finished HW3

HW3/Q2/Q2_part1.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def simulate_ddm(v, a=1.0, beta=0.5, tau=0.3, sigma=1.0, dt=0.001, max_steps=3000):
+    X = beta * a  # start position
+    t = 0.0
+    for _ in range(max_steps):
+        dW = np.random.normal(0, np.sqrt(dt))
+        dX = v * dt + sigma * dW
+        X += dX
+        t += dt
+        if X >= a:
+            return t + tau, 1  # upper bound hit
+        elif X <= 0:
+            return t + tau, 0  # lower bound hit
+    return max_steps * dt + tau, None  # Timeout (optional)
+
+
+# terrible params (upped in part 2)
+vs = np.linspace(0.5, 1.5, 25)  # drift rates for test
+n_trials = 2000
+
+# store
+upper_means, lower_means = [], []
+
+for v in vs:
+    upper_rts, lower_rts = [], []
+    for _ in range(n_trials):
+        rt, choice = simulate_ddm(v)
+        if choice == 1:
+            upper_rts.append(rt)
+        elif choice == 0:
+            lower_rts.append(rt)
+    # means (ignore cases where no hits)
+    upper_means.append(np.mean(upper_rts) if upper_rts else np.nan)
+    lower_means.append(np.mean(lower_rts) if lower_rts else np.nan)
+
+# plotting yay
+plt.figure(figsize=(10, 6))
+plt.plot(vs, upper_means, 'o-', label='Upper Boundary Mean RT')
+plt.plot(vs, lower_means, 's-', label='Lower Boundary Mean RT')
+plt.plot(vs, np.array(upper_means) - np.array(lower_means),
+         'd-', label='Mean Difference')
+plt.xlabel('Drift Rate (v)')
+plt.ylabel('Response Time (s)')
+plt.title('Effect of Drift Rate on RT Distributions')
+plt.legend()
+plt.grid(True)
+plt.savefig('part1.png')