### Import the new solver

Source: https://skscope.readthedocs.io/en/latest/_sources/contribute/ContributeCode.rst

Example of importing the newly implemented solver after installation.

```python
from skscope import NewSolver
```

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

### Install official release via pip

Source: https://skscope.readthedocs.io/en/latest/userguide/install.html

Recommended installation method for most users.

```bash
pip install skscope
```

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

### Basic Data Loading Example

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/LinearModelAndVariants/isotonic-regression.ipynb

Demonstrates how to load data from a CSV file using pandas. Ensure pandas is installed.

```python
import pandas as pd

df = pd.read_csv('data.csv')
print(df.head())
```

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

### Install documentation dependencies

Source: https://skscope.readthedocs.io/en/latest/_sources/contribute/ContributeDocs.rst

Install the required Python packages for building the documentation.

```bash
pip install -r docs/requirements.txt
```

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

### SKscope Example

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/Miscellaneous/exemplar-based-clustering.ipynb

A basic example demonstrating the usage of SKscope.

```python
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
```

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

### Compare Warm Start Strategies

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/GeneralizedLinearModels/logistic-regression.ipynb

Demonstrates the performance difference between default warm start and explicitly disabling it in ScopeSolver.

```python
# Record start time
start_time = time.time()
solver_ws = ScopeSolver(p, sparsity = range(10), sample_size = n, cv = 5,
                        split_method=lambda data, index: (data[0][index, :], data[1][index]))
solver_ws.solve(logistic_loss_cv, jit=True, data=(X, y))

# Calculate runtime
runtime = time.time() - start_time
print("Runtime:", runtime, "seconds")
print("True support set: ", (true_params.nonzero()[0]))
print("Estimated support set: ", (solver_ws.support_set))
```

```python
# Record start time
start_time = time.time()
solver_nws = ScopeSolver(p, sparsity = range(10), sample_size = n, cv = 5,
                        split_method=lambda data, index: (data[0][index, :], data[1][index]))
solver_nws.warm_start = False
solver_nws.solve(logistic_loss_cv, jit=True, data=(X, y))
# Calculate runtime
runtime = time.time() - start_time
print("Runtime:", runtime, "seconds")
print("True support set: ", (true_params.nonzero()[0]))
print("Estimated support set: ", (solver_nws.support_set))
```

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

### Logging Setup

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/FusionModels/depth-first-search-graph-trend-filtering.ipynb

Basic configuration for logging messages to a file. Logs will be appended to 'app.log'.

```python
import logging

def setup_logging():
    logging.basicConfig(
        level=logging.INFO,
        format='%(asctime)s - %(levelname)s - %(message)s',
        filename='app.log',
        filemode='a'
    )
    print("Logging configured. Messages will be written to app.log")

# Example usage:
# setup_logging()
# logging.info('Application started.')
```

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

### Basic JavaScript Example

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/FusionModels/piecewise-linear-trend-filtering.ipynb

A simple JavaScript snippet demonstrating a basic function. No specific setup or imports are required for this example.

```javascript
function example() {
  return true;
}
```

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

### Install Documentation Dependencies

Source: https://skscope.readthedocs.io/en/latest/contribute/ContributeCode.html

Install the necessary packages for developing Python API documentation using Sphinx and related tools. Ensure all packages in docs/requirements.txt are installed.

```bash
pip install -r docs/requirements.txt

```

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

### Database Connection Example

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/FusionModels/depth-first-search-graph-trend-filtering.ipynb

Illustrates establishing a connection to a PostgreSQL database. Replace placeholders with actual credentials. Requires 'psycopg2'.

```python
import psycopg2

def connect_db(db_params):
    try:
        conn = psycopg2.connect(**db_params)
        print("Database connection established successfully.")
        return conn
    except psycopg2.Error as e:
        print(f"Error connecting to database: {e}")
        return None

# Example usage:
# db_config = {
#     'database': 'mydatabase',
#     'user': 'myuser',
#     'password': 'mypassword',
#     'host': 'localhost',
#     'port': '5432'
# }
# connection = connect_db(db_config)
```

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

### Import Dependencies

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/LinearModelAndVariants/linear-mixed-model.ipynb

Initial setup for the environment, including necessary libraries for numerical computation and modeling.

```python
import numpy as np
import jax.numpy as jnp
import matplotlib.pyplot as plt
import seaborn as sns
from skscope import ScopeSolver

import warnings
warnings.filterwarnings('ignore')
```

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

### Install official release via conda

Source: https://skscope.readthedocs.io/en/latest/userguide/install.html

Alternative installation method for Linux or Mac users.

```bash
conda install skscope
```

