3_Slot_Based_Mixtures.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e921eaa3-f0cb-4973-90dd-73d505f5603e",
   "metadata": {},
   "source": [
    "# Slot-Based Mixture Modeling\n",
    "\n",
    "How to model mixtures with a slot-based approach instead of the traditional approach.\n",
    "\n",
    "Find more information here:\n",
    "- [Mixture Example](https://emdgroup.github.io/baybe/examples/Constraints_Discrete/mixture_constraints.html)\n",
    "- [BayBE GitHub](https://github.com/emdgroup/baybe)\n",
    "- [BayBE Userguide](https://emdgroup.github.io/baybe/userguide/userguide.html)\n",
    "\n",
    "<a target=\"_blank\" href=\"https://colab.research.google.com/github/emdgroup/baybe-ac24-workshop/blob/main/3_Slot_Based_Mixtures.ipynb\">\n",
    "  <img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/>\n",
    "</a>\n",
    "<a target=\"_blank\" href=\"https://mybinder.org/v2/gh/emdgroup/baybe-ac24-workshop/HEAD?labpath=3_Slot_Based_Mixtures.ipynb\">\n",
    "  <img src=\"https://mybinder.org/badge_logo.svg\" alt=\"Launch Binder\"/>\n",
    "</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80437ed4-6afb-4d5a-90aa-d840719a37cf",
   "metadata": {},
   "source": [
    "# Install and Import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9858f10e-f33a-414d-8bf5-fc51c6159a71",
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install 'baybe[chem]==0.10.0' seaborn matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1d060866-26e6-4f66-b7c7-93779cf38d79",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore', category = FutureWarning)\n",
    "warnings.filterwarnings('ignore', message = '.*BayBE.*')\n",
    "\n",
    "import baybe\n",
    "os.environ['BAYBE_CACHE_DIR']='' # turn descriptor caching off\n",
    "baybe.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "080a4d99-22a4-45b6-96c8-0fec919ce817",
   "metadata": {},
   "source": [
    "# Defining Mixture Substances\n",
    "\n",
    "Let us consider 6 common solvents and create an experimental campaign supposed to optimize their mixture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4d38e3cb-988e-4385-b874-e2c3c5961150",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "dict_solvents = {\n",
    "    \"Water\": \"O\",\n",
    "    \"Hexane\": \"CCCCCC\",\n",
    "    \"Toluene\": \"CC1=CC=CC=C1\",\n",
    "    \"DMF\": \"CN(C)C=O\",\n",
    "    \"Dioxane\": \"C1COCCO1\",\n",
    "    \"Ethanol\":\"CCO\",\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "377aec6d-33b7-4ff2-90e6-34368a28e610",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from rdkit import Chem\n",
    "from rdkit.Chem import Draw\n",
    "\n",
    "mols = [Chem.MolFromSmiles(smi) for smi in dict_solvents.values()]\n",
    "Draw.MolsToGridImage(mols, molsPerRow = 3, legends = dict_solvents.keys())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c9d2c7b-365b-4498-98e5-954a134af6df",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Traditional Mixture Search Space"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9df6c36-0c76-44d7-a3ff-05d703c4d4bb",
   "metadata": {},
   "source": [
    "In this example we use discrete setpoints for the concentrations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e6c955bf-d81c-4d5c-aecb-878e7843baf3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "setpoints = np.linspace(0.0, 1.0, 10+1).round(2).tolist()\n",
    "setpoints"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ca5d90f-0c73-49fd-92bd-16218492a895",
   "metadata": {},
   "source": [
    "Now we create a numerical parameter for each of the substances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f4e5f16c-d31e-4cf3-bcf0-e0a21b82585f",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from baybe.parameters import NumericalDiscreteParameter\n",
    "\n",
    "parameters = [\n",
    "    NumericalDiscreteParameter(\n",
    "        name=f'{name}',\n",
    "        values=setpoints\n",
    "    )\n",
    "    for name in dict_solvents\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "460e996b-3107-4a6a-9b42-cb1bc565874d",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Inspecting SearchSpaces"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29d509b2-4670-42da-b880-12306258568f",
   "metadata": {},
   "source": [
    "In BayBE, a search space is represented by a `discrete` and `continuous` part. These sub spaces manage all aspects dealing with translating the users-defined settings to something machine readable for the machine learning surrogate mdoel.\n",
