Matrices - Matrix Operations and Linear Algebra Library

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Matrices is a matrix operations and linear algebra library for Dart. It was developed to provide matrix operations support for projects such as Astable. All operations are currently implemented in Dart language. To use it, you need to import the matrices.dart file. Also, before using Matrices, you need to understand the concepts related to linear algebra.

Linear algebra is a branch of mathematics that deals with vectors, linear spaces, linear transformations and finite dimensional systems of linear equations. Linear algebra deals with linear relations. A linear relationship means that the relationship between mathematical objects is expressed in a one-time form. Since nonlinear models in scientific research can often be approximated as linear models, linear algebra is widely used in the natural and social sciences.

Getting Started

  /// Creating a matrix

  var mat = Matrix.fromList([
    [1, 2, 3],
    [4, 5, 6]
  ]);
  print( mat );

  // Matrix: 2x4
  // [1.0, 2.0, 3.0]
  // [4.0, 5.0, 6.0]

  /// Creating a matrix filled with 0’s

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

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

  /// Creating a matrix filled with 1’s

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

  /// Creating a matrix filled with certain value

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

  /// Creating a matrix from a flattened list
  
  // If the length of the flattened list is smaller than the expected matrix size,
  // zeros will be filled in the vacant position.
  
  var mat1 = Matrix.fromFlattenedList([1, 2, 3, 4], 2, 2);
  var mat2 = Matrix.fromFlattenedList([1, 2, 3, 4], 2, 3);
  print(mat1);
  print(mat2);

  // Matrix: 2x2
  // [1.0, 2.0]
  // [3.0, 4.0]

  // Matrix: 2x3
  // [1.0, 2.0, 3.0]
  // [4.0, 0.0, 0.0]

  /// Creating a matrix filled with random values

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

  /// Addition

  print( mat + 3 );
  print( mat + mat );

  // Matrix: 2x3
  // [4.0, 5.0, 6.0]
  // [7.0, 8.0, 9.0]

  // Matrix: 2x3
  // [2.0, 4.0, 6.0]
  // [8.0, 10.0, 12.0]

  /// Take the matrix mat as example
  Matrix mat 2x4
      [1, 2, 3, 4]
      [5, 6, 7, 8]

  /// Indexing a matrix element
  print( mat[1][2] );

  // 7.0

  /// Number of rows
  print( mat.rowCount );

  // 2

  /// Number of columns
  print( mat.columnCount );

  // 4

  /// Total number of elements
  print( mat.count );

  // 8


  /// Slicing a row

  print( mat.row(0) );

  // An easier slicing method
  print( mat[0] );

  // [1.0, 2.0, 3.0, 4.0]
  // [1.0, 2.0, 3.0, 4.0]

  /// Slicing a column
  print( mat.column(0) );

  // Here, we also provide an easier slicing method for columns
  // Add a minus before real column index to slice column (except the 1st column)

  // Slicing the 1st column
  print( mat[''] );

  // Slicing the 2nd column
  print( mat[-1] );

  // [1.0, 5.0]
  // [1.0, 5.0]
  // [2.0, 6.0]

  /// Transposing
  print( mat.transpose );

  // Matrix: 4x2
  // [1.0, 5.0]
  // [2.0, 6.0]
  // [3.0, 7.0]
  // [4.0, 8.0]

  /// Row Echelon Form
  print( mat.rowEchelonForm );

  // Matrix: 2x4
  // [1.0, 0.0, -1.00000, -2.00000]
  // [0.0, 1.0, 2.00000, 3.00000]


  /// Rank
  print( mat.rank );

  // 2

  /// Take the matrix mat as example, too.
  Matrix mat 2x4
      [1, 2, 3, 4]
      [5, 6, 7, 8]

  /// Modify an element
  mat[0][0] = 6;
  print( mat[0] );

  // [6.0, 2.0, 3.0, 4.0]

  /// Modify a row
  mat.setRow([6, 6, 6, 6], 0);
  print( mat[0] );

  // [6.0, 6.0, 6.0, 6.0]

  // A eaiser way to modify a row
  mat[0] = [8, 8, 8, 8];
  print( mat[0] );

  // [8.0, 8.0, 8.0, 8.0]

  /// Modify a column
  mat.setColumn([6, 6], 0);
  print( mat );

  // Matrix: 2x4
  // [6.0, 2.0, 3.0, 4.0]
  // [6.0, 6.0, 7.0, 8.0]

  // A eaiser way to modify a column
  // Add a minus before real column index to modify column (except the 1st column which requires an empty string)
  mat[''] = [8, 8];
  mat[-1] = [9, 9];
  print( mat );

  // Matrix: 2x4
  // [8.0, 9.0, 3.0, 4.0]
  // [8.0, 9.0, 7.0, 8.0]

  /// Subtraction

  var mat1 = Matrix.fromList([
    [1, 2, 1],
    [1, 2, 1]
  ]);
  print( mat - 3 );
  print( mat - mat1 );

  // Matrix: 2x3
  // [-2.0, -1.0, 0.0]
  // [1.0, 2.0, 3.0]

  // Matrix: 2x3
  // [0.0, 0.0, 2.0]
  // [3.0, 3.0, 5.0]


  /// Scalar Multiplication

  // Note: Scalar should be on the right position of the operator *
  print( mat * 3 );

  // Matrix: 2x3
  // [3.0, 6.0, 9.0]
  // [12.0, 15.0, 18.0]


  /// Matrix Product

  var mat2 = Matrix.fromList([
    [2, 3.5],
    [1, -2],
    [-4, 0.5]
  ]);
  print( mat * mat2 );

  // Matrix: 2x2
  // [-8.0, 1.0]
  // [-11.0, 7.0]

  /// This is only a small part of Matrices, please check the documentation for more usage !

User Guide

Find more functions and usage, please click Matrices Document to explore the exciting world of matrices

Who's using it?

  • Astable - A beautiful and powerful structural mechanics software

Libraries

matrices
test