102 lines
4 KiB
Python
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
|