euler_1d_raw.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "23b3ca67",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import numba"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b4d85ee",
   "metadata": {},
   "source": [
    "### Grid "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "38ee8260",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Grid:\n",
    "    def __init__(self, xmin: float, xmax: float, nx: int, n_ghost: int = 1):\n",
    "        self.xmin = xmin\n",
    "        self.xmax = xmax\n",
    "        self.nx = nx\n",
    "        self.tot_nx = nx + 2 * n_ghost\n",
    "        self.dx = (xmax - xmin) / (nx - 1)\n",
    "        self.x = np.linspace(xmin, xmax, nx)\n",
    "        self.x = np.insert(self.x, 0, self.x[0])\n",
    "        self.x = np.insert(self.x, self.x.shape[0], self.x[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8b7a1d0",
   "metadata": {},
   "source": [
    "### Primitive variables to conserved variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "aa482c99",
   "metadata": {},
   "outputs": [],
   "source": [
    "@numba.njit\n",
    "def prim_to_cons_vars(pv: np.ndarray) -> np.ndarray:\n",
    "    cv = np.zeros(pv.shape)\n",
    "    cv[:, 0] = pv[:, 0]\n",
    "    cv[:, 1] = pv[:, 0] * pv[:, 1]\n",
    "    cv[:, 2] = pv[:, 0] * (pv[:, 2] / (pv[:, 0] * (1.4 - 1)) + 0.5 * pv[:, 1] ** 2)\n",
    "\n",
    "    return cv"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2b6f0a0",
   "metadata": {},
   "source": [
    "### Conserved variables to primitive variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4ee818b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "@numba.njit\n",
    "def cons_to_prim_vars(cv: np.ndarray) -> np.ndarray:\n",
    "    pv = np.zeros(cv.shape)\n",
    "    pv[:, 0] = cv[:, 0]\n",
    "    pv[:, 1] = cv[:, 1] / cv[:, 0]\n",
    "    pv[:, 2] = (cv[:, 2] / cv[:, 0] - 0.5 * pv[:, 1] ** 2) * cv[:, 0] * (1.4 - 1)\n",
    "\n",
    "    return pv"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8004a4fa",
   "metadata": {},
   "source": [
    "### Conserved variables to flux"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "568be14c",
   "metadata": {},
   "outputs": [],
   "source": [
    "@numba.njit\n",
    "def conv_vars_to_flux(cv: np.ndarray) -> np.ndarray:\n",
    "    pv = cons_to_prim_vars(cv)\n",
    "    f = np.zeros(cv.shape)\n",
    "    f[:, 0] = cv[:, 1]\n",
    "    f[:, 1] = pv[:, 2] + cv[:, 1] * pv[:, 1]\n",
    "    f[:, 2] = pv[:, 2] * pv[:, 1] + cv[:, 2] * pv[:, 1]\n",
    "\n",
    "    return f"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51c2177f",
   "metadata": {},
   "source": [
    "### To compute time step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "46c7b070",
   "metadata": {},
   "outputs": [],
   "source": [
    "@numba.jit\n",
    "def time_step(cv: np.ndarray, dx: float, cfl: float = 0.2) -> np.ndarray:\n",
    "    pv = cons_to_prim_vars(cv)\n",
    "    a = np.sqrt(1.4 * pv[:, 2] / pv[:, 0])\n",
    "    eig_val = np.abs(pv[:, 1] + a)\n",
    "    dt = cfl * dx / eig_val\n",
    "    \n",
    "    return np.min(dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf5c8435",
   "metadata": {},
   "source": [
    "### To compute Rusanov (LLF) flux"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "857e55b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "@numba.njit\n",
    "def llf_flux(cv: np.ndarray) -> np.ndarray:\n",
    "    f = conv_vars_to_flux(cv)\n",
    "    pv = cons_to_prim_vars(cv)\n",
    "    a = np.sqrt(1.4 * pv[:, 2] / pv[:, 0])\n",
    "    f_iph=np.zeros(f.shape)\n",
    "    f_imh=np.zeros(f.shape)\n",
    "    for i in range(1, cv.shape[0]-1):\n",
    "        eig_val_l = np.abs(pv[i, 1]) + a[i]\n",
    "        eig_val_r = np.abs(pv[i+1, 1]) + a[i+1]\n",
    "        max_eig_val = np.maximum(eig_val_l, eig_val_r)\n",
    "        f_iph[i] = 0.5 * (f[i, :] + f[i+1, :]) - 0.5 * max_eig_val * (cv[i+1, :] - cv[i, :])\n",
    "\n",
    "    for i in range(1, cv.shape[0]-1):\n",
    "        eig_val_l = np.abs(pv[i-1, 1]) + a[i-1]\n",
    "        eig_val_r = np.abs(pv[i, 1]) + a[i]\n",
    "        max_eig_val = np.maximum(eig_val_l, eig_val_r)\n",
    "        f_imh[i] = 0.5 * (f[i, :] + f[i-1, :]) - 0.5 * max_eig_val * (cv[i, :] - cv[i-1, :])\n",
    "\n",
    "    return f_iph - f_imh"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06694378",
   "metadata": {},
   "source": [
    "### Initial and boundary conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0a1dee46",
   "metadata": {},
   "outputs": [],
   "source": [
    "def initialize(pv_l: np.ndarray, pv_r: np.ndarray, x: np.ndarray, pv: np.ndarray, xloc):\n",
    "    pv[np.argwhere(x <= xloc), :] = pv_l\n",
    "    pv[np.argwhere(x > xloc), :] = pv_r\n",
    "    \n",
    "def bc(cv: np.ndarray) -> np.ndarray:\n",
    "    pv = cons_to_prim_vars(cv)\n",
    "    pv[0,:] = pv[1,:]\n",
    "    pv[-1,:] = pv[-2,:]\n",
    "    con_var = prim_to_cons_vars(pv)\n",
    "\n",
    "    return con_var"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee1213b9",
   "metadata": {},
   "source": [
    "### Simulation parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0b89b92e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.          0.          0.        ]\n",
      " [ 0.          0.          0.        ]\n",
      " [ 0.          0.          0.        ]\n",
      " [ 0.47078198 -0.00629402  1.0287577 ]\n",
      " [-1.22078198 -1.45620598 -3.8646952 ]\n",
      " [ 0.          0.          0.        ]\n",
      " [ 0.          0.          0.        ]\n",
      " [ 0.          0.          0.        ]\n",
      " [ 0.          0.          0.        ]\n",
      " [ 0.          0.          0.        ]\n",
      " [ 0.          0.          0.        ]\n",
      " [ 0.          0.          0.        ]\n",
      " [ 0.          0.          0.        ]]\n"
     ]
    }
   ],
   "source": [
    "prim_var_l = np.array([1.0, 0.75, 1.0])\n",
    "prim_var_r = np.array([0.125, 0.0, 0.1])\n",
    "\n",
    "cfl_num = 0.9\n",
    "grid = Grid(0, 1, 11)\n",
    "x_grid = grid.x\n",
    "x_loc = 0.3\n",
    "prim_var = np.zeros((x_grid.size, 3))\n",
    "initialize(prim_var_l, prim_var_r, x_grid, prim_var, x_loc)\n",
    "\n",
    "cons_var = prim_to_cons_vars(prim_var)\n",
    "flux = conv_vars_to_flux(cons_var)\n",
    "prim_var = cons_to_prim_vars(cons_var)\n",
    "\n",
    "print(llf_flux(cons_var))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b97101da",
   "metadata": {},
   "source": [
    "### Run the simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "db27f072",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00010920828178686061\n",
      "0.00021841656140415513\n",
      "0.0003276248388466742\n",
      "0.0004368331141249236\n",
      "0.0005460413872318551\n",
      "0.000655249658175369\n",
      "0.0007644579269554385\n",
      "0.000873666193572945\n",
      "0.0009828744580348497\n",
      "0.0010920827203350486\n",
      "0.0012012909804838998\n",
      "0.0013104992384754628\n",
      "0.0014197074943165355\n",
      "0.001528915748008106\n",
      "0.001638123999550046\n",
      "0.0017473322489502396\n",
      "0.001856540496201665\n",
      "0.001965748741314542\n",
      "0.0020749569842840434\n",
      "0.0021841652251158583\n",
      "0.0022933734638119975\n",
      "0.0024025817003713156\n",
      "0.002511789934802628\n",
      "0.0026209981670979863\n",
      "0.0027302063972674804\n",
      "0.0028394146253073885\n",
      "0.0029486228512222994\n",
      "0.0030578310750152397\n",
      "0.003167039296684052\n",
      "0.0032762475162384794\n",
      "0.00338545573366965\n",
      "0.0034946639489875334\n",
      "0.0036038721621894933\n",
      "0.0037130803732790363\n",
      "0.003822288582260189\n",
      "0.003931496789129798\n",
      "0.004040704993897719\n",
      "0.0041499131965557715\n",
      "0.004259121397113009\n",
      "0.004368329595567858\n",
      "0.004477537791922766\n",
      "0.004586745986182735\n",
      "0.004695954178343641\n",
      "0.004805162368415233\n",
      "0.004914370556390437\n",
