clone + Zero> Matrix<T>

fn zeros(rows: usize, cols: usize) -> Matrix<T>

Constructs matrix of all zeros.

Requires both the row and the column dimensions.

Examples

use rulinalg::matrix::Matrix;

let mat = Matrix::<f64>::zeros(2,3);

fn from_diag(diag: &[T]) -> Matrix<T>

Constructs matrix with given diagonal.

Requires slice of diagonal elements.

Examples

use rulinalg::matrix::Matrix;

let mat = Matrix::from_diag(&vec![1.0,2.0,3.0,4.0]);

impl<T: Clone + One> Matrix<T>

fn ones(rows: usize, cols: usize) -> Matrix<T>

Constructs matrix of all ones.

Requires both the row and the column dimensions.

Examples

use rulinalg::matrix::Matrix;

let mat = Matrix::<f64>::ones(2,3);

impl<T: Clone + Zero + One> Matrix<T>

fn identity(size: usize) -> Matrix<T>

Constructs the identity matrix.

Requires the size of the matrix.

Examples

use rulinalg::matrix::Matrix;

let I = Matrix::<f64>::identity(4);

impl<T: Float + FromPrimitive> Matrix<T>

fn mean(&self, axis: Axes) -> Vector<T>

The mean of the matrix along the specified axis.

• Axis Row - Arithmetic mean of rows.
• Axis Col - Arithmetic mean of columns.

Calling mean() on an empty matrix will return an empty matrix.

Examples

use rulinalg::matrix::{Matrix, Axes};

let a = matrix![1.0, 2.0;
                3.0, 4.0];

let c = a.mean(Axes::Row);
assert_eq!(c, vector![2.0, 3.0]);

let d = a.mean(Axes::Col);
assert_eq!(d, vector![1.5, 3.5]);

fn variance(&self, axis: Axes) -> Result<Vector<T>, Error>

The variance of the matrix along the specified axis.

• Axis Row - Sample variance of rows.
• Axis Col - Sample variance of columns.

Examples

use rulinalg::matrix::{Matrix, Axes};

let a = matrix![1.0, 2.0;
                3.0, 4.0];

let c = a.variance(Axes::Row).unwrap();
assert_eq!(c, vector![2.0, 2.0]);

let d = a.variance(Axes::Col).unwrap();
assert_eq!(d, vector![0.5, 0.5]);

Failures

• There are one or fewer row/columns in the working axis.

impl<T: Any + Float> Matrix<T>

fn solve(self, y: Vector<T>) -> Result<Vector<T>, Error>

Solves the equation Ax = y.

Requires a Vector y as input.

The method performs an LU decomposition internally, consuming the matrix in the process. If solving the same system for multiple right-hand sides is desired, see PartialPivLu.

Examples

use rulinalg::matrix::Matrix;
use rulinalg::vector::Vector;

let a = matrix![2.0, 3.0;
                1.0, 2.0];
let y = vector![13.0, 8.0];

let x = a.solve(y).unwrap();

assert_eq!(x, vector![2.0, 3.0]);

Panics

• The matrix column count and vector size are different.
• The matrix is not square.

Failures

• The matrix cannot be decomposed into an LUP form to solve.
• There is no valid solution as the matrix is singular.

fn inverse(self) -> Result<Matrix<T>, Error>

Computes the inverse of the matrix.

Internally performs an LU decomposition.

Examples

use rulinalg::matrix::Matrix;

let a = matrix![2., 3.;
                1., 2.];
let inv = a.clone().inverse().expect("This matrix should have an inverse!");

let I = a * inv;

assert_matrix_eq!(I, matrix![1.0, 0.0; 0.0, 1.0]);

Panics

• The matrix is not square.

Failures

• The matrix could not be LUP decomposed.
• The matrix has zero determinant.

fn det(self) -> T

Computes the determinant of the matrix.

Examples

let a = matrix![1.0, 2.0, 0.0;
                0.0, 3.0, 4.0;
                5.0, 1.0, 2.0];

let det = a.det();

Panics

• The matrix is not square.

impl<T: ToPrimitive> Matrix<T>

fn try_into<U: NumCast>(self) -> Result<Matrix<U>, Error>

Attempts to convert the matrix into a new matrix of different scalar type.

Failures

• One or more of the elements in the matrix cannot be converted into the new type.