    "\n",
    "The `discrete` sub space has two dataframes representing all desired combinations resulting from discrete parameters.\n",
    "- `exp_rep`: The experimental representation, still containing labels for e.g. categories and substances. Recommendations given to the user will be in this representation.\n",
    "- `comp_rep`: The comutational representation, consisting of only numbers that result from the encoding of parameter labels and values.\n",
    "\n",
    "You can access the underlying data frames like `searchspace.discrete.exp_rep` and `searchspace.discrete.comp_rep`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "988d0609-5995-43ab-b12d-64bb62255b96",
   "metadata": {
    "tags": []
   },
   "source": [
    "## SearchSpace Via Constraint\n",
    "\n",
    "In this notebook we will limit us to create the correpsonding search space with discrete parameters, i.e. with concrete set points. But the traditional mixture representation in BayBE can also be achieved with continuous numerical parameters and corresponding linear equality constarints."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "b879c223-d4da-4fd0-a8e2-30b0239a73ad",
   "metadata": {
    "tags": []
   },
   "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>Water</th>\n",
       "      <th>Hexane</th>\n",
       "      <th>Toluene</th>\n",
       "      <th>DMF</th>\n",
       "      <th>Dioxane</th>\n",
       "      <th>Ethanol</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2998</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2999</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3000</th>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3001</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3002</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3003 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Water  Hexane  Toluene  DMF  Dioxane  Ethanol\n",
       "0       0.0     0.0      0.0  0.0      0.0      1.0\n",
       "1       0.0     0.0      0.0  0.0      0.1      0.9\n",
       "2       0.0     0.0      0.0  0.0      0.2      0.8\n",
       "3       0.0     0.0      0.0  0.0      0.3      0.7\n",
       "4       0.0     0.0      0.0  0.0      0.4      0.6\n",
       "...     ...     ...      ...  ...      ...      ...\n",
       "2998    0.0     0.0      0.9  0.0      0.1      0.0\n",
       "2999    0.0     0.0      0.9  0.1      0.0      0.0\n",
       "3000    0.1     0.0      0.9  0.0      0.0      0.0\n",
       "3001    0.0     0.1      0.9  0.0      0.0      0.0\n",
       "3002    0.0     0.0      1.0  0.0      0.0      0.0\n",
       "\n",
       "[3003 rows x 6 columns]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from baybe.constraints import DiscreteSumConstraint, ThresholdCondition\n",
    "from baybe.searchspace import SearchSpace\n",
    "\n",
    "sum_constraint = DiscreteSumConstraint(parameters = dict_solvents.keys(),\n",
    "                                       condition = ThresholdCondition(threshold = 1.0,\n",
    "                                                                      operator = '='))\n",
    "\n",
    "searchspace = SearchSpace.from_product(parameters = parameters,\n",
    "                                       constraints = [sum_constraint])\n",
    "searchspace.discrete.exp_rep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "1a7ca914-395d-4d7c-acd2-4e1a55a9996a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check that all rows sum to 1.0 (within a small tolerance)\n",
    "(searchspace.discrete\n",
    "            .exp_rep\n",
    "            .sum(axis = 1)\n",
    "            .apply(lambda x: x-1.0)\n",
    "            .abs()\n",
    "            .lt(0.001)\n",
    "            .all())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efb823ce-3215-4d06-996e-1f7b9625f41c",
   "metadata": {
    "tags": []
   },
   "source": [
    "## SearchSpace Via Simplex Constructor\n",
    "This constructor already incorporates the main sum constraint during the product creation and hence is much more efficient. It is always to be preferred for discrete mixture representations. This constructor, for isntance, also has the capability to include cardinality constraints (also known as n-choose-k or similar), which is useful when e.g. a minimum of `k1` and a maximum of `k2` components should be included in the mixture (`min_nonzero` and `max_nonzero` arguments, not used below).\n",
    "\n",
