public Dictionary<int, double> CrossCorrelation(Statistics s, bool normalize)
{
if (Length != s.Length)
return null;
double mean1 = Mean();
double mean2 = s.Mean();
double invdenominator = 1; // 1/denominator for normalization
int length = Length; // cache this - profiling shows a surprising cost for repeated access
var result = new Dictionary<int, double>(1 + (2 * length));
// Normalized cross-correlation = subtract the mean and divide by the standard deviation
if (normalize)
{
double sqsum1 = 0;
double sqsum2 = 0;
foreach (double v in _list)
sqsum1 += (v - mean1)*(v - mean1);
foreach (double v in s._list)
sqsum2 += (v - mean2)*(v - mean2);
// sigma_1 * sigma_2 * n
double denominator = Math.Sqrt(sqsum1*sqsum2); // find the demominator
if (denominator > 0)
{
invdenominator = 1.0/denominator; // for speed, we'll multiply by invdenominator rather than divide by denominator
}
else
{
// all datapoints are zero
for (int delay = -length; delay <= length; delay++)
{
result.Add(delay,0);
}
return result;
}
}
for (int delay = -length; delay <= length; delay++)
{
double sxy = 0;
int upper = Math.Min(length, length - delay); // i and i+delay must both be in range(0,length)
for (int i = Math.Max(0, -delay); i < upper; i++) // i and i+delay must both be in range(0,length)
{
if (normalize)
sxy += (_list[i] - mean1) * (s._list[i + delay] - mean2);
else
sxy += (_list[i]) * (s._list[i + delay]);
}
result.Add(delay, sxy * invdenominator);
}
return result;
}
/// <summary>
/// Calculates the variance for a set of numbers from a weighted mean.
/// See:
/// http://en.wikipedia.org/wiki/Weighted_mean
/// </summary>
/// <param name="weights">The weights</param>
/// <returns>Variance from weighted mean</returns>
public double Variance(Statistics weights)
{
if (_list.Length < 2)
return 0;
try
{
double s = 0;
for (int i = 0; i < _list.Length; i++)
s += weights._list[i] * Math.Pow(_list[i], 2);
return (s/weights.Mean() - _list.Length*Math.Pow(Mean(weights), 2)) / (_list.Length - 1);
}
catch (Exception)
{
return double.NaN;
}
}
/// <summary>
/// Calculates the covariance between two sets of numbers.
/// </summary>
/// <param name="s1">First set of numbers</param>
/// <param name="s2">Second set of numbers</param>
/// <returns></returns>
public static double Covariance(Statistics s1, Statistics s2)
{
try
{
if (s1.Length != s2.Length)
return double.NaN;
int len = s1.Length;
double sumMul = 0;
for (int i = 0; i < len; i++)
sumMul += (s1._list[i]*s2._list[i]);
return (sumMul - len*s1.Mean()*s2.Mean())/(len - 1);
}
catch (Exception)
{
return double.NaN;
}
}
public void QValueTest()
{
var statPvalues = new Statistics(STOREY_P_VALUES);
Assert.AreEqual(0.676341, statPvalues.PiZero(0.5), 1e-6);
Assert.AreEqual(0.671857, statPvalues.PiZero(), 1e-6);
// First try q values with 0.5 lambda from the paper
var qvalues = statPvalues.Qvalues(0.5);
Assert.AreEqual(STOREY_P_VALUES.Length, qvalues.Length);
Assert.AreEqual(STOREY_Q_VALUES.Length, qvalues.Length);
var deltas = new Statistics(qvalues.Select((v, i) => Math.Abs(v - STOREY_Q_VALUES[i])));
Assert.IsTrue(deltas.Mean() < 1.1e-5);
Assert.IsTrue(deltas.Max() < 4e-4);
// Then try it with automated lambda calculation
qvalues = statPvalues.Qvalues();
deltas = new Statistics(qvalues.Select((v, i) => Math.Abs(v - STOREY_Q_VALUES[i])));
Assert.IsTrue(deltas.Mean() < 2.6e-3);
Assert.IsTrue(deltas.Max() < 4.5e-3);
}
/// <summary>
/// Calculates the b term (y-intercept) of the linear
/// regression function (y = a*x + b) given the Y and X values.
/// </summary>
/// <param name="y">Y values</param>
/// <param name="x">X values</param>
/// <returns>The b coefficient of y = a*x + b</returns>
public static double BTerm2(Statistics y, Statistics x)
{
return y.Mean() - ATerm2(y, x)*x.Mean();
}
public SummaryValue(Statistics statistics)
{
Mean = statistics.Mean();
if (statistics.Length > 1)
{
Stdev = statistics.StdDev();
Cv = Stdev/Mean;
}
}
public void MeanWeightedTest()
{
Statistics s = new Statistics(80, 90);
Statistics weights = new Statistics(20, 30);
Assert.AreEqual(86, s.Mean(weights));
Assert.AreEqual(79.50, _interventionPercents.Mean(_interventionRequests), 0.01);
}
private string GetDotProductResultsText(TransitionGroupDocNode nodeGroup, int indexResult)
{
var replicateIndices = IndexOfReplicate(indexResult);
IEnumerable<float?> values;
switch (ExpectedVisible)
{
case AreaExpectedValue.library:
if (replicateIndices.IsEmpty)
{
values = new[] {nodeGroup.GetLibraryDotProduct(-1)};
}
else
{
values = replicateIndices.Select(nodeGroup.GetLibraryDotProduct);
}
break;
case AreaExpectedValue.isotope_dist:
if (replicateIndices.IsEmpty)
{
values = new[] {nodeGroup.GetIsotopeDotProduct(-1)};
}
else
{
values = replicateIndices.Select(nodeGroup.GetIsotopeDotProduct);
}
break;
default:
return null;
}
var statistics = new Statistics(values
.Select(value => value.HasValue ? (double?) value : null)
.Where(value=>value.HasValue)
.Cast<double>());
if (statistics.Length == 0)
{
return null;
}
return GetDotProductText((float) statistics.Mean());
}
private static PointPair CreatePointPair(int iGroup,
ICollection<double> listTimes,
IEnumerable<double> listStarts,
IEnumerable<double> listEnds,
IEnumerable<double> listFwhms,
ref double maxY,
ref double minY)
{
if (listTimes.Count == 0)
return RTPointPairMissing(iGroup);
var statTimes = new Statistics(listTimes);
var statStarts = new Statistics(listStarts);
var statEnds = new Statistics(listEnds);
var statFwhms = new Statistics(listFwhms);
double endY = statEnds.Mean();
double startY = statStarts.Mean();
var pointPair = HiLowMiddleErrorBarItem.MakePointPair(iGroup,
endY, startY, statTimes.Mean(), statFwhms.Mean());
maxY = Math.Max(maxY, endY);
minY = Math.Min(minY, startY);
return pointPair;
}
private static PointPair CreatePointPair(int iGroup, ICollection<double> listValues, ref double maxY)
{
if (listValues.Count == 0)
return PointPairMissing(iGroup);
var statValues = new Statistics(listValues);
PointPair pointPair;
if (Settings.Default.ShowPeptideCV)
{
double cvRatio = statValues.StdDev() / statValues.Mean();
if (!Settings.Default.PeakDecimalCv)
cvRatio *= 100;
pointPair = MeanErrorBarItem.MakePointPair(iGroup, cvRatio, 0);
}
else
pointPair = MeanErrorBarItem.MakePointPair(iGroup, statValues.Mean(), statValues.StdDev());
maxY = Math.Max(maxY, MeanErrorBarItem.GetYTotal(pointPair));
return pointPair;
}