runtime-comparisons.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5d406f20",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.linalg import eigh_tridiagonal\n",
    "from numpy.random import randint, rand\n",
    "from scipy.sparse import random\n",
    "from scipy.sparse import csr_matrix\n",
    "from matplotlib import pyplot as plt\n",
    "import time\n",
    "from numba import njit\n",
    "from lanczos import lanczos_eig\n",
    "import multiprocessing\n",
    "from tqdm.contrib.concurrent import process_map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "38d0eb71",
   "metadata": {},
   "outputs": [],
   "source": [
    "#qiskit colour palet\n",
    "darkpurple = (48/255, 19/255, 94/255)\n",
    "purple = (105/255, 40/255, 195/255)\n",
    "background2 = (242/255, 243/255, 248/255)\n",
    "background1 = (221/255, 225/255, 230/255)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5c98abb0-accc-4e29-87cc-3cd6898b64e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def rand_herm(size,sparsity):\n",
    "    sparsity = 1 - np.sqrt(1 - sparsity)\n",
    "    mat = np.zeros(size*size)\n",
    "    nonzero_num = int(size*size*sparsity)\n",
    "    nonzero_idx = randint(0, size**2, size=nonzero_num)\n",
    "    mat[nonzero_idx] = rand(nonzero_num)\n",
    "    mat = mat.reshape(size, size)\n",
    "    mat = mat + mat.T\n",
    "    return mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0463146f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def rand_herm_sparse(size,sparsity):\n",
    "    sparsity = 1 - np.sqrt(1 - sparsity)\n",
    "    mat = random(size,size,density=sparsity,format='csr')\n",
    "    mat = mat + mat.T\n",
    "    return mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c67e0c3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def LanczosVsNumpy(size, sparsity, k, repeats):\n",
    "    tlanc_list = []\n",
    "    teigh_list = []\n",
    "    fidelity_list = []\n",
    "    \n",
    "    for idx in range(repeats):\n",
    "        mat = rand_herm(size, sparsity)\n",
    "\n",
    "        t0 = time.time()\n",
    "\n",
    "        x = rand(size)\n",
    "        _, W1 = lanczos_eig(mat,x,k)\n",
    "        eiglanc = W1[:,0]\n",
    "\n",
    "        t1 = time.time()\n",
    "\n",
    "        _, W2 = np.linalg.eigh(mat)\n",
    "        eigres = W2[:,0]\n",
    "\n",
    "        t2 = time.time()\n",
    "\n",
    "        fidelity = np.abs(eigres @ eiglanc)\n",
    "        tlanc = t1 - t0\n",
    "        teigh = t2 - t1\n",
    "        \n",
    "        fidelity_list.append(fidelity)\n",
    "        tlanc_list.append(tlanc)\n",
    "        teigh_list.append(teigh)\n",
    "    \n",
    "    return np.mean(tlanc_list), np.mean(teigh_list), np.mean(fidelity_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c2e0921d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# LanczosVsNumpy(1000, 0.2, 40, 100)\n",
    "runtime_vals = []\n",
    "for size_idx in range(300,1500,20):\n",
    "    runtime_vals.append(LanczosVsNumpy(size_idx, 0.3, min(50+int(10*size_idx/1500),size_idx//10), 100))\n",
