{
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   "source": [
    "## HW3 Problem 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'numpy'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[1], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;21;01mnumpy\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[0;32m      2\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpyplot\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;28;01mas\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;21;01mplt\u001b[39;00m\n\u001b[0;32m      4\u001b[0m \u001b[38;5;66;03m# Baseline parameters\u001b[39;00m\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'numpy'"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Baseline parameters\n",
    "a = 2.0\n",
    "beta = 0.5\n",
    "tau = 0.5\n",
    "scale = 1.0\n",
    "max_time = 10.0\n",
    "dt = 1e-3\n",
    "num_sims = 2000\n",
    "\n",
    "# Vary drift rate\n",
    "v_values = np.linspace(0.5, 1.5, 25)\n",
    "mean_rt_upper = []\n",
    "mean_rt_lower = []\n",
    "\n",
    "for v in v_values:\n",
    "    data = simulate_diffusion_n(num_sims, v, a, beta, tau, dt, scale, max_time)\n",
    "    mean_rt_upper.append(data[data[:, 1] == 1, 0].mean())\n",
    "    mean_rt_lower.append(data[data[:, 1] == 0, 0].mean())\n",
    "\n",
    "# Plot results\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(v_values, mean_rt_upper, label='Upper Boundary (Correct)', color='maroon')\n",
    "plt.plot(v_values, mean_rt_lower, label='Lower Boundary (Incorrect)', color='gray')\n",
    "plt.xlabel('Drift Rate (v)')\n",
    "plt.ylabel('Mean Response Time (s)')\n",
    "plt.legend()\n",
    "plt.title('Effect of Drift Rate on Mean RTs')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Vary boundary separation (a)\n",
    "a_values = np.linspace(1.0, 3.0, 25)\n",
    "mean_rt_upper = []\n",
    "mean_rt_lower = []\n",
    "std_rt_upper = []\n",
    "std_rt_lower = []\n",
    "\n",
    "for a in a_values:\n",
    "    data = simulate_diffusion_n(num_sims, v, a, beta, tau, dt, scale, max_time)\n",
    "    mean_rt_upper.append(data[data[:, 1] == 1, 0].mean())\n",
    "    mean_rt_lower.append(data[data[:, 1] == 0, 0].mean())\n",
    "    std_rt_upper.append(data[data[:, 1] == 1, 0].std())\n",
    "    std_rt_lower.append(data[data[:, 1] == 0, 0].std())\n",
    "\n",
    "# Plot results\n",
    "plt.figure(figsize=(12, 6))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(a_values, mean_rt_upper, label='Upper Boundary (Correct)', color='maroon')\n",
    "plt.plot(a_values, mean_rt_lower, label='Lower Boundary (Incorrect)', color='gray')\n",
    "plt.xlabel('Boundary Separation (a)')\n",
    "plt.ylabel('Mean Response Time (s)')\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(a_values, std_rt_upper, label='Upper Boundary (Correct)', color='maroon')\n",
    "plt.plot(a_values, std_rt_lower, label='Lower Boundary (Incorrect)', color='gray')\n",
    "plt.xlabel('Boundary Separation (a)')\n",
    "plt.ylabel('Standard Deviation of RT (s)')\n",
    "plt.legend()\n",
    "\n",
    "plt.suptitle('Effect of Boundary Separation on RT Distributions')\n",
    "plt.show()"
   ]
  }
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