02_Analyze-data_project.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computational Mechanics Project #02 - Create specifications for a projectile robot\n",
    "\n",
    "On the first day of class, we threw $2\"\\times~2\"$ dampened paper (spitballs) at a target on the whiteboard. Now, we are going to analyze the accuracy of the class with some cool Python tools and design a robot that has the same accuracy and precision as the class, but we will have the robot move farther away from the target and use a simpler projectile i.e. a tennis ball so we don't need to worry about knuckle-ball physics. \n",
    "\n",
    "The goal of this project is to determine the precision of necessary components for a robot that can reproduce the class throwing distibution. We have generated pseudo random numbers using `numpy.random`, but the class target practice is an example of truly random distributions. If we repeated the exercise, there is a vanishingly small probability that we would hit the same points on the target, and there are no deterministic models that could take into account all of the factors that affected each hit on the board. \n",
    "\n",
    "<img src=\"../images/robot_design.png\" style=\"height: 250px;\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we ask ourselves some questions:\n",
    "\n",
    "1. How do we quantify the class accuracy and precision?\n",
    "\n",
    "2. If we design a robot, what design components can we control?\n",
    "\n",
    "3. How can we relate the controlled components to the class accuracy, and specify the component precision?\n",
    "\n",
    "The first question, we have some experience from our work in [02_Seeing_Stats](../notebooks/02_Seeing_Stats.ipynb). We can define the mean, standard deviation, measure the first, second, and third quartiles,  etc. \n",
    "\n",
    "The second question is a physical question. We cannot control the placement of the robot or the target those are chosen for us. We cannot control temperature, mechanical vibrations, etc. We *can* control the desired initial velocity. The initial velocity will have some speed and direction, and both will be subject to random noise. Once the speed and direction are set, the location on the target is determined by kinematic equations for an object in freefall, as such\n",
    "\n",
    "$x_{impact} = \\frac{v_x}{v_y}d + x(0)~~~~~~~~~~~~~~~~~~~~(1.a)$\n",
    "\n",
    "$z_{impact} = d\\left(\\frac{v_z(0)}{v_y}-\\frac{g}{2v_y^2}d\\right)+ z(0)~~~~~(1.b)$.\n",
    "\n",
    "Where the location of impact is at a $y$-distance of $d$ at a point on the target with coordinates $(x_{impact},~z_{impact})$, and the initial velocity is $\\bar{v}=v_x\\hat{i}+v_y\\hat{j}+v_z(0)\\hat{k}$, the object is released at an initial location $\\bar{r}(0)=x(0)\\hat{i}+0\\hat{j}+z(0)\\hat{k}$, and the only acceleration is due to gravity, $\\bar{a}=-g\\hat{k}$. Equation (1) becomes much easier to  evaluate if we assume that $v_x=0$, resulting in an evalution of the accuracy of the height of the impact, $z_{impact}$, as such\n",
