102 lines
4 KiB
Python
102 lines
4 KiB
Python
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import numpy as np
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import matplotlib.pyplot as plt
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class Walker:
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""" The Walker knows how to walk at random on a context map. """
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def __init__(self, sigma_i, sigma_j, size, map_type='flat'):
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self.sigma_i = sigma_i
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self.sigma_j = sigma_j
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self.size = size
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if map_type == 'flat':
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context_map = np.ones((size, size))
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elif map_type == 'hills':
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grid_ii, grid_jj = np.mgrid[0:size, 0:size]
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i_waves = np.sin(grid_ii / 130) + np.sin(grid_ii / 10)
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i_waves /= i_waves.max()
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j_waves = np.sin(grid_jj / 100) + np.sin(grid_jj / 50) + \
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np.sin(grid_jj / 10)
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j_waves /= j_waves.max()
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context_map = j_waves + i_waves
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elif map_type == 'labyrinth':
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context_map = np.ones((size, size))
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context_map[50:100, 50:60] = 0
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context_map[20:89, 80:90] = 0
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context_map[90:120, 0:10] = 0
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context_map[120:size, 30:40] = 0
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context_map[180:190, 50:60] = 0
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context_map[50:60, 50:200] = 0
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context_map[179:189, 80:130] = 0
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context_map[110:120, 0:190] = 0
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context_map[120:size, 30:40] = 0
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context_map[180:190, 50:60] = 0
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context_map /= context_map.sum()
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self.context_map = context_map
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# Pre-compute a 2D grid of coordinates for efficiency
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self._grid_ii, self._grid_jj = np.mgrid[0:size, 0:size]
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# --- Walker public interface
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def sample_next_step(self, current_i, current_j, random_state=np.random):
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""" Sample a new position for the walker. """
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# Combine the next-step proposal with the context map to get a
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# next-step probability map
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next_step_map = self._next_step_proposal(current_i, current_j)
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selection_map = self._compute_next_step_probability(next_step_map)
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# Draw a new position from the next-step probability map
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r = random_state.rand()
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cumulative_map = np.cumsum(selection_map)
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cumulative_map = cumulative_map.reshape(selection_map.shape)
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i_next, j_next = np.argwhere(cumulative_map >= r)[0]
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return i_next, j_next
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def plot_trajectory(self, trajectory):
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""" Plot a trajectory over a context map. """
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trajectory = np.asarray(trajectory)
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plt.matshow(self.context_map)
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plt.plot(trajectory[:, 1], trajectory[:, 0], color='r')
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plt.show()
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def plot_trajectory_hexbin(self, trajectory):
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""" Plot an hexagonal density map of a trajectory. """
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trajectory = np.asarray(trajectory)
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with plt.rc_context({'figure.figsize': (4, 4), 'axes.labelsize': 16,
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'xtick.labelsize': 14, 'ytick.labelsize': 14}):
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plt.hexbin(trajectory[:, 1], trajectory[:, 0], gridsize=30,
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extent=(0, 200, 0, 200), edgecolors='none', cmap='Reds')
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plt.gca().invert_yaxis()
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plt.xlabel('X')
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plt.ylabel('Y')
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# --- Walker non-public interface
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def _next_step_proposal(self, current_i, current_j):
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""" Create the 2D proposal map for the next step of the walker. """
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# 2D Gaussian distribution , centered at current position,
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# and with different standard deviations for i and j
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grid_ii, grid_jj = self._grid_ii, self._grid_jj
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sigma_i, sigma_j = self.sigma_i, self.sigma_j
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rad = (
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(((grid_ii - current_i) ** 2) / (sigma_i ** 2))
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+ (((grid_jj - current_j) ** 2) / (sigma_j ** 2))
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)
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p_next_step = np.exp(-(rad / 2.0)) / (2.0 * np.pi * sigma_i * sigma_j)
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return p_next_step / p_next_step.sum()
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def _compute_next_step_probability(self, next_step_map):
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""" Compute the next step probability map from next step proposal and
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context map. """
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next_step_probability = next_step_map * self.context_map
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next_step_probability /= next_step_probability.sum()
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return next_step_probability
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