2024-heraklion-scientific-p.../notebooks/walker/Step_2_plotting/walker.py
2024-08-27 15:52:41 +03:00

102 lines
4 KiB
Python

import numpy as np
import matplotlib.pyplot as plt
class Walker:
""" The Walker knows how to walk at random on a context map. """
def __init__(self, sigma_i, sigma_j, size, map_type='flat'):
self.sigma_i = sigma_i
self.sigma_j = sigma_j
self.size = size
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()
self.context_map = context_map
# Pre-compute a 2D grid of coordinates for efficiency
self._grid_ii, self._grid_jj = np.mgrid[0:size, 0:size]
# --- Walker public interface
def sample_next_step(self, current_i, current_j, 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
next_step_map = self._next_step_proposal(current_i, current_j)
selection_map = self._compute_next_step_probability(next_step_map)
# Draw a new position from the next-step probability map
r = random_state.rand()
cumulative_map = np.cumsum(selection_map)
cumulative_map = cumulative_map.reshape(selection_map.shape)
i_next, j_next = np.argwhere(cumulative_map >= r)[0]
return i_next, j_next
def plot_trajectory(self, trajectory):
""" Plot a trajectory over a context map. """
trajectory = np.asarray(trajectory)
plt.matshow(self.context_map)
plt.plot(trajectory[:, 1], trajectory[:, 0], color='r')
plt.show()
def plot_trajectory_hexbin(self, trajectory):
""" Plot an hexagonal density map of a trajectory. """
trajectory = np.asarray(trajectory)
with plt.rc_context({'figure.figsize': (4, 4), 'axes.labelsize': 16,
'xtick.labelsize': 14, 'ytick.labelsize': 14}):
plt.hexbin(trajectory[:, 1], trajectory[:, 0], gridsize=30,
extent=(0, 200, 0, 200), edgecolors='none', cmap='Reds')
plt.gca().invert_yaxis()
plt.xlabel('X')
plt.ylabel('Y')
# --- Walker non-public interface
def _next_step_proposal(self, current_i, current_j):
""" 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 = self._grid_ii, self._grid_jj
sigma_i, sigma_j = self.sigma_i, self.sigma_j
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(self, next_step_map):
""" Compute the next step probability map from next step proposal and
context map. """
next_step_probability = next_step_map * self.context_map
next_step_probability /= next_step_probability.sum()
return next_step_probability