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Differences Between: [Versions 310 and 401] [Versions 311 and 401] [Versions 39 and 401]

   1  <?php
   2  
   3  declare(strict_types=1);
   4  
   5  namespace Phpml\Math;
   6  
   7  use Phpml\Exception\InvalidArgumentException;
   8  use Phpml\Exception\MatrixException;
   9  use Phpml\Math\LinearAlgebra\LUDecomposition;
  10  
  11  class Matrix
  12  {
  13      /**
  14       * @var array
  15       */
  16      private $matrix = [];
  17  
  18      /**
  19       * @var int
  20       */
  21      private $rows;
  22  
  23      /**
  24       * @var int
  25       */
  26      private $columns;
  27  
  28      /**
  29       * @var float
  30       */
  31      private $determinant;
  32  
  33      /**
  34       * @throws InvalidArgumentException
  35       */
  36      public function __construct(array $matrix, bool $validate = true)
  37      {
  38          // When a row vector is given
  39          if (!is_array($matrix[0])) {
  40              $this->rows = 1;
  41              $this->columns = count($matrix);
  42              $matrix = [$matrix];
  43          } else {
  44              $this->rows = count($matrix);
  45              $this->columns = count($matrix[0]);
  46          }
  47  
  48          if ($validate) {
  49              for ($i = 0; $i < $this->rows; ++$i) {
  50                  if (count($matrix[$i]) !== $this->columns) {
  51                      throw new InvalidArgumentException('Matrix dimensions did not match');
  52                  }
  53              }
  54          }
  55  
  56          $this->matrix = $matrix;
  57      }
  58  
  59      public static function fromFlatArray(array $array): self
  60      {
  61          $matrix = [];
  62          foreach ($array as $value) {
  63              $matrix[] = [$value];
  64          }
  65  
  66          return new self($matrix);
  67      }
  68  
  69      public function toArray(): array
  70      {
  71          return $this->matrix;
  72      }
  73  
  74      public function toScalar(): float
  75      {
  76          return $this->matrix[0][0];
  77      }
  78  
  79      public function getRows(): int
  80      {
  81          return $this->rows;
  82      }
  83  
  84      public function getColumns(): int
  85      {
  86          return $this->columns;
  87      }
  88  
  89      /**
  90       * @throws MatrixException
  91       */
  92      public function getColumnValues(int $column): array
  93      {
  94          if ($column >= $this->columns) {
  95              throw new MatrixException('Column out of range');
  96          }
  97  
  98          return array_column($this->matrix, $column);
  99      }
 100  
 101      /**
 102       * @return float|int
 103       *
 104       * @throws MatrixException
 105       */
 106      public function getDeterminant()
 107      {
 108          if ($this->determinant !== null) {
 109              return $this->determinant;
 110          }
 111  
 112          if (!$this->isSquare()) {
 113              throw new MatrixException('Matrix is not square matrix');
 114          }
 115  
 116          $lu = new LUDecomposition($this);
 117  
 118          return $this->determinant = $lu->det();
 119      }
 120  
 121      public function isSquare(): bool
 122      {
 123          return $this->columns === $this->rows;
 124      }
 125  
 126      public function transpose(): self
 127      {
 128          if ($this->rows === 1) {
 129              $matrix = array_map(static function ($el): array {
 130                  return [$el];
 131              }, $this->matrix[0]);
 132          } else {
 133              $matrix = array_map(null, ...$this->matrix);
 134          }
 135  
 136          return new self($matrix, false);
 137      }
 138  
 139      public function multiply(self $matrix): self
 140      {
 141          if ($this->columns !== $matrix->getRows()) {
 142              throw new InvalidArgumentException('Inconsistent matrix supplied');
 143          }
 144  
 145          $array1 = $this->toArray();
 146          $array2 = $matrix->toArray();
 147          $colCount = $matrix->columns;
 148  
 149          /*
 150           - To speed-up multiplication, we need to avoid use of array index operator [ ] as much as possible( See #255 for details)
 151           - A combination of "foreach" and "array_column" works much faster then accessing the array via index operator
 152          */
 153          $product = [];
 154          foreach ($array1 as $row => $rowData) {
 155              for ($col = 0; $col < $colCount; ++$col) {
 156                  $columnData = array_column($array2, $col);
 157                  $sum = 0;
 158                  foreach ($rowData as $key => $valueData) {
 159                      $sum += $valueData * $columnData[$key];
 160                  }
 161  
 162                  $product[$row][$col] = $sum;
 163              }
 164          }
 165  
 166          return new self($product, false);
