new_features.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "36cbb85d-b0ed-437f-8c73-a339583b2287",
   "metadata": {},
   "source": [
    "# Feature thoughts"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35dc14dc-f9cb-4a01-8dfd-9ac72ad9f0ff",
   "metadata": {},
   "source": [
    "## Atom manipulation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcf973cb-0fc0-41b7-8877-61b7ef59d2da",
   "metadata": {},
   "source": [
    "A direction we want to go in is also atom manipulation in a robust manner. To this end we need a set of methods that can access atom and manipulate them."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "210bdbb8-1720-4ab3-9c80-47777e21f289",
   "metadata": {},
   "source": [
    "#### How to access atoms?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4ea65fe7-85c9-409f-b021-cf394da9220a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pyscal.crystal_structures as pcs\n",
    "from pyscal.core import System\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import warnings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f9deafb9-b879-4b6d-aa45-ad6153d271b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "atoms, box = pcs.make_crystal(structure=\"fcc\", repetitions=(5,5,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7dfcfc1c-89a0-4e86-85fd-6bc5ed05b228",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
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       "   [3.5, 3.5, 2.0],\n",
       "   [3.0, 3.0, 3.0],\n",
       "   [3.5, 3.0, 3.5],\n",
       "   [3.0, 3.5, 3.5],\n",
       "   [3.5, 3.5, 3.0],\n",
       "   [3.0, 3.0, 4.0],\n",
       "   [3.5, 3.0, 4.5],\n",
       "   [3.0, 3.5, 4.5],\n",
       "   [3.5, 3.5, 4.0],\n",
       "   [3.0, 4.0, 0.0],\n",
       "   [3.5, 4.0, 0.5],\n",
       "   [3.0, 4.5, 0.5],\n",
       "   [3.5, 4.5, 0.0],\n",
       "   [3.0, 4.0, 1.0],\n",
       "   [3.5, 4.0, 1.5],\n",
       "   [3.0, 4.5, 1.5],\n",
       "   [3.5, 4.5, 1.0],\n",
       "   [3.0, 4.0, 2.0],\n",
       "   [3.5, 4.0, 2.5],\n",
       "   [3.0, 4.5, 2.5],\n",
       "   [3.5, 4.5, 2.0],\n",
       "   [3.0, 4.0, 3.0],\n",
       "   [3.5, 4.0, 3.5],\n",
       "   [3.0, 4.5, 3.5],\n",
       "   [3.5, 4.5, 3.0],\n",
       "   [3.0, 4.0, 4.0],\n",
       "   [3.5, 4.0, 4.5],\n",
       "   [3.0, 4.5, 4.5],\n",
       "   [3.5, 4.5, 4.0],\n",
       "   [4.0, 0.0, 0.0],\n",
       "   [4.5, 0.0, 0.5],\n",
       "   [4.0, 0.5, 0.5],\n",
       "   [4.5, 0.5, 0.0],\n",
       "   [4.0, 0.0, 1.0],\n",
       "   [4.5, 0.0, 1.5],\n",
       "   [4.0, 0.5, 1.5],\n",
       "   [4.5, 0.5, 1.0],\n",
       "   [4.0, 0.0, 2.0],\n",
       "   [4.5, 0.0, 2.5],\n",
       "   [4.0, 0.5, 2.5],\n",
       "   [4.5, 0.5, 2.0],\n",
       "   [4.0, 0.0, 3.0],\n",
       "   [4.5, 0.0, 3.5],\n",
       "   [4.0, 0.5, 3.5],\n",
       "   [4.5, 0.5, 3.0],\n",
       "   [4.0, 0.0, 4.0],\n",
       "   [4.5, 0.0, 4.5],\n",
       "   [4.0, 0.5, 4.5],\n",
       "   [4.5, 0.5, 4.0],\n",
       "   [4.0, 1.0, 0.0],\n",
       "   [4.5, 1.0, 0.5],\n",
       "   [4.0, 1.5, 0.5],\n",
       "   [4.5, 1.5, 0.0],\n",
       "   [4.0, 1.0, 1.0],\n",
       "   [4.5, 1.0, 1.5],\n",
       "   [4.0, 1.5, 1.5],\n",
       "   [4.5, 1.5, 1.0],\n",
       "   [4.0, 1.0, 2.0],\n",
       "   [4.5, 1.0, 2.5],\n",
