https://github.com/luminsports/php-levenberg-marquardt

https://github.com/luminsports/php-levenberg-marquardt

php

Last synced: about 2 months ago
JSON representation

• Host: GitHub
• URL: https://github.com/luminsports/php-levenberg-marquardt
• Owner: luminsports
• License: mit
• Created: 2022-08-18T06:25:34.000Z (over 2 years ago)
• Default Branch: main
• Last Pushed: 2022-08-18T07:31:54.000Z (over 2 years ago)
• Last Synced: 2024-08-24T22:40:06.349Z (5 months ago)
• Topics: php
• Language: PHP
• Size: 22.5 KB
• Stars: 1
• Watchers: 0
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

Awesome Lists containing this project

README

        
# Levenberg Marquardt Curve Fitting

[![Code Style](https://github.com/luminsports/php-levenberg-marquardt/actions/workflows/php-cs-fixer.yml/badge.svg?branch=main)](https://github.com/luminsports/php-levenberg-marquardt/actions/workflows/php-cs-fixer.yml)

[![Tests](https://github.com/luminsports/php-levenberg-marquardt/actions/workflows/run-tests.yml/badge.svg?branch=main)](https://github.com/luminsports/php-levenberg-marquardt/actions/workflows/run-tests.yml)

This algorithm is based on the article [Brown, Kenneth M., and J. E. Dennis. "Derivative free analogues of the Levenberg-Marquardt and Gauss algorithms for nonlinear least squares approximation." Numerische Mathematik 18.4 (1971): 289-297.](https://doi.org/10.1007/BF01404679) and [http://people.duke.edu/~hpgavin/ce281/lm.pdf](http://people.duke.edu/~hpgavin/ce281/lm.pdf)

In order to get a general idea of the problem you could also check the [Wikipedia article](https://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm).

## Credit

This package is a PHP port of [mljs/levenberg-marquardt](https://github.com/mljs/levenberg-marquardt). As such, we have retained their MIT license.

## Installation

```composer require luminsports/levenberg-marquardt```

## Example

```php

use LuminSports\LevenbergMarquardt\LevenbergMarquardt;

// Set up the curve-fitting model

$model = (new LevenbergMarquardt)

    // the parameters and returns a function with the independent variable as a parameter

    ->setParameterizedFunction(function ($criticalPower, $pMax, $tau) {

        return fn (float $t) => ($pMax - $criticalPower) * exp(-$t / $tau) + $criticalPower;

    })

    

    // array of initial parameter values

    ->setInitialValues([

        'criticalPower' => $relative ? 4 : 300,

        'wPrime'        => $relative ? 285 : 20000,

        'tau'           => $relative ? 4 : 300,

    ])

    

    // minimum allowed values for parameters

    ->setMinValues([0, 0, 0])

    

    // maximum allowed values for parameters

    ->setMaxValues([1000, 600, 300])

    

    // Levenberg-Marquardt parameter, small values of the damping parameter λ result in a Gauss-Newton update and large values of λ result in a gradient descent update (default 1E-2)

    ->setDamping(1.5)

    

    // factor to reduce the damping (Levenberg-Marquardt parameter) when there is not an improvement when updating parameters (default: 9)

    ->setDampingStepDown(9)

    

    // factor to increase the damping (Levenberg-Marquardt parameter) when there is an improvement when updating parameters (default: 11)

    ->setDampingStepUp(11)

    

    // the threshold to define an improvement through an update of parameters (default: 1E-3)

    ->setImprovementThreshold(1E-3)

    

    // the step size to approximate the jacobian matrix (default: 10E-2)

    ->setGradientDifference(10E-2)

    

    // if true the jacobian matrix is approximated by central differences otherwise by forward differences (default: false)

    ->setCentralDifference(true)

    

    // maximum of allowed iterations (default: 100)

    ->setMaxIterations(1000)

    

    // minimum uncertainty allowed for each point (default: 10E-3)

    ->setErrorTolerance(10E-3);

    

$curve = $model->setXValues($knownXValues)

    ->setYValues($knownYValues)

    ->getCurve();

    

// outputs the parameters that formed the best fitting curve

$curve->getParameters(); 

// outputs the number of iterations it took to reach this solution

$curve->getIterations(); 

// the sum of the weighted squares of the errors (or weighted residuals) between the known y-coordinates and the curve-fit function.

$curve->getError(); 

// returns an array of points for the provided x-values, with the predicted y-values

$model->predict($xValuesToPredictFor);

```