Trait Implementations

impl<T> BaseMatrix<T> for Matrix<T>

fn rows(&self) -> usize

Rows in the matrix.

fn cols(&self) -> usize

Columns in the matrix.

fn row_stride(&self) -> usize

Row stride in the matrix.

fn is_empty(&self) -> bool

Returns true if the matrix contais no elements

fn as_ptr(&self) -> *const T

Top left index of the matrix.

fn into_matrix(self) -> Matrix<T> where T: Copy

Convert the matrix struct into a owned Matrix.

fn sum(&self) -> T where T: Copy + Zero + Add<T, Output=T>

The sum of all elements in the matrix

fn elemul(&self, m: &Self) -> Matrix<T> where T: Copy + Mul<T, Output=T>

The elementwise product of two matrices.

fn elediv(&self, m: &Self) -> Matrix<T> where T: Copy + Div<T, Output=T>

The elementwise division of two matrices.

fn vcat<S>(&self, m: &S) -> Matrix<T> where T: Copy, S: BaseMatrix<T>

Vertically concatenates two matrices. With self on top.

fn as_slice(&self) -> MatrixSlice<T>

Returns a MatrixSlice over the whole matrix.

unsafe fn get_unchecked(&self, index: [usize; 2]) -> &T

Get a reference to a point in the matrix without bounds checking.

fn col(&self, index: usize) -> Column<T>

Returns the column of a matrix at the given index. None if the index is out of bounds.

unsafe fn col_unchecked(&self, index: usize) -> Column<T>

Returns the column of a matrix at the given index without doing a bounds check.

fn row(&self, index: usize) -> Row<T>

Returns the row of a matrix at the given index.

unsafe fn row_unchecked(&self, index: usize) -> Row<T>

Returns the row of a matrix at the given index without doing unbounds checking

fn iter<'a>(&self) -> SliceIter<'a, T> where T: 'a

Returns an iterator over the matrix data.

fn col_iter(&self) -> Cols<T>

Iterate over the columns of the matrix.

fn row_iter(&self) -> Rows<T>

Iterate over the rows of the matrix.

fn diag_iter(&self, k: DiagOffset) -> Diagonal<T, Self>

Iterate over diagonal entries

fn sum_rows(&self) -> Vector<T> where T: Copy + Zero + Add<T, Output=T>

The sum of the rows of the matrix.

fn sum_cols(&self) -> Vector<T> where T: Copy + Zero + Add<T, Output=T>

The sum of the columns of the matrix.

fn norm<N: MatrixNorm<T, Self>>(&self, norm: N) -> T where T: Float

Compute given matrix norm for matrix.

fn metric<'a, 'b, B, M>(&'a self, mat: &'b B, metric: M) -> T where B: 'b + BaseMatrix<T>, M: MatrixMetric<'a, 'b, T, Self, B>

Compute the metric distance between two matrices.

fn min(&self, axis: Axes) -> Vector<T> where T: Copy + PartialOrd

The min of the specified axis of the matrix.

fn max(&self, axis: Axes) -> Vector<T> where T: Copy + PartialOrd

The max of the specified axis of the matrix.

fn select_rows<'a, I>(&self, rows: I) -> Matrix<T> where T: Copy,
        I: IntoIterator<Item=&'a usize>,
        I::IntoIter: ExactSizeIterator + Clone

Select rows from matrix

fn select_cols<'a, I>(&self, cols: I) -> Matrix<T> where T: Copy,
        I: IntoIterator<Item=&'a usize>,
        I::IntoIter: ExactSizeIterator + Clone

Select columns from matrix

fn select(&self, rows: &[usize], cols: &[usize]) -> Matrix<T> where T: Copy

Select block matrix from matrix

fn hcat<S>(&self, m: &S) -> Matrix<T> where T: Copy, S: BaseMatrix<T>

Horizontally concatenates two matrices. With self on the left.

fn diag(&self) -> Diagonal<T, Self>

Extract the diagonal of the matrix

fn transpose(&self) -> Matrix<T> where T: Copy

Tranposes the given matrix

fn is_diag(&self) -> bool where T: Zero + PartialEq

Checks if matrix is diagonal.

fn solve_u_triangular(&self, y: Vector<T>) -> Result<Vector<T>, Error> where T: Any + Float

Solves an upper triangular linear system.

