LUDecomposition.php in Loft Data Grids 6.2

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vendor/phpoffice/phpexcel/Classes/PHPExcel/Shared/JAMA/LUDecomposition.php

<?php

/**
 *	@package JAMA
 *
 *	For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
 *	unit lower triangular matrix L, an n-by-n upper triangular matrix U,
 *	and a permutation vector piv of length m so that A(piv,:) = L*U.
 *	If m < n, then L is m-by-m and U is m-by-n.
 *
 *	The LU decompostion with pivoting always exists, even if the matrix is
 *	singular, so the constructor will never fail. The primary use of the
 *	LU decomposition is in the solution of square systems of simultaneous
 *	linear equations. This will fail if isNonsingular() returns false.
 *
 *	@author Paul Meagher
 *	@author Bartosz Matosiuk
 *	@author Michael Bommarito
 *	@version 1.1
 *	@license PHP v3.0
 */
class PHPExcel_Shared_JAMA_LUDecomposition {
  const MatrixSingularException = "Can only perform operation on singular matrix.";
  const MatrixSquareException = "Mismatched Row dimension";

  /**
   *	Decomposition storage
   *	@var array
   */
  private $LU = array();

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

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

  /**
   *	Pivot sign.
   *	@var int
   */
  private $pivsign;

  /**
   *	Internal storage of pivot vector.
   *	@var array
   */
  private $piv = array();

  /**
   *	LU Decomposition constructor.
   *
   *	@param $A Rectangular matrix
   *	@return Structure to access L, U and piv.
   */
  public function __construct($A) {
    if ($A instanceof PHPExcel_Shared_JAMA_Matrix) {

      // Use a "left-looking", dot-product, Crout/Doolittle algorithm.
      $this->LU = $A
        ->getArray();
      $this->m = $A
        ->getRowDimension();
      $this->n = $A
        ->getColumnDimension();
      for ($i = 0; $i < $this->m; ++$i) {
        $this->piv[$i] = $i;
      }
      $this->pivsign = 1;
      $LUrowi = $LUcolj = array();

      // Outer loop.
      for ($j = 0; $j < $this->n; ++$j) {

        // Make a copy of the j-th column to localize references.
        for ($i = 0; $i < $this->m; ++$i) {
          $LUcolj[$i] =& $this->LU[$i][$j];
        }

        // Apply previous transformations.
        for ($i = 0; $i < $this->m; ++$i) {
          $LUrowi = $this->LU[$i];

          // Most of the time is spent in the following dot product.
          $kmax = min($i, $j);
          $s = 0.0;
          for ($k = 0; $k < $kmax; ++$k) {
            $s += $LUrowi[$k] * $LUcolj[$k];
          }
          $LUrowi[$j] = $LUcolj[$i] -= $s;
        }

        // Find pivot and exchange if necessary.
        $p = $j;
        for ($i = $j + 1; $i < $this->m; ++$i) {
          if (abs($LUcolj[$i]) > abs($LUcolj[$p])) {
            $p = $i;
          }
        }
        if ($p != $j) {
          for ($k = 0; $k < $this->n; ++$k) {
            $t = $this->LU[$p][$k];
            $this->LU[$p][$k] = $this->LU[$j][$k];
            $this->LU[$j][$k] = $t;
          }
          $k = $this->piv[$p];
          $this->piv[$p] = $this->piv[$j];
          $this->piv[$j] = $k;
          $this->pivsign = $this->pivsign * -1;
        }

        // Compute multipliers.
        if ($j < $this->m && $this->LU[$j][$j] != 0.0) {
          for ($i = $j + 1; $i < $this->m; ++$i) {
            $this->LU[$i][$j] /= $this->LU[$j][$j];
          }
        }
      }
    }
    else {
      throw new PHPExcel_Calculation_Exception(PHPExcel_Shared_JAMA_Matrix::ArgumentTypeException);
    }
  }

  //	function __construct()