    "More details on the simplex constructor [here](https://emdgroup.github.io/baybe/userguide/searchspace.html#creating-a-simplex-bound-discrete-subspace) and [here](https://emdgroup.github.io/baybe/_autosummary/baybe.searchspace.discrete.SubspaceDiscrete.html#baybe.searchspace.discrete.SubspaceDiscrete.from_simplex)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "20f22750-ab8f-4d0f-9b48-1fe680b46359",
   "metadata": {
    "tags": []
   },
   "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>Water</th>\n",
       "      <th>Hexane</th>\n",
       "      <th>Toluene</th>\n",
       "      <th>DMF</th>\n",
       "      <th>Dioxane</th>\n",
       "      <th>Ethanol</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2998</th>\n",
       "      <td>0.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2999</th>\n",
       "      <td>0.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3000</th>\n",
       "      <td>0.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3001</th>\n",
       "      <td>0.9</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3002</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3003 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Water  Hexane  Toluene  DMF  Dioxane  Ethanol\n",
       "0       0.0     0.0      0.0  0.0      0.0      1.0\n",
       "1       0.0     0.0      0.0  0.0      0.1      0.9\n",
       "2       0.0     0.0      0.0  0.0      0.2      0.8\n",
       "3       0.0     0.0      0.0  0.0      0.3      0.7\n",
       "4       0.0     0.0      0.0  0.0      0.4      0.6\n",
       "...     ...     ...      ...  ...      ...      ...\n",
       "2998    0.9     0.0      0.0  0.0      0.1      0.0\n",
       "2999    0.9     0.0      0.0  0.1      0.0      0.0\n",
       "3000    0.9     0.0      0.1  0.0      0.0      0.0\n",
       "3001    0.9     0.1      0.0  0.0      0.0      0.0\n",
       "3002    1.0     0.0      0.0  0.0      0.0      0.0\n",
       "\n",
       "[3003 rows x 6 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from baybe.searchspace import SubspaceDiscrete\n",
    "\n",
    "discrete_space2 = SubspaceDiscrete.from_simplex(1.0, # Overall sum we intend\n",
    "                                                parameters, # Our numerical parameters\n",
    "                                                product_parameters = None, # We have no other parameters\n",
    "                                                constraints = None, # We have no other constraints\n",
    "                                                boundary_only = True) # We only want entries on the bpundary of 1.0, not below\n",
    "searchspace2 = SearchSpace(discrete = discrete_space2)\n",
    "searchspace2.discrete.exp_rep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6d5f2007-2675-48f7-a843-e19f2d96ab4b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check that all rows sum to 1.0 (within a small tolerance)\n",
    "(searchspace2.discrete\n",
    "             .exp_rep\n",
    "             .sum(axis = 1)\n",
    "             .apply(lambda x: x-1.0)\n",
    "             .abs()\n",
    "             .lt(0.001)\n",
    "             .all())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62ca06d1-5048-4a05-84b9-84807f08e9f3",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Slot-Based Search Space"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4ce0eda-0f27-4d26-a3ac-34fb1b7dfaa4",
   "metadata": {},
   "source": [
    "Instead of one parameter per allowed substance, we will create slots. Each slot is represented by two parameters, one for the label of the substance that is in the slot, and another one for the concentration associated with that slot.\n",
    "\n",
    "To do this we must choose the maximum number of slots. This means we model a mixture that allows \"up to `N_SLOTS` substances\" being part of it. This comes with two distinct advantages:\n",
    "- We can use BayBE's label encoding to inform the model about the chemical properties of the substances in the slot\n",
    "- Since without additional constraints, slots are numered and thus imply an order, this automatically models the order of addition, too"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "0da19bed-188f-4bb8-ba39-82abf694c6ad",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from baybe.parameters import SubstanceParameter\n",
    "\n",
    "N_SLOTS = 3\n",
    "\n",
    "# Parameters fore the slot labels\n",
    "slots = [\n",
    "    SubstanceParameter(name = f'Slot_{k+1}', data = dict_solvents)\n",
    "    for k in range(N_SLOTS)\n",
