Matrix<T> class abstract base

A simple Dart implementation of a matrix whose size is m x n. Thanks to its generic nature, you can decide to work with int, double, Complex or any other kind of numerical type. This library implements:

By default, the cells of a matrix are initialized with zeroes. You can access elements of the matrix either by calling itemAt or by using the call method (which makes the object 'callable').

Implementers

Constructors

Matrix({required int rows, required int columns, required T defaultValue, required T identityOneValue, bool identity = false})
Creates a new N x M matrix where rows is N and columns is M. The matrix is filled with zeroes.
Matrix.diagonal({required int rows, required int columns, required T defaultValue, required T diagonalValue})
Creates a new N x M matrix where rows is N and columns is M. The matrix is filled with diagonalValue in the main diagonal and zeroes otherwise.
Matrix.fromData({required int rows, required int columns, required List<List<T>> data})
Creates a new N x M matrix where rows is N and columns is M. The matrix is filled with values from data.
Matrix.fromFlattenedData({required int rows, required int columns, required List<T> data})
Creates a new N x M matrix where rows is N and columns is M. The matrix is filled with values from data.

Properties

columnCount → int
The number of columns of the matrix.
final
flattenData → List<T>
An unmodifiable, flattened representation of the matrix data.
no setter
hashCode → int
The hash code for this object.
no setteroverride
isSquareMatrix → bool
Determines whether the matrix is square nor not.
no setter
rowCount → int
The number of rows of the matrix.
final
runtimeType → Type
A representation of the runtime type of the object.
no setterinherited

Methods

call(int row, int col) → T
Use this method to retrieve the element at a given position in the matrix. For example:
characteristicPolynomial() → Algebraic
The characteristic polynomial can only be computed if the matrix is square, meaning that it must have the same number of columns and rows.
choleskyDecomposition() → List<Matrix<T>>
Uses the the Cholesky decomposition algorithm to factor the matrix into the product of a lower triangular matrix and its conjugate transpose. In particular, this method returns the L and LT matrices of the
cofactorMatrix() → Matrix<T>
The matrix formed by all of the cofactors of a square matrix is called the "cofactor matrix" (also called "the matrix of cofactors").
determinant() → T
The determinant can only be computed if the matrix is square, meaning that it must have the same number of columns and rows.
eigenDecomposition() → List<Matrix<T>>
Computes the V, D and V' matrices of the eigendecomposition algorithm. In particular, this method returns the following matrices:
eigenvalues() → List<Complex>
Returns the eigenvalues associated to this matrix.
inverse() → Matrix<T>
Returns the inverse of this matrix.
isDiagonal() → bool
A diagonal matrix is a matrix in which the entries outside the main diagonal are all zero.
isIdentity() → bool
The identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by In, or simply by I.
isSymmetric() → bool
A symmetric matrix is a square matrix that is equal to its transpose. Because equal matrices have equal dimensions, only square matrices can be symmetric.
itemAt(int row, int col) → T
Use this method to retrieve the element at a given position in the matrix. For example:
luDecomposition() → List<Matrix<T>>
Factors the matrix as the product of a lower triangular matrix L and an upper triangular matrix U. The matrix must be square.
minor(int row, int col) → Matrix<T>
A minor of a matrix A is the determinant of some smaller square matrix, cut down from A by removing one or more of its rows and columns.
noSuchMethod(Invocation invocation) → dynamic
Invoked when a nonexistent method or property is accessed.
inherited
qrDecomposition() → List<Matrix<T>>
Computes the Q and R matrices of the QR decomposition algorithm. In particular, this method returns the Q and R matrices of the
rank() → int
The rank of a matrix A is the dimension of the vector space generated by its columns. This corresponds to the maximal number of linearly independent columns of A.
singleValueDecomposition() → List<Matrix<T>>
Computes the E, U and V matrices of the SVD (Single Value Decomposition) algorithm. In particular, this method returns the following matrices:
toList() → List<T>
Returns a modifiable "flattened" view of the matrix as a List<T> object.
toListOfList() → List<List<T>>
Returns a modifiable view of the matrix as a List<List<T>> object.
toString() → String
A string representation of this object.
override
trace() → T
The trace of a square matrix A, denoted tr(A), is defined to be the sum of elements on the main diagonal (from the upper left to the lower right).
transpose() → Matrix<T>
Returns the transpose of this matrix.
transposedValue(int row, int col) → T
Returns the value at (row, col) position as if this matrix were transposed. For example, let's say we have this matrix object:

Operators

operator *(Matrix<T> other) → Matrix<T>
Returns the product of two matrices.
operator +(Matrix<T> other) → Matrix<T>
Returns the sum of two matrices.
operator -(Matrix<T> other) → Matrix<T>
Returns the difference of two matrices.
operator /(Matrix<T> other) → Matrix<T>
Returns the division of two matrices.
operator ==(Object other) → bool
The equality operator.
override