  /**
   *	Get lower triangular factor.
   *
   *	@return array Lower triangular factor
   */
  public function getL() {
    for ($i = 0; $i < $this->m; ++$i) {
      for ($j = 0; $j < $this->n; ++$j) {
        if ($i > $j) {
          $L[$i][$j] = $this->LU[$i][$j];
        }
        elseif ($i == $j) {
          $L[$i][$j] = 1.0;
        }
        else {
          $L[$i][$j] = 0.0;
        }
      }
    }
    return new PHPExcel_Shared_JAMA_Matrix($L);
  }

  //	function getL()

  /**
   *	Get upper triangular factor.
   *
   *	@return array Upper triangular factor
   */
  public function getU() {
    for ($i = 0; $i < $this->n; ++$i) {
      for ($j = 0; $j < $this->n; ++$j) {
        if ($i <= $j) {
          $U[$i][$j] = $this->LU[$i][$j];
        }
        else {
          $U[$i][$j] = 0.0;
        }
      }
    }
    return new PHPExcel_Shared_JAMA_Matrix($U);
  }

  //	function getU()

  /**
   *	Return pivot permutation vector.
   *
   *	@return array Pivot vector
   */
  public function getPivot() {
    return $this->piv;
  }

  //	function getPivot()

  /**
   *	Alias for getPivot
   *
   *	@see getPivot
   */
  public function getDoublePivot() {
    return $this
      ->getPivot();
  }

  //	function getDoublePivot()

  /**
   *	Is the matrix nonsingular?
   *
   *	@return true if U, and hence A, is nonsingular.
   */
  public function isNonsingular() {
    for ($j = 0; $j < $this->n; ++$j) {
      if ($this->LU[$j][$j] == 0) {
        return false;
      }
    }
    return true;
  }

  //	function isNonsingular()

  /**
   *	Count determinants
   *
   *	@return array d matrix deterninat
   */
  public function det() {
    if ($this->m == $this->n) {
      $d = $this->pivsign;
      for ($j = 0; $j < $this->n; ++$j) {
        $d *= $this->LU[$j][$j];
      }
      return $d;
    }
    else {
      throw new PHPExcel_Calculation_Exception(PHPExcel_Shared_JAMA_Matrix::MatrixDimensionException);
    }
  }

  //	function det()

  /**
   *	Solve A*X = B
   *
   *	@param  $B  A Matrix with as many rows as A and any number of columns.
   *	@return  X so that L*U*X = B(piv,:)
   *	@PHPExcel_Calculation_Exception  IllegalArgumentException Matrix row dimensions must agree.
   *	@PHPExcel_Calculation_Exception  RuntimeException  Matrix is singular.
   */
  public function solve($B) {
    if ($B
      ->getRowDimension() == $this->m) {
      if ($this
        ->isNonsingular()) {

        // Copy right hand side with pivoting
        $nx = $B
          ->getColumnDimension();
        $X = $B
          ->getMatrix($this->piv, 0, $nx - 1);

        // Solve L*Y = B(piv,:)
        for ($k = 0; $k < $this->n; ++$k) {
          for ($i = $k + 1; $i < $this->n; ++$i) {
            for ($j = 0; $j < $nx; ++$j) {
              $X->A[$i][$j] -= $X->A[$k][$j] * $this->LU[$i][$k];
            }
          }
        }

        // Solve U*X = Y;
        for ($k = $this->n - 1; $k >= 0; --$k) {
          for ($j = 0; $j < $nx; ++$j) {
            $X->A[$k][$j] /= $this->LU[$k][$k];
          }
          for ($i = 0; $i < $k; ++$i) {
            for ($j = 0; $j < $nx; ++$j) {
              $X->A[$i][$j] -= $X->A[$k][$j] * $this->LU[$i][$k];
            }
          }
        }
        return $X;
      }
      else {
        throw new PHPExcel_Calculation_Exception(self::MatrixSingularException);
      }
    }
    else {
      throw new PHPExcel_Calculation_Exception(self::MatrixSquareException);
    }
  }

}

//	class PHPExcel_Shared_JAMA_LUDecomposition

Classes

Name	Description
PHPExcel_Shared_JAMA_LUDecomposition	@package JAMA