    "]\n",
    "\n",
    "# Parameters for the slot concentrations\n",
    "slot_amounts = [\n",
    "    NumericalDiscreteParameter(name = f'Slot_{k+1}_Amount', values = setpoints)\n",
    "    for k in range(N_SLOTS)\n",
    "]\n",
    "\n",
    "# We also need a sum constraint for the overal sum\n",
    "sum_constraint = DiscreteSumConstraint(\n",
    "    parameters = [p.name for p in slot_amounts],\n",
    "    condition = ThresholdCondition(\n",
    "        threshold = 1.0,\n",
    "        operator = '='\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b494b6c1-e8e9-4998-9d47-91c31a082b11",
   "metadata": {},
   "source": [
    "## Naive Result\n",
    "Without further consideration we get a search space that has several issues that need to be fixed, some of them not so obvious. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "bde717d4-c19e-486d-979d-0d0a608ecc7e",
   "metadata": {
    "tags": []
   },
   "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>Slot_1</th>\n",
       "      <th>Slot_2</th>\n",
       "      <th>Slot_3</th>\n",
       "      <th>Slot_1_Amount</th>\n",
       "      <th>Slot_2_Amount</th>\n",
       "      <th>Slot_3_Amount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Water</td>\n",
       "      <td>Water</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Water</td>\n",
       "      <td>Water</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Water</td>\n",
       "      <td>Water</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Water</td>\n",
       "      <td>Water</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Water</td>\n",
       "      <td>Water</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14251</th>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14252</th>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14253</th>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14254</th>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14255</th>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>14256 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        Slot_1   Slot_2   Slot_3  Slot_1_Amount  Slot_2_Amount  Slot_3_Amount\n",
       "0        Water    Water    Water            0.0            0.0            1.0\n",
       "1        Water    Water    Water            0.0            0.1            0.9\n",
       "2        Water    Water    Water            0.0            0.2            0.8\n",
       "3        Water    Water    Water            0.0            0.3            0.7\n",
       "4        Water    Water    Water            0.0            0.4            0.6\n",
       "...        ...      ...      ...            ...            ...            ...\n",
       "14251  Ethanol  Ethanol  Ethanol            0.8            0.1            0.1\n",
       "14252  Ethanol  Ethanol  Ethanol            0.8            0.2            0.0\n",
       "14253  Ethanol  Ethanol  Ethanol            0.9            0.0            0.1\n",
       "14254  Ethanol  Ethanol  Ethanol            0.9            0.1            0.0\n",
       "14255  Ethanol  Ethanol  Ethanol            1.0            0.0            0.0\n",
       "\n",
       "[14256 rows x 6 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "searchspace3a = SearchSpace.from_product(\n",
    "    parameters = slots + slot_amounts,\n",
    "    constraints = [sum_constraint]\n",
    ")\n",
    "\n",
    "searchspace3a.discrete.exp_rep"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b82dd6be-ef5f-4be4-9545-c390cb9965d0",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Avoid Duplicate Slots - `DiscreteNoLabelDuplicatesConstraint`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "7b71d63c-6d8e-4eb2-872b-1f9790bd24f9",
   "metadata": {
    "tags": []
   },
   "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>Slot_1</th>\n",
       "      <th>Slot_2</th>\n",
       "      <th>Slot_3</th>\n",
       "      <th>Slot_1_Amount</th>\n",
       "      <th>Slot_2_Amount</th>\n",
       "      <th>Slot_3_Amount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Toluene</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Toluene</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Toluene</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Toluene</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Toluene</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7915</th>\n",
       "      <td>DMF</td>\n",
       "      <td>Dioxane</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7916</th>\n",
