PYG_learning/week6-PYG实现GraphConv,GATConv,SAGEConv.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7a7be480-c1f3-47b4-bf94-bebc1ccfa606",
   "metadata": {
    "id": "YqM5Z7qKUgqS"
   },
   "source": [
    "In this week, you are required to implement a toy GATConv and SAGEConv based on document. Also, you need to implement both in PyG and DGL. In this work, you will get a further understanding of tensor-centric in PyG and graph-centric in DGL.."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "329fcfd6-bb73-464e-9b98-7cf9c49f7981",
   "metadata": {
    "id": "xeuAiMpRU719"
   },
   "source": [
    "## PYG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "510185d1-3a07-4f38-8d67-50f7ec1636af",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "\n",
    "os.environ[\"KMP_DUPLICATE_LIB_OK\"] = \"TRUE\"\n",
    "\n",
    "from torch_geometric.data import Data\n",
    "from torch_geometric.nn import MessagePassing\n",
    "from torch_geometric.utils import add_self_loops, degree, remove_self_loops\n",
    "from torch_geometric.utils import softmax as edge_softmax\n",
    "from torch_geometric.utils import to_networkx\n",
    "from torch_scatter import scatter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ee5efc29-71de-49e5-8976-1140e1565c1f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data(x=[6, 4], edge_index=[2, 8], edge_attr=[8])\n"
     ]
    },
    {
     "data": {
      "image/png": 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mAjwVcJU3/qrdunULXl5eZp2sVaPW4kZZDTRaAd8rc+Hu4YXhw4d3uJzORAFHEBfigyTVzQ5vVjYFB4bHA3sDAB4+fIjQ0FCMGjUKx48fh0Qiafd+w/l4g+Cx8HM8teWUPh9viK/hOaS9oARUgoLiKjyz7ZTVyq//Zi1Wv/5H3L9/H5s2bYIgCPqscENMycdr0vR9bJAXNk4Og7+Hwho/higo4AgAYO5uFTKul4nay0l4DqP6KNDzpyTs2bMHgvDrSiXP8zh16hTGjx/f6r7m+XgdaY+E5yDlOayfFIqZkQGi/Axio4AjABp7lIlbT0It4vK9XMojbdkE+HsosGDBAnz++edo+nXjOA5+fn64dOkSPDw89PfsSC8wOUXImJXxwVgSZ38bmingiN5X2UVY/a14u/s/nBKGGZEBuHfvHgYNGgS1Wt3qmjFjxiA7OxscxxmsX33vGmpyj6G+KBfaR8XgXXpA3jcEvZ6YCycPw29QbarfntBOE6I3MzIAK+ODRSlrVXyI/pf9ypUr0Gg0bV6Xk5ODn3/+2Wg+XqXyIGqvZsB5QDh6T1wIt/Dfof7WJdz7fCk0D24YbIMt8vE6ino40oqlc6iESaGtepbq6mo0NDRAp9NBEAT9/5dKpfD19TU6h6y/fQXyPkHgJE76zxrK7+Du7iVwHToeXi+sNNiecYGeSFoQZfLPYG30WIC0MjMyAOMHe+lXCSHoAN7wEn7TKuG4QE+Dq4TGDvhpysczxLn/sFafOXn0g8wrAA2ltwze1zwfL8jHPh4Z0JCStMnfQ4GkBVH41x/DUHUuBR5OWvw2Y44DMMBTgblRA5C27AkkLYgya0ne1Hy85hhj0NVWgFf0MHqdNfPxzEE9HDHqWvYplKftQl7SOrj39tLv9JBJeQz0dNXvILGEqfl4zdXknYCuqgy9Hn/J6HVN+XjrEGpJE0VDAUeMSklJwZgxY+Dn5wcACO3bsVy49piaj9dcQ9ktlKf+X8j7DYVr2NPtXt+UjyfGHwdL0ZCSGKTVanH06FE899xzVqvD1Hy8Jrrqhyg5sB683BVeL74Dzsjcsom18vHM0fkhT+yWSqXCw4cP8fzzz1utjo7kyQn1NSj+13sQ6mvgO+dDSN09rVKPNVEPRwxKTk6Gt7e3Vc/sNzVPjmk1KDmYAO3DO/D5w7uQeXXsgbbY+Xjmso9WELuUnJyMZ5991qpH0DXl4xnDBB0eHP4Q6rv58H5xNeT9Wj8mMMYa+XjmoiEladPt27dx8eJFrFmzxqr1mJKP9/D4btQVquASNBa6umpUX0pv8b3bCOOvqGqej9fZ7KMVxO6kpKRAIpEgPj7e6nW1l4+nKb4OAKgrzEJdYVar740FnITnEBfsI05DRUBbu0ibXnzxRZSXl+PUKevlyTWxdj5e2rInaKcJsV9qtRppaWlWXZ1s0tDQAGdNBWKDvDq826Q9Ep5DbJCX3QQbQENK0oaTJ0+ipqZG9Odvly9fxvnz53HlyhVcvnwZFy5cwPXr18EYw3fHM5B1w3hmd0dJeQ4bJ4eJVp4YKOBIKykpKfD398eIEeK9xzQ/Px+hoY3bq6RSKQRB0GeA+/r64rkJUah2uy1qPl7CpFC7O26BhpSkleTkZDz33HPgOPGGeMHBwZgwYQIkEgm0Wm2L4xb++c9/gud5jPXU4nl/nSj1Nc/HsycUcKSFgoICFBYWij5/43ken3zySYsglkgkiIyMRHh4OF5//XUEBQXhn0un4oMpYZBL+Q7P6SQ8B7mUx4dTwvBGnPF313UWGlKSFpKTkyGXy/HUU0+JWu7x48cxd+5cODs7o7q6GgCg0+ng4eGBwYMHQxAEMMYwfPjwVvl4pp7aZSwfz15QD0daSElJwZNPPglXV3F2Zmg0GqxevRoTJ07E0KFDkZ+fj4ULfz0S/dixY9DpdGCMged5/XO/pny81D8/gblRAzDAU2G1fDybYoT8oqqqislkMrZ9+3ZRyrt27RqLiIhgUqmUffTRR0yn0zHGGKuurmZ9+vRhaNzI3+L/9u/fb7C86voGdulOBTt3s5xdulPBqusbRGmnLVHAEb1Dhw4xAKywsNCicgRBYJ999hlzdXVlQ4YMYdnZ2a2uUavVbPHixa0C7tq1axbVbe9oSEn0UlJSEBISgsGDB5tdRkVFBWbOnIn58+djxowZOHfuHCIiIlpdJ5PJoNFo4OTkBJlMBgBwdXW1qO4uobMjntgHQRBYv3792LJly8wu49SpUywgIID17NmTff3110av/fTTTxkAtmfPHnbp0iUWGBjInn/+ebPr7ioo4AhjjLHz588zACwtLa3D9zY0NLB3332X8TzPYmNj2c2bN41ef/bsWSaXy9miRYv0n2m1WlZfX9/hursaCjjCGGPs/fffZ25ubkytVnfovuvXr7OYmBgmkUhYQkIC02q1Rq8vKytjAwcOZBEREayurs6SJndJ9ByOAGh8/vbMM8/o51Om2LdvH1577TV4eHjg9OnTiIkx/p44QRAwZ84cVFZW4sSJE3B2dra02V1PZ0c86XylpaWM53mWmJho0vWPHj1ic+fOZQDY7NmzWUVFhUn3rV+/nnEcx44ePWpJc7s0CjjCvvzySwaA3blzp91rlUolCwwMZO7u7iwpKcnkOo4ePco4jmPr16+3pKldHgUcYS+99BIbNWqU0Wu0Wi3bsGEDk0gkLCoqqkPP6m7cuME8PDzY73//e/3D7+6KAq6b02q1zNPTk61du9bgNUVFReyJJ55gHMextWvXMo1GY3L59fX1LCIigg0YMICVlZWJ0eQujRZNujmVSoWysjKD2QEHDx7EwoUL4erqivT0dEyYMKFD5S9duhS5ubk4c+ZMixcvdludHfGkc61du5Z5enq2Ws6vrq5mCxYsYADYtGnTWHl5eYfL3rNnDwPAPv30U7Ga2+VRwDkQczb3jhw5kr300kstPsvJyWHBwcFMoVCwxMREJghCh9ty/vx55uzszObNm2fW/Y6KTu3q4gqKq/ClqgjpV0tQVF7b4px+DkCAhwJxIT54KSoAQ3xbHqZz584d9O/fH/v27cOsWbMgCAK2bNmCNWvWICwsDPv27UNISEiH21RRUYGIiAi4u7sjIyMDLi4ulv2QDoQCrou6VV7b4QTN2CCvFgmaiYmJWLRoEUpKSqDRaPDyyy8jLS0Nq1atwoYNGzr0ELyJIAiYPHkyTp06hZycHAQGBpr9MzoiWjTpgpq/EhhAuyddNX2fcb0ME7eexPpJoZgZGYDk5GTExMQgIyMD8+fPh5OTE1JTUzFx4kSz2/bRRx/hyJEj+O677yjY2kA9XBezI70Am3+8ZnE5f35qMP46JRKhoaFQqVR44YUXsHv3bnh7e5td5rFjxxAfH4933nkHGzZssLiNjogCrgv5KrvI4DFygqYOlapvob57FZp71yDUV8PzuT/D7THDvVVZyj+gyT+Jbdu2YfHixRad0nX79m2MHj0a4eHhOHr0KCSS9t/b1h1RAmoXcau8Fu8dyTP4vVBbiUdn9qOh7BacfAa1XyBj8HhmMZJPKvHaa69ZFGwajQZ/+MMf4OzsjH379lGwGUFzuC5izaFc/ZytLRI3D/RfkgSJW2+o7xXg/hfLjBfIceClTvgiT4OJ0Za1beXKlcjJycHp06ctGpJ2B9TDdQEFxVU4XVhqdHGEkzpB4ta7Q+UyjsfpwlIUllSZ3bb9+/fjk08+wbZt2xAVFWV2Od0FBVwX8KWqSPQXXTSR8Bz2KovMujcvLw+vvvoq5syZg9dee03kljkmCrguIP1qiagvuWhOJzCkXyvp8H2VlZWYOnUqAgMDsXPnTlGPRXdkNIezc9VqLYqMvB1UDEVltahRa01+SyhjDPPnz8fdu3dx9uxZ0Q6N7Q6oh7NzN8tqYO3nNgzAjbIak6/fsmULvvnmG3zxxRcIDg62XsMcEAWcndNohfYvsmE9p06dwl/+8he8/fbbmDx5spVb5XhoSGkHVqxYgby8PDz11FOIi4vDqFGjIJU2/qeRSW3zN9GUeu7du4cZM2YgNjYW77//vg1a5Xgo4OzAxYsXkZaWhtTUVAiCAFdXV8TExGDw4MF4a/kqcIBVh5UcgIGexudhDQ0NmD59OjiOw1dffaX/g0A6hv7V7EB0dDTS09Oh0zW+jLCmpgZpaWlIS0tDVVUVAka+ipsmLJxU5nwHob4GuupyAEBdYRa0VaUAgB5jXgDv3HZQBXgq2l0wWb16NZRKJU6cOAFfX9+O/HikGQq4TlBaWgqVSoXMzEwolUpkZGTog625efPmYdeuXXj/+2tIUt1s99FApeoQdJW/LvHXXssArmUAANxC49oMOAnPIS7Yx2i5Bw8exJYtW7Bt2zaMHz/elB+RGECbl61Mq9UiNzdXH1xKpRIFBQUAAG9vb8TExCA8PBx/+9vfADS+FZTneXz22WeYM2cOgMadJs9sO2W1NqYtewJBPu5tfpefn4/IyEg8//zz2L9/Pz1vsxAFnMju37+vD6zMzEycPXsWtbW1kEqlGDlyJKKjoxETE4Po6GgMGjRI/wscFBSE//znP/Dz88N3333X6o0zc3erkHG9TNQH4BKew7hATyQtaHtLVnV1NaKiosAYQ1ZWFtzc3ESru7uyScDVqLW4UVYDjVaATMpjoKeryQ9Z7ZlGo8H58+f1waVUKnHjxg0AQJ8+fRATE6MPrtGjR0OhMPx2zvXr1+P06dPYu3cv/Pz8Wn1/q7wWE7eehFrExwRyKY+0ZRPafGsoYwyzZ8/Gv//9b2RlZWHYsGGi1dudWS3gLDlrw17dvn27xdAwJycHarUaMpkMY8aMQXR0tL4H69+/v+jDL2P5cOb4cEoYZkQGtPnd9u3bsXTpUnz99deYPn26aHV2d6IHnBhnbdiD+vp65OTktBge3rlzBwAwYMCAFkPDkSNHQi6X26RdYmV8r4oPwRtxQW1+l5GRgQkTJmDJkiXYunWrxXWRX4kacM3P2ujIXEPCc5DynP6sDVtjjOHGjRsthobnz59HQ0MDXFxcEBERoQ+u6Oho9OnTx+ZtbM7Sf+eESaEGe7bi4mKMHj0agYGBOH78OJycnMRqNoGIASfWX96V8cFYEjdEhBYZVlNTg7Nnz7YYHhYXFwNoXLxoPjQMCwuzy1+6jowkIOgAXtLuSEKr1SI+Ph6XL1/GuXPn0LdvXyu1vvsSJeAMzS3qb15E8f41bd7jN3cz5P2GtvmdsblFRzHGUFhY2CK4Ll68CJ1OBzc3N4wdO1bfe0VFRXW5jGX9XPlaCYrKWs+V+/WU4fKxg/jrzCexbMEso2WtXr0amzdvxrFjxzp8pDkxjcUBZ2z1rCng