fn solve_l_triangular(&self, y: Vector<T>) -> Result<Vector<T>, Error> where T: Any + Float

Solves a lower triangular linear system.

fn split_at(&self, mid: usize, axis: Axes) -> (MatrixSlice<T>, MatrixSlice<T>)

Split the matrix at the specified axis returning two MatrixSlices.

fn sub_slice<'a>(&self,
                 start: [usize; 2],
                 rows: usize,
                 cols: usize)
                 -> MatrixSlice<'a, T> where T: 'a

Produce a MatrixSlice from an existing matrix.

impl<T> BaseMatrixMut<T> for Matrix<T>

fn as_mut_ptr(&mut self) -> *mut T

Top left index of the slice.

fn as_mut_slice(&mut self) -> MatrixSliceMut<T>

Returns a MatrixSliceMut over the whole matrix.

unsafe fn get_unchecked_mut(&mut self, index: [usize; 2]) -> &mut T

Get a mutable reference to a point in the matrix without bounds checks.

fn iter_mut<'a>(&mut self) -> SliceIterMut<'a, T> where T: 'a

Returns a mutable iterator over the matrix.

fn col_mut(&mut self, index: usize) -> ColumnMut<T>

Returns a mutable reference to the column of a matrix at the given index. None if the index is out of bounds.

unsafe fn col_unchecked_mut(&mut self, index: usize) -> ColumnMut<T>

Returns a mutable reference to the column of a matrix at the given index without doing a bounds check.

fn row_mut(&mut self, index: usize) -> RowMut<T>

Returns a mutable reference to the row of a matrix at the given index. None if the index is out of bounds.

unsafe fn row_unchecked_mut(&mut self, index: usize) -> RowMut<T>

Returns a mutable reference to the row of a matrix at the given index without doing a bounds check.

fn swap_rows(&mut self, a: usize, b: usize)

Swaps two rows in a matrix.

fn swap_cols(&mut self, a: usize, b: usize)

Swaps two columns in a matrix.

fn col_iter_mut(&mut self) -> ColsMut<T>

Iterate over the mutable columns of the matrix.

fn row_iter_mut(&mut self) -> RowsMut<T>

Iterate over the mutable rows of the matrix.

fn diag_iter_mut(&mut self, k: DiagOffset) -> DiagonalMut<T, Self>

Iterate over diagonal entries mutably

fn set_to<M: BaseMatrix<T>>(self, target: M) where T: Copy

Sets the underlying matrix data to the target data.

fn apply(self, f: &Fn(T) -> T) -> Self where T: Copy

Applies a function to each element in the matrix.

fn split_at_mut(&mut self,
                mid: usize,
                axis: Axes)
                -> (MatrixSliceMut<T>, MatrixSliceMut<T>)

Split the matrix at the specified axis returning two MatrixSliceMuts.

fn sub_slice_mut<'a>(&mut self,
                     start: [usize; 2],
                     rows: usize,
                     cols: usize)
                     -> MatrixSliceMut<'a, T> where T: 'a

Produce a MatrixSliceMut from an existing matrix.

impl<T: Display> Display for Matrix<T>

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

Formats the Matrix for display.

impl<T> Index<[usize; 2]> for Matrix<T>

Indexes matrix.

Takes row index first then column.

type Output = T

The returned type after indexing

fn index(&self, idx: [usize; 2]) -> &T

The method for the indexing (container[index]) operation

impl<T> IndexMut<[usize; 2]> for Matrix<T>

Indexes mutable matrix.

Takes row index first then column.

fn index_mut(&mut self, idx: [usize; 2]) -> &mut T

The method for the mutable indexing (container[index]) operation

impl<T> Add<T> for Matrix<T> where T: Copy + Add<T, Output=T>

Scalar addition with matrix.

Will reuse the memory allocated for the existing matrix.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, f: T) -> Matrix<T>

The method for the + operator

impl<'a, T> Add<&'a T> for Matrix<T> where T: Copy + Add<T, Output=T>

Scalar addition with matrix.

Will reuse the memory allocated for the existing matrix.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, f: &T) -> Matrix<T>

The method for the + operator

impl<'a, T> Add<T> for &'a Matrix<T> where T: Copy + Add<T, Output=T>

Scalar addition with matrix.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, f: T) -> Matrix<T>

The method for the + operator

impl<'a, 'b, T> Add<&'b T> for &'a Matrix<T> where T: Copy + Add<T, Output=T>

Scalar addition with matrix.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, f: &T) -> Matrix<T>

The method for the + operator

impl<T> Mul<T> for Matrix<T> where T: Copy + Mul<T, Output=T>

Scalar multiplication with matrix.

