/**
* 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);
}