CETO-4-1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ae999e93",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "# Gruvbox theme for jupyter (can be deleted)\n",
    "from jupyterthemes import jtplot\n",
    "jtplot.style(theme='gruvboxd', context='notebook', ticks=True, grid=True)\n",
    "plt.rcParams['figure.dpi'] = 300\n",
    "plt.rcParams['savefig.dpi'] = 300"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c27218fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Average velocity calculator\n",
    "def v(N, probability):\n",
    "    t = 0 # Time in seconds\n",
    "    dist = 0 # Distance in meters\n",
    "    for i in range(0,N):\n",
    "        # Jump\n",
    "        t+=1        # 1 second for jumping\n",
    "        dist += 0.3 # move for 0.3 meters\n",
    "        # random.random() returns value from 0 to 1\n",
    "        if random.random() <= probability: # if cracked the leg, wait 30 seconds\n",
    "            t+=30\n",
    "    return dist/t   # calculate average velocity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "55a20ff7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x16e3b6bee20>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2400x2100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## First task - function velocity(amount of jumps) \n",
    "N = 100\n",
    "x = []\n",
    "x = [i*1000+500 for i in range(N)] \n",
    "    \n",
    "# Graph\n",
    "v = np.vectorize(v)\n",
    "vs = v(x, 0.2)\n",
    "plt.title(\"$v(N)$\")\n",
    "plt.ylabel('$v$')\n",
    "plt.xlabel('$N$')\n",
    "plt.plot(x, vs)\n",
    "\n",
    "# Expected velocity is 0.3/(1 + 30*0.2) = 0.04285 m/s\n",
    "# The more jumps there is, the more velocity goes to this value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7565eff5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x25c311d3610>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2400x2100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Second task - function velocity(probability) \n",
    "x = np.arange(0, 1, 0.1)\n",
    "x1 = np.arange(0, 1, 0.01)\n",
    "vtest = lambda x: 0.3/(1+30*x)\n",
    "\n",
    "# Graph\n",
    "v = np.vectorize(v)\n",
    "vs = v(100000, x)\n",
    "vtestgr = vtest(x1)\n",
    "plt.title(\"$v(p)$\")\n",
    "plt.ylabel('$v$')\n",
    "plt.xlabel('$probability$')\n",
    "# plt.plot(x1, vtestgr)\n",
    "plt.scatter(x, vs)\n",
    "\n",
    "# Dependancy is shown on the graph. We can see that average velocity falls very fast with increase of\n",
    "#probability of cracking. When p -> 0, than v -> 0.3; when p -> 1, than v -> 0.00967742"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5c18b60f",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Third task - broken horse\n",
    "def brokenV(N):\n",
    "    t = 0 # Time in seconds\n",
    "    dist = 0 # Distance in meters\n",
    "    for i in range(0,N):\n",
    "        # Jump\n",
    "        t+=1\n",
    "        if random.random() <= 0.3:\n",
    "            dist += 0.15\n",
    "        else:\n",
    "            dist += 0.3\n",
    "        \n",
    "        if random.random() <= 0.2: # if cracked the leg, wait 30 seconds\n",
    "            t+=30\n",
    "    return dist/t\n",
    "\n",
    "brokenV(5000000) # Result - average velocity: 0.0364 m/s\n",
    "eps = 0\n",
    "for i in range(0,10):\n",
    "    eps+=abs(brokenV(5000000)-0.036429)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bd9b1b3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.028030189664200372"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Fourth task - mad horse\n",
    "def madV(N):\n",
    "    t = 0 # Time in seconds\n",
    "    dist = 0 # Distance in meters\n",
    "    for i in range(0,N):\n",
    "        # Jump\n",
    "        t+=1\n",
    "        if random.random() <= 0.3:\n",
    "            dist += 0.15\n",
    "            if random.random() <= 0.2: # if cracked the leg, wait 30 seconds\n",
    "                t+=30\n",
    "        else:\n",
    "            dist += 0.3\n",
    "            if random.random() <= 0.3: # if cracked the leg, wait 30 seconds\n",
    "                t+=30\n",
    "        \n",
    "    return dist/t\n",
    "\n",
    "madV(5000000) # Result - average velocity: 0.028 m/s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2ffead1d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x26bdf4a4160>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2400x2100 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Fifth task - jumping every time T\n",
    "# Average velocity calculator\n",
    "def v5(N, T):\n",
    "    t = 0 # Time in seconds\n",
    "    dist = 0 # Distance in meters\n",
    "    for i in range(0, N):\n",
    "        # Jump\n",
    "        t+=T\n",
    "        dist += 0.3\n",
    "        \n",
    "        if random.random() <= 0.2: # if cracked the leg, wait 30 seconds\n",
    "            t+=30\n",
    "    return dist/t\n",
    "\n",
    "# Graph - average velocity dependancy by T\n",
    "T = np.arange(0, 25, 0.5)\n",
    "v5 = np.vectorize(v5)\n",
    "vs = v5(2000000, T)\n",
    "plt.title(\"$v(T)$\")\n",
    "plt.ylabel('$avg. velocity$')\n",
    "plt.xlabel('$time T$')\n",
    "plt.plot(T, vs)\n",
    "\n",
    "# From the graph, when T -> 0, than v -> ~0.05, as expected, because average time is 0.2*30=6 seconds\n",
    "#per jump, average distance is 0.3, velocity = 0.3/6=0.05 m/s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "15c0ab60",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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