    "\n",
    "$x_{impact} = x(0)~~~~~~~~~~~~~~~~~~~~(2.a)$\n",
    "\n",
    "$z_{impact} = \\frac{d}{\\cos{\\theta}}\\left(\\sin{\\theta}-\\frac{g}{2v_0^2\\cos{\\theta}}d\\right)+ z(0)~~~~~(2.b)$.\n",
    "\n",
    "Where $\\theta$ is the angle of the initial velocity and $v_0$ is the initial speed. Equation (2) restricts the analysis to height accuracy. You can incorporate the 2D impact analysis if you finish the 1D analysis. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The third question, is how we can relate equation (2) to the measured points of impact? For this, we can use Monte Carlo methods *(There are other methods, but Monte Carlo is one of the most straight-forward)*. Our Monte Carlo approach is as such, if we have a desired initial speed, $v_0$, and desired angle, $\\theta$, we can propagate the uncertainty of our actual speeds and angles into the $z_{impact}$ locations. Then, we can choose distributions in speed and angles that match the distributions in $z_{impact}$ locations. Here are the steps:\n",
    "\n",
    "1. Generate random $\\theta_i$ and $v_{0~i}$ variables\n",
    "\n",
    "2. Plug into eqn 2 for random $z_{impact~i}$ locations\n",
    "\n",
    "3. Compare to our measured $z_{impact}$ location statistics\n",
    "\n",
    "4. Repeat 1-3 until the predicted uncertainty matches the desired uncertainty, we can use a number of comparison metrics:\n",
    "    \n",
    "    - standard deviation\n",
    "    \n",
    "    - first, second, and third quartiles\n",
    "    \n",
    "    - visually, with box plots and histograms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Project Deliverables\n",
    "\n",
    "1. Statistical analysis of class accuracy and precision (x- and z-locations) data is in the csv file  [../data/target_data.csv](../data/target_data.csv) _Note: if you want to see how I turned the images into data check out the jupyter notebook [process_target_practice](./process_target_practice.ipynb)\n",
    "\n",
    "2. A Monte Carlo model to generate impact heights based upon uncertainty in $\\theta_0$ and $v_0$. \n",
    "\n",
    "3. The precision required to recreate the class accuracy and precision with a robot. \n",
    "**You must show some validation of your work**\n",
    "\n",
    "4. [BONUS] Repeat 2-3 taking into account the variation in $x_{impact}$ due to misalignment. \n",
    "\n",
    "Given constants and constraints:\n",
    "\n",
    "- $d=$3 m, distance to target\n",
    "\n",
    "- $g=$9.81 m/s$^2$, acceleration due to gravity\n",
    "\n",
    "- $z(0)=$0.3 m,  the initial height is 0.3 m above the bull's eye\n",
    "\n",
