Task #1892: error values on slope

CEP/DP3/AOFlagger/include/AOFlagger/quality/loghistogram.h

@@ -263,6 +263,34 @@ class LogHistogram : public Serializable
 			return (double) (sumOffset/(long double) n);
 		}
 		
+		double NormalizedSlopeStdDev(double startAmplitude, double endAmplitude, double slope, double offset) const
+		{
+			long double sqErrorSum = 0.0, xsqErrorSum = 0.0, xSum = 0.0;
+			unsigned long n = 0;
+			// determine the 'average' x
+			for(const_iterator i=begin();i!=end();++i)
+			{
+				if(i.value() >= startAmplitude && i.value() < endAmplitude)
+				{
+					xSum += log10(i.value());
+					++n;
+				}
+			}
+			const long double avgX = xSum / n;
+			for(const_iterator i=begin();i!=end();++i)
+			{
+				if(i.value() >= startAmplitude && i.value() < endAmplitude)
+				{
+					long double y = log10(i.normalizedCount());
+					long double x = log10(i.value());
+					long double ySlope = x*slope + offset;
+					sqErrorSum += (y-ySlope)*(y-ySlope);
+					xsqErrorSum += (x - avgX)*(x - avgX);
+				}
+			}
+			return (double) sqrtl(sqErrorSum/(xsqErrorSum * (long double) (n-2)));
+		}
+		
 		double PowerLawUpperLimit(double constrainingAmplitude, double exponent, double factor) const
 		{
 			const double count = NormalizedCountAbove(constrainingAmplitude);

CEP/DP3/AOFlagger/src/gui/quality/histogrampage.cpp

@@ -453,11 +453,13 @@ void HistogramPage::addSlopeText(std::stringstream &str, const LogHistogram &his
 	}
 	double rfiRatio = atof(_slopeRFIRatio.get_text().c_str());
 
-	double slope = histogram.NormalizedSlope(minRange, maxRange);
-	double offset = histogram.NormalizedSlopeOffset(minRange, maxRange, slope);
-	double upperLimit = histogram.PowerLawUpperLimit(minRange, slope, pow10(offset));
-	double lowerLimit = histogram.PowerLawLowerLimit(minRange, slope, pow10(offset), rfiRatio);
-	str << '\n' << slope << '[' << log10(lowerLimit) << ';' << log10(upperLimit) << ']';
+	const double
+		slope = histogram.NormalizedSlope(minRange, maxRange),
+		offset = histogram.NormalizedSlopeOffset(minRange, maxRange, slope),
+		error = histogram.NormalizedSlopeStdDev(minRange, maxRange, slope, offset),
+		upperLimit = histogram.PowerLawUpperLimit(minRange, slope, pow10(offset)),
+		lowerLimit = histogram.PowerLawLowerLimit(minRange, slope, pow10(offset), rfiRatio);
+	str << '\n' << slope << "±" << error << '[' << log10(lowerLimit) << ';' << log10(upperLimit) << ']';
 }
 
 void HistogramPage::updateDataWindow()