      "0.005023578742277202\n",
      "0.005132786926074977\n",
      "0.005241995107785192\n",
      "0.005351203287413788\n",
      "0.0054604114649557025\n",
      "0.005569619640420586\n",
      "0.005678827813802424\n",
      "0.005788035985108108\n",
      "0.005897244154338067\n",
      "0.0060064523214927515\n",
      "0.006115660486579002\n",
      "0.006224868649590861\n",
      "0.006334076810537882\n",
      "0.006443284969415063\n",
      "0.006552493126228285\n",
      "0.006661701280978909\n",
      "0.006770909433666458\n",
      "0.006880117584298622\n",
      "0.006989325732868595\n",
      "0.007098533879385838\n",
      "0.0072077420238463065\n",
      "0.007316950166254928\n",
      "0.00742615830661394\n",
      "0.007535366444921989\n",
      "0.007644574581187565\n",
      "0.007753782715403065\n",
      "0.007862990847577862\n",
      "0.007972198977708811\n",
      "0.008081407105799942\n",
      "0.008190615231854314\n",
      "0.008299823355869752\n",
      "0.008409031477855492\n",
      "0.008518239597803188\n",
      "0.00862744771572213\n",
      "0.00873665583161001\n",
      "0.00884586394547002\n",
      "0.00895507205730598\n",
      "0.00906428016711496\n",
      "0.009173488274906176\n",
      "0.009282696380672001\n",
      "0.009391904484420947\n",
      "0.00950111258615147\n",
      "0.009610320685866\n",
      "0.009719528783569048\n",
      "0.009828736879256991\n",
      "0.00993794497293897\n",
      "0.010047153064608131\n",
      "0.010156361154272212\n",
      "0.010265569241930372\n",
      "0.010374777327584338\n",
      "0.010483985411239252\n",
      "0.010593193492890863\n",
      "0.010702401572548235\n",
      "0.010811609650205221\n",
      "0.010920817725868856\n",
      "0.011030025799538929\n",
      "0.011139233871216537\n",
      "0.011248441940907381\n",
      "0.011357650008606649\n",
      "0.011466858074323337\n",
      "0.011576066138051929\n",
      "0.011685274199798826\n",
      "0.01179448225956438\n",
      "0.011903690317349128\n",
      "0.012012898373159263\n",
      "0.012122106426989479\n",
      "0.012231314478848704\n",
      "0.012340522528731981\n",
      "0.012449730576645153\n",
      "0.012558938622589062\n",
      "0.012668146666563752\n",
      "0.012777354708575842\n",
      "0.012886562748619598\n",
      "0.012995770786703885\n",
      "0.013104978822824234\n",
      "0.013214186856985997\n",
      "0.01332339488919044\n",
      "0.013432602919437184\n",
      "0.013541810947733202\n",
      "0.013651018974072405\n",
      "0.013760226998463593\n",
      "0.013869435020902715\n",
      "0.013978643041394704\n",
      "0.014087851059941179\n",
      "0.014197059076541407\n",
      "0.014306267091202645\n",
      "0.014415475103918522\n",
      "0.014524683114697772\n",
      "0.01463389112353669\n",
      "0.014743099130439865\n",
      "0.014852307135409191\n",
      "0.014961515138443657\n",
      "0.015070723139550738\n",
      "0.015179931138723842\n",
      "0.015289139135971644\n",
      "0.01539834713129071\n",
      "0.015507555124685355\n",
      "0.015616763116157686\n",
      "0.015725971105706477\n",
      "0.01583517909333935\n",
      "0.01594438707904957\n",
      "0.016053595062845746\n",
      "0.01616280304472465\n",
      "0.01627201102469039\n",
      "0.01638121900274522\n",
      "0.01649042697888776\n",
      "0.016599634953125726\n",
      "0.01670884292545229\n",
      "0.016818050895876003\n",
      "0.01692725886439378\n",
      "0.017036466831009584\n",
      "0.017145674795725745\n",
      "0.017254882758540813\n",
      "0.01736409071946251\n",
      "0.01747329867848399\n",
      "0.017582506635613754\n",
      "0.01769171459084878\n",
      "0.017800922544192965\n",
      "0.017910130495648647\n",
      "0.01801933844521436\n",
      "0.018128546392897783\n",
      "0.018237754338692114\n",
      "0.018346962282605794\n",
      "0.01845617022463581\n",
      "0.01856537816478605\n",
      "0.018674586103058798\n",
      "0.018783794039452642\n",
      "0.018893001973975143\n",
      "0.019002209906619615\n",
      "0.01911141783739444\n",
      "0.019220625766296545\n",
      "0.019329833693329877\n",
      "0.0194390416184966\n",
      "0.019548249541795418\n",
      "0.01965745746323372\n",
      "0.01976666538280499\n",
      "0.019875873300517554\n",
      "0.019985081216368217\n",
      "0.020094289130361043\n",
      "0.020203497042498023\n",
      "0.020312704952778034\n",
      "0.02042191286120823\n",
      "0.020531120767782327\n",
      "0.0206403286725086\n",
      "0.020749536575383667\n",
      "0.02085874447641177\n",
      "0.020967952375594665\n",
      "0.021077160272931463\n",
      "0.021186368168429025\n",
      "0.02129557606208136\n",
      "0.021404783953896684\n",
      "0.021513991843871375\n",
      "0.021623199732009917\n",
      "0.021732407618313767\n",
      "0.021841615502782328\n",
      "0.021950823385422116\n",
      "0.022060031266227482\n",
      "0.022169239145206587\n",
      "0.022278447022355513\n",
      "0.022387654897679042\n",
      "0.022496862771178273\n",
      "0.022606070642852964\n",
      "0.02271527851270922\n",
      "0.0228244863807418\n",
      "0.02293369424695881\n",
      "0.023042902111355977\n",
      "0.02315210997393843\n",
      "0.02326131783470687\n",
      "0.02337052569366145\n",
      "0.023479733550807822\n",
      "0.023588941406141192\n",
      "0.02369814925966962\n",
      "0.023807357111388427\n",
      "0.023916564961303143\n",
      "0.02402577280941401\n",
      "0.024134980655721637\n",
      "0.02424418850023117\n",
      "0.024353396342938316\n",
      "0.024462604183851083\n",
      "0.024571812022964334\n",
      "0.02468101986028405\n",
      "0.024790227695809974\n",
      "0.024899435529543212\n",
      "0.025008643361488357\n",
      "0.025117851191641668\n",
      "0.025227059020011097\n",
      "0.025336266846591005\n",
      "0.02544547467138788\n",
      "0.025554682494400897\n",
      "0.025663890315631724\n",
      "0.025773098135084344\n",
      "0.02588230595275562\n",
      "0.025991513768653447\n",
      "0.02610072158277164\n",
      "0.02620992939511723\n",
      "0.0263191372056888\n",
      "0.026428345014488604\n",
      "0.026537552821519983\n",
      "0.026646760626780442\n",
      "0.026755968430277825\n",
      "0.026865176232005353\n",
      "0.026974384031970645\n",
      "0.02708359183017164\n",
      "0.02719279962661124\n",
      "0.027302007421292084\n",
      "0.02741121521421237\n",
      "0.027520423005379425\n",
      "0.02762963079478676\n",
      "0.027738838582442162\n",
      "0.02784804636834289\n",
      "0.027957254152492516\n",
      "0.02806646193489296\n",
      "0.02817566971554314\n",
      "0.02828487749444961\n",
      "0.028394085271606653\n",
      "0.028503293047022007\n",
      "0.0286125008206922\n",
      "0.028721708592621534\n",
      "0.028830916362811147\n",
      "0.028940124131260733\n",
      "0.02904933189797602\n",
      "0.02915853966295211\n",
      "0.029267747426196686\n",
      "0.029376955187705518\n",
      "0.02948616294748366\n",
      "0.029595370705531452\n",
      "0.029704578461849384\n",
      "0.029813786216442338\n",
      "0.029922993969306255\n",
      "0.03003220172044877\n",
      "0.03014140946986486\n",
      "0.03025061721756037\n",
      "0.03035982496353479\n",
      "0.030469032707789456\n",
      "0.03057824045032836\n",
      "0.03068744819114833\n",
      "0.030796655930256947\n",
      "0.030905863667648352\n",
      "0.031015071403329222\n",
      "0.031124279137298178\n",
      "0.031233486869557413\n",
      "0.03134269460011001\n",
      "0.03145190232895371\n",
      "0.03156111005609603\n",
      "0.03167031778153027\n",
      "0.03177952550526395\n",
      "0.03188873322729479\n",
      "0.03199794094762589\n",
      "0.032107148666259376\n",
      "0.032216356383193936\n",
      "0.032325564098436094\n",
      "0.03243477181198014\n",
      "0.03254397952383355\n",
      "0.03265318723399309\n",
      "0.0327623949424628\n",
      "0.03287160264924383\n",
      "0.032980810354335845\n",
