2010-08-26 19:14:53 +00:00
|
|
|
<?php
|
|
|
|
|
/**
|
|
|
|
|
* @package JAMA
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
define('RAND_MAX', mt_getrandmax());
|
|
|
|
|
define('RAND_MIN', 0);
|
|
|
|
|
|
|
|
|
|
/** PHPExcel root directory */
|
|
|
|
|
if (!defined('PHPEXCEL_ROOT')) {
|
|
|
|
|
/**
|
|
|
|
|
* @ignore
|
|
|
|
|
*/
|
|
|
|
|
define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../../');
|
|
|
|
|
require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
|
|
|
|
|
PHPExcel_Autoloader::Register();
|
|
|
|
|
PHPExcel_Shared_ZipStreamWrapper::register();
|
|
|
|
|
// check mbstring.func_overload
|
|
|
|
|
if (ini_get('mbstring.func_overload') & 2) {
|
|
|
|
|
throw new Exception('Multibyte function overloading in PHP must be disabled for string functions (2).');
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/utils/Error.php';
|
|
|
|
|
require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/utils/Maths.php';
|
|
|
|
|
require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/CholeskyDecomposition.php';
|
|
|
|
|
require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/LUDecomposition.php';
|
|
|
|
|
require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/QRDecomposition.php';
|
|
|
|
|
require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/EigenvalueDecomposition.php';
|
|
|
|
|
require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/SingularValueDecomposition.php';
|
|
|
|
|
require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/String.php';
|
|
|
|
|
require_once PHPEXCEL_ROOT . 'PHPExcel/Calculation/Functions.php';
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* Matrix class
|
|
|
|
|
*
|
|
|
|
|
* @author Paul Meagher
|
|
|
|
|
* @author Michael Bommarito
|
|
|
|
|
* @author Lukasz Karapuda
|
|
|
|
|
* @author Bartek Matosiuk
|
|
|
|
|
* @version 1.8
|
|
|
|
|
* @license PHP v3.0
|
|
|
|
|
* @see http://math.nist.gov/javanumerics/jama/
|
|
|
|
|
*/
|
|
|
|
|
class Matrix {
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* Matrix storage
|
|
|
|
|
*
|
|
|
|
|
* @var array
|
|
|
|
|
* @access public
|
|
|
|
|
*/
|
|
|
|
|
public $A = array();
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* Matrix row dimension
|
|
|
|
|
*
|
|
|
|
|
* @var int
|
|
|
|
|
* @access private
|
|
|
|
|
*/
|
|
|
|
|
private $m;
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* Matrix column dimension
|
|
|
|
|
*
|
|
|
|
|
* @var int
|
|
|
|
|
* @access private
|
|
|
|
|
*/
|
|
|
|
|
private $n;
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* Polymorphic constructor
|
|
|
|
|
*
|
|
|
|
|
* As PHP has no support for polymorphic constructors, we hack our own sort of polymorphism using func_num_args, func_get_arg, and gettype. In essence, we're just implementing a simple RTTI filter and calling the appropriate constructor.
|
|
|
|
|
*/
|
|
|
|
|
public function __construct() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
//Square matrix - n x n
|
|
|
|
|
case 'integer':
|
|
|
|
|
$this->m = $args[0];
|
|
|
|
|
$this->n = $args[0];
|
|
|
|
|
$this->A = array_fill(0, $this->m, array_fill(0, $this->n, 0));
|
|
|
|
|
break;
|
|
|
|
|
//Rectangular matrix - m x n
|
|
|
|
|
case 'integer,integer':
|
|
|
|
|
$this->m = $args[0];
|
|
|
|
|
$this->n = $args[1];
|
|
|
|
|
$this->A = array_fill(0, $this->m, array_fill(0, $this->n, 0));
|
|
|
|
|
break;
|
|
|
|
|
//Rectangular matrix constant-filled - m x n filled with c
|
|
|
|
|
case 'integer,integer,integer':
|
|
|
|
|
$this->m = $args[0];
|
|
|
|
|
$this->n = $args[1];
|
|
|
|
|
$this->A = array_fill(0, $this->m, array_fill(0, $this->n, $args[2]));
|
|
|
|
|
break;
|
|
|
|
|
//Rectangular matrix constant-filled - m x n filled with c
|
|
|
|
|
case 'integer,integer,double':
|
|
|
|
|
$this->m = $args[0];
|
|
|
|
|
$this->n = $args[1];
|
|
|
|
|
$this->A = array_fill(0, $this->m, array_fill(0, $this->n, $args[2]));
|
|
|
|
|
break;
|
|
|
|
|
//Rectangular matrix - m x n initialized from 2D array
|
|
|
|
|
case 'array':
|
|
|
|
|
$this->m = count($args[0]);
|
|
|
|
|
$this->n = count($args[0][0]);
|
|
|
|
|
$this->A = $args[0];
|
|
|
|
|
break;
|
|
|
|
|
//Rectangular matrix - m x n initialized from 2D array
|
|
|
|
|
case 'array,integer,integer':
|
|
|
|
|
$this->m = $args[1];
|
|
|
|
|
$this->n = $args[2];
|
|
|
|
|
$this->A = $args[0];
|
|
|
|
|
break;
|
|
|
|
|
//Rectangular matrix - m x n initialized from packed array
|
|
|
|
|
case 'array,integer':
|
|
|
|
|
$this->m = $args[1];
|
|
|
|
|
if ($this->m != 0) {
|
|
|
|
|
$this->n = count($args[0]) / $this->m;
|
|
|
|
|
} else {
|
|
|
|
|
$this->n = 0;
|
|
|
|
|
}
|
|
|
|
|
if (($this->m * $this->n) == count($args[0])) {
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$this->A[$i][$j] = $args[0][$i + $j * $this->m];
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(ArrayLengthException));
|
|
|
|
|
}
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
}
|
|
|
|
|
} // function __construct()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* getArray
|
|
|
|
|
*
|
|
|
|
|
* @return array Matrix array
|
|
|
|
|
*/
|
|
|
|
|
public function getArray() {
|
|
|
|
|
return $this->A;
|
|
|
|
|
} // function getArray()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* getArrayCopy
|
|
|
|
|
*
|
|
|
|
|
* @return array Matrix array copy
|
|
|
|
|
*/
|
|
|
|
|
public function getArrayCopy() {
|
|
|
|
|
return $this->A;
|
|
|
|
|
} // function getArrayCopy()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* constructWithCopy
|
|
|
|
|
* Construct a matrix from a copy of a 2-D array.
