2024-heraklion-scientific-patterns/notebooks/walker/Step_0_Introduction/Step_0_Introduction.ipynb

In [1]:

%matplotlib inline

import matplotlib.pyplot as plt

from walker import create_context_map, next_step_proposal, plot_trajectory, sample_next_step

Examples of how the code works¶

The walker code works in the following way:

The function next_step_proposal to creates a map of the probability of ending up in any position, given the current position, some map parameters, and the size of the map

In [2]:

proposal = next_step_proposal(current_i=100, current_j=50, sigma_i=10, sigma_j=5, size=200)
plt.matshow(proposal)

Out[2]:

<matplotlib.image.AxesImage at 0x7fc6b6844400>

The function create_context_map creates a context map that tell us regions in the image with a higher probability of being looked at (e.g., very bright spots in an image)

In [3]:

context_map = create_context_map(size=150, map_type='hills')
plt.matshow(context_map)
plt.colorbar()

Out[3]:

<matplotlib.colorbar.Colorbar at 0x7fc6b68df080>

The function sample_next_step calls next_step_proposal, combines it with the context map that is passed to it (in compute_next_step_probability), and then stochastically selects the next step.

How to simulate a trajectory¶

in order to use the walker, the user has to create a context map. Then, for a number of timesteps, sample a step, always passing along the new position information.

In [4]:

i, j = 100, 50  # initial position
sigma_i, sigma_j = 3, 4  # parameters of the next step map
size = 200  # size of the image
context_map = create_context_map(size, 'hills')  # fixed context map

# Sample a next step 1000 times
trajectory = []
for _ in range(1000):
    i, j = sample_next_step(i, j, sigma_i, sigma_j, context_map)
    trajectory.append((i, j))

In [5]:

plot_trajectory(trajectory, context_map)

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