      "0.03309001805774434\n",
      "0.03319922575946463\n",
      "0.033308433459504135\n",
      "0.03341764115785866\n",
      "0.033526848854533206\n",
      "0.03363605654952791\n",
      "0.03374526424284343\n",
      "0.03385447193448424\n",
      "0.03396367962444667\n",
      "0.03407288731273811\n",
      "0.03418209499935336\n",
      "0.03429130268429841\n",
      "0.03440051036757238\n",
      "0.03450971804917694\n",
      "0.0346189257291155\n",
      "0.03472813340738545\n",
      "0.03483734108399413\n",
      "0.03494654875893534\n",
      "0.03505575643221606\n",
      "0.03516496410383436\n",
      "0.03527417177379297\n",
      "0.03538337944209419\n",
      "0.03549258710873651\n",
      "0.035601794773726464\n",
      "0.03571100243705832\n",
      "0.03582021009873935\n",
      "0.03592941775876653\n",
      "0.03603862541714367\n",
      "0.036147833073871954\n",
      "0.03625704072895099\n",
      "0.036366248382386133\n",
      "0.03647545603417282\n",
      "0.03658466368431827\n",
      "0.036693871332818366\n",
      "0.03680307897967801\n",
      "0.036912286624897234\n",
      "0.0370214942684768\n",
      "0.03713070191042087\n",
      "0.03723990955072607\n",
      "0.03734911718939956\n",
      "0.037458324826436094\n",
      "0.0375675324618417\n",
      "0.037676740095615245\n",
      "0.037785947727758645\n",
      "0.03789515535827488\n",
      "0.03800436298716175\n",
      "0.03811357061442632\n",
      "0.03822277824006231\n",
      "0.03833198586407682\n",
      "0.038441193486467566\n",
      "0.03855040110723761\n",
      "0.03865960872638874\n",
      "0.03876881634391994\n",
      "0.03887802395983705\n",
      "0.03898723157413501\n",
      "0.03909643918682089\n",
      "0.0392056467978912\n",
      "0.0393148544073502\n",
      "0.039424062015198436\n",
      "0.039533269621436135\n",
      "0.03964247722606786\n",
      "0.03975168482908981\n",
      "0.03986089243050901\n",
      "0.03997010003032077\n",
      "0.040079307628530535\n",
      "0.040188515225137625\n",
      "0.04029772282014349\n",
      "0.04040693041355142\n",
      "0.0405161380053589\n",
      "0.04062534559557288\n",
      "0.04073455318418747\n",
      "0.040843760771209325\n",
      "0.040952968356636504\n",
      "0.041062175940471714\n",
      "0.04117138352271696\n",
      "0.041280591103371\n",
      "0.04138979868243976\n",
      "0.04149900625991808\n",
      "0.04160821383581286\n",
      "0.0417174214101209\n",
      "0.041826628982846156\n",
      "0.04193583655398934\n",
      "0.04204504412355049\n",
      "0.04215425169153423\n",
      "0.042263459257936696\n",
      "0.042372666822764755\n",
      "0.04248187438601393\n",
      "0.04259108194768945\n",
      "0.04270028950779071\n",
      "0.04280949706631906\n",
      "0.04291870462327778\n",
      "0.043027912178664335\n",
      "0.04313711973248555\n",
      "0.04324632728473567\n",
      "0.043355534835421185\n",
      "0.04346474238454019\n",
      "0.04357394993209535\n",
      "0.043683157478088576\n",
      "0.043792365022518695\n",
      "0.04390157256539144\n",
      "0.044010780106701834\n",
      "0.044119987646456624\n",
      "0.04422919518465258\n",
      "0.04433840272129368\n",
      "0.04444761025638047\n",
      "0.044556817789913154\n",
      "0.044666025321896057\n",
      "0.04477523285232559\n",
      "0.04488444038120846\n",
      "0.04499364790854009\n",
      "0.04510285543432579\n",
      "0.04521206295856476\n",
      "0.04532127048125854\n",
      "0.04543047800241007\n",
      "0.04553968552201714\n",
      "0.04564889304008642\n",
      "0.045758100556612\n",
      "0.04586730807160052\n",
      "0.0459765155850498\n",
      "0.04608572309696275\n",
      "0.046194930607340916\n",
      "0.04630413811618348\n",
      "0.046413345623495694\n",
      "0.04652255312927304\n",
      "0.046631760633522125\n",
      "0.0467409681362394\n",
      "0.046850175637429145\n",
      "0.0469593831370915\n",
      "0.047068590635227045\n",
      "0.047177798131839595\n",
      "0.04728700562692607\n",
      "0.04739621312049302\n",
      "0.04750542061253553\n",
      "0.047614628103059234\n",
      "0.04772383559206288\n",
      "0.04783304307954844\n",
      "0.04794225056551831\n",
      "0.04805145804997082\n",
      "0.04816066553291198\n",
      "0.048269873014336495\n",
      "0.04837908049425089\n",
      "0.048488287972652484\n",
      "0.04859749544954466\n",
      "0.048706702924928374\n",
      "0.04881591039880339\n",
      "0.04892511787117425\n",
      "0.049034325342037124\n",
      "0.04914353281139848\n",
      "0.04925274027925424\n",
      "0.04936194774560919\n",
      "0.04947115521046283\n",
      "0.049580362673816374\n",
      "0.0496895701356729\n",
      "0.04979877759603003\n",
      "0.049907985054894195\n",
      "0.050017192512259896\n",
      "0.050126399968133326\n",
      "0.05023560742251256\n",
      "0.05034481487540023\n",
      "0.05045402232679795\n",
      "0.05056322977670481\n",
      "0.05067243722512595\n",
      "0.05078164467205694\n",
      "0.05089085211750413\n",
      "0.051000059561464174\n",
      "0.051109267003941125\n",
      "0.05121847444493513\n",
      "0.05132768188444675\n",
      "0.051436889322479626\n",
      "0.05154609675903082\n",
      "0.05165530419410663\n",
      "0.05176451162770228\n",
      "0.05187371905982324\n",
      "0.05198292649046821\n",
      "0.052092133919639204\n",
      "0.052201341347338365\n",
      "0.05231054877356424\n",
      "0.05241975619832244\n",
      "0.05252896362160805\n",
      "0.05263817104342733\n",
      "0.05274737846377751\n",
      "0.05285658588266205\n",
      "0.05296579330008163\n",
      "0.05307500071603626\n",
      "0.05318420813053004\n",
      "0.05329341554355957\n",
      "0.053402622955131054\n",
      "0.05351183036524027\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.053621037773892134\n",
      "0.05373024518108583\n",
      "0.053839452586822864\n",
      "0.05394865999110581\n",
      "0.05405786739393278\n",
      "0.05416707479530974\n",
      "0.0542762821952314\n",
      "0.05438548959370394\n",
      "0.05449469699072506\n",
      "0.054603904386297725\n",
      "0.05471311178042303\n",
      "0.054822319173100556\n",
      "0.05493152656433476\n",
      "0.05504073395412188\n",
      "0.05514994134246803\n",
      "0.05525914872936945\n",
      "0.05536835611483057\n",
      "0.05547756349885098\n",
      "0.05558677088143178\n",
      "0.055695978262575885\n",
      "0.05580518564228105\n",
      "0.055914393020553343\n",
      "0.05602360039738754\n",
      "0.05613280777278954\n",
      "0.05624201514675744\n",
      "0.05635122251929381\n",
      "0.05646042989040005\n",
      "0.056569637260075446\n",
      "0.056678844628324676\n",
      "0.056788051995143723\n",
      "0.05689725936053861\n",
      "0.05700646672450595\n",
      "0.05711567408704979\n",
      "0.05722488144817003\n",
      "0.05733408880786744\n",
      "0.05744329616614518\n",
      "0.05755250352300076\n",
      "0.05766171087844015\n",
      "0.057770918232458494\n",
      "0.05788012558506131\n",
      "0.05798933293624699\n",
      "0.058098540286017804\n",
      "0.05820774763437539\n",
      "0.05831695498131878\n",
      "0.05842616232685283\n",
      "0.05853536967097334\n",
      "0.05864457701368624\n",
      "0.058753784354988424\n",
      "0.05886299169488365\n",
      "0.05897219903337203\n",
      "0.059081406370454115\n",
      "0.05919061370613322\n",
      "0.05929982104040668\n",
      "0.05940902837328038\n",
      "0.05951823570474973\n",
      "0.059627443034819975\n",
      "0.059736650363489706\n",
      "0.059845857690760985\n",
      "0.05995506501663559\n",
      "0.06006427234111239\n",
      "0.06017347966419634\n",
      "0.060282686985883134\n",
      "0.06039189430617861\n",
      "0.06050110162507987\n",
      "0.06061030894259046\n",
      "0.06071951625871063\n",
      "0.060828723573440775\n",
      "0.0609379308867843\n",
      "0.06104713819873845\n",
      "0.061156345509309006\n",
      "0.06126555281849158\n",
      "0.061374760126291214\n",
