The amount of ram required for dense vs sparse matrix

matrix-ram-requirement.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3237eabc-88f8-40cd-b4a1-a942753d48a9",
   "metadata": {},
   "source": ["https://abhigupta.io/2022/01/31/please-use-sparse-matrices.html"]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "88537f4c-d0e9-4d5e-a5bf-db4b672144d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import sparse\n",
    "from scipy.sparse import diags\n",
    "from scipy.stats import uniform\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "dof = np.linspace(10,10000,10,dtype = int)\n",
    "size_full=[]\n",
    "size_sparse=[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "38b724ef-1e42-4436-9751-fec3b771ebe6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of full matrix with zeros: 7.63e-04 MB\n",
      "Size of sparse csr_matrix: 4.27e-04 MB\n",
      "------------------------------------------------------------\n",
      "Size of full matrix with zeros: 9.57e+00 MB\n",
      "Size of sparse csr_matrix: 5.12e-02 MB\n",
      "------------------------------------------------------------\n",
      "Size of full matrix with zeros: 3.79e+01 MB\n",
      "Size of sparse csr_matrix: 1.02e-01 MB\n",
      "------------------------------------------------------------\n",
      "Size of full matrix with zeros: 8.51e+01 MB\n",
      "Size of sparse csr_matrix: 1.53e-01 MB\n",
      "------------------------------------------------------------\n",
      "Size of full matrix with zeros: 1.51e+02 MB\n",
      "Size of sparse csr_matrix: 2.04e-01 MB\n",
      "------------------------------------------------------------\n",
      "Size of full matrix with zeros: 2.36e+02 MB\n",
      "Size of sparse csr_matrix: 2.54e-01 MB\n",
      "------------------------------------------------------------\n",
      "Size of full matrix with zeros: 3.39e+02 MB\n",
      "Size of sparse csr_matrix: 3.05e-01 MB\n",
      "------------------------------------------------------------\n",
      "Size of full matrix with zeros: 4.62e+02 MB\n",
      "Size of sparse csr_matrix: 3.56e-01 MB\n",
      "------------------------------------------------------------\n",
      "Size of full matrix with zeros: 6.03e+02 MB\n",
      "Size of sparse csr_matrix: 4.07e-01 MB\n",
      "------------------------------------------------------------\n",
      "Size of full matrix with zeros: 7.63e+02 MB\n",
      "Size of sparse csr_matrix: 4.58e-01 MB\n",
      "------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "for n in dof:\n",
    "    data = uniform.rvs(size=n**2, loc = 0, scale=2)\n",
    "    data = np.reshape(data, (n, n))\n",
    "\n",
    "    data = [np.diag(data),np.diag(data),np.diag(data)]\n",
    "    diagonal = diags(data, [0, -1, 1]).toarray()\n",
    "\n",
    "    data = diagonal\n",
    "    data_size = data.nbytes/(1024**2)\n",
    "    print('Size of full matrix with zeros: '+ '{:.2e}'.format(data_size) + ' MB')\n",
    "    size_full.append(data_size)\n",
    "\n",
    "    data_csr = sparse.coo_matrix(data)\n",
    "    data_csr_size = (data_csr.data.nbytes+data_csr.row.nbytes+data_csr.col.nbytes)/(1024**2)\n",
    "    print('Size of sparse csr_matrix: '+ '{:.2e}'.format(data_csr_size) + ' MB')\n",
    "    size_sparse.append(data_csr_size)\n",
    "    print('-'*60)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "95867a06-5ad7-49da-901d-8e337fec9b24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12bf1bc70>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xscale(\"log\")\n",
    "# plt.yscale(\"log\")\n",
    "plt.plot(dof,size_full)\n",
    "plt.plot(dof, size_sparse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "eb0cb788-fab1-453c-bf45-eab735e815b0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 7.45e-09 4.58e-05 \n",
      "10 7.45e-07 4.58e-04 \n",
      "100 7.45e-05 4.58e-03 \n",
      "1000 7.45e-03 4.58e-02 \n",
      "10000 7.45e-01 4.58e-01 \n",
      "100000 7.45e+01 4.58e+00 \n",
      "1000000 7.45e+03 4.58e+01 \n",
      "10000000 7.45e+05 4.58e+02 \n",
      "100000000 7.45e+07 4.58e+03 \n",
      "1000000000 7.45e+09 4.58e+04 \n"
     ]
    }
   ],
   "source": [
    "table_data=[]\n",
    "for i in range(10):\n",
    "    n=10**i\n",
    "    _dense = n**2*8/1024**3\n",
    "    _sparse = 3*(n*8+n*4+n*4)/1024**2\n",
    "    table_data.append(['1e'+str(i),_dense,_sparse])\n",
    "    print(\"{:} {:.2e} {:.2e} \".format(n,_dense,_sparse))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "14b81d8b-2193-4c86-9be3-cabe61ca1a54",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|             dof |      dense (GB) |   sparse (MB) |\n",
      "|-----------------+-----------------+---------------|\n",
      "|          1.0000 |          0.0000 |        0.0000 |\n",
      "|         10.0000 |          0.0000 |        0.0005 |\n",
      "|        100.0000 |          0.0001 |        0.0046 |\n",
      "|       1000.0000 |          0.0075 |        0.0458 |\n",
      "|      10000.0000 |          0.7451 |        0.4578 |\n",
      "|     100000.0000 |         74.5058 |        4.5776 |\n",
      "|    1000000.0000 |       7450.5806 |       45.7764 |\n",
      "|   10000000.0000 |     745058.0597 |      457.7637 |\n",
      "|  100000000.0000 |   74505805.9692 |     4577.6367 |\n",
      "| 1000000000.0000 | 7450580596.9238 |    45776.3672 |\n"
     ]
    }
   ],
   "source": [
    "from tabulate import tabulate\n",
    "\n",
    "print(tabulate(table_data, headers=['dof', 'dense (GB)', 'sparse (MB)'], tablefmt='orgtbl',floatfmt=\".4f\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3c581c86-6813-4569-be3c-d07053d18914",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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