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

### Install skscope via Package Managers

Source: https://skscope.readthedocs.io/en/latest/_sources/userguide/install.rst

Standard installation methods for official releases using pip or conda.

```Bash
pip install skscope
```

```Bash
conda install skscope
```

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

### Importing skscope dependencies

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/SparsityLevelSelection/supported-information-criteria-and-cross-validation.ipynb

Initial setup for using skscope solvers and utilities with JAX and NumPy.

```python
import numpy as np
import jax.numpy as jnp
from skscope import ScopeSolver, utilities
from sklearn.datasets import make_regression

import warnings
warnings.filterwarnings('ignore')
```

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

### Build skscope from Source

Source: https://skscope.readthedocs.io/en/latest/_sources/userguide/install.rst

Install the package in editable mode to allow for development changes without rebuilding.

```Bash
pip install -e .
```

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

### Import Libraries for Sparse Matrix Example

Source: https://skscope.readthedocs.io/en/latest/feature/ComputationalTips.html

Import necessary libraries including numpy, jax.numpy, jax.experimental.sparse, skscope, and scipy.sparse. Filter warnings for cleaner output.

```python
import numpy as np
import jax.numpy as jnp
from jax.experimental import sparse
from skscope import ScopeSolver
import scipy.sparse as sp

import warnings
warnings.filterwarnings('ignore')

```

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

### Bash: Scripting Example

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/FusionModels/depth-first-search-graph-trend-filtering.ipynb

A simple Bash script for automating tasks. Ensure correct permissions and environment variables are set.

```bash
#!/bin/bash
echo "Hello, World!"
```

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

### File Path Example in JavaScript

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/FusionModels/piecewise-linear-trend-filtering.ipynb

Illustrates how to define a file path string in JavaScript, including handling backslashes. This is useful for path manipulation.

```javascript
const path = "C:\\Users\\file";

```

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

### Install JAX with CUDA Support

Source: https://skscope.readthedocs.io/en/latest/_sources/feature/ComputationalTips.rst

To utilize GPU acceleration with JAX and skscope, install the appropriate JAX version matching your CUDA toolkit. This command installs JAX with CUDA 12 support.

```bash
pip install -U "jax[cuda12]"
```

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

### Build documentation locally

Source: https://skscope.readthedocs.io/en/latest/_sources/contribute/ContributeDocs.rst

Generate the HTML documentation from the Jupyter notebooks in the docs directory.

```bash
make html
```

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

### Configuration File Loading

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/FusionModels/depth-first-search-graph-trend-filtering.ipynb

Shows how to load configuration settings from a JSON file. Assumes a 'config.json' file exists in the same directory.

```python
import json

def load_config(filepath='config.json'):
    try:
        with open(filepath, 'r') as f:
            config = json.load(f)
        return config
    except FileNotFoundError:
        print(f"Error: Configuration file '{filepath}' not found.")
        return None
    except json.JSONDecodeError:
        print(f"Error: Could not decode JSON from '{filepath}'.")
        return None

# Example usage:
# app_config = load_config()
```

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

### Cross Validation Output Example

Source: https://skscope.readthedocs.io/en/latest/gallery/SparsityLevelSelection/supported-information-criteria-and-cross-validation.html

Example output showing sparsity and active set results for cross-validation.

```text
sparsity: 5
active set: [10, 16, 20, 28, 45]
```

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

### Import Necessary Libraries

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/GraphicalModels/sparse-precision-matrix.ipynb

Initializes the environment by importing required libraries for numerical computation, optimization, and visualization.

```python
from skscope import ScopeSolver
import jax.numpy as jnp
import numpy as np
from sklearn.datasets import make_sparse_spd_matrix
import cvxpy as cp
import matplotlib.pyplot as plt
import seaborn as sns
import scipy.linalg as la
```

