vectorize the peak fitting

[rmflight]

I don't think we can vectorize getting coefficients of $intensity = a + m/z + m/z^2$, however, I think we could vectorize getting the center and intensity, because the number of coefficients is the same, and the only bit we need otherwise is the mean of the m/z's, I think

model_peak_center_intensity = function(x, coefficients){
  mn_x = mean(x)
  # this is all on the coefficients
  peak_center = ((-1 * coefficients[2]) / (2 * coefficients[3]))
  # this is just center from above, and then coefficients
  center_int = coefficients[1] + coefficients[2] * peak_center +
    (coefficients[3] * (peak_center ^ 2))
  c(ObservedMZ = peak_center + mn_x, Height = center_int)
}

So looking at this, if we passed in a vector of means, and a matrix of coefficients, we should be able to generate a whole lot of peak centers and heights all in one go. This would be good, because one of the big penalties we currently take is writing data-frame, and right now we do it row by row (using purrr mostly, so it's trying to do pre-allocation, but it's still not going to be as good as a whole lot at once I think).

[rmflight]

This may be a relevant stats thread for trying to vectorize the fitting of coefficients

https://stats.stackexchange.com/questions/135621/what-is-the-proper-way-to-do-vector-based-linear-regression-in-r

[rmflight]

I don't think we need to vectorize this, but we can do two things to make it a bit faster.

1. Remove zero points, as that removes the zero weighting, which does mean more lines evaluated by lm.fit
2. Put the coefficient regression and center calculation in the same function. It makes no sense to have them split up, and saves us a function call.