List Operators

Introduction

The package list_operators uses Dart Extensions to provide operators and utility methods for objects of type List and Iterable. Note: The operators and methods listed below are generative in the sense that they return a new object. For example the unary negation operator -a applied to a list a returns a new list and does not modify the elements of a in place.

Extensions on List<T extends num> make the following vector-style operators and methods availabe:

• subtraction a-b: element by element,
• unary negation -a: negates every element,
• scalar multiplication a*x: x is a num,
• scalar division a/x: x is a num,
• integer division a~/x: x is a num,
• a.plus(b): addition, element by element,
• a.innerProd(b): the inner product Σ_i (a_i · b_i),
• a.distance(b): distance using an Euclidian metric,
• a.distanceFromOrigin(),
• a.sphericalToCartesian: transforms Polar Spherical coordinates to Cartesian coordinates,
• a.cartesianToSpherical: transforms Cartesian coordinates to Polar Spherical coordinates,
• a.cartesianToCylindrical: transforms Cartesian coordinates to Cylindrical coordinates, a.cylindricalToCartesian: transforms Cylindrical coordinates to Cartesian coordinates.
• a.equal(b): Returns true if a[i] == b[i] for each index i,
• a.match(b, precision): Returns true if (a[i] - b[i]) <= precision for each index i. Note: The corresponding matcher is named CloseToList in analogy with the package matcher.

For objects of type Iterable<T extends num>, which includes lists and sets, the following methods are provided:

• a.abs(): absolute value,
• a.pow(): power,
• a.exp(): exponentiation,
• a.min(): minimum value,
• a.max(): maximum value,
• a.mean(): mean of all elements,
• a.stdDev(): standard deviation,
• a.sum(): sum of all elements,
• a.prod(): product of all elements.

For objects of type List<T extends Comparable> the library introduces the comparison operators a < b, a <= b, a > b, a >= b.

Usage

Include list_operatos as a dependency in your pubspec.yaml file. The programs below demonstrates how to use operators and methods defined by the library list_operators.

Methods and Operators For Objects of Type List<num>:

import 'package:list_operators/list_operators.dart';

void main() {
  final a = [1, 2, 3];
  final b = [11, 12, 13];

  /// Use with List<num>
  print('Absolute value:');
  print((a - b).abs());
  print('');

  print('Addition:');
  print(a.plus(b));
  print('');

  print('Subtraction:');
  print(b - a);
  print('');

  print('Inner product:');
  print(a.innerProd(b));
  print('');

  print('Multiplication with a number:');
  print(a * 10);
  print('');

  print('Power');
  print(a.pow(2));
  print('');

  print('Exponentiation');
  print(a.exp());
  print(a.exp(2));
  print('');

  print('b.distanceFromOrigin()');
  print(b.distanceFromOrigin);
  print('');

  print('b.distance(a)');
  print(b.distance(a));
  print('');

  /// Dart built-in operator:
  print('Concatenation:');
  print(a + b);
  print('');

  // Creating an unmodifiable list view (recursively)
  print('\nCreating an unmodifiable list of an object of type List<List<T>>:');
  final list = [
    ['one'],
    ['two'],
  ];

  // Extension works for objects of type List<T> and List<List<T>>
  final listView = list.unmodifiable;

  // Prints: UnmodifiableListView<UnmodifiableListView<String>>
  print(listView.runtimeType);
}

$ dart numerical_list_example.dart
Absolute value:
[10, 10, 10]

Addition:
[12, 14, 16]

Subtraction:
[10, 10, 10]

Inner product:
74

Multiplication with a number:
[10, 20, 30]

Power
[1, 4, 9]

Exponentiation
[2.718281828459045, 7.38905609893065, 20.085536923187668]
[7.38905609893065, 54.598150033144236, 403.4287934927351]

b.distanceFromOrigin()
20.83266665599966

b.distance(a)
17.320508075688775

Concatenation:
[1, 2, 3, 11, 12, 13]

Creating an unmodifiable list of an object of type List<List<T>>:
UnmodifiableListView<UnmodifiableListView<String>>

Methods For Objects of Type Iterable<num>:

import 'package:list_operators/list_operators.dart';

void main() {
  final b = [11, 12, 13];

  // Operators and method that work with Iterable<num>
  print('Minimum: b.min()');
  print(b.min());
  print('');

  print('Maximum: b.max()');
  print(b.max());
  print('');

  print('Mean: b.mean()');
  print(b.mean());
  print('');

  print('Product of all entries: b.prod()');
  print(b.prod());
  print('');

  print('Standard deviation: b.stdDev()');
  print(b.stdDev());prod()
  print('');

  print('Sum: b.sum()');
  print(b.sum());
}

$ dart numerical_iterable_example.dart
Minimum: b.min()
11

Maximum: b.max()
13

Mean: b.mean()
12.0

Product of all entries: b.prod()
1716

Standard deviation: b.stdDev()
1.0

Sum: b.sum()
36

Operators For Objects of Type List<T extends Comparable>:

import 'package:list_operators/list_operators.dart';

void main() {
  final a = [1, 2, 3];
  final b = [11, 12, 13];

  // Operators that work with List<T extends Comparable>
  print('a < b:');
  print(a < b);
  print('');

  print('a <= b:');
  print(a <= b);
  print('');

  print('a > b:');
  print(a > b);
  print('');

  print('b >= b:');
  print(b >= b);
  print('');

  final s1 = ['a1', 'a2'];
  final s2 = ['b1', 'b2'];

  print('s1 <= s2');
  print(s1 < s2);
}

$ dart comparable_list_example.dart
a < b:
true

a <= b:
true

a > b:
false

b >= b:
true

s1 <= s2
true

Methods for Exporting Numerical Lists as a String:

import 'package:list_operators/list_operators.dart';
void main() {
  final a = [1, 2, 3];

  /// Exporting numerical lists to a `String` object.
  print('Exporting lists to String:');
  print(a.export(
    label: '<<Sample label>>',
    delimiter: ', ',
    precision: 4,
  ));

  print('Exporting an object of type List<List<num>> to String:');
  print('Each inner list is exported as a row.');
  print([
    [1, 2, 3],
    [101, 102, 103]
  ].export(label: '<<Sample label>>', precision: 6));

  print('Exporting an object of type List<List<num>> to String.');
  print('Inner lists are exported as columns.');
  print([
    [1, 2, 3],
    [101, 102, 103]
  ].export(
    label: '<<Sample label>>',
    precision: 6,
    flip: true,
  ));
}

$ dart export_to_string_example.dart
Exporting lists to String:
<<Sample label>>
1.000,
2.000,
3.000,

Exporting an object of type List<List<num>> to String:
Each inner list is exported as a row.
<<Sample label>>
1.00000 2.00000 3.00000prod()
101.000 102.000 103.000

Exporting an object of type List<List<num>> to String.
Inner lists are exported as columns.
<<Sample label>>
1.00000 101.000
2.00000 102.000
3.00000 103.000

Limitations

In its current version, Dart does not support function (and implicitly operator) overloading. For this reason some numerical operations introduced by list_operators are not symmetrical, even though intuitively they should be:

• The expression [1, 2, 3] * 10 is well defined and the result is [10, 20, 30].
• The expression 10 * [1, 2, 3] is not defined since the operator * for objects of type int expects a second operand of type num.

Note: The + operator (concatenates two lists) is already defined by Dart's abstract class List and cannot be overridden by an extension on List. To add two numerical lists element by element use the method: List<num> plus(List<num> other).

Examples

The programs shown above are included in the folder example.

Features and bugs

Please file feature requests and bugs at the issue tracker.