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 // Copyright ©2017 The Gonum Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package fd import ( "math" "runtime" "sync" ) // Derivative estimates the derivative of the function f at the given location. // The finite difference formula, the step size, and other options are // specified by settings. If settings is nil, the first derivative will be // estimated using the Forward formula and a default step size. func Derivative(f func(float64) float64, x float64, settings *Settings) float64 { // Default settings. formula := Forward step := formula.Step var originValue float64 var originKnown, concurrent bool // Use user settings if provided. if settings != nil { if !settings.Formula.isZero() { formula = settings.Formula step = formula.Step checkFormula(formula) } if settings.Step != 0 { step = settings.Step } originKnown = settings.OriginKnown originValue = settings.OriginValue concurrent = settings.Concurrent } var deriv float64 if !concurrent || runtime.GOMAXPROCS(0) == 1 { for _, pt := range formula.Stencil { if originKnown && pt.Loc == 0 { deriv += pt.Coeff * originValue continue } deriv += pt.Coeff * f(x+step*pt.Loc) } return deriv / math.Pow(step, float64(formula.Derivative)) } wg := &sync.WaitGroup{} mux := &sync.Mutex{} for _, pt := range formula.Stencil { if originKnown && pt.Loc == 0 { mux.Lock() deriv += pt.Coeff * originValue mux.Unlock() continue } wg.Add(1) go func(pt Point) { defer wg.Done() fofx := f(x + step*pt.Loc) mux.Lock() defer mux.Unlock() deriv += pt.Coeff * fofx }(pt) } wg.Wait() return deriv / math.Pow(step, float64(formula.Derivative)) }