 167      }
 168  
 169      /**
 170       * @param float|int $value
 171       */
 172      public function divideByScalar($value): self
 173      {
 174          $newMatrix = [];
 175          for ($i = 0; $i < $this->rows; ++$i) {
 176              for ($j = 0; $j < $this->columns; ++$j) {
 177                  $newMatrix[$i][$j] = $this->matrix[$i][$j] / $value;
 178              }
 179          }
 180  
 181          return new self($newMatrix, false);
 182      }
 183  
 184      /**
 185       * @param float|int $value
 186       */
 187      public function multiplyByScalar($value): self
 188      {
 189          $newMatrix = [];
 190          for ($i = 0; $i < $this->rows; ++$i) {
 191              for ($j = 0; $j < $this->columns; ++$j) {
 192                  $newMatrix[$i][$j] = $this->matrix[$i][$j] * $value;
 193              }
 194          }
 195  
 196          return new self($newMatrix, false);
 197      }
 198  
 199      /**
 200       * Element-wise addition of the matrix with another one
 201       */
 202      public function add(self $other): self
 203      {
 204          return $this->sum($other);
 205      }
 206  
 207      /**
 208       * Element-wise subtracting of another matrix from this one
 209       */
 210      public function subtract(self $other): self
 211      {
 212          return $this->sum($other, -1);
 213      }
 214  
 215      public function inverse(): self
 216      {
 217          if (!$this->isSquare()) {
 218              throw new MatrixException('Matrix is not square matrix');
 219          }
 220  
 221          $LU = new LUDecomposition($this);
 222          $identity = $this->getIdentity();
 223          $inverse = $LU->solve($identity);
 224  
 225          return new self($inverse, false);
 226      }
 227  
 228      public function crossOut(int $row, int $column): self
 229      {
 230          $newMatrix = [];
 231          $r = 0;
 232          for ($i = 0; $i < $this->rows; ++$i) {
 233              $c = 0;
 234              if ($row != $i) {
 235                  for ($j = 0; $j < $this->columns; ++$j) {
 236                      if ($column != $j) {
 237                          $newMatrix[$r][$c] = $this->matrix[$i][$j];
 238                          ++$c;
 239                      }
 240                  }
 241  
 242                  ++$r;
 243              }
 244          }
 245  
 246          return new self($newMatrix, false);
 247      }
 248  
 249      public function isSingular(): bool
 250      {
 251          return $this->getDeterminant() == 0;
 252      }
 253  
 254      /**
 255       * Frobenius norm (Hilbert–Schmidt norm, Euclidean norm) (‖A‖F)
 256       * Square root of the sum of the square of all elements.
 257       *
 258       * https://en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm
 259       *
 260       *          _____________
 261       *         /ᵐ   ⁿ
 262       * ‖A‖F = √ Σ   Σ  |aᵢⱼ|²
 263       *         ᵢ₌₁ ᵢ₌₁
 264       */
 265      public function frobeniusNorm(): float
 266      {
 267          $squareSum = 0;
 268          for ($i = 0; $i < $this->rows; ++$i) {
 269              for ($j = 0; $j < $this->columns; ++$j) {
 270                  $squareSum += $this->matrix[$i][$j] ** 2;
 271              }
 272          }
 273  
 274          return $squareSum ** .5;
 275      }
 276  
 277      /**
 278       * Returns the transpose of given array
 279       */
 280      public static function transposeArray(array $array): array
 281      {
 282          return (new self($array, false))->transpose()->toArray();
 283      }
 284  
 285      /**
 286       * Returns the dot product of two arrays<br>
 287       * Matrix::dot(x, y) ==> x.y'
 288       */
 289      public static function dot(array $array1, array $array2): array
 290      {
 291          $m1 = new self($array1, false);
 292          $m2 = new self($array2, false);
 293  
 294          return $m1->multiply($m2->transpose())->toArray()[0];
 295      }
 296  
 297      /**
 298       * Element-wise addition or substraction depending on the given sign parameter
 299       */
 300      private function sum(self $other, int $sign = 1): self
 301      {
 302          $a1 = $this->toArray();
 303          $a2 = $other->toArray();
 304  
 305          $newMatrix = [];
 306          for ($i = 0; $i < $this->rows; ++$i) {
 307              for ($k = 0; $k < $this->columns; ++$k) {
 308                  $newMatrix[$i][$k] = $a1[$i][$k] + $sign * $a2[$i][$k];
 309              }
 310          }
 311  
 312          return new self($newMatrix, false);
 313      }
 314  
 315      /**
 316       * Returns diagonal identity matrix of the same size of this matrix
 317       */
 318      private function getIdentity(): self
 319      {
 320          $array = array_fill(0, $this->rows, array_fill(0, $this->columns, 0));
 321          for ($i = 0; $i < $this->rows; ++$i) {
 322              $array[$i][$i] = 1;
 323          }
 324  
 325          return new self($array, false);
 326      }
 327  }