    "- 4 m/s$<v_0<$12 m/s, the initial velocity is always higher than 9 mph and less than 27 mph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import random as random\n",
    "\n",
    "#Import rcParams to set font styles\n",
    "from matplotlib import rcParams\n",
    "\n",
    "#Set font style and size \n",
    "rcParams['font.family'] = 'sans'\n",
    "rcParams['font.size'] = 16\n",
    "rcParams['lines.linewidth'] = 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f771a965dd8>"
      ]
     },
     "execution_count": 412,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "target_data = pd.read_csv(\"../data/target_data.csv\")\n",
    "class_x_pos = target_data[' x position (m)'].values\n",
    "class_y_pos = target_data[' y position (m)'].values\n",
    "plt.figure(figsize=(8,8))\n",
    "plt.scatter(class_x_pos, class_y_pos) \n",
    "plt.title('Scatter plot of Classroom Shots\\n')\n",
    "plt.xlabel('x positions (m)')\n",
    "plt.ylabel('y positions (m)')\n",
    "plt.plot(0,0,'o',label='origin',color=(0,0, 0, 1),markersize=10)\n",
    "plt.plot(np.mean(class_x_pos),0,'o',label='X Mean',color=(0,0.5, 0, 0.7),markersize=10)\n",
    "plt.plot(0,np.mean(class_y_pos),'o',label='Y Mean',color=(1,0, 0, ),markersize=10)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "m = target_data.hist(column=' x position (m)', bins=25, density=True, edgecolor='white')\n",
    "plt.title('x positions \\n');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "m = target_data.hist(column=' y position (m)',bins=25, density=True,edgecolor='white' )\n",
    "plt.title('y positions \\n');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# It looks like the plots follow a something close to a normal distribution, we will now get the standard deviation and mean positions to see how those two plots look superimposed on one another."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "from scipy.stats import norm\n",
    "\n",
    "target_data.hist(column=' y position (m)',bins=25, density=True,edgecolor='white' )\n",
    "plt.title('y positions \\n');\n",
    "xmin, xmax = plt.xlim()\n",
    "x = np.linspace(xmin, xmax, 100)\n",
    "mu = np.mean(class_y_pos)\n",
    "std = np.std(class_y_pos)\n",
    "p = norm.pdf(x, mu, std)\n",
    "plt.plot(x, p, 'k', linewidth=2)\n",
    "title = \"x Positions: mean = %.2f,  std = %.2f\" % (mu, std)\n",
    "plt.title(title)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "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": [
    "from scipy.stats import norm\n",
    "\n",
    "m = target_data.hist(column=' x position (m)',bins=25, density=True,edgecolor='white' )\n",
    "plt.title('x positions \\n');\n",
    "xmin, xmax = plt.xlim()\n",
    "x = np.linspace(xmin, xmax, 100)\n",
    "mu = np.mean(class_x_pos)\n",
    "std = np.std(class_x_pos)\n",
    "p = norm.pdf(x, mu, std)\n",
    "plt.plot(x, p, 'k', linewidth=2)\n",