Will reuse the memory allocated for the existing matrix.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, f: T) -> Matrix<T>

The method for the * operator

impl<'a, T> Mul<&'a T> for Matrix<T> where T: Copy + Mul<T, Output=T>

Scalar multiplication with matrix.

Will reuse the memory allocated for the existing matrix.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, f: &T) -> Matrix<T>

The method for the * operator

impl<'a, T> Mul<T> for &'a Matrix<T> where T: Copy + Mul<T, Output=T>

Scalar multiplication with matrix.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, f: T) -> Matrix<T>

The method for the * operator

impl<'a, 'b, T> Mul<&'b T> for &'a Matrix<T> where T: Copy + Mul<T, Output=T>

Scalar multiplication with matrix.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, f: &T) -> Matrix<T>

The method for the * operator

impl<T> Sub<T> for Matrix<T> where T: Copy + Sub<T, Output=T>

Scalar subtraction with matrix.

Will reuse the memory allocated for the existing matrix.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, f: T) -> Matrix<T>

The method for the - operator

impl<'a, T> Sub<&'a T> for Matrix<T> where T: Copy + Sub<T, Output=T>

Scalar subtraction with matrix.

Will reuse the memory allocated for the existing matrix.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, f: &T) -> Matrix<T>

The method for the - operator

impl<'a, T> Sub<T> for &'a Matrix<T> where T: Copy + Sub<T, Output=T>

Scalar subtraction with matrix.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, f: T) -> Matrix<T>

The method for the - operator

impl<'a, 'b, T> Sub<&'b T> for &'a Matrix<T> where T: Copy + Sub<T, Output=T>

Scalar subtraction with matrix.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, f: &T) -> Matrix<T>

The method for the - operator

impl<T> Div<T> for Matrix<T> where T: Copy + Div<T, Output=T>

Scalar division with matrix.

Will reuse the memory allocated for the existing matrix.

type Output = Matrix<T>

The resulting type after applying the / operator

fn div(self, f: T) -> Matrix<T>

The method for the / operator

impl<'a, T> Div<&'a T> for Matrix<T> where T: Copy + Div<T, Output=T>

Scalar division with matrix.

Will reuse the memory allocated for the existing matrix.

type Output = Matrix<T>

The resulting type after applying the / operator

fn div(self, f: &T) -> Matrix<T>

The method for the / operator

impl<'a, T> Div<T> for &'a Matrix<T> where T: Copy + Div<T, Output=T>

Scalar division with matrix.

type Output = Matrix<T>

The resulting type after applying the / operator

fn div(self, f: T) -> Matrix<T>

The method for the / operator

impl<'a, 'b, T> Div<&'b T> for &'a Matrix<T> where T: Copy + Div<T, Output=T>

Scalar division with matrix.

type Output = Matrix<T>

The resulting type after applying the / operator

fn div(self, f: &T) -> Matrix<T>

The method for the / operator

impl<T> Mul<Vector<T>> for Matrix<T> where T: Copy + Zero + Mul<T, Output=T> + Add<T, Output=T>

Multiplies matrix by vector.

type Output = Vector<T>

The resulting type after applying the * operator

fn mul(self, m: Vector<T>) -> Vector<T>

The method for the * operator

impl<'a, T> Mul<Vector<T>> for &'a Matrix<T> where T: Copy + Zero + Mul<T, Output=T> + Add<T, Output=T>

Multiplies matrix by vector.

type Output = Vector<T>

The resulting type after applying the * operator

fn mul(self, m: Vector<T>) -> Vector<T>

The method for the * operator

impl<'a, T> Mul<&'a Vector<T>> for Matrix<T> where T: Copy + Zero + Mul<T, Output=T> + Add<T, Output=T>

Multiplies matrix by vector.

type Output = Vector<T>

The resulting type after applying the * operator

fn mul(self, m: &Vector<T>) -> Vector<T>

The method for the * operator

impl<'a, 'b, T> Mul<&'b Vector<T>> for &'a Matrix<T> where T: Copy + Zero + Mul<T, Output=T> + Add<T, Output=T>