       "   [4.0, 1.5, 2.5],\n",
       "   [4.5, 1.5, 2.0],\n",
       "   [4.0, 1.0, 3.0],\n",
       "   [4.5, 1.0, 3.5],\n",
       "   [4.0, 1.5, 3.5],\n",
       "   [4.5, 1.5, 3.0],\n",
       "   [4.0, 1.0, 4.0],\n",
       "   [4.5, 1.0, 4.5],\n",
       "   [4.0, 1.5, 4.5],\n",
       "   [4.5, 1.5, 4.0],\n",
       "   [4.0, 2.0, 0.0],\n",
       "   [4.5, 2.0, 0.5],\n",
       "   [4.0, 2.5, 0.5],\n",
       "   [4.5, 2.5, 0.0],\n",
       "   [4.0, 2.0, 1.0],\n",
       "   [4.5, 2.0, 1.5],\n",
       "   [4.0, 2.5, 1.5],\n",
       "   [4.5, 2.5, 1.0],\n",
       "   [4.0, 2.0, 2.0],\n",
       "   [4.5, 2.0, 2.5],\n",
       "   [4.0, 2.5, 2.5],\n",
       "   [4.5, 2.5, 2.0],\n",
       "   [4.0, 2.0, 3.0],\n",
       "   [4.5, 2.0, 3.5],\n",
       "   [4.0, 2.5, 3.5],\n",
       "   [4.5, 2.5, 3.0],\n",
       "   [4.0, 2.0, 4.0],\n",
       "   [4.5, 2.0, 4.5],\n",
       "   [4.0, 2.5, 4.5],\n",
       "   [4.5, 2.5, 4.0],\n",
       "   [4.0, 3.0, 0.0],\n",
       "   [4.5, 3.0, 0.5],\n",
       "   [4.0, 3.5, 0.5],\n",
       "   [4.5, 3.5, 0.0],\n",
       "   [4.0, 3.0, 1.0],\n",
       "   [4.5, 3.0, 1.5],\n",
       "   [4.0, 3.5, 1.5],\n",
       "   [4.5, 3.5, 1.0],\n",
       "   [4.0, 3.0, 2.0],\n",
       "   [4.5, 3.0, 2.5],\n",
       "   [4.0, 3.5, 2.5],\n",
       "   [4.5, 3.5, 2.0],\n",
       "   [4.0, 3.0, 3.0],\n",
       "   [4.5, 3.0, 3.5],\n",
       "   [4.0, 3.5, 3.5],\n",
       "   [4.5, 3.5, 3.0],\n",
       "   [4.0, 3.0, 4.0],\n",
       "   [4.5, 3.0, 4.5],\n",
       "   [4.0, 3.5, 4.5],\n",
       "   [4.5, 3.5, 4.0],\n",
       "   [4.0, 4.0, 0.0],\n",
       "   [4.5, 4.0, 0.5],\n",
       "   [4.0, 4.5, 0.5],\n",
       "   [4.5, 4.5, 0.0],\n",
       "   [4.0, 4.0, 1.0],\n",
       "   [4.5, 4.0, 1.5],\n",
       "   [4.0, 4.5, 1.5],\n",
       "   [4.5, 4.5, 1.0],\n",
       "   [4.0, 4.0, 2.0],\n",
       "   [4.5, 4.0, 2.5],\n",
       "   [4.0, 4.5, 2.5],\n",
       "   [4.5, 4.5, 2.0],\n",
       "   [4.0, 4.0, 3.0],\n",
       "   [4.5, 4.0, 3.5],\n",
       "   [4.0, 4.5, 3.5],\n",
       "   [4.5, 4.5, 3.0],\n",
       "   [4.0, 4.0, 4.0],\n",
       "   [4.5, 4.0, 4.5],\n",
       "   [4.0, 4.5, 4.5],\n",
       "   [4.5, 4.5, 4.0]],\n",
       "  'ids': [1,\n",
       "   2,\n",
       "   3,\n",
       "   4,\n",
       "   5,\n",
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       "   False]},\n",
       " [[5.0, 0, 0], [0, 5.0, 0], [0, 0, 5.0]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "atoms,box"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0416a949-0b34-47dc-9e96-3fec4df0591d",
   "metadata": {},
   "source": [
    "Atoms are dicts. Thats fine. Atoms could be class inherited from dict, so we have extra methods that are useful. Lets try this approach. But first we do a simple calculation to benchmark the speed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4f9ceb9a-712b-4319-b3fc-9b16a7681454",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Atoms(dict):\n",
    "    def __init__(self):\n",
    "        pass\n",
    "    \n",
    "    @property\n",
    "    def positions(self):\n",
    "        return self[\"positions\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8b0321d1-a452-46e1-926f-03c43192d67a",
   "metadata": {},
   "outputs": [],
   "source": [
    "rep = 5\n",