    "    \n",
    "# np.save('lanc_comp2.npy', np.array(runtime_vals))\n",
    "runtime_vals = np.load('simdata/lanc_comp2.npy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "697df108-7538-482e-a6fa-c21fb18879bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams['axes.facecolor']=background2\n",
    "\n",
    "plt.figure(figsize=(21,9),dpi=300,facecolor=background1)\n",
    "plt.plot(range(300,1500,20), np.array(runtime_vals)[:,0],'-o', markersize=1, linewidth=3,label='lanczos $|\\ell \\\\rangle$',color=purple)\n",
    "plt.plot(range(300,1500,20), np.array(runtime_vals)[:,1],'-o', markersize=1, linewidth=3,label='linalg.eigh $|e \\\\rangle$',color=darkpurple)\n",
    "plt.xlabel('Array Dimension',fontsize=15)\n",
    "plt.ylabel('Run Time',fontsize=15)\n",
    "plt.title('$ \\langle Run Time \\\\rangle_{100} $ vs Array Dimension',fontsize=20)\n",
    "plt.legend(fontsize=15)\n",
    "plt.tick_params(axis='both', which='major', labelsize=12)\n",
    "plt.savefig('lanczos-vs-numpy-eigh.png',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4555661a-e6ad-4034-b833-9f2adcf2eb82",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams['axes.facecolor']=background2\n",
    "plt.figure(figsize=(21,9),dpi=300,facecolor=background1)\n",
    "\n",
    "plt.plot(range(300,1500,20), np.array(runtime_vals)[:,2], color = purple)\n",
    "plt.xlabel('Array Dimension')\n",
    "plt.ylabel('Fidelity $\\langle e | \\ell \\\\rangle$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2688d3c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def DenseVsSparse(size, sparsity, k, repeats):\n",
    "    tdense_list = []\n",
    "    tsparse_list = []\n",
    "    fidelity_list = []\n",
    "    sparsity = 6.3/size\n",
    "    for idx in range(repeats):\n",
    "        matsp = rand_herm_sparse(size, sparsity)\n",
    "        mat = matsp.A\n",
    "        x1 = rand(size)\n",
    "        x2 = x1.copy()\n",
    "        \n",
    "        t0 = time.time()\n",
    "\n",
    "        _, W1 = lanczos_eig(mat,x1,k)\n",
    "        eig_dense = W1[:,0]\n",
    "\n",
    "        t1 = time.time()\n",
    "\n",
    "        _, W2 = lanczos_eig(matsp,x2,k)\n",
    "        eig_sparse = W2[:,0]\n",
    "\n",
    "        t2 = time.time()\n",
    "\n",
    "        fidelity = np.abs(eig_dense @ eig_sparse)\n",
    "        tdense = t1 - t0\n",
    "        tsparse = t2 - t1\n",
    "        \n",
    "        fidelity_list.append(fidelity)\n",
    "        tdense_list.append(tdense)\n",
    "        tsparse_list.append(tsparse)\n",
    "    \n",
    "    return np.mean(tdense_list), np.mean(tsparse_list), np.mean(fidelity_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "602e34b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "493731e694c0443eb33026742b761956",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/182 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.07 s, sys: 439 ms, total: 1.51 s\n",
      "Wall time: 1h 39min 38s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "def parallel_func(value):\n",
    "    size_idx = value\n",
    "    try:\n",
