/// <summary>
/// Calculates a Variance of a sample (set of numbers).
/// </summary>
/// <remarks>
/// https://en.wikipedia.org/wiki/Variance
/// Variance measures how far the set of numbers are spread out.
/// Variance == 0 indicates that all numbers are identical.
/// Variance is always non-negative.
/// Variance close to 0 indicates that the numbers tend to be very close to the mean (and hence to each other).
/// </remarks>
/// <param name="samples">array of samples</param>
/// <param name="mode">calculation mode (biased or unbiased)</param>
/// <param name="algorithm">algorithm to use for calculations</param>
public static VarianceInfo Calculate(IReadOnlyList<double> samples, VarianceMode mode, VarianceAlgorithm algorithm)
{
if (mode == VarianceMode.Biased && samples.Count <= 0)
return VarianceInfo.NaN;
else if (mode == VarianceMode.Unbiased && samples.Count <= 1)
return VarianceInfo.NaN;
//# https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
var partial_variance_info = new VarianceInfo();
if (algorithm == VarianceAlgorithm.Online)
partial_variance_info = M1M2_OnlineAlgorithm(samples);
else if (algorithm == VarianceAlgorithm.SumsAndSumSquares)
partial_variance_info = M1M2_SumsAndSquares(samples);
else if (algorithm == VarianceAlgorithm.SumsAndSumSquaresWithShift)
partial_variance_info = M1M2_SumsAndSumSquaresWithShift(samples);
else
throw new NotSupportedException($"{algorithm} is not supported");
if (mode == VarianceMode.Biased)
partial_variance_info.M2Denominator = samples.Count;
else
partial_variance_info.M2Denominator = (samples.Count - 1);
return partial_variance_info;
}
static IObservable<VarianceInfo> M1M2_SumsAndSquares(IObservable<double> samples)
{
// sum of samples
var sum_x = 0.0;
// sum of sample squares
var sum_x2 = 0.0;
var m1m2 = new VarianceInfo();
return samples.Select(x =>
{
sum_x += x;
sum_x2 += x * x;
m1m2.Count++;
m1m2.M1 = sum_x / m1m2.Count;
m1m2.M2 = ((sum_x * sum_x) / m1m2.Count);
return m1m2;
});
}
/// <summary>
/// Calculates a Variance of a sample (set of numbers).
/// </summary>
/// <remarks>
/// https://en.wikipedia.org/wiki/Variance
/// Variance measures how far the set of numbers are spread out.
/// Variance == 0 indicates that all numbers are identical.
/// Variance is always non-negative.
/// Variance close to 0 indicates that the numbers tend to be very close to the mean (and hence to each other).
/// </remarks>
/// <param name="samples">observable samples</param>
/// <param name="mode">calculation mode (biased or unbiased)</param>
/// <param name="algorithm">algorithm to use for calculations</param>
public static IObservable<VarianceInfo> Calculate(IObservable<double> samples, VarianceMode mode, VarianceAlgorithm algorithm)
{
return Observable.Create<VarianceInfo>(o =>
{
var count = 0;
VarianceInfo m1m2 = new VarianceInfo();
var M2_Observable = (IObservable<VarianceInfo>)null;
if (algorithm == VarianceAlgorithm.Online)
M2_Observable = M1M2_OnlineAlgorithm(samples);
else
throw new NotSupportedException($"{algorithm} is not supported");
M2_Observable.Subscribe(M2 =>
{
count++;
if (mode == VarianceMode.Biased && count <= 0)
{
m1m2 = VarianceInfo.NaN;
o.OnNext(m1m2);
return;
}
else if (mode == VarianceMode.Unbiased && count <= 1)
{
m1m2 = VarianceInfo.NaN;
o.OnNext(m1m2);
return;
}
if (mode == VarianceMode.Biased)
m1m2.M2Denominator = count;
else
m1m2.M2Denominator = (count - 1);
o.OnNext(m1m2);
});
return Disposable.Empty;
});
}
static IObservable<VarianceInfo> M1M2_OnlineAlgorithm(IObservable<double> samples)
{
var m1m2 = new VarianceInfo();
return samples.Select(x =>
{
m1m2.Count++;
var delta = x - m1m2.M1;
m1m2.M1 += delta / m1m2.Count;
m1m2.M2 += delta * (x - m1m2.M1);
return m1m2;
});
}
static VarianceInfo()
{
NaN = new VarianceInfo(0, double.NaN, double.NaN, double.NaN);
}