Refactor systemQuality function and write nan-compatible equation for system and fragment quality

[comcon1]

systemQuality function doesn't do it's job. The equation presented in Hanne's piece of documentation
https://nmrlipids.github.io/FAIRMD_lipids/latest/quality.html
is not nan-compatible. Dealing with missing values (the most important and non-trivial part of this value evaluation) is completely skipped in both documentation and in the original paper.

[ohsOllila]

Documentation is saying "𝐹frag⁡[lipid] is the percentage of order parameters for which the quality is available within the fragment." This penalizes if the qualities for some segments are missing.

[comcon1]

I would not say that the code works like this. Let's put it here to see. Maybe it does but just organized a bit non-trivial.

def systemQuality(system_fragment_qualities, simulation):
    system_dict = {}
    lipid_dict = {}
    w_nan = []

    for lipid in system_fragment_qualities:
        # copy keys to new dictionary
        lipid_dict = dict.fromkeys(system_fragment_qualities[lipid].keys(), 0)

        w = simulation.molar_fraction(lipid)

        for key, value in system_fragment_qualities[lipid].items():
            if not np.isnan(value):
                lipid_dict[key] += w * value
            else:
                # save 1 - w of a lipid into a list if the fragment quality is nan
                w_nan.append(1 - w)

        system_dict[lipid] = lipid_dict

    system_quality = {}

    headgroup = 0
    tails = 0
    total = 0

    for lipid_key in system_dict:
        for key, value in system_dict[lipid_key].items():
            if key == "total":
                total += value
            elif key == "headgroup":
                headgroup += value
            elif key == "sn-1" or key == "sn-2":
                tails += value / 2
            else:
                tails += value

    if np.prod(w_nan) > 0:
        # multiply all elements of w_nan and divide the sum by the product
        system_quality["headgroup"] = headgroup * np.prod(w_nan)
        system_quality["tails"] = tails * np.prod(w_nan)
        system_quality["total"] = total * np.prod(w_nan)
    else:
        system_quality["headgroup"] = headgroup
        system_quality["tails"] = tails
        system_quality["total"] = total

    print("system_quality")
    print(system_quality)

    return system_quality

[comcon1]

Regarding the fragment, I see the penalization (1-w)^N(nan) where w is the molar fraction. I don't understand it. Is there any sense to this? So, if I slice the lipid into many pieces, it will penalize more than smaller pieces.

Also, I would say that I disagree with the weight of quality linearly proportional to the lipid composition. It's not fair. If you have 90%PC and 10% cholesterol, cholesterol's quality should not contribute 10%. If there are two these systems and one has quality only for PC and the other - only for cholesterol, the second cannot weight 10% of the first. Maybe it should weight less but not THAT less. Maybe "sqrt(mass fraction)" or even "^(1/3)".

[ohsOllila]

Regarding the fragment, I see the penalization (1-w)^N(nan) where w is the molar fraction. I don't understand it. Is there any sense to this? So, if I slice the lipid into many pieces, it will penalize more than smaller pieces.

1 is no penalty, 0 is full penalty. With bigger the number is smaller meaning bigger penalty.

Also, I would say that I disagree with the weight of quality linearly proportional to the lipid composition.

Yes, this is an ad hoc decision. Also some other decision can be done. I doubt that this would have practical relevance for the ranking.

Dealing with missing values (the most important and non-trivial part of this value evaluation) is completely skipped in both documentation and in the original paper.

Now it seems to me that the penalty due to missing values is indeed missing from the fourth equation in the documentation. It should be there in similar fashion as in the third.