3Me8AFmflrvKXQJHQ6Lo2WaZxlbP2lNZWYmsrKwWw8Py8sadF0OHDtUHV0xMDIYPH+5Q528cP3UGqxI+ws5/JkLhLMNAT1d8tfcLLFy4ECUlJfD09DR47+HDhzF58mRs2rQJK1eutGGruxeL1+bbO2sDAOT+oXAd+rjJZWoFhjWHcg0+H2oiCALy8/NbBFdeXh4YY+jVqxeioqLw5ptvIiYmBmPHjkXv3h07gqArYYzhjUWvIj8/HxfTj2Dq1KlwlUuRnJyM6Ohoo8FWUFCAV155BVOmTMGKFSts2Orux6KAazprwxSCuhackxwc336PohOY/qyN5jsgysvLoVKp9ENDlUqFR48egeM4jBgxAuPGjcPy5csRHR2NkJAQ8Hz3yT767rvvkJ+fDwBYtmwZFi5ciKioKOTk5GDRokVgjLX5mKK2thZTp06Fr68vPv/8c9pJYmUWDSnXHckzusevaUjJyVzANHUAx0PuH4recfMh72N8YUTCc3h2sCsea/i1B7t69SoAwMvLq8XCRmRkJNzdu8azPGtQq9UYOnQobt68ieb/OTmO0//vPn36YMWKFS16MMYYXnnlFXzzzTdQqVQYMWKEzdve3VjUw7V71obECYqQcXAJjACv6ImG0iJUZh1C8Zd/gd+cTZD5DTZ4q05gOKy6hl2730B4eDgmTpyI//mf/0F0dDQGDx5Mf4mb+eSTT1oEG8/zYI1vRtJfc+/ePeTk5LS4b9euXUhKSsLevXsp2GzE7B6uWq1F2LofOpyn1fDwLu7tfhNy/1D4zkho9/rsv8TCu1cPc5rYLZSUlCAwMBA1NYaPSJBIJBg7dizS0tL028uysrIQGxuLP/3pT9ixY4etmtvtmT3JMfesDafefeEyJAr1RRfBhNYpKb9VUkt7q405d+6c0WDjeR5Dhw5FSkqKPthKS0sxbdo0jBo1Clu2bLFVUwksCDhLztqQ9vACdFqwBrVV6+kOnn32WZSUlODq1auIiYnBuHHjcPDgQX1Gdr9+/ZCWloZevXoBAHQ6HWbPno26ujocOHDArFdSEfOZPYez5KwNbcV9cFIZOJmzVevpLry9veHt7Q2O4zBkyBBMnToVXl5eKC8vx8mTJ1tkH6xbtw7Hjh3Djz/+CH9//05sdfdkdsAN9HRt96wNXe2jVg+3NcXXUVuQBZfAMeA448Fkylkb5Nf0pzpXXzj5DEKNWovU1FTIZDIMGvTriz2Sk5OxYcMGvP/++3j66ac7scXdl0WPBSZsSjd61sb9fWvAO8kg7zfsl1XKW6i+cBTgpegzdzOcvIz/hR3gqcDJlXHmNs+hdTT96fr16xgzZgxiY2Nx+PDhbvWM0p5Y9Tlc5dkjqMk7Ae3DexA0tZAoesJ5QDh6Pj4LTr2Nb4yV8BzmRg3Aukmh5jbPIZmT/vR4kCdyP1uD6vs3kZOTo5/PEduzKOA686yN7sj8tBxA0GrxepQ3Vk0ZZ8UWkvZYNK4Y4uuO2CAv0d/sIuE5xAZ5UbA1syO9AKu/zYVaK3T4XBOdADBeiv+T/RA70gus1EJiCqtmC5jLkmwBR2TsaAWmbUDF6b2oyUuHUF8NJ++B6PXEXLgMGmWwPDHTn0jHWDxz9vdQYL3I86yESaEUbL9o71XDpclbUZl9GK7Dn0TviQvB8TxKDqxD/S3D97x7JA+3rPxGHtI2UZaqZkYGYGW8OG9RWRUfQn99mzGW/qS+exW1V06h14RX0Pup+XAf+Sx8Z22EtIcPKk58brDMpvQnYnuirQ0viRuCD6aEQS7lOzynk/Ac5FIeH04JM3iwTXfU3quGa6+eATge7iOf1X/GSWVwC38G6jv50FY+aPO+5ulPxLZEfRgzMzIAacsmYFxgY7Jje4HX9P24QE+kLZtAPdtvtPeqYU3xdTh59AMvbzn8bsqu1xRfN3ivJa8aJuYT/TRWfw8FkhZEtXvWRoCnAnHBPpgTHUCrkQa0l/6kqy6HxK11FrvEzUP/vcF7f3nV8DrQc05bstrxx0N83bFuUijWIdRhT162JlNeNcy0GkDS+kQxTir79XsjOvqqYWI5m/xLu8qlCO3b9oFBpG2mpD9xUhmga2j1eVOgNQWeIU2vGqb/NrZDG+rslClpSRI3D+iqH7b6vGko2TS0tLQeIh4KODtlSlqSzCcQDeV3IKhbDj01dxsP5JX5BopSDxEP/Wvbqab0J2MUQ8cDTEDV+aP6z5i2AdW5qZD1DYG0h/FDbSn9yfZotmynXOVSBHgojKY/yfuGQDH0cVSc/AJCbQWkvfuiJvcYtI9K4Pv7pe3WYcqrhom4qIezY3EhPu0+y/T6r+XoEfHfqLmUjvLUXWCCFj7T3oVzgPFTuEx51TARH70B1Y5R+pPjoR7OjlH6k+OhgLNzGyeHQSpywEl5Dhsnh4laJjENBZydo/Qnx0IB1wVQ+pPjoEWTLsSarxomtkEB18WYc2pXe68aJrZDAddFUfpT10QB5wAo/anroIAjxIZolZIQG6KAI8SGKOAIsSEKOEJsiAKOEBuigCPEhijgCLEhCjhCbIgCjhAbooAjxIYo4AixIQo4Qmzo/wNUZaP+dWk3VgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 定义图\n",
    "edge_index = torch.LongTensor(\n",
    "    [\n",
    "        [0, 0, 1, 2, 4, 4, 4, 5],\n",
    "        [1, 2, 2, 3, 0, 2, 3, 1],\n",
    "    ]\n",
    ")\n",
    "feat = torch.FloatTensor(\n",
    "    [\n",
    "        [0, 0, 0, 0],\n",
    "        [1, 1, 1, 1],\n",
    "        [2, 2, 2, 2],\n",
    "        [3, 3, 3, 3],\n",
    "        [4, 4, 4, 4],\n",
    "        [5, 5, 5, 5],\n",
    "    ]\n",
    ")\n",
    "data = Data(x=feat, edge_index=edge_index)\n",
    "edge_attr = torch.ones(data.num_edges) * 2\n",
    "data.edge_attr = edge_attr\n",
    "\n",
    "in_feats = data.num_features\n",
    "out_feats = 3\n",
    "\n",
    "print(data)\n",
    "nxg = to_networkx(data)\n",
    "plt.figure(figsize=(2, 2))\n",
