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<?php |
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declare(strict_types=1); |
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namespace Np; |
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use Np\core\{nd,blas,lapack}; |
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use Np\linAlgb\reductions\{ref,rref}; |
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use Np\linAlgb\decompositions\{lu,svd,eigen,cholesky}; |
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/** |
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* Matrix |
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* |
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* @package Np |
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* @category Scientific Computing |
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* @author ghost (Shubham Chaudhary) |
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* @email [email protected] |
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* @copyright (c) 2020-2021, Shubham Chaudhary |
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*/ |
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class matrix extends nd { |
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use ops,linAlgb\linAlg; |
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/** |
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* create empty 2d matrix for given data type |
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* @param int $row num of rows |
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* @param int $col num of cols |
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* @return \Np\matrix |
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*/ |
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public static function factory(int $row, int $col): matrix { |
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return new self($row, $col); |
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} |
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/** |
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* create 2d matrix using php array |
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* @param array $data |
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* @return \Np\matrix |
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*/ |
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public static function ar(array $data): matrix { |
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if (is_array($data) && is_array($data[0])) { |
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$ar = self::factory(count($data), count($data[0])); |
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$ar->setData($data); |
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unset($data); |
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return $ar; |
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} else { |
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self::_err('given array is not rank-2 or given is not an array'); |
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} |
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} |
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/** |
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* create one like 2d matrix |
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* @param int $row |
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* @param int $col |
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* @return \Np\matrix |
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*/ |
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public static function ones(int $row, int $col): matrix { |
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$ar = self::factory($row, $col); |
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for ($i = 0; $i < $ar->ndim; ++$i) { |
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$ar->data[$i] = 1; |
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} |
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return $ar; |
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} |
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/** |
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* Create Matrix with random values |
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* @param int $row |
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* @param int $col |
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* @return \Np\matrix |
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*/ |
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public static function randn(int $row, int $col): matrix { |
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$ar = self::factory($row, $col); |
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$max = getrandmax(); |
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for ($i = 0; $i < $ar->ndim; ++$i) { |
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$ar->data[$i] = rand() / $max; |
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} |
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return $ar; |
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} |
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/** |
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* Return 2d matrix with uniform values |
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* @param int $row |
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* @param int $col |
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* @return \Np\matrix |
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*/ |
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public static function uniform(int $row, int $col): matrix { |
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$ar = self::factory($row, $col); |
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$max = getrandmax(); |
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for ($i = 0; $i < $ar->ndim; ++$i) { |
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$ar->data[$i] = rand(-$max, $max) / $max; |
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} |
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return $ar; |
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} |
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/** |
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* Return a zero matrix with the given dimensions. |
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* @param int $row |
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* @param int $col |
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* @return \Np\matrix |
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*/ |
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public static function zeros(int $row, int $col): matrix { |
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$ar = self::factory($row, $col); |
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for ($i = 0; $i < $ar->ndim; ++$i) { |
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$ar->data[$i] = 0.0; |
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} |
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return $ar; |
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} |
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/** |
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* create a null like 2d matrix |
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* @param int $row |
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* @param int $col |
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* @return \Np\matrix |