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

### OMPSolver Initialization and Usage

Source: https://skscope.readthedocs.io/en/latest/autoapi/solver.html

This snippet demonstrates how to initialize and use the OMPSolver class to find a sparse optimal solution.

```APIDOC
## OMPSolver

### Description
Get sparse optimal solution of convex objective function by Orthogonal Matching Pursuit (OMP) algorithm. Specifically, `OMPSolver` aims to tackle this problem: minx∈Rpf(x) s.t. ||x||0≤s, where f(x) is a convex objective function and s is the sparsity level. Each element of x can be seen as a variable, and the nonzero elements of x are the selected variables.

### Method
__init__

### Parameters
#### Path Parameters
- **dimensionality** (int) - Required - Dimension of the optimization problem, which is also the total number of variables that will be considered to select or not, denoted as p.

#### Query Parameters
- **sparsity** (int or array of int, optional) - The sparsity level, which is the number of nonzero elements of the optimal solution, denoted as s. Default is `range(int(p/log(log(p))/log(p)))`.
- **sample_size** (int, default=1) - Sample size, denoted as n.
- **threshold** (float, default=0.0) - The threshold to determine whether a variable is selected or not.
- **strict_sparsity** (bool, default=True) - Whether to strictly control the sparsity level to be `sparsity` or not.
- **preselect** (array of int, default=[]) - An array contains the indexes of variables which must be selected.
- **numeric_solver** (callable, optional) - A solver for the convex optimization problem. `OMPSolver` will call this function to solve the convex optimization problem in each iteration. It should have the same interface as `skscope.convex_solver_LBFGS`.
- **max_iter** (int, default=100) - Maximum number of iterations taken for converging.
- **group** (array of shape (dimensionality,), default=range(dimensionality)) - The group index for each variable, and it must be an incremental integer array starting from 0 without gap. The variables in the same group must be adjacent, and they will be selected together or not. Here are wrong examples: `[0,2,1,2]` (not incremental), `[1,2,3,3]` (not start from 0), `[0,2,2,3]` (there is a gap). It’s worth mentioning that the concept “a variable” means “a group of variables” in fact. For example,``sparsity=[3]`` means there will be 3 groups of variables selected rather than 3 variables, and `always_include=[0,3]` means the 0-th and 3-th groups must be selected.
- **ic_method** (callable, optional) - A function to calculate the information criterion for choosing the sparsity level. `ic(loss, p, s, n) -> ic_value`, where `loss` is the value of the objective function, `p` is the dimensionality, `s` is the sparsity level and `n` is the sample size. Used only when `sparsity` is array and `cv` is 1. Note that `sample_size` must be given when using `ic_method`.
- **cv** (int, default=1) - The folds number when use the cross-validation method. - If `cv` = 1, the sparsity level will be chosen by the information criterion. - If `cv` > 1, the sparsity level will be chosen by the cross-validation method.
- **cv_fold_id** (array of shape (sample_size,), optional) - An array indicates different folds in CV, which samples in the same fold should be given the same number. The number of different elements should be equal to `cv`. Used only when cv > 1.
- **split_method** (callable, optional) - A function to get the part of data used in each fold of cross-validation. Its interface should be `(data, index) -> part_data` where `index` is an array of int.
- **random_state** (int, optional) - The random seed used for cross-validation.

### Returns
- **params** (array of shape(dimensionality,)) - The sparse optimal solution.
- **objective_value** (float) - The value of objective function on the solution.
- **support_set** (array of int) - The indices of selected variables, sorted in ascending order.

### References
Yuan X T, Li P, Zhang T. Gradient Hard Thresholding Pursuit[J]. J. Mach. Learn. Res., 2017, 18(1): 6027-6069.
```

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

### Example Output for BIC

Source: https://skscope.readthedocs.io/en/latest/gallery/SparsityLevelSelection/supported-information-criteria-and-cross-validation.html

This is an example output showing the sparsity and active set identified after applying the BIC criterion for model selection.

```text
sparsity: 3
active set: [10, 20, 45]
```

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

### Error Handling Example

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/FusionModels/1d-trend-filtering.ipynb

Provides an example of how Skscope handles errors during processing. This snippet is for illustrative purposes and may not reflect all error scenarios.

```python
from skscope import Scope
import pandas as pd

df = pd.DataFrame({'col1': [1, 'a', 3]})
scope = Scope(df)
try:
    scope.process_data()
except Exception as e:
    print(f"An error occurred: {e}")
```

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

### Initialize Solver with Cross-Validation

Source: https://skscope.readthedocs.io/en/latest/feature/DataScienceTool.html

Configure the solver with sample size, split method, and fold count to enable cross-validation.

```python
solver = ScopeSolver(
    dimensionality=p,          ## there are p parameters
    sparsity=[1, 2, 3, 4, 5],  ## we want to select 1-5 variables
    sample_size=n,             ## the number of samples
    split_method=split_method, ## use split_method to split data
    cv=10,                     ## use 10-fold cross validation
)

params = solver.solve(custom_objective, data = (X, y))
```

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

### Import required libraries

Source: https://skscope.readthedocs.io/en/latest/gallery/GraphicalModels/sparse-gaussian-precision-matrix.html

Initializes the environment with necessary libraries for optimization, data handling, and visualization.

```python
from scope import ScopeSolver
import jax.numpy as jnp
import numpy as np
from sklearn.datasets import make_sparse_spd_matrix
from sklearn.covariance import GraphicalLassoCV
import cvxpy as cp
import matplotlib.pyplot as plt
import matplotlib.cm as cm
import seaborn as sns
import networkx as nx
import scipy.linalg as la
import warnings

warnings.filterwarnings("ignore", message="invalid value encountered in subtract")
```

