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add example jupyter notebook of permitation algorithms
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‎examples/basic_algorithms.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "b42d0808",
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"metadata": {
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"id": "b42d0808"
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},
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"source": [
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"Usage of algorithms for symmetry analysis\n",
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"=========================================\n",
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"\n",
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"In order to determine the geometric symmetry, posym implements diferent algorithms to compute the permutation of atoms that minimize the CSM"
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]
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},
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{
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"cell_type": "markdown",
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"id": "7d4340db",
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"metadata": {
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"id": "7d4340db"
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},
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"source": [
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"Setup environment\n",
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"----------------------"
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]
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},
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{
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"cell_type": "markdown",
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"id": "65af4b5c",
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"metadata": {
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"id": "65af4b5c"
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},
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"source": [
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"Install required packages"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "6368cc0b",
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "6368cc0b",
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"outputId": "d8389a23-86de-44e5-b89a-f1039e74e74a"
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},
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"outputs": [],
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"source": [
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"try:\n",
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" import posym\n",
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"except ImportError:\n",
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" ! pip install git+https://github.com/abelcarreras/posym.git@development\n",
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"try:\n",
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" import pyscf\n",
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"except ImportError:\n",
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" ! pip install pyscf\n",
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"try:\n",
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" import matplotlib\n",
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"except ImportError:\n",
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" ! pip install matplotlib"
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]
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},
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{
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"cell_type": "markdown",
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"id": "42420111",
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"metadata": {
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"id": "42420111"
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},
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"source": [
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"Import required modules"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "5b788bc8",
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"metadata": {
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"id": "5b788bc8"
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},
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"outputs": [],
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"source": [
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"from posym import SymmetryMolecule\n",
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"from posym.tools import get_basis_set_pyscf, build_density, build_orbital\n",
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"from posym.algebra import norm\n",
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"from posym.config import Configuration\n",
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"import numpy as np\n",
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"import time\n",
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"import matplotlib.pyplot as plt"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ECd689yd1Fzg",
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"metadata": {
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"id": "ECd689yd1Fzg"
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},
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"source": [
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"helper function for timing"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "LeCfugrjiN20",
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"metadata": {
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"id": "LeCfugrjiN20"
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},
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"outputs": [],
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"source": [
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"class TimeIt:\n",
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" def __init__(self):\n",
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" self._time_ini = 0\n",
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" self._time_fin = 0\n",
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"\n",
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" def __enter__(self):\n",
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" # Record the start time\n",
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" self._time_ini = time.time()\n",
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" return self # So that `as f` receives this object\n",
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"\n",
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" def __exit__(self, exc_type, exc_value, traceback):\n",
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" # Record the end time\n",
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" self._time_fin = time.time()\n",
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"\n",
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" @property\n",
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" def elapsed(self):\n",
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" # Return the elapsed time\n",
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" return self._time_fin - self._time_ini"
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]
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},
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{
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"cell_type": "markdown",
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"id": "CIQ8B_XraLqk",
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"metadata": {
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"id": "CIQ8B_XraLqk"
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},
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"source": [
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"Algorithms to compute CSM\n",
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"-------------------------"
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]
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},
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{
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"cell_type": "markdown",
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"id": "Xt1jmD6Agi2w",
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"metadata": {
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"id": "Xt1jmD6Agi2w"
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},
