This small library allows a computation of mean, variance and covariance without keeping track in memory of each individual sample. The library is intended for Arduino applications, however it may be used in any C++ program.

Based on Welford's online algorithm.

Check code commentaries for further information.

There is a class template, MeanAndVar, that should be instantiated to a signed numerical data type. Typical uses are (for example):

#include<MeanAndVarOnTheFly.h>

MeanAndVar<int> integerPopulation;
MeanAndVar<float> realNumberPopulation;

Check the examples folder for some usage cases, mostly filters for ADC readings.

You can reuse an existing object to compute a new mean and variance by calling reset(). Add samples to your population using add(), then retrieve the mean and variance with getMean(), getUnbiasedVariance() and getVariance(). Call getCount() to know the size of the statistical population.

There is a class template, CovarianceMatrix, that should be instantiated to int32_t, int64_t or double (no other types are allowed). Include the proper header in your sketch:

#include<CovarianceOnTheFly.h>

You must provide the count of statistical variables in the covariance matrix at the class constructor:

CovarianceMatrix<double> example(4); // Creates a 4x4 (symmetrical) covariance matrix for 4 statistical variables

Add samples to your population using add(), one argument for each statistical variable, in ascending order of index. For example:

CovarianceMatrix<double> example(4); // four statistical variables
example.add( 1.0, 30.3, 1.2, 30.9); // four arguments are mandatory (first,second,third,fourth).

Then you may retrieve the covariance for any pair of statistical variables with getCovariance(). Arguments to this function are 0-based indices of the involved statistical variables. For example:

CovarianceMatrix<double> example(4); // four statistical variables

auto cov1_2 = example.getCovariance(1,2) // covariance of second and third variables.
auto cov0_3 = example.getCovariance(0,3) // covariance of first and fourth variables.

You can reuse an existing object to compute a new covariance matrix by calling reset(). Call getCount() to know the size of the statistical population. Call getMean() to retrieve the mean of a single statistical variable.