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   "source": [
    "##  NUMERICAL ROTATIONS in 3D with numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
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   "source": [
    "def Rx(theta,V):\n",
    "    \"\"\"\n",
    "    Rotation of a 3d vector V\n",
    "    of an angle theta around\n",
    "    the x-axis\n",
    "    \"\"\"\n",
    "    c = np.cos(theta)\n",
    "    s = np.sin(theta)\n",
    "    R = np.matrix(\n",
    "        [[1, 0, 0], \n",
    "         [0, c, -s], \n",
    "         [0, s, c]]\n",
    "    )\n",
    "    return R*V\n"
   ]
  },
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   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
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   "source": [
    "def Ry(theta,V):\n",
    "    \"\"\"\n",
    "    Rotation of a 3d vector V\n",
    "    of an angle theta around\n",
    "    the y-axis\n",
    "    \"\"\"\n",
    "    c = np.cos(theta)\n",
    "    s = np.sin(theta)\n",
    "    R = np.matrix(\n",
    "        [[c, 0, s],\n",
    "         [0, 1, 0],\n",
    "         [-s, 0, c]]\n",
    "    )\n",
    "    return R*V\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Rz(theta,V):\n",
    "    \"\"\"\n",
    "    Rotation of a 3d vector V\n",
    "    of an angle theta around\n",
    "    the z-axis\n",
    "    \"\"\"\n",
    "    c = np.cos(theta)\n",
    "    s = np.sin(theta)\n",
    "    R = np.matrix(\n",
    "        [[c, -s, 0], \n",
    "         [s, c, 0],\n",
    "         [0, 0, 1]]\n",
    "    )\n",
    "    return R*V\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A little demo of how the functions in this module can be used:\n",
      "Original vector V:\n",
      "[[1]\n",
      " [2]\n",
      " [3]]\n",
      "V rotated of pi/2 araund the x-axis: Rx(np.pi/2.,V)\n",
      "[[ 1.]\n",
      " [-3.]\n",
      " [ 2.]]\n",
      "V rotated of pi/4 araund the z-axis: Rz(np.pi/4.,V)\n",
      "[[-0.70710678]\n",
      " [ 2.12132034]\n",
      " [ 3.        ]]\n"
     ]
    }
   ],
   "source": [
    "if __name__ == \"__main__\":\n",
    "    print(\"A little demo of how the functions in this module can be used:\")\n",
    "    V = np.matrix([[1],[2],[3]])\n",
    "    print(\"Original vector V:\\n\" + str(V))\n",
    "    V1 = Rx(np.pi/2.,V)\n",
    "    print(\"V rotated of pi/2 around the x-axis: Rx(np.pi/2.,V)\\n\" + str(V1))\n",
    "    V2 = Rz(np.pi/4,V)\n",
    "    print(\"V rotated of pi/4 around the z-axis: Rz(np.pi/4.,V)\\n\" + str(V2))\n"
   ]
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