    "atoms, box = pcs.make_crystal(structure=\"fcc\", repetitions=(rep,rep,rep))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "20a108d9-030a-4cb3-a57b-c04cba11dad9",
   "metadata": {},
   "outputs": [],
   "source": [
    "sys = System()\n",
    "sys.box = box\n",
    "sys.atoms = atoms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "ac3b8131-f586-4455-8a3a-b1fc8341a954",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "373 ms ± 8.08 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "sys.find_neighbors(method=\"cutoff\", cutoff=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "03b9a5ad-f028-4c3f-8682-451d56fa0677",
   "metadata": {},
   "outputs": [],
   "source": [
    "at = Atoms()\n",
    "for key, val in atoms.items():\n",
    "    at[key] = val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "e433826b-36d0-4627-ac2e-8243d491314f",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
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       " [1.5, 4.5, 10.0],\n",
       " [1.0, 4.0, 11.0],\n",
       " [1.5, 4.0, 11.5],\n",
       " [1.0, 4.5, 11.5],\n",
       " [1.5, 4.5, 11.0],\n",
       " [1.0, 5.0, 0.0],\n",
       " [1.5, 5.0, 0.5],\n",
       " [1.0, 5.5, 0.5],\n",
       " [1.5, 5.5, 0.0],\n",
       " [1.0, 5.0, 1.0],\n",
       " [1.5, 5.0, 1.5],\n",
       " [1.0, 5.5, 1.5],\n",
       " [1.5, 5.5, 1.0],\n",
       " [1.0, 5.0, 2.0],\n",
       " [1.5, 5.0, 2.5],\n",
       " [1.0, 5.5, 2.5],\n",
       " [1.5, 5.5, 2.0],\n",
       " [1.0, 5.0, 3.0],\n",
       " [1.5, 5.0, 3.5],\n",
       " [1.0, 5.5, 3.5],\n",
       " [1.5, 5.5, 3.0],\n",
       " [1.0, 5.0, 4.0],\n",
       " [1.5, 5.0, 4.5],\n",
       " [1.0, 5.5, 4.5],\n",
       " [1.5, 5.5, 4.0],\n",
       " [1.0, 5.0, 5.0],\n",
       " [1.5, 5.0, 5.5],\n",
       " [1.0, 5.5, 5.5],\n",
       " [1.5, 5.5, 5.0],\n",
       " [1.0, 5.0, 6.0],\n",
       " [1.5, 5.0, 6.5],\n",
       " [1.0, 5.5, 6.5],\n",
       " [1.5, 5.5, 6.0],\n",
       " [1.0, 5.0, 7.0],\n",
       " [1.5, 5.0, 7.5],\n",
       " [1.0, 5.5, 7.5],\n",
       " [1.5, 5.5, 7.0],\n",
       " [1.0, 5.0, 8.0],\n",
       " [1.5, 5.0, 8.5],\n",
       " [1.0, 5.5, 8.5],\n",
       " [1.5, 5.5, 8.0],\n",
       " [1.0, 5.0, 9.0],\n",
       " [1.5, 5.0, 9.5],\n",
       " [1.0, 5.5, 9.5],\n",
       " [1.5, 5.5, 9.0],\n",
       " [1.0, 5.0, 10.0],\n",
       " [1.5, 5.0, 10.5],\n",
       " [1.0, 5.5, 10.5],\n",
       " [1.5, 5.5, 10.0],\n",
       " [1.0, 5.0, 11.0],\n",
       " [1.5, 5.0, 11.5],\n",
       " [1.0, 5.5, 11.5],\n",
       " [1.5, 5.5, 11.0],\n",
       " [1.0, 6.0, 0.0],\n",
       " [1.5, 6.0, 0.5],\n",
       " [1.0, 6.5, 0.5],\n",
       " [1.5, 6.5, 0.0],\n",
       " [1.0, 6.0, 1.0],\n",
       " [1.5, 6.0, 1.5],\n",
       " [1.0, 6.5, 1.5],\n",
       " [1.5, 6.5, 1.0],\n",
       " [1.0, 6.0, 2.0],\n",
       " [1.5, 6.0, 2.5],\n",
       " [1.0, 6.5, 2.5],\n",
       " [1.5, 6.5, 2.0],\n",
       " [1.0, 6.0, 3.0],\n",
       " [1.5, 6.0, 3.5],\n",
       " [1.0, 6.5, 3.5],\n",
       " [1.5, 6.5, 3.0],\n",
       " [1.0, 6.0, 4.0],\n",
       " [1.5, 6.0, 4.5],\n",
       " [1.0, 6.5, 4.5],\n",
       " [1.5, 6.5, 4.0],\n",
       " [1.0, 6.0, 5.0],\n",
       " [1.5, 6.0, 5.5],\n",
       " [1.0, 6.5, 5.5],\n",
       " [1.5, 6.5, 5.0],\n",
       " [1.0, 6.0, 6.0],\n",
