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A Dart matrix computing library, providing basic operations of linear algebra

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Matrices - Dart Matrix Computing Library

中文文档    中文文档(Gitee)
Grayscale releases are marked with '!'
Unimplemented functions are marked with '*'
Usage: https://pub.dev/packages/matrices

CONTENT

Matrices introduction #

Matrices is a matrix library written purely in Dart. It is developed to provide support for projects like Astable which requires mathematical computation.

Matrix class #

The matrix class provides all the methods shared by any types of matrix like vector, square matrix or non-square matrix. For example, methods are provided to create a matrix, to query or update element at certain position, to append a row or column to the existing matrix, etc. However, it does not provides methods special for a square matrix. Importing 'Matrix.dart' is required before using methods listed below.

Illustrations of Matrix class #

The Matrix class only has one public field - 'Matrix' whose runtimetype is List<List< double >>. Thus, the operation of updating the matrix is the same as the operation on a 'list' instance. We do not provide the concept of vectors, please use the List< double > type instead. However, you are NOT ALLOWED to initialize a Matrix instance through Matrix() conctructor. Instead, a few named constructors are provided for initialization of a Matrix instance.

Create a Matrix instance #

Create a matrix

  /// Matrix.fromList(List<List<double>> lists)

  var mat = Matrix.fromList([
    [2, 3, 3, 3],
    [9, 9, 8, 6],
    [1, 1, 2, 9]
  ]);
  print( mat );

  // Matrix: 3x4
  // [2.0, 3.0, 3.0, 3.0]
  // [9.0, 9.0, 8.0, 6.0]
  // [1.0, 1.0, 2.0, 9.0]

Matrix of zeros

  /// Matrix.zero(int row, int column)

  var mat = Matrix.zero(2, 3);
  print( mat );

  // Matrix: 2x3
  // [0.0, 0.0, 0.0]
  // [0.0, 0.0, 0.0]

Matrix of ones

  /// Matrix.one(int row, int column)

  var mat = Matrix.one(2, 3);
  print( mat );
  
  // Matrix: 2x3
  // [1.0, 1.0, 1.0]
  // [1.0, 1.0, 1.0]

Matrix of a certain number

  /// Matrix.number(double number, int row, int column)

  var mat = Matrix.number(9, 2, 3);
  print( mat );
  
  // Matrix: 2x3
  // [9.0, 9.0, 9.0]
  // [9.0, 9.0, 9.0]

Matrix of random numbers

  /// Matrix.random(int row, int column)

  var mat = Matrix.random(2, 3);
  print( mat );
  
  // Matrix: 2x3
  // [0.38224693703597046, 0.5412146597032305, 0.6424342222644003]
  // [0.8491145735932242, 0.6236773300386973, 0.25269555696856316]

Select #

Taking the matrix 'mat' as example.

Matrix mat 3x4
    [2, 3, 3, 3]
    [9, 9, 8, 6]
    [1, 1, 2, 9]

Access item

  print( mat.matrix[1][2] );

  // 8.0

Access row

  print( mat.row(0) );    

  // [2.0, 3.0, 3.0, 3.0]

Access column

  /// List<double> column(int column)

  print( mat.column(0) );

  // [2.0, 9.0, 1.0]

Transpose

  /// Matrix transpose()

  print( mat.transpose() );

  // Matrix: 4x3
  // [2.0, 9.0, 1.0]
  // [3.0, 9.0, 1.0]
  // [3.0, 8.0, 2.0]
  // [3.0, 6.0, 9.0]

Row-echelon form

  /// Matrix rowEchelonForm()

  print( mat.rowEchelonForm() );

  // Matrix: 3x4
  // [1.0, 0.0, 0.0, 1.5]
  // [0.0, 1.0, 0.0, -7.5]
  // [0.0, 0.0, 1.0, 7.5]

Rank

  /// int rank()

  print( mat.rank() );

  // 3

Update #

Taking the matrix 'mat' as example.