      "0.06148396743270664\n",
      "0.061593174737739766\n",
      "0.061702382041392445\n",
      "0.06181158934366346\n",
      "0.06192079664455779\n",
      "0.0620300039440711\n",
      "0.06213921124220913\n",
      "0.06224841853896911\n",
      "0.06235762583435445\n",
      "0.06246683312836549\n",
      "0.06257604042100252\n",
      "0.06268524771226898\n",
      "0.06279445500216206\n",
      "0.06290366229068747\n",
      "0.06301286957784095\n",
      "0.0631220768636274\n",
      "0.06323128414804563\n",
      "0.06334049143109745\n",
      "0.06344969871278475\n",
      "0.06355890599310628\n",
      "0.06366811327206696\n",
      "0.06377732054966251\n",
      "0.06388652782589856\n",
      "0.06399573510077243\n",
      "0.06410494237428745\n",
      "0.06421414964644395\n",
      "0.06432335691724222\n",
      "0.06443256418668564\n",
      "0.06454177145477144\n",
      "0.06465097872150524\n",
      "0.06476018598688286\n",
      "0.06486939325090911\n",
      "0.06497860051358281\n",
      "0.06508780777490576\n",
      "0.06519701503487979\n",
      "0.06530622229350369\n",
      "0.0654154295507823\n",
      "0.0655246368067114\n",
      "0.06563384406129656\n",
      "0.0657430513145351\n",
      "0.0658522585664303\n",
      "0.06596146581698249\n",
      "0.06607067306619197\n",
      "0.06617988031406202\n",
      "0.06628908756058999\n",
      "0.06639829480578137\n",
      "0.06650750204963202\n",
      "0.0666167092921467\n",
      "0.06672591653332423\n",
      "0.0668351237731664\n",
      "0.06694433101167498\n",
      "0.06705353824884881\n",
      "0.06716274548469262\n",
      "0.06727195271920229\n",
      "0.06738115995238332\n",
      "0.067490367184233\n",
      "0.06759957441475463\n",
      "0.06770878164394845\n",
      "0.06781798887181484\n",
      "0.06792719609835694\n",
      "0.06803640332357222\n",
      "0.06814561054746611\n",
      "0.0682548177700344\n",
      "0.06836402499128193\n",
      "0.06847323221120737\n",
      "0.06858243942981262\n",
      "0.06869164664709931\n",
      "0.06880085386306642\n",
      "0.06891006107771845\n",
      "0.06901926829105151\n",
      "0.06912847550307098\n",
      "0.06923768271377408\n",
      "0.06934688992316418\n",
      "0.06945609713124139\n",
      "0.0695653043380062\n",
      "0.06967451154346159\n",
      "0.06978371874760518\n",
      "0.06989292595044233\n",
      "0.07000213315196877\n",
      "0.07011134035218934\n",
      "0.07022054755110266\n",
      "0.07032975474871071\n",
      "0.07043896194501495\n",
      "0.07054816914001452\n",
      "0.0706573763337137\n",
      "0.07076658352610882\n",
      "0.07087579071720516\n",
      "0.07098499790699984\n",
      "0.07109420509549634\n",
      "0.07120341228269458\n",
      "0.07131261946859524\n",
      "0.07142182665320106\n",
      "0.07153103383650987\n",
      "0.07164024101852695\n",
      "0.07174944819924792\n",
      "0.07185865537867772\n",
      "0.07196786255681481\n",
      "0.07207706973366133\n",
      "0.07218627690921851\n",
      "0.07229548408348571\n",
      "0.07240469125646694\n",
      "0.07251389842815877\n",
      "0.07262310559856641\n",
      "0.07273231276768682\n",
      "0.07284151993552364\n",
      "0.07295072710207658\n",
      "0.0730599342673465\n",
      "0.07316914143133589\n",
      "0.07327834859404285\n",
      "0.07338755575547254\n",
      "0.07349676291562045\n",
      "0.07360597007449167\n",
      "0.07371517723208446\n",
      "0.07382438438840112\n",
      "0.07393359154344267\n",
      "0.07404279869720869\n",
      "0.0741520058497029\n",
      "0.07426121300092216\n",
      "0.07437042015087159\n",
      "0.07447962729954796\n",
      "0.07458883444695508\n",
      "0.07469804159309244\n",
      "0.07480724873796113\n",
      "0.07491645588156334\n",
      "0.07502566302389745\n",
      "0.07513487016496836\n",
      "0.07524407730477176\n",
      "0.0753532844433127\n",
      "0.07546249158058921\n",
      "0.07557169871660384\n",
      "0.07568090585135731\n",
      "0.07579011298484947\n",
      "0.07589932011708374\n",
      "0.07600852724805726\n",
      "0.07611773437777508\n",
      "0.07622694150623377\n",
      "0.07633614863343734\n",
      "0.076445355759385\n",
      "0.07655456288407811\n",
      "0.07666377000751856\n",
      "0.076772977129705\n",
      "0.07688218425064201\n",
      "0.0769913913703256\n",
      "0.07710059848876073\n",
      "0.07720980560594522\n",
      "0.07731901272188182\n",
      "0.077428219836571\n",
      "0.07753742695001285\n",
      "0.07764663406221047\n",
      "0.07775584117316132\n",
      "0.0778650482828704\n",
      "0.07797425539133401\n",
      "0.0780834624985564\n",
      "0.07819266960453651\n",
      "0.07830187670927595\n",
      "0.0784110838127763\n",
      "0.07852029091503653\n",
      "0.07862949801606084\n",
      "0.07873870511584559\n",
      "0.07884791221439569\n",
      "0.07895711931170867\n",
      "0.07906632640778755\n",
      "0.07917553350263247\n",
      "0.07928474059624385\n",
      "0.07939394768862441\n",
      "0.07950315477977199\n",
      "0.07961236186969146\n",
      "0.07972156895837891\n",
      "0.07983077604583881\n",
      "0.07993998313206982\n",
      "0.08004919021707382\n",
      "0.08015839730085207\n",
      "0.08026760438340386\n",
      "0.08037681146473301\n",
      "0.08048601854483625\n",
      "0.08059522562371843\n",
      "0.08070443270137677\n",
      "0.08081363977781458\n",
      "0.08092284685303167\n",
      "0.08103205392702878\n",
      "0.08114126099980826\n",
      "0.08125046807136829\n",
      "0.0813596751417137\n",
      "0.0814688822108403\n",
      "0.0815780892787528\n",
      "0.08168729634544958\n",
      "0.08179650341093281\n",
      "0.08190571047520337\n",
      "0.08201491753826093\n",
      "0.08212412460010889\n",
      "0.08223333166074437\n",
      "0.08234253872017215\n",
      "0.08245174577838917\n",
      "0.082560952835399\n",
      "0.08267015989120113\n",
      "0.08277936694579663\n",
      "0.08288857399918745\n",
      "0.08299778105137218\n",
      "0.08310698810235527\n",
      "0.08321619515213279\n",
      "0.08332540220070947\n",
      "0.08343460924808335\n",
      "0.08354381629425692\n",
      "0.0836530233392307\n",
      "0.08376223038300472\n",
      "0.08387143742558197\n",
      "0.08398064446695996\n",
      "0.0840898515071434\n",
      "0.08419905854612893\n",
      "0.08430826558392042\n",
      "0.08441747262051699\n",
      "0.08452667965226383\n",
      "0.08463588668647497\n",
      "0.08474509371949313\n",
      "0.08485430075132235\n",
      "0.08496350778195912\n",
      "0.08507271481140809\n",
      "0.08518192183966697\n",
      "0.08529112886673858\n",
      "0.08540033589262305\n",
      "0.08550954291732078\n",
      "0.08561874994083435\n",
      "0.08572795696316168\n",
      "0.08583716398430741\n",
      "0.08594637100426784\n",
      "0.08605557802304718\n",
      "0.08616478504064418\n",
      "0.0862739920570606\n",
      "0.08638319906564923\n",
      "0.0864924060797062\n",
      "0.08660161309258668\n",
      "0.08671082010428763\n",
      "0.08682002711481362\n",
      "0.08692923412416202\n",
      "0.08703844113233597\n",
      "0.08714764813933525\n",
      "0.08725685514516059\n",
      "0.08736606214981417\n",
      "0.08747526915165756\n",
      "0.08758447615396886\n",
      "0.08769368315510727\n",
      "0.08780289015507732\n",
      "0.08791209715387739\n",
      "0.0880213041515096\n",
      "0.08813051114797474\n",
      "0.08823971813502733\n",
      "0.08834892512916093\n",
      "0.08845813212212769\n",
      "0.08856733911393214\n",
      "0.08867654610457126\n",
      "0.08878575309404858\n",
      "0.08889496008236346\n",
      "0.08900416706951703\n",
      "0.08911337405551102\n",
      "0.08922258104034421\n",
      "0.08933178801198473\n",
      "0.08944099499450092\n",
      "0.08955020197586129\n",
      "0.08965940895606384\n",
      "0.08976861593511105\n",
      "0.0898778229130033\n",
      "0.08998702988974072\n",
      "0.09009623685687959\n",
      "0.09020544383131056\n",
      "0.09031465080459165\n",