    "title = \"x Positions: mean = %.2f,  std = %.2f\" % (mu, std)\n",
    "plt.title(title)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean class x-position was -0.047\n",
      "The first quartile is -0.169, the second quartile is 0.028 and the third quartile is 0.167\n"
     ]
    },
    {
     "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": [
    "Quartiles = [np.percentile(class_x_pos, q=25), np.percentile(class_x_pos, q=50), np.percentile(class_x_pos, q=75)]\n",
    "print('The mean class x-position was {:.3f}'.format(np.mean(class_y_pos)))\n",
    "print('The first quartile is {:.3f}, the second quartile is {:.3f} and the third quartile is {:.3f}'.format(Quartiles[0],Quartiles[1],Quartiles[2]))\n",
    "plt.boxplot(class_x_pos, labels=['Class Throws x-Distribution']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean class x-position was -0.047\n",
      "The first quartile is -0.218, the second quartile is -0.071 and the third quartile is 0.132\n"
     ]
    },
    {
     "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": [
    "Quartiles = [np.percentile(class_y_pos, q=25), np.percentile(class_y_pos, q=50), np.percentile(class_y_pos, q=75)]\n",
    "print('The mean class x-position was {:.3f}'.format(np.mean(class_y_pos)))\n",
    "print('The first quartile is {:.3f}, the second quartile is {:.3f} and the third quartile is {:.3f}'.format(Quartiles[0],Quartiles[1],Quartiles[2]))\n",
    "plt.boxplot(class_y_pos, labels=['Class Throws y-Distribution']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 405,
   "metadata": {},
   "outputs": [],
   "source": [
    "def z_impact(d,theta,Vo,Z_initial):\n",
    "    \"\"\"\n",
    "    This function calculates the x position of the impact of a projectile\n",
    "    Inputs:\n",
    "    ----------------------------------------\n",
    "    d - distande from release to the target as measured in the y direction\n",
    "    theta - angle of the initial velocity\n",
    "    Vo - initial speed\n",
    "    Z_initial - height of release\n",
    "    Outputs:\n",
    "    ----------------------------------------\n",
    "    z_impact - x position of projectile on impact surface\n",
    "    \"\"\"\n",
    "    g = 9.81\n",
    "    z_impact = (d/np.cos(theta))*(np.sin(theta)-(g*d)/(2*(Vo**2)*np.cos(theta)))+Z_initial\n",
    "    return z_impact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 406,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['throw #', ' x position (m)', ' y position (m)',\n",
       "       'picture x position (pixel)', ' picture y position (pixel)',\n",
       "       'target x position (pixel)', ' target y position (pixel)', ' image #'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 406,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "target_data = pd.read_csv(\"../data/target_data.csv\")\n",
    "d = 3\n",