Matrix mat 3x4
    [2, 3, 3, 3]
    [9, 9, 8, 6]
    [1, 1, 2, 9]

Update item

  mat.matrix[0][0] = 3;
  print( mat.matrix[0] );

  // [3.0, 3.0, 3.0, 3.0]

Update row

  /// setRow(List<double> list, int row)

  mat.setRow([1, 4, 5, 0], 0);
  print( mat.matrix[0] );

  // [1.0, 4.0, 5.0, 0.0]

Update column

  /// setColumn(List<double> list, int column)

  mat.setColumn([1, 4, 5], 0);
  print( mat );

  // Matrix: 3x4
  // [1.0, 3.0, 3.0, 3.0]
  // [4.0, 9.0, 8.0, 6.0]
  // [5.0, 1.0, 2.0, 9.0]

Insert #

Taking the matrix 'mat' as example.

Matrix mat 3x4
    [2, 3, 3, 3]
    [9, 9, 8, 6]
    [1, 1, 2, 9]

Insert row

  /// addRow(List<double> list, int index)

  mat.addRow([8,8,8,8], 0);
  print( mat );

  // Matrix: 4x4
  // [8.0, 8.0, 8.0, 8.0]
  // [2.0, 3.0, 3.0, 3.0]
  // [9.0, 9.0, 8.0, 6.0]
  // [1.0, 1.0, 2.0, 9.0]

Insert column

  /// addColumn(List<double> list, int index)

  mat.addColumn([8, 8, 8], 4);
  print( mat );

  // Matrix: 3x5
  // [2.0, 3.0, 3.0, 3.0, 8.0]
  // [9.0, 9.0, 8.0, 6.0, 8.0]
  // [1.0, 1.0, 2.0, 9.0, 8.0]

Append rows

  /// appendRows(Matrix injected)

  var tail = Matrix.fromList([
    [8, 8, 8, 8],
    [8, 8, 8, 8]
  ]);
  mat.appendRows(tail);
  print( mat );

  // Matrix: 5x4
  // [2.0, 3.0, 3.0, 3.0]
  // [9.0, 9.0, 8.0, 6.0]
  // [1.0, 1.0, 2.0, 9.0]
  // [8.0, 8.0, 8.0, 8.0]
  // [8.0, 8.0, 8.0, 8.0]

Append columns

  /// appendColumns(Matrix injected)

  var tail = Matrix.fromList([
    [8, 8],
    [8, 8],
    [8, 8]
  ]);
  mat.appendColumns(tail);
  print( mat );

  // Matrix: 3x6
  // [2.0, 3.0, 3.0, 3.0, 8.0, 8.0]
  // [9.0, 9.0, 8.0, 6.0, 8.0, 8.0]
  // [1.0, 1.0, 2.0, 9.0, 8.0, 8.0]

Delete #

Taking the matrix 'mat' as example.

Matrix mat 3x4
    [2, 3, 3, 3]
    [9, 9, 8, 6]
    [1, 1, 2, 9]

Delete row

  /// deleteRow(int index)

  mat.deleteRow(0);
  print( mat );

  // Matrix: 2x4
  // [9.0, 9.0, 8.0, 6.0]
  // [1.0, 1.0, 2.0, 9.0]

Delete column

  /// deleteColumn(int index)

  mat.deleteColumn(0);
  print( mat );
  
  // Matrix: 3x3
  // [3.0, 3.0, 3.0]
  // [9.0, 8.0, 6.0]
  // [1.0, 2.0, 9.0]

Delete rows

PS: While deleting rows, the indexs MUST be put in order FROM SMALLEST TO LARGEST.

  /// deleteRows(List<int> list)

  mat.deleteRows([0, 1]);
  print( mat );

  // Matrix: 1x4
  // [1.0, 1.0, 2.0, 9.0]

Delete columns

PS: While deleting columns, the indexs MUST be put in order FROM SMALLEST TO LARGEST.