       "      <td>DMF</td>\n",
       "      <td>Dioxane</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7917</th>\n",
       "      <td>DMF</td>\n",
       "      <td>Dioxane</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7918</th>\n",
       "      <td>DMF</td>\n",
       "      <td>Dioxane</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7919</th>\n",
       "      <td>DMF</td>\n",
       "      <td>Dioxane</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>7920 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       Slot_1   Slot_2   Slot_3  Slot_1_Amount  Slot_2_Amount  Slot_3_Amount\n",
       "0     Toluene   Hexane    Water            0.0            0.0            1.0\n",
       "1     Toluene   Hexane    Water            0.0            0.1            0.9\n",
       "2     Toluene   Hexane    Water            0.0            0.2            0.8\n",
       "3     Toluene   Hexane    Water            0.0            0.3            0.7\n",
       "4     Toluene   Hexane    Water            0.0            0.4            0.6\n",
       "...       ...      ...      ...            ...            ...            ...\n",
       "7915      DMF  Dioxane  Ethanol            0.8            0.1            0.1\n",
       "7916      DMF  Dioxane  Ethanol            0.8            0.2            0.0\n",
       "7917      DMF  Dioxane  Ethanol            0.9            0.0            0.1\n",
       "7918      DMF  Dioxane  Ethanol            0.9            0.1            0.0\n",
       "7919      DMF  Dioxane  Ethanol            1.0            0.0            0.0\n",
       "\n",
       "[7920 rows x 6 columns]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from baybe.constraints import DiscreteNoLabelDuplicatesConstraint\n",
    "\n",
    "no_label_duplicate_constraint = DiscreteNoLabelDuplicatesConstraint(\n",
    "    parameters = [p.name for p in slots]\n",
    ")\n",
    "\n",
    "searchspace3b = SearchSpace.from_product(\n",
    "    parameters = slots + slot_amounts,\n",
    "    constraints = [sum_constraint,\n",
    "                   no_label_duplicate_constraint])\n",
    "\n",
    "searchspace3b.discrete.exp_rep"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6668ff6a-451a-441d-b30b-a4fad8e2c6e3",
   "metadata": {},
   "source": [
    "## Avoid Degenerate Points Caused by a Dependency - `DiscreteDependenciesConstraint`\n",
    "\n",
    "By \"dependency\" we mean a situation where the values of a parameter only matter if another parameter has a certain value.\n",
    "\n",
    "This is, for instance, the case in our slot-based mixture approach, because the slot label does not matter if the slot amount is 0.\n",
    "\n",
    "Another example for this is a switch that turns on certain parts of the equipment which have their own settings. However, these settings only matter if the switch is actually 'on'. If not, these settings can take any value without affecting the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "ad5c5d02-c7f7-4751-82b2-2fb423fcb2ef",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def show_degenerate_points(df, point):\n",
    "    \"\"\"Returns degenerate equivalents of `point` that are found in `df`.\n",
    "    \n",
    "    This assumes that 0.0 is the degeneracy-causing value on the amounts.\n",
    "    \"\"\"\n",
    "    \n",
    "    idxs = []\n",
    "    for ind, row in df.iterrows():\n",
    "        mask = (row['Slot_1_Amount'] == 0.0) or (row['Slot_1'] == point['Slot_1'].values[0])\n",
    "        mask &= (row['Slot_2_Amount'] == 0.0) or (row['Slot_2'] == point['Slot_2'].values[0])\n",
    "        mask &= (row['Slot_3_Amount'] == 0.0) or (row['Slot_3'] == point['Slot_3'].values[0])\n",
    "        mask &= row['Slot_1_Amount'] == point['Slot_1_Amount'].values[0]\n",
    "        mask &= row['Slot_2_Amount'] == point['Slot_2_Amount'].values[0]\n",
    "        mask &= row['Slot_3_Amount'] == point['Slot_3_Amount'].values[0]\n",
    "        if mask:\n",
    "            idxs.append(ind)\n",
    "\n",
    "    return df.loc[idxs]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11206689-701d-4727-8c96-fe0d703a246b",
   "metadata": {},
   "source": [
    "Lets take a look at the degenerate equivalents of the first search space entry. (if you pick en entry that has no 0.0 in the amounts, no degenerate points are expected)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "1685348c-8d6a-4e8b-a273-fc8c6f6fc8e7",
   "metadata": {
    "tags": []
   },