       " [1.5, 6.0, 6.5],\n",
       " [1.0, 6.5, 6.5],\n",
       " [1.5, 6.5, 6.0],\n",
       " [1.0, 6.0, 7.0],\n",
       " [1.5, 6.0, 7.5],\n",
       " [1.0, 6.5, 7.5],\n",
       " [1.5, 6.5, 7.0],\n",
       " [1.0, 6.0, 8.0],\n",
       " [1.5, 6.0, 8.5],\n",
       " [1.0, 6.5, 8.5],\n",
       " [1.5, 6.5, 8.0],\n",
       " [1.0, 6.0, 9.0],\n",
       " [1.5, 6.0, 9.5],\n",
       " [1.0, 6.5, 9.5],\n",
       " [1.5, 6.5, 9.0],\n",
       " [1.0, 6.0, 10.0],\n",
       " [1.5, 6.0, 10.5],\n",
       " [1.0, 6.5, 10.5],\n",
       " [1.5, 6.5, 10.0],\n",
       " [1.0, 6.0, 11.0],\n",
       " [1.5, 6.0, 11.5],\n",
       " [1.0, 6.5, 11.5],\n",
       " [1.5, 6.5, 11.0],\n",
       " [1.0, 7.0, 0.0],\n",
       " [1.5, 7.0, 0.5],\n",
       " [1.0, 7.5, 0.5],\n",
       " [1.5, 7.5, 0.0],\n",
       " [1.0, 7.0, 1.0],\n",
       " [1.5, 7.0, 1.5],\n",
       " [1.0, 7.5, 1.5],\n",
       " [1.5, 7.5, 1.0],\n",
       " [1.0, 7.0, 2.0],\n",
       " [1.5, 7.0, 2.5],\n",
       " [1.0, 7.5, 2.5],\n",
       " [1.5, 7.5, 2.0],\n",
       " [1.0, 7.0, 3.0],\n",
       " [1.5, 7.0, 3.5],\n",
       " [1.0, 7.5, 3.5],\n",
       " [1.5, 7.5, 3.0],\n",
       " [1.0, 7.0, 4.0],\n",
       " [1.5, 7.0, 4.5],\n",
       " [1.0, 7.5, 4.5],\n",
       " [1.5, 7.5, 4.0],\n",
       " [1.0, 7.0, 5.0],\n",
       " [1.5, 7.0, 5.5],\n",
       " [1.0, 7.5, 5.5],\n",
       " [1.5, 7.5, 5.0],\n",
       " [1.0, 7.0, 6.0],\n",
       " [1.5, 7.0, 6.5],\n",
       " [1.0, 7.5, 6.5],\n",
       " [1.5, 7.5, 6.0],\n",
       " [1.0, 7.0, 7.0],\n",
       " [1.5, 7.0, 7.5],\n",
       " [1.0, 7.5, 7.5],\n",
       " [1.5, 7.5, 7.0],\n",
       " [1.0, 7.0, 8.0],\n",
       " [1.5, 7.0, 8.5],\n",
       " [1.0, 7.5, 8.5],\n",
       " [1.5, 7.5, 8.0],\n",
       " [1.0, 7.0, 9.0],\n",
       " [1.5, 7.0, 9.5],\n",
       " [1.0, 7.5, 9.5],\n",
       " [1.5, 7.5, 9.0],\n",
       " [1.0, 7.0, 10.0],\n",
       " [1.5, 7.0, 10.5],\n",
       " [1.0, 7.5, 10.5],\n",
       " [1.5, 7.5, 10.0],\n",
       " [1.0, 7.0, 11.0],\n",
       " [1.5, 7.0, 11.5],\n",
       " [1.0, 7.5, 11.5],\n",
       " [1.5, 7.5, 11.0],\n",
       " [1.0, 8.0, 0.0],\n",
       " [1.5, 8.0, 0.5],\n",
       " [1.0, 8.5, 0.5],\n",
       " [1.5, 8.5, 0.0],\n",
       " [1.0, 8.0, 1.0],\n",
       " [1.5, 8.0, 1.5],\n",
       " [1.0, 8.5, 1.5],\n",
       " [1.5, 8.5, 1.0],\n",
       " [1.0, 8.0, 2.0],\n",
       " [1.5, 8.0, 2.5],\n",
       " [1.0, 8.5, 2.5],\n",
       " [1.5, 8.5, 2.0],\n",
       " [1.0, 8.0, 3.0],\n",
       " [1.5, 8.0, 3.5],\n",
       " [1.0, 8.5, 3.5],\n",
       " [1.5, 8.5, 3.0],\n",
       " [1.0, 8.0, 4.0],\n",
       " [1.5, 8.0, 4.5],\n",
       " [1.0, 8.5, 4.5],\n",
       " [1.5, 8.5, 4.0],\n",
       " [1.0, 8.0, 5.0],\n",
       " [1.5, 8.0, 5.5],\n",
       " [1.0, 8.5, 5.5],\n",
       " [1.5, 8.5, 5.0],\n",
       " [1.0, 8.0, 6.0],\n",
       " [1.5, 8.0, 6.5],\n",
       " [1.0, 8.5, 6.5],\n",
       " [1.5, 8.5, 6.0],\n",
       " [1.0, 8.0, 7.0],\n",
       " [1.5, 8.0, 7.5],\n",
       " [1.0, 8.5, 7.5],\n",
       " [1.5, 8.5, 7.0],\n",
       " [1.0, 8.0, 8.0],\n",
       " [1.5, 8.0, 8.5],\n",
       " [1.0, 8.5, 8.5],\n",
       " [1.5, 8.5, 8.0],\n",
       " [1.0, 8.0, 9.0],\n",
       " [1.5, 8.0, 9.5],\n",
       " [1.0, 8.5, 9.5],\n",
