Numerical Integration

simpsons.go

package main

import (
	"fmt"
	"math"
)

// Simpson's Rule for numerical integration of f from a to b using n steps
// Port of python code: http://stackoverflow.com/questions/16001157/simpsons-rule-in-python
func simpsons(f func(float64) float64, a, b float64, n int) float64 {
	h := (b - a) / float64(n)
	k := 0.0
	x := a + h
	for i := 1; i < (n/2)+1; i++ {
		k += 4 * f(x)
		x += 2 * h
	}
	x = a + 2*h
	for i := 1; i < n/2; i++ {
		k += 2 * f(x)
		x += 2 * h
	}
	return (h / 3) * (f(a) + f(b) + k)
}

func main() {
	// Should be e-1 (~1.7183)
	fmt.Println(simpsons(math.Exp, 0.0, 1.0, 100))
}