{
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  {
   "cell_type": "markdown",
   "id": "a950b9af",
   "metadata": {},
   "source": [
    "**This script is simply for me to calculate the location of IceCube relative to the origin of any ARA station**\n",
    "\n",
    "The relevant documentation to understand the definitions after the imports can be found in https://elog.phys.hawaii.edu/elog/ARA/130712_170712/doc.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b926e2e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "901b442b",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Definitions of translations in surveyor's coordinates:\n",
    "\n",
    "t_IC_to_ARAg = np.array([-24100, 1700, 6400])\n",
    "t_ARAg_to_A1 = np.array([16401.71, -2835.37, -25.67])\n",
    "t_ARAg_to_A2 = np.array([13126.7, -8519.62, -18.72])\n",
    "t_ARAg_to_A3 = np.array([9848.35, -2835.19, -12.7])\n",
    "\n",
    "#Definitions of rotations from surveyor's axes to the ARA Station's coordinate systems\n",
    "\n",
    "R1 = np.array([[-0.598647, 0.801013, -0.000332979], [-0.801013, -0.598647, -0.000401329], \\\n",
    "               [-0.000520806, 0.0000264661, 1]])\n",
    "R2 = np.array([[-0.598647, 0.801013, -0.000970507], [-0.801007, -0.598646,-0.00316072 ], \\\n",
    "               [-0.00311277, -0.00111477, 0.999995]])\n",
    "R3 = np.array([[-0.598646, 0.801011, -0.00198193],[-0.801008, -0.598649,-0.00247504], \\\n",
    "               [-0.00316902, 0.000105871, 0.999995]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab2d3206",
   "metadata": {},
   "source": [
    "**Using these definitions, I should be able to calculate the location of IceCube relative to each ARA station by:**\n",
    "\n",
    "$$\n",
    "\\vec{r}_{A 1}^{I C}=-R_1\\left(\\vec{t}_{I C}^{A R A}+\\vec{t}_{A R A}^{A 1}\\right)\n",
    "$$\n",
    "\n",
    "We have a write-up of how to get this. Contact salcedogomez.1@osu.edu if you need that.\n",
    "\n",
    "Alex had done this already, he got that \n",
    "\n",
    "$$\n",
    "\\vec{r}_{A 1}^{I C}=-3696.99^{\\prime} \\hat{x}-6843.56^{\\prime} \\hat{y}-6378.31^{\\prime} \\hat{z}\n",
    "$$\n",
    "\n",
    "Let me verify that I get the same"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "912163d2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IC coordinates relative to A1 (in):  [-3696.98956579 -6843.55800868 -6378.30926681]\n",
      "IC coordinates relative to A1 (m):  [-1127.13096518 -2086.4506124  -1944.60648378]\n",
      "Distance of IC from A1 (m):  3066.788996234438\n"
     ]
    }
   ],
   "source": [
    "IC_A1 = -R1 @ np.add(t_ARAg_to_A1, t_IC_to_ARAg).T\n",
    "print(\"IC coordinates relative to A1 (in): \", IC_A1)\n",
    "print(\"IC coordinates relative to A1 (m): \", IC_A1/3.28)\n",
    "print(\"Distance of IC from A1 (m): \", np.sqrt((IC_A1[0]/3.28)**2 + (IC_A1[1]/3.28)**2 + (IC_A1[2]/3.28)**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9c9f252",
   "metadata": {},
   "source": [
    "Looks good!\n",
    "\n",
    "Now, I just get the other ones:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8afa27c6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IC coordinates relative to A2 (in):  [ -1100.33577313 -12852.0589083   -6423.00776043]\n",
      "IC coordinates relative to A2 (m):  [ -335.46822352 -3918.31064277 -1958.2340733 ]\n",
      "Distance of IC from A2 (m):  4393.219537890439\n"
     ]
    }
   ],
   "source": [
    "IC_A2 = -R2 @ np.add(t_ARAg_to_A2, t_IC_to_ARAg).T\n",
    "print(\"IC coordinates relative to A2 (in): \", IC_A2)\n",
    "print(\"IC coordinates relative to A2 (m): \", IC_A2/3.28)\n",
    "print(\"Distance of IC from A2 (m): \", np.sqrt((IC_A2[0]/3.28)**2 + (IC_A2[1]/3.28)**2 + (IC_A2[2]/3.28)**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9959d0a4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IC coordinates relative to A3 (in):  [ -7609.73440732 -12079.45719852  -6432.31164368]\n",
      "IC coordinates relative to A3 (m):  [-2320.04097784 -3682.76134101 -1961.07062307]\n",
      "Distance of IC from A3 (m):  4774.00452685144\n"
     ]
    }
   ],
   "source": [
    "IC_A3 = -R3 @ np.add(t_ARAg_to_A3, t_IC_to_ARAg).T\n",
    "print(\"IC coordinates relative to A3 (in): \", IC_A3)\n",
    "print(\"IC coordinates relative to A3 (m): \", IC_A3/3.28)\n",
    "print(\"Distance of IC from A3 (m): \", np.sqrt((IC_A3[0]/3.28)**2 + (IC_A3[1]/3.28)**2 + (IC_A3[2]/3.28)**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "093dff67",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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