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*/ |
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public static function null(int $row, int $col): matrix { |
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$ar = self::factory($row, $col); |
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for ($i = 0; $i < $ar->ndim; ++$i) { |
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$ar->data[$i] = null; |
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} |
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return $ar; |
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} |
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/** |
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* create a 2d matrix with given scalar value |
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* @param int $row |
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* @param int $col |
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* @param int|float $val |
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* @return \Np\matrix |
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*/ |
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public static function full(int $row, int $col, int|float $val): matrix { |
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$ar = self::factory($row, $col); |
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for ($i = 0; $i < $ar->ndim; ++$i) { |
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$ar->data[$i] = $val; |
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} |
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return $ar; |
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} |
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/** |
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* create a diagonal 2d matrix with given 1d array; |
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* @param array $elements |
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* @return \Np\matrix |
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*/ |
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public static function diagonal(array $elements): matrix { |
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$n = count($elements); |
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$ar = self::factory($n, $n); |
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for ($i = 0; $i < $n; ++$i) { |
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$ar->data[$i * $n + $i] = $elements[$i]; #for ($j = 0; $j < $n; ++$j) {$i === $j ? $elements[$i] : 0;#} |
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} |
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return $ar; |
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} |
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/** |
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* Generate a m x n matrix with elements from a Poisson distribution. |
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* @param int $row |
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* @param int $col |
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* @param float $lambda |
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* @return \Np\matrix |
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*/ |
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public static function poisson(int $row, int $col, float $lambda = 1.0): matrix { |
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$ar = self::factory($row, $col); |
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$max = getrandmax(); |
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$l = exp(-$lambda); |
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for ($i = 0; $i < $row; ++$i) { |
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for ($j = 0; $j < $col; ++$j) { |
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$k = 0; |
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$p = 1.0; |
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while ($p > $l) { |
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++$k; |
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$p = $p * rand() / $max; |
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} |
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$ar->data[$i * $col + $j] = $k - 1; |
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} |
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} |
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return $ar; |
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} |
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/** |
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* Return a standard normally distributed random matrix i.e values |
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* between -1 and 1. |
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* @param int $row |
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* @param int $col |
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* @return \Np\matrix |
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*/ |
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public static function gaussian(int $row, int $col): matrix { |
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$max = getrandmax(); |
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$a = $extras = []; |
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while (count($a) < $row) { |
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$rowA = []; |
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if (!empty($extras)) { |
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$rowA[] = array_pop($extras); |
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} |
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while (count($rowA) < $col) { |
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$r = sqrt(-2.0 * log(rand() / $max)); |
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$phi = rand() / $max * self::TWO_PI; |
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$rowA[] = $r * sin($phi); |
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$rowA[] = $r * cos($phi); |
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} |
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if (count($rowA) > $col) { |
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$extras[] = array_pop($rowA); |
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} |
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$a[] = $rowA; |
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} |
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return self::ar($a); |
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} |
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/** |
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* create an identity matrix with the given dimensions. |
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* @param int $n |
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* @return matrix |
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* @throws \InvalidArgumentException |
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*/ |
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public static function identity(int $n): matrix { |
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if ($n < 1) { |
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self::_dimensionaMisMatchErr('dimensionality must be greater than 0 on all axes.'); |
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} |
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$ar = self::factory($n, $n); |
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for ($i = 0; $i < $n; ++$i) { |
