Separability; Distributions for neuron parameters

SimpleCell.ipynb

@@ -545,9 +545,7 @@
     }
    },
    "outputs": [],
-   "source": [
+   "source": []
-    "sp.latex?"
-   ]
   },
   {
    "cell_type": "code",

model/sym_model.py

@@ -13,7 +13,7 @@ sp.init_printing()
 k, x0, y0, phi_rf, theta_rf, sigma_x, sigma_y, sigma, x, y, theta_grating, phi_grating = sp.symbols(r'k x_0 y_0 \phi_{rf} \theta_{rf} \sigma_x \sigma_y \sigma x y \theta_{grating} \phi_{grating}')
 defaults = {
     k: 6,
-    sigma: 0.2,
+    sigma: 1,
     phi_rf: sp.pi / 2,
     phi_grating: sp.pi / 2,
     theta_grating: 0,
@@ -46,6 +46,31 @@ xy_split = np.arange(-1, 1, 0.05)
 phi_split = np.arange(0, 2 * np.pi, np.pi / 100)
 theta_split = np.arange(0, np.pi, np.pi / 100)
 
+# The second option is (the distribution function, the function that takes the size and returns the step and the starting point)
+Distribution = typing.Union[float, typing.Dict[float, float], typing.Tuple[typing.Callable[[float], float], typing.Callable[[int], typing.Tuple[float, float]]]]
+
+
+def sample_distribution(distribution: Distribution, size: int = 1) -> np.ndarray:
+    if isinstance(distribution, float) or isinstance(distribution, int):
+        return np.array([float(distribution)] * size)
+    if isinstance(distribution, dict):
+        return np.random.choice(list(distribution.keys()), size, p=list(distribution.values()))
+    elif isinstance(distribution, tuple):
+        step, start = distribution[1](size)
+        res = [start]
+        for i in range(size):
+            res.append(res[-1] + step / distribution[0](res[-1]))
+        return np.array(res)
+    else:
+        raise ValueError(f'Unknown distribution type: {type(distribution)}')
+
+
+def get_uniform_dist(start: float, stop: float) -> Distribution:
+    return (lambda _x: 1, lambda size: ((stop - start) / (size - 1 or 1), start))
+
+phi_dist_uni = get_uniform_dist(0, 2 * np.pi)
+theta_dist_uni = get_uniform_dist(0, np.pi)
+
 
 def sigmoid(x):
     return 1 / (1 + np.exp(-x))
@@ -60,22 +85,6 @@ class Cell:
     y0_val: float = defaults[y0]
     k_val: float = defaults[k]
 
-    @classmethod
-    def random(cls,
-               phi_dist: np.ndarray = np.ones(len(phi_split)),
-               theta_dist: np.ndarray = np.ones(len(theta_split)),
-               sigma_dist: np.ndarray = np.ones(len(sigma_split)),
-               k_val: float = defaults[k],
-               xy_dist: np.ndarray = np.ones(len(xy_split))):
-        return cls(
-            sigma_val=1, # np.random.choice(sigma_split, p=sigma_dist / np.sum(sigma_dist)),
-            phi_val=np.random.choice(phi_split, p=phi_dist / np.sum(phi_dist)),
-            theta_val=np.random.choice(theta_split, p=theta_dist / np.sum(theta_dist)),
-            x0_val=0,  # np.random.choice(xy_split, p=xy_dist / np.sum(xy_dist)),
-            y0_val=0,  # np.random.choice(xy_split, p=xy_dist / np.sum(xy_dist)),
-            k_val=k_val,
-        )
-
     @property
     def sympy_func(self) -> sp.Expr:
         return receptive_field\
@@ -135,12 +144,20 @@ class Population:
 
     @classmethod
     def random(cls, n: int, 
-               phi_dist: np.ndarray = np.ones(len(phi_split)),
+               phi_dist: Distribution = phi_dist_uni,
-               theta_dist: np.ndarray = np.ones(len(theta_split)),
+               theta_dist: Distribution = theta_dist_uni,
-               sigma_dist: np.ndarray = np.ones(len(sigma_split)),
+               sigma_dist: Distribution = defaults[sigma],
                k_val: float = defaults[k],
-               xy_dist: np.ndarray = np.ones(len(xy_split))):
+               xy_dist: Distribution = get_uniform_dist(-5, 5)):
-        return cls(cells=[Cell.random(phi_dist, theta_dist, sigma_dist, k_val, xy_dist) for _ in range(n)])
+        return cls(cells=[
+            Cell(phi_val=phi_val, theta_val=theta_val, sigma_val=sigma_val, x0_val=x0_val, y0_val=y0_val, k_val=k_val) 
+            for phi_val, theta_val, sigma_val, x0_val, y0_val in zip(
+                sample_distribution(phi_dist, n),
+                sample_distribution(theta_dist, n),
+                sample_distribution(sigma_dist, n),
+                sample_distribution(xy_dist, n),
+                sample_distribution(xy_dist, n))
+        ])
 
     def get_response(self, phi_deg: float, theta_deg: float, coef: float = 4, use_sigmoid: bool = True) -> np.ndarray:
         return (sigmoid if use_sigmoid else (lambda x: x))(np.array([cell.get_value(theta_deg, phi_deg) for cell in self.cells]) * coef)