Exchange_money_DGL.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6fbe6c39-8c82-40a3-b9f6-0ffad3bcbd69",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "eb485a6b-4ac5-481d-9698-065078a1153d",
   "metadata": {},
   "outputs": [],
   "source": [
    "os.environ[\"DGLBACKEND\"] = \"pytorch\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4afb538b-7c04-47cc-b18f-1005f1c69307",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch \n",
    "import pandas as pd\n",
    "import dgl\n",
    "from dgl.data import DGLDataset\n",
    "import dgl.function as fn\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2993410a-471e-43de-a127-9cdb4d5010d3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Done loading data from cached files.\n"
     ]
    }
   ],
   "source": [
    "ds = dgl.data.CSVDataset('./DGL_playground/toy_dataset/')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d0caa888-26ee-4d09-87ff-ca5e9bbe80d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "g = ds[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "cd74092f-5caa-4cd9-966c-8e81ef278bdb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Graph(num_nodes=10, num_edges=20,\n",
      "      ndata_schemes={' na2': Scheme(shape=(), dtype=torch.int64), ' na1': Scheme(shape=(), dtype=torch.int64)}\n",
      "      edata_schemes={'ea2': Scheme(shape=(), dtype=torch.int64), 'ea1': Scheme(shape=(), dtype=torch.int64), 'w': Scheme(shape=(), dtype=torch.int64)})\n"
     ]
    }
   ],
   "source": [
    "print(g)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "d45b3df4",
   "metadata": {},
   "source": [
    "### Define Weights\n",
    "\n",
    "The weights need to be constant along any bi-directed edge. DGL does not provide a function to ensure this happens. Currently a for loop is being used to ensure identical weights along edges - a better solution needs to be found to ensure scalability of the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7a85ae11-826b-464e-8a7f-4bd367ad2db4",
   "metadata": {},
   "outputs": [],
   "source": [
    "g.edata['w'] = torch.rand(g.num_edges(),1)\n",
    "# g.edata['w']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1a79e7ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0, 0, 0, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8]),\n",
       " tensor([1, 2, 3, 0, 2, 0, 1, 0, 4, 5, 3, 5, 3, 4, 7, 8, 6, 8, 6, 7]),\n",
       " tensor([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,\n",
       "         18, 19]))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g.edges(\"all\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.1062],\n",
       "        [0.1417],\n",
       "        [0.7484],\n",
       "        [0.1062],\n",
       "        [0.2712],\n",
       "        [0.1417],\n",
       "        [0.2712],\n",
       "        [0.7484],\n",
       "        [0.4586],\n",
       "        [0.9633],\n",
       "        [0.4586],\n",
       "        [0.3179],\n",
       "        [0.9633],\n",
       "        [0.3179],\n",
       "        [0.6236],\n",
       "        [0.5601],\n",
       "        [0.6236],\n",
       "        [0.0011],\n",
       "        [0.5601],\n",
       "        [0.0011]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Obtain source, destination and edge ids for all edges\n",
    "[src, dst, eid] = g.edges(form = 'all')\n",
    "\n",
    "# Loop through edges to identify bi-directional edges to then assign same weights\n",
    "# This loop can be optimized but ideally needs to be replaced with an parallelisable function\n",
    "for i in eid:\n",
    "    for j in eid:\n",
    "        if (src[i] == dst[j] and dst[i] == src[j]): #For edges with same nodes\n",
    "            g.edata['w'][j] = g.edata['w'][i]\n",
    "            break\n",
    "g.edata['w']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d5359e8e",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Create wealth per node/agent in the network as a node feature/attribute\n",
    "g.ndata['k'] = torch.rand(g.num_nodes(),1)*1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "37bb7a8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Create savings propensity as a node features per agent\n",
    "g.ndata['lambda'] = torch.rand(g.num_nodes(),1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7534fd4f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Initialize some base node attributes (0s, and 1s)\n",
    "g.ndata['zeros'] = torch.zeros(g.num_nodes(),1)\n",
    "g.ndata['ones'] = torch.ones(g.num_nodes(),1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c4375e49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[3.],\n",
       "        [2.],\n",
       "        [2.],\n",
       "        [3.],\n",
       "        [2.],\n",
       "        [2.],\n",
       "        [2.],\n",
       "        [2.],\n",
       "        [2.],\n",
