{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Circuit models 101\n",
    "\n",
    "In this notebook, we will explore the basics of circuit models in AutoEIS. We will start by importing the necessary libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-06T14:44:55.527926Z",
     "iopub.status.busy": "2024-06-06T14:44:55.527292Z",
     "iopub.status.idle": "2024-06-06T14:44:59.815071Z",
     "shell.execute_reply": "2024-06-06T14:44:59.814561Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import autoeis as ae\n",
    "ae.visualization.set_plot_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Circuit representation\n",
    "\n",
    "In AutoEIS, circuits are represented as strings. Please refer to [circuit notation](../circuit.md) for the syntax of the circuit string. Now, let's create a sample circuit string:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-06T14:44:59.818272Z",
     "iopub.status.busy": "2024-06-06T14:44:59.818075Z",
     "iopub.status.idle": "2024-06-06T14:44:59.826120Z",
     "shell.execute_reply": "2024-06-06T14:44:59.825771Z"
    }
   },
   "outputs": [],
   "source": [
    "circuit = \"R1-[P2,R3]-C4-[[R5,C6],[L7,R8]]-R2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the circuit model using the `draw_circuit` function, which requires the `lcapy` package to be installed, and a working LaTeX installation. See [here](https://lcapy.readthedocs.io/en/latest/install.html) for more details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-06T14:44:59.828192Z",
     "iopub.status.busy": "2024-06-06T14:44:59.828089Z",
     "iopub.status.idle": "2024-06-06T14:45:01.978652Z",
     "shell.execute_reply": "2024-06-06T14:45:01.977827Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Suggestion: add a constraint between nodes (25, 27) and (28, 26) for vertical graph\n"
     ]
    },
    {
     "data": {
      "image/png": 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     },
     "metadata": {
      "image/png": {
       "height": 688,
       "width": 1787
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = ae.visualization.draw_circuit(circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Querying circuit strings\n",
    "\n",
    "Once you have the circuit string, you can run different queries on it. We're not going to explore all of available queries here, but we'll show you a few of the most common ones. To see the full list of available queries, check out the [API reference](../modules.rst).\n",
    "\n",
    "To get the list of components in the circuit, you can use the `get_component_labels` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-06T14:45:01.981944Z",
     "iopub.status.busy": "2024-06-06T14:45:01.981264Z",
     "iopub.status.idle": "2024-06-06T14:45:01.985385Z",
     "shell.execute_reply": "2024-06-06T14:45:01.984889Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['R1', 'P2', 'R3', 'C4', 'R5', 'C6', 'L7', 'R8', 'R2']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ae.parser.get_component_labels(circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(The impedance of) Each component is represented by one or more parameters. To get the list of parameters that fully describe the circuit, use the `get_parameter_labels` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-06T14:45:01.987898Z",
     "iopub.status.busy": "2024-06-06T14:45:01.987790Z",
     "iopub.status.idle": "2024-06-06T14:45:01.990889Z",
     "shell.execute_reply": "2024-06-06T14:45:01.990377Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['R1', 'P2w', 'P2n', 'R3', 'C4', 'R5', 'C6', 'L7', 'R8', 'R2']"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ae.parser.get_parameter_labels(circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that components and parameters are not the same, despite the fact that for single-parameter components they're represented by the same string. For instance, `R1` is both a parameter and a component, but `P2` is a component, which is described by the parameters `P2w` and `P2n`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also validate the circuit using the `validate_circuit` function in case you're not sure if the circuit is valid:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-06T14:45:01.993066Z",
     "iopub.status.busy": "2024-06-06T14:45:01.992942Z",
     "iopub.status.idle": "2024-06-06T14:45:02.001546Z",
     "shell.execute_reply": "2024-06-06T14:45:02.001179Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ae.parser.validate_circuit(circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try to validate an invalid circuit string:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-06T14:45:02.003388Z",
     "iopub.status.busy": "2024-06-06T14:45:02.003294Z",
     "iopub.status.idle": "2024-06-06T14:45:02.212646Z",
