/** Calculates Sn as estimator of scale for given vector
*
* This method implements a naive calculation of Sn, as defined by Rousseeuw
*and Croux (http://dx.doi.org/10.2307%2F2291267).
* In contrast to standard deviation, this is more robust towards outliers.
*
* @param begin :: Beginning of vector.
* @param end :: End of vector.
* @return Sn of supplied data.
*/
double PoldiPeakSearch::getSn(MantidVec::const_iterator begin,
MantidVec::const_iterator end) const {
size_t numberOfPoints = std::distance(begin, end);
MantidVec absoluteDifferenceMedians(numberOfPoints);
PARALLEL_FOR_NO_WSP_CHECK()
for (int i = 0; i < static_cast<int>(numberOfPoints); ++i) {
double currentValue = *(begin + i);
MantidVec temp;
temp.reserve(numberOfPoints - 1);
for (int j = 0; j < static_cast<int>(numberOfPoints); ++j) {
if (j != i) {
temp.push_back(fabs(*(begin + j) - currentValue));
}
}
std::sort(temp.begin(), temp.end());
absoluteDifferenceMedians[i] =
getMedianFromSortedVector(temp.begin(), temp.end());
}
std::sort(absoluteDifferenceMedians.begin(), absoluteDifferenceMedians.end());
return 1.1926 * getMedianFromSortedVector(absoluteDifferenceMedians.begin(),
absoluteDifferenceMedians.end());
}
/** Computes a background estimation with an error
*
* This method computes an estimate of the average background along with its deviation. Since the background does not
* follow a normal distribution and may contain outliers, instead of computing the average and standard deviation,
* the median is used as location estimator and Sn is used as scale estimator. For details regarding the latter
* refer to PoldiPeakSearch::getSn.
*
* @param peakPositions :: Peak positions.
* @param correlationCounts :: Data from which the peak positions were extracted.
* @return Background estimation with error.
*/
UncertainValue PoldiPeakSearch::getBackgroundWithSigma(std::list<MantidVec::const_iterator> peakPositions, const MantidVec &correlationCounts) const
{
MantidVec background = getBackground(peakPositions, correlationCounts);
/* Instead of using Mean and Standard deviation, which are appropriate
* for data originating from a normal distribution (which is not the case
* for background of POLDI correlation spectra), the more robust measures
* Median and Sn are used.
*/
std::sort(background.begin(), background.end());
double meanBackground = getMedianFromSortedVector(background.begin(), background.end());
double sigmaBackground = getSn(background.begin(), background.end());
return UncertainValue(meanBackground, sigmaBackground);
}