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"source": [
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"Define molecule (distorted ethane)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "JA918EMggsu6",
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"metadata": {
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"id": "JA918EMggsu6"
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},
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"outputs": [],
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"source": [
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"coordinates = [[-0.7560, 0.0000, 0.0000],\n",
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" [ 0.7560, 0.0000, 0.0000],\n",
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" [-4.1404, 0.6586, 0.7845],\n",
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" [-2.1404, 0.3501, -0.9626],\n",
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" [-1.1405, -1.0087, 0.1781],\n",
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" [ 1.1404, -0.3501, 0.9626],\n",
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" [ 2.1405, 1.0087, -0.1781],\n",
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" [ 4.1404, -0.6586, -0.7845]]\n",
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"\n",
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"symbols = ['C','C','H','H','H','H','H','H']"
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]
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},
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{
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"cell_type": "markdown",
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"id": "Fr36QEM8g90G",
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"metadata": {
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"id": "Fr36QEM8g90G"
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},
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"source": [
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"**Hungarian algorithm** : very fast, coherence only garanteed if close to exact symmetry (lower bound for the real CSM)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "VP3xB3G9g0jq",
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "VP3xB3G9g0jq",
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"outputId": "40720b40-7af9-4966-acce-073a56877854"
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},
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"outputs": [],
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"source": [
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"Configuration().algorithm = 'hungarian'\n",
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"Configuration().label_tolerance = 1.0\n",
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"\n",
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"with TimeIt() as f:\n",
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" mb = SymmetryMolecule('C2h', coordinates, symbols, orientation_angles=[-90, 0.0, 109.987640])\n",
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" print('CSM: ', mb.measure)\n",
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" print('Coor measure: ', mb, '(', norm(mb), ')')\n",
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" print(mb._symbols_restricted)\n",
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"print('time:', f.elapsed)\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "HmrmyMgIhDEG",
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"metadata": {
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"id": "HmrmyMgIhDEG"
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},
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"source": [
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"**Exact algorithm** : very slow but exact for any geometry and any group"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "Dh6WJ3BfZgJd",
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "Dh6WJ3BfZgJd",
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"outputId": "13e7906c-3afd-409a-ce09-62b9e082ce8a"
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},
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"outputs": [],
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"source": [
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"\n",
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"Configuration().algorithm = 'exact'\n",
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"Configuration().label_tolerance = 1.0\n",
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"\n",
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"with TimeIt() as f:\n",
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" mb = SymmetryMolecule('C2h', coordinates, symbols, orientation_angles=[-90, 0.0, 109.987640])\n",
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" print('CSM: ', mb.measure)\n",
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" print('Coor measure: ', mb, '(', norm(mb), ')')\n",
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" print(mb._symbols_restricted)\n",
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"print('time:', f.elapsed)\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "WeQA4lOVhGNc",
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"metadata": {
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"id": "WeQA4lOVhGNc"
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},
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"source": [
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"**Exact algorithm with tolerance label**: faster as tolerance get close to zero, will yield overstimated CSM if tolerance label is too low (upper bound for the CSM)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "vtVZFvlXhGk2",
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "vtVZFvlXhGk2",
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"outputId": "d6eb415f-82a0-4608-c450-366fb85c7b7c"
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},
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"outputs": [],
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"source": [
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"Configuration().algorithm = 'exact'\n",
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"Configuration().label_tolerance = 0.2\n",
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"\n",
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"with TimeIt() as f:\n",
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" mb = SymmetryMolecule('C2h', coordinates, symbols, orientation_angles=[-90, 0.0, 109.987640])\n",
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" print('CSM: ', mb.measure)\n",
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" print('Coor measure: ', mb, '(', norm(mb), ')')\n",
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" print(mb._symbols_restricted)\n",
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"print('time:', f.elapsed)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "8HJZpn-5tmei",
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "8HJZpn-5tmei",
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"outputId": "bcd03258-0493-4bc4-db22-9ab0da056563"
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},
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"outputs": [],
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"source": [
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"Configuration().algorithm = 'exact'\n",
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"Configuration().label_tolerance = 0.1\n",
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"\n",
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"with TimeIt() as f:\n",
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" mb = SymmetryMolecule('C2h', coordinates, symbols, orientation_angles=[-90, 0.0, 109.987640])\n",
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" print('CSM: ', mb.measure)\n",
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" print('Coor measure: ', mb, '(', norm(mb), ')')\n",
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" print(mb._symbols_restricted)\n",
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"print('time:', f.elapsed)"
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]
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}
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],
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"metadata": {
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"colab": {
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"provenance": []
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},
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.9"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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