go-discrepancy
Go package for approximating star discrepancy, which can be expressed as,
where Q is a rectangular solid in [0, 1]^s, and we have N points (x_1, ..., x_N) in the s-dimensional unit cube.
This code is directly translated from John Burkardt's implementation of "Eric Thiemard, An Algorithm to Compute Bounds for the Star Discrepancy, Journal of Complexity, Volume 17, pages 850-880, 2001."
John Burkardt's implementation: https://people.sc.fsu.edu/~jburkardt/cpp_src/star_discrepancy/star_discrepancy.html
Installation
go get github.com/ArmanMaesumi/go-discrepancy
Usage
package main
import (
"fmt"
"github.com/ArmanMaesumi/go-discrepancy/star"
)
func main() {
epsilon := 0.5
points := [][]float64 {
{0.1, 0.3},
{0.2, 0.5},
}
/**
Parameters:
ep - 0.0 < epsilon < 1.0 (resolution of approximation)
pts - matrix of n points in [0, 1]^s
numerator - optional balance numerator, use 1 as default
denominator - optional balance denominator, use 2 as default
0.0 < numerator / denominator < 1.0
returns: float64 (lower bound), float64 (upper bound)
**/
lower, upper := star.StarDiscrepancy(epsilon, points, 1, 2)
fmt.Println(lower)
fmt.Println(upper)
}
Output:
0.9
1
Benchmarks
Random point sets with N=100 are generated with S={2,5,10}. See star/discrepancy_test.go for more details
BenchmarkStarDiscrepancyDimensions2-16 146623 8585 ns/op
BenchmarkStarDiscrepancyDimensions5-16 5468 213480 ns/op
BenchmarkStarDiscrepancyDimensions10-16 54 19662859 ns/op