|
|
|
|
|
*
|
|
|
|
|
* @param double A[][] Two-dimensional array of doubles.
|
|
|
|
|
* @exception IllegalArgumentException All rows must have the same length
|
|
|
|
|
*/
|
|
|
|
|
public function constructWithCopy($A) {
|
|
|
|
|
$this->m = count($A);
|
|
|
|
|
$this->n = count($A[0]);
|
|
|
|
|
$newCopyMatrix = new Matrix($this->m, $this->n);
|
|
|
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
if (count($A[$i]) != $this->n) {
|
|
|
|
|
throw new Exception(JAMAError(RowLengthException));
|
|
|
|
|
}
|
|
|
|
|
for ($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$newCopyMatrix->A[$i][$j] = $A[$i][$j];
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $newCopyMatrix;
|
|
|
|
|
} // function constructWithCopy()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* getColumnPackedCopy
|
|
|
|
|
*
|
|
|
|
|
* Get a column-packed array
|
|
|
|
|
* @return array Column-packed matrix array
|
|
|
|
|
*/
|
|
|
|
|
public function getColumnPackedCopy() {
|
|
|
|
|
$P = array();
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
array_push($P, $this->A[$j][$i]);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $P;
|
|
|
|
|
} // function getColumnPackedCopy()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* getRowPackedCopy
|
|
|
|
|
*
|
|
|
|
|
* Get a row-packed array
|
|
|
|
|
* @return array Row-packed matrix array
|
|
|
|
|
*/
|
|
|
|
|
public function getRowPackedCopy() {
|
|
|
|
|
$P = array();
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
array_push($P, $this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $P;
|
|
|
|
|
} // function getRowPackedCopy()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* getRowDimension
|
|
|
|
|
*
|
|
|
|
|
* @return int Row dimension
|
|
|
|
|
*/
|
|
|
|
|
public function getRowDimension() {
|
|
|
|
|
return $this->m;
|
|
|
|
|
} // function getRowDimension()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* getColumnDimension
|
|
|
|
|
*
|
|
|
|
|
* @return int Column dimension
|
|
|
|
|
*/
|
|
|
|
|
public function getColumnDimension() {
|
|
|
|
|
return $this->n;
|
|
|
|
|
} // function getColumnDimension()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* get
|
|
|
|
|
*
|
|
|
|
|
* Get the i,j-th element of the matrix.
|
|
|
|
|
* @param int $i Row position
|
|
|
|
|
* @param int $j Column position
|
|
|
|
|
* @return mixed Element (int/float/double)
|
|
|
|
|
*/
|
|
|
|
|
public function get($i = null, $j = null) {
|
|
|
|
|
return $this->A[$i][$j];
|
|
|
|
|
} // function get()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* getMatrix
|
|
|
|
|
*
|
|
|
|
|
* Get a submatrix
|
|
|
|
|
* @param int $i0 Initial row index
|
|
|
|
|
* @param int $iF Final row index
|
|
|
|
|
* @param int $j0 Initial column index
|
|
|
|
|
* @param int $jF Final column index
|
|
|
|
|
* @return Matrix Submatrix
|
|
|
|
|
*/
|
|
|
|
|
public function getMatrix() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
//A($i0...; $j0...)
|
|
|
|
|
case 'integer,integer':
|
|
|
|
|
list($i0, $j0) = $args;
|
|
|
|
|
if ($i0 >= 0) { $m = $this->m - $i0; } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
if ($j0 >= 0) { $n = $this->n - $j0; } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
$R = new Matrix($m, $n);
|
|
|
|
|
for($i = $i0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = $j0; $j < $this->n; ++$j) {
|
|
|
|
|
$R->set($i, $j, $this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $R;
|
|
|
|
|
break;
|
|
|
|
|
//A($i0...$iF; $j0...$jF)
|
|
|
|
|
case 'integer,integer,integer,integer':
|
|
|
|
|
list($i0, $iF, $j0, $jF) = $args;
|
|
|
|
|
if (($iF > $i0) && ($this->m >= $iF) && ($i0 >= 0)) { $m = $iF - $i0; } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
if (($jF > $j0) && ($this->n >= $jF) && ($j0 >= 0)) { $n = $jF - $j0; } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
$R = new Matrix($m+1, $n+1);
|
|
|
|
|
for($i = $i0; $i <= $iF; ++$i) {
|
|
|
|
|
for($j = $j0; $j <= $jF; ++$j) {
|
|
|
|
|
$R->set($i - $i0, $j - $j0, $this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $R;
|
|
|
|
|
break;
|
|
|
|
|
//$R = array of row indices; $C = array of column indices
|
|
|
|
|
case 'array,array':
|
|
|
|
|
list($RL, $CL) = $args;
|
|
|
|
|
if (count($RL) > 0) { $m = count($RL); } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
if (count($CL) > 0) { $n = count($CL); } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
$R = new Matrix($m, $n);
|
|
|
|
|
for($i = 0; $i < $m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $n; ++$j) {
|
|
|
|
|
$R->set($i - $i0, $j - $j0, $this->A[$RL[$i]][$CL[$j]]);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $R;
|
|
|
|
|
break;
|
|
|
|
|
//$RL = array of row indices; $CL = array of column indices
|
|
|
|
|
case 'array,array':
|
|
|
|
|
list($RL, $CL) = $args;
|
|
|
|
|
if (count($RL) > 0) { $m = count($RL); } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