   "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>Slot_1</th>\n",
       "      <th>Slot_2</th>\n",
       "      <th>Slot_3</th>\n",
       "      <th>Slot_1_Amount</th>\n",
       "      <th>Slot_2_Amount</th>\n",
       "      <th>Slot_3_Amount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Toluene</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>DMF</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>133</th>\n",
       "      <td>Dioxane</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Slot_1  Slot_2 Slot_3  Slot_1_Amount  Slot_2_Amount  Slot_3_Amount\n",
       "1    Toluene  Hexane  Water            0.0            0.1            0.9\n",
       "67       DMF  Hexane  Water            0.0            0.1            0.9\n",
       "133  Dioxane  Hexane  Water            0.0            0.1            0.9\n",
       "199  Ethanol  Hexane  Water            0.0            0.1            0.9"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_degenerate_points(df = searchspace3b.discrete.exp_rep,\n",
    "                       point = searchspace3b.discrete.exp_rep.iloc[[1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "bf2bf2e1-7e76-45d2-8796-82cea140194e",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from baybe.constraints import DiscreteDependenciesConstraint\n",
    "\n",
    "dependency_constraint = DiscreteDependenciesConstraint(\n",
    "    parameters = [\"Slot_1_Amount\",\n",
    "                  \"Slot_2_Amount\",\n",
    "                  \"Slot_3_Amount\"],\n",
    "    affected_parameters = [[\"Slot_1\"], # depends on Slot_1_Amount being > 0.0\n",
    "                           [\"Slot_2\"], # depends on Slot_2_Amount being > 0.0\n",
    "                           [\"Slot_3\"]],# depends on Slot_3_Amount being > 0.0\n",
    "    conditions = [\n",
    "        ThresholdCondition(threshold = 0.0, operator = \">\"), # the affected parameters are only relevant is this condition is True\n",
    "        ThresholdCondition(threshold = 0.0, operator = \">\"),\n",
    "        ThresholdCondition(threshold = 0.0, operator = \">\"),\n",
    "    ],\n",
    ")\n",
    "\n",
    "searchspace3c = SearchSpace.from_product(parameters = slots + slot_amounts,\n",
    "                                         constraints = [sum_constraint,\n",
    "                                                        no_label_duplicate_constraint,\n",
    "                                                        dependency_constraint])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "962c37e3-7d20-48b0-86ba-4cd5cbaf91be",
   "metadata": {},
   "source": [
    "Lets check again whether there are any degenerate points left after including the constraint. There should be none."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "4091f7d3-43c6-4fbe-9572-238f4d249e28",
   "metadata": {
    "tags": []
   },
   "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>Slot_1</th>\n",
       "      <th>Slot_2</th>\n",
       "      <th>Slot_3</th>\n",
       "      <th>Slot_1_Amount</th>\n",
       "      <th>Slot_2_Amount</th>\n",
       "      <th>Slot_3_Amount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Toluene</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Slot_1  Slot_2 Slot_3  Slot_1_Amount  Slot_2_Amount  Slot_3_Amount\n",
       "1  Toluene  Hexane  Water            0.0            0.1            0.9"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_degenerate_points(df = searchspace3c.discrete.exp_rep, \n",
    "                       point = searchspace3c.discrete.exp_rep.iloc[[1]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a61d5fa8-7af6-4991-9181-c0952d3c2a16",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Avoid Permutation Duplicates - `DiscretePermutationInvarianceConstraint`\n",
    "\n",
    "Since the slots are numbered you can see that as natural order of addition. In that case there is no permutation invariance. But if the order does not matter we need to remove permutation invariant search space entries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "8ad33bbf-f10a-4d66-a80d-7a46b34f77fd",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from itertools import permutations\n",
    "\n",
    "def show_permutation_equivalent_points(df, point):\n",
    "    \"\"\"Returns permutation equivalents of `point` that are found in `df`.\"\"\"\n",
    "    \n",
    "    slot_cols = ['Slot_1','Slot_2','Slot_3']\n",
    "    amount_cols = ['Slot_1_Amount','Slot_2_Amount','Slot_3_Amount']\n",