       "        [0.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Calculate number of neighbours (tot_nbr) each node has using built-in functions\n",
    "g.update_all(fn.u_add_v('zeros','ones','tot_nbr'), fn.sum('tot_nbr', 'tot_nbr'))\n",
    "g.ndata['tot_nbr']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bb03321",
   "metadata": {},
   "source": [
    "### Wealth Transfer Method 1: To all neighbours based on edge weights "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2.1111],\n",
       "        [1.7020],\n",
       "        [1.3924],\n",
       "        [1.2572],\n",
       "        [1.3032],\n",
       "        [1.2873],\n",
       "        [1.4322],\n",
       "        [0.9703],\n",
       "        [0.5404],\n",
       "        [0.0000]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Calculate total weight of all incoming (or outgoing, equivalent bidirectional graph) edges to each node\n",
    "g.ndata['tot_wgt'] = torch.zeros(g.num_nodes(),1)\n",
    "g.update_all(fn.u_add_e('tot_wgt','w','tot_wgt'), fn.sum('tot_wgt', 'tot_wgt'))\n",
    "g.ndata['tot_wgt']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ba23e1bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.4164],\n",
       "        [0.2698],\n",
       "        [0.3138],\n",
       "        [0.5165],\n",
       "        [0.4835],\n",
       "        [0.4090],\n",
       "        [0.5910],\n",
       "        [0.5270],\n",
       "        [0.2428],\n",
       "        [0.2302],\n",
       "        [0.2343],\n",
       "        [0.7657],\n",
       "        [0.2248],\n",
       "        [0.7752],\n",
       "        [0.6501],\n",
       "        [0.3499],\n",
       "        [0.9596],\n",
       "        [0.0404],\n",
       "        [0.9274],\n",
       "        [0.0726]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# e_div_u divides the edge feature by the feature of the source node for outgoing edges\n",
    "# However, u_add_e addes the features of edges with source node for incoming edges\n",
    "# Not sure if this discrepancy is intentional\n",
    "g.apply_edges(fn.e_div_u('w','tot_wgt','per_wgt'))\n",
    "g.edata['per_wgt']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "9fd3f8cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[218.4663],\n",
       "        [ 26.4017],\n",
       "        [ 91.8854],\n",
       "        [227.9832],\n",
       "        [ 17.4198],\n",
       "        [893.2269],\n",
       "        [216.5609],\n",
       "        [ 68.1918],\n",
       "        [146.3507],\n",
       "        [366.8424]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate disposable wealth depending on savings propensity (lambda) and wealth (k)\n",
    "g.ndata['disp_wealth'] = g.ndata['lambda']*g.ndata['k']\n",
    "g.ndata['disp_wealth']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b7c0870a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[ 90.9696],\n",
       "        [ 58.9324],\n",
       "        [ 68.5644],\n",
       "        [ 13.6364],\n",
       "        [ 12.7652],\n",
       "        [ 37.5808],\n",
       "        [ 54.3046],\n",
       "        [120.1447],\n",
       "        [ 55.3564],\n",
       "        [ 52.4822],\n",
       "        [  4.0806],\n",
       "        [ 13.3391],\n",
       "        [200.8192],\n",
       "        [692.4078],\n",
       "        [140.7790],\n",
       "        [ 75.7819],\n",
       "        [ 65.4344],\n",
       "        [  2.7574],\n",
       "        [135.7258],\n",
       "        [ 10.6249]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Calculate income to be transferred along an edge\n",
    "g.apply_edges(fn.e_mul_u('per_wgt','disp_wealth','trfr_wealth'))\n",
    "g.edata['trfr_wealth']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "fb3aa4a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[171.3618],\n",
       "        [145.2742],\n",
       "        [ 71.6976],\n",
       "        [273.4642],\n",
       "        [747.7642],\n",
       "        [ 65.8213],\n",
       "        [201.1602],\n",
       "        [151.4039],\n",
       "        [ 78.5393],\n",
       "        [  0.0000]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Message passing along edges to sum total income obtained from neighbours for each node/agent\n",
    "g.update_all(fn.v_add_e('zeros','trfr_wealth','delta_inc'), fn.sum('delta_inc', 'delta_inc'))\n",
    "g.ndata['delta_inc']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "815c3d42",
   "metadata": {},
   "source": [
    "### Wealth Transfer Method 2: To one random neighbour from list of neighbours"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b3ef1cc8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[ 65.7963],\n",
       "        [ 22.1956],\n",
       "        [211.9366],\n",
       "        [ 40.2728],\n",
       "        [ 97.5574],\n",
       "        [ 38.6332],\n",
       "        [  2.4555],\n",
       "        [174.4195],\n",
