A tiny library for linear interpolation. O(log(N)) per evaluation for N control points (and O(1) in a special case).
import "github.com/sgreben/piecewiselinear"go get -u "github.com/sgreben/piecewiselinear"import "github.com/sgreben/piecewiselinear"
func main() {
f := piecewiselinear.Function{Y:[]float64{0,1,0}} // range: "hat" function
f.X = []float64{0, 0.5, 1} // domain: equidistant points along X axis
fmt.Println(
f.At(0), // f.At(x) evaluates f at x
f.At(0.25),
f.At(0.5),
f.At(0.75),
f.At(1.0),
f.At(123.0), // outside its domain X the function is constant 0
f.At(-123.0), //
f.Area(),
f.AreaUpTo(0.5),
)
// Output:
// 0 0.5 1 0.5 0 0 0 0.5 0.25
}If the control points are uniformly spaced, piecewiselinear.FunctionUniform is much faster (no search required):
import "github.com/sgreben/piecewiselinear"
func main() {
f := piecewiselinear.FunctionUniform{Y: []float64{0, 1, 0}} // range: "hat" function
f.Xmin, f.Xmax = 0, 1 // domain: equidistant points along X axis
fmt.Println(
f.At(0), // f.At(x) evaluates f at x
f.At(0.25),
f.At(0.5),
f.At(0.75),
f.At(1.0),
f.At(123.0), // outside its domain X the function is constant 0
f.At(-123.0), //
f.Area(),
f.AreaUpTo(0.5),
)
// Output:
// 0 0.5 1 0.5 0 0 0 0.5 0.25
}On an Apple M1 Pro:
- 6ns per evaluation (
.At(x)) for 10 control points - 320ns per evaluation for 10 million control points.
and, for FunctionUniform, 2ns per evaluation regardless of the number of control points.
goos: darwin
goarch: arm64
pkg: github.com/sgreben/piecewiselinear
BenchmarkAt4-10 230890022 5.499 ns/op 0 B/op 0 allocs/op
BenchmarkAt8-10 199668106 6.084 ns/op 0 B/op 0 allocs/op
BenchmarkAt10-10 192352903 6.206 ns/op 0 B/op 0 allocs/op
BenchmarkAt100-10 138742411 8.613 ns/op 0 B/op 0 allocs/op
BenchmarkAt1k-10 46360660 25.50 ns/op 0 B/op 0 allocs/op
BenchmarkAt10k-10 16649996 70.02 ns/op 0 B/op 0 allocs/op
BenchmarkAt100k-10 11696936 100.4 ns/op 0 B/op 0 allocs/op
BenchmarkAt1M-10 8512652 140.6 ns/op 0 B/op 0 allocs/op
BenchmarkAt10M-10 3769648 320.4 ns/op 0 B/op 0 allocs/op
BenchmarkUniformAt10M-10 571224222 2.185 ns/op 0 B/op 0 allocs/op