Fix sum_hills overflows when doing projections

[GiovanniBussi]

Description

I am trying to resolve a problem of sum_hills with overflow in exponential when projecting a grid to lower dimension.

I cc people that might be familiar with that part of the code: @carlocamilloni @gtribello @valsson. I noticed that Omar has a copy of this code in ves module, maybe he wants to update it as well.

Changes I did:

• I made the BiasWeight class store a variable (shift) which is the maximum beta*v seen seen so far
• at the end of the projection, I add back the shift to the logarithm and reset the shift.
• I merged two loops here. This is crucial since in this manner the logarithm is taken for one point at a time (and not for all the grid points at the end, as it was before).

As you can see in the regtest, the aim is to be able to integrate a free energy with very large values (note that kBT is very low (0.01)). With the current master branch, the resulting fes.dat would look like this:

#! FIELDS d1 projection
#! SET min_d1 0.726691
#! SET max_d1 1.4841
#! SET nbins_d1  23
#! SET periodic_d1 false
    0.7266910   -0.3044524
    0.7611187   -0.9426032
    0.7955464   -3.8206172
    0.8299740  -11.1560780
    0.8644017  -26.8774481
    0.8988294  -56.3034760
    0.9332571         -inf
    0.9676848         -inf
    1.0021125         -inf
    1.0365401         -inf
    1.0709678         -inf
    1.1053955         -inf
    1.1398232         -inf
    1.1742509         -inf
    1.2086785         -inf
    1.2431062         -inf
    1.2775339         -inf
    1.3119616  -43.4845150
    1.3463893  -19.9096343
    1.3808170   -7.8582589
    1.4152446   -2.4672329
    1.4496723   -0.5443036
    1.4841000   -0.3044522

With the fix, it looks like this

#! FIELDS d1 projection
#! SET min_d1 0.726691
#! SET max_d1 1.4841
#! SET nbins_d1  23
#! SET periodic_d1 false
    0.7266910   -0.3044524
    0.7611187   -0.9426032
    0.7955464   -3.8206172
    0.8299740  -11.1560780
    0.8644017  -26.8774481
    0.8988294  -56.3034760
    0.9332571 -104.1750364
    0.9676848 -171.1615119
    1.0021125 -250.2626861
    1.0365401 -325.9693625
    1.0709678 -378.4433089
    1.1053955 -391.7742547
    1.1398232 -361.7430008
    1.1742509 -297.9659459
    1.2086785 -218.9493543
    1.2431062 -143.4879780
    1.2775339  -83.7886778
    1.3119616  -43.4845150
    1.3463893  -19.9096343
    1.3808170   -7.8582589
    1.4152446   -2.4672329
    1.4496723   -0.5443036
    1.4841000   -0.3044522

All current regtests are not affected.

I think this is a bug fix, so I would merge it to v2.8 and then even check if I can backport to v2.7.

Target release

I would like my code to appear in release v2.8 (possibly v2.7)

[gtribello]

This looks cool. :-)