# linalg #

A Simple Linear Algebra Package.

This package is intended to be a portable, easy to use linear algebra package. The library does not have any dependencies outside of Dart itself, thus making it portable and easy to integrate. Internally all numbers are stored as Dart Doubles ( 64 bit as specified in the IEEE 754 standard ).

Our goal is to keep the code readable, documented and maintainable.

## Short Example #

Just a quick example on how to do matrix multiplication.

``````final Matrix a = Matrix([[1, 2], [3, 4]]);
final Vector b = Vector.column([2, 3]);
final Matrix e = Matrix([[8], [18]]);
Matrix result = a * b;
print(result);
print(result == e);
``````

This prints

``````[[8.0], [18.0]]
true
``````

## Complete Example #

A more extensive example with various matrix operations. See the Matrix API and Vector API for the full details.

``````import 'package:linalg/linalg.dart';

void example() {
// *****************************
// Lets solve a linear equation.
// *****************************
//
// A * B = E
//
// We have B and E, we have to find A.
//
// A * B * B' = E * B'
//
// Were B' = inverse of B.
//
// A * I = E * B'
//
// Where I = identity matrix
//
// A = E * B'
final Matrix B = Matrix([[2, 0], [1, 2]]);
final Matrix E = Matrix([[4, 4], [10, 8]]);

Matrix Bi = B.inverse();
Matrix A_calc = E * Bi;

final Matrix A = Matrix([[1, 2], [3, 4]]);
print("The calculated A_calc = \$A_calc, the expected A is \$A, they are \${A_calc==A?'':'not'} the same.");
// Expected: The calculated A = [[1.0, 2.0], [3.0, 4.0]], the expected A is [[1.0, 2.0], [3.0, 4.0]], they are  the same.

// *****************************
// Lets do some more matrix math
// *****************************
//
// Next let multiply Matrix A by 3.
Matrix Am = A * 3.0;
print(Am);
// Expecting: [[3.0, 6.0], [9.0, 12.0]]

// Now add matrix B to A
Matrix AmPlusB = Am + B;
print(AmPlusB);
// Expecting: [[5.0, 6.0], [10.0, 14.0]]

// What is the determinant of the A matrix?
print("The determinant of A = \${A.det()}");
// Expecting The determinant of A = -2.0
}
``````

## Installation #

``````dependencies:
linalg: ^0.3.2
``````

``````import 'package:linalg/linalg.dart';
``````

Original code came from: https://pub.dartlang.org/packages/toaster_linear

We ended up rewriting considerable parts of the code and adding tests and documentation.

## [0.3.2] -- 5/9/2019 #

• Updated Coverage collection to work with recent dart builds.

## [0.3.1] -- 12/24/2018 #

• Fixed Vector.toList and Vector.toMatrix to return deepCopies by default. Added optional parameters to return references where possible for optimization use.

## [0.3.0] -- 12/24/2018 #

• Added matrix.columnVector, Matrix.rowVector and Matrix.copy
• Changed toVector to create a deep copy by default, but allowed it to reuse Matrix storage for performance.

## [0.2.0] -- 12/15/2018 #

• Added Vector.sum, Vector.mean, Vector.norm, Vector.manhattanNorm and Vector.toList with tests and docs.
• Deprecated Vector.distance for the better name Vector.norm.

## [0.1.1] -- 11/27/2018 #

• Added Matrix.trace, Vector.crossProduct and Vector.dotProduct

## [0.1.0] -- 11/26/2018 #

• Slight documentation modifications.

## [0.0.5] -- 11/21/2018 #

• Dart minimum back to 2.0.0 fixed linter errors.

## [0.0.4] -- 11/21/2018 #

• Increased Dart minimum to 2.1.0 to allow int to double assignments.

## [0.0.3] -- 11/21/2018 #

• Removed flutter dependency

## [0.0.1] - 11/21/2018. #

• Initial release

example/example.dart

``````import 'package:linalg/linalg.dart';

final Matrix a = Matrix([
[1, 2],
[3, 4]
]);
final Vector b = Vector.column([2, 3]);
final Matrix e = Matrix([
[8],
[18]
]);
Matrix result = a * b;
print(result);
print(result == e);
}

/// Example code for using the Matrix class.
void main() {

// *****************************
// Lets solve a linear equation.
// *****************************
//
// A * B = E
//
// We have B and E, we have to find A.
//
// A * B * B' = E * B'
//
// Were B' = inverse of B.
//
// A * I = E * B'
//
// Where I = identity matrix
//
// A = E * B'
final Matrix B = Matrix([
[2.0, 0.0],
[1.0, 2.0]
]);
final Matrix E = Matrix([
[4.0, 4.0],
[10.0, 8.0]
]);

Matrix Bi = B.inverse();
Matrix A_calc = E * Bi;

final Matrix A = Matrix([
[1.0, 2.0],
[3.0, 4.0]
]);
print(
"The calculated A = \$A_calc, the expected A is \$A, they are \${A_calc == A ? '' : 'not'} the same.");
// Expected: The calculated A = [[1.0, 2.0], [3.0, 4.0]], the expected A is [[1.0, 2.0], [3.0, 4.0]], they are  the same.

// *****************************
// Lets do some more matrix math
// *****************************
//
// Next let multiply Matrix A by 3.
Matrix Am = A * 3.0;
print(Am);
// Expecting: [[3.0, 6.0], [9.0, 12.0]]

// Now add matrix B to A
Matrix AmPlusB = Am + B;
print(AmPlusB);
// Expecting: [[5.0, 6.0], [10.0, 14.0]]

// What is the determinant of the A matrix?
print("The determinant of A = \${A.det()}");
// Expecting The determinant of A = -2.0
}
``````

## Use this package as a library

### 1. Depend on it

``````
dependencies:
linalg: ^0.3.2

``````

### 2. Install it

You can install packages from the command line:

with pub:

``````
\$ pub get

``````

with Flutter:

``````
\$ flutter pub get

``````

Alternatively, your editor might support `pub get` or `flutter pub get`. Check the docs for your editor to learn more.

### 3. Import it

Now in your Dart code, you can use:

``````
import 'package:linalg/linalg.dart';
``````
 Popularity: Describes how popular the package is relative to other packages. [more] 65 Health: Code health derived from static analysis. [more] 94 Maintenance: Reflects how tidy and up-to-date the package is. [more] 100 Overall: Weighted score of the above. [more] 81

We analyzed this package on Apr 1, 2020, and provided a score, details, and suggestions below. Analysis was completed with status completed using:

• Dart: 2.7.1
• pana: 0.13.6

#### Health suggestions

Fix `lib/matrix.dart`. (-5.36 points)

Analysis of `lib/matrix.dart` reported 11 hints, including:

line 151 col 7: DO use curly braces for all flow control structures.

line 159 col 7: DO use curly braces for all flow control structures.

line 159 col 13: Unnecessary new keyword.

line 160 col 23: Unnecessary new keyword.

line 174 col 7: DO use curly braces for all flow control structures.

Fix `lib/vector.dart`. (-0.50 points)

Analysis of `lib/vector.dart` reported 1 hint:

line 352 col 23: Unnecessary new keyword.

#### Dependencies

Package Constraint Resolved Available
Direct dependencies
Dart SDK >=2.0.0 <3.0.0
Dev dependencies
coverage ^0.12.3
grinder ^0.8.3
grinder_coveralls ^0.2.0
test ^1.5.0