Model measurement and error in NumPy

问题

I'd like to try the SciPy suite instead of Octave for doing the statistics in my lab experiments. Most of my questions were answered here, there is just another thing left:

I usually have an error attached to the measurements, in Octave I just did the following:

R.val = 10;
R.err = 0.1;

U.val = 4;
U.err = 0.1;

And then I would calculate I with it like so:

I.val = U.val / R.val;
I.err = sqrt(
    (1 / R.val * U.err)^2
    + (U.val / R.val^2 * R.err)^2
);

When I had a bunch of measurements, I usually used a structure array, like this:

R(0).val = 1;
R(0).err = 0.1;
…
R(15).val = 100;
R(15).err = 9;

Then I could do R(0).val or directly access all of them using R.val and I had a column vector with all the values, for mean(R.val) for instance.

How could I represent this using SciPy/NumPy/Python?

回答1:

The easiest is indeed to use NumPy structured arrays, that give you the possibility to define arrays of homogeneous elements (a record) composed of other homogeneous elements (fields).

For example, you could define

R = np.empty(15, dtype=[('val',float),('err',float)])

and then fill the corresponding columns:

R['val'] = ...
R['err'] = ...

Alternatively, you could define the array at once if you have your val and err in two lists:

R = np.array(zip(val_list, err_list), dtype=[('val',float),('err',float)])

In both cases, you can access individual elements by indices, like R[0] (which would give you a specific object, a np.void, that still gives you the possibility to access the fields separately), or by slices R[1:-1]...

With your example, you could do:

I = np.empty_like(R)
I['val'] = U['val'] / R['val']
I['err'] = np.sqrt((1 / R['val'] * U['err'])**2 + (U['val'] / R['val']**2 * R['err'])**2)

You could also use record array, which are basic structured array with the __getattr__ and __setattr__ methods overloaded in such way that you can access the fields as attributes (like in R.val) as well as indices (like the standard R['val']). Of course, as these basic methods are overloaded, record arrays are not as efficient as structured arrays.

回答2:

This kind of error propagation is exactly what the uncertainties Python package does. It does so transparently and by correctly handling correlations:

from uncertainties import ufloat

R = ufloat(10, 0.1)
U = ufloat(4, 0.1)
I = U/R

print I

prints 0.4+/-0.0107703296143, after automatically determining and calculating the error formula that you typed manually in your example. Also, I.n and I.s are respectively the nominal value (your val) and the standard deviation (your err).

Arrays holding numbers with uncertainties can also be used (http://pythonhosted.org/uncertainties/numpy_guide.html).

(Disclaimer: I'm the author of this package.)

回答3:

For just one measurement probably simple namedtuple would suffice.

And instead of structure arrays you can use numpy's record arrays. Seems to be little bit more mouthful though.

Also google cache of NumPy for Matlab Users (direct link doesn't work for me atm) can help with some counterparts of basic operations.

回答4:

There is a package for representing quantities along with uncertainties in Python. It is called quantities ! (also on PyPI).

来源：https://stackoverflow.com/questions/12351837/model-measurement-and-error-in-numpy

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python

numpy

scipy

octave