Multiplies matrix by vector.

type Output = Vector<T>

The resulting type after applying the * operator

fn mul(self, v: &Vector<T>) -> Vector<T>

The method for the * operator

impl<'a, T> Add<MatrixSlice<'a, T>> for Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, s: MatrixSlice<T>) -> Matrix<T>

The method for the + operator

impl<'a, 'b, T> Add<MatrixSlice<'a, T>> for &'b Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, s: MatrixSlice<T>) -> Matrix<T>

The method for the + operator

impl<'a, 'b, T> Add<&'b MatrixSlice<'a, T>> for Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, s: &MatrixSlice<T>) -> Matrix<T>

The method for the + operator

impl<'a, 'b, 'c, T> Add<&'c MatrixSlice<'a, T>> for &'b Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, s: &MatrixSlice<T>) -> Matrix<T>

The method for the + operator

impl<'a, T> Add<MatrixSliceMut<'a, T>> for Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, s: MatrixSliceMut<T>) -> Matrix<T>

The method for the + operator

impl<'a, 'b, T> Add<MatrixSliceMut<'a, T>> for &'b Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, s: MatrixSliceMut<T>) -> Matrix<T>

The method for the + operator

impl<'a, 'b, T> Add<&'b MatrixSliceMut<'a, T>> for Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, s: &MatrixSliceMut<T>) -> Matrix<T>

The method for the + operator

impl<'a, 'b, 'c, T> Add<&'c MatrixSliceMut<'a, T>> for &'b Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, s: &MatrixSliceMut<T>) -> Matrix<T>

The method for the + operator

impl<'a, T> Sub<MatrixSlice<'a, T>> for Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, s: MatrixSlice<T>) -> Matrix<T>

The method for the - operator

impl<'a, 'b, T> Sub<MatrixSlice<'a, T>> for &'b Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, s: MatrixSlice<T>) -> Matrix<T>

The method for the - operator

impl<'a, 'b, T> Sub<&'b MatrixSlice<'a, T>> for Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, s: &MatrixSlice<T>) -> Matrix<T>

The method for the - operator

impl<'a, 'b, 'c, T> Sub<&'c MatrixSlice<'a, T>> for &'b Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, s: &MatrixSlice<T>) -> Matrix<T>

The method for the - operator

impl<'a, T> Sub<MatrixSliceMut<'a, T>> for Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, s: MatrixSliceMut<T>) -> Matrix<T>

The method for the - operator

impl<'a, 'b, T> Sub<MatrixSliceMut<'a, T>> for &'b Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, s: MatrixSliceMut<T>) -> Matrix<T>

The method for the - operator

impl<'a, 'b, T> Sub<&'b MatrixSliceMut<'a, T>> for Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, s: &MatrixSliceMut<T>) -> Matrix<T>

The method for the - operator

impl<'a, 'b, 'c, T> Sub<&'c MatrixSliceMut<'a, T>> for &'b Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction between Matrix and MatrixSlice.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, s: &MatrixSliceMut<T>) -> Matrix<T>

The method for the - operator

impl<T> Add<Matrix<T>> for Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition between two matrices.

This will reuse allocated memory from self.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, m: Matrix<T>) -> Matrix<T>

The method for the + operator

impl<'a, T> Add<Matrix<T>> for &'a Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition between two matrices.

This will reuse allocated memory from m.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, m: Matrix<T>) -> Matrix<T>

The method for the + operator

impl<'a, T> Add<&'a Matrix<T>> for Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition between two matrices.

This will reuse allocated memory from self.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, m: &Matrix<T>) -> Matrix<T>

The method for the + operator

impl<'a, 'b, T> Add<&'b Matrix<T>> for &'a Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition between two matrices.

type Output = Matrix<T>

The resulting type after applying the + operator

fn add(self, m: &Matrix<T>) -> Matrix<T>

The method for the + operator

impl<T> Sub<Matrix<T>> for Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction between two matrices.

This will reuse allocated memory from self.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, m: Matrix<T>) -> Matrix<T>

The method for the - operator

impl<'a, T> Sub<Matrix<T>> for &'a Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction between two matrices.

This will reuse allocated memory from m.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, m: Matrix<T>) -> Matrix<T>

The method for the - operator

impl<'a, T> Sub<&'a Matrix<T>> for Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction between two matrices.

