Dealing with correlations about uncertainties

[apuignav]

Ciao Mauro,

I think this is not working because you're using relative errors, and therefore saying that one error has a larger impact breaks the 100% correlation. I think you may need to use a summed error

Therefore, for the second consideration, you probably need to use absolute errors (this is a simple example, but I think it may be the proper way to attack the problem):

>>> sys = ufloat(0.0, 0.2)
>>> val_y = 10
>>> y = ufloat(val_y, 0.0) + val_y * sys
>>> val_z = 10
>>> z = ufloat(val_z, 0.0) + val_z * sys * 2 # Two times larger
>>> y + z
20.0+/-0.6

Or something like this...

Albert

[apuignav]

Sorry, I forgot the x part

>>> val_x = 5
>>> x = ufloat(val_x, 0.0) + val_x * sys
>>> x + y
15.0+/-0.3
>>> x/y
0.5+/-0
>>> y/x
2.0+/-0

Albert

[lebigot]

Mauro, the behavior that you observe is perfectly correct, since each number created with ufloat() is an independent random variable (I updated https://pythonhosted.org/uncertainties/user_guide.html#creating-numbers-with-uncertainties so as to make this clearer).

Albert's approach is a good idea: since you need a single independent variable, there should be a single ufloat() with a non-zero uncertainty. Albert's solution can be made simpler, though: there is no need to use ufloat(val_x, 0.0), as it can be written directly as val_x.

If I were to code what you want, I would do:

>>> from uncertainties import ufloat
>>> percent_error = ufloat(0, 0.01)  # Error of 1 percentage point
>>> x = 5*(1+2*percent_error)  # 2 % error
>>> x
5.0+/-0.1
>>> y = 10*(1+2*percent_error)  # 2 % correlated error
>>> y/x
2.0+/-0
>>> x+y
15.0+/-0.3
>>> z = 10*(1+4*percent_error)  # 4 % correlated error
>>> y+z
20.0+/-0.6

In general, you can create correlated random variables with the correlated_values() function (http://pythonhosted.org/uncertainties/user_guide.html#index-9).