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for ($j = 0; $j < $n; ++$j) { |
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$ar->data[$i * $n + $j] = $i === $j ? 1 : 0; |
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} |
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} |
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return $ar; |
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} |
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/** |
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* Return a row as vector from the matrix. |
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* @param int $index |
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* @return \Np\vector |
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*/ |
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public function rowAsVector(int $index): vector { |
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$vr = vector::factory($this->col); |
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for ($j = 0; $j < $this->col; ++$j) { |
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$vr->data[$j] = $this->data[$index * $this->col + $j]; |
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} |
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return $vr; |
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} |
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/** |
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* Return a col as vector from the matrix. |
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* @param int $index |
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* @return \Np\vector |
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*/ |
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public function colAsVector(int $index): vector { |
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$vr = vector::factory($this->row); |
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for ($i = 0; $i < $this->row; ++$i) { |
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$vr->data[$i] = $this->data[$i * $this->row + $index]; |
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} |
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return $vr; |
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} |
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/** |
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* Return the diagonal elements of a square matrix as a vector. |
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* @return \Np\vector |
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*/ |
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public function diagonalAsVector(): vector { |
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if ($this->isSquare()) { |
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$vr = vector::factory($this->row); |
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for ($i = 0; $i < $this->row; ++$i) { |
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$vr->data[$i] = $this->getDiagonalVal($i); |
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} |
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return $vr; |
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} |
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self::_err('Can not trace of a none square matrix'); |
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} |
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/** |
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* Flatten i.e unravel the matrix into a vector. |
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* |
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* @return \Np\vector |
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*/ |
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public function asVector(): vector { |
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$vr = vector::factory($this->ndim); |
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for ($i = 0; $i < $this->ndim; ++$i) { |
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$vr->data[$i] = $this->data[$i]; |
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} |
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return $vr; |
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} |
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/** |
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* 2D convolution between a matrix ma and kernel kb, with a given stride. |
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* @param \Np\matrix $m |
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* @param int $stride |
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* @return matrix |
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*/ |
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public function convolve(matrix $m, int $stride = 1): matrix { |
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return convolve::conv2D($this, $m, $stride); |
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} |
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/** |
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* Calculate the determinant of the matrix. |
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* @return float |
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*/ |
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public function det(): float { |
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if (!$this->isSquare()) { |
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self::_err('determinant is undefined for a non square matrix'); |
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} |
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$lu = $this->lu(); |
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$nSwaps = $lu->p()->diagonalAsVector()->subtract($lu->p()->diagonalAsVector()->sum())->col - 1; |
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$detP = (-1) ** $nSwaps; |
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$detL = $lu->l()->diagonalAsVector()->product(); |
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$detU = $lu->u()->diagonalAsVector()->product(); |
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unset($lu); |
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return ($detP * $detL * $detU); |
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} |
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/** |
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* Return the trace of the matrix i.e the sum of all diagonal elements of a square matrix. |
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* @return float |
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*/ |
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public function trace(): float { |
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if (!$this->isSquare()) { |
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self::_err('Error::matrix is not a squared can not Trace!'); |
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} |
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$trace = 0.0; |
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for ($i = 0; $i < $this->row; ++$i) { |
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for ($j = 0; $j < $this->col; ++$j) { |
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if ($i == $j) { |
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326
|
|
|
$trace += $this->data[$i * $this->col + $i]; |
|
327
|
|
|
} |
|
328
|
|
|
} |
|
329
|
|
|
} |
|
330
|
|
|
return $trace; |
|
331
|
|
|
} |
|
332
|
|
|
|
|
333
|
|
|
/** |
|
334
|
|
|
* dignoalInterChange |
|
335
|
|
|
*/ |
|
336
|
|
|
