Material for ASPP 2024

notebooks/walker/Step_6_loading_parameters_from_file/solution/context_maps.py

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+""" CONTEXT MAP BUILDERS """
+import numpy as np
+
+
+
+def flat_context_map_builder(size):
+    """ A context map where all positions are equally likely. """
+    return np.ones((size, size))
+
+
+def hills_context_map_builder(size):
+    """ A context map with bumps and valleys. """
+    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
+    return context_map
+
+
+def labyrinth_context_map_builder(size):
+    """ A context map that looks like a 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
+
+    return context_map
+
+
+# Register map builders
+map_builders = {
+    "flat": flat_context_map_builder,
+    "hills": hills_context_map_builder,
+    "labyrinth": labyrinth_context_map_builder,
+}

notebooks/walker/Step_6_loading_parameters_from_file/solution/inputs.json

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+{
+    "seed": 42,
+    "sigma_i": 3,
+    "sigma_j": 4,
+    "size": 200,
+    "map_type": "hills",
+    "start_i": 50,
+    "start_j": 100,
+    "n_iterations": 1000
+}

notebooks/walker/Step_6_loading_parameters_from_file/solution/plotting.py

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+import matplotlib.pyplot as plt
+import numpy as np
+
+
+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()
+
+
+def plot_trajectory_hexbin(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')

notebooks/walker/Step_6_loading_parameters_from_file/solution/run.py

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+import json
+import time
+
+import git
+import numpy as np
+
+from walker import Walker
+from context_maps import map_builders
+
+
+with open("inputs.json", 'r') as f:
+    inputs = json.load(f)
+
+random_state = np.random.RandomState(inputs["seed"])
+n_iterations = inputs["n_iterations"]
+
+
+
+context_map_builder = map_builders[inputs["map_type"]]
+context_map = context_map_builder(inputs["size"])
+walker = Walker(inputs["sigma_i"], inputs["sigma_j"], context_map)
+
+
+trajectory = []
+for _ in range(n_iterations):
+    i, j = walker.sample_next_step(inputs["start_i"], inputs["start_j"],
+                                   random_state)
+    trajectory.append((i, j))
+
+# STEP 4: Save the trajectory
+curr_time = time.strftime("%Y%m%d-%H%M%S")
+np.save(f"sim_{curr_time}", trajectory)
+
+
+# STEP 5: Save the metadata
+# lookup git repository
+repo = git.Repo(search_parent_directories=True)
+sha = repo.head.object.hexsha
+
+with open('meta.txt', 'w') as f:
+    f.write(f'I estimated parameters at {curr_time}.\n')
+    f.write(f'The git repo was at commit {sha}')

notebooks/walker/Step_6_loading_parameters_from_file/solution/show

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+

notebooks/walker/Step_6_loading_parameters_from_file/solution/walker.py

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+import numpy as np
+
+
+class Walker:
+    """ The Walker knows how to walk at random on a context map. """
+
+    def __init__(self, sigma_i, sigma_j, context_map):
+        self.sigma_i = sigma_i
+        self.sigma_j = sigma_j
+        self.size = context_map.shape[0]
+        # Make sure that the context map is normalized
+        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:self.size, 0:self.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
+