README

Tools for working with simple polynomial models.

Installation

$ composer require filmtools/polynomial

Upgrading from v1

From v2 on, this package now uses SplFixedArrays wherever possible. This will likely affect all your CoefficientProviderInterface implementations, as they now are required to return \SplFixedArray.

Wherever you calculate with FromCoefficientsInterpolator or MultipleInterpolator, you get \SplFixedArray results. When you rely on array results, just call $result->toArray() as defined in SplFixedArray methods API.

What's in the package

Interfaces

CoefficientsProviderInterface: Returns the coefficients of the polynomial model.

public function getCoefficients(): \SplFixedArray;

InterpolatorInterface: Find an y value for a given x coordinate.

public function interpolate( float $x ): float;

XFinderInterface: Find an x for a given y, as opposite to InterpolatorInterface::interpolate

public function findX( float $y ) : float;

PolynomialModelInterface extends the above InterpolatorInterface, XFinderInterface, and CoefficientsProviderInterface

PolynomialModelProviderInterface returns a polynomial model interface instance.

public function getPolynomialModel(): PolynomialModelInterface;

FromCoefficientsInterpolator

This callable class interpolates a iterable with X values using the coefficients given on invokation:

<?php
use FilmTools\PolynomialModel\FromCoefficientsInterpolator;

// Use these X values every time:
$x_iterable = array(1,2,3);
$fci = new FromCoefficientsInterpolator( $x_iterable );

// Now find Y for each X
$coefficients_iterable = [
  0 => 2, 
  1 => 3
];

$interpolated = $fci( $coefficients_iterable ); 
// SplFixedArray [ 5, 8, 11 ]

You may also pass custom X values on invokation:

$fci = new FromCoefficientsInterpolator;

$coefficients = array(2,3);
$x_values = array(1,2,3);

// Now find Y for each X
$interpolated = $fci( $coefficients, $x_values); 
// SplFixedArray [ 5, 8, 11 ]

The interpolation method also accepts CoefficientsProviderInterface:

use FilmTools\PolynomialModel\CoefficientsProviderInterface;
use FilmTools\PolynomialModel\FromCoefficientsInterpolator;

class MyModel implements CoefficientsProviderInterface
{
  public function getCoefficients(): \SplFixedArray
  {
    return \SplFixedArray::fromArray(array(2,3));
  }
}

$x_values = array(1,2,3);
$fci = new FromCoefficientsInterpolator( $x_values );
$interpolated = $fci( new MyModel ); 
// SplFixedArray [ 5, 8, 11 ]

MultipleInterpolator

Interpolates iterables of X values using the same default coefficients. The interpolation method returns a SplFixedArray. The Constructor accepts a numbers iterable as well as CoefficientsProviderInterface:

<?php
use FilmTools\PolynomialModel\MultipleInterpolator;

$coefficients = array(2,3);
$mi = new MultipleInterpolator( $coefficients );

$x_iterable = array(1,2,3);
$interpolated = $mi->interpolate( $x_iterable );
$interpolated = $mi( $x_values );
// SplFixedArray [ 5, 8, 11 ]

DerivativeCoefficientsProvider

Calculates the coefficients for a derivative polynomial on a given a set of coefficients (either array or Provider).

<?php
use FilmTools\PolynomialModel\DerivativeCoefficientsProvider;
use FilmTools\PolynomialModel\CoefficientsProviderInterface;

class MyModel implements CoefficientsProviderInterface
{
  public function getCoefficients(): \SplFixedArray
  {
    // Keys are exponents, values are factors!
    return \SplFixedArray::fromArray( [0=>16, 1=>30, 2=>5, 3=> 18 ]);
  }
}
$my_provider = new MyModel;

$derivation_provider = new DerivativeCoefficientsProvider( $my_provider );
$coefficients = $derivation_provider->getCoefficients();
// SplFixedArray( 0 => 30, 1 => 10, 2 => 54)

The class itself implements CoefficientsProviderInterface, and thus works excellent in conjunction with MultipleInterpolator. Here an example using the above MyModel class:

use FilmTools\PolynomialModel\DerivativeCoefficientsProvider;
use FilmTools\PolynomialModel\MultipleInterpolator;

$derivated_coefficients = new DerivativeCoefficientsProvider( new MyModel );
$interpolator = new MultipleInterpolator( $derivated_coefficients );

$x_values = array(1,2,3);
$slopes = $interpolator->interpolate( $x_values );
// SplFixedArray 94, 266, 546

Exceptions

The PolynomialModelException extends \Exception and implements PolynomialModelExceptionInterface.

The NotEnoughPointsException as well as XNotFoundException and YNotFoundException extend from PolynomialModelException. All these have PolynomialModelExceptionInterface in common. Use these whenever something fails.