This will reuse allocated memory from self.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, m: &Matrix<T>) -> Matrix<T>

The method for the - operator

impl<'a, 'b, T> Sub<&'b Matrix<T>> for &'a Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction between two matrices.

type Output = Matrix<T>

The resulting type after applying the - operator

fn sub(self, m: &Matrix<T>) -> Matrix<T>

The method for the - operator

impl<T> AddAssign<T> for Matrix<T> where T: Copy + Add<T, Output=T>

Performs addition assignment between a matrix and a scalar.

fn add_assign(&mut self, _rhs: T)

The method for the += operator

impl<'a, T> AddAssign<&'a T> for Matrix<T> where T: Copy + Add<T, Output=T>

Performs addition assignment between a matrix and a scalar.

fn add_assign(&mut self, _rhs: &T)

The method for the += operator

impl<T> SubAssign<T> for Matrix<T> where T: Copy + Sub<T, Output=T>

Performs subtraction assignment between a matrix and a scalar.

fn sub_assign(&mut self, _rhs: T)

The method for the -= operator

impl<'a, T> SubAssign<&'a T> for Matrix<T> where T: Copy + Sub<T, Output=T>

Performs subtraction assignment between a matrix and a scalar.

fn sub_assign(&mut self, _rhs: &T)

The method for the -= operator

impl<T> DivAssign<T> for Matrix<T> where T: Copy + Div<T, Output=T>

Performs division assignment between a matrix and a scalar.

fn div_assign(&mut self, _rhs: T)

The method for the /= operator

impl<'a, T> DivAssign<&'a T> for Matrix<T> where T: Copy + Div<T, Output=T>

Performs division assignment between a matrix and a scalar.

fn div_assign(&mut self, _rhs: &T)

The method for the /= operator

impl<T> MulAssign<T> for Matrix<T> where T: Copy + Mul<T, Output=T>

Performs multiplication assignment between a matrix and a scalar.

fn mul_assign(&mut self, _rhs: T)

The method for the *= operator

impl<'a, T> MulAssign<&'a T> for Matrix<T> where T: Copy + Mul<T, Output=T>

Performs multiplication assignment between a matrix and a scalar.

fn mul_assign(&mut self, _rhs: &T)

The method for the *= operator

impl<T> AddAssign<Matrix<T>> for Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition assignment between two matrices.

fn add_assign(&mut self, _rhs: Matrix<T>)

The method for the += operator

impl<'a, T> AddAssign<&'a Matrix<T>> for Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition assignment between two matrices.

fn add_assign(&mut self, _rhs: &Matrix<T>)

The method for the += operator

impl<T> SubAssign<Matrix<T>> for Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction assignment between two matrices.

fn sub_assign(&mut self, _rhs: Matrix<T>)

The method for the -= operator

impl<'a, T> SubAssign<&'a Matrix<T>> for Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction assignment between two matrices.

fn sub_assign(&mut self, _rhs: &Matrix<T>)

The method for the -= operator

impl<'a, T> AddAssign<MatrixSlice<'a, T>> for Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition assignment between two matrices.

fn add_assign(&mut self, _rhs: MatrixSlice<T>)

The method for the += operator

impl<'a, 'b, T> AddAssign<&'b MatrixSlice<'a, T>> for Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition assignment between two matrices.

fn add_assign(&mut self, _rhs: &MatrixSlice<T>)

The method for the += operator

impl<'a, T> SubAssign<MatrixSlice<'a, T>> for Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction assignment between two matrices.

fn sub_assign(&mut self, _rhs: MatrixSlice<T>)

The method for the -= operator

impl<'a, 'b, T> SubAssign<&'b MatrixSlice<'a, T>> for Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction assignment between two matrices.

fn sub_assign(&mut self, _rhs: &MatrixSlice<T>)

The method for the -= operator

impl<'a, T> AddAssign<MatrixSliceMut<'a, T>> for Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition assignment between two matrices.

fn add_assign(&mut self, _rhs: MatrixSliceMut<T>)

The method for the += operator

impl<'a, 'b, T> AddAssign<&'b MatrixSliceMut<'a, T>> for Matrix<T> where T: Copy + Add<T, Output=T>

Performs elementwise addition assignment between two matrices.

fn add_assign(&mut self, _rhs: &MatrixSliceMut<T>)

