### Clone and Setup pyimpspec Development Environment

Source: https://github.com/vyrjana/pyimpspec/blob/main/README.md

Commands to clone the repository from GitHub and install the necessary development dependencies using pip. This is the standard procedure for setting up a local development environment for the project.

```bash
git clone https://github.com/vyrjana/pyimpspec.git
pip install -r ./dev-requirements.txt
```

--------------------------------

### Install Optional Dependencies with pip (Bash)

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_installing.md

Installs optional dependencies, such as 'cvxopt', for pyimpspec using pip. This is typically done by specifying extras in the install command.

```bash
pip install pyimpspec[cvxopt]
```

--------------------------------

### Check pip Installation (Bash)

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_installing.md

Verifies if pip is installed on the system. This is a prerequisite for installing Python packages.

```bash
pip --version
```

--------------------------------

### Install pyimpspec using pipx (Bash)

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_installing.md

Installs pyimpspec and its dependencies using pipx, which automatically manages virtual environments.

```bash
pipx install pyimpspec
```

--------------------------------

### Install Optional Dependencies with pipx (Bash)

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_installing.md

Installs optional dependencies, such as 'cvxopt', into an existing pyimpspec installation managed by pipx.

```bash
pipx inject pyimpspec cvxopt
```

--------------------------------

### Install pyimpspec using pip (Bash)

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_installing.md

Installs pyimpspec and its dependencies using pip. This method requires manual management of Python virtual environments.

```bash
pip install pyimpspec
```

--------------------------------

### Performing a Kramers-Kronig Test

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_kramers_kronig.md

This example demonstrates how to perform a full Kramers-Kronig test on a dataset. It shows both the high-level wrapper function and the manual step-by-step workflow involving evaluation, RC suggestion, and representation selection.

```python
from pyimpspec import (
  DataSet,
  KramersKronigResult,
  generate_mock_data,
  perform_kramers_kronig_test,
)
from pyimpspec.analysis.kramers_kronig import (
  evaluate_log_F_ext,
  suggest_num_RC,
  suggest_representation,
)
from typing import Dict, List, Tuple

data: DataSet = generate_mock_data("CIRCUIT_1", noise=5e-2, seed=42)[0]

# High-level test execution
test: KramersKronigResult = perform_kramers_kronig_test(data)

# Manual workflow equivalent
Z_evaluations = evaluate_log_F_ext(data, admittance=False)
Z_suggested_F_ext, Z_tests, Z_minimized_statistic = Z_evaluations[0]
Z_suggestion = suggest_num_RC(Z_tests)

Y_evaluations = evaluate_log_F_ext(data, admittance=True)
Y_tests = Y_evaluations[0][1]
Y_suggestion = suggest_num_RC(Y_tests)

suggestion = suggest_representation([Z_suggestion, Y_suggestion])
test, scores, lower_limit, upper_limit = suggestion
```

--------------------------------

### Import pyimpspec in Python

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_installing.md

Demonstrates how to import the pyimpspec library in a Python script or interactive session after installation and activation of the virtual environment.

```python
import pyimpspec
```

--------------------------------

### Check pipx Installation (Bash)

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_installing.md

Verifies if pipx is installed. pipx is a tool for managing Python applications in isolated environments.

```bash
pipx --version
```

--------------------------------

### Perform DRT Analysis using pyimpspec

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_drt.md

Demonstrates how to generate mock impedance data and perform DRT analysis using either specific method functions (e.g., TR-NNLS) or the general wrapper function. The example shows the import of necessary classes and functions, data generation, and the execution of the analysis.

```python
from pyimpspec import (
  DataSet,
  DRTResult,
  calculate_drt,
  generate_mock_data,
)
from pyimpspec.analysis.drt import (
  BHTResult,
  LMResult,
  MRQFitResult,
  TRNNLSResult,
  TRRBFResult,
  calculate_drt_bht,
  calculate_drt_lm,
  calculate_drt_mrq_fit,
  calculate_drt_tr_nnls,
  calculate_drt_tr_rbf,
)

data: DataSet = generate_mock_data("CIRCUIT_1", noise=5e-2, seed=42)[0]
drt: TRNNLSResult = calculate_drt_tr_nnls(data, lambda_value=1e-4)
drt: DRTResult = calculate_drt(data, method="tr-nnls", lambda_value=1e-4)
assert isinstance(drt, TRNNLSResult)
```