  /// deleteColumns(List<int> list)

  mat.deleteColumns([0, 2]);
  print( mat );

  // Matrix: 3x2
  // [3.0, 3.0]
  // [9.0, 6.0]
  // [1.0, 9.0]

Arithmetic operations #

Addition

  var mat = Matrix.fromList([
    [2, 3, 3],
    [1, 2, 9]
  ]);
  print( mat + 3 );
  print( mat + mat );

Subtraction

  var mat = Matrix.fromList([
    [2, 3, 3],
    [1, 2, 9]
  ]);
  print( mat - 3 );

Multiplication

  // Scalar matrix multiplication (the scalar number MUST be in the right position)
  var mat = Matrix.fromList([
    [2, 3, 3],
    [1, 2, 9]
  ]);
  print( mat * 3 );

  // Matrix: 2x3
  // [6.0, 9.0, 9.0]
  // [3.0, 6.0, 27.0]

  // Matrix multiplication
  var multi = Matrix.fromList([
    [2, 3.5],
    [1, -2],
    [-4, 0.5]
  ]);
  print( mat * multi );

  // Matrix: 2x2
  // [-5.0, 2.5]
  // [-32.0, 4.0]

Caution! #

Follow-up plan #

SquareMatrix class #

The SquareMatrix class has methods special for square matrix, like creating a squarematrix instance, calculating the determinant, the inverse, the eigen values and the eigen vectors, etc. Importing 'SquareMatrix.dart' is required before using methods listed below.

Illustrations of SquareMatrix class #

Createa a SquareMatrix instance #

Create a square matrix

  /// SquareMatrix.fromList(List<List<double>> lists)

  var mat = SquareMatrix.fromList([
    [2, 3, 3],
    [1, 2, 9],
    [9, 8, 6]
  ]);
  print( mat );

  // Matrix: 3x3
  // [6.0, 9.0, 9.0]
  // [3.0, 6.0, 27.0]
  // [27.0, 24.0, 18.0]

SquareMatrix of zeros

  /// SquareMatrix.zero(int row)

  var mat = SquareMatrix.zero(3);
  print( mat );

  // SquareMatrix: 3x3
  // [0.0, 0.0, 0.0]
  // [0.0, 0.0, 0.0]
  // [0.0, 0.0, 0.0]

SquareMatrix of ones

  /// SquareMatrix.one(int row)

  var mat = SquareMatrix.one(3);
  print( mat );

  // SquareMatrix: 3x3
  // [1.0, 1.0, 1.0]
  // [1.0, 1.0, 1.0]
  // [1.0, 1.0, 1.0]

SquareMatrix of a certain number

  /// SquareMatrix.number(double number, int row)

  var mat = SquareMatrix.number(2, 3);
  print( mat );

  // SquareMatrix: 3x3
  // [2.0, 2.0, 2.0]
  // [2.0, 2.0, 2.0]
  // [2.0, 2.0, 2.0]

SquareMatrix of random numbers

  /// SquareMatrix.random(int row)

  var mat = SquareMatrix.random(3);
  print( mat );

  // SquareMatrix: 3x3
  // [0.2666268534804871, 0.607635195280705, 0.581392153915932]
  // [0.3590813328566256, 0.8098420655296595, 0.015949886001227154]
  // [0.6670401483574298, 0.3054732396044414, 0.3113168618967712]

Create diagonal square matrix from list

  /// SquareMatrix.diagonal(List<double> list)

  var mat = SquareMatrix.diagonal([1,2,3]);
  print( mat );

  // SquareMatrix: 3x3
  // [1.0, 0.0, 0.0]
  // [0.0, 2.0, 0.0]
  // [0.0, 0.0, 3.0]

Create diagonal square matrix from number

  /// SquareMatrix.diagonalFromNumber(double num, int row)

  var mat = SquareMatrix.diagonalFromNumber(2,3);
  print( mat );

  // SquareMatrix: 3x3
  // [2.0, 0.0, 0.0]
  // [0.0, 2.0, 0.0]
  // [0.0, 0.0, 2.0]

Special properties of square matrix #

Determinant

  /// double determinant()

  var dett = SquareMatrix.fromList([
    [1, 2],
    [1, 1]
  ]);
  print(dett.determinant());

  // -1.0

Inverse

  /// SquareMatrix inverse()

  var dett = SquareMatrix.fromList([
    [1, 2],
    [1, 1]
  ]);
  print(dett.inverse());

  // SquareMatrix: 2x2
  // [1.0, -1.0]
  // [1.0, -1.0]

Eigenvalues *

  /// double eigenvalue()

Eigenvectors *

  /// Matrix eigenvector()

Caution! #

Follow-up plan #

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A Dart matrix computing library, providing basic operations of linear algebra

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