The method for the += operator

impl<'a, T> SubAssign<MatrixSliceMut<'a, T>> for Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction assignment between two matrices.

fn sub_assign(&mut self, _rhs: MatrixSliceMut<T>)

The method for the -= operator

impl<'a, 'b, T> SubAssign<&'b MatrixSliceMut<'a, T>> for Matrix<T> where T: Copy + Sub<T, Output=T>

Performs elementwise subtraction assignment between two matrices.

fn sub_assign(&mut self, _rhs: &MatrixSliceMut<T>)

The method for the -= operator

impl<T> Neg for Matrix<T> where T: Neg<Output=T> + Copy

Gets negative of matrix.

type Output = Matrix<T>

The resulting type after applying the - operator

fn neg(self) -> Matrix<T>

The method for the unary - operator

impl<'a, T> Neg for &'a Matrix<T> where T: Neg<Output=T> + Copy

Gets negative of matrix.

type Output = Matrix<T>

The resulting type after applying the - operator

fn neg(self) -> Matrix<T>

The method for the unary - operator

impl<'a, T: 'a + Copy> FromIterator<&'a [T]> for Matrix<T>

Creates a Matrix from an iterator over slices.

Each of the slices produced by the iterator will become a row in the matrix.

Panics

Will panic if the iterators items do not have constant length.

Examples

We can create a new matrix from some data.

use rulinalg::matrix::{Matrix, BaseMatrix};

let a : Matrix<f64> = vec![4f64; 16].chunks(4).collect();

assert_eq!(a.rows(), 4);
assert_eq!(a.cols(), 4);

We can also do more interesting things.

use rulinalg::matrix::{Matrix, BaseMatrix};

let a = Matrix::new(4,2, (0..8).collect::<Vec<usize>>());

// Here we skip the first row and take only those
// where the first entry is less than 6.
let b = a.row_iter()
         .skip(1)
         .filter(|x| x[0] < 6)
         .collect::<Matrix<usize>>();

// We take the middle rows
assert_eq!(b.into_vec(), vec![2,3,4,5]);

fn from_iter<I: IntoIterator<Item=&'a [T]>>(iterable: I) -> Self

Creates a value from an iterator.

impl<'a, T: 'a + Copy> FromIterator<Row<'a, T>> for Matrix<T>

fn from_iter<I: IntoIterator<Item=Row<'a, T>>>(iterable: I) -> Self

Creates a value from an iterator.

impl<'a, T: 'a + Copy> FromIterator<RowMut<'a, T>> for Matrix<T>

fn from_iter<I: IntoIterator<Item=RowMut<'a, T>>>(iterable: I) -> Self

Creates a value from an iterator.

impl<'a, T: Any + Copy + Zero + Add<T, Output=T> + Mul<T, Output=T>> Mul<Matrix<T>> for Matrix<T>

Multiplies two matrices together.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, m: Matrix<T>) -> Matrix<T>

The method for the * operator

impl<'a, 'b, T> Mul<&'a Matrix<T>> for Matrix<T> where T: Any + Copy + Zero + Add<T, Output=T> + Mul<T, Output=T>

Multiplies two matrices together.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, m: &Matrix<T>) -> Matrix<T>

The method for the * operator

impl<'a, T> Mul<Matrix<T>> for &'a Matrix<T> where T: Any + Copy + Zero + Add<T, Output=T> + Mul<T, Output=T>

Multiplies two matrices together.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, m: Matrix<T>) -> Matrix<T>

The method for the * operator

impl<'a, 'b, T> Mul<&'b Matrix<T>> for &'a Matrix<T> where T: Any + Copy + Zero + Add<T, Output=T> + Mul<T, Output=T>

Multiplies two matrices together.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, m: &Matrix<T>) -> Matrix<T>

The method for the * operator

impl<'a, T> Mul<MatrixSlice<'a, T>> for Matrix<T> where T: Any + Copy + Zero + Add<T, Output=T> + Mul<T, Output=T>

Multiplies two matrices together.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, m: MatrixSlice<T>) -> Matrix<T>

The method for the * operator

impl<'a, 'b, T> Mul<&'b MatrixSlice<'a, T>> for Matrix<T> where T: Any + Copy + Zero + Add<T, Output=T> + Mul<T, Output=T>

Multiplies two matrices together.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, m: &MatrixSlice<T>) -> Matrix<T>