public function dignoalInterChange() { |
|
337
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
338
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
339
|
|
|
$tmp = $this->data[$i * $this->col - $j]; |
|
340
|
|
|
$this->data[$i * $this->col - $j] = $tmp; |
|
341
|
|
|
} |
|
342
|
|
|
} |
|
343
|
|
|
} |
|
344
|
|
|
|
|
345
|
|
|
//---------------Arthmetic Opreations----------------------------------- |
|
346
|
|
|
|
|
347
|
|
|
/** |
|
348
|
|
|
* multiply this matrix with another matrix|scalar element-wise |
|
349
|
|
|
* Matrix Scalar\Matrix multiplication |
|
350
|
|
|
* @param int|float|matrix|vector $m |
|
351
|
|
|
* @return matrix|vector |
|
352
|
|
|
*/ |
|
353
|
|
|
public function multiply(int|float|matrix|vector $m): matrix|vector { |
|
354
|
|
|
if ($m instanceof self) { |
|
355
|
|
|
return $this->multiplyMatrix($m); |
|
356
|
|
|
} else if ($m instanceof vector) { |
|
357
|
|
|
return $this->multiplyVector($m); |
|
358
|
|
|
} else { |
|
359
|
|
|
return $this->scale($m); |
|
360
|
|
|
} |
|
361
|
|
|
} |
|
362
|
|
|
|
|
363
|
|
|
/** |
|
364
|
|
|
* |
|
365
|
|
|
* @param \Np\vector $v |
|
366
|
|
|
* @return matrix |
|
367
|
|
|
*/ |
|
368
|
|
|
protected function multiplyVector(vector $v): matrix { |
|
369
|
|
|
if ($this->checkDimensions($v, $this)) { |
|
370
|
|
|
$ar = matrix::factory($this->row, $this->col); |
|
371
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
372
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
373
|
|
|
$ar->data[$i * $this->col + $j] = $v->data[$j] * $this->data[$i * $this->col + $j]; |
|
374
|
|
|
} |
|
375
|
|
|
} |
|
376
|
|
|
return $ar; |
|
377
|
|
|
} |
|
378
|
|
|
} |
|
379
|
|
|
|
|
380
|
|
|
/** |
|
381
|
|
|
* |
|
382
|
|
|
* @param \Np\matrix $m |
|
383
|
|
|
* @return matrix |
|
384
|
|
|
*/ |
|
385
|
|
|
protected function multiplyMatrix(matrix $m): matrix { |
|
386
|
|
|
if ($this->checkShape($this, $m)) { |
|
387
|
|
|
$ar = self::factory($this->row, $this->col); |
|
388
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
389
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
390
|
|
|
$ar->data[$i * $this->col + $j] = $this->data[$i * $this->col + $j] * $m->data[$i * $this->col + $j]; |
|
391
|
|
|
} |
|
392
|
|
|
} |
|
393
|
|
|
return $ar; |
|
394
|
|
|
} |
|
395
|
|
|
} |
|
396
|
|
|
|
|
397
|
|
|
/** |
|
398
|
|
|
* Sum of two matrix, vector or a scalar to current matrix |
|
399
|
|
|
* |
|
400
|
|
|
* @param int|float|matrix|vector $m |
|
401
|
|
|
* @return matrix |
|
402
|
|
|
*/ |
|
403
|
|
|
public function sum(int|float|matrix|vector $m): matrix { |
|
404
|
|
|
if ($m instanceof self) { |
|
405
|
|
|
return $this->sumMatrix($m); |
|
406
|
|
|
} elseif ($m instanceof vector) { |
|
407
|
|
|
return $this->sumVector($m); |
|
408
|
|
|
} else { |
|
409
|
|
|
return $this->sumScalar($m); |
|
410
|
|
|
} |
|
411
|
|
|
} |
|
412
|
|
|
|
|
413
|
|
|
protected function sumScalar(int|float $s): matrix { |
|
414
|
|
|
$ar = self::factory($this->row, $this->col); |
|
415
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
416
|
|
|
$ar->data[$i] = $this->data[$i] + $s; |
|
417
|
|
|
} |
|
418
|
|
|
return $ar; |
|
419
|
|
|
} |
|
420
|
|
|
|
|
421
|
|
|
protected function sumMatrix(matrix $m): matrix { |
|
422
|
|
|
if ($this->checkShape($this, $m)) { |
|
423
|
|
|
$ar = self::factory($this->row, $this->col); |
|
424
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
425
|
|
|
$ar->data[$i] = $this->data[$i] + $m->data[$i]; |
|
426
|
|
|
} |
|
427
|
|
|
return $ar; |
|
428
|
|
|
} |
|
429
|
|
|
} |
|
430
|
|
|
|
|
431
|
|
|
protected function sumVector(vector $v): matrix { |
|
432
|
|
|
if ($this->checkDimensions($v, $this)) { |
|
433
|
|
|
$ar = self::factory($this->row, $this->col); |
|
434
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
435
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
436
|
|
|
$ar->data[$i * $this->col + $j] = $v->data[$j] + $this->data[$i * $this->col + $j]; |
|
437
|
|
|
} |
|
438
|
|
|
} |
|
439
|
|
|
return $ar; |
|
440
|
|
|
} |
|
441
|
|
|
} |
|
442
|
|
|
|
|
443
|
|
|
/** |
|
444
|
|
|
* Sum of Rows of matrix |
|
445
|
|
|
* @return vector |
|
446
|
|
|
*/ |
|
447
|
|
|
public function sumRows(): vector { |
|
448
|
|
|
$vr = vector::factory($this->row); |
|
449
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
450
|
|
|
$sum = 0.0; |
|
451
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
452
|
|
|
$sum += $this->data[$i * $this->col + $j]; |
|
453
|
|
|
} |
|
454
|
|
|
$vr->data[$i] = $sum; |
|
455
|
|
|
} |
|
456
|
|
|
return $vr; |
|
457
|
|
|
} |
|
458
|
|
|
|
|
459
|
|
|
/** |
|
460
|
|
|
* subtract another matrix, vector or a scalar to this matrix |
|
461
|
|
|
* @param int|float|matrix|vector $d matrix|$scalar to subtract this matrix |
|
462
|
|
|
* @return \Np\matrix |
|
463
|
|
|
*/ |
|
464
|
|
|
public function subtract(int|float|matrix|vector $d): matrix { |
|
465
|
|
|
if ($d instanceof self) { |
|
466
|
|
|
return $this->subtractMatrix($d); |
|
467
|
|
|
} elseif ($d instanceof vector) { |
|
468
|
|
|
return $this->subtractVector($d); |
|
469
|
|
|
} else { |
|
470
|
|
|
return $this->subtractScalar($d); |
|
471
|
|
|
} |
|
472
|
|
|
} |
|
473
|
|
|
|
|
474
|
|
|
protected function subtractScalar(int|float $s): matrix { |
|
475
|
|
|
$ar = self::factory($this->row, $this->col); |
|
476
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
477
|
|
|
$ar->data[$i] = $this->data[$i] - $s; |
|
478
|
|
|
} |
|
479
|
|
|
return $ar; |
|
480
|
|
|
} |
|
481
|
|
|
|
|
482
|
|
|
/** |
|
483
|
|
|
* |
|
484
|
|
|
* @param matrix $m |
|
485
|
|
|
* @return matrix |
|
486
|
|
|
*/ |
|
487
|
|
|
protected function subtractMatrix(matrix $m): matrix { |
|
488
|
|
|
if ($this->checkShape($this, $m)) { |
|
489
|
|
|
$ar = self::factory($this->row, $this->col); |
|
490
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
491
|
|
|
$ar->data[$i] = $this->data[$i] - $m->data[$i]; |
|
492
|
|
|
} |
|
493
|
|
|
return $ar; |
|
494
|
|
|
} |
|
495
|
|
|
} |
|
496
|
|
|
|
|
497
|
|
|
/** |
|
498
|
|
|
* |
|
499
|
|
|
* @param vector $v |
|
500
|
|
|
* @return matrix |
|
501
|
|
|
*/ |
|
502
|
|
|
protected function subtractVector(vector $v): matrix { |
|
503
|
|
|
if ($this->checkDimensions($v, $this)) { |
|
504
|
|
|
$ar = self::factory($this->row, $this->col); |
|
505
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
506
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
507
|
|
|
$ar->data[$i * $this->col + $j] = $this->data[$i * $this->col + $j] - $v->data[$j]; |
|
508
|
|
|
} |
|
509
|
|
|
} |
|
510
|
|
|
return $ar; |
|
511
|
|
|
} |
|
512
|
|
|
} |
|
513
|
|
|
|
|
514
|
|
|
/** |
|
515
|
|
|
* |
|
516
|
|
|
* @param vector $v |
|
517
|
|
|
* @return matrix |
|
518
|
|
|
*/ |
|
519
|
|
|
public function subtractColumnVector(vector $v): matrix { |
|
520
|
|
|
if ($this->checkDimensions($v, $this)) { |
|
521
|
|
|
$ar = self::factory($this->row, $this->col); |
|
522
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
523
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
524
|
|
|
$ar->data[$i * $this->col + $j] = $this->data[$i * $this->col + $j] - $v->data[$i]; |
|
525
|
|
|
} |
|
526
|
|
|
} |
|
527
|
|
|
return $ar; |
|
528
|
|
|
} |
|
529
|
|
|
} |
|
530
|
|
|
|
|
531
|
|
|
/** |
|
532
|
|
|
* Return the division of two elements, element-wise. |
|
533
|
|
|
* @param int|float|matrix $d |
|
534
|
|
|
* @return matrix |
|
535
|
|
|
*/ |
|
536
|
|
|
public function divide(int|float|matrix|vector $d): matrix { |
|
537
|
|
|
if ($d instanceof self) { |
|
538
|
|
|
return $this->divideMatrix($d); |
|
539
|
|
|
} elseif ($d instanceof vector) { |
|
540
|
|
|
return $this->divideVector($d); |
|
541
|
|
|
} else { |
|
542
|
|
|
