Add user option for similarity measures

[erikscheurer]

Closes #24

This PR adds options for different similarity measures. Currently L1 and L2 are supported.

[erikscheurer]

When implementing a relative L1 norm for example, by which quantity do we divide? For example, we have the two simulation with states 1 and 2, then data=[1,2]. (So still a single scalar value to compare simulations)
If we then calculate the distances between the two we would have diff =[[0 , 1-2],[2-1, 0]] if we do not normalize. How would this look normalized? Normalization by the maximum of the two? If we do a pointwise division with a vector, we would not get a symmetric matrix which does not make much sense right?

[erikscheurer]

I see two options now:

1. Divide by the mean, this would mean, that different units for example would be cancelled out while preserving the symmetry in the distances. In our example this would be diff=[[0 (1-2)/1.5], [(2-1)/1.5, 0]]
2. Divide by the metric of the "fist" simulation. Divide the matrix row-wise with the vector. diff=[[0, (1-2)/1], [(1-2)/2, 0]]. This would make sense to do because the check if the simulation should be turned active or inactive is done using the row index. To check if the simulation number 0 with data 1 should be turned off, we check if diff[0,:]<tol, therefore we should divide row 0 by the data of simulation 0

[IshaanDesai]

Lets go for the second option, so dividing my the data value of one of the simulations. Which one to pick is our choice, we should only be consistent. As for vectorial quantities, lets say we have a quantity $v$ which we want to use for the comparison. For two micro simulations 1 and 2, this would mean that we have two vectors to compare, $v^1_x, v^1_y, v^1_z$ and $v^2_x, v^2_y, v^2_z$. Let us do a component-wise relative computation then, so we do $\frac{abs(v^1_x - v^2_x)}{v^1_x}$ for all components, and then sum up the relative errors.

[erikscheurer]

This should work now as we discussed, do we want unit tests for this?

[IshaanDesai]

Thanks for this! These additions will expand the adaptivity functionality significantly. Minor changes from my side.

[erikscheurer]

In the future we may want to switch to a different method of selecting functions. As suggested in #24, the user could provide their own similarity functions which cannot easily be realized with the string-selection.

[erikscheurer]

Do we want to merge this or wait for the documentation and the unit tests? Some documentation would be necessary for the similarity functions.

[IshaanDesai]

Do we want to merge this or wait for the documentation and the unit tests? Some documentation would be necessary for the similarity functions.

Let me finish the documentation PR, and then we can add documentation here, and merge it.

[IshaanDesai]

Looks good 👍 only a few documentation related comments from my side. After adding the documentation we can merge.