Reference

class smup.smup.Smup[source]

Main interface with two main methods: compute() and display().

compute(x=1024, y=720, s=20, norm=2, provisioning=1.0, heterogeneous_areas=False, seed=None)[source]
Parameters

  • x (int) – Width of the picture (in pixels)

  • y (int) – Height of the picture (in pixels)

  • s (int) – Number of areas to display in the picture

  • norm (int or str or float or callable.) – Distance function to use. If norm is a positive float p (or string representation of), the p-norm will (which is not a norm if p<1). Optimized for 1, 2, or ‘inf’ but arbitrary positive float can be used If norm is a callable (must be jittable with proper signature), it will be used as such (not need to be an actual norm or even distance).

  • provisioning (float) – Quotas slack. Values < 1 will make holes in the covering, while large values will make a Voronoi diagram.

  • heterogeneous_areas (bool) – Tells if the surfaces of site try to have same area or not. If False, each area will have the same size up to roundings (about x*y/s). If True, (s-1) integers between 0 and x*y are draw uniformly independently. The sizes are given by the s intervals generated on [0, x*y].

  • seed (int, optional) – Random seed

Returns

Return type

None

Examples

We will use ASCII display for these examples. With the chosen seen, the site 0 should be a ball.

With Euclidian distance, the ball is a disk.

>>> my_smup = Smup()
>>> my_smup.compute(x=30, y=20, s=3, norm=2, seed=42)
>>> txt = ascii_display(my_smup.picture, my_smup.centers)
>>> print(txt) 
1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 X 2 2 2 1 1 1 X 1
1 1 1 1 1 2 2 2 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 1 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1

With Manhattan distance, the ball is a diamond.

>>> my_smup.compute(x=30, y=20, s=3, norm=1, seed=42)
>>> txt = ascii_display(my_smup.picture, my_smup.centers)
>>> print(txt) 
1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 2 2 2 2 2 2 0 0 0 0 2 2 2 2 2 2 2 2 X 2 2 2 1 1 1 X 1
1 1 1 2 2 2 2 2 2 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 2 2 2 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1
1 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1

With Inf-norm distance, the ball is a (partial) square.

>>> my_smup.compute(x=30, y=20, s=3, norm="inf", seed=42)
>>> txt = ascii_display(my_smup.picture, my_smup.centers)
>>> print(txt) 
1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 X 2 2 2 1 1 1 X 1
1 1 2 2 2 2 0 2 2 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 2 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 1 1 1 1 1 1
1 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1 1 1
1 1 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 1 1 1
1 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 1 1 1 1 1 1 1 1
1 2 2 2 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 2 1 1 1 1 1 1 1 1 1 1
1 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1
1 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1
1 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1
1 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1
1 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1
1 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1
1 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1
1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Arbitrary power can be used for the norm (which may not be a norm in the end).

>>> my_smup.compute(x=30, y=20, s=3, norm=.5, seed=42)
>>> txt = ascii_display(my_smup.picture, my_smup.centers)
>>> print(txt) 
1 1 1 1 1 1 2 2 2 2 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 2 2 2 2 2 2 2 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
2 2 2 2 2 2 2 2 2 2 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
2 2 2 2 2 2 2 2 2 2 0 0 2 2 2 2 2 2 2 2 2 X 2 2 2 1 1 1 X 1
1 1 2 2 2 2 2 2 2 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 2 2 2 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 2 2 2 0 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 2 1 1 1 1 1
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 1 1 1 1 1 1

You can also specify a custom function and use it. The function, which may not be a norm of even a distance, must be numba compatible with a signature (2,), (2, X) -> (X,). Example:

>>> def diagonal_polarization(center, points):
...     return (points[0, :] - center[0] + points[1, :] - center[1])**2
>>> my_smup.compute(x=30, y=20, s=3, norm=diagonal_polarization, seed=42)
>>> txt = ascii_display(my_smup.picture, my_smup.centers)
>>> print(txt) 
2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1
2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1
2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1
2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 X 2 2 2 1 1 1 X 1
2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 1
2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 1 1
2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 1 1 1
2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 1 1 1 1
2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 1 1 1 1 1
2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1
2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1
2 2 0 0 0 0 0 0 0 0 0 X 0 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1
2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2
0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2
0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2
0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2
0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2
0 0 0 0 0 0 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2
0 0 0 0 0 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2

Unclear norm defaults to Euclidian norm (and a warning is issued).