      "0.0904238577767195\n",
      "0.09053306474769797\n",
      "0.09064227171752604\n",
      "0.09075147868620521\n",
      "0.09086068565373681\n",
      "0.09096989262012002\n",
      "0.09107909958535847\n",
      "0.09118830652832352\n",
      "0.09129751349127059\n",
      "0.0914067204530718\n",
      "0.09151592741373\n",
      "0.09162513437324515\n",
      "0.09173434133161781\n",
      "0.0918435482888502\n",
      "0.0919527552377125\n",
      "0.09206196219266524\n",
      "0.09217116914647665\n",
      "0.0922803760991509\n",
      "0.09238958305068658\n",
      "0.09249879000108562\n",
      "0.09260799695034887\n",
      "0.09271720389847594\n",
      "0.09282641084547001\n",
      "0.0929356177913284\n",
      "0.09304482470716026\n",
      "0.0931540316507532\n",
      "0.09326323859321528\n",
      "0.09337244553454603\n",
      "0.09348165247474641\n",
      "0.0935908594138182\n",
      "0.0937000663517601\n",
      "0.09380927328398671\n",
      "0.09391848021967338\n",
      "0.09402768715423494\n",
      "0.09413689408766959\n",
      "0.09424610101997963\n",
      "0.09435530795116548\n",
      "0.09446451488122719\n",
      "0.09457372181016745\n",
      "0.09468292873798405\n",
      "0.09479213566468125\n",
      "0.09490134255493295\n",
      "0.09501054947938872\n",
      "0.0951197564027247\n",
      "0.09522896332494224\n",
      "0.09533817024604269\n",
      "0.09544737716602518\n",
      "0.09555658408489327\n",
      "0.09566579100212706\n",
      "0.09577499791876444\n",
      "0.09588420483428636\n",
      "0.09599341174285551\n",
      "0.0961026186561519\n",
      "0.09621182556833599\n",
      "0.09632103247941\n",
      "0.09643023938937219\n",
      "0.09653944629822676\n",
      "0.0966486532059702\n",
      "0.09675786007219996\n",
      "0.09686706697772779\n",
      "0.09697627388214895\n",
      "0.09708548078546432\n",
      "0.09719468768767348\n",
      "0.0973038945887795\n",
      "0.09741310148877978\n",
      "0.0975223083876785\n",
      "0.09763151528547305\n",
      "0.09774072218216649\n",
      "0.09784992905835417\n",
      "0.09795913595284544\n",
      "0.09806834284623783\n",
      "0.09817754973853005\n",
      "0.09828675662972601\n",
      "0.09839596351982227\n",
      "0.09850517040882296\n",
      "0.09861437725259393\n",
      "0.09872358413940223\n",
      "0.09883279102511586\n",
      "0.09894199790973485\n",
      "0.0990512047932618\n",
      "0.09916041167569456\n",
      "0.09926961855703724\n",
      "0.09937882543728685\n",
      "0.09948803231644684\n",
      "0.09959723919451637\n",
      "0.09970644603977351\n",
      "0.099815652915666\n",
      "0.0999248597904698\n",
      "0.10003406666418832\n",
      "0.10014327353681861\n",
      "0.10025248040836472\n",
      "0.10036168727882454\n",
      "0.10047089410172101\n",
      "0.1005801009700134\n",
      "0.10068930783722252\n",
      "0.10079851470335051\n",
      "0.1009077215683957\n",
      "0.10101692843236212\n",
      "0.1011261352952464\n",
      "0.10123534215705236\n",
      "0.10134454901777874\n",
      "0.10145375587742726\n",
      "0.10156296269322329\n",
      "0.10167216955071738\n",
      "0.101781376407137\n",
      "0.10189058326247967\n",
      "0.1019997901167494\n",
      "0.10210899696994365\n",
      "0.1022182038220654\n",
      "0.10232741062567965\n",
      "0.10243661747565642\n",
      "0.1025458243245628\n",
      "0.10265503117239758\n",
      "0.10276423801916448\n",
      "0.10287344486486025\n",
      "0.10298265170948882\n",
      "0.10309185855304853\n",
      "0.10320106539554151\n",
      "0.10331027223696815\n",
      "0.10341947902478643\n",
      "0.10352868586408295\n",
      "0.10363789270231363\n",
      "0.10374709953948241\n",
      "0.10385630637558638\n",
      "0.10396551321062888\n",
      "0.10407472004460908\n",
      "0.10418392683053894\n",
      "0.10429313366239829\n",
      "0.10440234049319706\n",
      "0.10451154732293852\n",
      "0.10462075415161985\n",
      "0.10472996097924496\n",
      "0.10483916780581176\n",
      "0.10494837463132278\n",
      "0.10505758145577797\n",
      "0.10516678827917782\n",
      "0.10527599504051503\n",
      "0.10538520186180662\n",
      "0.1054944086820472\n",
      "0.10560361550123344\n",
      "0.1057128223193691\n",
      "0.10582202913645289\n",
      "0.10593123595248655\n",
      "0.10604044272233493\n",
      "0.10614964953626946\n",
      "0.10625885634915704\n",
      "0.10636806314485814\n",
      "0.10647726995565102\n",
      "0.10658647676539598\n",
      "0.10669568357409595\n",
      "0.10680489038175044\n",
      "0.10691409718836037\n",
      "0.10702330399392726\n",
      "0.10713251073027938\n",
      "0.10724171753376154\n",
      "0.1073509243362\n",
      "0.10746013113759859\n",
      "0.1075693379379556\n",
      "0.10767854473727317\n",
      "0.10778775153555159\n",
      "0.10789695829092082\n",
      "0.10800616508712348\n",
      "0.10811537188228756\n",
      "0.10822457864487683\n",
      "0.10833378543796843\n",
      "0.10844299223002565\n",
      "0.1085521990210476\n",
      "0.1086614058110356\n",
      "0.10877061259999073\n",
      "0.10887981938791233\n",
      "0.10898902610080435\n",
      "0.10909823288666239\n",
      "0.10920743967149109\n",
      "0.10931664645528835\n",
      "0.1094258532380567\n",
      "0.109535060019796\n",
      "0.10964426680050682\n",
      "0.10975347354301132\n",
      "0.1098626803216674\n",
      "0.10997188709929916\n",
      "0.11008109383016691\n",
      "0.11019030060574715\n",
      "0.11029950738030216\n",
      "0.11040871415383367\n",
      "0.1105179209263423\n",
      "0.11062712769782787\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.11073633446829291\n",
      "0.1108455411592619\n",
      "0.11095474792768535\n",
      "0.11106395469508736\n",
      "0.11117316146147083\n",
      "0.1112823682268352\n",
      "0.11139157499118145\n",
      "0.11150078175451095\n",
      "0.1116099884857666\n",
      "0.11171919524706397\n",
      "0.11182840200734406\n",
      "0.1119376087078976\n",
      "0.11204681546614874\n",
      "0.11215602222338669\n",
      "0.11226522897961162\n",
      "0.11237443573482377\n",
      "0.11248364248902522\n",
      "0.1125928492422143\n",
      "0.11270205591280616\n",
      "0.11281126266397491\n",
      "0.11292046941413536\n",
      "0.1130296761632865\n",
      "0.11313888291142975\n",
      "0.11324808965856599\n",
      "0.11335729640469475\n",
      "0.11346650312631734\n",
      "0.11357570987043433\n",
      "0.11368491661354786\n",
      "0.11379412328521066\n",
      "0.11390333002631553\n",
      "0.1140125367664171\n",
      "0.11412174350551602\n",
      "0.1142309502436139\n",
      "0.11434015698070957\n",
      "0.11444936371680647\n",
      "0.1145585703685757\n",
      "0.11466777710267254\n",
      "0.11477698383576973\n",
      "0.11488619056504452\n",
      "0.11499539729614651\n",
      "0.11510460402625106\n",
      "0.1152138107553605\n",
      "0.115323017468965\n",
      "0.11543222419608395\n",
      "0.1155414309222069\n",
      "0.11565063756641607\n",
      "0.11575984429055221\n",
      "0.11586905101369568\n",
      "0.11597825773584766\n",
      "0.11608746445700738\n",
      "0.11619667117717786\n",
      "0.11630587789635648\n",
      "0.11641508453086469\n",
      "0.11652429124806485\n",
      "0.11663349796427708\n",
      "0.11674270465836599\n",
      "0.1168519113726028\n",
      "0.11696111808585394\n",
      "0.11707032479811795\n",
      "0.11717953150531712\n",
      "0.11728873821561098\n",
      "0.11739794492492159\n",
      "0.11750715154311943\n",
      "0.1176163582504629\n",
      "0.11772556495682428\n",
      "0.11783477166220321\n",
      "0.11794397836660227\n",
      "0.11805318507001927\n",
      "0.11816239177245773\n",
      "0.11827159839127036\n",
      "0.11838080509174988\n",
      "0.11849001179125085\n",
      "0.11859921845145632\n",
      "0.11870842514900316\n",
      "0.11881763184557263\n",
      "0.11892683854116794\n",
      "0.11903604523578626\n",
