examples/example-1.1-custom-parameter-exploration.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A simple parameter exploration\n",
    "\n",
    "This notebook demonstrates a very simple parameter exploration of a custom function that we have defined. It is a simple function that returns the distance to a unit circle, so we expect our parameter exploration to resemble a circle. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# change to the root directory of the project\n",
    "import os\n",
    "if os.getcwd().split(\"/\")[-1] == \"examples\":\n",
    "    os.chdir('..')\n",
    "    \n",
    "# This will reload all imports as soon as the code changes\n",
    "%load_ext autoreload\n",
    "%autoreload 2    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "try:\n",
    "    import matplotlib.pyplot as plt\n",
    "except ImportError:\n",
    "    import sys\n",
    "    !{sys.executable} -m pip install matplotlib\n",
    "    import matplotlib.pyplot as plt\n",
    "    \n",
    "import numpy as np\n",
    "\n",
    "from neurolib.utils.parameterSpace import ParameterSpace\n",
    "from neurolib.optimize.exploration import BoxSearch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the evaluation function\n",
    "Here we define a very simple evaluation function. The function needs to take in `traj` as an argument, which is the pypet trajectory. This is how the function knows what parameters were assigned to it. Using the builtin function `search.getParametersFromTraj(traj)` we can then retrieve the parameters for this run. They are returned as a dictionary and can be accessed in the function. \n",
    "\n",
    "In the last step, we use `search.saveToPypet(result_dict, traj)` to save the results to the pypet trajectory and to an HDF. In between, the computational magic happens!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def explore_me(traj):\n",
    "    pars = search.getParametersFromTraj(traj)\n",
    "    # let's calculate the distance to a circle\n",
    "    computation_result = abs((pars['x']**2 + pars['y']**2) - 1)\n",
    "    result_dict = {\"distance\" : computation_result}\n",
    "    search.saveToPypet(result_dict, traj)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the parameter space and exploration\n",
    "\n",
    "Here we define which space we want to cover. For this, we use the builtin class `ParameterSpace` which provides a very easy interface to the exploration. To initialize the exploration, we simply pass the evaluation function and the parameter space to the `BoxSearch` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "parameters = ParameterSpace({\"x\": np.linspace(-2, 2, 2), \"y\": np.linspace(-2, 2, 2)})\n",
    "# info: chose np.linspace(-2, 2, 40) or more, values here are low for testing\n",
    "search = BoxSearch(evalFunction = explore_me, parameterSpace = parameters, filename=\"example-1.1.hdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Run\n",
    "\n",
    "And off we go!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "search.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get results\n",
    "\n",
    "We can easily obtain the results from pypet. First we call `search.loadResults()` to make sure that the results are loaded from the hdf file to our instance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "search.loadResults()\n",
    "print(\"Number of results: {}\".format(len(search.results)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The runs are also ordered in a simple pandas dataframe called `search.dfResults`. We cycle through all results by calling `search.results[i]` and loading the desired result (here the distance to the circle) into the dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>distance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-2.0</td>\n",
       "      <td>-2.000000</td>\n",
       "      <td>7.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-2.0</td>\n",
       "      <td>-1.897436</td>\n",
       "      <td>6.600263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-2.0</td>\n",
       "      <td>-1.794872</td>\n",
       "      <td>6.221565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-2.0</td>\n",
       "      <td>-1.692308</td>\n",
       "      <td>5.863905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2.0</td>\n",
       "      <td>-1.589744</td>\n",
       "      <td>5.527285</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1595</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1.589744</td>\n",
       "      <td>5.527285</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1596</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1.692308</td>\n",
       "      <td>5.863905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1597</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1.794872</td>\n",
       "      <td>6.221565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1598</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1.897436</td>\n",
       "      <td>6.600263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1599</th>\n",
       "      <td>2.0</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>7.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1600 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        x         y  distance\n",
       "0    -2.0 -2.000000  7.000000\n",
       "1    -2.0 -1.897436  6.600263\n",
       "2    -2.0 -1.794872  6.221565\n",
       "3    -2.0 -1.692308  5.863905\n",
       "4    -2.0 -1.589744  5.527285\n",
       "...   ...       ...       ...\n",
       "1595  2.0  1.589744  5.527285\n",
       "1596  2.0  1.692308  5.863905\n",
       "1597  2.0  1.794872  6.221565\n",
       "1598  2.0  1.897436  6.600263\n",
       "1599  2.0  2.000000  7.000000\n",
       "\n",
       "[1600 rows x 3 columns]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for i in search.dfResults.index:\n",
    "    search.dfResults.loc[i, 'distance'] = search.results[i]['distance']\n",
    "    \n",
    "search.dfResults"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And of course a plot can visualize the results very easily."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x124a71588>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(search.dfResults.pivot_table(values='distance', index = 'x', columns='y'), \\\n",
    "           extent = [min(search.dfResults.x), max(search.dfResults.x),\n",
    "                     min(search.dfResults.y), max(search.dfResults.y)], origin='lower')\n",
    "plt.colorbar(label='Distance to the unit circle')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "py36",
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