>>> my_smup.compute(x=30, y=20, s=3, norm="??", seed=42)
>>> txt = ascii_display(my_smup.picture, my_smup.centers)
>>> print(txt) 
1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 X 2 2 2 1 1 1 X 1
1 1 1 1 1 2 2 2 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 1 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 1

Heterogeneous areas make site quotas uneven.

>>> my_smup.compute(x=30, y=20, s=3, heterogeneous_areas=True, seed=42)
>>> txt = ascii_display(my_smup.picture, my_smup.centers)
>>> print(txt)
1 1 1 1 1 1 2 2 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 1 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 1 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 1 1 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 X 2 2 2 1 1 1 X 1
1 1 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 1 1 1 1 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 1 1 1 1 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 1 1 1 1 1 1

Underprovisioned quotas will create holes.

>>> my_smup.compute(x=30, y=20, s=3, provisioning=.4, seed=42)
>>> txt = ascii_display(my_smup.picture, my_smup.centers)
>>> print(txt)
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 1 1 1 1 1
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 1 1 1 1 1
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 1 1 1 1 1
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 X 2 2 2 1 1 1 X 1
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 1 1 1 1 1
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 1 1 1 1 1
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 1 1 1 1 1
3 3 3 3 3 3 3 3 3 0 0 0 0 3 3 3 3 2 2 2 2 2 2 2 2 1 1 1 1 1
3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 3 3 3 2 2 2 2 2 2 2 1 1 1 1 1
3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 3 3 3 3 1 2 2 1 1 1 1 1 1 1
3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 1 1 1 1 1 1 1 1 1
3 3 3 3 3 3 0 0 0 0 0 X 0 0 0 0 3 3 3 3 3 3 1 1 1 1 1 1 1 1
3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 1 1 1 1 1 1
3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 1 1 1 1
3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Overprovisioned quotas will create a Voronoi diagram.

>>> my_smup.compute(x=30, y=20, s=3, provisioning=4, seed=42)
>>> txt = ascii_display(my_smup.picture, my_smup.centers)
>>> print(txt)
0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 X 2 2 2 1 1 1 X 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 2 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1
display(cmap='jet', draw_centers=False, center_size=20, save=None)[source]
Parameters

  • cmap (str) – Matplotlib colormap to use. Defaults to ‘jet’

  • draw_centers (bool) – Draw centers of areas. Defaults to False.

  • center_size (int) – Size of centers, if drawn. Defaults to 20.

  • save (str ot Path, optional) – Filename for saving picture.

Returns

Return type

None

Examples

See Using SMUP for graphical examples. Here we just show the file saving feature.

>>> from pathlib import Path
>>> import tempfile
>>> my_smup = Smup()
>>> my_smup.compute(x=30, y=20, s=3, norm=2, seed=42)
>>> with tempfile.TemporaryDirectory() as tmpdirname:
...     fn = tmpdirname/Path("picture.png")
...     my_smup.display(draw_centers=True, save=fn)
...     size=fn.stat().st_size
>>> size
55984
smup.smup.ascii_display(picture, centers)[source]
Parameters

  • picture (ndarray) – A xXy array populated with integers 0, …, s-1 that indicate the area of each pixel. Non covered pixels, if any, are represented by s.

  • centers (ndarray) – Coordinates of the area centers

Returns

ASCII display of the matching.