--------------------------------

### GPL Interactive Mode Notice

Source: https://github.com/vyrjana/pyimpspec/blob/main/LICENSES/LICENSE-cvxopt.txt

This snippet displays the standard copyright and licensing notice that appears when a program licensed under the GNU GPL starts in interactive mode. It informs users about the program's origin, warranty, and redistribution conditions.

```text
<program>  Copyright (C) <year>  <name of author>
This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
under certain conditions; type `show c' for details.
```

--------------------------------

### Define Circuit Elements in pyimpspec

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs_circuit.md

Examples of how to instantiate common circuit elements within the pyimpspec framework. These classes represent physical components used to build impedance models.

```python
from pyimpspec.circuit.elements import Resistor, Inductor, Gerischer, HavriliakNegami

# Instantiate a standard resistor
r = Resistor(R=1000)

# Instantiate an ideal inductor
l = Inductor(L=1e-6)

# Instantiate a Gerischer element
g = Gerischer(Y=1, k=1)

# Instantiate a Havriliak-Negami element
hn = HavriliakNegami(dC=1e-6, tau=1, a=0.9, b=0.9)
```

--------------------------------

### Process EIS Data using Pyimpspec Command-Line Interface (Bash)

Source: https://context7.com/vyrjana/pyimpspec/llms.txt

Demonstrates various command-line operations provided by Pyimpspec for parsing, plotting, testing, fitting, and analyzing EIS data. These commands allow users to perform common EIS tasks directly from the terminal without writing Python scripts. Examples include parsing data files, generating Bode plots, performing Kramers-Kronig tests, fitting equivalent circuits, and calculating DRT.

```Bash
# Parse data file and output as CSV
pyimpspec parse "data.dta" \
  --output-to \
  --output-format csv \
  --output-dir "./output"

# Plot impedance data as Bode plot
pyimpspec plot "data.dta" \
  --type bode \
  --output-to \
  --plot-format svg

# Perform Kramers-Kronig test
pyimpspec test "data.dta" \
  --no-capacitance \
  --mu-criterion 0.7

# Fit circuit to data
pyimpspec fit "data.dta" \
  --circuit "R(RC)(RW)"

# Calculate DRT
pyimpspec drt "data.dta" \
  --method tr-nnls \
  --lambda 1e-4

# Perform Z-HIT analysis
pyimpspec zhit "data.dta"

# Use mock data with wildcards
pyimpspec zhit "<CIRCUIT_* >"

# Mock data with custom parameters
pyimpspec zhit "<CIRCUIT_1:noise=5e-2,num_per_decade=9,seed=42>"

# Generate/view configuration file
pyimpspec config -h
```

--------------------------------

### Access Configuration Help

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_cli.md

Displays the help menu for the configuration subcommand to manage default arguments.

```bash
pyimpspec config -h
```

--------------------------------

### Use Circuit Placeholders and Wildcards

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_cli.md

Shows how to use built-in circuit placeholders and wildcards to process multiple immittance spectra.

```bash
pyimpspec zhit "<CIRCUIT_*>"
pyimpspec zhit "<CIRCUIT_*:noise=5e-2,num_per_decade=9,seed=42,drift=1.1,log_min_f=-1.0,log_max_f=4.0>"
```

--------------------------------

### Initialize pyimpspec library

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs.md

Demonstrates how to import the main pyimpspec module and the matplotlib-based plotting sub-module for impedance spectroscopy tasks.

```python
import pyimpspec
from pyimpspec import mpl
```

--------------------------------

### Registering a Custom Circuit Element

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_circuit.md

Demonstrates how to define a new circuit element by subclassing Element, implementing the _impedance method, and registering it with metadata including parameters and equations.

```python
from pyimpspec import (
    ComplexImpedances,
    Frequencies,
    Circuit,
    Element,
    ElementDefinition,
    ParameterDefinition,
    register_element,
    parse_cdc,
)
from numpy import pi, inf

class SomeNewElement(Element):
    def _impedance(self, f: Frequencies, X: float, a: float) -> ComplexImpedances:
        return 1 / (X * (1j * 2 * pi * f)**a)

register_element(
    ElementDefinition(
        Class=SomeNewElement,
        symbol="Ude",
        name="Some new element",
        description="User-defined element of some type.",
        equation="1/(X*(2*pi*f*I)^a)",
        parameters=[
            ParameterDefinition(
                symbol="X",
                unit="Some unit",
                description="Description of this parameter",
                value=1e-6,
                lower_limit=1e-24,
                upper_limit=inf,
                fixed=False,
            ),
            ParameterDefinition(
                symbol="a",
                unit="",
                description="Some exponent",
                value=0.5,
                lower_limit=0.0,
                upper_limit=1.0,
                fixed=False,
            ),
        ],
    ),
)

circuit: Circuit = parse_cdc("Ude")
```