      "0.11914525192943104\n",
      "0.1192544586221008\n",
      "0.11936366521576092\n",
      "0.11947287190648469\n",
      "0.1195820785962357\n",
      "0.11969128528501605\n",
      "0.11980049197282402\n",
      "0.11990969865966307\n",
      "0.12001890534553059\n",
      "0.12012811195022136\n",
      "0.12023731863415098\n",
      "0.12034652531711243\n",
      "0.12045573194475848\n",
      "0.12056493862578498\n",
      "0.12067414530584646\n",
      "0.12078335198494054\n",
      "0.12089255866307064\n",
      "0.12100176534023487\n",
      "0.12111097201643549\n",
      "0.12122017858704573\n",
      "0.12132938526131941\n",
      "0.12143859193463152\n",
      "0.1215477986069808\n",
      "0.12165700527837062\n",
      "0.12176621194879801\n",
      "0.12187541861826633\n",
      "0.12198462521041592\n",
      "0.12209383187796527\n",
      "0.12220303854455648\n",
      "0.12231224514098833\n",
      "0.12242145180566522\n",
      "0.12253065846938417\n",
      "0.12263986513214853\n",
      "0.12274907179395604\n",
      "0.12285827845480934\n",
      "0.12296748511470793\n",
      "0.12307669166376853\n",
      "0.12318589832176068\n",
      "0.12329510497879938\n",
      "0.12340431163488759\n",
      "0.12351351829002273\n",
      "0.12362272494420812\n",
      "0.12373193159744217\n",
      "0.12384113817863784\n",
      "0.1239503448299733\n",
      "0.12405955148035977\n",
      "0.12416875804694333\n",
      "0.12427796469543405\n",
      "0.12438717134297944\n",
      "0.12449637798957688\n",
      "0.12460558463522937\n",
      "0.12471479127993601\n",
      "0.12482399792369807\n",
      "0.12493320445272035\n",
      "0.12504241109459444\n",
      "0.12515161773552683\n",
      "0.12526082437433958\n",
      "0.1253700266447283\n",
      "0.12547920532502568\n",
      "0.12558836669828913\n",
      "0.12569752332545864\n",
      "0.12580667570360848\n",
      "0.12591583039257484\n",
      "0.12602498873704526\n",
      "0.12613415047338156\n",
      "0.12624331501872976\n",
      "0.12635248195938853\n",
      "0.126461650907162\n",
      "0.12657082159711436\n",
      "0.126679993786268\n",
      "0.1267891673002259\n",
      "0.12689834197931732\n",
      "0.12700751770331853\n",
      "0.1271166943624336\n",
      "0.12722587187055379\n",
      "0.12733505014921656\n",
      "0.1274442291347511\n",
      "0.12755340876920493\n",
      "0.12766258900419822\n",
      "0.12777176979568464\n",
      "0.12788095110602082\n",
      "0.1279901329008829\n",
      "0.12809931515036363\n",
      "0.12820849782712382\n",
      "0.12831768090695936\n",
      "0.1284268643676723\n",
      "0.1285360481893502\n",
      "0.12864523235366318\n",
      "0.1287544168439889\n",
      "0.12886360164496594\n",
      "0.12897278674253745\n",
      "0.12908197212366138\n",
      "0.12919115777631274\n",
      "0.12930034368929139\n",
      "0.12940952985220477\n",
      "0.12951871625533723\n",
      "0.12962790288962503\n",
      "0.12973708974656512\n",
      "0.1298462768181884\n",
      "0.12995546409699446\n",
      "0.13006465157592595\n",
      "0.13017383924832066\n",
      "0.1302830271078882\n",
      "0.13039221514867408\n",
      "0.13050140336503915\n",
      "0.13061059175163187\n",
      "0.13071978030337053\n",
      "0.13082896901542154\n",
      "0.13093815788318405\n",
      "0.13104734690227265\n",
      "0.1311565360685042\n",
      "0.1312657253778837\n",
      "0.13137491482659308\n",
      "0.13148410441097957\n",
      "0.13159329412754606\n",
      "0.13170248397294135\n",
      "0.13181167394395196\n",
      "0.1319208640374939\n",
      "0.13203005425060552\n",
      "0.13213924458044063\n",
      "0.1322484350242622\n",
      "0.13235762557943653\n",
      "0.13246681624342782\n",
      "0.13257600701379302\n",
      "0.13268519788817718\n",
      "0.13279438886430892\n",
      "0.13290357993999644\n",
      "0.13301277111312354\n",
      "0.133121962381646\n",
      "0.13323115374358824\n",
      "0.13334034519704005\n",
      "0.13344953674015364\n",
      "0.13355872837114077\n",
      "0.13366792008827016\n",
      "0.1337771118898649\n",
      "0.13388630377430014\n",
      "0.13399549574000078\n",
      "0.13410468778543946\n",
      "0.1342138799091345\n",
      "0.13432307210964803\n",
      "0.1344322643855842\n",
      "0.13454145673558746\n",
      "0.134650649158341\n",
      "0.13475984165256513\n",
      "0.13486903421701602\n",
      "0.13497822685048408\n",
      "0.13508741955179282\n",
      "0.13519661231979754\n",
      "0.1353058051533842\n",
      "0.1354149980514682\n",
      "0.13552419101299337\n",
      "0.13563338403693093\n",
      "0.13574257712227852\n",
      "0.13585177026805925\n",
      "0.1359609634733208\n",
      "0.13607015673713457\n",
      "0.13617935005859494\n",
      "0.13628854343681837\n",
      "0.13639773687094273\n",
      "0.13650693036012657\n",
      "0.13661612390354844\n",
      "0.13672531750040623\n",
      "0.13683451114991654\n",
      "0.1369437048513141\n",
      "0.1370528986038512\n",
      "0.13716209240679705\n",
      "0.13727128625943738\n",
      "0.13738048016107385\n",
      "0.13748967411102353\n",
      "0.13759886810861854\n",
      "0.13770806215320552\n",
      "0.13781725624414518\n",
      "0.13792645038081192\n",
      "0.13803564456259346\n",
      "0.13814483878889036\n",
      "0.1382540330591157\n",
      "0.13836322737269477\n",
      "0.1384724217290646\n",
      "0.13858161612767375\n",
      "0.13869081056798194\n",
      "0.13880000504945972\n",
      "0.13890919957158818\n",
      "0.1390183941338587\n",
      "0.1391275887357726\n",
      "0.13923678337684098\n",
      "0.1393459780565843\n",
      "0.1394551727745323\n",
      "0.1395643675302236\n",
      "0.13967356232320569\n",
      "0.1397827571530344\n",
      "0.1398919520192739\n",
      "0.14000114692149648\n",
      "0.1401103418592822\n",
      "0.14021953683221886\n",
      "0.1403287318399017\n",
      "0.14043792688193324\n",
      "0.14054712195792315\n",
      "0.140656317067488\n",
      "0.1407655122102511\n",
      "0.14087470738584243\n",
      "0.14098390259389834\n",
      "0.14109309783406151\n",
      "0.1412022931059808\n",
      "0.14131148840931093\n",
      "0.1414206837437126\n",
      "0.14152987910885223\n",
      "0.14163907450440175\n",
      "0.14174826993003858\n",
      "0.14185746538544552\n",
      "0.14196666087031054\n",
      "0.14207585638432668\n",
      "0.14218505192719202\n",
      "0.1422942474986095\n",
      "0.14240344309828679\n",
      "0.14251263872593625\n",
      "0.1426218343812748\n",
      "0.1427310300640238\n",
      "0.14284022577390898\n",
      "0.14294942151066037\n",
      "0.14305861727401215\n",
      "0.14316781306370258\n",
      "0.14327700887947395\n",
      "0.14338620472107247\n",
      "0.14349540058824817\n",
      "0.14360459648075485\n",
      "0.14371379239835003\n",
      "0.14382298834079477\n",
      "0.1439321843078537\n",
      "0.14404138029929492\n",
      "0.1441505763148899\n",
      "0.14425977235441345\n",
      "0.14436896841764366\n",
      "0.1444781645043618\n",
      "0.14458736061435226\n",
      "0.1446965567474025\n",
      "0.14480575290330303\n",
      "0.14491494908184724\n",
      "0.1450241452828315\n",
      "0.14513334150605497\n",
      "0.14524253775131962\n",
      "0.14535173401843016\n",
      "0.14546093030719395\n",
      "0.145570126617421\n",
      "0.1456793229489239\n",
      "0.14578851930151784\n",
      "0.14589771567502038\n",
      "0.14600691206925162\n",
      "0.14611610848403403\n",
      "0.14622530491919242\n",
      "0.14633450137455392\n",
      "0.14644369784994796\n",
      "0.14655289434520616\n",
      "0.14666209086016235\n",
      "0.14677128739465253\n",
      "0.14688048394851477\n",
      "0.14698968052158928\n",
      "0.14709887711371827\n",
      "0.14720807372474595\n",
      "0.14731727035451853\n",
      "0.14742646700288412\n",
      "0.14753566366969276\n",
      "0.14764486035479638\n",
      "0.1477540570580487\n",
      "0.1478632537793053\n",
      "0.1479724505184235\n",
