Function bisectionMethod

util.go:1158–1183

func lookupMin(f func(float64) float64, xmin, xmax float64) float64 { const MaxIterations = 1000 min := math.Inf(1) for i := 0; i <= MaxIterations; i++ { t := float64(i) / float64(MaxIterations) x := xmin + t*(xmax-xmin) y := f(x) if y < min { min = y } } return min } func gradien

(f func(float64) float64, y, xmin, xmax float64)

// find value x for which f(x) = y in the interval x in [xmin, xmax] using the bisection method
func bisectionMethod(f func(float64) float64, y, xmin, xmax float64) float64 {
	const MaxIterations = 100
	const Tolerance = 0.001 // 0.1%

	n := 0
	toleranceX := math.Abs(xmax-xmin) * Tolerance
	toleranceY := math.Abs(f(xmax)-f(xmin)) * Tolerance

	var x float64
	for {
		x = (xmin + xmax) / 2.0
		if n >= MaxIterations {
			return x
		}

		dy := f(x) - y
		if math.Abs(dy) < toleranceY || math.Abs(xmax-xmin)/2.0 < toleranceX {
			return x
		} else if dy > 0.0 {
			xmax = x
		} else {
			xmin = x
		}
		n++
	}
}

// polynomialApprox returns a function y(x) that maps the parameter x [xmin,xmax] to the integral of fp. For a circle tmin and tmax would be 0 and 2PI respectively for example. It also returns the total length of the curve. Implemented using M. Walter, A. Fournier, Approximate Arc Length Parametrization, Anais do IX SIBGRAPHI, p. 143--150, 1996, see https://www.visgraf.impa.br/sibgrapi96/trabs/pdf/a14.pdf
//func polynomialApprox3(gaussLegendre gaussLegendreFunc, fp func(float64) float64, xmin, xmax float64) (func(float64) float64, float64) {