       " [1.5, 8.5, 9.0],\n",
       " ...]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "at.positions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "82da973d-b761-45b3-8e61-bc3377f72933",
   "metadata": {},
   "outputs": [],
   "source": [
    "sys2 = System()\n",
    "sys2.box = box\n",
    "sys2.atoms = at"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "67b569d3-f96c-4f68-91dd-ee3ec9fdf77a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "406 ms ± 27.4 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "sys2.find_neighbors(method=\"cutoff\", cutoff=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "b05ae9f3-9952-43a6-a9c0-df69f5328d18",
   "metadata": {},
   "outputs": [],
   "source": [
    "at.head = sys2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "b11331ff-2bdc-42ad-b6df-263a58984a57",
   "metadata": {},
   "outputs": [],
   "source": [
    "at.mapdict = {\"ghostx\":\"ghost\"}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "9861bb94-8668-497e-8cff-18f1d466990c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['positions', 'ids', 'types', 'ghost', 'mask_1', 'mask_2', 'condition', 'head', 'neighbors', 'neighbordist', 'temp_neighbors', 'temp_neighbordist', 'neighborweight', 'diff', 'r', 'theta', 'phi', 'cutoff'])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "at.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5ee451f1-59ac-4f54-a354-c666a8e8035a",
   "metadata": {},
   "outputs": [],
   "source": [
    "repetitions = [2, 5, 7, 10, 12]\n",
    "at_dict = [68.9, 31.6, 68, 258, 449]\n",
    "at_class = [73, 32.5, 70, 250, 441]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b93ab21a-bc6d-44ca-ba82-821c525aadeb",
   "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": [
    "plt.plot(repetitions, at_dict, \"-o\");\n",
    "plt.plot(repetitions, at_class, \"-o\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05a2db7f-38a3-4aa1-9962-3d4539b3ab58",
   "metadata": {},
   "source": [
    "This is quite nice and fine; the way therefore is to draft a new class with convenient properties aimed at the user. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "16b4e87f-0cd7-4976-92d6-c3e1c9b37176",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Atoms(dict):\n",
    "    def __init__(self, *args, **kwargs):\n",
    "        self.update(*args, **kwargs)\n",
    "\n",
    "    def __getitem__(self, key):\n",
    "        if isinstance(key, slice):\n",
    "            return self._get_atoms(key)\n",
    "        elif isinstance(key, int):\n",
    "            return self._get_atoms(key)\n",
    "        else:\n",
    "            val = dict.__getitem__(self, key)\n",
    "            return val\n",
    "\n",
    "    def __setitem__(self, key, val):\n",
    "        dict.__setitem__(self, key, val)\n",
    "\n",
    "    def __repr__(self):\n",
    "        dictrepr = dict.__repr__(self)\n",
    "        return '%s(%s)' % (type(self).__name__, dictrepr)\n",
    "        \n",
    "    def update(self, *args, **kwargs):\n",
    "        for k, v in dict(*args, **kwargs).items():\n",
    "            self[k] = v\n",
    "    \n",
    "    def _get_atoms(self, index):\n",
    "        atom_dict = {}\n",
    "        for key in self.keys():\n",
    "            atom_dict[key] = self[key][index]\n",