if (count($CL) > 0) { $n = count($CL); } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
$R = new Matrix($m, $n);
|
|
|
|
|
for($i = 0; $i < $m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $n; ++$j) {
|
|
|
|
|
$R->set($i, $j, $this->A[$RL[$i]][$CL[$j]]);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $R;
|
|
|
|
|
break;
|
|
|
|
|
//A($i0...$iF); $CL = array of column indices
|
|
|
|
|
case 'integer,integer,array':
|
|
|
|
|
list($i0, $iF, $CL) = $args;
|
|
|
|
|
if (($iF > $i0) && ($this->m >= $iF) && ($i0 >= 0)) { $m = $iF - $i0; } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
if (count($CL) > 0) { $n = count($CL); } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
$R = new Matrix($m, $n);
|
|
|
|
|
for($i = $i0; $i < $iF; ++$i) {
|
|
|
|
|
for($j = 0; $j < $n; ++$j) {
|
|
|
|
|
$R->set($i - $i0, $j, $this->A[$RL[$i]][$j]);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $R;
|
|
|
|
|
break;
|
|
|
|
|
//$RL = array of row indices
|
|
|
|
|
case 'array,integer,integer':
|
|
|
|
|
list($RL, $j0, $jF) = $args;
|
|
|
|
|
if (count($RL) > 0) { $m = count($RL); } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
if (($jF >= $j0) && ($this->n >= $jF) && ($j0 >= 0)) { $n = $jF - $j0; } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
$R = new Matrix($m, $n+1);
|
|
|
|
|
for($i = 0; $i < $m; ++$i) {
|
|
|
|
|
for($j = $j0; $j <= $jF; ++$j) {
|
|
|
|
|
$R->set($i, $j - $j0, $this->A[$RL[$i]][$j]);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $R;
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
}
|
|
|
|
|
} // function getMatrix()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* setMatrix
|
|
|
|
|
*
|
|
|
|
|
* Set a submatrix
|
|
|
|
|
* @param int $i0 Initial row index
|
|
|
|
|
* @param int $j0 Initial column index
|
|
|
|
|
* @param mixed $S Matrix/Array submatrix
|
|
|
|
|
* ($i0, $j0, $S) $S = Matrix
|
|
|
|
|
* ($i0, $j0, $S) $S = Array
|
|
|
|
|
*/
|
|
|
|
|
public function setMatrix() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
case 'integer,integer,object':
|
|
|
|
|
if ($args[2] instanceof Matrix) { $M = $args[2]; } else { throw new Exception(JAMAError(ArgumentTypeException)); }
|
|
|
|
|
if (($args[0] + $M->m) <= $this->m) { $i0 = $args[0]; } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
if (($args[1] + $M->n) <= $this->n) { $j0 = $args[1]; } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
for($i = $i0; $i < $i0 + $M->m; ++$i) {
|
|
|
|
|
for($j = $j0; $j < $j0 + $M->n; ++$j) {
|
|
|
|
|
$this->A[$i][$j] = $M->get($i - $i0, $j - $j0);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
break;
|
|
|
|
|
case 'integer,integer,array':
|
|
|
|
|
$M = new Matrix($args[2]);
|
|
|
|
|
if (($args[0] + $M->m) <= $this->m) { $i0 = $args[0]; } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
if (($args[1] + $M->n) <= $this->n) { $j0 = $args[1]; } else { throw new Exception(JAMAError(ArgumentBoundsException)); }
|
|
|
|
|
for($i = $i0; $i < $i0 + $M->m; ++$i) {
|
|
|
|
|
for($j = $j0; $j < $j0 + $M->n; ++$j) {
|
|
|
|
|
$this->A[$i][$j] = $M->get($i - $i0, $j - $j0);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
}
|
|
|
|
|
} // function setMatrix()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* checkMatrixDimensions
|
|
|
|
|
*
|
|
|
|
|
* Is matrix B the same size?
|
|
|
|
|
* @param Matrix $B Matrix B
|
|
|
|
|
* @return boolean
|
|
|
|
|
*/
|
|
|
|
|
public function checkMatrixDimensions($B = null) {
|
|
|
|
|
if ($B instanceof Matrix) {
|
|
|
|
|
if (($this->m == $B->getRowDimension()) && ($this->n == $B->getColumnDimension())) {
|
|
|
|
|
return true;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(MatrixDimensionException));
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(ArgumentTypeException));
|
|
|
|
|
}
|
|
|
|
|
} // function checkMatrixDimensions()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* set
|
|
|
|
|
*
|
|
|
|
|
* Set the i,j-th element of the matrix.
|
|
|
|
|
* @param int $i Row position
|
|
|
|
|
* @param int $j Column position
|
|
|
|
|
* @param mixed $c Int/float/double value
|
|
|
|
|
* @return mixed Element (int/float/double)
|
|
|
|
|
*/
|
|
|
|
|
public function set($i = null, $j = null, $c = null) {
|
|
|
|
|
// Optimized set version just has this
|
|
|
|
|
$this->A[$i][$j] = $c;
|
|
|
|
|
/*
|
|
|
|
|
if (is_int($i) && is_int($j) && is_numeric($c)) {
|
|
|
|
|
if (($i < $this->m) && ($j < $this->n)) {
|
|
|
|
|
$this->A[$i][$j] = $c;
|
|
|
|
|
} else {
|
|
|
|
|
echo "A[$i][$j] = $c<br />";
|
|
|
|
|
throw new Exception(JAMAError(ArgumentBoundsException));
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(ArgumentTypeException));
|
|
|
|
|
}
|
|
|
|
|
*/
|
|
|
|
|
} // function set()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* identity
|
|
|
|
|
*
|
|
|
|
|
* Generate an identity matrix.
