added analysis helpers

Author: codegithubka

docs/prompts.md

@@ -28,3 +28,5 @@ Finally, make sure to add an expected type for each argument and define the retu
 6. Create a time series analysis plot of the evolution of prey and predator density vs. time. Make sure enough time steps all visible to see how the system eventually stabilizes.
 
 7. Create a bifuracation diagram to confirm the monotonic relationship for a varying prey death rate vs. equilibrium density. 
+
+###

models/__init__.py

@@ -1 +1,2 @@
-from .mean_field import MeanFieldModel
+from .mean_field import MeanFieldModel
+from .CA import CA

models/helpers.py

@@ -0,0 +1,78 @@
+import numpy as np
+from scipy.ndimage import label
+
+def find_clusters(grid: np.ndarray, state: int = 1, connectivity: int = 'moore'):
+    """Locate connected clusters of a given state."""
+    if connectivity == 'moore':
+        structure = np.ones((3, 3), dtype=int)
+    else:
+        structure =  ([[0, 1, 0],
+                       [1, 1, 1],
+                      [0, 1, 0]])
+        
+    binary_mask = (grid == state).astype(int)
+    labeled_array, num_clusters = label(binary_mask, structure=structure)
+    
+    return labeled_array, num_clusters
+
+def get_cluster_sizes(grid: np.ndarray, state: int = 1):
+    """Returns an array containing the sizes of all detected clusters."""
+    labeled, n = find_clusters(grid, state)
+    
+    if n == 0:
+        return np.array([])
+    
+    sizes = np.bincount(labeled.ravel())[1:]  # Exclude background count
+    
+    return sizes
+
+def fit_power_law_mle(sizes: np.ndarray, s_min: float = 1.0):
+    """
+    Maximum Likelihood Estimator for the power-law exponent.
+    """
+    # Filter sizes below the minimum threshold
+    sizes = sizes[sizes >= s_min]
+    
+    if len(sizes) < 10:
+        return {'tau': np.nan, 'tau_err': np.nan, 'n_samples': len(sizes)}
+    
+    n = len(sizes)
+    
+    # Standard MLE formula for power-law index
+    tau = 1 + n / np.sum(np.log(sizes / s_min))
+    tau_err = (tau - 1) / np.sqrt(n)
+    
+    return {
+        'tau': tau, 
+        'tau_err': tau_err, 
+        'n_samples': n
+    }
+
+def detect_hydra_effect(d_r_vals: np.ndarray, R_vals: np.ndarray):
+    """Detects hydra effect by identifying increase in prey population with increased death rate."""
+    
+    dR = np.gradient(R_vals, d_r_vals)
+    hydra_mask = dR > 0
+    
+    if not np.any(hydra_mask):
+        return {
+            'detected': False,
+            'region': None,
+            'max_strength': 0.0
+        }
+    hydra_indices = np.where(hydra_mask)[0]
+    
+    results = {
+        'detected': True,
+        'd_r_start': d_r_vals[hydra_indices[0]],
+        'd_r_end': d_r_vals[hydra_indices[-1]],
+        'max_slope': np.max(dR),
+        'd_r_at_max_slope': d_r_vals[np.argmax(dR)],
+        'peak_density': np.max(R_vals[hydra_mask])
+    }
+    
+    return results
+
+def find_spatial_correlation(d_r_vals, ca_results):
+    """ca_results: List of grids (np.ndarray) at equilibrium of each d_r value."""
+    pass

notebooks/mf.ipynb

@@ -2,4 +2,5 @@ matplotlib
 numpy
 scipy
 pytest
-seaborn
+seaborn
+black

requirements.txt

@@ -0,0 +1,21 @@
+"""Cellular Automaton tests."""
+
+import pytest
+import numpy as np
+from models.CA import CA
+
+# @pytest.fixture
+def ca_instance():
+    pass
+
+def test_initialization():
+    pass
+
+def test_invalid_parameters():
+    pass
+
+def test_grid_filling():
+    pass
+
+def test_neighborhood_types():
+    pass