Material for ASPP 2024

notebooks/walker/Step_1_classes/solution/walker.py

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+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
+
+    # --- 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
+
+
+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()