Lagrange interpolation PHP Decorator (Интерполяционные полиномы Лагранжа на PHP Декораторе)

Dataset.php

<?php

interface Dataset
{
    public function output();
}

Decorator.php

<?php

class Decorator implements Dataset
{
    protected $dataset;
    
    public function __construct(Dataset $dataset)
    {
        $this->dataset = $dataset;
    }
    
    public function output()
    {
        $this->dataset->output();
    }
}

index.php

<?php

require('Dataset.php');
require('PointDataset.php');
require('Decorator.php');
require('Lagrange.php');

$pointDataset = new PointDataset([
    [0, 0],
    [1, 0.5],
    [2, 1],
]);

echo (new Lagrange($pointDataset))->setStep(0.01)->output();

Lagrange.php

<?php

/**
 *
 * $pointDataset = new PointDataset([
 *     [0, 0],
 *     [1, 0.5],
 *     [2, 1],
 * ]);
 *
 * echo (new Lagrange($pointDataset))->setStep(0.1)->output();
 *
 */

class Lagrange extends Decorator
{
    private $step = 0.1;
    
    public function setStep($step)
    {
        $this->step = $step;
        return $this;
    }

    public function output()
    {
        $this->dataset->setPoints($this->interpolate($this->step));
        parent::output();
    }
    
    private function polynomial($i, $x)
    {
        $p = 1;

        for ($j = 0, $k = $this->dataset->count(); $j < $k; $j++)
        {
            if ($j === $i) continue;
            
            $p *= ($x - $this->dataset->x($j)) / ($this->dataset->x($i) - $this->dataset->x($j));
        }
        
        return $p;
    }
    
    private function value($x)
    {
        $sum = 0;
    
        for ($i = 0, $n = $this->dataset->count(); $i < $n; $i++)
        {
            $sum += $this->dataset->y($i) * $this->polynomial($i, $x);
        }
        
        return $sum;
    }
    
    public function interpolate($step)
    {
        if (is_null($this->dataset->getPoints()))
            return null;

        $xs = $this->dataset->x(0);
        $xe = $this->dataset->x($this->dataset->count());
        $points = [];
        
        for ($x = $xs; $x <= $xe; $x += $step)
        {
            $points[] = [
                $x,
                $this->value($x),
            ];
        }
        
        return $points;
    }
}

PointDataset.php

<?php

class PointDataset implements Dataset
{
    private $points;
    
    public function __construct($points)
    {
        $this->setPoints($points);
    }
    
    public function getPoints()
    {
        return $this->points;
    }
    
    public function setPoints($points)
    {
        $this->points = $points;
    }
    
    public function x($i)
    {
        return $this->points[$i][0];
    }
    
    public function y($i)
    {
        return $this->points[$i][1];
    }
    
    public function count()
    {
        return count($this->points) - 1;
    }

    public function output()
    {
        foreach ($this->points as $point)
        {
            echo "{$point[0]};{$point[1]}<br>";
        }
    }
}