    "    \n",
    "    idxs = []\n",
    "    for perm in permutations([0,1,2]):\n",
    "        slots_permuted = [slot_cols[k] for k in perm]\n",
    "        amount_permuted = [amount_cols[k] for k in perm]\n",
    "        mask = (df[slot_cols].values == point[slots_permuted].values).all(axis=1)\n",
    "        mask &= (df[amount_cols].values == point[amount_permuted].values).all(axis=1)\n",
    "        idxs += df.index[mask].to_list()\n",
    "    \n",
    "    return df.loc[idxs]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1c7189d-db32-4f45-9aa4-9c088c3a3164",
   "metadata": {
    "tags": []
   },
   "source": [
    "Lets check out the permutaiton-equivalent points of a random entry."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "917e0ace-3569-4a6b-95e5-338d6d2bff78",
   "metadata": {
    "tags": []
   },
   "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>Slot_1</th>\n",
       "      <th>Slot_2</th>\n",
       "      <th>Slot_3</th>\n",
       "      <th>Slot_1_Amount</th>\n",
       "      <th>Slot_2_Amount</th>\n",
       "      <th>Slot_3_Amount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3712</th>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Water</td>\n",
       "      <td>Dioxane</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>805</th>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Dioxane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4207</th>\n",
       "      <td>Water</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Dioxane</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5012</th>\n",
       "      <td>Water</td>\n",
       "      <td>Dioxane</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>962</th>\n",
       "      <td>Dioxane</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4484</th>\n",
       "      <td>Dioxane</td>\n",
       "      <td>Water</td>\n",
       "      <td>Ethanol</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Slot_1   Slot_2   Slot_3  Slot_1_Amount  Slot_2_Amount  Slot_3_Amount\n",
       "3712  Ethanol    Water  Dioxane            0.7            0.2            0.1\n",
       "805   Ethanol  Dioxane    Water            0.7            0.1            0.2\n",
       "4207    Water  Ethanol  Dioxane            0.2            0.7            0.1\n",
       "5012    Water  Dioxane  Ethanol            0.2            0.1            0.7\n",
       "962   Dioxane  Ethanol    Water            0.1            0.7            0.2\n",
       "4484  Dioxane    Water  Ethanol            0.1            0.2            0.7"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_permutation_equivalent_points(df = searchspace3c.discrete.exp_rep,\n",
    "                                   point = searchspace3c.discrete.exp_rep.sample(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdab3868-68e6-4c6d-8dea-0c12f615c2c4",
   "metadata": {},
   "source": [
    "All of these points are equivalent. \n",
    "All except 1 must be removed from the searchspace.\n",
    "This is what `DiscretePermutationInvarianceConstraint` does."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "52162b71-79a9-44f0-8751-d57df0051481",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from baybe.constraints import DiscretePermutationInvarianceConstraint\n",
    "\n",
    "perm_inv_constraint = DiscretePermutationInvarianceConstraint(\n",
    "    parameters = [p.name for p in slots],\n",
    "    dependencies = dependency_constraint\n",
    ")\n",
    "\n",
    "searchspace3d = SearchSpace.from_product(parameters = slots + slot_amounts,\n",
    "                                         constraints = [sum_constraint,\n",
    "                                                        no_label_duplicate_constraint,\n",
    "                                                        perm_inv_constraint])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "102cf4d4-939b-495c-9284-7af35da4ab48",
   "metadata": {
    "tags": []
   },
   "source": [
    "Lets re-check whether there are any permutaiton-invariant entries left."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "8b6af99a-bae4-423a-8a32-0e92450480b3",
   "metadata": {
    "tags": []
   },
   "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>Slot_1</th>\n",
       "      <th>Slot_2</th>\n",
       "      <th>Slot_3</th>\n",
       "      <th>Slot_1_Amount</th>\n",
       "      <th>Slot_2_Amount</th>\n",
       "      <th>Slot_3_Amount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>Toluene</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Slot_1  Slot_2 Slot_3  Slot_1_Amount  Slot_2_Amount  Slot_3_Amount\n",
