Cartans in Clifford-G3C.ipynb

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  {
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   "source": [
    "# Cartan's Rotation Algorithms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from clifford import eps\n",
    "from clifford.tools import orthoFrames2Verser\n",
    "from clifford.tools.g3c import * \n",
    "from scipy import e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "works\n"
     ]
    }
   ],
   "source": [
    "def generate_rotation_rotor():\n",
    "    B = e123.project(random_bivector())\n",
    "    return e**B\n",
    "\n",
    "def generate_translation_rotor():\n",
    "    a = e123.project(layout.randomV())\n",
    "    return (1 + ninf *a / 2)\n",
    "\n",
    "# generates random vectors in g3\n",
    "euc_vector = lambda: e123.project(layout.randomV())\n",
    "\n",
    "# Create random euclidean transformation from translations  and rotation\n",
    "T = generate_translation_rotor()\n",
    "R = generate_rotation_rotor()\n",
    "V = T*R \n",
    "\n",
    "\n",
    "a = [euc_vector() for k in range(4)] # create set of 4 vectors\n",
    "A = list(map(up,a)) #\n",
    "# homo() ==down/up roundtrip. observations are in g3, not g3c, so \n",
    "# this is represented by doing a down/up round trip, which is just homo()\n",
    "B = [homo(V*k*~V) for k in A] \n",
    "\n",
    "V_found,rs = orthoFrames2Verser(A=A,B=B, remove_scaling=1, det=1)\n",
    "\n",
    "if (min( abs(V_found+V),abs(V_found-V)) <eps() ):\n",
    "        print('works',)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.59732 + (0.37407^e12) + (0.10978^e13) - (0.523^e14) - (0.523^e15) + (0.70088^e23) + (0.27335^e24) + (0.27335^e25) + (1.03019^e34) + (1.03019^e35) + (0.01875^e1234) + (0.01875^e1235),\n",
       " -0.59732 + (0.37407^e12) + (0.10978^e13) - (0.523^e14) - (0.523^e15) + (0.70088^e23) + (0.27335^e24) + (0.27335^e25) + (1.03019^e34) + (1.03019^e35) + (0.01875^e1234) + (0.01875^e1235))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V_found,V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 13.26 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "100 loops, best of 3: 3.56 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "orthoFrames2Verser(A=A,B=B, remove_scaling=1, det=1)"
   ]
  }
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