{
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   "cell_type": "code",
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   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $sigmoid(x) = \\frac{1}{1+e^{(-x)}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    \"\"\"\n",
    "    Compute the sigmoid function for the input here.\n",
    "\n",
    "    Arguments:\n",
    "    x -- A scalar or numpy array.\n",
    "\n",
    "    Return:\n",
    "    s -- sigmoid(x)\n",
    "    \"\"\"\n",
    "\n",
    "    ### YOUR CODE HERE\n",
    "    s = 1 / (1 + np.exp(-x))\n",
    "    ### END YOUR CODE\n",
    "\n",
    "    return s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# sigmoid_grad\n",
    "- $\\sigma(-x) = \\frac{1}{1 + e^{x}} = \\frac{e^x+1}{e^x + 1} - \\frac{e^x}{e^x + 1}=1-\\sigma(x)$\n",
    "\n",
    "- $\\sigma' = \\sigma(x) \\times (1 - \\sigma(x))$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid_grad(s):\n",
    "    \"\"\"\n",
    "    Compute the gradient for the sigmoid function here. Note that\n",
    "    for this implementation, the input s should be the sigmoid\n",
    "    function value of your original input x.\n",
    "\n",
    "    Arguments:\n",
    "    s -- A scalar or numpy array.\n",
    "\n",
    "    Return:\n",
    "    ds -- Your computed gradient.\n",
    "    \"\"\"\n",
    "\n",
    "    ### YOUR CODE HERE\n",
    "    ds = s * (1-s)\n",
    "    ### END YOUR CODE\n",
    "\n",
    "    return ds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running basic tests...\n",
      "[[0.73105858 0.88079708]\n",
      " [0.26894142 0.11920292]]\n",
      "[[0.19661193 0.10499359]\n",
      " [0.19661193 0.10499359]]\n",
      "You should verify these results by hand!\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def test_sigmoid_basic():\n",
    "    \"\"\"\n",
    "    Some simple tests to get you started.\n",
    "    Warning: these are not exhaustive.\n",
    "    \"\"\"\n",
    "    print(\"Running basic tests...\")\n",
    "    x = np.array([[1, 2], [-1, -2]])\n",
    "    f = sigmoid(x)\n",
    "    g = sigmoid_grad(f)\n",
    "    print(f)\n",
    "    f_ans = np.array([\n",
    "        [0.73105858, 0.88079708],\n",
    "        [0.26894142, 0.11920292]])\n",
    "    assert np.allclose(f, f_ans, rtol=1e-05, atol=1e-06)\n",
    "    print(g)\n",
    "    g_ans = np.array([\n",
    "        [0.19661193, 0.10499359],\n",
    "        [0.19661193, 0.10499359]])\n",
    "    assert np.allclose(g, g_ans, rtol=1e-05, atol=1e-06)\n",
    "    print(\"You should verify these results by hand!\\n\")\n",
    "\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    test_sigmoid_basic();"
   ]
  }
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