    "        data = DenseVsSparse(size_idx, 0.01, size_idx//3, 200)\n",
    "    except :\n",
    "        data = [float('nan'), float('nan'), float('nan')]\n",
    "    return data\n",
    "# with multiprocessing.Pool() as execute:\n",
    "#     runtime_vals = execute.map(parallel_func, range(200,2015,10))\n",
    "runtime_vals = process_map(parallel_func, range(200,2015,10))\n",
    "# runtime_vals = np.array(runtime_vals)\n",
    "# np.save('simdata/dense-vs-sparse.npy',runtime_vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "edd6ae27",
   "metadata": {},
   "outputs": [],
   "source": [
    "runtime_vals = np.load('simdata/dense-vs-sparse.npy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "43fec65d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "       [1.15193347, 0.30824081, 0.86212667],\n",
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       "       [1.60148981, 0.39497692, 0.83328649],\n",
       "       [1.66097151, 0.40759842, 0.74193155],\n",
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       "       [1.88183768, 0.45236823, 0.74828013],\n",
       "       [2.07327398, 0.47417908, 0.82554289],\n",
       "       [       nan,        nan,        nan],\n",
       "       [2.27308264, 0.49847305, 0.72443442],\n",
       "       [       nan,        nan,        nan],\n",
       "       [2.45967794, 0.5411404 , 0.72814865],\n",
       "       [2.53040684, 0.52716498, 0.75526306],\n",
       "       [2.5161378 , 0.55701036, 0.79073798],\n",
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       "       [2.63361147, 0.58915507, 0.81213548],\n",
       "       [2.66941232, 0.58273491, 0.77337971],\n",
       "       [2.71739661, 0.57696549, 0.79782166],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [2.48541974, 0.56350808, 0.77483547],\n",
       "       [2.51605819, 0.5957093 , 0.81274053],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [2.7518197 , 0.60906778, 0.6405493 ],\n",
       "       [2.7537808 , 0.64376508, 0.66633606],\n",
       "       [2.88042775, 0.62507173, 0.75141831],\n",
       "       [2.87103827, 0.646209  , 0.6327487 ],\n",
       "       [2.9015733 , 0.65184703, 0.73409607],\n",
       "       [2.96044317, 0.67537451, 0.7060931 ],\n",
       "       [       nan,        nan,        nan],\n",
       "       [3.08793093, 0.67789238, 0.71199764],\n",
       "       [3.09359723, 0.70489826, 0.62657912],\n",
       "       [3.2722819 , 0.69869608, 0.79512706],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [3.36591914, 0.74897274, 0.73907288],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [3.46284604, 0.78538852, 0.67991297],\n",
       "       [       nan,        nan,        nan],\n",
       "       [3.57876001, 0.82850328, 0.70821348],\n",
       "       [3.61565941, 0.80355014, 0.83493258],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
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       "       [       nan,        nan,        nan],\n",
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       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan],\n",