    "nx.draw(nxg, pos=nx.spring_layout(nxg), with_labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f978247f-ee48-4cc9-b37d-bf29f094ab94",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "06d41b64-0ae3-4157-abe3-f7d55f6a86de",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "attachments": {
    "a41a4576-7867-4e6b-9fd3-91bd34fcb681.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "11031ed5-7c1f-4bb9-a777-aa95d97935ad",
   "metadata": {},
   "source": [
    "### GraphConv(GCNConv)\n",
    "\n",
    "![image.png](attachment:a41a4576-7867-4e6b-9fd3-91bd34fcb681.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "5f579de8-8ed6-4b3a-ad92-f77c34626866",
   "metadata": {},
   "outputs": [],
   "source": [
    "class PyG_GraphConv(MessagePassing):\n",
    "    def __init__(self, in_feats, out_feats):\n",
    "        super(PyG_GraphConv, self).__init__(aggr=\"add\")\n",
    "        self.w = nn.Linear(in_feats, out_feats, bias=False)\n",
    "        self.reset_parameters()\n",
    "\n",
    "    def reset_parameters(self):\n",
    "        torch.nn.init.ones_(self.w.weight)\n",
    "\n",
    "    def forward(self, x, edge_index, edge_attr):\n",
    "        edge_index, edge_attr = remove_self_loops(edge_index, edge_attr)\n",
    "        edge_index, edge_attr = add_self_loops(edge_index, edge_attr)\n",
    "\n",
    "        out_deg = degree(edge_index[0], num_nodes=x.shape[0]).view(-1, 1).pow(-0.5)\n",
    "        in_deg = degree(edge_index[1], num_nodes=x.shape[0]).view(-1, 1).pow(-0.5)\n",
    "\n",
    "        out = self.propagate(\n",
    "            edge_index, x=x, edge_attr=edge_attr, in_deg=in_deg, out_deg=out_deg\n",
    "        )\n",
    "        return self.w(out)\n",
    "\n",
    "    def message(self, x_j, edge_index, edge_attr, out_deg_j, in_deg_i):\n",
    "\n",
    "        norm = out_deg_j * in_deg_i\n",
    "        edge_attr = edge_attr.view(-1, 1)\n",
    "\n",
    "        return norm * edge_attr * x_j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "98fcffdb-58d4-4c20-9415-3325931d0664",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[11.3137, 11.3137, 11.3137],\n",
      "        [17.9629, 17.9629, 17.9629],\n",
      "        [13.6569, 13.6569, 13.6569],\n",
      "        [22.6978, 22.6978, 22.6978],\n",
      "        [ 8.0000,  8.0000,  8.0000],\n",
      "        [14.1421, 14.1421, 14.1421]])\n"
     ]
    }
   ],
   "source": [
    "my_graphconv = PyG_GraphConv(in_feats, out_feats)\n",
    "with torch.no_grad():\n",
    "    out = my_graphconv(data.x, data.edge_index, data.edge_attr)\n",
    "    print(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2a5d2058-692e-46cb-9bf8-b53bdfba3096",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4b7c083e-f5f5-4641-8859-76c5e09bdf9f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "29e8dfcf-085f-489a-bb4f-7610b2d1dd70",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[18.4752, 18.4752, 18.4752],\n",
      "        [18.6885, 18.6885, 18.6885],\n",
      "        [14.5900, 14.5900, 14.5900],\n",
      "        [19.4153, 19.4153, 19.4153],\n",
      "        [16.0000, 16.0000, 16.0000],\n",
      "        [20.0000, 20.0000, 20.0000]])\n"
     ]
    }
   ],
   "source": [
    "from torch_geometric.nn import GCNConv\n",
    "\n",
    "gcnconv = GCNConv(in_feats, out_feats, bias=False, normalize=True, add_self_loops=True)\n",
    "torch.nn.init.ones_(gcnconv.lin.weight)\n",
