function pleac_Multiplying_Matrices()
{
// PHP offers no native support for matrices. However, a 'Math_Matrix' class
// is available for download from PEAR: [http://pear.php.net/package/Math_Matrix].
// Note the following 'include' directives are required:
//
// include_once('Math/Matrix.php');
$a = new Math_Matrix(array(array(3, 2, 3), array(5, 9, 8)));
$b = new Math_Matrix(array(array(4, 7), array(9, 3), array(8, 1)));
echo $a->toString() . "\n";
echo $b->toString() . "\n";
// NOTE: When I installed this package I had to rename the 'clone' method else
// it would not load, so I chose to rename it to 'clone_', and this usage is
// shown below. This bug may well be fixed by the time you obtain this package
$c = $a->clone_();
$c->multiply($b);
echo $c->toString() . "\n";
}
echo "\nA\n" . $a->toString('%8.4f') . "\n";
echo "B " . $b->toString() . "\n";
echo "Solution " . $x->toString() . "\n";
echo "\nSolving with error correction\n";
$x = Math_Matrix::solveEC($a, $b);
echo "EC Solution " . $x->toString() . "\n";
$Adata = array(array(1, 1, 2), array(2, 3, 4));
$Bdata = array(array(-1, 3), array(-3, 4), array(-5, 2));
$A = new Math_Matrix($Adata);
$A1 = $A->clone();
$B = new Math_Matrix($Bdata);
$B1 = $B->clone();
$A1->multiply($B1);
$B->multiply($A);
echo $A1->toString() . "\n";
echo $B->toString() . "\n";
/*
echo "\n";
$data = array (
array(1,0,1),
array(1,1,1),
array(1,1,0),
);
$m = new Math_Matrix($data);
echo $m->toString()."\n";
$det = $m->determinant();
echo "Determinant = $det\n";
echo "Euclidean Norm = ".$m->norm()."\n";
echo "Normalized Determinant = ".$m->normalizedDeterminant()."\n";
echo "\n";
public function create($array)
{
// test conditions
// TODO: test min/max
// test area
if ($this->minArea * ($this->minWidth * $this->minHeight) >= $this->maxArea * ($this->maxWidth * $this->maxHeight)) {
throw new Exception('Min/max area overlap, please adjust settings');
}
// create matrix
$this->matrix = Math_Matrix::makeMatrix($this->ysize, $this->xsize, -1);
// variable to define whether filling is active
$fill = false;
// return array
$positions = array();
foreach ($array as $k => $v) {
// get next empty space
$pos = $this->searchNextPosition();
// fill horizontal?
if ($pos[1] == 0) {
// are we at the top?
if ($pos[0] != 0) {
// are we not at [0,0] ?
if (rand(1, $this->fillTopProbability) == 1) {
// roll a dice for top position fill
// calculate fill position
$fill = $this->searchXBoundFrom($pos[0]) + $this->minWidth;
if ($this->debug) {
echo 'fill from top x=' . $fill . '<br/>';
}
} else {
$fill = false;
}
}
} elseif ($fill === false) {
// fill from halfway?
if (rand(1, $this->fillHalfwayProbability) == 1) {
// roll a dice halfway position fill
// calculate fill position
$fill = $this->searchXBoundFrom($pos[0]) + $this->minWidth;
if ($this->debug) {
echo 'fill x=' . $fill . '<br/>';
}
}
}
// get dimensions
$rand = $this->randomDimensions();
$randWidth = $rand['width'];
$randHeight = $rand['height'];
if ($fill !== false) {
$randWidth = $fill - $pos[0];
}
// height available?
$heightAvailable = $this->availableHeightFrom($pos[0], $pos[1]);
if ($heightAvailable <= $this->minHeight) {
$height = $heightAvailable;
} else {
if ($heightAvailable <= $this->minHeight * 2) {
$height = $heightAvailable;
} else {
$height = min($randHeight, $heightAvailable - $this->minHeight);
}
}
// random width
$width = $randWidth;
// debug
if ($this->debug) {
echo $k . ': ' . $height . '(' . $heightAvailable . ')x' . $width . ' @ [' . $pos[0] . ', ' . $pos[1] . ']<br/>';
}
// set ids
for ($x = $pos[0]; $x < $width + $pos[0]; $x++) {
for ($y = $pos[1]; $y < $height + $pos[1]; $y++) {
$this->matrix->setElement($y, $x, $k);
}
}
// set item position
$positions[$k] = array('x' => $pos[0] * $this->multiplier, 'y' => $pos[1] * $this->multiplier, 'w' => $width * $this->multiplier, 'h' => $height * $this->multiplier);
}
// debug: print matrix
if ($this->debug) {
echo '<pre>' . $this->matrix->toString('%3.0f') . '</pre>';
die;
}
// return array
return $positions;
}
function testMakeHankel()
{
$data = array(array(1, 2, 3, 3), array(2, 3, 3, 5), array(3, 3, 5, 7));
$c = array(1, 2, 3);
$r = array(1, 3, 5, 7);
$res = new Math_Matrix($data);
$hankel = Math_Matrix::makeHankel($c, $r);
$this->assertEquals($res->toString(), $hankel->toString());
}
function testMultiply()
{
$Adata = array(array(1, 1, 2), array(2, 3, 4));
$Bdata = array(array(-1, 3), array(-3, 4), array(-5, 2));
$ABdata = array(array(-14, 11), array(-31, 26));
$BAdata = array(array(5, 8, 10), array(5, 9, 10), array(-1, 1, -2));
$A = new Math_Matrix($Adata);
$A1 = $A->clone();
$B = new Math_Matrix($Bdata);
$B1 = $B->clone();
$A1->multiply($B);
$B1->multiply($A);
$AB = new Math_Matrix($ABdata);
$BA = new Math_Matrix($BAdata);
$this->assertEquals($A1->toString(), $AB->toString());
$this->assertEquals($B1->toString(), $BA->toString());
}
<?php
/**
* Example of using the Math_Matrix class
* @author Jesus M. Castagnetto
*
* $Id: ex_math_matrix.php,v 1.1 2003/05/16 22:28:18 jmcastagnetto Exp $
*/
require_once 'Math/Matrix.php';
$data = array(array(1.0, 2.0, 3.0, 4.0), array(5.0, 6.0, 7.0, 8.0), array(1.0, 4.0, 5.0, 7.0), array(2.0, 3.0, -3.0, 4.0));
$m = new Math_Matrix($data);
//print_r($m);
echo $m->toString() . "\n";
$det = $m->determinant();
echo "Determinant = {$det}\n";
echo "Trace = " . $m->trace() . "\n";
echo "Euclidean Norm = " . $m->norm() . "\n";
echo "Normalized Determinant = " . $m->normalizedDeterminant() . "\n";
echo "\nSubmatrix(1,1,2,2)\n";
$n = $m->getSubMatrix(1, 1, 2, 2);
echo $n->toString() . "\n";
$det = $n->determinant();
echo "Determinant = {$det}\n";
echo "Euclidean Norm = " . $n->norm() . "\n";
echo "Normalized Determinant = " . $n->normalizedDeterminant() . "\n";
echo "\nWriting original matrix\n";
$e = Math_Matrix::writeToFile($m, 'writetest.mat', 'csv');
echo "... Reading from file\n";
$p = Math_Matrix::readFromFile('writetest.mat', 'csv');
echo $p->toString() . "\n";
$det = $p->determinant();
