fit: consider exposing Grad

[sbinet]

right now, the fit.Func1D and fit.FuncND automatically compute the gradient of the provided function to fit, using gonum/diff/fd (a package that applies numerical differentiation to approximate the derivatives).

we should probably consider exposing the Grad field, making it optional, so users could provide an implementation - perhaps generated with gonum/autodiff. (we should probably provide such an example.)

[jordanrule]

I took a crack at this and ended up with this:

// FuncSettings describes the methods of derivation for a function
type FuncSettings struct {
    Grad func(fct func(ps []float64) float64) func(grad []float64, ps []float64)
    Hess func(fct func(ps []float64) float64) func(hess *mat.SymDense, x []float64)
}

func (settings *FuncSettings) init() {
    if settings.Grad == nil {
        settings.Grad = func(fct func(ps []float64) float64) func(grad []float64, ps []float64) {
            return func(grad []float64, ps []float64) {
                fd.Gradient(grad, fct, ps, nil)
            }
        }
    }

    if settings.Hess == nil {
        settings.Hess = func(fct func(ps []float64) float64) func(hess *mat.SymDense, x []float64) {
            return func(hess *mat.SymDense, x []float64) {
                fd.Hessian(hess, fct, x, nil)
            }
        }
    }
}

Which was the cleanest way I could come up with to expose the cost function external to the constructor of Func*D. Then I went to look for other implementation of gradient computation, and was surprised to not find anything in pure Go other than your gonum/autodiff (I am new to scientific computing in golang). This looks like a good implementation, but would likely require writing the cost function out to a temporary file, which doesn't seem ideal for reliability.

In conclusion, I don't think anything I wrote is an improvement on what exists in the codebase, and am going to try to pick up a different first-issue.

[sbinet]

hi @jordanrule and thanks for your interest in Go-HEP.

when I filed that issue I was probably thinking of simply s/grad/Grad/ (the same for hess) and modifying Func1D.init to set Grad with fd.Gradient if it was nil.

one could then provide a simple example with a well-known Grad function.

w.r.t. autofd, I guess one could just put the result of the autofd command in a dedicated file, adding the exact command used to generate it (and/or add it as a //go:generate directive).