Auxiliary Functions¶

Download this as a Jupyter notebook

This notebook covers the usage of the auxiliary function provided in pyXla.

A key feature of the pyXla framework is the separation of sampling and analysis. A set of functions are provided to support sampling. They are:

Each function corresponds to a given input file as indicated by it suffix.

When a sample is loaded declaratively via domain and function specification (method 3 in Loading and Sampling), these function are used under the hood. These function are available to the user for finer control over sampling.

The auxiliary functions are all imported from pyxla.util:

from pyxla.util import sample_X, compute_F, compute_V, compute_D, compute_N

One can generate an X file as below:

from pyxla.sampling import HilbertCurveSampler

sampler = HilbertCurveSampler(
    sample_size=100, dim=2, return_neighbourhood=True # will return an N file too
)

X, N = sample_X(sampler)
X.head()

	x0	x1
0	6.453459	12.845543
1	3.665404	25.092207
2	18.456522	15.515011
3	19.369122	10.219224
4	15.620123	8.727153

Specifying return_neighbourhood=True generates an N file as well:

N.head()

	id1	id2
0	0	1
1	1	2
2	2	3
3	3	4
4	4	5

The F file can be generated from the X file by specifying an objective function or multiple objective functions:

def sphere(X):
    return X[0]**2 + X[1]**2

def summation(X):
    return X.sum()

F = compute_F([sphere, summation], X)
F.head()

	f0	f1
0	206.655109	19.299002
1	643.054056	28.757612
2	581.358767	33.971533
3	479.595420	29.588346
4	320.151425	24.347275

The process is similar for the V file:

V = compute_V([lambda X: sphere(X) - 2], X)
V.head()

	v0
0	204.655109
1	641.054056
2	579.358767
3	477.595420
4	318.151425

Computing a D file is straightforward:

D = compute_D({"X": X}, metric='canberra') # you can define a function or specify any of scipy's distance functions
D.head()

		d
id1	id2
0	1	0.598340
	2	0.575984
	3	0.614037
	4	0.606185
	5	1.430009

The N file is equally straightforward; either specify a neighbourhood function of supply the literal "hilbert-curve" to use the Hilbert curve to efficiently generate neighbourhood information (see pyxla.sampling.hilbert_curve_neighbour_sampling()).

def randomly_neighbours(a, b):
    import random
    return random.choice([True, False])

N = compute_N({"X": X}, neighbourhood_func=randomly_neighbours)
N.head()

	id1	id2
0	0	1
1	0	2
2	0	3
3	0	4
4	0	5