     "shell.execute_reply": "2024-06-06T14:45:02.212263Z"
    },
    "tags": [
     "raises-exception"
    ]
   },
   "outputs": [
    {
     "ename": "AssertionError",
     "evalue": "Duplicate elements found: {'R1'}",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[7], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mae\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mparser\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mvalidate_circuit\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mR1-[R2,P3]-R1\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/work/AutoEIS/AutoEIS/src/autoeis/parser.py:56\u001b[0m, in \u001b[0;36mvalidate_circuit\u001b[0;34m(circuit)\u001b[0m\n\u001b[1;32m     54\u001b[0m components \u001b[38;5;241m=\u001b[39m get_component_labels(circuit)\n\u001b[1;32m     55\u001b[0m duplicates \u001b[38;5;241m=\u001b[39m [e \u001b[38;5;28;01mfor\u001b[39;00m e \u001b[38;5;129;01min\u001b[39;00m components \u001b[38;5;28;01mif\u001b[39;00m components\u001b[38;5;241m.\u001b[39mcount(e) \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m1\u001b[39m]\n\u001b[0;32m---> 56\u001b[0m \u001b[38;5;28;01massert\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m duplicates, \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mDuplicate elements found: \u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mset\u001b[39m(duplicates)\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     57\u001b[0m \u001b[38;5;66;03m# Test circuit is not empty\u001b[39;00m\n\u001b[1;32m     58\u001b[0m \u001b[38;5;28;01massert\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(circuit) \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m0\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mCircuit string is empty.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n",
      "\u001b[0;31mAssertionError\u001b[0m: Duplicate elements found: {'R1'}"
     ]
    }
   ],
   "source": [
    "ae.parser.validate_circuit(\"R1-[R2,P3]-R1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another useful query is to compare two circuits to see if they are structurally equivalent. For instance, one would expect that `R1-R2` and `R2-R1` and `R5-R0` are equivalent, i.e., neither the order of appearance of the components nor the labels matter. This is useful for filtering out duplicate circuits, which may (and will) arise during circuit generation using evolutionary algorithms. You can do this using the `are_circuits_equivalent` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-06T14:45:02.214901Z",
     "iopub.status.busy": "2024-06-06T14:45:02.214750Z",
     "iopub.status.idle": "2024-06-06T14:45:02.221751Z",
     "shell.execute_reply": "2024-06-06T14:45:02.221357Z"
    }
   },
   "outputs": [],
   "source": [
    "circuit1 = \"R1-[P2,R3]-C4\"\n",
    "circuit2 = \"C4-R1-[R3,P2]\"\n",
    "circuit3 = \"C0-R5-[R9,P0]\"\n",
    "\n",
    "assert ae.utils.are_circuits_equivalent(circuit1, circuit2)\n",
    "assert ae.utils.are_circuits_equivalent(circuit1, circuit3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluating circuit strings\n",
    "\n",
    "Once you have a valid circuit string, you can calculate the EIS spectra of the circuit model by evaluating it at the frequency range of interest. To do this, you need to convert the circuit string to a function using the `generate_circuit_fn` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-06T14:45:02.223601Z",
     "iopub.status.busy": "2024-06-06T14:45:02.223505Z",
     "iopub.status.idle": "2024-06-06T14:45:02.225503Z",
     "shell.execute_reply": "2024-06-06T14:45:02.225152Z"
    }
   },
   "outputs": [],
   "source": [
    "circuit_fn = ae.utils.generate_circuit_fn(circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's calculate the EIS spectra for a few frequencies. For this, we also need to pass the parameters of the circuit model, for which we can use random values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-06T14:45:02.227375Z",
     "iopub.status.busy": "2024-06-06T14:45:02.227288Z",
     "iopub.status.idle": "2024-06-06T14:45:02.237558Z",
     "shell.execute_reply": "2024-06-06T14:45:02.237199Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.21883079-2.24443252e+02j, 1.2175161 -4.83386010e+01j,\n",
       "       1.2507572 -1.03434596e+01j, 1.38312962-2.19648084e+00j,\n",
       "       1.37171398-5.63043052e-01j, 1.19447804-2.53134306e-01j,\n",
       "       1.07605597-9.78569732e-02j, 1.03376487-4.21266919e-02j,\n",
       "       1.01152567-2.01285355e-02j, 1.0002327 -9.77043145e-03j])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freq = np.logspace(-3, 3, 10)\n",
    "num_params = ae.parser.count_parameters(circuit)\n",
    "p = np.random.rand(num_params)\n",
    "Z = circuit_fn(freq, p)\n",
    "Z"
   ]
  }
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