return $this->divideScalar($d); |
|
543
|
|
|
} |
|
544
|
|
|
} |
|
545
|
|
|
|
|
546
|
|
|
protected function divideMatrix(matrix $m): matrix { |
|
547
|
|
|
if ($this->checkShape($this, $m)) { |
|
548
|
|
|
$ar = self::factory($this->row, $this->col); |
|
549
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
550
|
|
|
$ar->data[$i] = $this->data[$i] / $m->data[$i]; |
|
551
|
|
|
} |
|
552
|
|
|
return $ar; |
|
553
|
|
|
} |
|
554
|
|
|
} |
|
555
|
|
|
|
|
556
|
|
|
protected function divideVector(vector $v): matrix { |
|
557
|
|
|
if ($this->checkDimensions($v, $this)) { |
|
558
|
|
|
$ar = self::factory($this->row, $this->col); |
|
559
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
560
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
561
|
|
|
$ar->data[$i * $this->col + $j] = $this->data[$i * $this->col + $j] / $v->data[$j]; |
|
562
|
|
|
} |
|
563
|
|
|
} |
|
564
|
|
|
return $ar; |
|
565
|
|
|
} |
|
566
|
|
|
} |
|
567
|
|
|
|
|
568
|
|
|
protected function divideScalar(int|float $s): matrix { |
|
569
|
|
|
$ar = self::factory($this->row, $this->col); |
|
570
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
571
|
|
|
$ar->data[$i] = $this->data[$i] / $s; |
|
572
|
|
|
} |
|
573
|
|
|
return $ar; |
|
574
|
|
|
} |
|
575
|
|
|
|
|
576
|
|
|
/** |
|
577
|
|
|
* |
|
578
|
|
|
* Raise this matrix to the power of the element-wise entry in another matrix. |
|
579
|
|
|
* |
|
580
|
|
|
* @param int|float|matrix $m |
|
581
|
|
|
* @return matrix |
|
582
|
|
|
*/ |
|
583
|
|
|
public function pow(int|float|matrix|vector $d): matrix { |
|
584
|
|
|
if ($d instanceof self) { |
|
585
|
|
|
return $this->powMatrix($d); |
|
586
|
|
|
} else if ($d instanceof vector) { |
|
587
|
|
|
return $this->powVector($d); |
|
588
|
|
|
} else { |
|
589
|
|
|
return $this->powScalar($d); |
|
590
|
|
|
} |
|
591
|
|
|
} |
|
592
|
|
|
|
|
593
|
|
|
protected function powMatrix(matrix $m): matrix { |
|
594
|
|
|
if ($this->checkShape($this, $m)) { |
|
595
|
|
|
$ar = self::factory($this->row, $this->col); |
|
596
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
597
|
|
|
$ar->data[$i] = $this->data[$i] ** $m->data[$i]; |
|
598
|
|
|
} |
|
599
|
|
|
return $ar; |
|
600
|
|
|
} |
|
601
|
|
|
} |
|
602
|
|
|
|
|
603
|
|
|
protected function powVector(vector $v): matrix { |
|
604
|
|
|
if ($this->checkDimensions($v, $this)) { |
|
605
|
|
|
$ar = self::factory($this->row, $this->col); |
|
606
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
607
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
608
|
|
|
$ar->data[$i * $this->col + $j] = $this->data[$i * $this->col + $j] ** $v->data[$j]; |
|
609
|
|
|
} |
|
610
|
|
|
} |
|
611
|
|
|
return $ar; |
|
612
|
|
|
} |
|
613
|
|
|
} |
|
614
|
|
|
|
|
615
|
|
|
protected function powScalar(int|float $s): matrix { |
|
616
|
|
|
$ar = $this->copy(); |
|
617
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
618
|
|
|
$ar->data[$i] **= $s; |
|
619
|
|
|
} |
|
620
|
|
|
return $ar; |
|
621
|
|
|
} |
|
622
|
|
|
|
|
623
|
|
|
/** |
|
624
|
|
|
* Calculate the modulus i.e remainder of division between this matrix and another matrix. |
|
625
|
|
|
* @param int|float|matrix|vector $d |
|
626
|
|
|
* @return matrix |
|
627
|
|
|
*/ |
|
628
|
|
|
public function mod(int|float|matrix|vector $d): matrix { |
|
629
|
|
|
if ($d instanceof self) { |
|
630
|
|
|
$this->modMatrix($d); |
|
631
|
|
|
} else if ($d instanceof vector) { |
|
632
|
|
|
$this->modVector($d); |
|
633
|
|
|
} else { |
|
634
|
|
|
$this->modScalar($d); |
|
635
|
|
|
} |
|
636
|
|
|
} |
|
637
|
|
|
|
|
638
|
|
|
protected function modMatrix(matrix $m): matrix { |
|
639
|
|
|
if ($this->checkShape($this, $m)) { |
|
640
|
|
|
$ar = self::factory($this->row, $this->col); |
|
641
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
642
|
|
|
$ar->data[$i] = $this->data[$i] % $m->data[$i]; |
|
643
|
|
|
} |
|
644
|
|
|
return $ar; |
|
645
|
|
|
} |
|
646
|
|
|
} |
|
647
|
|
|
|
|
648
|
|
|
protected function modVector(vector $v): matrix { |
|
649
|
|
|
if ($this->checkDimensions($v, $this)) { |
|
650
|
|
|
$ar = self::factory($this->row, $this->col); |
|
651
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
652
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
653
|
|
|
$ar->data[$i * $this->col + $j] = $this->data[$i * $this->col + $j] % $v->data[$j]; |
|
654
|
|
|
} |
|
655
|
|
|
} |
|
656
|
|
|
return $ar; |
|
657
|
|
|
} |
|
658
|
|
|
} |
|
659
|
|
|
|
|
660
|
|
|
protected function modScalar(int|float $s): matrix { |
|
661
|
|
|
$ar = $this->copy(); |
|
662
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
663
|
|
|
$ar->data[$i] %= $s; |
|
664
|
|
|
} |
|
665
|
|
|
return $ar; |
|
666
|
|
|
} |
|
667
|
|
|
|
|
668
|
|
|
/** |
|
669
|
|
|
* Return the element-wise reciprocal of the matrix. |
|
670
|
|
|
* |
|
671
|
|
|
* @return matrix |
|
672
|
|
|
*/ |
|
673
|
|
|
public function reciprocal(): matrix { |
|
674
|
|
|
return self::ones($this->row, $this->col)->divideMatrix($this); |
|
675
|
|
|
} |
|
676
|
|
|
|
|
677
|
|
|
/** |
|
678
|
|
|
* Transpose the matrix i.e row become cols and cols become rows. |
|
679
|
|
|
* @return \Np\matrix |
|
680
|
|
|
*/ |
|
681
|
|
|
public function transpose(): matrix { |
|
682
|
|
|
$ar = self::factory($this->col, $this->row); |
|
683
|
|
|
for ($i = 0; $i < $ar->row; ++$i) { |
|
684
|
|
|
for ($j = 0; $j < $ar->col; ++$j) { |
|
685
|
|
|
$ar->data[$i * $ar->col + $j] = $this->data[$j * $this->col + $i]; |
|
686
|
|
|
} |
|
687
|
|
|
} |
|
688
|
|
|
return $ar; |
|
689
|
|
|
} |
|
690
|
|
|
|
|
691
|
|
|
/** |
|
692
|
|
|
* swap specific values in matrix |
|
693
|
|
|
* @param int $i1 |
|
694
|
|
|
* @param int $i2 |
|
695
|
|
|
*/ |
|
696
|
|
|
public function swapValue(int $i1, int $i2) { |
|
697
|
|
|
$tmp = $this->data[$i1]; |
|
698
|
|
|
$this->data[$i1] = $this->data[$i2]; |
|
699
|
|
|
$this->data[$i2] = $tmp; |
|
700
|
|
|
} |
|
701
|
|
|
|
|
702
|
|
|
/** |
|
703
|
|
|
* swap specific rows in matrix |
|
704
|
|
|
* @param int $r1 |
|
705
|
|
|
* @param int $r2 |
|
706
|
|
|
*/ |
|
707
|
|
|
public function swapRows(int $r1, int $r2) { |
|
708
|
|
|
for ($i = 0; $i < $this->col; ++$i) { |
|
709
|
|
|
$tmp = $this->data[$r1 * $this->col + $i]; |
|
710
|
|
|
$this->data[$r1 * $this->col + $i] = $this->data[$r2 * $this->col + $i]; |
|
711
|
|
|
$this->data[$r2 * $this->col + $i] = $tmp; |
|
712
|
|
|
} |
|
713
|
|
|
} |
|
714
|
|
|
|
|
715
|
|
|
/** |
|
716
|
|
|
* swap specific cols in matrix |
|
717
|
|
|
* @param int $c1 |
|
718
|
|
|
* @param int $c2 |
|
719
|
|
|
*/ |
|
720
|
|
|
public function swapCols(int $c1, int $c2) { |
|
721
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
722
|
|
|
$tmp = $this->data[$i * $this->row + $c1]; |
|
723
|
|
|
$this->data[$i * $this->row + $c1] = $this->data[$i * $this->row + $c2]; |
|
724
|
|
|
$this->data[$i * $this->row + $c2] = $tmp; |
|
725
|
|
|
} |
|
726
|
|
|
} |
|
727
|
|
|
|
|
728
|
|
|
/** |
|
729
|
|
|
* |
|
730
|
|
|
* @param int|float $scalar |
|
731
|
|
|
* @return matrix |
|
732
|
|
|
*/ |
|
733
|
|
|
public function scale(int|float $scalar): matrix { |
|
734
|
|
|
if ($scalar == 0) { |
|
735
|
|
|
return self::zeros($this->row, $this->col); |
|
736
|
|
|
} |
|
737
|
|
|
|
|
738
|
|
|
$ar = $this->copy(); |
|
739
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
740
|
|
|
$ar->data[$i] *= $scalar; |
|
741
|
|
|
} |
|
742
|
|
|
|
|
743
|
|
|
return $ar; |
|
744
|
|
|
} |
|
745
|
|
|
|
|
746
|
|
|
/** |
|
747
|
|
|
* scale all the elements of a row |
|
748
|
|
|
* @param int $row |
|
749
|
|
|
* @param int|float $c |
|
750
|
|
|
*/ |
|
751
|
|
|
public function scaleRow(int $row, int|float $c) { |
|
752
|
|
|
for ($i = 0; $i < $this->col; ++$i) { |
|
753
|
|
|