--------------------------------

### Circuit Fitting Workflow

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_fitting.md

Demonstrates the complete workflow for fitting circuit parameters using PyImpSpec, from data generation to exporting fitted parameters as a markdown table.

```APIDOC
## Circuit Fitting Workflow

### Description
This example illustrates the process of fitting an electrical circuit using the `pyimpspec` library. It covers generating mock data, defining a circuit structure, performing the fit, and visualizing the results.

### Method
This is a conceptual workflow and does not map to a single HTTP request. It involves sequential execution of Python code.

### Endpoint
N/A

### Parameters
N/A

### Request Example
```python
from schemdraw import Drawing
from pandas import DataFrame
from pyimpspec import (
  Circuit,
  DataSet,
  FitResult,
  fit_circuit,
  generate_mock_data,
)
from pyimpspec.utils import parse_cdc

# Generate mock data for a circuit
data: DataSet = generate_mock_data("CIRCUIT_1", noise=5e-2, seed=42)[0]

# Define the circuit structure
circuit: Circuit = parse_cdc("R(RC)(RW)")

# Fit the circuit to the data
fit: FitResult = fit_circuit(circuit, data)

# Get the SymPy representation of the circuit
print(fit.circuit.to_sympy())

# Generate a drawing of the fitted circuit with running counts
drawing: Drawing = fit.circuit.to_drawing(running=True)

# Export fitted parameters to a pandas DataFrame and then to markdown
df: DataFrame = fit.to_parameters_dataframe(running=True)
parameters: str = df.to_markdown(index=False)
print(parameters)
```

### Response
#### Success Response (200)
This workflow produces output to the console and potentially generates image files (e.g., circuit drawings). The primary textual output is the markdown table of fitted parameters.

#### Response Example
```
R_0 + 1/(2*I*pi*C_2*f + 1/R_1) + 1/(Y_4*(2*I*pi*f)**n_4 + 1/R_3)
| Element   | Parameter   |         Value |   Std. err. (%) | Unit      | Fixed   |
|:----------|:------------|--------------:|----------------:|:----------|:--------|
| R_0       | R           |  99.9526      |      0.0270415  | ohm       | No      |
| R_1       | R           | 200.295       |      0.0161802  | ohm       | No      |
| C_2       | C           |   7.98617e-07 |      0.00251256 | F         | No      |
| R_3       | R           | 499.93        |      0.0228977  | ohm       | No      |
| W_4       | Y           |   0.000400664 |      0.0303443  | S*s^(1/2) | No      |
```
```

--------------------------------

### Install pyimpspec in editable mode

Source: https://github.com/vyrjana/pyimpspec/blob/main/tests/README.md

Installs the current package in editable mode, allowing changes to the source code to be reflected immediately without re-installation. This is a prerequisite for running tests locally.

```bash
pip install --editable .
```

--------------------------------

### TransmissionLineModelBlockingOpen

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs_circuit.md

Initializes a blocking porous electrode transmission line model with a perfectly reflective inner boundary.

```APIDOC
## POST /circuit/elements/TransmissionLineModelBlockingOpen

### Description
Creates a model for a blocking porous electrode with a perfectly reflective inner boundary (Model b).

### Method
POST

### Endpoint
/circuit/elements/TransmissionLineModelBlockingOpen

### Parameters
#### Request Body
- **R_i** (float) - Optional - Ionic resistance
- **Y** (float) - Optional - Interfacial admittance
- **n** (float) - Optional - Phase angle
- **L** (float) - Required - Pore length

### Request Example
{
  "R_i": 1.0,
  "Y": 0.005,
  "n": 0.8,
  "L": 1.0
}

### Response
#### Success Response (200)
- **model** (string) - Tlmbo
```

