Discrepancy Test

August 1, 2019 · View on GitHub

Source Code: /src/families/_1d/tests/discrepancy/

Discrepancy is a real number given to a sampling sequence that describes how the points clump together or leave holes.

Discrepancy is calculated by finding the region with the largest difference between actual density of points and expected density if the points were evenly spaced. The region with the largest difference may be either too dense, or too sparse. That difference between actual and expected density in that region is the discrepancy.

In higher dimensions, the same process is followed with rectangular regions. Sometimes this process will be simplified to just considering regions where one point is at the origin, which is an approximation of discrepancy calculated more quickly, called "Star Discrepancy", which is written as D*.

CalculateDiscrepancy() calculates discrepancy assuming that 0 and 1 do not wrap around and are "hard walls".

The right most empty section that it checks for discrepancy is between the right most point and 1.0.

For a while, I had a torroidal (wrap around) discrepancy calculation test, to analyze sequences for times when you are sampling something that wraps around, like angles on a circle. It ended up being fairly rare that the "wrap around region" was the region with the largest discrepancy so i removed the test, since the graph looked virtually identical to the non wrap around version.