    "with torch.no_grad():\n",
    "    out = gcnconv(data.x, data.edge_index, data.edge_attr)\n",
    "    print(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "11ca07a3-948e-4e71-8ea3-aee75ae3e086",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "36140e7d-1315-47d2-a0fb-df98f023258a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d112a4ed-9b0c-4043-96b9-d2b90f03729e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6742ad5c-1a6f-4c1e-b791-4b6caea680d6",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "36b1cdd1-6ca1-45b3-90de-a071383efb65",
   "metadata": {},
   "source": [
    "### GATConv\n",
    "$$\n",
    "        \\mathbf{x}^{\\prime}_i = \\alpha_{i,i}\\mathbf{\\Theta}_{s}\\mathbf{x}_{i} +\n",
    "        \\sum_{j \\in \\mathcal{N}(i)}\n",
    "        \\alpha_{i,j}\\mathbf{\\Theta}_{t}\\mathbf{x}_{j},\n",
    "$$\n",
    "    where the attention coefficients $\\alpha_{i,j}$ are computed as\n",
    "\n",
    "$$\n",
    "        \\alpha_{i,j} =\n",
    "        \\frac{\n",
    "        \\exp\\left(\\mathrm{LeakyReLU}\\left(\n",
    "        \\mathbf{a}^{\\top}_{s} \\mathbf{\\Theta}_{s}\\mathbf{x}_i\n",
    "        + \\mathbf{a}^{\\top}_{t} \\mathbf{\\Theta}_{t}\\mathbf{x}_j\n",
    "        \\right)\\right)}\n",
    "        {\\sum_{k \\in \\mathcal{N}(i) \\cup \\{ i \\}}\n",
    "        \\exp\\left(\\mathrm{LeakyReLU}\\left(\n",
    "        \\mathbf{a}^{\\top}_{s} \\mathbf{\\Theta}_{s}\\mathbf{x}_i\n",
    "        + \\mathbf{a}^{\\top}_{t}\\mathbf{\\Theta}_{t}\\mathbf{x}_k\n",
    "        \\right)\\right)}.\n",
    "$$\n",
    "    If the graph has multi-dimensional edge features $\\mathbf{e}_{i,j}$,\n",
    "    the attention coefficients $\\alpha_{i,j}$ are computed as\n",
    "\n",
    "$$\n",
    "        \\alpha_{i,j} =\n",
    "        \\frac{\n",
    "        \\exp\\left(\\mathrm{LeakyReLU}\\left(\n",
    "        \\mathbf{a}^{\\top}_{s} \\mathbf{\\Theta}_{s}\\mathbf{x}_i\n",
    "        + \\mathbf{a}^{\\top}_{t} \\mathbf{\\Theta}_{t}\\mathbf{x}_j\n",
    "        + \\mathbf{a}^{\\top}_{e} \\mathbf{\\Theta}_{e} \\mathbf{e}_{i,j}\n",
    "        \\right)\\right)}\n",
    "        {\\sum_{k \\in \\mathcal{N}(i) \\cup \\{ i \\}}\n",
    "        \\exp\\left(\\mathrm{LeakyReLU}\\left(\n",
    "        \\mathbf{a}^{\\top}_{s} \\mathbf{\\Theta}_{s}\\mathbf{x}_i\n",
    "        + \\mathbf{a}^{\\top}_{t} \\mathbf{\\Theta}_{t}\\mathbf{x}_k\n",
    "        + \\mathbf{a}^{\\top}_{e} \\mathbf{\\Theta}_{e} \\mathbf{e}_{i,k}\n",
    "        \\right)\\right)}.\n",
    "$$\n",
    "    If the graph is not bipartite, $\\mathbf{\\Theta}_{s} =\n",
    "    \\mathbf{\\Theta}_{t}$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4e948b15-9e4c-46f0-93b7-de2cb2ab3b84",
   "metadata": {
    "id": "mclJkxgsUbRY"
   },
   "outputs": [],
   "source": [
    "class PyG_GATConv(MessagePassing):\n",
    "    def __init__(self, in_feats, out_feats, edge_dim):\n",
    "        super(PyG_GATConv, self).__init__()\n",
    "        self.w_node = nn.Linear(in_feats, out_feats, bias=False)\n",
    "        self.w_edge = nn.Linear(edge_dim, out_feats, bias=False)\n",
    "\n",
    "        self.a_self = nn.Linear(out_feats, 1, bias=False)\n",
    "        self.a_neih = nn.Linear(out_feats, 1, bias=False)\n",
    "        self.a_edge = nn.Linear(out_feats, 1, bias=False)\n",
    "        self.edge_dim = edge_dim\n",
    "\n",
