Golden ratio

[sebasv]

Golden ratio search code and a performance improvement for the approx_fprime routine by skipping vector addition in the loop. cargo bench gave a 3-4 time speedup on 10-1000 dimensional testfunctions with random data.

Bench code:

    #[bench]
    fn speed_approx_fprime(bench: &mut Bencher) {
        let n = 1000;
        let mut rng = thread_rng();
        let rand = Normal::new(0.0, 1.0);
        let x = Array1::from_shape_fn(n, |_| rand.sample(&mut rng));
        let eps = Array1::from_shape_fn(n, |_| rand.sample(&mut rng)/1e8);
        let f = |x: ArrayView1<f64>| x.mapv(|xi| xi*xi).scalar_sum();

        bench.iter(|| approx_fprime(x.view(), &f, eps.view()));
    }

• [x] Ready for review

[to266]

I added a checkbox to ease the communication when a PR is ready to be merged / for review :)

[sebasv]

This PR is ready for review. I have added a method to search around an initial guess. If this method is used on a monotone function, it will return nan.

[sebasv]

In addition, feel free to add the bench to the repo as well

I quickly looked into this. cargo bench currently only works on nightly, so we could include a separate benches directory that should be compiled on nightly. Alternatively we could use Criterion, which would add a dev depencency. What are your thoughts?

[to266]

I'd say include the nightly benches. Currently we'd not run them on CI anyway, and each dev can switch to nightly for the benchmarks. These can be done in a separate PR as well, to not pollute this :)