       "30  Toluene  Hexane  Water            0.3            0.0            0.7"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_permutation_equivalent_points(df = searchspace3d.discrete.exp_rep,\n",
    "                                   point = searchspace3d.discrete.exp_rep.sample(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0a758a5-ecb1-4cdf-ac4c-f6726c215a6c",
   "metadata": {
    "tags": []
   },
   "source": [
    "## A Look at the Final Search Space\n",
    "\n",
    "It is much smaller than the original one that did not consider the various invariances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "ea57ed4b-899a-4df8-a7a5-b730b964b517",
   "metadata": {
    "tags": []
   },
   "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>Slot_1</th>\n",
       "      <th>Slot_2</th>\n",
       "      <th>Slot_3</th>\n",
       "      <th>Slot_1_Amount</th>\n",
       "      <th>Slot_2_Amount</th>\n",
       "      <th>Slot_3_Amount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Toluene</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Toluene</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Toluene</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Toluene</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Toluene</td>\n",
       "      <td>Hexane</td>\n",
       "      <td>Water</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>856</th>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Dioxane</td>\n",
       "      <td>DMF</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>857</th>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Dioxane</td>\n",
       "      <td>DMF</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>858</th>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Dioxane</td>\n",
       "      <td>DMF</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>859</th>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Dioxane</td>\n",
       "      <td>DMF</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>860</th>\n",
       "      <td>Ethanol</td>\n",
       "      <td>Dioxane</td>\n",
       "      <td>DMF</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>861 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Slot_1   Slot_2 Slot_3  Slot_1_Amount  Slot_2_Amount  Slot_3_Amount\n",
       "0    Toluene   Hexane  Water            0.0            0.0            1.0\n",
       "1    Toluene   Hexane  Water            0.0            0.1            0.9\n",
       "2    Toluene   Hexane  Water            0.0            0.2            0.8\n",
       "3    Toluene   Hexane  Water            0.0            0.3            0.7\n",
       "4    Toluene   Hexane  Water            0.0            0.4            0.6\n",
       "..       ...      ...    ...            ...            ...            ...\n",
       "856  Ethanol  Dioxane    DMF            0.6            0.2            0.2\n",
       "857  Ethanol  Dioxane    DMF            0.6            0.3            0.1\n",
       "858  Ethanol  Dioxane    DMF            0.7            0.1            0.2\n",
       "859  Ethanol  Dioxane    DMF            0.7            0.2            0.1\n",
       "860  Ethanol  Dioxane    DMF            0.8            0.1            0.1\n",
       "\n",
       "[861 rows x 6 columns]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "searchspace3d.discrete.exp_rep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "717b9f4c-119c-4813-a87a-ff58a5126c9d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "d4e648b7-4b74-4e80-bf6c-710dc465e63d",
   "metadata": {
    "tags": []
   },
   "source": [
    "# In Progress: Bringing it All Togehter"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0a05645-f39e-4e98-b214-61091441d9cb",
   "metadata": {},
   "source": [
    "To model slot-based mixtures we will soon provide a custom constructor. This will take care of creation the necessary constraints automatically\n",
    "```python\n",
    "discrete_subspace = SubspaceDiscrete.from_slot_based_mixture(\n",
    "    slots, # parameters that can be arbitrarily encoded\n",
    "    setpoints,\n",
    "    permutation_invariant = True # when order of addition does not matter\n",
    ")\n",
    "```\n",
    "\n",
    "(not yet executable)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "BayBE-dev",
   "language": "python",
   "name": "baybe-dev"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}