The mode is the point in the kernel density estimate with the highest
frequency, i.e. the time which correlates with the highest peak.
If there are two or more modes (i.e. bimodal, trimodal, etc) then we
could take the average of these modes.
NOTE: If the kde estimate of the population is multi-modal (it has two
points with exactly the same value) then the mean mode is returned. This
is potentially misleading, but When benchmarking this should be a very
rare occurance.
/**
* Calculate and set the deviation from the mean time for each iteration. If
* the deviation is greater than the rejection threshold, then mark the iteration as
* rejected.
*/
public function computeStats()
{
$this->rejects = array();
if (0 === count($this->iterations)) {
return;
}
$times = array();
foreach ($this->iterations as $iteration) {
$times[] = $iteration->getResult()->getTime() / $iteration->getRevolutions();
}
// standard deviation for T Distribution
$this->stats['stdev'] = Statistics::stdev($times);
// mean of the times
$this->stats['mean'] = Statistics::mean($times);
// mode based on the kernel distribution function
$this->stats['mode'] = Statistics::kdeMode($times);
// relative standard error
$this->stats['rstdev'] = $this->stats['stdev'] / $this->stats['mean'] * 100;
// variance
$this->stats['variance'] = Statistics::variance($times);
// min and max
$this->stats['min'] = min($times);
$this->stats['max'] = max($times);
foreach ($this->iterations as $iteration) {
// deviation is the percentage different of the value from the mean of the set.
$deviation = 100 / $this->stats['mean'] * ($iteration->getResult()->getTime() / $iteration->getRevolutions() - $this->stats['mean']);
$iteration->setDeviation($deviation);
// the Z-Value represents the number of standard deviations this
// value is away from the mean.
$revTime = $iteration->getResult()->getTime() / $iteration->getRevolutions();
$zValue = $this->stats['stdev'] ? ($revTime - $this->stats['mean']) / $this->stats['stdev'] : 0;
$iteration->setZValue($zValue);
if (null !== $this->rejectionThreshold) {
if (abs($deviation) >= $this->rejectionThreshold) {
$this->rejects[] = $iteration;
}
}
}
$this->computed = true;
}
/**
* @dataProvider provideKdeMode
*/
public function testKdeMode($population, $space, $bandwidth, $expected)
{
$result = Statistics::kdeMode($population, $space, $bandwidth);
$this->assertEquals($expected, round($result, 2));
}
/**
* Return the mode time.
*
* @return float
*/
public function getModeTime()
{
return Statistics::kdeMode($this->getTimes());
}