    "        return atom_dict        "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b39da9a5-0390-4a8d-93cf-19714bc2134d",
   "metadata": {},
   "source": [
    "Speedtest this class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "fe32ef44-d11f-43f6-99ed-c8345338649e",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "rep = 12\n",
    "atoms, box = pcs.make_crystal(structure=\"fcc\", repetitions=(rep,rep,rep))\n",
    "at = Atoms()\n",
    "for key, val in atoms.items():\n",
    "    at[key] = val\n",
    "sys = System()\n",
    "sys.box = box\n",
    "sys.atoms = atoms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "8fdad6e7-0ba9-4940-bb69-f81113a34061",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "473 ms ± 44.1 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "sys.find_neighbors(method=\"cutoff\", cutoff=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8ab0b9f8-6c27-4aac-a7bb-0496037559a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "at_class_v2 = [72, 32, 68, 260, 473]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7ecd8415-de22-428e-8c05-b2b26425b6e9",
   "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": [
    "plt.plot(repetitions, at_dict, \"-o\");\n",
    "plt.plot(repetitions, at_class, \"-o\");\n",
    "plt.plot(repetitions, at_class_v2, \"-o\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "366e2003-19cd-447b-a28e-3b2c57dfc9dd",
   "metadata": {},
   "source": [
    "It is not particularly more expensive, we go with this definition and extend it."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5942b5cd-fb38-4899-a1c8-df86c327f3a2",
   "metadata": {},
   "source": [
    "We have to use the very new type-converted class and see if it affects the speed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "1a4f666e-2235-4af8-883a-6bd0764e4e6b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rep = 10\n",
    "atoms, box = pcs.make_crystal(structure=\"bcc\", lattice_constant=3.147, repetitions=(rep,rep,rep))\n",
    "sys = System()\n",
    "sys.box = box\n",
    "sys.atoms = atoms\n",
    "atoms.natoms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "ac2fe53f-dce6-4cbf-87e8-b45365433dd1",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "sys.find_neighbors(method=\"cutoff\", cutoff=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "d33902b1-9b3b-4073-809b-37d223daf9e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pyscal.attributes.MyList"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(sys.atoms[\"positions\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1b576b0a-5bc3-41de-94ae-6054e25dc7f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "at_class_v3 = [1.6, 6.21, 17.6] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6f7cb589-5671-488d-9f45-75ebf427a1d7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "080f4a91-c410-4a0a-8896-2b8506711ae0",
   "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": [
    "plt.plot(repetitions, at_dict, \"-o\");\n",
    "plt.plot(repetitions, at_class, \"-o\");\n",
    "plt.plot(repetitions, at_class_v2, \"-o\");\n",
    "plt.plot(repetitions, at_class_v3, \"-o\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d9600b53-d596-4b4e-b230-65535da2a742",
   "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": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}