n = $n; $this->m = $m; for ($i = 0; $i < $m; ++$i) { $this->matrix[$i] = \array_fill(0, $n, 0); } } /** * Set value. * * @param int $m Row * @param int $n Column * @param int $value Value * * @return void * * @throws InvalidDimensionException * * @since 1.0.0 */ public function set(int $m, int $n, $value) : void { if (!isset($this->matrix[$m], $this->matrix[$m][$n])) { throw new InvalidDimensionException($m . 'x' . $n); } $this->matrix[$m][$n] = $value; } /** * Get value. * * @param int $m Row * @param int $n Column * * @return mixed * * @throws InvalidDimensionException * * @since 1.0.0 */ public function get(int $m, int $n) { if (!isset($this->matrix[$m], $this->matrix[$m][$n])) { throw new InvalidDimensionException($m . 'x' . $n); } return $this->matrix[$m][$n]; } /** * Transpose matrix. * * @return Matrix * * @since 1.0.0 */ public function transpose() : self { $matrix = new self($this->n, $this->m); $matrix->setMatrix(\array_map(null, ...$this->matrix)); return $matrix; } /** * Get matrix array. * * @return array> * * @since 1.0.0 */ public function getMatrix() : array { return $this->matrix; } /** * Get sub matrix array. * * @param int $iRow Start row * @param int $lRow End row * @param int $iCol Start col * @param int $lCol End col * * @return Matrix * * @since 1.0.0 */ public function getSubMatrix(int $iRow, int $lRow, int $iCol, int $lCol) : self { $X = [[]]; for ($i = $iRow; $i <= $lRow; ++$i) { for ($j = $iCol; $j <= $lCol; ++$j) { $X[$i - $iRow][$j - $iCol] = $this->matrix[$i][$j]; } } $matrix = new self(); $matrix->setMatrix($X); return $matrix; } /** * Get sub matrix array. * * @param array $rows Row indices * @param array $cols Row indices * * @return Matrix * * @since 1.0.0 */ public function getSubMatrixByColumnsRows(array $rows, array $cols) : self { $X = [[]]; $rlength = \count($rows); $clength = \count($cols); for ($i = 0; $i < $rlength; ++$i) { for ($j = 0; $j < $clength; ++$j) { $X[$i][$j] = $this->matrix[$rows[$i]][$cols[$j]]; } } $matrix = new self(); $matrix->setMatrix($X); return $matrix; } /** * Get sub matrix array. * * @param int $iRow Start row * @param int $lRow End row * @param array $cols Row indices * * @return Matrix * * @since 1.0.0 */ public function getSubMatrixByColumns(int $iRow, int $lRow, array $cols) : self { $X = [[]]; $length = \count($cols); for ($i = $iRow; $i <= $lRow; ++$i) { for ($j = 0; $j < $length; ++$j) { $X[$i - $iRow][$j] = $this->matrix[$i][$cols[$j]]; } } $matrix = new self(); $matrix->setMatrix($X); return $matrix; } /** * Get sub matrix array. * * @param array $rows Row indices * @param int $iCol Start col * @param int $lCol End col * * @return Matrix * * @since 1.0.0 */ public function getSubMatrixByRows(array $rows, int $iCol, int $lCol) : self { $X = [[]]; $length = \count($rows); for ($i = 0; $i < $length; ++$i) { for ($j = $iCol; $j <= $lCol; ++$j) { $X[$i][$j - $iCol] = $this->matrix[$rows[$i]][$j]; } } $matrix = new self(); $matrix->setMatrix($X); return $matrix; } /** * Get matrix array. * * @return array> * * @since 1.0.0 */ public function toArray() : array { return $this->matrix; } /** * Is symmetric. * * @return bool * * @since 1.0.0 */ public function isSymmetric() : bool { $isSymmetric = true; for ($j = 0; ($j < $this->m) & $isSymmetric; ++$j) { for ($i = 0; ($i < $this->n) & $isSymmetric; ++$i) { $isSymmetric = ($this->matrix[$i][$j] === $this->matrix[$j][$i]); } } return $isSymmetric; } /** * Get matrix rank. * * @return int * * @since 1.0.0 */ public function rank() : int { $matrix = $this->matrix; $mDim = $this->m; $nDim = $this->n; if ($this->m > $this->n) { $mDim = $this->n; $nDim = $this->m; $matrix = \array_map(null, ...