PhpSpreadsheet/Classes/PHPExcel/Shared/JAMA/QRDecomposition.php

<?php
/**
 *	@package JAMA
 *
 *	For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n
 *	orthogonal matrix Q and an n-by-n upper triangular matrix R so that
 *	A = Q*R.
 *
 *	The QR decompostion always exists, even if the matrix does not have
 *	full rank, so the constructor will never fail.  The primary use of the
 *	QR decomposition is in the least squares solution of nonsquare systems
 *	of simultaneous linear equations.  This will fail if isFullRank()
 *	returns false.
 *
 *	@author  Paul Meagher
 *	@license PHP v3.0
 *	@version 1.1
 */
class QRDecomposition {

	/**
	 *	Array for internal storage of decomposition.
	 *	@var array
	 */
	private $QR = array();

	/**
	 *	Row dimension.
	 *	@var integer
	 */
	private $m;

	/**
	*	Column dimension.
	*	@var integer
	*/
	private $n;

	/**
	 *	Array for internal storage of diagonal of R.
	 *	@var  array
	 */
	private $Rdiag = array();


	/**
	 *	QR Decomposition computed by Householder reflections.
	 *
	 *	@param matrix $A Rectangular matrix
	 *	@return Structure to access R and the Householder vectors and compute Q.
	 */
	public function __construct($A) {
		if($A instanceof Matrix) {
			// Initialize.
			$this->QR = $A->getArrayCopy();
			$this->m  = $A->getRowDimension();
			$this->n  = $A->getColumnDimension();
			// Main loop.
			for ($k = 0; $k < $this->n; ++$k) {
				// Compute 2-norm of k-th column without under/overflow.
				$nrm = 0.0;
				for ($i = $k; $i < $this->m; ++$i) {
					$nrm = hypo($nrm, $this->QR[$i][$k]);
				}
				if ($nrm != 0.0) {
					// Form k-th Householder vector.
					if ($this->QR[$k][$k] < 0) {
						$nrm = -$nrm;
					}
					for ($i = $k; $i < $this->m; ++$i) {
						$this->QR[$i][$k] /= $nrm;
					}
					$this->QR[$k][$k] += 1.0;
					// Apply transformation to remaining columns.
					for ($j = $k+1; $j < $this->n; ++$j) {
						$s = 0.0;
						for ($i = $k; $i < $this->m; ++$i) {
							$s += $this->QR[$i][$k] * $this->QR[$i][$j];
						}
						$s = -$s/$this->QR[$k][$k];
						for ($i = $k; $i < $this->m; ++$i) {
							$this->QR[$i][$j] += $s * $this->QR[$i][$k];
						}
					}
				}
				$this->Rdiag[$k] = -$nrm;
			}
		} else {
			throw new Exception(JAMAError(ArgumentTypeException));
		}
	}	//	function __construct()


	/**
	 *	Is the matrix full rank?
	 *
	 *	@return boolean true if R, and hence A, has full rank, else false.
	 */
	public function isFullRank() {
		for ($j = 0; $j < $this->n; ++$j) {
			if ($this->Rdiag[$j] == 0) {
				return false;
			}
		}
		return true;
	}	//	function isFullRank()


	/**
	 *	Return the Householder vectors
	 *
	 *	@return Matrix Lower trapezoidal matrix whose columns define the reflections
	 */
	public function getH() {
		for ($i = 0; $i < $this->m; ++$i) {
			for ($j = 0; $j < $this->n; ++$j) {
				if ($i >= $j) {
					$H[$i][$j] = $this->QR[$i][$j];
				} else {
					$H[$i][$j] = 0.0;
				}
			}
		}
		return new Matrix($H);
	}	//	function getH()


	/**
	 *	Return the upper triangular factor
	 *
	 *	@return Matrix upper triangular factor
	 */
	public function getR() {
		for ($i = 0; $i < $this->n; ++$i) {
			for ($j = 0; $j < $this->n; ++$j) {
				if ($i < $j) {
					$R[$i][$j] = $this->QR[$i][$j];
				} elseif ($i == $j) {
					$R[$i][$j] = $this->Rdiag[$i];
				} else {
					$R[$i][$j] = 0.0;
				}
			}
		}
		return new Matrix($R);
	}	//	function getR()


	/**
	 *	Generate and return the (economy-sized) orthogonal factor
	 *
	 *	@return Matrix orthogonal factor
	 */
	public function getQ() {
		for ($k = $this->n-1; $k >= 0; --$k) {
			for ($i = 0; $i < $this->m; ++$i) {
				$Q[$i][$k] = 0.0;
			}
			$Q[$k][$k] = 1.0;
			for ($j = $k; $j < $this->n; ++$j) {
				if ($this->QR[$k][$k] != 0) {
					$s = 0.0;
					for ($i = $k; $i < $this->m; ++$i) {
						$s += $this->QR[$i][$k] * $Q[$i][$j];
					}
					$s = -$s/$this->QR[$k][$k];
					for ($i = $k; $i < $this->m; ++$i) {
						$Q[$i][$j] += $s * $this->QR[$i][$k];
					}
				}
			}
		}
		/*
		for($i = 0; $i < count($Q); ++$i) {
			for($j = 0; $j < count($Q); ++$j) {
				if(! isset($Q[$i][$j]) ) {
					$Q[$i][$j] = 0;
				}
			}
		}
		*/
		return new Matrix($Q);
	}	//	function getQ()


	/**
	 *	Least squares solution of A*X = B
	 *
	 *	@param Matrix $B A Matrix with as many rows as A and any number of columns.
	 *	@return Matrix Matrix that minimizes the two norm of Q*R*X-B.
	 */
	public function solve($B) {
		if ($B->getRowDimension() == $this->m) {
			if ($this->isFullRank()) {
				// Copy right hand side
				$nx = $B->getColumnDimension();
				$X  = $B->getArrayCopy();
				// Compute Y = transpose(Q)*B
				for ($k = 0; $k < $this->n; ++$k) {
					for ($j = 0; $j < $nx; ++$j) {
						$s = 0.0;
						for ($i = $k; $i < $this->m; ++$i) {
							$s += $this->QR[$i][$k] * $X[$i][$j];
						}
						$s = -$s/$this->QR[$k][$k];
						for ($i = $k; $i < $this->m; ++$i) {
							$X[$i][$j] += $s * $this->QR[$i][$k];
						}
					}
				}
				// Solve R*X = Y;
				for ($k = $this->n-1; $k >= 0; --$k) {
					for ($j = 0; $j < $nx; ++$j) {
						$X[$k][$j] /= $this->Rdiag[$k];
					}
					for ($i = 0; $i < $k; ++$i) {
						for ($j = 0; $j < $nx; ++$j) {
							$X[$i][$j] -= $X[$k][$j]* $this->QR[$i][$k];
						}
					}
				}
				$X = new Matrix($X);
				return ($X->getMatrix(0, $this->n-1, 0, $nx));
			} else {
				throw new Exception(JAMAError(MatrixRankException));
			}
		} else {
			throw new Exception(JAMAError(MatrixDimensionException));
		}
	}	//	function solve()

}	//	class QRDecomposition