    "Z_initial = 0.3\n",
    "N = 53\n",
    "\n",
    "initial_velocities = np.random.rand(53)*8 + 4\n",
    "initial_angles = np.random.rand(53)*(np.pi/12)\n",
    "\n",
    "target_data.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
   "metadata": {},
   "outputs": [],
   "source": [
    "impact_locations = z_impact(3,initial_angles,initial_velocities,0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot of velocities with random distribution shown below does not accurately represent what the class did. We have to adjust the right skew as well at the standard deviation. Instead of using a purely random distribution we will use a normal distribution for both the velocities and angles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 408,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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K+tvCPDchXYJ7jPR4QjGebSTtpMIr6SRtJOmlFbFL0mdJO8mfFO9hK72d5WrSwck/RMRVQ2xDq9t/q75DOiMpX1E4gubvVyJpX0nPK5WNJV0dgFWX+RuX1ft9PyPiftL9ylfkfV7RKbR5oN9CjJXybYi5wA6Snrs3mLffU/N/v1Ga/iZ5e9qkNLlvkrbvDxb33Xmf/WHSdn9hof7VpLPLv5P02kL9dVl122HuYPEPZjRdhr0deJ2kG0hHHtuSnrNZQeqO3PBD0pfjU5KmkXqjTSM9XP0D0s3p50TErZI+SXqY/C5JF5K6FW9BOvr5CukZS0gL++PAmZLmknrA/SoiLm0i/nEa+F2OSyLiBNKbLQ4C3peflbqW9IU4lLQRvqfUIeZdpBvs38sb3i9Jl6p2I91fa+yc/oN0ZnBD7gCyMrdtXdIZ+a6leK4hHeX/S75X9HiO8XtVwedOW+8h3bu7StL3Sffw9iE9V3UTo/xNKxFxmaQvkC7ZLZJ0OelxjEmko849SI889OX2nkm6Z3OLpEtJO4uDSOus6R3kMPk+sELS9aQj43GkZxc3B06t6ETVtIj4i6SjgMtI20/xdXdbAkeUO7aQDoz2AV7Lqk5fLwRulnQz6bnlB3LZXqTl+wfSs4NFV5Geg7sWeHXFgdijUXpmegCtbv+t+hKpI8mH8ve28ZzlG0gd8Jq5+gPpWdCtlH6koI+U2PYj9cb+TqPjX0SskPRLYB9J3yAdRAfw9ZyMPkQ6gP2+pOJzlluS9qO7MHRNxVjjkzme2ZJmsup1d7uT3thUfgbzg6QDkZNYldSIiPskHZdjulXp/eTPkk4sXkTqzXxXof5fJR1BOgC8XNIFpO3w70jL5KekBDw0TXTfnczgj45Mrhinj1J37dK05pTKg1Vv8LmQdGT1BGlD7NfVl3Rp5QekTkGPk460ZjLAGynyOK8jdS1eRkpMfaQbw9NK9T5N2jj/UhXrAMuoj9W7ypf/bi3U3Yh0drKIdNT0cG5zvzcV5fpbkt6C1JfrP5iX1T+W6r2V1LvvSVKHmzmko/n5VHQlJ/UIW8iqx3zml9dHxTi75VgfzrEsym3ZsFSvcj3XDRtk2Ta9LeVhg20Hryd1X38ot+H3pIOHfwY2KdRbj/SKtsabk+4lfZHXq1o+Ay3numEVdU+k/6Mjx5AOEu/PsTxISjADvrGq1T/S5cQrSGeST5CucBw0WHtKMY4nXTG5Lm9/fyF9N28mnfH0ex6Uwb8zUbXeB4m/6e2/ahnXDSMdVH0zbzeN5TNjsGlVTPtQ0oHPvTnOh0m3B44Gxpbq7kTqrLS8sDwmF4a/NK+vJ0j7tAtIJxitbGuH0//RkaZjrJn2VqTnPh8k7WN+Teo0VPV2pMYyPHGAab0pL+8Vub0/Z5BHAUmJ8QekK2jPkE6ojqfNR6+UJ941+T7lb0lf0kbvu+0ioq+JcdcnfRHfRbrncSvwqRjafQ8zM7NKo+GeZaPX1Eoqnh2qcQ5wJOkM4CDSKfflknYbdCwzM7MWjIYzy3VIvb+uId1IP5smzixzz6pbSff5vpXLxpIuLf4mImZ1Mm4zM+sdXT+zjKF3TphFui9yfmFaK0kvmp5Z7tFlZmY2VF1PlpAemo6IGS2ONg1YHBHlHyleSOqEMdBDsWZmZi0ZTY+OtGoi1T9H80hh+GpyF/mjAMaPH7/7TjvtVK5iZmaDuOmmmx6KiIHeuLbWWpOTpah+We+Ar/aKiNmklxQwffr0WLBgQYdCMzNbO0ka8ltw1mSj4jLsED1Cxdkj6dchGsPNzMzatiYny4XAdsVXbmVTWfXAvJmZWdvW5GQ5j/QSg7c0CvKjI4cCV0TEM90KzMzM1i6j4p6lpDfnfzZ+a+z1Sj8gvTQirpG0Len1SydHxMnw3DtfzwfOyC/KXUx6Ldh2wDtHtgVmZrY2GxXJktKvGgD/lT+vIb1/UaQX+pbPhI8A/oX0NvuNSS9NPiAiyr/LZ2ZmNmSjIlnG4D9OS36bT786kX4N+9j8Z2Zm