--------------------------------

### GET /fitted_parameter

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs_fitting.md

Methods for interacting with individual FittedParameter objects.

```APIDOC
## GET /fitted_parameter

### Description
Accessors for individual parameter properties such as value, error, and fixed status.

### Methods
- **get_value()**: Returns the fitted value (float).
- **get_error()**: Returns the absolute standard error (float).
- **get_relative_error()**: Returns the relative standard error (float).
- **get_unit()**: Returns the parameter unit (str).
- **is_fixed()**: Returns whether the parameter was fixed (bool).
```

--------------------------------

### Perform Kramers-Kronig Tests

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_cli.md

Demonstrates running Kramers-Kronig tests on impedance spectra with specific parameters like mu-criterion.

```bash
pyimpspec test "path to some file" --no-capacitance --mu-criterion 0.7
```

--------------------------------

### GET /to_statistics_dataframe

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs_fitting.md

Retrieves the statistical summary of the circuit fit.

```APIDOC
## GET /to_statistics_dataframe

### Description
Returns a pandas DataFrame containing statistics related to the circuit fit process.

### Method
GET

### Endpoint
/to_statistics_dataframe

### Response
#### Success Response (200)
- **DataFrame** (pandas.DataFrame) - A table containing fit statistics.
```

--------------------------------

### GET /pyimpspec/elements

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs_circuit.md

Retrieve a mapping of element symbols to their corresponding classes.

```APIDOC
## GET /pyimpspec/elements

### Description
Returns a dictionary that maps element symbols to their corresponding classes.

### Method
GET

### Endpoint
pyimpspec.get_elements(default_only=False, private=False)

### Parameters
#### Query Parameters
- **default_only** (bool) - Optional - Return only default elements.
- **private** (bool) - Optional - Include private elements.

### Response
#### Success Response (200)
- **result** (Dict[str, Type[Element]]) - Mapping of symbols to element classes.
```

--------------------------------

### GET /to_peaks_dataframe

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs_drt.md

Exports peak data into a pandas DataFrame format.

```APIDOC
## GET /to_peaks_dataframe

### Description
Get the peaks as a pandas.DataFrame object.

### Method
GET

### Endpoint
/to_peaks_dataframe

### Parameters
#### Query Parameters
- **threshold** (float) - Optional - Minimum peak height threshold.
- **columns** (List[str]) - Optional - Labels for column headers.

### Response
#### Success Response (200)
- **dataframe** (pandas.DataFrame) - The resulting peak data table.
```

--------------------------------

### Fit Circuit and Generate Parameters DataFrame (Python)

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_fitting.md

This snippet demonstrates fitting a circuit to generated data using PyImpSpec. It shows how to generate mock data, parse a circuit definition, perform the fit, convert the fitted circuit to a SymPy expression, and then generate a markdown-formatted DataFrame of the fitted parameters with running counts.

```python
from schemdraw import Drawing
from pandas import DataFrame
from pyimpspec import (
  Circuit,
  DataSet,
  FitResult,
  fit_circuit,
  generate_mock_data,
)

data: DataSet = generate_mock_data("CIRCUIT_1", noise=5e-2, seed=42)[0]
circuit: Circuit = parse_cdc("R(RC)(RW)")
fit: FitResult = fit_circuit(circuit, data)

fit.circuit.to_sympy()
drawing: Drawing = fit.circuit.to_drawing(running=True)

df: DataFrame = fit.to_parameters_dataframe(running=True)
parameters: str = df.to_markdown(index=False)
```

--------------------------------

### GET /to_parameters_dataframe

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs_fitting.md

Retrieves the fitted parameters and their estimated errors as a pandas DataFrame.

```APIDOC
## GET /to_parameters_dataframe

### Description
Returns a pandas DataFrame containing fitted parameters and their corresponding estimated standard errors.

### Method
GET

### Endpoint
/to_parameters_dataframe

### Parameters
#### Query Parameters
- **running** (bool) - Optional - Whether or not to use running counts as the lower indices of elements.

### Response
#### Success Response (200)
- **DataFrame** (pandas.DataFrame) - A table containing parameter values and errors.
```