$matrix); } $rank = $mDim; for ($row = 0; $row < $rank; ++$row) { if (isset($matrix[$row][$row]) && $matrix[$row][$row] !== 0) { for ($col = 0; $col < $mDim; ++$col) { if ($col !== $row) { $mult = $matrix[$col][$row] / $matrix[$row][$row]; for ($i = 0; $i < $rank; ++$i) { $matrix[$col][$i] -= $mult * $matrix[$row][$i]; } } } } else { $reduce = true; for ($i = $row + 1; $i < $mDim; ++$i) { if (isset($matrix[$i][$row]) && $matrix[$i][$row] !== 0) { $this->swapRow($matrix, $row, $i, $rank); $reduce = false; break; } } if ($reduce) { --$rank; for ($i = 0; $i < $mDim; ++$i) { $matrix[$i][$row] = $matrix[$i][$rank]; } --$row; } } } return $rank; } /** * Swap values in rows * * @param array $matrix Matrix reference to modify * @param int $row1 Row to swap * @param int $row2 Row to swap * @param int $col Max col to swap to * * @return void * * @since 1.0.0 */ private function swapRow(array &$matrix, int $row1, int $row2, int $col) : void { for ($i = 0; $i < $col; ++$i) { $temp = $matrix[$row1][$i]; $matrix[$row1] = $matrix[$row2][$i]; $matrix[$row2] = $temp; } } /** * Set matrix array. * * @param array> $matrix Matrix * * @return Matrix * * @throws \Exception * * @since 1.0.0 */ public function setMatrix(array $matrix) : self { $this->m = \count($matrix); $this->n = !\is_array($matrix[0] ?? 1) ? 1 : \count($matrix[0]); $this->matrix = $matrix; return $this; } /** * Subtract right. * * @param mixed $value Value * * @return Matrix * * @throws \InvalidArgumentException * * @since 1.0.0 */ public function sub($value) : self { if ($value instanceof self) { return $this->add($value->mult(-1)); } elseif (!\is_string($value) && \is_numeric($value)) { return $this->add(-$value); } throw new \InvalidArgumentException('Type'); } /** * Add right. * * @param mixed $value Value * * @return Matrix * * @throws \InvalidArgumentException * * @since 1.0.0 */ public function add($value) : self { if ($value instanceof self) { return $this->addMatrix($value); } elseif (!\is_string($value) && \is_numeric($value)) { return $this->addScalar($value); } throw new \InvalidArgumentException(); } /** * Add matrix. * * @param Matrix $matrix Matrix to add * * @return Matrix * * @throws \Exception * * @since 1.0.0 */ private function addMatrix(self $matrix) : self { if ($this->m !== $matrix->getM() || $this->n !== $matrix->getN()) { throw new InvalidDimensionException($matrix->getM() . 'x' . $matrix->getN()); } $matrixArr = $matrix->getMatrix(); $newMatrixArr = $this->matrix; foreach ($newMatrixArr as $i => $vector) { foreach ($vector as $j => $value) { $newMatrixArr[$i][$j] += $matrixArr[$i][$j]; } } $newMatrix = new self($this->m, $this->n); $newMatrix->setMatrix($newMatrixArr); return $newMatrix; } /** * Get matrix rows. * * @return int * * @since 1.0.0 */ public function getM() : int { return $this->m; } /** * Get matrix columns. * * @return int * * @since 1.0.0 */ public function getN() : int { return $this->n; } /** * Add scalar. * * @param mixed $scalar Scalar * * @return Matrix * * @throws \Exception * * @since 1.0.0 */ private function addScalar($scalar) : self { $newMatrixArr = $this->matrix; foreach ($newMatrixArr as $i => $vector) { foreach ($vector as $j => $value) { $newMatrixArr[$i][$j] += $scalar; } } $newMatrix = new self($this->m, $this->n); $newMatrix->setMatrix($newMatrixArr); return $newMatrix; } /** * Multiply right. * * @param mixed $value Factor * * @return Matrix * * @throws \InvalidArgumentException * * @since 1.0.0 */ public function mult($value) : self { if ($value instanceof self) { return $this->multMatrix($value); } elseif (!