       "        [216.1678],\n",
       "        [842.2933]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate disposable wealth depending on savings propensity (lambda) and wealth (k)\n",
    "g.ndata['disp_wealth'] = g.ndata['lambda']*g.ndata['k']\n",
    "g.ndata['disp_wealth']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1134736b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Graph(num_nodes=10, num_edges=9,\n",
       "      ndata_schemes={' na2': Scheme(shape=(), dtype=torch.int64), ' na1': Scheme(shape=(), dtype=torch.int64), 'k': Scheme(shape=(1,), dtype=torch.float32), 'lambda': Scheme(shape=(1,), dtype=torch.float32), 'zeros': Scheme(shape=(1,), dtype=torch.float32), 'ones': Scheme(shape=(1,), dtype=torch.float32), 'tot_nbr': Scheme(shape=(1,), dtype=torch.float32), 'disp_wealth': Scheme(shape=(1,), dtype=torch.float32)}\n",
       "      edata_schemes={'ea2': Scheme(shape=(), dtype=torch.int64), 'ea1': Scheme(shape=(), dtype=torch.int64), 'w': Scheme(shape=(1,), dtype=torch.float32), '_ID': Scheme(shape=(), dtype=torch.int64)})"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Using dgl sample_neighbours function to create sub-graph with 1 edge for each node (i.e. choose a random edge for each node as needed for the Boltzmann wealth model)\n",
    "# Syntax:\n",
    "#   dgl.sampling.sample_neighbors(g, nodes, fanout, edge_dir='in', prob=None, replace=False, copy_ndata=True, copy_edata=True, _dist_training=False, exclude_edges=None, output_device=None)\n",
    "\n",
    "g_subset = dgl.sampling.sample_neighbors(g, g.nodes(), 1, edge_dir='out', copy_ndata = True) #copy_ndata ensures data from g is transferred to g_subset\n",
    "g_subset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "dfd9a7cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([234.1322,  65.7963,   0.0000, 136.1905,  40.2728,   0.0000,   0.0000,\n",
       "        216.1678, 176.8750,   0.0000])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g_subset.ndata['delta_inc'] = torch.zeros(g.num_nodes(),1)\n",
    "g_subset.update_all(fn.u_add_v('disp_wealth','zeros','delta_inc'), fn.sum('delta_inc', 'delta_inc'))\n",
    "torch.squeeze(g_subset.ndata['delta_inc'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a09d0a7",
   "metadata": {},
   "source": [
    "### Update wealth at time t+1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "d01c0ab6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[ True],\n",
       "        [ True],\n",
       "        [ True],\n",
       "        [ True],\n",
       "        [ True],\n",
       "        [ True],\n",
       "        [ True],\n",
       "        [ True],\n",
       "        [ True],\n",
       "        [False]])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a mask to check if a given node has atleast 1 associated edge to give money\n",
    "g_subset.ndata['mask'] = torch.zeros(g_subset.num_nodes(),1)\n",
    "g_subset.ndata['mask'] = torch.tensor([i in src for i in g_subset.nodes()])[:,None]\n",
    "g_subset.ndata['mask']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "ee1cce1e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Update income for next time-step\n",
    "# This and the previous step can be simplified by directly updating k in the final model\n",
    "# The use of mask is necessary to ensure that updated wealths do not change for nodes with no edges\n",
    "g_subset.ndata['k_new'] = g_subset.ndata['k'] - g_subset.ndata['disp_wealth']*g_subset.ndata['mask'] + g_subset.ndata['delta_inc']\n",
    "g.ndata['k_new'] = g_subset.ndata['k_new']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "d2affd6d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([251.8720, 126.4798, 238.9267, 956.5364,  98.2575, 382.0890,   7.2087,\n",
       "        429.0481, 527.9481, 984.7639])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.squeeze(g.ndata['k_new'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e685a41",
   "metadata": {},
   "source": [
    "### Analyse wealth exchange by plotting wealth at time t ('k') and time t+1 ('k_new') \n",
    "\n",
    "Ensuring continuity by checking that total wealth is consistent between time t and t+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "2abf9140",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2fc70ce090>]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting current wealth and updated wealth for each agent for one time-step\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.plot(g.ndata['k'])\n",
    "plt.plot(g.ndata['k_new'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "350d99e4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([-0.0002])\n"
     ]
    }
   ],
   "source": [
    "#Checking for continuity of wealth\n",
    "print (sum(g.ndata['k']) - sum(g.ndata['k_new']))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "ptm",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}