--------------------------------

### GET /generate_fit_identifiers

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs_fitting.md

Generates the mapping of circuit elements to lmfit-compatible parameter identifiers.

```APIDOC
## GET /generate_fit_identifiers

### Description
Generates identifiers for circuit elements that can be used to define constraints in the fitting process.

### Method
GET

### Endpoint
/generate_fit_identifiers

### Parameters
#### Query Parameters
- **circuit** (Circuit) - Required - The circuit object to process.

### Request Example
{
  "circuit": "R1-C1"
}

### Response
#### Success Response (200)
- **identifiers** (dict) - A dictionary mapping elements to FitIdentifiers.

#### Response Example
{
  "R1": {"R": "R1_R"},
  "C1": {"C": "C1_C"}
}
```

--------------------------------

### Get Time Constants - PyImpspec

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs_kramers_kronig.md

Retrieves the time constants that were utilized during the fitting process.

```python
def get_time_constants():
    """Get the time constants that were used during fitting.

    * **Return type:**
      [`TimeConstants`](apidocs_typing.md#pyimpspec.TimeConstants)
    """
    pass
```

--------------------------------

### GET /statistics/dataframe

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs_drt.md

Retrieves statistical data related to the DRT analysis as a pandas DataFrame.

```APIDOC
## GET /statistics/dataframe

### Description
Returns the statistical summary of the DRT analysis as a pandas DataFrame.

### Method
GET

### Endpoint
/to_statistics_dataframe

### Response
#### Success Response (200)
- **dataframe** (pandas.DataFrame) - A DataFrame containing the statistical metrics.

#### Response Example
{
  "dataframe": "| Metric | Value |\n|---|---|\n| Mean | 0.45 |\n| Std Dev | 0.12 |"
```

--------------------------------

### Suggest Optimal RC Elements (Method 6 - Log-Sum Apex)

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs_kramers_kronig.md

Suggests the optimal number of RC elements by analyzing the approximate position of the apex in a plot of log-sum of impedance components versus the number of RC elements. This method accounts for the trade-off between increasing the number of RC elements and the resulting decrease in component magnitudes, which can lead to overfitting.

```python
def suggest_num_RC_method_6(tests, lower_limit=0, upper_limit=0, relative_scores=True):
    """Suggest the optimal number of RC elements to use based on the approximate position of the apex in a plot of $\log{\Sigma_{k=1}^{N_\tau} |\tau_k / R_k|}$ versus the number of RC elements.
    If the tests were performed on the admittance representation of the immittance data, then $C_k$ is substituted for $R_k$.
    The sum grows initially as the number of RC elements increases.
    However, the magnitudes of the fitted $R_k$ (or $C_k$) also tend to increase, which causes the magnitudes of the corresponding $C_k$ (or $R_k$) to decrease.
    Thus, the sum begins to decline despite the increasing number of RC elements and the fitted impedance spectrum begins to oscillate (i.e., overfitting takes place).
    The apex should coincide with or be near the optimum.

    References:

    - [V. Yrjänä and J. Bobacka, 2024, Electrochim. Acta, 504, 144951](https://doi.org/10.1016/j.electacta.2024.144951)

    * **Parameters:**
      * **tests** (List[[`KramersKronigResult`](#pyimpspec.KramersKronigResult)]) – The test results to evaluate.
      * **lower_limit** (*int* *,* *optional*) – The lower limit to enforce for the number of RC elements.
        If this value is less than one, then no limit is enforced.
        If both the lower and upper limit are greater than zero, then the lower limit must have a smaller value than the upper limit.
      * **upper_limit** (*int* *,* *optional*) – The upper limit to enforce for the number of RC elements.
        If this value is less than one, then no limit is enforced.
        If both the lower and upper limit are greater than zero, then the upper limit must have a greater value than the lower limit.
      * **relative_scores** (*bool* *,* *optional*) – Return relative scores ranging from 0.0 to 1.0 (from worst to best) rather than the raw values.
    * **Returns:**
      A dictionary mapping the number of RC elements to its corresponding score.
    * **Return type:**
      Dict[int, float]
    """
    pass
```