$this->data[$row * $this->col + $i] *= $c; |
|
754
|
|
|
} |
|
755
|
|
|
} |
|
756
|
|
|
|
|
757
|
|
|
/** |
|
758
|
|
|
* scale all the elements of |
|
759
|
|
|
* @param int $col |
|
760
|
|
|
* @param int|float $c |
|
761
|
|
|
*/ |
|
762
|
|
|
public function scaleCol(int $col, int|float $c) { |
|
763
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
764
|
|
|
$this->data[$i * $this->col + $col] *= $c; |
|
765
|
|
|
} |
|
766
|
|
|
} |
|
767
|
|
|
|
|
768
|
|
|
/** |
|
769
|
|
|
* Scale digonally |
|
770
|
|
|
* @param int|float $c |
|
771
|
|
|
* @param bool $lDig |
|
772
|
|
|
*/ |
|
773
|
|
|
public function scaleDigonalCol(int|float $c, bool $lDig = true) { |
|
774
|
|
|
if ($lDig) { |
|
775
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
776
|
|
|
$this->data[$i * $this->col + $i] *= $c; |
|
777
|
|
|
} |
|
778
|
|
|
} else { |
|
779
|
|
|
for ($i = $this->row; $i > 0; --$i) { |
|
780
|
|
|
$this->data[$i * $this->col - $i] *= $c; |
|
781
|
|
|
} |
|
782
|
|
|
} |
|
783
|
|
|
} |
|
784
|
|
|
|
|
785
|
|
|
/** |
|
786
|
|
|
* |
|
787
|
|
|
* @param int $r1 |
|
788
|
|
|
* @param int $r2 |
|
789
|
|
|
* @param float $c |
|
790
|
|
|
*/ |
|
791
|
|
|
public function addScaleRow(int $r1, int $r2, float $c) { |
|
792
|
|
|
for ($i = 0; $i < $this->col; ++$i) { |
|
793
|
|
|
$this->data[$r2 * $this->col + $i] += $this->data[$r1 * $this->col + $i] * $c; |
|
794
|
|
|
} |
|
795
|
|
|
} |
|
796
|
|
|
|
|
797
|
|
|
/** |
|
798
|
|
|
* Attach given matrix to the left of this matrix. |
|
799
|
|
|
* |
|
800
|
|
|
* @param \Np\matrix $m |
|
801
|
|
|
* @return \Np\matrix |
|
802
|
|
|
*/ |
|
803
|
|
|
public function joinLeft(matrix $m): matrix { |
|
804
|
|
|
if ($this->row == $m->row) { |
|
805
|
|
|
$col = $this->col + $m->col; |
|
806
|
|
|
$ar = self::factory($this->row, $col); |
|
807
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
808
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
809
|
|
|
$ar->data[$i * $col + $j] = $this->data[$i * $this->col + $j]; |
|
810
|
|
|
} |
|
811
|
|
|
for ($j = 0; $j < $m->col; ++$j) { |
|
812
|
|
|
$ar->data[$i * $col + ($this->col + $j)] = $m->data[$i * $m->col + $j]; |
|
813
|
|
|
} |
|
814
|
|
|
} |
|
815
|
|
|
return $ar; |
|
816
|
|
|
} |
|
817
|
|
|
self::_err('Error::Invalid size! or DataType!'); |
|
818
|
|
|
} |
|
819
|
|
|
|
|
820
|
|
|
/** |
|
821
|
|
|
* Join matrix m to the Right of this matrix. |
|
822
|
|
|
* @param \Np\matrix $m |
|
823
|
|
|
* @return matrix |
|
824
|
|
|
*/ |
|
825
|
|
|
public function joinRight(matrix $m): matrix { |
|
826
|
|
|
if ($this->row == $m->row) { |
|
827
|
|
|
self::_err('Error::Invalid size! or DataType!'); |
|
828
|
|
|
} |
|
829
|
|
|
$col = $this->col + $m->col; |
|
830
|
|
|
$ar = self::factory($this->row, $col); |
|
831
|
|
|
for ($i = 0; $i < $m->row; ++$i) { |
|
832
|
|
|
for ($j = 0; $j < $m->col; ++$j) { |
|
833
|
|
|
$ar->data[$i * $col + $j] = $m->data[$i * $m->col + $j]; |
|
834
|
|
|
} |
|
835
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
836
|
|
|
$ar->data[$i * $col + ($this->col + $j)] = $this->data[$i * $this->col + $j]; |
|
837
|
|
|
} |
|
838
|
|
|
} |
|
839
|
|
|
return $ar; |
|
840
|
|
|
} |
|
841
|
|
|
|
|
842
|
|
|
/** |
|
843
|
|
|
* Join matrix m Above this matrix. |
|
844
|
|
|
* @param \Np\matrix $m |
|
845
|
|
|
* @return matrix |
|
846
|
|
|
*/ |
|
847
|
|
|
public function joinAbove(matrix $m): matrix { |
|
848
|
|
|
if ($this->col == $m->col) { |
|
849
|
|
|
$row = $this->row + $m->row; |
|
850
|
|
|
$ar = self::factory($row, $this->col); |
|
851
|
|
|
for ($i = 0; $i < $m->row; ++$i) { |
|
852
|
|
|
for ($j = 0; $j < $m->col; ++$j) { |
|
853
|
|
|
$ar->data[$i * $m->col + $j] = $m->data[$i * $m->col + $j]; |
|
854
|
|
|
} |
|
855
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
856
|
|
|
$ar->data[($i + $this->row) * $this->col + $j] = $this->data[$i * $this->col + $j]; |
|
857
|
|
|
} |
|
858
|
|
|
} |
|
859
|
|
|
return $ar; |
|
860
|
|
|
} |
|
861
|
|
|
self::_err('Error::Invalid size! or DataType!'); |
|
862
|
|
|
} |
|
863
|
|
|
|
|
864
|
|
|
/** |
|
865
|
|
|
* Join matrix m below this matrix. |
|
866
|
|
|
* @param \Np\matrix $m |
|
867
|
|
|
* @return matrix |
|
868
|
|
|
*/ |
|
869
|
|
|
public function joinBelow(matrix $m): matrix { |
|
870
|
|
|
if ($this->col == $m->col) { |
|
871
|
|
|
$row = $this->row + $m->row; |
|
872
|
|
|
$ar = self::factory($row, $this->col); |
|
873
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
874
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
875
|
|
|
$ar->data[$i * $this->col + $j] = $this->data[$i * $this->col + $j]; |
|
876
|
|
|
} |
|
877
|
|
|
for ($j = 0; $j < $m->col; ++$j) { |
|
878
|
|
|
$ar->data[($i + $m->row) * $m->col + $j] = $m->data[$i * $m->col + $j]; |
|
879
|
|
|
} |
|
880
|
|
|
} |
|
881
|
|
|
return $ar; |
|
882
|
|
|
} |
|
883
|
|
|
self::_err('Error::Invalid size! or DataType!'); |
|
884
|
|
|
} |
|
885
|
|
|
|
|
886
|
|
|
/** |
|
887
|
|
|
* |
|
888
|
|
|
* @param int $cols |
|
889
|
|
|
* @return \Np\matrix |
|
890
|
|
|
*/ |
|
891
|
|
|
public function diminish_left(int $cols): matrix { |
|
892
|
|
|
$ar = self::factory($this->row, $cols); |
|
893
|
|
|
for ($i = 0; $i < $ar->row; ++$i) { |
|
894
|
|
|
for ($j = 0; $j < $ar->col; ++$j) { |
|
895
|
|
|
$ar->data[$i * $ar->col + $j] = $this->data[$i * $this->col + $j]; |
|
896
|
|
|
} |
|
897
|
|
|
} |
|
898
|
|
|
return $ar; |
|
899
|
|
|
} |
|
900
|
|
|
|
|
901
|
|
|
/** |
|
902
|
|
|
* |
|
903
|
|
|
* @param int $cols |
|
904
|
|
|
* @return \Np\matrix |
|
905
|
|
|
*/ |
|
906
|
|
|
public function diminish_right(int $cols): matrix { |
|
907
|
|
|
$ar = self::factory($this->row, $cols); |
|
908
|
|
|
for ($i = 0; $i < $ar->row; ++$i) { |
|
909
|
|
|
for ($j = 0; $j < $ar->col; ++$j) { |
|
910
|
|
|
$ar->data[$i * $ar->col + $j] = $this->data[$i * $this->col - $cols + $j]; |
|
911
|
|
|
} |
|
912
|
|
|
} |
|
913
|
|
|
return $ar; |
|
914
|
|
|
} |
|
915
|
|
|
|
|
916
|
|
|
/** |
|
917
|
|
|
* Return the index of the maximum element in every row of the matrix. |
|
918
|
|
|
* @return \Np\vector int |
|
919
|
|
|
*/ |
|
920
|
|
|
public function argMax(): vector { |
|
921
|
|
|
$v = vector::factory($this->row, vector::INT); |
|
922
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
923
|
|
|
$v->data[$i] = blas::max($this->rowAsVector($i)); |
|
924
|
|
|
} |
|
925
|
|
|
return $v; |
|
926
|
|
|
} |
|
927
|
|
|
|
|
928
|
|
|
/** |
|
929
|
|
|
* Return the index of the minimum element in every row of the matrix. |
|
930
|
|
|
* @return \Np\vector int |
|
931
|
|
|
*/ |
|
932
|
|
|
public function argMin(): vector { |
|
933
|
|
|
$v = vector::factory($this->row, vector::INT); |
|
934
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
935
|
|
|
$v->data[$i] = blas::min($this->rowAsVector($i)); |
|
936
|
|
|
} |
|
937
|
|
|
|
|
938
|
|
|
return $v; |
|
939
|
|
|
} |
|
940
|
|
|
|
|
941
|
|
|
/** |
|
942
|
|
|
* Set given data in matrix |
|
943
|
|
|
* @param int|float|array $data |
|
944
|
|
|
* @param bool $dignoal |
|
945
|
|
|
* @return void |
|
946
|
|
|
*/ |
|
947
|
|
|
public function setData(int|float|array $data): void { |
|
948
|
|
|
|
|
949
|
|
|
if (is_array($data) && is_array($data[0])) { |
|
950
|
|
|
$f = $this->flattenArray($data); |
|
951
|
|
|
foreach ($f as $k => $v) { |
|
952
|
|
|
$this->data[$k] = $v; |
|
953
|
|
|
} |
|
954
|
|
|
} elseif (is_numeric($data)) { |
|
955
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
956
|
|
|
$this->data[$i] = $data; |
|
957
|
|
|
} |
|
958
|
|
|
} elseif (is_array($data) && !is_array($data[0])) { |
|
959
|
|
|
foreach ($data as $i => $v) { |
|
960
|
|
|
$this->data[$i] = $v; |
|
961
|
|
|
} |
|
962
|
|
|
} |
|
963
|
|
|
} |
|
964
|
|
|
|
|
965