|
|
|
|
|
* @param int $m Row dimension
|
|
|
|
|
* @param int $n Column dimension
|
|
|
|
|
* @return Matrix Identity matrix
|
|
|
|
|
*/
|
|
|
|
|
public function identity($m = null, $n = null) {
|
|
|
|
|
return $this->diagonal($m, $n, 1);
|
|
|
|
|
} // function identity()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* diagonal
|
|
|
|
|
*
|
|
|
|
|
* Generate a diagonal matrix
|
|
|
|
|
* @param int $m Row dimension
|
|
|
|
|
* @param int $n Column dimension
|
|
|
|
|
* @param mixed $c Diagonal value
|
|
|
|
|
* @return Matrix Diagonal matrix
|
|
|
|
|
*/
|
|
|
|
|
public function diagonal($m = null, $n = null, $c = 1) {
|
|
|
|
|
$R = new Matrix($m, $n);
|
|
|
|
|
for($i = 0; $i < $m; ++$i) {
|
|
|
|
|
$R->set($i, $i, $c);
|
|
|
|
|
}
|
|
|
|
|
return $R;
|
|
|
|
|
} // function diagonal()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* filled
|
|
|
|
|
*
|
|
|
|
|
* Generate a filled matrix
|
|
|
|
|
* @param int $m Row dimension
|
|
|
|
|
* @param int $n Column dimension
|
|
|
|
|
* @param int $c Fill constant
|
|
|
|
|
* @return Matrix Filled matrix
|
|
|
|
|
*/
|
|
|
|
|
public function filled($m = null, $n = null, $c = 0) {
|
|
|
|
|
if (is_int($m) && is_int($n) && is_numeric($c)) {
|
|
|
|
|
$R = new Matrix($m, $n, $c);
|
|
|
|
|
return $R;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(ArgumentTypeException));
|
|
|
|
|
}
|
|
|
|
|
} // function filled()
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* random
|
|
|
|
|
*
|
|
|
|
|
* Generate a random matrix
|
|
|
|
|
* @param int $m Row dimension
|
|
|
|
|
* @param int $n Column dimension
|
|
|
|
|
* @return Matrix Random matrix
|
|
|
|
|
*/
|
|
|
|
|
public function random($m = null, $n = null, $a = RAND_MIN, $b = RAND_MAX) {
|
|
|
|
|
if (is_int($m) && is_int($n) && is_numeric($a) && is_numeric($b)) {
|
|
|
|
|
$R = new Matrix($m, $n);
|
|
|
|
|
for($i = 0; $i < $m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $n; ++$j) {
|
|
|
|
|
$R->set($i, $j, mt_rand($a, $b));
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $R;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(ArgumentTypeException));
|
|
|
|
|
}
|
|
|
|
|
} // function random()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* packed
|
|
|
|
|
*
|
|
|
|
|
* Alias for getRowPacked
|
|
|
|
|
* @return array Packed array
|
|
|
|
|
*/
|
|
|
|
|
public function packed() {
|
|
|
|
|
return $this->getRowPacked();
|
|
|
|
|
} // function packed()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* getMatrixByRow
|
|
|
|
|
*
|
|
|
|
|
* Get a submatrix by row index/range
|
|
|
|
|
* @param int $i0 Initial row index
|
|
|
|
|
* @param int $iF Final row index
|
|
|
|
|
* @return Matrix Submatrix
|
|
|
|
|
*/
|
|
|
|
|
public function getMatrixByRow($i0 = null, $iF = null) {
|
|
|
|
|
if (is_int($i0)) {
|
|
|
|
|
if (is_int($iF)) {
|
|
|
|
|
return $this->getMatrix($i0, 0, $iF + 1, $this->n);
|
|
|
|
|
} else {
|
|
|
|
|
return $this->getMatrix($i0, 0, $i0 + 1, $this->n);
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(ArgumentTypeException));
|
|
|
|
|
}
|
|
|
|
|
} // function getMatrixByRow()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* getMatrixByCol
|
|
|
|
|
*
|
|
|
|
|
* Get a submatrix by column index/range
|
|
|
|
|
* @param int $i0 Initial column index
|
|
|
|
|
* @param int $iF Final column index
|
|
|
|
|
* @return Matrix Submatrix
|
|
|
|
|
*/
|
|
|
|
|
public function getMatrixByCol($j0 = null, $jF = null) {
|
|
|
|
|
if (is_int($j0)) {
|
|
|
|
|
if (is_int($jF)) {
|
|
|
|
|
return $this->getMatrix(0, $j0, $this->m, $jF + 1);
|
|
|
|
|
} else {
|
|
|
|
|
return $this->getMatrix(0, $j0, $this->m, $j0 + 1);
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(ArgumentTypeException));
|
|
|
|
|
}
|
|
|
|
|
} // function getMatrixByCol()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* transpose
|
|
|
|
|
*
|
|
|
|
|
* Tranpose matrix
|
|
|
|
|
* @return Matrix Transposed matrix
|
|
|
|
|
*/
|
|
|
|
|
public function transpose() {
|
|
|
|
|
$R = new Matrix($this->n, $this->m);
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$R->set($j, $i, $this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $R;
|
|
|
|
|
} // function transpose()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* norm1
|
|
|
|
|
*
|
|
|
|
|
* One norm
|
|
|
|
|
* @return float Maximum column sum
|
|
|
|
|
*/
|
|
|
|
|
public function norm1() {
|
|
|
|
|
$r = 0;
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$s = 0;
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
$s += abs($this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
$r = ($r > $s) ? $r : $s;
|
|
|
|
|
}
|
|
|
|
|
return $r;
|
|
|
|
|
} // function norm1()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* norm2
|
|
|
|
|
*
|
|
|
|
|
* Maximum singular value
|
|
|
|
|
* @return float Maximum singular value
|
|
|
|
|
*/
|
|
|
|
|
public function norm2() {
|
|
|
|
|
} // function norm2()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* normInf
|
|
|
|
|
*
|
|
|
|
|
* Infinite norm
|
|
|
|
|
* @return float Maximum row sum
|
|
|
|
|
*/
|
|
|
|
|
public function normInf() {
|
|
|
|
|
$r = 0;
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
$s = 0;
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$s += abs($this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
$r = ($r > $s) ? $r : $s;
|
|
|
|
|
}
|
|
|
|
|
return $r;
|
|
|
|
|
} // function normInf()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* normF
|
|
|
|
|
*
|
|
|
|
|
* Frobenius norm
|
|
|
|
|
* @return float Square root of the sum of all elements squared
|
|
|
|
|
*/
|
|
|
|
|
public function normF() {
|
|
|
|
|
$f = 0;
|
|
|
|
|
for ($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for ($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$f = hypo($f,$this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $f;
|
|
|
|
|
} // function normF()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* Matrix rank
|
|
|
|
|
*
|
|
|
|
|
* @return effective numerical rank, obtained from SVD.
