82 lines
3 KiB
Python
82 lines
3 KiB
Python
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import numpy as np
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import matplotlib.pyplot as plt
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def sample_next_step(current_i, current_j, sigma_i, sigma_j, context_map,
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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 next-step
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# probability map
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size = context_map.shape[0]
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next_step_map = next_step_proposal(current_i, current_j, sigma_i, sigma_j,
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size)
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next_step_probability = compute_next_step_probability(next_step_map,
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context_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(next_step_probability)
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cumulative_map = cumulative_map.reshape(next_step_probability.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 next_step_proposal(current_i, current_j, sigma_i, sigma_j, size):
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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 = np.mgrid[0:size, 0:size]
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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(next_step_map, context_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 * 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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def create_context_map(size, map_type='flat'):
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""" Create a fixed context map. """
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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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return context_map
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def plot_trajectory(trajectory, context_map):
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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(context_map)
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plt.plot(trajectory[:, 1], trajectory[:, 0], color='r')
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plt.show()
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