Return type

str

smup.smup.compute(x, y, s, distance_function, provisioning=1.0, heterogeneous_areas=False, seed=None)[source]

Main function of the package. Computes the pictures.

Parameters

  • x (int) – Width of the picture (in pixels)

  • y (int) – Height of the picture (in pixels)

  • s (int) – Number of areas to display in the picture

  • distance_function (callable) – Functions that computes distances between a center and points

  • provisioning (float) – Quota under/over provisioning. Values < 1 will make holes in the covering, while large values will make a Voronoi diagram.

  • heterogeneous_areas (bool) – Tells if the surfaces of site try to have same area or not.

  • seed (int, optional) – Random seed

Returns

  • picture (ndarray) – A xXy array populated with integers 0, …, s-1 that indicate the area of each pixel. Non covered pixels, if any, are represented by s.

  • centers (ndarray) – Coordinates of the area centers

smup.smup.dist_1(center, points)[source]
Parameters

  • center (ndarray) – 2-D coordinate of the center.

  • points (ndarray) – 2-D coordinates of the points

Returns

Manhattan distances between center and points.

Return type

ndarray

Examples

Manhattan distances between the origin and the points (0.3, 0.4), (1, 0), and (2, 1):

>>> center = np.array([0, 0])
>>> points = np.array([ [0.3, 1, 2], [0.4, 0, 1] ])
>>> dist_1(center, points)
array([0.7, 1. , 3. ])
smup.smup.dist_2(center, points)[source]
Parameters

  • center (ndarray) – 2-D coordinate of the center.

  • points (ndarray) – 2-D coordinates of the points

Returns

Square of Euclidian distances between center and points.

Return type

ndarray

Examples

Square distances between the origin and the points (0.3, 0.4), (1, 0), and (2, 1):

>>> center = np.array([0, 0])
>>> points = np.array([ [0.3, 1, 2], [0.4, 0, 1] ])
>>> dist_2(center, points)
array([0.25, 1.  , 5.  ])
smup.smup.dist_inf(center, points)[source]
Parameters

  • center (ndarray) – 2-D coordinate of the center.

  • points (ndarray) – 2-D coordinates of the points

Returns

Inf-norm distances between center and points.

Return type

ndarray

Examples

Inf-norm distances between the origin and the points (0.3, 0.4), (1, 0), and (2, 1):

>>> center = np.array([0, 0])
>>> points = np.array([ [0.3, 1, 2], [0.4, 0, 1] ])
>>> dist_inf(center, points)
array([0.4, 1. , 2. ])
smup.smup.isfloat(value)[source]
Parameters

value (object) –

Returns

Can the object be converted to float?

Return type

bool

Examples

>>> isfloat(3)
True
>>> isfloat("3.145")
True
>>> isfloat("Hello")
False
>>> isfloat("1+1")
False
smup.smup.make_dist_p(p=2.0)[source]
Parameters

p (float) – Power to apply.

Returns

A jitted function that computes the sum of individual coordinate distances to the power of p. Correspond to a norm (up to re-scaling by 1/p) if p greater or equal to 1.

Return type

callable

Examples

Let us fix a center and some points.

>>> center = np.array([0, 0])
>>> points = np.array([ [0.3, 1, 2], [0.4, 0, 1] ])

Square distances between the origin and the points (0.3, 0.4), (1, 0), and (2, 1) (equivalent to dist_2())

>>> my_dist = make_dist_p(p=2)
>>> my_dist(center, points)
array([0.25, 1.  , 5.  ])

Power of 1 (equivalent to dist_1()):

>>> my_dist = make_dist_p(p=1)
>>> my_dist(center, points)
array([0.7, 1. , 3. ])

Power of 3:

>>> my_dist = make_dist_p(p=3)
>>> my_dist(center, points)
array([0.091, 1.   , 9.   ])

Power of .5 (not a norm; convexity is lost):

>>> my_dist = make_dist_p(p=.5)
>>> my_dist(center, points)
array([1.18017809, 1.        , 2.41421356])