File Source for Matrix.php

<?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 {
$this->A[$i][$j] = PHPExcel_Calculation_Functions::NaN();
}
}
}
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

Source for file Matrix.php