public function testSetOptions()
{
$options = array('max_iteration' => 20, 'divergent_skip' => false);
$o = Math_Numerical_RootFinding::factory('Bisection', $options);
$this->assertTrue($o instanceof Math_Numerical_RootFinding_Bisection);
$this->assertEquals($o->get('max_iteration'), $options['max_iteration']);
$this->assertFalse($o->get('divergent_skip'));
}
public function testCompute()
{
$o = Math_Numerical_RootFinding::factory('Secant');
$res = $o->compute(array(get_class($this), 'Fx'), 0, 1);
if (PEAR::isError($res)) {
$this->fail('Error has returned from compute(): ' . $res->getMessage());
}
$exact_root = 0.56714329;
$this->assertLessThanOrEqual($o->get('max_iteration'), $o->getIterationCount(), 'Invalid iteration count');
$this->assertLessThanOrEqual($o->get('err_tolerance'), $o->getEpsError());
$this->assertGreaterThanOrEqual($exact_root - $o->get('err_tolerance'), $o->getRoot());
$this->assertLessThanOrEqual($exact_root + $o->get('err_tolerance'), $o->getRoot());
}
* Math_Numerical_RootFinding class.
*/
require_once 'Math/Numerical/RootFinding.php';
/**
* f(x) callback function.
*
* @param float $x Variable value.
*
* @return float
*/
function gx($x)
{
return pow(M_E, -$x);
}
// Create new instance of Math_Numerical_RootFinding_Fixedpoint.
$mroot = Math_Numerical_RootFinding::factory('fixedpoint');
if (PEAR::isError($mroot)) {
die($mroot->toString());
}
// Calculate the root using Fixed Point's method.
$root = $mroot->compute('gx', 0);
if (PEAR::isError($root)) {
die($root->toString());
}
print "<h1>Root Finding::Fixed Point Method</h1>\n";
$mroot->infoCompute();
print "<h2>Case</h2>\n";
print "f(x) = e<sup>-x</sup> - x<br />\n";
print "g(x) = e<sup>-x</sup><br />\n";
print "<h3>Parameters</h3>\n";
print "<b>Initial guest</b> = 0<br />\n";
*/
require_once 'Math/Numerical/RootFinding.php';
/**
* f(x) callback function.
*
* @param float $x Variable value.
*
* @return float
* @ignore
*/
function fx($x)
{
return pow(M_E, -$x) - $x;
}
// Create new instance of Math_Numerical_RootFinding_Falseposition.
$mroot = Math_Numerical_RootFinding::factory('falseposition');
if (PEAR::isError($mroot)) {
die($mroot->toString());
}
// Calculate the root using False Position's method.
$root = $mroot->compute('fx', 0, 1);
if (PEAR::isError($root)) {
die($root->toString());
}
print "<h1>Root Finding::False Position Method</h1>\n";
$mroot->infoCompute();
print "<h2>Case</h2>\n";
print "f(x) = e<sup>-x</sup> - x<br />\n";
print "<h3>Parameters</h3>\n";
print "<b>First initial guest</b> = 0<br />\n";
print "<b>Second initial guest</b> = 1<br />\n";
return pow($x, 3) - 5 * pow($x, 2) + 7 * $x - 3;
}
/**
* f'(x) callback function.
*
* @param float $x Variable value.
*
* @return float
* @ignore
*/
function dx($x)
{
return 3 * pow($x, 2) - 10 * $x + 7;
}
// Create new instance of Math_Numerical_RootFinding_Ralstonrabinowitz.
$mroot = Math_Numerical_RootFinding::factory('RalstonRabinowitz');
if (PEAR::isError($mroot)) {
die($mroot->toString());
}
// Calculate the root using Ralston and Rabinowitz's method.
$root = $mroot->compute('fx', 'dx', 0, 4);
if (PEAR::isError($root)) {
die($root->toString());
}
print "<h1>Root Finding::Ralston and Rabinowitz Method</h1>\n";
$mroot->infoCompute();
print "<h2>Case</h2>\n";
print "f(x) = x<sup>3</sup> - 5x<sup>2</sup> + 7x - 3<br />\n";
print "f'(x) = 3x<sup>2</sup> - 10x + 7<br />\n";
print "<h3>Parameters</h3>\n";
print "<b>First initial guest</b> (<u>\$xR0</u>) = 0<br />\n";
*/
require_once 'Math/Numerical/RootFinding.php';
/**
* f(x) callback function.
*
* @param float $x Variable value.
*
* @return float
* @ignore
*/
function fx($x)
{
return pow(M_E, -$x) - $x;
}
// Create new instance of Math_Numerical_RootFinding_Bisection.
