Fix files format

[datejada]

Pull request details

Describe the changes made in this pull request

Fixing files format according to the pre-commit hooks

List of related issues or pull requests

Closes #1

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[datejada]

@abelsiqueira would you mind double-checking that all is in place for this package? I think after fixing the formats, the basic set up is there, but just to double-check. Thanks!

[abelsiqueira]

Looks right to me. I made a small comment on the equation, but that is a separate issue.

[abelsiqueira]

It would be useful to write the math for this in the docs. Something like

$$\min \qquad \bigg(\mu h - \sum_{i = 1}^h p_i^x\bigg)^2$$

It would also make it easier to read with less parenthesis, that's why I moved things around.
I had the impression the problem was

$$\min \qquad \sum_{i=1}^h (\mu - p_i^x)^2,$$

i.e., you want each p_i^x to be close to \mu.

[abelsiqueira]

Never mind my comment, I read that you are just worried about the mean of the new p_i^x, not the individual p_i^x value, so the first definition is correct. I would maybe write as

$$\min \qquad \frac{1}{2}\bigg(\mu - \frac{1}{h}\sum_{i=1}^h p_i^x\bigg)^2$$

[abelsiqueira]

I realized something about the problem. You are doing nonlinear least squares of a single variable with a single equation. So it makes sense to ask whether the equation already has a solution. Under conditions on the profile values and the target_mean, it has, and in that case it would be simpler to use a root-finding algorithm.
For instance:

using Roots
profile_values = [0.2, 0.5, 0.9, 1.0, 0.4, 0.1, 0.0] 
target_mean = 0.5
find_zero(
	x -> sum(profile_values .^ x .- target_mean),
	[1e-2, 1.0],
)

Depending on what you want, and the assumptions that you can make, this can be used.

[datejada]

@abelsiqueira Thanks for the proposal. German and I have reviewed it and we think it makes sense to have the solution from the find_zero function. We believe that in most cases, there will be a solution to the equation. However, in the unlikely event that there is no solution, we want to at least have the coefficient that minimizes the error. Therefore, we want to modify the function to start with the "find_zero" function and if it cannot find a solution, then go for the optimization. What do you think? In any case, I will create an issue for it. 😄