Interpolating a 2D array given value of certain points

Question

Let’s say I have a 2D array of that represents the signal strength of a network, like so:

d = np.array([[ 0,  0,  0,  3],
              [ 0,  2,  0,  3],
              [ 0,  0,  0,  0],
              [ 0,  0,  0,  3]])

I know the signal strength of specific transmission nodes in the network, and the ones I don’t know will default to 0. The rules for the network strength is that for every node travelled by the signal, the signal strength decays by 1, and I should get

d = np.array([[ 0,  1,  2,  3],
              [ 1,  2,  2,  3],
              [ 0,  1,  1,  2],
              [ 0,  1,  2,  3]])

as a result. What would be the best way to obtain the 2nd array from the first?

Asked By: ChronoVortex

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Source

Answer 1

I suspect you’re not interpolating, but instead applying a max of the effects from each station. Extend to a three dimensional matrix where the added dimension is the number of stations, and then do a max over that dimension. The following produces the same output (made non-square to avoid transposition errors):

import numpy as np

input_stations = np.array((
    ( 0,  0,  0,  3),
    ( 0,  2,  0,  3),
    ( 0,  0,  0,  0),
    ( 0,  0,  0,  3),
    ( 0,  0,  0,  0),
))
coords = input_stations.nonzero()
stations = input_stations[coords]
station_y, station_x = input_stations.nonzero()
m, n = input_stations.shape

# stations by y by x
station_strengths = np.clip(
    stations[:, np.newaxis, np.newaxis]
    - np.abs(
        np.arange(m)[np.newaxis, :, np.newaxis] - station_y[:, np.newaxis, np.newaxis]
    )
    - np.abs(
        np.arange(n)[np.newaxis, np.newaxis, :] - station_x[:, np.newaxis, np.newaxis]
    ),
    a_min=0, a_max=None,
)
strengths = station_strengths.max(axis=0)

expected = np.array((
    ( 0,  1,  2,  3),
    ( 1,  2,  2,  3),
    ( 0,  1,  1,  2),
    ( 0,  1,  2,  3),
    ( 0,  0,  1,  2),
))

assert np.all(expected == strengths)

Answered By: Reinderien

Interpolating a 2D array given value of certain points

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