|
|
|
|
|
*/
|
|
|
|
|
public function rank () {
|
|
|
|
|
$svd = new SingularValueDecomposition($this);
|
|
|
|
|
return $svd->rank();
|
|
|
|
|
} // function rank ()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* Matrix condition (2 norm)
|
|
|
|
|
*
|
|
|
|
|
* @return ratio of largest to smallest singular value.
|
|
|
|
|
*/
|
|
|
|
|
public function cond () {
|
|
|
|
|
$svd = new SingularValueDecomposition($this);
|
|
|
|
|
return $svd->cond();
|
|
|
|
|
} // function cond ()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* trace
|
|
|
|
|
*
|
|
|
|
|
* Sum of diagonal elements
|
|
|
|
|
* @return float Sum of diagonal elements
|
|
|
|
|
*/
|
|
|
|
|
public function trace() {
|
|
|
|
|
$s = 0;
|
|
|
|
|
$n = min($this->m, $this->n);
|
|
|
|
|
for($i = 0; $i < $n; ++$i) {
|
|
|
|
|
$s += $this->A[$i][$i];
|
|
|
|
|
}
|
|
|
|
|
return $s;
|
|
|
|
|
} // function trace()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* uminus
|
|
|
|
|
*
|
|
|
|
|
* Unary minus matrix -A
|
|
|
|
|
* @return Matrix Unary minus matrix
|
|
|
|
|
*/
|
|
|
|
|
public function uminus() {
|
|
|
|
|
} // function uminus()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* plus
|
|
|
|
|
*
|
|
|
|
|
* A + B
|
|
|
|
|
* @param mixed $B Matrix/Array
|
|
|
|
|
* @return Matrix Sum
|
|
|
|
|
*/
|
|
|
|
|
public function plus() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
case 'object':
|
|
|
|
|
if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); }
|
|
|
|
|
break;
|
|
|
|
|
case 'array':
|
|
|
|
|
$M = new Matrix($args[0]);
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
$this->checkMatrixDimensions($M);
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$M->set($i, $j, $M->get($i, $j) + $this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $M;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
}
|
|
|
|
|
} // function plus()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* plusEquals
|
|
|
|
|
*
|
|
|
|
|
* A = A + B
|
|
|
|
|
* @param mixed $B Matrix/Array
|
|
|
|
|
* @return Matrix Sum
|
|
|
|
|
*/
|
|
|
|
|
public function plusEquals() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
case 'object':
|
|
|
|
|
if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); }
|
|
|
|
|
break;
|
|
|
|
|
case 'array':
|
|
|
|
|
$M = new Matrix($args[0]);
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
$this->checkMatrixDimensions($M);
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$validValues = True;
|
|
|
|
|
$value = $M->get($i, $j);
|
|
|
|
|
if ((is_string($this->A[$i][$j])) && (strlen($this->A[$i][$j]) > 0) && (!is_numeric($this->A[$i][$j]))) {
|
|
|
|
|
$this->A[$i][$j] = trim($this->A[$i][$j],'"');
|
|
|
|
|
$validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
if ((is_string($value)) && (strlen($value) > 0) && (!is_numeric($value))) {
|
|
|
|
|
$value = trim($value,'"');
|
|
|
|
|
$validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($value);
|
|
|
|
|
}
|
|
|
|
|
if ($validValues) {
|
|
|
|
|
$this->A[$i][$j] += $value;
|
|
|
|
|
} else {
|
|
|
|
|
$this->A[$i][$j] = PHPExcel_Calculation_Functions::NaN();
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $this;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
}
|
|
|
|
|
} // function plusEquals()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* minus
|
|
|
|
|
*
|
|
|
|
|
* A - B
|
|
|
|
|
* @param mixed $B Matrix/Array
|
|
|
|
|
* @return Matrix Sum
|
|
|
|
|
*/
|
|
|
|
|
public function minus() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
case 'object':
|
|
|
|
|
if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); }
|
|
|
|
|
break;
|
|
|
|
|
case 'array':
|
|
|
|
|
$M = new Matrix($args[0]);
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
$this->checkMatrixDimensions($M);
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$M->set($i, $j, $M->get($i, $j) - $this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $M;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
}
|
|
|
|
|
} // function minus()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* minusEquals
|
|
|
|
|
*
|
|
|
|
|
* A = A - B
|
|
|
|
|
* @param mixed $B Matrix/Array
|
|
|
|
|
* @return Matrix Sum
|
|
|
|
|
*/
|
|
|
|
|
public function minusEquals() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
case 'object':
|
|
|
|
|
if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); }
|
|
|
|
|
break;
|
|
|
|
|
case 'array':
|
|
|
|
|
$M = new Matrix($args[0]);
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
$this->checkMatrixDimensions($M);
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$validValues = True;
|
|
|
|
|
$value = $M->get($i, $j);
|
|
|
|
|
if ((is_string($this->A[$i][$j])) && (strlen($this->A[$i][$j]) > 0) && (!is_numeric($this->A[$i][$j]))) {
|
|
|
|
|
$this->A[$i][$j] = trim($this->A[$i][$j],'"');
|
|
|
|
|
$validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
if ((is_string($value)) && (strlen($value) > 0) && (!is_numeric($value))) {
|
|
|
|
|
$value = trim($value,'"');
|
|
|
|
|
$validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($value);
|
|
|
|
|
}
|
|
|
|
|
if ($validValues) {
|
|
|
|
|
$this->A[$i][$j] -= $value;
|
|
|
|
|
} else {
|
|
|
|
|
$this->A[$i][$j] = PHPExcel_Calculation_Functions::NaN();