      "0.1480816472752624\n",
      "0.1481908440496828\n",
      "0.1483000408415472\n",
      "0.14840923765071976\n",
      "0.14851843447706628\n",
      "0.14862763132045415\n",
      "0.14873682818075237\n",
      "0.1488460250578315\n",
      "0.14895522195156363\n",
      "0.1490644188618223\n",
      "0.14917361578848265\n",
      "0.14928281273142116\n",
      "0.14939200969051583\n",
      "0.14950120666564604\n",
      "0.14961040365669254\n",
      "0.1497196006635375\n",
      "0.14982879768606444\n",
      "0.14993799472415817\n",
      "0.1500471917777048\n",
      "0.1501563888465918\n",
      "0.15026558593070782\n",
      "0.15037478302994284\n",
      "0.15048398014418798\n",
      "0.15059317727333568\n",
      "0.15070237441727946\n",
      "0.1508115715759141\n",
      "0.15092076874913551\n",
      "0.15102996593684073\n",
      "0.15113916313892792\n",
      "0.15124836035529637\n",
      "0.15135755758584646\n",
      "0.1514667548304796\n",
      "0.15157595208909835\n",
      "0.1516851493616062\n",
      "0.15179434664790778\n",
      "0.15190354394790864\n",
      "0.1520127412615154\n",
      "0.15212193858863562\n",
      "0.15223113592917786\n",
      "0.1523403332830516\n",
      "0.15244953065016734\n",
      "0.1525587280304364\n",
      "0.1526679254237711\n",
      "0.15277712283008466\n",
      "0.15288632024929116\n",
      "0.15299551768130557\n",
      "0.15310471512604373\n",
      "0.15321391258342237\n",
      "0.15332311005335902\n",
      "0.15343230753577203\n",
      "0.15354150503058062\n",
      "0.1536507025377048\n",
      "0.15375990005706536\n",
      "0.15386909758858391\n",
      "0.15397829513218284\n",
      "0.15408749268778527\n",
      "0.1541966902553151\n",
      "0.15430588783469698\n",
      "0.1544150854258563\n",
      "0.15452428302871915\n",
      "0.1546334806432124\n",
      "0.15474267826926355\n",
      "0.15485187590680086\n",
      "0.15496107355575328\n",
      "0.1550702712160504\n",
      "0.15517946888762252\n",
      "0.15528866657040058\n",
      "0.15539786426431618\n",
      "0.15550706196930159\n",
      "0.1556162596852897\n",
      "0.15572545741221402\n",
      "0.15583465515000872\n",
      "0.15594385289860854\n",
      "0.15605305065794886\n",
      "0.15616224842796567\n",
      "0.1562714462085955\n",
      "0.15638064399977555\n",
      "0.15648984180144354\n",
      "0.15659903961353774\n",
      "0.15670823743599704\n",
      "0.15681743526876085\n",
      "0.15692663311176913\n",
      "0.15703583096496243\n",
      "0.15714502882828177\n",
      "0.15725422670166875\n",
      "0.15736342458506547\n",
      "0.15747262247841456\n",
      "0.1575818203816592\n",
      "0.15769101829474297\n",
      "0.15780021621761003\n",
      "0.15790941415020504\n",
      "0.15801861209247312\n",
      "0.15812781004435986\n",
      "0.15823700800581136\n",
      "0.15834620597677418\n",
      "0.15845540395719535\n",
      "0.15856460194702232\n",
      "0.15867379994620306\n",
      "0.15878299795468595\n",
      "0.1588921959724198\n",
      "0.1590013939993539\n",
      "0.15911059203543795\n",
      "0.1592197900806221\n",
      "0.15932898813485688\n",
      "0.1594381861980933\n",
      "0.15954738427028273\n",
      "0.15965658235137697\n",
      "0.15976578044132828\n",
      "0.1598749785400892\n",
      "0.15998417664761277\n",
      "0.1600933747638524\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.16020257288876188\n",
      "0.16031177102229538\n",
      "0.16042096916440746\n",
      "0.16053016731505304\n",
      "0.16063936547418742\n",
      "0.16074856364176623\n",
      "0.16085776181774555\n",
      "0.16096696000208174\n",
      "0.16107615819473156\n",
      "0.1611853563956521\n",
      "0.1612945546048008\n",
      "0.16140375282213545\n",
      "0.16151295104761418\n",
      "0.16162214928119542\n",
      "0.16173134752283802\n",
      "0.16184054577250107\n",
      "0.16194974403014403\n",
      "0.16205894229572668\n",
      "0.1621681405692091\n",
      "0.16227733885055173\n",
      "0.1623865371397153\n",
      "0.1624957354366608\n",
      "0.16260493374134957\n",
      "0.1627141320537433\n",
      "0.1628233303738039\n",
      "0.1629325287014936\n",
      "0.16304172703677497\n",
      "0.1631509253796108\n",
      "0.16326012372996418\n",
      "0.16336932208779856\n",
      "0.16347852045307756\n",
      "0.1635877188257652\n",
      "0.16369691720582566\n",
      "0.16380611559322347\n",
      "0.1639153139879234\n",
      "0.1640245123898905\n",
      "0.16413371079909006\n",
      "0.16424290921548768\n",
      "0.16435210763904917\n",
      "0.16446130606974063\n",
      "0.16457050450752841\n",
      "0.1646797029523791\n",
      "0.16478890140425956\n",
      "0.1648980998631369\n",
      "0.1650072983289784\n",
      "0.1651164968017517\n",
      "0.16522569528142458\n",
      "0.16533489376796515\n",
      "0.16544409226134166\n",
      "0.16555329076152267\n",
      "0.16566248926847693\n",
      "0.1657716877821734\n",
      "0.16588088630258135\n",
      "0.1659900848296702\n",
      "0.1660992833634096\n",
      "0.16620848190376944\n",
      "0.16631768045071985\n",
      "0.16642687900423112\n",
      "0.16653607756427377\n",
      "0.16664527613081856\n",
      "0.16675447470383645\n",
      "0.1668636732832986\n",
      "0.16697287186917636\n",
      "0.16708207046144133\n",
      "0.16719126906006526\n",
      "0.16730046766502016\n",
      "0.16740966627627818\n",
      "0.16751886489381168\n",
      "0.16762806351759324\n",
      "0.16773726214759563\n",
      "0.16784646078379178\n",
      "0.16795565942615487\n",
      "0.16806485807465818\n",
      "0.16817405672927524\n",
      "0.16828325538997976\n",
      "0.16839245405674563\n",
      "0.1685016527295469\n",
      "0.1686108514083578\n",
      "0.16872005009315275\n",
      "0.16882924878390637\n",
      "0.16893844748059342\n",
      "0.16904764618318885\n",
      "0.16915684489166777\n",
      "0.16926604360600547\n",
      "0.1693752423261774\n",
      "0.1694844410521592\n",
      "0.16959363978392666\n",
      "0.1697028385214557\n",
      "0.16981203726472247\n",
      "0.16992123601370324\n",
      "0.17003043476837443\n",
      "0.17013963352871264\n",
      "0.17024883229469465\n",
      "0.17035803106629735\n",
      "0.1704672298434978\n",
      "0.1705764286262732\n",
      "0.17068562741460094\n",
      "0.17079482620845854\n",
      "0.17090402500782367\n",
      "0.17101322381267414\n",
      "0.17112242262298794\n",
      "0.17123162143874313\n",
      "0.17134082025991798\n",
      "0.1714500190864909\n",
      "0.17155921791844042\n",
      "0.17166841675574523\n",
      "0.17177761559838414\n",
      "0.17188681444633608\n",
      "0.17199601329958017\n",
      "0.17210521215809563\n",
      "0.17221441102186183\n",
      "0.17232360989085826\n",
      "0.1724328087650646\n",
      "0.17254200764446054\n",
      "0.172651206529026\n",
      "0.172760405418741\n",
      "0.1728696043135857\n",
      "0.17297880321354037\n",
      "0.1730880021185854\n",
      "0.17319720102870134\n",
      "0.17330639994386884\n",
      "0.17341559886406865\n",
      "0.1735247977892817\n",
      "0.173633996719489\n",
      "0.1737431956546717\n",
      "0.17385239459481103\n",
      "0.17396159353988838\n",
      "0.17407079248988525\n",
      "0.17417999144478324\n",
      "0.1742891904045641\n",
      "0.17439838936920962\n",
      "0.1745075883387018\n",
      "0.17461678731302271\n",
      "0.17472598629215452\n",
      "0.1748351852760795\n",
      "0.17494438426478007\n",
      "0.17505358325823872\n",
      "0.17516278225643808\n",
      "0.1752719812593609\n",
      "0.17538118026698996\n",
      "0.17549037927930825\n",
      "0.17559957829629877\n",
      "0.17570877731794468\n",
      "0.17581797634422924\n",
      "0.1759271753751358\n",
      "0.17603637441064782\n",
      "0.17614557345074883\n",
      "0.17625477249542248\n",
      "0.17636397154465258\n",
      "0.17647317059842293\n",
      "0.1765823696567175\n",
      "0.17669156871952035\n",
      "0.1768007677868156\n",
      "0.17690996685858754\n",
