util.go

package evalue

import "math"

// findBracketMono finds a bracket interval [a, b] where f(a)f(b) < 0.
// f must be a monotonically increasing function.
func findBracketMono(f func(float64) float64, guess float64) (float64, float64) {
	// Make sure initial guess has the same sign as the root.
	f0 := f(0)
	if (guess < 0 && f0 < 0) || (guess > 0 && f0 > 0) {
		guess *= -1
	}

	// r is the rate in which we adjust the interval.
	var r float64
	a, fa := guess, f(guess)
	if (a > 0) == (fa < 0) {
		r = 2
	} else {
		r = 1. / 2
	}

	b := a * r
	fb := f(b)
	for range 200 {
		if math.Signbit(fa) != math.Signbit(fb) || fa == 0 || fb == 0 {
			break
		}
		a, fa = b, fb
		b *= r
		fb = f(b)
	}

	return a, b
}