    "        self.reset_parameters()\n",
    "\n",
    "    def reset_parameters(self):\n",
    "        torch.nn.init.ones_(self.w_node.weight)\n",
    "        torch.nn.init.ones_(self.w_edge.weight)\n",
    "        torch.nn.init.ones_(self.a_self.weight)\n",
    "        torch.nn.init.ones_(self.a_neih.weight)\n",
    "        torch.nn.init.ones_(self.a_edge.weight)\n",
    "\n",
    "    def forward(self, x, edge_index, edge_attr, get_attention=False):\n",
    "        edge_index, edge_attr = remove_self_loops(edge_index, edge_attr)\n",
    "        edge_index, edge_attr = add_self_loops(\n",
    "            edge_index, edge_attr, num_nodes=x.shape[0], fill_value=\"mean\"\n",
    "        )\n",
    "\n",
    "        edge_attr = edge_attr.view(-1, self.edge_dim)\n",
    "\n",
    "        wx = self.w_node(x)\n",
    "        we = self.w_edge(edge_attr)\n",
    "        alpha = self.edge_updater(edge_index, we=we, wx=wx)\n",
    "        out = self.propagate(edge_index, wx=wx, alpha=alpha)\n",
    "\n",
    "        if get_attention:\n",
    "            return out, alpha\n",
    "        else:\n",
    "            return out\n",
    "\n",
    "    def message(self, wx_j, alpha):\n",
    "        return alpha * wx_j\n",
    "\n",
    "    def edge_update(self, edge_index, wx_i, wx_j, we):\n",
    "        e = self.a_neih(wx_j) + self.a_self(wx_i) + self.a_edge(we)\n",
    "        e = F.leaky_relu(e)\n",
    "        alpha = edge_softmax(e, edge_index[1])\n",
    "        return alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ad70ebd5-765b-4629-a833-d110afe8e840",
   "metadata": {},
   "outputs": [],
   "source": [
    "my_gatconv = PyG_GATConv(in_feats, out_feats, edge_dim=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "fd703148-e604-4492-82f9-e6ec250912c4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[16.0000, 16.0000, 16.0000],\n",
      "        [20.0000, 20.0000, 20.0000],\n",
      "        [16.0000, 16.0000, 16.0000],\n",
      "        [16.0000, 16.0000, 16.0000],\n",
      "        [16.0000, 16.0000, 16.0000],\n",
      "        [20.0000, 20.0000, 20.0000]])\n",
      "tensor([[8.7565e-27],\n",
      "        [1.4252e-21],\n",
      "        [2.3195e-16],\n",
      "        [3.7751e-11],\n",
      "        [1.0000e+00],\n",
      "        [1.0000e+00],\n",
      "        [9.9999e-01],\n",
      "        [1.0000e+00],\n",
      "        [1.4252e-21],\n",
      "        [1.4252e-21],\n",
      "        [3.7751e-11],\n",
      "        [6.1442e-06],\n",
      "        [1.0000e+00],\n",
      "        [1.0000e+00]])\n"
     ]
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    out, attention = my_gatconv(\n",
    "        data.x, data.edge_index, data.edge_attr, get_attention=True\n",
    "    )\n",
    "    print(out)\n",
    "    print(attention)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c85f396-9f0e-4605-8eb9-ea0baf52b539",
   "metadata": {},
   "source": [
    "#### 对比"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "01cb413f-9952-47f7-acce-09862ac56841",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[16.0000, 16.0000, 16.0000],\n",
      "        [20.0000, 20.0000, 20.0000],\n",
      "        [16.0000, 16.0000, 16.0000],\n",
      "        [16.0000, 16.0000, 16.0000],\n",
      "        [16.0000, 16.0000, 16.0000],\n",
      "        [20.0000, 20.0000, 20.0000]])\n",
      "tensor([[8.7565e-27],\n",
