{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "16ed33ab-de49-411d-860d-3a07dcc44ecd",
   "metadata": {},
   "source": [
    "# Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "212e287a-44cb-4376-864c-3e201445389e",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "import itertools\n",
    "import copy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "974f7d5a-60d3-4f61-a7b8-851536ba2337",
   "metadata": {},
   "source": [
    "# Shooting method"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7258a55-baee-4e4d-a1ad-74e2151f63d9",
   "metadata": {},
   "source": [
    "We are going to solve the problem proposed in the slides, which is slightly easier than the one covered in class.\\\n",
    "The ball is thrown upward from an initial height y(t=0)=0 m, and needs to be at a height of 10 m after 3 s, y(t=3)=10 m.\\\n",
    "We are asked to find the necessary initial velocity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6ef562be-e509-4453-9071-b70570ad90c5",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "g_grav = 9.81\n",
    "\n",
    "def projectile(y, t):\n",
    "    return np.array([y[1], -g_grav])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2df7a0f5-7c12-4b73-8edc-e1d29cd9488b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_trajectory(yi, vi, ti, tf, target_yf=None):\n",
    "\n",
    "    ts = np.linspace(ti,tf)\n",
    "    ys = scipy.integrate.odeint(projectile,np.array([yi,vi]),ts)\n",
    "\n",
    "    if(target_yf is not None):\n",
    "        plt.axhline(target_yf, lw=0.7, c=\"k\", dashes=[3,3])  \n",
    "    \n",
    "    print(\"yf=\",ys[-1,0])\n",
    "\n",
    "    plt.plot(ts, ys[:,0], label=\"y(t) [m]\")\n",
    "    plt.plot(ts, ys[:,1], label=\"v(t) [m/s]\")\n",
    "    \n",
    "    plt.legend(frameon=False)\n",
    "    plt.xlabel(\"t [s]\")\n",
    "    plt.xlim([ts[0],ts[-1]])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3fbb86d2-abca-47e8-88ce-95f8c433980e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yf= -29.145000000501\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_trajectory(yi=0., vi=5., ti=0., tf=3.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa0265a1-59e3-413f-89f0-7abd48a5dcea",
   "metadata": {},
   "source": [
    "Now that we have a set of functions that work, we can start shooting for the correct initial conditions.\\\n",
    "First order of business is to braket our solution. We can do an very coarse grid search to find a suitable braket."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f9417637-7f76-4296-beff-24392b8edca9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v0 = 0  -> yf = -44.14500000040266\n",
      "v0 = 10  -> yf = -14.145000000398568\n",
      "v0 = 20  -> yf = 15.854999999780787\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ts = np.linspace(0,3)\n",
    "\n",
    "for v0 in [0, 10, 20]:\n",
    "    ys = scipy.integrate.odeint(projectile,np.array([0,v0]),ts)\n",
    "    print(\"v0 =\", v0, \" -> yf =\", ys[-1,0])\n",
    "    plt.plot(ts, ys[:,0], label=\"v0=\"+str(v0)+\" m/s\")\n",
    "    \n",
    "plt.axhline(10, lw=0.7, c=\"k\", dashes=[3,3])    \n",
    "\n",
    "plt.legend(frameon=False)\n",
    "plt.xlabel(\"t [s]\")\n",
    "plt.ylabel(\"y [m]\")\n",
    "plt.xlim([ts[0],ts[-1]])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91a541fe-738f-4580-958c-73e141de8847",
   "metadata": {},
   "source": [
    "Thus, we infer that $v0 \\in [0, 20]$ braket our solution (indeed, even [10, 20] would have), . We can refine our search there."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "50adafb2-df4a-4510-8c6c-ffce100aad21",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_y(v0, tf, yf):\n",
    "    ts = np.linspace(0,tf,2)\n",
    "    ys = scipy.integrate.odeint(projectile,np.array([0,v0]),ts)\n",
    "    return ys[-1,0] - yf"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f1323e0-8f4d-45d4-9d3d-95973fe4cabb",
   "metadata": {},
   "source": [
    "Any root finder is fair game. A good one provided in scipy.optimize is ridder.\n",
    "You can use one of the ones explained in class instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2ad17367-73df-4d4d-a1f9-6202e7190ca9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "target_vi= 18.04833333348188\n"
     ]
    }
   ],
   "source": [
    "target_vi = scipy.optimize.ridder(get_y, 0, 20, args=(3, 10))\n",
    "print(\"target_vi=\", target_vi)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d3ed124-ccb0-498b-9506-eaef8c19c7c4",
   "metadata": {},
   "source": [
    "If scipy.optimize.ridder did not accept an optional argument with the \"args\" to be passed to the function, we could implement a workaround"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "416ee242-9a5a-4434-b6f9-ac7a6be04f78",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_y_at_tf(tf, yf):\n",
    "    def get_y(v0):\n",
    "        ts = np.linspace(0,tf,2)\n",
    "        ys = scipy.integrate.odeint(projectile,np.array([0,v0]),ts)\n",
    "        return ys[-1,0] - yf\n",
    "    return get_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f66528ef-a1b3-41af-abf5-3cb597ff7173",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18.04833333348188"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scipy.optimize.ridder(get_y_at_tf(tf=3, yf=10), 0, 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "725b6e5d-d861-4c68-8dc6-0c63a6c6ef0e",
   "metadata": {},
   "source": [
    "Either way, we now have the desired initial conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "cc8f133d-acda-4b9b-ad68-08986907cfdd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "yf= 10.000000000198966\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_trajectory(yi=0., vi=target_vi, ti=0., tf=3., target_yf=10.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "260be495-95d3-47fe-bf26-7551340c8264",
   "metadata": {},
   "source": [
    "Bullseye"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "968c7cf8-3370-41da-adaa-5c5b98cbd721",
   "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",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
