# Dart Data

Dart Data is a fast and space efficient library to deal with data in Dart, Flutter and the web. As of today this mostly includes data structures and algorithms for vectors and matrices, but at some point might also include graphs and other mathematical structures.

This library is open source, stable and well tested. Development happens on GitHub. Feel free to report issues or create a pull-request there. General questions are best asked on StackOverflow.

The package is hosted on dart packages. Up-to-date class documentation is created with every release.

## Tutorial

Below are step-by-step instructions of how to use this library. More elaborate examples are included with the examples.

### Installation

Follow the installation instructions on dart packages.

Import the core-package into your Dart code using:

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

### How to solve a linear equation?

Solve 'A * x = b', where 'A' is a matrix and 'b' a vector:

```
final a = Matrix<double>.fromRows(DataType.float64, [
[2, 1, 1],
[1, 3, 2],
[1, 0, 0],
]);
final b = Vector<double>.fromList(DataType.float64, [4, 5, 6]);
final x = a.solve(b.columnMatrix).column(0);
print(x.format(valuePrinter: Printer.fixed()); // prints '6 15 -23'
```

### How to find the eigenvalues of a matrix?

Find the eigenvalues of a matrix 'A':

```
final a = Matrix<double>.fromRows(DataType.float64, [
[1, 0, 0, -1],
[0, -1, 0, 0],
[0, 0, 1, -1],
[-1, 0, -1, 0],
]);
final decomposition = a.eigenvalue;
final eigenvalues = Vector<double>.fromList(
DataType.float64, decomposition.realEigenvalues);
print(eigenvalues.format(valuePrinter: Printer.fixed(precision: 1))); // prints '-1.0 -1.0 1.0 2.0'
```

### How to find all the roots of a polynomial?

To find the roots of `x^5 + -8x^4 + -72x^3 + 242x^2 + 1847x + 2310`

:

```
final polynomial = Polynomial.fromCoefficients(DataType.int32, [1, -8, -72, 242, 1847, 2310]);
final roots = polynomial.roots;
print(roots.map((root) => root.real)); // [-5, -3, -2, 7, 11]
print(roots.map((root) => root.imaginary)); // [0, 0, 0, 0, 0]
```

### How to do a polynomial regression?

To find the best fitting third degree polynomial through a list of points:

```
final height = [1.47, 1.50, 1.52, 1.55, 1.57, 1.60, 1.63, 1.65, 1.68, 1.70, 1.73, 1.75, 1.78, 1.80, 1.83].toVector();
final mass = [52.21, 53.12, 54.48, 55.84, 57.20, 58.57, 59.93, 61.29, 63.11, 64.47, 66.28, 68.10, 69.92, 72.19, 74.46].toVector();
final fitter = PolynomialRegression(degree: 2);
final result = fitter.fit(xs: height, ys: mass);
print(result.polynomial.format(valuePrinter: FixedNumberPrinter(precision: 3))); // 61.960x^2 + -143.162x + 128.813
```

### How to numerically integrate a function?

In both examples we specify a custom depth, since these integrals are tricky at the upper bound (very steep for the first one, very flat for the second one).

```
// Compute the area of a circle by iterating over a quarter circle:
final pi = 4 * integrate((x) => sqrt(1 - x * x), 0, 1, depth: 30);
print(pi); // 3.1415925673846368 ~ pi
// Compute an improper integral:
final one = integrate((x) => exp(-x), 0, double.infinity, depth: 30);
print(one); // 1.0000000904304227 ~ 1
```

## Misc

### License

The MIT License, see LICENSE.

Some of the matrix decomposition algorithms are a port of the JAMA: A Java Matrix Package released under public domain.

- In particular, the singular value decomposition algorithm comes from the Math.Net Numerics released under MIT.

Some of the distributions and special functions are a port of the JavaScript Statistical Library released under MIT.

The Levenberg-Marquardt least squares curve fitting is a port of levenberg-marquardt released under MIT.

## Libraries

- data
- All data packages in a single import.
- matrix
- Matrix data type and algorithms.
- numeric
- Numeric algorithms and solutions.
- polynomial
- Polynomial data type and algorithms.
- special
- Particular mathematical functions.
- stats
- Statistical computations and algorithms.
- tensor
- Tensor data structure.
- type
- Data types and their base functions.
- vector
- Vector data type and algorithms.