149 lines
4.2 KiB
PHP
149 lines
4.2 KiB
PHP
<?php
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declare(strict_types=1);
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namespace Phpml\Math\Statistic;
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use Phpml\Exception\InvalidArgumentException;
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class Covariance
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{
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/**
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* Calculates covariance from two given arrays, x and y, respectively
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*
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* @throws InvalidArgumentException
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*/
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public static function fromXYArrays(array $x, array $y, bool $sample = true, ?float $meanX = null, ?float $meanY = null): float
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{
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$n = count($x);
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if ($n === 0 || count($y) === 0) {
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throw new InvalidArgumentException('The array has zero elements');
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}
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if ($sample && $n === 1) {
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throw new InvalidArgumentException('The array must have at least 2 elements');
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}
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if ($meanX === null) {
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$meanX = Mean::arithmetic($x);
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}
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if ($meanY === null) {
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$meanY = Mean::arithmetic($y);
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}
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$sum = 0.0;
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foreach ($x as $index => $xi) {
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$yi = $y[$index];
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$sum += ($xi - $meanX) * ($yi - $meanY);
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}
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if ($sample) {
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--$n;
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}
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return $sum / $n;
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}
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/**
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* Calculates covariance of two dimensions, i and k in the given data.
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*
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* @throws InvalidArgumentException
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* @throws \Exception
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*/
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public static function fromDataset(array $data, int $i, int $k, bool $sample = true, ?float $meanX = null, ?float $meanY = null): float
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{
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if (count($data) === 0) {
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throw new InvalidArgumentException('The array has zero elements');
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}
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$n = count($data);
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if ($sample && $n === 1) {
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throw new InvalidArgumentException('The array must have at least 2 elements');
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}
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if ($i < 0 || $k < 0 || $i >= $n || $k >= $n) {
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throw new InvalidArgumentException('Given indices i and k do not match with the dimensionality of data');
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}
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if ($meanX === null || $meanY === null) {
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$x = array_column($data, $i);
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$y = array_column($data, $k);
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$meanX = Mean::arithmetic($x);
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$meanY = Mean::arithmetic($y);
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$sum = 0.0;
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foreach ($x as $index => $xi) {
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$yi = $y[$index];
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$sum += ($xi - $meanX) * ($yi - $meanY);
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}
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} else {
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// In the case, whole dataset given along with dimension indices, i and k,
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// we would like to avoid getting column data with array_column and operate
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// over this extra copy of column data for memory efficiency purposes.
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//
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// Instead we traverse through the whole data and get what we actually need
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// without copying the data. This way, memory use will be reduced
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// with a slight cost of CPU utilization.
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$sum = 0.0;
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foreach ($data as $row) {
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$val = [0, 0];
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foreach ($row as $index => $col) {
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if ($index == $i) {
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$val[0] = $col - $meanX;
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}
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if ($index == $k) {
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$val[1] = $col - $meanY;
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}
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}
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$sum += $val[0] * $val[1];
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}
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}
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if ($sample) {
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--$n;
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}
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return $sum / $n;
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}
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/**
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* Returns the covariance matrix of n-dimensional data
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*
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* @param array|null $means
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*/
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public static function covarianceMatrix(array $data, ?array $means = null): array
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{
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$n = count($data[0]);
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if ($means === null) {
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$means = [];
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for ($i = 0; $i < $n; ++$i) {
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$means[] = Mean::arithmetic(array_column($data, $i));
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}
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}
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$cov = [];
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for ($i = 0; $i < $n; ++$i) {
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for ($k = 0; $k < $n; ++$k) {
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if ($i > $k) {
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$cov[$i][$k] = $cov[$k][$i];
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} else {
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$cov[$i][$k] = self::fromDataset(
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$data,
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$i,
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$k,
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true,
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$means[$i],
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$means[$k]
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);
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}
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}
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}
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return $cov;
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}
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}
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