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124 lines
3.4 KiB
PHP
124 lines
3.4 KiB
PHP
<?php
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/**
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* Orange Management
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*
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* PHP Version 7.4
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*
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* @package phpOMS\Math\Numerics\Interpolation
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* @copyright Dennis Eichhorn
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* @license OMS License 1.0
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* @version 1.0.0
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* @link https://orange-management.org
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*/
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declare(strict_types=1);
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namespace phpOMS\Math\Numerics\Interpolation;
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use phpOMS\Math\Matrix\Vector;
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/**
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* Linear spline interpolation.
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*
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* @package phpOMS\Math\Numerics\Interpolation
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* @license OMS License 1.0
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* @link https://orange-management.org
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* @since 1.0.0
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*/
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final class LinearInterpolation implements InterpolationInterface
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{
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/**
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* Points for spline interpolation
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*
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* @var array
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* @since 1.0.0
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*/
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private array $points = [];
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/**
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* Parameter a of cubic spline
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*
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* @var Vector
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* @since 1.0.0
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*/
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private Vector $solveA;
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/**
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* Parameter b of cubic spline
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*
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* @var Vector
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* @since 1.0.0
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*/
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private Vector $solveB;
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/**
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* Parameter c of cubic spline
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*
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* @var Vector
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* @since 1.0.0
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*/
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private Vector $solveC;
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/**
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* Constructor.
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*
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* @param array $points Points to create the interpolation with
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*
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* @since 1.0.0
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*/
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public function __construct(array $points) {
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$this->points = $points;
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$n = \count($this->points);
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$this->solveA = new Vector($n);
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$this->solveB = new Vector($n);
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$this->solveC = new Vector($n);
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for ($i = 0; $i < $n - 1; ++$i) {
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$this->solveA->setV($i, 0.0);
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$this->solveB->setV($i, 0.0);
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$this->solveC->setV($i, ($this->points[$i + 1]['y'] - $this->points[$i]['y']) / ($this->points[$i + 1]['x'] - $this->points[$i]['x']));
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}
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for ($i = 0; $i < $n - 1; ++$i) {
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$this->solveA->setV($i, 1.0 / 3.0 * ($this->solveB->getV($i + 1) - $this->solveB->getV($i)) / ($this->points[$i + 1]['x'] - $this->points[$i]['x']));
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$this->solveC->setV($i,
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($this->points[$i + 1]['y'] - $this->points[$i]['y']) / ($this->points[$i + 1]['x'] - $this->points[$i]['x'])
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- 1.0 / 3.0 * (2 * $this->solveB->getV($i) + $this->solveB->getV($i + 1)) * ($this->points[$i + 1]['x'] - $this->points[$i]['x']));
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}
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$h = $this->points[$n - 1]['x'] - $this->points[$n - 2]['x'];
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$this->solveA->setV($n - 1, 0.0);
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$this->solveC->setV($n - 1, 3.0 * $this->solveA->getV($n - 2) * $h ** 2 + 2.0 * $this->solveB->getV($n - 2) * $h + $this->solveC->getV($n - 2));
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}
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/**
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* {@inheritdoc}
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*/
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public function interpolate($x) : float
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{
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$n = \count($this->points);
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$xPos = $n - 1;
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foreach ($this->points as $key => $point) {
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if ($x <= $point['x']) {
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$xPos = $key;
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break;
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}
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}
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$xPos = \max($xPos - 1, 0);
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$h = $x - $this->points[$xPos]['x'];
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if ($x < $this->points[0]['x']) {
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return ($this->solveB->getV(0) * $h + $this->solveC->getV(0)) * $h + $this->points[0]['y'];
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} elseif ($x > $this->points[$n - 1]['x']) {
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return ($this->solveB->getV($n - 1) * $h + $this->solveC->getV($n - 1) * $h + $this->points[$n - 1]['y']);
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}
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return (($this->solveA->getV($xPos) * $h + $this->solveB->getV($xPos)) * $h + $this->solveC->getV($xPos)) * $h + $this->points[$xPos]['y'];
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}
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}
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