--------------------------------

### GET /peaks/dataframe

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs_drt.md

Converts peak data into a pandas DataFrame for easier analysis and reporting.

```APIDOC
## GET /peaks/dataframe

### Description
Returns the DRT peaks as a pandas DataFrame object, suitable for generating tables or further data manipulation.

### Method
GET

### Endpoint
/to_peaks_dataframe

### Parameters
#### Query Parameters
- **threshold** (float) - Optional - The minimum peak height threshold.
- **columns** (List[str]) - Optional - Custom labels for the DataFrame column headers.

### Response
#### Success Response (200)
- **dataframe** (pandas.DataFrame) - A DataFrame containing the peak data.

#### Response Example
{
  "dataframe": "| Time Constant | Gamma |\n|---|---|\n| 0.01 | 0.5 |\n| 0.1 | 1.2 |"
```

--------------------------------

### GET /get_peaks

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs_drt.md

Retrieves time constants and gammas for peaks exceeding a specified magnitude threshold.

```APIDOC
## GET /get_peaks

### Description
Get the time constants (in seconds) and gammas (in ohms) of peaks with magnitudes greater than the threshold.

### Method
GET

### Endpoint
/get_peaks

### Parameters
#### Query Parameters
- **threshold** (float) - Optional - Minimum peak height threshold relative to the tallest peak.

### Response
#### Success Response (200)
- **data** (Tuple[TimeConstants, Gammas, TimeConstants, Gammas]) - Returns peak data.
```

--------------------------------

### Create Circuit Elements Directly in PyImpspec

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_circuit.md

Demonstrates how to build a circuit by directly instantiating and nesting Element and Connection objects like Resistor, Capacitor, Series, and Parallel. This method provides granular control over circuit construction.

```python
from pyimpspec import Circuit, Series, Parallel, Resistor, Capacitor, Warburg
from numpy import inf, sqrt

R_sol: Resistor = (
  Resistor(R=20)
  .set_fixed(R=True)
  .set_label("sol")
)
C_dl: Capacitor = (
  Capacitor()
  .set_label("dl")
  .set_values(C=25e-6)
  .set_lower_limits(C=-inf)
  .set_upper_limits(C=1e-3)
)
R_ct: Resistor = (
  Resistor(R=100)
  .set_label("ct")
  .set_lower_limits(R=50)
  .set_upper_limits(R=200)
)
W_diff: Warburg = (
  Warburg(Y=1/(sqrt(2)*300))
  .set_label("diff")
  .set_lower_limits(Y=-inf)
  .set_upper_limits(Y=1.5*1/(sqrt(2)*300))
)
inner_series: Series = Series([R_ct, W_diff])
parallel: Parallel = Parallel([C_dl, inner_series])
outer_series: Series = Series([R_sol, parallel])
circuit: Circuit = Circuit(outer_series)
circuit.to_string(3)
```

--------------------------------

### GET /circuit/serialize

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_circuit.md

Serializes a circuit object into a CDC string, including metadata and versioning for compatibility.

```APIDOC
## GET /circuit/serialize

### Description
Serializes a circuit object into a versioned CDC string. This is useful for storing circuits while ensuring compatibility across different API versions.

### Method
GET

### Endpoint
/circuit/serialize

### Parameters
#### Query Parameters
- **decimals** (integer) - Optional - Number of decimal places for numerical values. Defaults to 12.

### Request Example
GET /circuit/serialize?decimals=3

### Response
#### Success Response (200)
- **serialized_string** (string) - The versioned CDC string representation.

#### Response Example
{
  "serialized_string": "!V=1![R{R=2.000E+01F...}]"
}
```

--------------------------------

### Perform Kramers-Kronig Test and Suggest RC Elements

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_kramers_kronig.md

Demonstrates how to execute a Kramers-Kronig test on a dataset and manually tune the RC element suggestion process using the mu-criterion. This approach allows for fine-grained control over the optimization parameters.

```python
from pyimpspec import (DataSet, KramersKronigResult, generate_mock_data, perform_kramers_kronig_test)
from pyimpspec.analysis.kramers_kronig import (evaluate_log_F_ext, suggest_num_RC)
from typing import List, Tuple

mu_criterion: float = 0.85
data: DataSet = generate_mock_data("CIRCUIT_1", noise=5e-2, seed=42)[0]

test: KramersKronigResult = perform_kramers_kronig_test(data, mu_criterion=mu_criterion)

evaluations: List[Tuple[float, List[KramersKronigResult], float]] = evaluate_log_F_ext(data)
optimum_log_Fext: Tuple[float, List[KramersKronigResult], float] = evaluations[0]
tests: List[KramersKronigResult] = optimum_log_Fext[1]

suggestion: Tuple[KramersKronigResult, Dict[int, float], int, int] = suggest_num_RC(tests, mu_criterion=mu_criterion)
test, scores, lower_limit, upper_limit = suggestion
```

