Improve num_regression with changes in percent

[arthursoprana]

Add relative change, use sign on errors

The first idea would be to add a fourth column besides obtained_..., expected_... and diff: relative change. It would print the relative error of the obtained, in relation with the expected. It would also change to use a sign on the error.

Example:

    obtained_U_gas [m/s]  expected_U_gas [m/s]              abs. diff         rel. diff (%)
E       1   0.00000526006928701   0.00092027745031029  -0.000915017381023 -99.428425711698500
E       2   0.00109742144185932   0.05314025093428264  -0.052042829492423 -97.934858374650000
E       3   0.10233425003713974   0.83767265449607820  -0.735338404458939 -87.783503557400900
E       4   1.50587844448218111   2.46949341632139818  -0.963614971839210 -39.020754842692900
E       5   3.85292939530965661   4.17226524036200175  -0.319335845052350  -7.653776225996680
E       6   6.48537098006507318   6.44999832744570334   0.035372652619370   0.548413361114436
E       7  10.33851199361759932   9.96422211906309130   0.374289874554410   3.756338127372090
E       8  15.91086496866478051  15.83790607275804696   0.072958895906700   0.460659986058339
E       9  28.43953100878306728  28.31184178336182455   0.127689225421200   0.451009956887510

Note: using rel_error_in_percent = (obtained - expected) / abs(expected) * 100. There may be other better equations.

How it is currently:

E          obtained_U_gas [m/s]  expected_U_gas [m/s]                 diff
E       1   0.00000526006928701   0.00092027745031029  0.00091501738102328
E       2   0.00109742144185932   0.05314025093428264  0.05204282949242332
E       3   0.10233425003713974   0.83767265449607820  0.73533840445893850
E       4   1.50587844448218111   2.46949341632139818  0.96361497183921707
E       5   3.85292939530965661   4.17226524036200175  0.31933584505234514
E       6   6.48537098006507318   6.44999832744570334  0.03537265261936984
E       7  10.33851199361759932   9.96422211906309130  0.37428987455450802
E       8  15.91086496866478051  15.83790607275804696  0.07295889590673355
E       9  28.43953100878306728  28.31184178336182455  0.12768922542124272

Add changes on statistical properties

Sometimes it maybe useful to only look at variations in statistical properties, so this could be added to the output:

    obtained_U_gas [m/s]  expected_U_gas [m/s]              abs. diff         rel. diff (%)
E       1   0.00000526006928701   0.00092027745031029  -0.000915017381023 -99.428425711698500
(...)
E       9  28.43953100878306728  28.31184178336182455   0.127689225421200   0.451009956887510
E     min   0.000005260069287     0.000920277450310    -0.000915017381023 -99.428425711698500
E     max  28.439531008783000    28.311841783361800     0.127689225421200   0.451009956887510
E     avg   7.404058191385600     7.566384460243630    -0.162326268858032  -2.145361099623600
E     std   9.582861811894490     9.369144876763070     0.213716935131419   2.281071943518240

I'll mention @tadeu here since he's the original author of this request 😃

[tadeu]

Nice! Perhaps abs. diff might be confusing, since it's not an absolute value anymore (as in "using abs()")? Could it be called obtained - expected?

Good idea about the statistical properties. avg might be misleading over possibly negative values, as it could be near 0.0 in a case with plenty of errors symmetrically distributed.