      "0.17701916593482045\n",
      "0.17712836501549878\n",
      "0.17723756410060706\n",
      "0.1773467631901299\n",
      "0.17745596228405203\n",
      "0.17756516138235823\n",
      "0.17767436048503338\n",
      "0.1777835595920625\n",
      "0.1778927587034306\n",
      "0.1780019578191229\n",
      "0.17811115693912463\n",
      "0.17822035606342113\n",
      "0.1783295551919978\n",
      "0.1784387543248402\n",
      "0.17854795346193383\n",
      "0.17865715260326445\n",
      "0.1787663517488178\n",
      "0.17887555089857973\n",
      "0.17898475005253617\n",
      "0.17909394921067315\n",
      "0.17920314837297674\n",
      "0.17931234753943312\n",
      "0.17942154671002855\n",
      "0.17953074588474938\n",
      "0.179639945063582\n",
      "0.17974914424651292\n",
      "0.17985834343352872\n",
      "0.17996754262461603\n",
      "0.1800767418197616\n",
      "0.18018594101895224\n",
      "0.18029514022217483\n",
      "0.18040433942941633\n",
      "0.18051353864066377\n",
      "0.18062273785590424\n",
      "0.18073193707512494\n",
      "0.18084113629831314\n",
      "0.18095033552545614\n",
      "0.18105953475654135\n",
      "0.18116873399155625\n",
      "0.18127793323048838\n",
      "0.18138713247332536\n",
      "0.18149633172005486\n",
      "0.18160553097066467\n",
      "0.1817147302251426\n",
      "0.18182392948347653\n",
      "0.18193312874565445\n",
      "0.18204232801166437\n",
      "0.1821515272814944\n",
      "0.1822607265551327\n",
      "0.18236992583256753\n",
      "0.18247912511378717\n",
      "0.18258832439877998\n",
      "0.1826975236875344\n",
      "0.18280672298003892\n",
      "0.1829159222762821\n",
      "0.18302512157625256\n",
      "0.183134320879939\n",
      "0.18324352018733017\n",
      "0.1833527194984149\n",
      "0.18346191881318205\n",
      "0.18357111813162055\n",
      "0.18368031745371943\n",
      "0.18378951677946773\n",
      "0.18389871610885458\n",
      "0.18400791544186917\n",
      "0.18411711477850073\n",
      "0.18422631411873858\n",
      "0.18433551346257204\n",
      "0.18444471280999059\n",
      "0.18455391216098366\n",
      "0.18466311151554082\n",
      "0.18477231087365165\n",
      "0.1848815102353058\n",
      "0.184990709600493\n",
      "0.18509990896920298\n",
      "0.18520910834142557\n",
      "0.18531830771715066\n",
      "0.18542750709636818\n",
      "0.18553670647906814\n",
      "0.18564590586524055\n",
      "0.1857551052548755\n",
      "0.1858643046479632\n",
      "0.18597350404449378\n",
      "0.18608270344445754\n",
      "0.1861919028478448\n",
      "0.18630110225464588\n",
      "0.18641030166485123\n",
      "0.1865195010784513\n",
      "0.18662870049543664\n",
      "0.1867378999157978\n",
      "0.18684709933952542\n",
      "0.18695629876661013\n",
      "0.18706549819704268\n",
      "0.18717469763081385\n",
      "0.18728389706791446\n",
      "0.18739309650833538\n",
      "0.18750229595206755\n",
      "0.1876114953991019\n",
      "0.1877206948494295\n",
      "0.18782989430304137\n",
      "0.18793909375992865\n",
      "0.18804829322008249\n",
      "0.1881574926834941\n",
      "0.18826669215015476\n",
      "0.18837589162005577\n",
      "0.18848509109318848\n",
      "0.18859429056954427\n",
      "0.18870349004911458\n",
      "0.1888126895318909\n",
      "0.1889218890178648\n",
      "0.18903108850702782\n",
      "0.1891402879993716\n",
      "0.18924948749488782\n",
      "0.18935868699356817\n",
      "0.18946788649540441\n",
      "0.18957708600038836\n",
      "0.18968628550851185\n",
      "0.18979548501976679\n",
      "0.18990468453414508\n",
      "0.19001388405163872\n",
      "0.1901230835722397\n",
      "0.1902322830959401\n",
      "0.19034148262273198\n",
      "0.19045068215260755\n",
      "0.19055988168555893\n",
      "0.19066908122157838\n",
      "0.19077828076065817\n",
      "0.19088748030279057\n",
      "0.19099667984796795\n",
      "0.1911058793961827\n",
      "0.19121507894742726\n",
      "0.1913242785016941\n",
      "0.19143347805897568\n",
      "0.19154267761926458\n",
      "0.1916518771825534\n",
      "0.19176107674883475\n",
      "0.1918702763181013\n",
      "0.19197947589034575\n",
      "0.19208867546556083\n",
      "0.1921978750437393\n",
      "0.19230707462487404\n",
      "0.19241627420895785\n",
      "0.19252547379598364\n",
      "0.19263467338594434\n",
      "0.19274387297883291\n",
      "0.19285307257464235\n",
      "0.1929622721733657\n",
      "0.19307147177499606\n",
      "0.19318067137952652\n",
      "0.19328987098695022\n",
      "0.19339907059726036\n",
      "0.19350827021045017\n",
      "0.19361746982651287\n",
      "0.19372666944544178\n",
      "0.19383586906723022\n",
      "0.19394506869187153\n",
      "0.19405426831935912\n",
      "0.19416346794968642\n",
      "0.1942726675828469\n",
      "0.19438186721883405\n",
      "0.1944910668576414\n",
      "0.19460026649926251\n",
      "0.194709466143691\n",
      "0.1948186657909205\n",
      "0.19492786544094465\n",
      "0.19503706509375715\n",
      "0.19514626474935176\n",
      "0.19525546440772223\n",
      "0.19536466406886235\n",
      "0.19547386373276596\n",
      "0.1955830633994269\n",
      "0.1956922630688391\n",
      "0.19580146274099647\n",
      "0.19591066241589294\n",
      "0.1960198620935225\n",
      "0.1961290617738792\n",
      "0.19623826145695708\n",
      "0.19634746114275023\n",
      "0.19645666083125274\n",
      "0.19656586052245878\n",
      "0.1966750602163625\n",
      "0.19678425991295811\n",
      "0.19689345961223986\n",
      "0.197002659314202\n",
      "0.19711185901883882\n",
      "0.19722105872614465\n",
      "0.19733025843611385\n",
      "0.19743945814874078\n",
      "0.19754865786401987\n",
      "0.19765785758194557\n",
      "0.19776705730251232\n",
      "0.19787625702571465\n",
      "0.19798545675154708\n",
      "0.19809465648000416\n",
      "0.19820385621108047\n",
      "0.19831305594477067\n",
      "0.19842225568106933\n",
      "0.19853145541997116\n",
      "0.19864065516147086\n",
      "0.19874985490556316\n",
      "0.1988590546522428\n",
      "0.19896825440150456\n",
      "0.19907745415334324\n",
      "0.1991866539077537\n",
      "0.1992958536647308\n",
      "0.1994050534242694\n",
      "0.19951425318636443\n",
      "0.19962345295101083\n",
      "0.1997326527182036\n",
      "0.19984185248793768\n",
      "0.19995105226020815\n",
      "0.20006025203501002\n",
      "CPU times: user 2.27 s, sys: 96.8 ms, total: 2.37 s\n",
      "Wall time: 2.31 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "time = 0\n",
    "while time <= 0.2:\n",
    "    t_dt = time_step(cons_var, grid.dx, cfl_num)\n",
    "    flux = llf_flux(cons_var)\n",
    "    cv_new = cons_var - (t_dt / grid.dx) * flux\n",
    "    cons_var = bc(cv_new)\n",
    "    time += t_dt\n",
    "    print(time)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "705d52c5",
   "metadata": {},
   "source": [
    "### Plot results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "aa868f03",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0. , 0.2, 0.4, 0.6, 0.8, 1. , 1.2]),\n",
       " [Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, ''),\n",
       "  Text(0, 0, '')])"
      ]
     },
     "execution_count": 15,
     "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": [
    "prim_var = cons_to_prim_vars(cons_var)\n",
    "analytical = np.loadtxt('/mnt/external_data/maruthi/my_codes/compressible_euler_1d/output/shock_tube.dat')\n",
    "plt.plot(x_grid, prim_var[:, 0], label='LLF')\n",
    "plt.plot(analytical[:, 0], analytical[:, 1], label='Analytical')\n",
    "plt.xlabel('x', fontsize=16)\n",
    "plt.ylabel(r'$\\rho $', fontsize=16)\n",
    "plt.legend(fontsize=16)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.yticks(fontsize=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "32d9fe31",
   "metadata": {},
   "outputs": [],
   "source": [
    "# !numba -s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c72e951c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}