--------------------------------

### Perform Z-HIT Analysis

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_zhit.md

Demonstrates how to generate mock immittance data and perform the Z-HIT analysis using the pyimpspec library.

```python
from pyimpspec import DataSet, ZHITResult, generate_mock_data, perform_zhit

data: DataSet = generate_mock_data("CIRCUIT_2_INVALID", noise=5e-2, seed=42)[0]
zhit: ZHITResult = perform_zhit(data)
```

--------------------------------

### Upgrade pyimpspec with pip (Bash)

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_installing.md

Upgrades an existing pyimpspec installation to the latest version using pip.

```bash
pip install pyimpspec --upgrade
```

--------------------------------

### GET /peaks

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs_drt.md

Retrieves time constants and gamma values for peaks exceeding a specified relative magnitude threshold.

```APIDOC
## GET /peaks

### Description
Retrieves the time constants (in seconds) and gamma values (in ohms) for peaks with magnitudes greater than the specified threshold.

### Method
GET

### Endpoint
/get_peaks

### Parameters
#### Query Parameters
- **threshold** (float) - Optional - The minimum peak height threshold (relative to the height of the tallest peak).

### Response
#### Success Response (200)
- **result** (Tuple[TimeConstants, Gammas]) - A tuple containing the time constants and gamma values.

#### Response Example
{
  "time_constants": [0.01, 0.1, 1.0],
  "gammas": [0.5, 1.2, 0.8]
}
```

--------------------------------

### Build Circuits with CircuitBuilder Context Manager in PyImpspec

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_circuit.md

Illustrates using the CircuitBuilder context manager for a more intuitive and hierarchical way to construct circuits. This method simplifies the process of nesting connections and adding elements.

```python
from pyimpspec import Circuit, CircuitBuilder, Resistor, Capacitor, Warburg
from numpy import inf, sqrt

with CircuitBuilder() as outer_series:
  outer_series.add(
    Resistor(R=20)
    .set_label("sol")
    .set_fixed(R=True)
  )
  with outer_series.parallel() as parallel:
    parallel.add(
      Capacitor(C=25e-6)
      .set_label("dl")
      .set_lower_limits(C=-inf)
      .set_upper_limits(C=1e-3)
    )
    with parallel.series() as inner_series:
      inner_series.add(
        Resistor(R=100)
        .set_label("ct")
        .set_lower_limits(R=50)
        .set_upper_limits(R=200)
      )
      inner_series.add(
        Warburg(Y=1/(sqrt(2)*300))
        .set_label("diff")
        .set_lower_limits(Y=-inf)
        .set_upper_limits(Y=1.5*1/(sqrt(2)*300))
      )
circuit: Circuit = outer_series.to_circuit()
circuit.to_string(3)
```

--------------------------------

### POST /analysis/kramers-kronig/suggest-rc-method-6

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/apidocs_kramers_kronig.md

Suggests the optimal number of RC elements based on the apex position of the log sum of time constants versus RC element count.

```APIDOC
## POST /analysis/kramers-kronig/suggest-rc-method-6

### Description
Suggests the optimal number of RC elements by identifying the apex in a plot of log sum of time constants, helping to detect the onset of overfitting.

### Method
POST

### Endpoint
/analysis/kramers-kronig/suggest-rc-method-6

### Parameters
#### Request Body
- **tests** (List[KramersKronigResult]) - Required - The test results to evaluate.
- **lower_limit** (int) - Optional - Lower limit for the number of RC elements.
- **upper_limit** (int) - Optional - Upper limit for the number of RC elements.
- **relative_scores** (bool) - Optional - Return relative scores (0.0 to 1.0) instead of raw values.

### Response
#### Success Response (200)
- **result** (Dict[int, float]) - A dictionary mapping the number of RC elements to its corresponding score.
```

--------------------------------

### Upgrade pyimpspec with pipx (Bash)

Source: https://github.com/vyrjana/pyimpspec/blob/main/docs/source/guide_installing.md

Upgrades an existing pyimpspec installation to the latest version using pipx, including any injected dependencies.

```bash
pipx upgrade pyimpspec --include-injected
```