|
|
|
/** |
|
966
|
|
|
* get the matrix data type |
|
967
|
|
|
* @return int |
|
968
|
|
|
*/ |
|
969
|
|
|
public function getDtype(): int { |
|
970
|
|
|
return $this->dtype; |
|
971
|
|
|
} |
|
972
|
|
|
|
|
973
|
|
|
/** |
|
974
|
|
|
* get the shape of matrix |
|
975
|
|
|
* @return object |
|
976
|
|
|
*/ |
|
977
|
|
|
public function getShape(): object { |
|
978
|
|
|
return (object) ['m' => $this->row, 'n' => $this->col]; |
|
979
|
|
|
} |
|
980
|
|
|
|
|
981
|
|
|
/** |
|
982
|
|
|
* get the number of elements in the matrix. |
|
983
|
|
|
* @return int |
|
984
|
|
|
*/ |
|
985
|
|
|
public function getSize(): int { |
|
986
|
|
|
return $this->ndim; |
|
987
|
|
|
} |
|
988
|
|
|
|
|
989
|
|
|
/** |
|
990
|
|
|
* Is the matrix symmetric i.e. is it equal to its own transpose? |
|
991
|
|
|
* |
|
992
|
|
|
* @return bool |
|
993
|
|
|
*/ |
|
994
|
|
|
public function isSymmetric(): bool { |
|
995
|
|
|
if (!$this->isSquare()) { |
|
996
|
|
|
return false; |
|
997
|
|
|
} |
|
998
|
|
|
$ar = $this->transpose(); |
|
999
|
|
|
for ($i = 0; $i < $ar->ndim; ++$i) { |
|
1000
|
|
|
if ($ar->data[$i] != $this->data[$i]) { |
|
1001
|
|
|
unset($ar); |
|
1002
|
|
|
return false; |
|
1003
|
|
|
} |
|
1004
|
|
|
} |
|
1005
|
|
|
unset($ar); |
|
1006
|
|
|
return true; |
|
1007
|
|
|
} |
|
1008
|
|
|
|
|
1009
|
|
|
/** |
|
1010
|
|
|
* is matrix squred |
|
1011
|
|
|
* @return bool |
|
1012
|
|
|
*/ |
|
1013
|
|
|
public function isSquare(): bool { |
|
1014
|
|
|
if ($this->row === $this->col) { |
|
1015
|
|
|
return true; |
|
1016
|
|
|
} |
|
1017
|
|
|
return false; |
|
1018
|
|
|
} |
|
1019
|
|
|
|
|
1020
|
|
|
/** |
|
1021
|
|
|
* |
|
1022
|
|
|
* @param int|float $d |
|
1023
|
|
|
* @return bool |
|
1024
|
|
|
*/ |
|
1025
|
|
|
public static function is_zero($d): bool { |
|
1026
|
|
|
if (abs($d) < self::EPSILON) { |
|
1027
|
|
|
return true; |
|
1028
|
|
|
} |
|
1029
|
|
|
return false; |
|
1030
|
|
|
} |
|
1031
|
|
|
|
|
1032
|
|
|
/** |
|
1033
|
|
|
* is row zero |
|
1034
|
|
|
* @param int $row |
|
1035
|
|
|
* @return bool |
|
1036
|
|
|
*/ |
|
1037
|
|
|
public function is_rowZero(int $row): bool { |
|
1038
|
|
|
for ($i = 0; $i < $this->col; ++$i) { |
|
1039
|
|
|
if ($this->data[$row * $this->col + $i] != 0) { |
|
1040
|
|
|
return false; |
|
1041
|
|
|
} |
|
1042
|
|
|
} |
|
1043
|
|
|
return true; |
|
1044
|
|
|
} |
|
1045
|
|
|
|
|
1046
|
|
|
/** |
|
1047
|
|
|
* |
|
1048
|
|
|
* @return bool |
|
1049
|
|
|
*/ |
|
1050
|
|
|
public function has_ZeroRow(): bool { |
|
1051
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
1052
|
|
|
if ($this->is_rowZero($i)) { |
|
1053
|
|
|
return true; |
|
1054
|
|
|
} |
|
1055
|
|
|
} |
|
1056
|
|
|
return false; |
|
1057
|
|
|
} |
|
1058
|
|
|
|
|
1059
|
|
|
/** |
|
1060
|
|
|
* Return the elements of the matrix in a 2-d array. |
|
1061
|
|
|
* @return array |
|
1062
|
|
|
*/ |
|
1063
|
|
|
public function asArray(): array { |
|
1064
|
|
|
$ar = array_fill(0, $this->row, array_fill(0, $this->col, null)); |
|
1065
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
1066
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
1067
|
|
|
$ar[$i][$j] = $this->data[$i * $this->col + $j]; |
|
1068
|
|
|
} |
|
1069
|
|
|
} |
|
1070
|
|
|
return $ar; |
|
1071
|
|
|
} |
|
1072
|
|
|
|
|
1073
|
|
|
/** |
|
1074
|
|
|
* get a diagonal value from matrix |
|
1075
|
|
|
* @param int $i |
|
1076
|
|
|
* @return float |
|
1077
|
|
|
*/ |
|
1078
|
|
|
public function getDiagonalVal(int $i) { |
|
1079
|
|
|
if ($this->isSquare()) { |
|
1080
|
|
|
return $this->data[$i * $this->row + $i]; |
|
1081
|
|
|
} |
|
1082
|
|
|
} |
|
1083
|
|
|
|
|
1084
|
|
|
/** |
|
1085
|
|
|
* Calculate the row echelon form of the matrix. |
|
1086
|
|
|
* Return the reduced matrix. |
|
1087
|
|
|
* |
|
1088
|
|
|
* @return matrix|null |
|
1089
|
|
|
*/ |
|
1090
|
|
|
public function ref(): matrix|null { |
|
1091
|
|
|
return ref::factory($this); |
|
1092
|
|
|
} |
|
1093
|
|
|
|
|
1094
|
|
|
/** |
|
1095
|
|
|
* Return the lower triangular matrix of the Cholesky decomposition. |
|
1096
|
|
|
* |
|
1097
|
|
|
* @return matrix|null |
|
1098
|
|
|
*/ |
|
1099
|
|
|
public function cholesky(): matrix|null { |
|
1100
|
|
|
return cholesky::factory($this); |
|
1101
|
|
|
} |
|
1102
|
|
|
|
|
1103
|
|
|
/** |
|
1104
|
|
|
* FIXME-------------- |
|
1105
|
|
|
* RREF |
|
1106
|
|
|
* The reduced row echelon form (RREF) of a matrix. |
|
1107
|
|
|
* @return \Np\matrix |
|
1108
|
|
|
*/ |
|
1109
|
|
|
public function rref(): matrix { |
|
1110
|
|
|
return rref::factory($this); |
|
1111
|
|
|
} |
|
1112
|
|
|
|
|
1113
|
|
|
/** |
|
1114
|
|
|
* Compute the singular value decomposition of a matrix and |
|
1115
|
|
|
* return an object of the singular values and unitary matrices |
|
1116
|
|
|
* |
|
1117
|
|
|
* @return object (u,s,v) |
|
1118
|
|
|
*/ |
|
1119
|
|
|
public function svd(): svd { |
|
1120
|
|
|
return svd::factory($this); |
|
1121
|
|
|
} |
|
1122
|
|
|
|
|
1123
|
|
|
/** |
|
1124
|
|
|
* Compute the eigen decomposition of a general matrix. |
|
1125
|
|
|
* return the eigenvalues and eigenvectors as object |
|
1126
|
|
|
* |
|
1127
|
|
|
* @param bool $symmetric |
|
1128
|
|
|
* @return eigen |
|
1129
|
|
|
*/ |
|
1130
|
|
|
public function eign(bool $symmetric = false): eigen { |
|
1131
|
|
|
return eigen::factory($this, $symmetric); |
|
1132
|
|
|
} |
|
1133
|
|
|
|
|
1134
|
|
|
/** |
|
1135
|
|
|
* |
|
1136
|
|
|
* Compute the LU factorization of matrix. |
|
1137
|
|
|
* return lower, upper, and permutation matrices as object. |
|
1138
|
|
|
* |
|
1139
|
|
|
* @return lu |
|
1140
|
|
|
*/ |
|
1141
|
|
|
public function lu(): lu { |
|
1142
|
|
|
return lu::factory($this); |
|
1143
|
|
|
} |
|
1144
|
|
|
|
|
1145
|
|
|
/** |
|
1146
|
|
|
* Return the L1 norm of the matrix. |
|
1147
|
|
|
* @return float |
|
1148
|
|
|
*/ |
|
1149
|
|
|
public function normL1(): float { |
|
1150
|
|
|
return lapack::lange('l', $this); |
|
1151
|
|
|
} |
|
1152
|
|
|
|
|
1153
|
|
|
/** |
|
1154
|
|
|
* Return the L2 norm of the matrix. |
|
1155
|
|
|
* @return float |
|
1156
|
|
|
*/ |
|
1157
|
|
|
public function normL2(): float { |
|
1158
|
|
|
return lapack::lange('f', $this); |
|
1159
|
|
|
} |
|
1160
|
|
|
|
|
1161
|
|
|
/** |
|
1162
|
|
|
* Return the L1 norm of the matrix. |
|
1163
|
|
|
* @return float |
|
1164
|
|
|
*/ |
|
1165
|
|
|
public function normINF(): float { |
|
1166
|
|
|
return lapack::lange('i', $this); |
|
1167
|
|
|
} |
|
1168
|
|
|
|
|
1169
|
|
|
/** |
|
1170
|
|
|
* Return the Frobenius norm of the matrix. |
|
1171
|
|
|
* @return float |
|
1172
|
|
|
*/ |
|
1173
|
|
|
public function normFrob(): float { |
|
1174
|
|
|
return $this->normL2(); |
|
1175
|
|
|
} |
|
1176
|
|
|
|
|
1177
|
|
|
/** |
|
1178
|
|
|
* Compute the means of each row and return them in a vector. |
|
1179
|
|
|
* |
|
1180
|
|
|
* @return vector |
|
1181
|
|
|
*/ |
|
1182
|
|
|
public function mean(): vector { |
|
1183
|
|
|
return $this->sumRows()->divide($this->col); |
|
1184
|
|
|
} |
|
1185
|
|
|
|
|
1186
|
|
|
/** |
|
1187
|
|
|
* Compute the row variance of the matrix. |
|
1188
|
|
|
* |
|
1189
|
|
|
* @param vector|null $mean |
|
1190
|
|
|
* @return vector |
|
1191
|
|
|
*/ |
|
1192
|
|
|
public function variance(vector|null $mean = null): vector { |
|
1193
|
|
|
if (isset($mean)) { |
|
1194
|
|
|
if (!$mean instanceof vector) { |
|
|
|
|
|
|
1195
|
|
|
self::_invalidArgument('mean must be a vector!'); |
|
1196
|
|
|
} |
|
1197
|
|
|
if ($this->row !== $mean->col) { |
|
1198
|
|
|
self::_err('Err:: given mean vector dimensionality mismatched!'); |
|
1199
|
|
|
} |
|
1200
|
|
|
} else { |
|
1201
|
|
|
$mean = $this->mean(); |
|
1202
|
|
|
} |
|
1203
|
|
|