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $this;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
}
|
|
|
|
|
} // function minusEquals()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* arrayTimes
|
|
|
|
|
*
|
|
|
|
|
* Element-by-element multiplication
|
|
|
|
|
* Cij = Aij * Bij
|
|
|
|
|
* @param mixed $B Matrix/Array
|
|
|
|
|
* @return Matrix Matrix Cij
|
|
|
|
|
*/
|
|
|
|
|
public function arrayTimes() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
case 'object':
|
|
|
|
|
if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); }
|
|
|
|
|
break;
|
|
|
|
|
case 'array':
|
|
|
|
|
$M = new Matrix($args[0]);
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
$this->checkMatrixDimensions($M);
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$M->set($i, $j, $M->get($i, $j) * $this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $M;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
}
|
|
|
|
|
} // function arrayTimes()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* arrayTimesEquals
|
|
|
|
|
*
|
|
|
|
|
* Element-by-element multiplication
|
|
|
|
|
* Aij = Aij * Bij
|
|
|
|
|
* @param mixed $B Matrix/Array
|
|
|
|
|
* @return Matrix Matrix Aij
|
|
|
|
|
*/
|
|
|
|
|
public function arrayTimesEquals() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
case 'object':
|
|
|
|
|
if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); }
|
|
|
|
|
break;
|
|
|
|
|
case 'array':
|
|
|
|
|
$M = new Matrix($args[0]);
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
$this->checkMatrixDimensions($M);
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$validValues = True;
|
|
|
|
|
$value = $M->get($i, $j);
|
|
|
|
|
if ((is_string($this->A[$i][$j])) && (strlen($this->A[$i][$j]) > 0) && (!is_numeric($this->A[$i][$j]))) {
|
|
|
|
|
$this->A[$i][$j] = trim($this->A[$i][$j],'"');
|
|
|
|
|
$validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
if ((is_string($value)) && (strlen($value) > 0) && (!is_numeric($value))) {
|
|
|
|
|
$value = trim($value,'"');
|
|
|
|
|
$validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($value);
|
|
|
|
|
}
|
|
|
|
|
if ($validValues) {
|
|
|
|
|
$this->A[$i][$j] *= $value;
|
|
|
|
|
} else {
|
|
|
|
|
$this->A[$i][$j] = PHPExcel_Calculation_Functions::NaN();
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $this;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
}
|
|
|
|
|
} // function arrayTimesEquals()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* arrayRightDivide
|
|
|
|
|
*
|
|
|
|
|
* Element-by-element right division
|
|
|
|
|
* A / B
|
|
|
|
|
* @param Matrix $B Matrix B
|
|
|
|
|
* @return Matrix Division result
|
|
|
|
|
*/
|
|
|
|
|
public function arrayRightDivide() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
case 'object':
|
|
|
|
|
if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); }
|
|
|
|
|
break;
|
|
|
|
|
case 'array':
|
|
|
|
|
$M = new Matrix($args[0]);
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
$this->checkMatrixDimensions($M);
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$validValues = True;
|
|
|
|
|
$value = $M->get($i, $j);
|
|
|
|
|
if ((is_string($this->A[$i][$j])) && (strlen($this->A[$i][$j]) > 0) && (!is_numeric($this->A[$i][$j]))) {
|
|
|
|
|
$this->A[$i][$j] = trim($this->A[$i][$j],'"');
|
|
|
|
|
$validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
if ((is_string($value)) && (strlen($value) > 0) && (!is_numeric($value))) {
|
|
|
|
|
$value = trim($value,'"');
|
|
|
|
|
$validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($value);
|
|
|
|
|
}
|
|
|
|
|
if ($validValues) {
|
|
|
|
|
if ($value == 0) {
|
|
|
|
|
// Trap for Divide by Zero error
|
|
|
|
|
$M->set($i, $j, '#DIV/0!');
|
|
|
|
|
} else {
|
|
|
|
|
$M->set($i, $j, $this->A[$i][$j] / $value);
|
|
|
|
|
}
|
|
|
|
|
} else {
|
2010-08-30 11:58:47 +00:00
|
|
|
$M->set($i, $j, PHPExcel_Calculation_Functions::NaN());
|
2010-08-26 19:14:53 +00:00
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $M;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
}
|
|
|
|
|
} // function arrayRightDivide()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* arrayRightDivideEquals
|
|
|
|
|
*
|
|
|
|
|
* Element-by-element right division
|
|
|
|
|
* Aij = Aij / Bij
|
|
|
|
|
* @param mixed $B Matrix/Array
|
|
|
|
|
* @return Matrix Matrix Aij
|
|
|
|
|
*/
|
|
|
|
|
public function arrayRightDivideEquals() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
case 'object':
|
|
|
|
|
if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); }
|
|
|
|
|
break;
|
|
|
|
|
case 'array':
|
|
|
|
|
$M = new Matrix($args[0]);
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
$this->checkMatrixDimensions($M);
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$this->A[$i][$j] = $this->A[$i][$j] / $M->get($i, $j);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $M;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
}
|
|
|
|
|
} // function arrayRightDivideEquals()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* arrayLeftDivide
|
|
|
|
|
*
|
|
|
|
|
* Element-by-element Left division
|
|
|
|
|
* A / B
|
|
|
|
|
* @param Matrix $B Matrix B
|
|
|
|
|
* @return Matrix Division result
|
|
|
|