The method for the * operator

impl<'a, 'b, T> Mul<MatrixSlice<'a, T>> for &'b Matrix<T> where T: Any + Copy + Zero + Add<T, Output=T> + Mul<T, Output=T>

Multiplies two matrices together.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, m: MatrixSlice<T>) -> Matrix<T>

The method for the * operator

impl<'a, 'b, 'c, T> Mul<&'c MatrixSlice<'a, T>> for &'b Matrix<T> where T: Any + Copy + Zero + Add<T, Output=T> + Mul<T, Output=T>

Multiplies two matrices together.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, m: &MatrixSlice<T>) -> Matrix<T>

The method for the * operator

impl<'a, T> Mul<MatrixSliceMut<'a, T>> for Matrix<T> where T: Any + Copy + Zero + Add<T, Output=T> + Mul<T, Output=T>

Multiplies two matrices together.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, m: MatrixSliceMut<T>) -> Matrix<T>

The method for the * operator

impl<'a, 'b, T> Mul<&'b MatrixSliceMut<'a, T>> for Matrix<T> where T: Any + Copy + Zero + Add<T, Output=T> + Mul<T, Output=T>

Multiplies two matrices together.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, m: &MatrixSliceMut<T>) -> Matrix<T>

The method for the * operator

impl<'a, 'b, T> Mul<MatrixSliceMut<'a, T>> for &'b Matrix<T> where T: Any + Copy + Zero + Add<T, Output=T> + Mul<T, Output=T>

Multiplies two matrices together.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, m: MatrixSliceMut<T>) -> Matrix<T>

The method for the * operator

impl<'a, 'b, 'c, T> Mul<&'c MatrixSliceMut<'a, T>> for &'b Matrix<T> where T: Any + Copy + Zero + Add<T, Output=T> + Mul<T, Output=T>

Multiplies two matrices together.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, m: &MatrixSliceMut<T>) -> Matrix<T>

The method for the * operator

impl<T> Mul<PermutationMatrix<T>> for Matrix<T>

Right-multiply a matrix by a permutation matrix.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, rhs: PermutationMatrix<T>) -> Matrix<T>

The method for the * operator

impl<'a, T> Mul<&'a PermutationMatrix<T>> for Matrix<T> where T: Clone

Right-multiply a matrix by a permutation matrix.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, rhs: &'a PermutationMatrix<T>) -> Matrix<T>

The method for the * operator

impl<'a, 'm, T> Mul<PermutationMatrix<T>> for &'a Matrix<T> where T: Zero + Clone

Right-multiply a matrix by a permutation matrix.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, rhs: PermutationMatrix<T>) -> Matrix<T>

The method for the * operator

impl<'a, 'b, 'm, T> Mul<&'b PermutationMatrix<T>> for &'a Matrix<T> where T: Zero + Clone

Right-multiply a matrix by a permutation matrix.

type Output = Matrix<T>

The resulting type after applying the * operator

fn mul(self, rhs: &'b PermutationMatrix<T>) -> Matrix<T>

The method for the * operator

impl<T: Debug> Debug for Matrix<T>

fn fmt(&self, __arg_0: &mut Formatter) -> Result

Formats the value using the given formatter.

impl<T: Clone> Clone for Matrix<T>

fn clone(&self) -> Matrix<T>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: PartialEq> PartialEq for Matrix<T>

fn eq(&self, __arg_0: &Matrix<T>) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, __arg_0: &Matrix<T>) -> bool

This method tests for !=.

impl<T: Eq> Eq for Matrix<T>

impl<T: Hash> Hash for Matrix<T>

fn hash<__HT: Hasher>(&self, __arg_0: &mut __HT)

Feeds this value into the state given, updating the hasher as necessary.

fn hash_slice<H>(data: &[Self], state: &mut H) where H: Hasher

Feeds a slice of this type into the state provided.

impl<T> From<Vector<T>> for Matrix<T>

fn from(vector: Vector<T>) -> Self

Performs the conversion.

impl<'a, T: Copy> From<MatrixSlice<'a, T>> for Matrix<T>

fn from(slice: MatrixSlice<'a, T>) -> Self

Performs the conversion.

impl<'a, T: Copy> From<MatrixSliceMut<'a, T>> for Matrix<T>

fn from(slice: MatrixSliceMut<'a, T>) -> Self

Performs the conversion.