Numeric algorithms and constants module
#include "diplib/accumulators.h"
dip::CovarianceAccumulator class

CovarianceAccumulator computes covariance and correlation of pairs of samples by accumulating the first two central moments and cross-moments.

Reference

Samples are added one pair at the time, using the Push method. Other members are used to retrieve the results. The accumulator uses a stable algorithm to prevent catastrophic cancellation.

The covariance matrix is formed by

| cov.VarianceX()   cov.Covariance() |
| cov.Covariance()  cov.VarianceY()  |

The Regression method returns the parameters to the least squares fit of the equation , where is the first sample in each pair and is the second (this is linear regression), is the intercept and is the slope. The Slope method computes only the slope component.

It is possible to accumulate samples in different objects (e.g. when processing with multiple threads), and add the accumulators together using the + operator.

Aliases

using RegressionResult = dip::RegressionParameters: Copying type for backward compatibility.

Functions

auto Correlation() const -> dip::dfloat: Estimator of correlation between the two variables
auto Covariance() const -> dip::dfloat: Unbiased estimator of population covariance
auto MeanX() const -> dip::dfloat: Unbiased estimator of population mean for first variable
auto MeanY() const -> dip::dfloat: Unbiased estimator of population mean for second variable
auto Number() const -> dip::uint: Number of samples
void Push(dip::dfloat x, dip::dfloat y): Add a pair of samples to the accumulator
auto Regression() const -> dip::CovarianceAccumulator::RegressionResult: Computes the slope and intercept of the regression line
void Reset(): Reset the accumulator, leaving it as if newly allocated.
auto Slope() const -> dip::dfloat: Computes the slope of the regression line
auto StandardDeviationX() const -> dip::dfloat: Estimator of population standard deviation for first variable (it is not possible to derive an unbiased estimator)
auto StandardDeviationY() const -> dip::dfloat: Estimator of population standard deviation for second variable (it is not possible to derive an unbiased estimator)
auto VarianceX() const -> dip::dfloat: Unbiased estimator of population variance for first variable
auto VarianceY() const -> dip::dfloat: Unbiased estimator of population variance for second variable