Covariance   A
last analyzed

Complexity

Total Complexity 31

Size/Duplication

Total Lines 140
Duplicated Lines 0 %

Coupling/Cohesion

Components 0
Dependencies 2

Importance

Changes 0
Metric Value
wmc 31
lcom 0
cbo 2
dl 0
loc 140
rs 9.92
c 0
b 0
f 0

3 Methods

Rating   Name   Duplication   Size   Complexity  
B fromXYArrays() 0 31 9
C fromDataset() 0 57 16
B covarianceMatrix() 0 31 6
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<?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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