       "       [       nan,        nan,        nan]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "runtime_vals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "437369d0",
   "metadata": {},
   "outputs": [
    {
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yQAAq3KxZM5NizZo3L/TOhPHjk2K777FnqervsedeKfJ/U0T95PPKrA8AAFRfU6ZMjttvvWnT69q1a8d1199YrjXMTAAAQHXx/vvvJrxOT0+Pnj33LuDp8mNuAgAAqoO999k3KfbO22+VOM+7b7+Z8DozMzP2KuQfMJmZAACALd3WPveMT3G+Rynr75myfvL3FwAA2PrMTLFHonnzFkXeMzMBQNEyqroBALZsGzZsiLGvvZoU32XX3Qq9N23a90mxbbbpUKoeWrdpExkZGbFhw4ZNsenTpxV6Z3qq+h06lqr+Nik+gXlGEfUBAIDqacOGDfGnP1wQ69at2xT74yV/jnbt25drHTMTAABQHaxatSqmTP4uIdZl2+2iXv36m17PmjUznnlqTHz04Qcxbdr3sWL58qhVu3Y0atQ4WrduE3vvs2/07nNAkX+39EvmJgAAoDo48KC+0aZt2/hh7txNseFPPBannX5WtGnbtlg5nn/umZg4cUJC7PgTTowGDRoWeMfMBAAAbOm29rmnPOu3T/F9K+rrBwAAtnzLli2NcR9/lBTfeeddi7xrZgKAoqVXdQMAbNneeP21WLRoYUKsYcNGhX4qcUTED3PnJMWK+2bHX6pRo0a0aNkyIfbj/Pmxfv36Au/MTVW/Tenqt2jZKmrUqJEQmz17VqlyAQAAm7e77/xPwqdL7bHnXnHqaWeWex0zEwAAUB1Mmfxd5OfnJ8S67bhTRESsWbMmrv7LZdH3gP3i9ltvjk8/GRdLfvopNmzYECtXrIjZs2bGxx99ELfc9O844dgjY9BJ/eKzT8cVu7a5CQAAqA4yMjLir3+/LiG2Zs2aOP3UQcVacPfaqy/Hn//0h4RY02bN4uJLLy/0npkJAADY0m3tc0/q+m1KVb916+R7c8xdAACw1Xty9KhYl5ubENt+h27Rrn37Iu+amQCgaJYDAlBhcnNy4oZ/X5sUP3HASZGRkVHo3V8uFIyIaNWqdal7+eXdjRs3xtIlSwqpv6jc6teoUSOaNW+eEPtp8eJS5QIAADZf3307Ke78z62bXmdlZcf1N9wc6enl//+CMzMBAADVwZzZs5NiLVu2jBkzpsdRh/eNxx/7b+Tl5RUr1yfjPo6BA/rFXXfcXqznzU0AAEB1ceBBB8dV1/w90tLSNsWmT5sWRx9xSPzl8kvj3XfejsWLFsX69etj7do1MXv2rHju2afj9FMHx3m/OitycnI23WvcuHE88uiwaNKkSaE1zUwAAMCWbmufe355npaWFi1atipV/ZatWiXMrBERixcnf30AAMDWY8mSn+LuO5Pfy3fywMHFum9mAoCiFb6ZCQDK4IZ/Xxczpk9PiDVo0DDOPe93Rd5dtmxZUqxOnTql7qV27eS7S5ctjeYtWqR8fnmK+rXLUL/OL+qvW7cuVq9eXaavCQAA2HysX78+/vSHCxI+Cfj3F14UnTp3qZB6ZiYAAKA6WLhwQVIsIyMjzjx1SNIn86anp0ezZs2jfv36sXTZ0vhp8eLIz89PeCY/Pz9uuuFfsXDhgrjmb/8stLa5CQAAqE5OO+Os6Nipc1x5+aUxd+6ciIjIycmJ4U88FsOfeKxYOfoecmj87Z//ihYtWhb5rJkJAADY0m3Nc8+qVasS3ssYEZGdnR01atQoVe2MjIzIzMyK3Nz/v5x+2dKlpcoFAABsGS7/859i6S/mgvbbdIiTBw0p1n0zEwAUzXJAACrEKy+9GA8/eH9S/LIrrizyU4kjItauXZMUy8rOLnU/2Snu5qxdW+Dza1LUT5WjLPXXrl3rzYcAALCFuPM/t8akSRM3vd5p513inHN/U2H1zEwAAEB1sHz58qTY/ffek/AmuFatW8f5v78oDj38iGjUqPGm+I8/zo8Xnns27rrj9li+fFlCjsf++3DsvMuucWL/kwqsbW4CAACqm959Dog33vkgXnrhuRg1ckR89OH7Rd5JT0+PkwYOjqGnnBY7dNux2LXMTAAAwJZua5571q4p39r/u//zv+NbW8jXDgAAbNkevP/eeP3VVxJiaWlp8Y9rr4+srKxi5TAzAUDR0qu6AQC2PBPGfxN/+uMFSfHDjzgqBpw8qFg5NqzfkBQr7jCYSqqBbP36dYXUX58UK0v9VH+BWFh9AACg+pg4YXzcfed/Nr2uWbNmXH/DzaX+xKjiMDMBAADVwbp1uUmxn78Bbt/99o9Xx74TJw8akrAYMCKiZctWcfavfh2vjn07um6/Q1Kev151RSxbVvCn65qbAACA6iY/Pz/eefvNeOrJ0fH5Z58U605eXl6MGTUirr/uH/HuO28Xu5aZCQAA2NJtzXPP+g2papd90UVi7eQaAADAlu+tN8bG9df9Iyl+5tm/in3327/YecxMAFA0ywEBKFezZ8+Ks884Ndb8YmN6585d4vobbylT7rS0tHK9m59f1fVL2AAAALDZWbduXfzpjxfGhg3//42Ev/7N72L7HbpVei9mJgAAYLNTyP+s79Jl27j/wf+m/GTen2vWvHk8+viIaNw4cXng6tWr45GHHihRO+YmAABgczV79qwYOOCE+NVZp8d7774T69Yl/mOlxo0bR+fOXWKbDh2jfv0GCWcbNmyI9959J844dXCce84ZsWTJT6XqwcwEAABs6bbquaf0pVPWN3MBAMDW5+uvvozf/+7XsXHjxoR4z157xyV/vqLM+c1MAJDIckAAys2PP86PUwefHIsWLUyIt2zVKh5+dFjUrVu32LkyamYkxXJyckrdW6q7NWvWLKR+8ll518+smVnqfAAAwObh9ltvjsnffbvp9XZdt4/f/O6CCq9rZgIAAKqDVLPL//ztn/9K+Wm9qTRt1iz