      "        [1.4252e-21],\n",
      "        [2.3195e-16],\n",
      "        [3.7751e-11],\n",
      "        [1.0000e+00],\n",
      "        [1.0000e+00],\n",
      "        [9.9999e-01],\n",
      "        [1.0000e+00],\n",
      "        [1.4252e-21],\n",
      "        [1.4252e-21],\n",
      "        [3.7751e-11],\n",
      "        [6.1442e-06],\n",
      "        [1.0000e+00],\n",
      "        [1.0000e+00]])\n"
     ]
    }
   ],
   "source": [
    "from torch_geometric.nn import GATConv\n",
    "\n",
    "gat = GATConv(in_feats, out_feats, edge_dim=1, bias=False)\n",
    "\n",
    "torch.nn.init.ones_(gat.lin.weight)\n",
    "torch.nn.init.ones_(gat.lin_edge.weight)\n",
    "torch.nn.init.ones_(gat.att_dst.data)\n",
    "torch.nn.init.ones_(gat.att_edge.data)\n",
    "torch.nn.init.ones_(gat.att_src.data)\n",
    "\n",
    "with torch.no_grad():\n",
    "    out, attention = gat(\n",
    "        data.x, data.edge_index, edge_attr=data.edge_attr, return_attention_weights=True\n",
    "    )\n",
    "    print(out)\n",
    "    print(attention[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "5eef8e4f-8771-47ad-8d17-c0aaa8a09241",
   "metadata": {},
   "outputs": [],
   "source": [
    "# tensor([[16.0000, 16.0000, 16.0000],\n",
    "#         [20.0000, 20.0000, 20.0000],\n",
    "#         [16.0000, 16.0000, 16.0000],\n",
    "#         [16.0000, 16.0000, 16.0000],\n",
    "#         [16.0000, 16.0000, 16.0000],\n",
    "#         [20.0000, 20.0000, 20.0000]])\n",
    "# tensor([[8.7565e-27],\n",
    "#         [1.4252e-21],\n",
    "#         [2.3195e-16],\n",
    "#         [3.7751e-11],\n",
    "#         [1.0000e+00],\n",
    "#         [1.0000e+00],\n",
    "#         [9.9999e-01],\n",
    "#         [1.0000e+00],\n",
    "#         [1.4252e-21],\n",
    "#         [1.4252e-21],\n",
    "#         [3.7751e-11],\n",
    "#         [6.1442e-06],\n",
    "#         [1.0000e+00],\n",
    "#         [1.0000e+00]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8a744d05-b829-4f68-a7f3-254d4846683e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "71cdd66a-b80e-4c08-b1ea-d36b9cea6c12",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "703454b0-8f39-4016-9be9-d52dada76735",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "294ba3a6-c31f-4ea1-a15f-94103f7d7825",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2b5a55f2-6cd8-4f01-95c1-dab7ec42353a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bff895e1-7c13-46db-a253-f737197fdd1c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a7c79a1d-5397-4940-addb-5c82bd0bb4b1",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "50395eed-8adf-4a3a-b807-9c55642da846",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dd4fa6f5-9e00-4999-83d0-ec696e0a9117",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6fd79b88-3ad9-4ed3-9d96-73b1f1c4c428",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "be633001-0c31-47df-a2c5-aebce2947c33",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "93d03002-9659-4524-86e8-e2f579ea98f3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "d0625720-2811-4a95-820e-c4c028ac2388",
   "metadata": {},
   "source": [
    "### SAGEConv\n",
    "$$\n",
    "\\begin{align}\\begin{aligned}\n",
    "h_{\\mathcal{N}(i)}^{(l+1)} &= \\mathrm{aggregate}\\left(\\{h_{j}^{l}, \\forall j \\in \\mathcal{N}(i) \\}\\right)\\\\\\\\\n",