$mroot = Math_Numerical_RootFinding::factory('Bisection');
if (PEAR::isError($mroot)) {
die($mroot->toString());
}
// Calculate the root using Bisection's method.
$root = $mroot->compute('fx', 0, 1);
if (PEAR::isError($root)) {
die($root->toString());
}
print "<h1>Root Finding::Bisection Method</h1>\n";
$mroot->infoCompute();
print "<h2>Case</h2>\n";
print "f(x) = e<sup>-x</sup> - x<br />\n";
print "<h3>Parameters</h3>\n";
print "<b>Lower guest</b> = 0<br />\n";
print "<b>Upper guest</b> = 1<br />\n";
*/
require_once 'Math/Numerical/RootFinding.php';
/**
* f(x) callback function
*
* @param float $x Variable value.
*
* @return float
* @ignore
*/
function fx($x)
{
return pow(M_E, -$x) - $x;
}
// Create new instance of Math_Numerical_RootFinding_Secant.
$mroot = Math_Numerical_RootFinding::factory('Secant');
if (PEAR::isError($mroot)) {
die($mroot->toString());
}
// Calculate the root using Secant's method.
$root = $mroot->compute('fx', 0, 1);
if (PEAR::isError($root)) {
die($root->toString());
}
print "<h1>Root Finding::Secant Method</h1>\n";
$mroot->infoCompute();
print "<h2>Case</h2>\n";
print "<b>Case:</b><br />\n";
print "f(x) = e<sup>-x</sup> - x<br />\n";
print "<h3>Parameters</h3>\n";
print "<b>First initial guest</b> = 0<br />\n";
return pow(M_E, -$x) - $x;
}
/**
* f'(x) callback function.
*
* @param float $x Variable value.
*
* @return float
* @ignore
*/
function dx($x)
{
return -pow(M_E, -$x) - 1;
}
// Create new instance of Math_Numerical_RootFinding_Newtonraphson.
$mroot = Math_Numerical_RootFinding::factory('NewtonRaphson');
if (PEAR::isError($mroot)) {
die($mroot->toString());
}
// Calculate the root using Newton-Raphson's method.
$root = $mroot->compute('fx', 'dx', 0);
if (PEAR::isError($root)) {
die($root->toString());
}
print "<h1>Root Finding::Newton-Raphson Method</h1>\n";
$mroot->infoCompute();
print "<h2>Case</h2>\n";
print "f(x) = e<sup>-x</sup> - x<br />\n";
print "f'(x) = -e<sup>-x</sup> - x<br />\n";
print "<h3>Parameters</h3>\n";
print "<b>Initial guest</b> = 0<br />\n";
/**
* Estimate and return the roots of a high-degree Polynomial ( degree 5 or greater )
*
* This function uses Newton's method using the Math_Numerical_RootFinding
* PEAR package to estimate the real roots of high-degree Polynomials. If
* you already have estimates of where the roots might be, you can pass in
* an array of guesses. Otherwise, the method will try to calculate some
* good initial guesses for you.
*
* You must have the Math_Numerical_RootFinding package installed for this
* method to work!
*
* @see Math_PolynomialOp::getRoots(), Math_Numerical_RootFinding
*
* @access public
*
* @param object $m
* @param array $guesses
* @return array
*/
function getRootsHighDegree($p, $guesses = array())
{
require_once 'Math/Numerical/RootFinding.php';
if (!is_a($p, 'Math_Polynomial')) {
$p = new Math_Polynomial($p);
}
$arr = array();
// Array to store the roots
$fx = Math_PolynomialOp::createFunction($p);
$dx = Math_PolynomialOp::createFunction(Math_PolynomialOp::getDerivative($p));
$newton = Math_Numerical_RootFinding::factory('Newtonraphson');
if (PEAR::isError($newton)) {
return PEAR::raiseError('Math_Numeric_RootFinding could not be instantiated, message was: ' . $newton->toString());
}
// We need to find some initial guesses for finding the roots
if (count($guesses)) {
// User has provided guesses for us
foreach ($guesses as $guess) {
$arr[] = $newton->compute($fx, $dx, $guess);
}
} else {
// We need to find the guesses ourselves... yuck.
$criticals = Math_PolynomialOp::getCriticalPoints($p);
$arr[] = $newton->compute($fx, $dx, $criticals[0] - 0.1);
$count = count($criticals);
for ($i = 1; $i < $count; $i++) {
$arr[] = $newton->compute($fx, $dx, ($criticals[$i - 1] + $criticals[$i]) / 2);
}
$arr[] = $newton->compute($fx, $dx, end($criticals) + 0.1);
$arr = array_unique($arr);
}
return Math_PolynomialOp::_round($arr);
}