1hFr8j1LMzOzEeFkaWZmVsPJ0szMrMaouGdpZra2mnzcpS2P03fagR2IxNrhM0szM7MaTpZmZmY1nCzNzMxqOFmamZnVcLI0MzOr4WRpZmZWw8nSzMyshpOlmZlZDSdLMzOzGk6WZmZmNZwszczMajhZmpmZ1XCyNDMzq+FkaWZmVsPJ0szMrIaTpZmZWQ0nSzMzsxpOlmZmZjWcLM3MzGo4WZqZmdVwsjQzM6vhZGlmZlbDydLMzKyGk6WZmVkNJ0szM7MaTpZmZmY1nCzNzMxqdD1ZStpa0lxJyyU9JulCSds0Oe42kr4taYmkJyXdLelUSeM7HbeZmfWOsd2cuaRxwFXAM8BhQACnAldL2iUinhhk3PHAT4F1gc8CS4CXAycBOwCHdjZ6MzPrFV1NlsCRwBRgx4hYBCDpduAe4Gjg9EHG3ZOUFGdGxBW57GpJE4GPSxoXEU92LnQzM+sV3b4MOwu4sZEoASJiMXADcHDNuOvlz8dK5Y+S2qXhCtLMzHpbt5PlNOCOivKFwNSacX9KOgP9oqSpkjaUtC/wEeDMwS7hmpmZtaLbyXIisKyi/BFgwmAjRsTTwF6kNiwEHgeuBC4BPlg1jqSjJC2QtGDp0qXtxG1mZj2k28kSUqeestpLqJLWB84HNgXeDewDfILUsec/K2cUMTsipkfE9EmTJg09YjMz6ynd7uCzjHR2WTaB6jPOon8CZgDbR8S9uexaScuB2ZLOjIjbhi1SMzPrWd0+s1xIum9ZNhW4s2bclwDLComy4Rf5c+c2YzMzMwO6nyznAXtImtIokDSZ9FjIvJpx/whMkLR9qfyV+fP3wxSjmZn1uG4ny7OBPuBiSQdLmgVcDPwWOKtRSdK2klZKOqEw7hxSp57LJB0m6bWSPgF8BbiJ9PiJmZlZ27qaLPPjHfsCdwPnAt8FFgP7RsSKQlUBYyjEGxF9wB7AraS3/lxGesnBbGD/iHh2BJpgZmY9oNsdfIiIJcAhNXX6qOghGxF3Am/tTGRmZmZJ15Ol2dpk8nGXtlS/77QDOxRJ72p1HZg1o9v3LM3MzEY9J0szM7MaTpZmZmY1nCzNzMxqOFmamZnVcLI0MzOr4WRpZmZWw8nSzMyshpOlmZlZDSdLMzOzGk6WZmZmNZwszczMajhZmpmZ1XCyNDMzq+FkaWZmVsPJ0szMrIaTpZmZWQ0nSzMzsxpOlmZmZjWcLM3MzGo4WZqZmdVwsjQzM6vhZGlmZlbDydLMzKyGk6WZmVkNJ0szM7MaTpZmZmY1nCzNzMxqOFmamZnV6HqylLS1pLmSlkt6TNKFkrZpYfydJf2vpIckPSXpN5I+0smYzcyst4zt5swljQOuAp4BDgMCOBW4WtIuEfFEzfjT8/jzgfcCy4EdgA07GLaZmfWYriZL4EhgCrBjRCwCkHQ7cA9wNHD6QCNKWgf4NnBlRLyxMOjqzoVrZma9qNuXYWcBNzYSJUBELAZuAA6uGXcGMJVBEqqZmdlw6HaynAbcUVG+kJQIB7NX/lxf0o2S/iLpQUn/JmmDYY3SzMx6WreT5URgWUX5I8CEmnG3yJ/nA1cA+wNfIt27/F7VCJKOkrRA0oKlS5cOLWIzM+s53b5nCalTT5maGK+R6L8TESfkf8+XNAY4TdLUiLhztRlFzAZmA0yfPr1qvmZmZv10+8xyGenssmwC1WecRQ/nz5+Uyq/In7u1EZeZmdlzup0sF5LuW5ZNBe6sKC+PC/3PTBtnpc+2EZeZmdlzup0s5wF7SJrSKJA0GdgzDxvMj0jPZx5QKp+ZPxcMT4hmZtbrup0szwb6gIslHSxpFnAx8FvgrEYlSdtKWimpcW+SiHgY+ALwPkmfl7SfpOOAE4BvFx9HMTMza0dXO/hExBOS9gW+BpxLuoR6JfDRiFhRqCpgDP2T+8nA48D7gY8DDwBfBk7pcOhmZtZDut4bNiKWAIfU1OmjoodsRATppQR+McEoNPm4S1uq33fagR2KpHe1ug5GgtdzPX93Rp9uX4Y1MzMb9ZwszczMajhZmpmZ1XCyNDMzq+FkaWZmVsPJ0szMrIaTpZmZWQ0nSzMzsxpOlmZmZjWcLM3MzGo4WZqZmdVwsjQzM6vhZGlmZlbDydLMzKyGk6WZmVkNJ0szM7MaTpZmZmY1nCzNzMxqOFmamZnVcLI0MzOr4WRpZmZWw8nSzMyshpOlmZlZDSdLMzOzGk6WZmZmNZwszczMajhZmpmZ1XCyNDMzq+FkaWZmVsPJ0szMrIaTpZmZWY2uJ0tJW0uaK2m5pMckXShpmyFM59OSQtL1nYjTzMx6V1eTpaRxwFXATsBhwLuBHYCrJY1vYTpTgM8AD3YiTjMz621juzz/I4EpwI4RsQhA0u3APcDRwOlNTufrwHeBHel+m8zMbC3T7cuws4AbG4kSICIWAzcABzczAUnvAF4GfLojEZqZWc/rdrKcBtxRUb4QmFo3sqQJwNeAT0bEI8Mcm5mZGdD9ZDkRWFZR/ggwoYnxvwzcDcxpZmaSjpK0QNKCpUuXNh2kmZn1tm4nS4CoKFPdSJL2Bv4ROCYiqqbRf0YRsyNiekRMnzRpUothmplZr+p2Z5hlpLPLsglUn3EWnQWcA/xO0sa5bCwwJv//qYh4ZtgiNTOzntXtZLmQdN+ybCpwZ824O+e/91UMWwZ8DDijrejMzMzofrKcB3xF0pSIuA9A0mRgT+C4mnFfW1F2BjAG+BCwqGL4WmvycZe2VL/vtAM7FIl1UqvreTRaG9ow2vj733ndTpZnAx8ELpZ0POn+5SnAb0mXWQGQtC1wL3ByRJwMEBHzyxOT9CgwtmqYmZnZUHW1g09EPAHsS+rRei7pxQKLgX0jYkWhqkhnjKOhQ5KZmfWYbp9