\is_string($value) && \is_numeric($value)) { return $this->multScalar($value); } throw new \InvalidArgumentException('Type'); } /** * Multiply matrix. * * @param Matrix $matrix Matrix to multiply with * * @return Matrix * * @throws \Exception * * @since 1.0.0 */ private function multMatrix(self $matrix) : self { $nDim = $matrix->getN(); $mDim = $matrix->getM(); $matrixArr = $matrix->getMatrix(); $newMatrix = new self($this->m, $nDim); $newMatrixArr = $newMatrix->getMatrix(); for ($i = 0; $i < $this->m; ++$i) { // Row of $this for ($c = 0; $c < $nDim; ++$c) { // Column of $matrix $temp = 0; for ($j = 0; $j < $mDim; ++$j) { // Row of $matrix $temp += ($this->matrix[$i][$j] ?? 0) * ($matrixArr[$j][$c] ?? 0); } $newMatrixArr[$i][$c] = $temp; } } $newMatrix->setMatrix($newMatrixArr); return $newMatrix; } /** * Multiply matrix. * * @param mixed $scalar Scalar value * * @return Matrix * * @throws \Exception * * @since 1.0.0 */ private function multScalar($scalar) : self { $newMatrixArr = $this->matrix; foreach ($newMatrixArr as $i => $vector) { foreach ($vector as $j => $value) { $newMatrixArr[$i][$j] *= $scalar; } } $newMatrix = new self($this->m, $this->n); $newMatrix->setMatrix($newMatrixArr); return $newMatrix; } /** * Upper triangulize matrix. * * @return Matrix * * @since 1.0.0 */ public function upperTriangular() : self { $matrix = new self($this->n, $this->n); $matrixArr = $this->matrix; $this->upperTrianglize($matrixArr); $matrix->setMatrix($matrixArr); return $matrix; } /** * Trianglize matrix. * * @param array> $arr Matrix to trianglize * * @return int Det sign * * @since 1.0.0 */ private function upperTrianglize(array &$arr) : int { $n = $this->n; $sign = 1; for ($i = 0; $i < $n; ++$i) { $max = 0; for ($j = $i; $j < $n; ++$j) { if (\abs($arr[$j][$i]) > \abs($arr[$max][$i])) { $max = $j; } } if ($max) { $sign = -$sign; $temp = $arr[$i]; $arr[$i] = $arr[$max]; $arr[$max] = $temp; } if (!$arr[$i][$i]) { return 0; } for ($j = $i + 1; $j < $n; ++$j) { $r = $arr[$j][$i] / $arr[$i][$i]; if (!$r) { continue; } for ($c = $i; $c < $n; ++$c) { $arr[$j][$c] -= $arr[$i][$c] * $r; } } } return $sign; } /** * Inverse matrix. * * @return Matrix * * @throws InvalidDimensionException * * @since 1.0.0 */ public function inverse() : self { return $this->solve(new IdentityMatrix($this->m)); } /** * Solve matrix * * @param Matrix $B Matrix/Vector b * * @return Matrix * * @since 1.0.0 */ public function solve(self $B) : self { $M = $this->m === $this->n ? new LUDecomposition($this) : new QRDecomposition($this); return $M->solve($B); } /** * Calculate det. * * @return float * * @since 1.0.0 */ public function det() : float { $L = new LUDecomposition($this); return $L->det(); } /** * {@inheritdoc} */ public function current() { return $this->offsetGet($this->position); } /** * {@inheritdoc} */ public function offsetGet($offset) { $row = (int) ($offset / $this->m); return $this->matrix[$row][$offset - $row * $this->n]; } /** * {@inheritdoc} */ public function next() : void { ++$this->position; } /** * {@inheritdoc} */ public function key() { return $this->position; } /** * {@inheritdoc} */ public function valid() { return $this->offsetExists($this->position); } /** * {@inheritdoc} */ public function offsetExists($offset) { $row = (int) ($offset / $this->m); return isset($this->matrix[$row][$offset - $row * $this->n]); } /** * {@inheritdoc} */ public function rewind() : void { $this->position = 0; } /** * {@inheritdoc} */ public function offsetSet($offset, $value) : void { $row = (int) ($offset / $this->m); $this->matrix[$row][$offset - $row * $this->n] = $value; } /** * {@inheritdoc} */ public function offsetUnset($offset) : void { $row = (int) ($offset / $this->m); unset($this->matrix[$row][$offset - $row * $this->n]); } }