+dOnlSfERw54oUW1zEwAAsDn67ttJceJxR8Vnn36SEN+mQ8f42z+uiw/GfR6ffjkhXnvz3XjznQ/iy/HfxhvvfBCX/PnyaN68RcKdsa+9GoMG9ItFCxPfw/dLZiYAAGBLtzXPPTUzkmvnlqF2qvo1zVwAALBVmTz5uzjr9KGxZs2ahPj2O3SLu+97MDIyCn6vYCpmJgAomuWAAJSLxYsXx6mDT445c2YnxJs2axaPDxsVbdq2LVG+Wtm1kmJlGapSDXS1atcuUf2yDJSpei+sPgAAsPn75puv4/5779r0ukaNGnH9DTdHZmbF/wWOmQkAAKgOatVK/b/ru26/Q/TstXeJch13fL9o0KBhQmzRooUx7fupqWubmwAAgGpg2bKlcdbpp8SSJUsS4gNOGhgvv/pGDDnltGjZslXSvQ4dOsa55/0uXhn7Vhxw4MEJZ99/PzV+/7tfR15eXoF1zUwAAMCWbmuee7JrlW/t/7u/NuF17drJNQAAgC3TjOnT4rQhA2Pp0qUJ8c6du8R/Hx+R9L6+4jAzAUDRLAcEoMyWLl0Spw45OaZN+z4h3rhx43hs2Kjo2KlziXM2bNQoKbZ69epS97hmTfLdRg2TaxRWf00Z6q/+Rf3MzMyoU6dOqfMBAABVKzc3Ny7544WxYcOGTbEzz/5V7LLrbpVS38wEAABUB41SzA4REfvt37vEubKys6N7jx5J8c8+/STl8+YmAACgOvj3v66NH3+cnxA77PAj47p/3xRZ2dlF3m/QoGHcde8DsdvueyTEPxn3cTw5emSB98xMAADAlm5rnnvq1asXNWvWTIjl5ubGxo0bS1V7w4YNkZubmxBL9fUBAABbntmzZ8XQQSfFokULE+Ltt+kQjw0fFU2bNi1VXjMTABTNckAAymT58mVx2pCBMfm7bxPiDRs2ikefGBnbbde1VHmbNm2WFPvlmyBLYv68eQmv09PTo1HjxoXUTx5ES1t/48aNsWhh4sDbpJSDLgAAsHl45OEHYuqUyZted+jYKS76w58qrb6ZCQAAqA6aNW+RMr7jjjuXKl+3HXdKii1cuCDls+YmAABgc7dkyU/x9FNjEmJZWdlx1V//HmlpacXOk5WVFVf/7Z9J8YcfeqDAO2YmAABgS7e1zz1NmiSe5+XlxYIFP5aq/oIff4z8/PyEWKrvLwAAsGX5Ye7cGDpoQNIs07Ztu3hi+Kho0aJlqXObmQCgaBlV3QAA1dfKFSvi1CEDY+LECQnx+vUbxCOPD48duu1Y6txt27VPiv0wd26pcqUaxlq2apW00f3n2rVrH59/9mlS/e49epa4/oIFP8aGDRuS8gMAANXXwgWJyydWr1oVJ55wdLHvr1+3Pik2/puv4+gj+ibFX3h5bFLMzAQAAFQH7dun/t/2pf1U3IYNk+8tXbo05bPmJgAAYHP3wfvvxbrc3ITYvvvtFy1btipxrl122TW23a5rwodbTf7u21iw4MeU/zDLzAQAAGzptva5p227dkmLNeb9MDdat25T4vrz5v2QIr+5CwAAtmTz5v0QQwb2T5qjWrVuHY8PHx2t27QtU34zEwAUzXJAAEpl5cqVcdopg2LC+G8S4nXr1YtHHhsWO++8S5nyd+rUOSk2a9bMUuWa98MPsX594uKNzp27FHqnY8r6M0pVf/asWUmxTkXUBwAAqpdFixbGokULi36wEGvWrIlvJ00q1rNmJgAAoDro0LFj1KhRIzZu3JgQz8zMLFW+rOzspFjuLxZp/I+5CQAA2NxN/u7bpNhuu+9Z6ny7775HwnLA/6vxXcrlgGYmAABgS7e1zz2dOnWOzz79JCE2c+bM2Kt7yRdtpPq+FfX1AwAA1dePP86PIQMHxJw5sxPiLVu2iidGjIl2BXxocEmYmQCgaOlV3QAA1c+qVavijFMGx9dffZkQr1u3bjzy6LDYdbfdy1xjpxTLBb/84rNS5fri80+TYjvutHMp6n9eyvrJfRdVHwAAoDBmJgAAoDqoVat2dNl2u6T4ypUrSpVvxfLlSbFGjRqlfNbcBAAAbO6WLl2aFGvcpEmp86W6u2xZco0IMxMAALDl29rnnqquDwAAVE8LFvwYQwYOiNm/WHjXokXLeHzE6Nhmmw7lUqeqZ5aqrg8AxWE5IAAlsnr16jjj1MHx5Ze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      "text/plain": [
       "<Figure size 6300x2700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['axes.facecolor']=background2\n",
    "\n",
    "plt.figure(figsize=(21,9),dpi=300,facecolor=background1)\n",
    "plt.plot(range(200,2015,10), np.array(runtime_vals)[:,0],'-o', markersize=1, linewidth=3,label='dense $|d \\\\rangle$',color=purple)\n",
    "plt.plot(range(200,2015,10), np.array(runtime_vals)[:,1],'-o', markersize=1, linewidth=3,label='sparse $|s \\\\rangle$',color=darkpurple)\n",
    "plt.xlabel('Array Dimension',fontsize=15)\n",
    "plt.ylabel('Run Time',fontsize=15)\n",
    "plt.title('$ \\langle Run Time \\\\rangle_{100} $ vs Array Dimension',fontsize=20)\n",
    "plt.legend(fontsize=15)\n",
    "plt.tick_params(axis='both', which='major', labelsize=12)\n",
    "plt.savefig('dense-vs-sparse.png',bbox_inches='tight')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}