|
*/
|
|
|
|
|
public function arrayLeftDivide() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
case 'object':
|
|
|
|
|
if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); }
|
|
|
|
|
break;
|
|
|
|
|
case 'array':
|
|
|
|
|
$M = new Matrix($args[0]);
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
$this->checkMatrixDimensions($M);
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$M->set($i, $j, $M->get($i, $j) / $this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $M;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
}
|
|
|
|
|
} // function arrayLeftDivide()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* arrayLeftDivideEquals
|
|
|
|
|
*
|
|
|
|
|
* Element-by-element Left division
|
|
|
|
|
* Aij = Aij / Bij
|
|
|
|
|
* @param mixed $B Matrix/Array
|
|
|
|
|
* @return Matrix Matrix Aij
|
|
|
|
|
*/
|
|
|
|
|
public function arrayLeftDivideEquals() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
case 'object':
|
|
|
|
|
if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); }
|
|
|
|
|
break;
|
|
|
|
|
case 'array':
|
|
|
|
|
$M = new Matrix($args[0]);
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
$this->checkMatrixDimensions($M);
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$this->A[$i][$j] = $M->get($i, $j) / $this->A[$i][$j];
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $M;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
}
|
|
|
|
|
} // function arrayLeftDivideEquals()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* times
|
|
|
|
|
*
|
|
|
|
|
* Matrix multiplication
|
|
|
|
|
* @param mixed $n Matrix/Array/Scalar
|
|
|
|
|
* @return Matrix Product
|
|
|
|
|
*/
|
|
|
|
|
public function times() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
case 'object':
|
|
|
|
|
if ($args[0] instanceof Matrix) { $B = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); }
|
|
|
|
|
if ($this->n == $B->m) {
|
|
|
|
|
$C = new Matrix($this->m, $B->n);
|
|
|
|
|
for($j = 0; $j < $B->n; ++$j) {
|
|
|
|
|
for ($k = 0; $k < $this->n; ++$k) {
|
|
|
|
|
$Bcolj[$k] = $B->A[$k][$j];
|
|
|
|
|
}
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
$Arowi = $this->A[$i];
|
|
|
|
|
$s = 0;
|
|
|
|
|
for($k = 0; $k < $this->n; ++$k) {
|
|
|
|
|
$s += $Arowi[$k] * $Bcolj[$k];
|
|
|
|
|
}
|
|
|
|
|
$C->A[$i][$j] = $s;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $C;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(MatrixDimensionMismatch));
|
|
|
|
|
}
|
|
|
|
|
break;
|
|
|
|
|
case 'array':
|
|
|
|
|
$B = new Matrix($args[0]);
|
|
|
|
|
if ($this->n == $B->m) {
|
|
|
|
|
$C = new Matrix($this->m, $B->n);
|
|
|
|
|
for($i = 0; $i < $C->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $C->n; ++$j) {
|
|
|
|
|
$s = "0";
|
|
|
|
|
for($k = 0; $k < $C->n; ++$k) {
|
|
|
|
|
$s += $this->A[$i][$k] * $B->A[$k][$j];
|
|
|
|
|
}
|
|
|
|
|
$C->A[$i][$j] = $s;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $C;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(MatrixDimensionMismatch));
|
|
|
|
|
}
|
|
|
|
|
return $M;
|
|
|
|
|
break;
|
|
|
|
|
case 'integer':
|
|
|
|
|
$C = new Matrix($this->A);
|
|
|
|
|
for($i = 0; $i < $C->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $C->n; ++$j) {
|
|
|
|
|
$C->A[$i][$j] *= $args[0];
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $C;
|
|
|
|
|
break;
|
|
|
|
|
case 'double':
|
|
|
|
|
$C = new Matrix($this->m, $this->n);
|
|
|
|
|
for($i = 0; $i < $C->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $C->n; ++$j) {
|
|
|
|
|
$C->A[$i][$j] = $args[0] * $this->A[$i][$j];
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $C;
|
|
|
|
|
break;
|
|
|
|
|
case 'float':
|
|
|
|
|
$C = new Matrix($this->A);
|
|
|
|
|
for($i = 0; $i < $C->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $C->n; ++$j) {
|
|
|
|
|
$C->A[$i][$j] *= $args[0];
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $C;
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(PolymorphicArgumentException);
|
|
|
|
|
}
|
|
|
|
|
} // function times()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* power
|
|
|
|
|
*
|
|
|
|
|
* A = A ^ B
|
|
|
|
|
* @param mixed $B Matrix/Array
|
|
|
|
|
* @return Matrix Sum
|
|
|
|
|
*/
|
|
|
|
|
public function power() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
case 'object':
|
|
|
|
|
if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); }
|
|
|
|
|
break;
|
|
|
|
|
case 'array':
|
|
|
|
|
$M = new Matrix($args[0]);
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
$this->checkMatrixDimensions($M);
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
$validValues = True;
|
|
|
|
|
$value = $M->get($i, $j);
|
|
|
|
|
if ((is_string($this->A[$i][$j])) && (strlen($this->A[$i][$j]) > 0) && (!is_numeric($this->A[$i][$j]))) {
|
|
|
|
|
$this->A[$i][$j] = trim($this->A[$i][$j],'"');
|
|
|
|
|
$validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($this->A[$i][$j]);
|
|
|
|
|
}
|
|
|
|
|
if ((is_string($value)) && (strlen($value) > 0) && (!is_numeric($value))) {
|
|
|
|
|
$value = trim($value,'"');
|
|
|
|
|
$validValues &= PHPExcel_Shared_String::convertToNumberIfFraction($value);
|
|
|
|
|
}
|
|
|
|
|
if ($validValues) {
|
|
|
|
|
$this->A[$i][$j] = pow($this->A[$i][$j],$value);
|
|
|
|
