Fix \phi_0 and d\phi_0 values

[anriseth]

The values of ϕ_0 and dϕ_0 are ϕ(0), dϕ(0), not ϕ(\alpha_0)).

It is a bit confusing to use α_0 as the initial guess, because it means that we think ϕ_0 refers to the value at the initial guess. Maybe we should change all α0 / α_0's to αinitial?

[codecov]

Codecov Report

Merging #118 into master will decrease coverage by 0.06%.
The diff coverage is 50%.

@@            Coverage Diff             @@
##           master     #118      +/-   ##
==========================================
- Coverage   60.68%   60.62%   -0.07%     
==========================================
  Files           8        8              
  Lines         646      645       -1     
==========================================
- Hits          392      391       -1     
  Misses        254      254

Impacted Files	Coverage Δ
src/backtracking.jl	81.57% <0%> (ø)	⬆️
src/morethuente.jl	55.08% <50%> (+0.05%)	⬆️
src/hagerzhang.jl	52.42% <75%> (-0.24%)	⬇️

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[pkofod]

Hm, I don't think I agree with this change. phi_0 zero is meant to be the initial phi (and dphi as well), so those calculations were just meant to calculate the values if they weren't provided already. Or am I missing something?

[anriseth]

No, phi_0 and dphi_0 that the line stretch algorithms use are the values of phi at alpha=0. That is what Optim passes to the line searches.

[pkofod]

Ah, right, sorry, it's the numbers used to check armijo/wolfe/.../conditions ... good catch :)