2024-heraklion-scientific-p.../notebooks/walker/Step_1_classes/walker.py
2024-08-27 15:52:41 +03:00

82 lines
3 KiB
Python

import numpy as np
import matplotlib.pyplot as plt
def sample_next_step(current_i, current_j, sigma_i, sigma_j, context_map,
random_state=np.random):
""" Sample a new position for the walker. """
# Combine the next-step proposal with the context map to get a next-step
# probability map
size = context_map.shape[0]
next_step_map = next_step_proposal(current_i, current_j, sigma_i, sigma_j,
size)
next_step_probability = compute_next_step_probability(next_step_map,
context_map)
# Draw a new position from the next-step probability map
r = random_state.rand()
cumulative_map = np.cumsum(next_step_probability)
cumulative_map = cumulative_map.reshape(next_step_probability.shape)
i_next, j_next = np.argwhere(cumulative_map >= r)[0]
return i_next, j_next
def next_step_proposal(current_i, current_j, sigma_i, sigma_j, size):
""" Create the 2D proposal map for the next step of the walker. """
# 2D Gaussian distribution , centered at current position,
# and with different standard deviations for i and j
grid_ii, grid_jj = np.mgrid[0:size, 0:size]
rad = (
(((grid_ii - current_i) ** 2) / (sigma_i ** 2))
+ (((grid_jj - current_j) ** 2) / (sigma_j ** 2))
)
p_next_step = np.exp(-(rad / 2.0)) / (2.0 * np.pi * sigma_i * sigma_j)
return p_next_step / p_next_step.sum()
def compute_next_step_probability(next_step_map, context_map):
""" Compute the next step probability map from next step proposal and
context map. """
next_step_probability = next_step_map * context_map
next_step_probability /= next_step_probability.sum()
return next_step_probability
def create_context_map(size, map_type='flat'):
""" Create a fixed context map. """
if map_type == 'flat':
context_map = np.ones((size, size))
elif map_type == 'hills':
grid_ii, grid_jj = np.mgrid[0:size, 0:size]
i_waves = np.sin(grid_ii / 130) + np.sin(grid_ii / 10)
i_waves /= i_waves.max()
j_waves = np.sin(grid_jj / 100) + np.sin(grid_jj / 50) + \
np.sin(grid_jj / 10)
j_waves /= j_waves.max()
context_map = j_waves + i_waves
elif map_type == 'labyrinth':
context_map = np.ones((size, size))
context_map[50:100, 50:60] = 0
context_map[20:89, 80:90] = 0
context_map[90:120, 0:10] = 0
context_map[120:size, 30:40] = 0
context_map[180:190, 50:60] = 0
context_map[50:60, 50:200] = 0
context_map[179:189, 80:130] = 0
context_map[110:120, 0:190] = 0
context_map[120:size, 30:40] = 0
context_map[180:190, 50:60] = 0
context_map /= context_map.sum()
return context_map
def plot_trajectory(trajectory, context_map):
""" Plot a trajectory over a context map. """
trajectory = np.asarray(trajectory)
plt.matshow(context_map)
plt.plot(trajectory[:, 1], trajectory[:, 0], color='r')
plt.show()