ZEhFLgENq6vTRRA/ZiJgxPFGZmZmt4jM1MzOzGk6WZmZmNZwszczMajhZmpmZ1XCyNDMzq+FkaWZmVsPJ0szMrIaTpZmZWQ0nSzMzsxpOlmZmZjWcLM3MzGo4WZqZmdVwsjQzM6vhZGlmZlbDydLMzKyGk6WZmVkNJ0szM7MaTpZmZmY1nCzNzMxqOFmamZnVcLI0MzOr4WRpZmZWw8nSzMyshpOlmZlZDSdLMzOzGk6WZmZmNZwszczMajhZmpmZ1XCyNDMzq+FkaWZmVqPryVLS1pLmSlou6TFJF0raponxpkuaLekuSU9KWiLpu5K2G4m4zcysd3Q1WUoaB1wF7AQcBrwb2AG4WtL4mtHfBkwD/g14PXAc8DJggaStOxa0mZn1nLFdnv+RwBRgx4hYBCDpduAe4Gjg9EHG/WJELC0WSLoBWJyne0JHIjYzs57T7cuws4AbG4kSICIWAzcABw82YjlR5rL7gaXAlsMcp5mZ9bBuJ8tpwB0V5QuBqa1OTNLOwKbAr9uMy8zM7DndTpYTgWUV5Y8AE1qZkKSxwJmkM8tzBqhzlKQFkhYsXdrvxNTMzKxSt5MlQFSUaQjT+Q/g1cC7IqIqARMRsyNiekRMnzRp0hBmYWZmvajbHXyWkc4uyyZQfcZZSdIXgKOAwyLiimGKbVCTj7t0JGbTMUOJv++0AzsQydCt6evAzNYc3U6WC0n3LcumAnc2MwFJnyE9NvLhiDh3GGMzMzMDun8Zdh6wh6QpjQJJk4E987BBSfowcCrwmYj49w7FaGZmPa7byfJsoA+4WNLBkmYBFwO/Bc5qVJK0raSVkk4olL0NOAP4MXCVpD0Kfy33pDUzMxtIVy/DRsQTkvYFvgacS+rYcyXw0YhYUagqYAyrJ/cDcvkB+a/oGmBGh8I2M7Me0+17lkTEEuCQmjp9lHrIRsThwOGdisvMzKyh25dhzczMRj0nSzMzsxpOlmZmZjWcLM3MzGo4WZqZmdVwsjQzM6vhZGlmZlbDydLMzKyGk6WZmVkNJ0szM7MaTpZmZmY1nCzNzMxqOFmamZnVcLI0MzOr4WRpZmZWw8nSzMyshpOlmZlZDSdLMzOzGk6WZmZmNZwszczMajhZmpmZ1XCyNDMzq+FkaWZmVsPJ0szMrIaTpZmZWQ0nSzMzsxpOlmZmZjWcLM3MzGo4WZqZmdVwsjQzM6vhZGlmZlaj68lS0taS5kpaLpOG7HkAAAawSURBVOkxSRdK2qbJcdeX9GVJD0h6StLPJb2m0zGbmVlv6WqylDQOuArYCTgMeDewA3C1pPFNTOIc4EjgBOAg4AHgckm7dSZiMzPrRWO7PP8jgSnAjhGxCEDS7cA9wNHA6QONKGlX4B3AeyLiW7nsGmAhcDIwq7Ohm5lZr+j2ZdhZwI2NRAkQEYuBG4CDmxj3L8D5hXFXAucBMyU9b/jDNTOzXtTtZDkNuKOifCEwtYlxF0fEkxXjrgds3354ZmZm3b8MOxFYVlH+CDChjXEbw1cj6SjgqPzfFZJ+02Sca4NNgIfamYC+OEyRjOz02253J/VimzuoF9s9pDa3ud1t29bYa6huJ0uAqChTE+Op1XEjYjYwu8m41iqSFkTE9G7HMdJ6sd292GbozXb3Ypu7pduXYZdRcQZIOqusOmssemSQcRvDzczM2tbtZLmQdO+xbCpwZxPjbpcfPymP+2dgUf9RzMzMWtftZDkP2EPSlEaBpMnAnnlY3bjrAm8pjDsWOBS4IiKeGe5g13A9efmZ3mx3L7YZerPdvdjmrlBE1W2/EZp5evHAbcBTwPGke5CnABsBu0TEilxvW+Be4OSIOLkw/nnATOATwGLgGNLLCV4dETePYFPMzGwt1tUzy4h4AtgXuBs4F/guKent20iUmYAx9I/3COBbwKnApcDWwAFOlGZmNpy6emZpZma2Juj2PUvrEEnHSvphfsl8SDqxhXHn5HHKf2d0MOS2tdPmPP4/SLpF0tOS7pd0vKQxHQp32EhaR9KnJfXl2G+TdEiT447qdd2rP7TQZrur1mf4ndntGQ3PWVpnHAk8BlwEvG8I4y+l//t1H2g3qA4bcpslzQQuIL2c/1jgpcDnSffPPzW8YQ67U4CPA58BbgLeBvyvpIMi4rImxh+V67rwQwvPkH5oIUi3XK6WtEu+jTOYc4ADSX0a7gM+QPqhhVdFxK2di7w9w9BugDnAWaWyu4czzp4TEf5bC/+AdfLnWNKX7cQWxp0D/K7bbRjhNt8CXFMqO4H0GNKLut22QeLelLRTPalUfiVw+5q8roGPAH8Fti+UbQesBI6tGXfXvA0cUSgbC/wGmNfttnWq3bluAKd2ux1r258vw66lIuLZbscw0obaZklbA7sB3ykNOpf0eNLr2wytk2aS3oVcjv07wEskbTfyIQ2bXv2hhXbabR3iZGkD2VTSQ5JWSrpb0qfWhPt3Q9R4McZqL/XPO6gnqX+pfzdNI51Zll/CsTB/NhP7aF3XvfpDC+20u+EYSc9IelLSVZL2Hr7wepPvWVqVW0n3vhYC6wNvBL5A+mHu93Yxrk5pvDax6hWLA72ScbSYCDwa+fpbwYA/KFAymtf1iP7QwijSTrshXVW4BPgD6aXnnwCukrR/RMwfriB7jZPlGkDSfsBPmqh6TUTMaHd+EVHuCXmZpBXARyV9MSLuaXcedUa4zY2X7w/1pf7DZgjtbvkHBYpGw7quMWI/tDDKtLNO313473WSLiadqZ4K7DUMsfUkJ8s1w8+AnZuoV77kNJz+B/goMB0YiR3oSLZ5sLONjRnZl/K32u5HgAmSVDq7bOcHBUZ6XQ+k3R9aqHrUYk34oYV22t1PRDwu6VLgn9oNrJc5Wa4B8n2Xu7ocxmBnX8NuhNvcuL83Dfh5ozC/p3gc9S/1HzZDaPdC4HnAi1n9vmXj3tZQYh/RdT2Idn9o4Y2SxpXuW64JP7TQTrsHMtCZtjXJHXysWe8gfdl+2e1AhltELCG9o/idpUHvIvWo/NGIB9W8H5N2/lWx35E7KbVqtKzrXv2hhXba3Y+k55OeN/2/YYqvN3X72RX/deaPdAntzcBbSTu+7+f/vxkYV6h3JbCo8P9tgWuB9wOvA94AfBN4Fvh6t9vViTbnsr/PbTwLmAF8DHga+HK329VEu0/LsR6bY/96bssbSvXWqHUNjCedAf6K9MjELNJBzX3AhqV2rAROKI1/Humy5XuBvwPm5uX0sm63rVPtJr2c4mzSAc8M0ksNfkU6oNq7221bk/+6HoD/OrRi08PmMcDf5EK9+UBf4f8TSW/AuT/vWJ4CbgY+SH7of7T+DbXNhfI35Z3SM8AS0ksJxnS7XU20ewzpV3vuz7HfDry5ot4at65J9x0vIL2Z6fEc7+RSnclUvIQC2AA4Hfhjbt//ATO63aZOtpt0wHMD8BDpqsjDpLPRV3S7TWv6n1+kbmZmVsP3LM3MzGo4WZqZmdVwsjQzM6vhZGlmZlbDydLMzKyGk6WZmVkNJ0szM7MaTpZmZmY1/j8Fw7C0QZFeLwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(impact_locations,25,density=True);\n",
    "plt.title('Impact Location mean is {:.2f} and std is {:.2f} '.format(np.mean(impact_locations),np.std(impact_locations)));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 436,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_velocities = np.random.normal(8,1,size=53)\n",
    "initial_angles = np.random.normal(np.pi/17.5,0.09,size=53)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# This plot shows a more accurate representation of what he class did."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 437,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Robot  positions: mean = 0.12,  std = 0.33')"
      ]
     },
     "execution_count": 437,
     "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": [
    "impact_locations = z_impact(3,initial_angles,initial_velocities,0.3)\n",
    "plt.hist(impact_locations,25,density=True);\n",
    "plt.title('Robot y positions \\n');\n",
    "xmin, xmax = plt.xlim()\n",
    "x = np.linspace(xmin, xmax, 100)\n",
    "mu = np.mean(impact_locations)\n",
    "std = np.std(impact_locations)\n",
    "p = norm.pdf(x, mu, std)\n",
    "plt.plot(x, p, 'k', linewidth=2)\n",
    "title = \"Robot  positions: mean = %.2f,  std = %.2f\" % (mu, std)\n",
    "plt.title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 438,
   "metadata": {},
   "outputs": [],
   "source": [
    "rand_x_locations = np.random.normal(0,0.25,size=53)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3/4 Validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 440,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f7719ffbbe0>"
      ]
     },
     "execution_count": 440,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,8))\n",
    "plt.scatter(class_x_pos, class_y_pos,label='Class Shots')\n",
    "plt.scatter(rand_x_locations,impact_locations,label='Robot Shots',color=(1,0, 0,1))\n",
    "plt.title('Scatter plot of Classroom Shots and Robot Similated Shots\\n')\n",
    "plt.xlabel('x positions (m)')\n",
    "plt.ylabel('y positions (m)')\n",
    "plt.plot(0,0,'o',label='origin',color=(0,0, 0, 1),markersize=10)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}