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<?php |
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|
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namespace Matrix\Decomposition; |
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|
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use Matrix\Exception; |
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use Matrix\Matrix; |
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|
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class QR |
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{ |
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private $qrMatrix; |
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private $rows; |
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private $columns; |
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|
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private $rDiagonal = []; |
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|
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public function __construct(Matrix $matrix) |
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{ |
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$this->qrMatrix = $matrix->toArray(); |
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$this->rows = $matrix->rows; |
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$this->columns = $matrix->columns; |
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|
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$this->decompose(); |
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} |
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|
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public function getHouseholdVectors() |
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{ |
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$householdVectors = []; |
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for ($row = 0; $row < $this->rows; ++$row) { |
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for ($column = 0; $column < $this->columns; ++$column) { |
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if ($row >= $column) { |
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$householdVectors[$row][$column] = $this->qrMatrix[$row][$column]; |
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} else { |
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$householdVectors[$row][$column] = 0.0; |
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} |
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} |
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} |
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|
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return new Matrix($householdVectors); |
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} |
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|
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public function getQ() |
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{ |
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$qGrid = []; |
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|
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$rowCount = $this->rows; |
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for ($k = $this->columns - 1; $k >= 0; --$k) { |
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for ($i = 0; $i < $this->rows; ++$i) { |
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$qGrid[$i][$k] = 0.0; |
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} |
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$qGrid[$k][$k] = 1.0; |
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if ($this->columns > $this->rows) { |
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$qGrid = array_slice($qGrid, 0, $this->rows); |
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} |
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|
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for ($j = $k; $j < $this->columns; ++$j) { |
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if (isset($this->qrMatrix[$k], $this->qrMatrix[$k][$k]) && $this->qrMatrix[$k][$k] != 0.0) { |
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$s = 0.0; |
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for ($i = $k; $i < $this->rows; ++$i) { |
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$s += $this->qrMatrix[$i][$k] * $qGrid[$i][$j]; |
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} |
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$s = -$s / $this->qrMatrix[$k][$k]; |
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for ($i = $k; $i < $this->rows; ++$i) { |
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$qGrid[$i][$j] += $s * $this->qrMatrix[$i][$k]; |
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} |
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} |
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} |
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} |
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|
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array_walk( |
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$qGrid, |
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function (&$row) use ($rowCount) { |
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$row = array_reverse($row); |
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$row = array_slice($row, 0, $rowCount); |
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} |
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); |
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|
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return new Matrix($qGrid); |
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} |
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|
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public function getR() |
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{ |
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$rGrid = []; |
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|
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for ($row = 0; $row < $this->columns; ++$row) { |
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for ($column = 0; $column < $this->columns; ++$column) { |
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if ($row < $column) { |
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$rGrid[$row][$column] = isset($this->qrMatrix[$row][$column]) ? $this->qrMatrix[$row][$column] : 0.0; |
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} elseif ($row === $column) { |
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$rGrid[$row][$column] = isset($this->rDiagonal[$row]) ? $this->rDiagonal[$row] : 0.0; |
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} else { |
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$rGrid[$row][$column] = 0.0; |
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} |
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} |
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} |
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|
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if ($this->columns > $this->rows) { |
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$rGrid = array_slice($rGrid, 0, $this->rows); |
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} |
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|
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return new Matrix($rGrid); |
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} |
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|
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private function hypo($a, $b) |
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{ |
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if (abs($a) > abs($b)) { |
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$r = $b / $a; |
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$r = abs($a) * sqrt(1 + $r * $r); |
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} elseif ($b != 0.0) { |
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$r = $a / $b; |
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$r = abs($b) * sqrt(1 + $r * $r); |
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} else { |
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$r = 0.0; |
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} |
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|
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return $r; |
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} |
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|
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/** |
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* QR Decomposition computed by Householder reflections. |
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*/ |
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private function decompose() |
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{ |
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for ($k = 0; $k < $this->columns; ++$k) { |
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// Compute 2-norm of k-th column without under/overflow. |
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$norm = 0.0; |
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for ($i = $k; $i < $this->rows; ++$i) { |
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$norm = $this->hypo($norm, $this->qrMatrix[$i][$k]); |
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} |
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if ($norm != 0.0) { |
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// Form k-th Householder vector. |
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if ($this->qrMatrix[$k][$k] < 0.0) { |
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$norm = -$norm; |
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} |
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for ($i = $k; $i < $this->rows; ++$i) { |
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$this->qrMatrix[$i][$k] /= $norm; |
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} |
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$this->qrMatrix[$k][$k] += 1.0; |
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// Apply transformation to remaining columns. |
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for ($j = $k + 1; $j < $this->columns; ++$j) { |
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$s = 0.0; |
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for ($i = $k; $i < $this->rows; ++$i) { |
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$s += $this->qrMatrix[$i][$k] * $this->qrMatrix[$i][$j]; |
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} |
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$s = -$s / $this->qrMatrix[$k][$k]; |
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for ($i = $k; $i < $this->rows; ++$i) { |
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$this->qrMatrix[$i][$j] += $s * $this->qrMatrix[$i][$k]; |
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} |
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} |
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} |
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$this->rDiagonal[$k] = -$norm; |
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} |
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} |
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|
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/** |
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* @return bool |
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*/ |
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public function isFullRank() |
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{ |
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for ($j = 0; $j < $this->columns; ++$j) { |
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if ($this->rDiagonal[$j] == 0.0) { |
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return false; |
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} |
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} |
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|
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return true; |
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} |
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|
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/** |
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* Least squares solution of A*X = B. |
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* |
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* @param Matrix $B a Matrix with as many rows as A and any number of columns |
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* |
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* @throws Exception |
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* |
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* @return Matrix matrix that minimizes the two norm of Q*R*X-B |
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*/ |
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public function solve(Matrix $B) |
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{ |
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if ($B->rows !== $this->rows) { |
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throw new Exception('Matrix row dimensions are not equal'); |
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} |
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|
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if (!$this->isFullRank()) { |
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throw new Exception('Can only perform this operation on a full-rank matrix'); |
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} |
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|
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// Compute Y = transpose(Q)*B |
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$Y = $this->getQ()->transpose() |
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->multiply($B); |
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// Solve R*X = Y; |
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return $this->getR()->inverse() |
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->multiply($Y); |
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} |
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} |
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|