|
} else {
|
|
|
|
|
$this->A[$i][$j] = PHPExcel_Calculation_Functions::NaN();
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $this;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
}
|
|
|
|
|
} // function power()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* concat
|
|
|
|
|
*
|
|
|
|
|
* A = A & B
|
|
|
|
|
* @param mixed $B Matrix/Array
|
|
|
|
|
* @return Matrix Sum
|
|
|
|
|
*/
|
|
|
|
|
public function concat() {
|
|
|
|
|
if (func_num_args() > 0) {
|
|
|
|
|
$args = func_get_args();
|
|
|
|
|
$match = implode(",", array_map('gettype', $args));
|
|
|
|
|
|
|
|
|
|
switch($match) {
|
|
|
|
|
case 'object':
|
|
|
|
|
if ($args[0] instanceof Matrix) { $M = $args[0]; } else { throw new Exception(JAMAError(ArgumentTypeException)); }
|
|
|
|
|
case 'array':
|
|
|
|
|
$M = new Matrix($args[0]);
|
|
|
|
|
break;
|
|
|
|
|
default:
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
break;
|
|
|
|
|
}
|
|
|
|
|
$this->checkMatrixDimensions($M);
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
// $this->A[$i][$j] = '"'.trim($this->A[$i][$j],'"').trim($M->get($i, $j),'"').'"';
|
|
|
|
|
$this->A[$i][$j] = trim($this->A[$i][$j],'"').trim($M->get($i, $j),'"');
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
return $this;
|
|
|
|
|
} else {
|
|
|
|
|
throw new Exception(JAMAError(PolymorphicArgumentException));
|
|
|
|
|
}
|
|
|
|
|
} // function concat()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* chol
|
|
|
|
|
*
|
|
|
|
|
* Cholesky decomposition
|
|
|
|
|
* @return Matrix Cholesky decomposition
|
|
|
|
|
*/
|
|
|
|
|
public function chol() {
|
|
|
|
|
return new CholeskyDecomposition($this);
|
|
|
|
|
} // function chol()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* lu
|
|
|
|
|
*
|
|
|
|
|
* LU decomposition
|
|
|
|
|
* @return Matrix LU decomposition
|
|
|
|
|
*/
|
|
|
|
|
public function lu() {
|
|
|
|
|
return new LUDecomposition($this);
|
|
|
|
|
} // function lu()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* qr
|
|
|
|
|
*
|
|
|
|
|
* QR decomposition
|
|
|
|
|
* @return Matrix QR decomposition
|
|
|
|
|
*/
|
|
|
|
|
public function qr() {
|
|
|
|
|
return new QRDecomposition($this);
|
|
|
|
|
} // function qr()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* eig
|
|
|
|
|
*
|
|
|
|
|
* Eigenvalue decomposition
|
|
|
|
|
* @return Matrix Eigenvalue decomposition
|
|
|
|
|
*/
|
|
|
|
|
public function eig() {
|
|
|
|
|
return new EigenvalueDecomposition($this);
|
|
|
|
|
} // function eig()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* svd
|
|
|
|
|
*
|
|
|
|
|
* Singular value decomposition
|
|
|
|
|
* @return Singular value decomposition
|
|
|
|
|
*/
|
|
|
|
|
public function svd() {
|
|
|
|
|
return new SingularValueDecomposition($this);
|
|
|
|
|
} // function svd()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* Solve A*X = B.
|
|
|
|
|
*
|
|
|
|
|
* @param Matrix $B Right hand side
|
|
|
|
|
* @return Matrix ... Solution if A is square, least squares solution otherwise
|
|
|
|
|
*/
|
|
|
|
|
public function solve($B) {
|
|
|
|
|
if ($this->m == $this->n) {
|
|
|
|
|
$LU = new LUDecomposition($this);
|
|
|
|
|
return $LU->solve($B);
|
|
|
|
|
} else {
|
|
|
|
|
$QR = new QRDecomposition($this);
|
|
|
|
|
return $QR->solve($B);
|
|
|
|
|
}
|
|
|
|
|
} // function solve()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* Matrix inverse or pseudoinverse.
|
|
|
|
|
*
|
|
|
|
|
* @return Matrix ... Inverse(A) if A is square, pseudoinverse otherwise.
|
|
|
|
|
*/
|
|
|
|
|
public function inverse() {
|
|
|
|
|
return $this->solve($this->identity($this->m, $this->m));
|
|
|
|
|
} // function inverse()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* det
|
|
|
|
|
*
|
|
|
|
|
* Calculate determinant
|
|
|
|
|
* @return float Determinant
|
|
|
|
|
*/
|
|
|
|
|
public function det() {
|
|
|
|
|
$L = new LUDecomposition($this);
|
|
|
|
|
return $L->det();
|
|
|
|
|
} // function det()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* Older debugging utility for backwards compatability.
|
|
|
|
|
*
|
|
|
|
|
* @return html version of matrix
|
|
|
|
|
*/
|
|
|
|
|
public function mprint($A, $format="%01.2f", $width=2) {
|
|
|
|
|
$m = count($A);
|
|
|
|
|
$n = count($A[0]);
|
|
|
|
|
$spacing = str_repeat(' ',$width);
|
|
|
|
|
|
|
|
|
|
for ($i = 0; $i < $m; ++$i) {
|
|
|
|
|
for ($j = 0; $j < $n; ++$j) {
|
|
|
|
|
$formatted = sprintf($format, $A[$i][$j]);
|
|
|
|
|
echo $formatted.$spacing;
|
|
|
|
|
}
|
|
|
|
|
echo "<br />";
|
|
|
|
|
}
|
|
|
|
|
} // function mprint()
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/**
|
|
|
|
|
* Debugging utility.
|
|
|
|
|
*
|
|
|
|
|
* @return Output HTML representation of matrix
|
|
|
|
|
*/
|
|
|
|
|
public function toHTML($width=2) {
|
|
|
|
|
print('<table style="background-color:#eee;">');
|
|
|
|
|
for($i = 0; $i < $this->m; ++$i) {
|
|
|
|
|
print('<tr>');
|
|
|
|
|
for($j = 0; $j < $this->n; ++$j) {
|
|
|
|
|
print('<td style="background-color:#fff;border:1px solid #000;padding:2px;text-align:center;vertical-align:middle;">' . $this->A[$i][$j] . '</td>');
|
|
|
|
|
}
|
|
|
|
|
print('</tr>');
|
|
|
|
|
}
|
|
|
|
|
print('</table>');
|
|
|
|
|
} // function toHTML()
|
|
|
|
|
|
|
|
|
|
} // class Matrix
|