return $this->subtractColumnVector($mean)->square() |
|
1204
|
|
|
->sumRows()->divide($this->row); |
|
1205
|
|
|
} |
|
1206
|
|
|
|
|
1207
|
|
|
/** |
|
1208
|
|
|
* Return the median vector of this matrix. |
|
1209
|
|
|
* @return vector |
|
1210
|
|
|
*/ |
|
1211
|
|
|
public function median(): vector { |
|
1212
|
|
|
$mid = intdiv($this->col, 2); |
|
1213
|
|
|
$odd = $this->col % 2 === 1; |
|
1214
|
|
|
$vr = vector::factory($this->row); |
|
1215
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
1216
|
|
|
$a = $this->rowAsVector($i)->sort(); |
|
1217
|
|
|
if ($odd) { |
|
1218
|
|
|
$median = $a->data[$mid]; |
|
1219
|
|
|
} else { |
|
1220
|
|
|
$median = ($a->data[$mid - 1] + $a->data[$mid]) / 2.0; |
|
1221
|
|
|
} |
|
1222
|
|
|
$vr->data[$i] = $median; |
|
1223
|
|
|
} |
|
1224
|
|
|
unset($a); |
|
1225
|
|
|
return $vr; |
|
1226
|
|
|
} |
|
1227
|
|
|
|
|
1228
|
|
|
/** |
|
1229
|
|
|
* Compute the covariance matrix. |
|
1230
|
|
|
* |
|
1231
|
|
|
* @param vector|null $mean |
|
1232
|
|
|
* @return matrix |
|
1233
|
|
|
*/ |
|
1234
|
|
|
public function covariance(vector|null $mean = null): matrix { |
|
1235
|
|
|
if (isset($mean)) { |
|
1236
|
|
|
if ($mean->col !== $this->row) { |
|
1237
|
|
|
self::_err('Err:: given mean vector dimensionality mismatched!'); |
|
1238
|
|
|
} |
|
1239
|
|
|
} else { |
|
1240
|
|
|
$mean = $this->mean(); |
|
1241
|
|
|
} |
|
1242
|
|
|
|
|
1243
|
|
|
$b = $this->subtractColumnVector($mean); |
|
1244
|
|
|
|
|
1245
|
|
|
return $b->dot($b->transpose()) |
|
1246
|
|
|
->divideScalar($this->row); |
|
1247
|
|
|
} |
|
1248
|
|
|
|
|
1249
|
|
|
/** |
|
1250
|
|
|
* Square of matrix |
|
1251
|
|
|
* @return matrix |
|
1252
|
|
|
*/ |
|
1253
|
|
|
public function square(): matrix { |
|
1254
|
|
|
return $this->multiplyMatrix($this); |
|
1255
|
|
|
} |
|
1256
|
|
|
|
|
1257
|
|
|
/** |
|
1258
|
|
|
* |
|
1259
|
|
|
* @param int|float|matrix|vector $d |
|
1260
|
|
|
* @return matrix |
|
1261
|
|
|
*/ |
|
1262
|
|
|
public function equal(int|float|matrix|vector $d): matrix { |
|
1263
|
|
|
if ($d instanceof self) { |
|
1264
|
|
|
return $this->equalMatrix($d); |
|
1265
|
|
|
} |
|
1266
|
|
|
if ($d instanceof vector) { |
|
1267
|
|
|
return $this->equalVector($d); |
|
1268
|
|
|
} |
|
1269
|
|
|
return $this->equalScalar($d); |
|
1270
|
|
|
} |
|
1271
|
|
|
|
|
1272
|
|
|
protected function equalMatrix(matrix $m): matrix { |
|
1273
|
|
|
if ($this->checkShape($this, $m)) { |
|
1274
|
|
|
$ar = self::factory($this->row, $this->col); |
|
1275
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
1276
|
|
|
$ar->data[$i] = $this->data[$i] == $m->data[$i] ? 1 : 0; |
|
1277
|
|
|
} |
|
1278
|
|
|
return $ar; |
|
1279
|
|
|
} |
|
1280
|
|
|
} |
|
1281
|
|
|
|
|
1282
|
|
|
protected function equalVector(vector $v): matrix { |
|
1283
|
|
|
if ($this->checkDimensions($v, $this)) { |
|
1284
|
|
|
$ar = self::factory($this->row, $this->col); |
|
1285
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
1286
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
1287
|
|
|
$ar->data[$i * $this->col + $j] = $this->data[$i * $this->col + $j] == $v->data[$j] ? 1 : 0; |
|
1288
|
|
|
} |
|
1289
|
|
|
} |
|
1290
|
|
|
return $ar; |
|
1291
|
|
|
} |
|
1292
|
|
|
} |
|
1293
|
|
|
|
|
1294
|
|
|
protected function equalScalar(int|float $s): matrix { |
|
1295
|
|
|
$ar = self::factory($this->row, $this->col); |
|
1296
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
1297
|
|
|
$ar->data[$i] = $this->data[$i] == $s ? 1 : 0; |
|
1298
|
|
|
} |
|
1299
|
|
|
return $ar; |
|
1300
|
|
|
} |
|
1301
|
|
|
|
|
1302
|
|
|
/** |
|
1303
|
|
|
* |
|
1304
|
|
|
* @param int|float|matrix|vector $d |
|
1305
|
|
|
* @return matrix |
|
1306
|
|
|
*/ |
|
1307
|
|
|
public function greater(int|float|matrix|vector $d): matrix { |
|
1308
|
|
|
if ($d instanceof self) { |
|
1309
|
|
|
return $this->greaterMatrix($d); |
|
1310
|
|
|
} |
|
1311
|
|
|
if ($d instanceof vector) { |
|
1312
|
|
|
return $this->greaterVector($d); |
|
1313
|
|
|
} |
|
1314
|
|
|
return $this->greaterScalar($d); |
|
1315
|
|
|
} |
|
1316
|
|
|
|
|
1317
|
|
|
protected function greaterMatrix(matrix $m): matrix { |
|
1318
|
|
|
if ($this->checkShape($this, $m)) { |
|
1319
|
|
|
$ar = self::factory($this->row, $this->col); |
|
1320
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
1321
|
|
|
$ar->data[$i] = $this->data[$i] > $m->data[$i] ? 1 : 0; |
|
1322
|
|
|
} |
|
1323
|
|
|
return $ar; |
|
1324
|
|
|
} |
|
1325
|
|
|
} |
|
1326
|
|
|
|
|
1327
|
|
|
protected function greaterVector(vector $v): matrix { |
|
1328
|
|
|
if ($this->checkDimensions($v, $this)) { |
|
1329
|
|
|
$ar = self::factory($this->row, $this->col); |
|
1330
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
1331
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
1332
|
|
|
$ar->data[$i * $this->col + $j] = $this->data[$i * $this->col + $j] > $v->data[$j] ? 1 : 0; |
|
1333
|
|
|
} |
|
1334
|
|
|
} |
|
1335
|
|
|
return $ar; |
|
1336
|
|
|
} |
|
1337
|
|
|
} |
|
1338
|
|
|
|
|
1339
|
|
|
protected function greaterScalar(int|float $s): matrix { |
|
1340
|
|
|
$ar = self::factory($this->row, $this->col); |
|
1341
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
1342
|
|
|
$ar->data[$i] = $this->data[$i] > $s ? 1 : 0; |
|
1343
|
|
|
} |
|
1344
|
|
|
return $ar; |
|
1345
|
|
|
} |
|
1346
|
|
|
|
|
1347
|
|
|
/** |
|
1348
|
|
|
* |
|
1349
|
|
|
* @param int|float|matrix $m |
|
1350
|
|
|
* @return matrix |
|
1351
|
|
|
*/ |
|
1352
|
|
|
public function less(int|float|matrix $m): matrix { |
|
1353
|
|
|
$ar = self::factory($this->row, $this->col); |
|
1354
|
|
|
if ($m instanceof self) { |
|
1355
|
|
|
if ($this->checkShape($this, $m)) { |
|
1356
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
1357
|
|
|
$ar->data[$i] = $this->data[$i] < $m->data[$i] ? 1 : 0; |
|
1358
|
|
|
} |
|
1359
|
|
|
return $ar; |
|
1360
|
|
|
} |
|
1361
|
|
|
} else { |
|
1362
|
|
|
for ($i = 0; $i < $this->ndim; ++$i) { |
|
1363
|
|
|
$ar->data[$i] = $this->data[$i] < $m ? 1 : 0; |
|
1364
|
|
|
} |
|
1365
|
|
|
return $ar; |
|
1366
|
|
|
} |
|
1367
|
|
|
} |
|
1368
|
|
|
|
|
1369
|
|
|
/** |
|
1370
|
|
|
* print the matrix in consol |
|
1371
|
|
|
*/ |
|
1372
|
|
|
public function printMatrix() { |
|
1373
|
|
|
echo __CLASS__ . PHP_EOL; |
|
1374
|
|
|
for ($i = 0; $i < $this->row; ++$i) { |
|
1375
|
|
|
for ($j = 0; $j < $this->col; ++$j) { |
|
1376
|
|
|
printf('%lf ', $this->data[$i * $this->col + $j]); |
|
1377
|
|
|
} |
|
1378
|
|
|
echo PHP_EOL; |
|
1379
|
|
|
} |
|
1380
|
|
|
} |
|
1381
|
|
|
|
|
1382
|
|
|
public function __toString() { |
|
1383
|
|
|
return (string) $this->printMatrix(); |
|
1384
|
|
|
} |
|
1385
|
|
|
|
|
1386
|
|
|
private function flattenArray(array $ar) { |
|
1387
|
|
|
if (is_array($ar) && is_array($ar[0])) { |
|
1388
|
|
|
$a = []; |
|
1389
|
|
|
foreach ($ar as $y => $value) { |
|
1390
|
|
|
foreach ($value as $k => $v) { |
|
1391
|
|
|
$a[] = $v; |
|
1392
|
|
|
} |
|
1393
|
|
|
} |
|
1394
|
|
|
return $a; |
|
1395
|
|
|
} |
|
1396
|
|
|
} |
|
1397
|
|
|
|
|
1398
|
|
|
/** |
|
1399
|
|
|
* |
|
1400
|
|
|
* @param int $row |
|
1401
|
|
|
* @param int $col |
|
1402
|
|
|
* @param int $dtype |
|
1403
|
|
|
* @return $this |
|
1404
|
|
|
*/ |
|
1405
|
|
|
protected function __construct(public int $row, public int $col, int $dtype = self::DOUBLE) { |
|
1406
|
|
|
if ($this->row < 1 || $this->col < 1) { |
|
1407
|
|
|
self::_invalidArgument('* To create Numphp/Matrix row & col must be greater than 0!, Op Failed! * '); |
|
1408
|
|
|
} |
|
1409
|
|
|
parent::__construct($this->row * $this->col, $dtype); |
|
1410
|
|
|
return $this; |
|
1411
|
|
|
} |
|
1412
|
|
|
} |
|
1413
|
|
|
|
ghostjat /
Np
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