    "h_{i}^{(l+1)} &= \\sigma \\left(W \\cdot \\mathrm{concat}(h_{i}^{l}, h_{\\mathcal{N}(i)}^{l+1}) \\right)\\\\\\\\\n",
    "h_{i}^{(l+1)} &= \\mathrm{norm}(h_{i}^{(l+1)})\\\\\\\\\n",
    "\\mathrm{norm}(v) &= \\frac{v}{\\max(\\lVert v \\rVert_p,\\epsilon)}\n",
    "\\end{aligned}\\end{align}\n",
    "$$\n",
    "\n",
    "If a weight tensor on each edge is provided, the aggregation becomes:\n",
    "$$\n",
    "h_{\\mathcal{N}(i)}^{(l+1)} = \\mathrm{aggregate}\n",
    "\\left(\\{e_{ji} h_{j}^{l}, \\forall j \\in \\mathcal{N}(i) \\}\\right)\n",
    "$$\n",
    "where $e_{ji}$ is the scalar weight on the edge from node $j$ to node $i$.\n",
    "    Please make sure that $e_{ji}$ is broadcastable with $h_j^{l}$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "8399ad00-b6e9-49e3-b2c4-fee160f7e2d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "class PyG_SAGEConv(MessagePassing):\n",
    "    def __init__(self, in_feats, out_feats):\n",
    "        super(PyG_SAGEConv, self).__init__(aggr=\"mean\")\n",
    "        self.W = nn.Linear(2 * in_feats, out_feats, bias=False)\n",
    "\n",
    "        self.reset_parameters()\n",
    "\n",
    "    def reset_parameters(self):\n",
    "        nn.init.ones_(self.W.weight)\n",
    "\n",
    "    def forward(self, x, edge_index):\n",
    "        hN = self.propagate(edge_index, x=x)\n",
    "        h_cat = torch.cat([x, hN], dim=1)\n",
    "\n",
    "        h = self.W(h_cat)\n",
    "        h = F.normalize(h, dim=1)\n",
    "        return h\n",
    "\n",
    "    def message(self, x_j, edge_index):\n",
    "        return x_j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "1c79b384-caa0-4acb-b5aa-a9344d182961",
   "metadata": {},
   "outputs": [],
   "source": [
    "my_sage = PyG_SAGEConv(in_feats, out_feats)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "63ab02cd-8e86-41fd-ba05-f4b2dac10e79",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[0.5774, 0.5774, 0.5774],\n",
      "        [0.5774, 0.5774, 0.5774],\n",
      "        [0.5774, 0.5774, 0.5774],\n",
      "        [0.5774, 0.5774, 0.5774],\n",
      "        [0.5774, 0.5774, 0.5774],\n",
      "        [0.5774, 0.5774, 0.5774]])\n"
     ]
    }
   ],
   "source": [
    "with torch.no_grad():\n",
    "    out = my_sage(data.x, data.edge_index)\n",
    "    print(out)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4571f9b6-6b25-467b-8efe-11dd64eb14a3",
   "metadata": {},
   "source": [
    "#### 对比"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "d4e1a541-f858-4ca4-8bd0-bc3f469f604f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[0.5774, 0.5774, 0.5774],\n",
      "        [0.5774, 0.5774, 0.5774],\n",
      "        [0.5774, 0.5774, 0.5774],\n",
      "        [0.5774, 0.5774, 0.5774],\n",
      "        [0.5774, 0.5774, 0.5774],\n",
      "        [0.5774, 0.5774, 0.5774]])\n"
     ]
    }
   ],
   "source": [
    "from torch_geometric.nn import SAGEConv\n",
    "\n",
    "sage = SAGEConv(in_feats, out_feats, aggr=\"mean\", normalize=True, bias=False)\n",
    "nn.init.ones_(sage.lin_l.weight)\n",
    "nn.init.ones_(sage.lin_r.weight)\n",
    "\n",
    "with torch.no_grad():\n",
    "    out = sage(data.x, data.edge_index)\n",
    "    print(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6e5e7dac-5518-43a0-a241-5bf60a6f7079",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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