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

### Install JAX with CUDA Support

Source: https://skscope.readthedocs.io/en/latest/feature/ComputationalTips.html

To utilize GPU acceleration, install a JAX version that matches your CUDA toolkit. This allows skscope to leverage GPU computation transparently.

```bash
pip install -U "jax[cuda12]"

```

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

### Skscope Solver with Warm Start Enabled

Source: https://skscope.readthedocs.io/en/latest/gallery/GeneralizedLinearModels/logistic-regression.html

Initializes and solves using the skscope solver with the default warm-start strategy enabled. Records and prints the runtime and estimated support set.

```python
# Record start time
start_time = time.time()
solver_ws = ScopeSolver(p, sparsity = range(10), sample_size = n, cv = 5,
                        split_method=lambda data, index: (data[0][index, :], data[1][index]))
solver_ws.solve(logistic_loss_cv, jit=True, data=(X, y))

# Calculate runtime
untime = time.time() - start_time
print("Runtime:", runtime, "seconds")
print("True support set: ", (true_params.nonzero()[0]))
print("Estimated support set: ", (solver_ws.support_set))
```

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

### GET /websites/skscope_readthedocs_io_en

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/Miscellaneous/exemplar-based-clustering.ipynb

Retrieves the documentation content for the SKScope project.

```APIDOC
## GET /websites/skscope_readthedocs_io_en

### Description
Retrieves the documentation content for the SKScope project.

### Method
GET

### Endpoint
/websites/skscope_readthedocs_io_en

### Response
#### Success Response (200)
- **content** (string) - The documentation content for the project.

#### Response Example
{
  "content": "Project: /websites/skscope_readthedocs_io_en..."
}
```

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

### GET /get_support

Source: https://skscope.readthedocs.io/en/latest/_modules/skscope/base_solver.html

Retrieves the support set of the optimal parameters.

```APIDOC
## GET /get_support

### Description
Returns the support set indices of the optimal parameters.

### Method
GET

### Response
#### Success Response (200)
- **support_set** (array) - The indices of the support set.
```

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

### Initialize Solver with Sparse Matrix Support

Source: https://skscope.readthedocs.io/en/latest/_sources/feature/ComputationalTips.rst

Import necessary libraries including `jax.numpy`, `jax.experimental.sparse`, and `scipy.sparse` to work with sparse matrices in skscope. This setup is demonstrated for linear regression.

```python
import numpy as np
import jax.numpy as jnp
from jax.experimental import sparse
from skscope import ScopeSolver
import scipy.sparse as sp

import warnings
warnings.filterwarnings('ignore')
```

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

### GET /get_config

Source: https://skscope.readthedocs.io/en/latest/_modules/skscope/base_solver.html

Retrieves the configuration parameters for the solver instance.

```APIDOC
## GET /get_config

### Description
Returns the parameters configured for the current solver instance.

### Method
GET

### Parameters
#### Query Parameters
- **deep** (boolean) - Optional - Whether to return parameters of sub-objects.
```

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

### Initialize and Run ScopeSolver

Source: https://skscope.readthedocs.io/en/latest/_sources/feature/ComputationalTips.rst

Configures the ScopeSolver with a specified sparsity level and executes the optimization.

```python
solver = ScopeSolver(p, sparsity=3)
params_skscope = solver.solve(ols_loss, jit=True)
```

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

### Initialize and execute data generation

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/GeneralizedLinearModels/gamma-regression.ipynb

Demonstrates usage of the data generation function with 500 observations and 5 active variables.

```python
n = 500
p = 500
s = 5
x, y, coef_ = make_gamma_data(n=n, p=p, k=s)

print("The predictor variables of the first five samples:",'\n',x[:,:5])
print("The first five noisy observations:", '\n', y[:5])
```

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

### GET /get_config

Source: https://skscope.readthedocs.io/en/latest/_modules/skscope/solver.html

Retrieves the current configuration parameters for the Skscope solver.

```APIDOC
## GET /get_config

### Description
Returns a dictionary containing the parameters for the current solver instance.

### Method
GET

### Endpoint
/get_config

### Parameters
#### Query Parameters
- **deep** (bool) - Optional - If True, returns parameters for this solver and contained subobjects that are estimators. Default is True.

### Response
#### Success Response (200)
- **params** (dict) - A dictionary of the solver's configuration parameters.

#### Response Example
{
  "dimensionality": 100,
  "sparsity": null,
  "thread": 1,
  "splicing_type": "halve"
}
```

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

### Initialize Support Set and Parameters

Source: https://skscope.readthedocs.io/en/latest/_modules/skscope/base_solver.html

Validates the initial support set and sets up random parameter initialization if required.

```python
if init_support_set is None:
            init_support_set = np.array([], dtype="int32")
        else:
            init_support_set = np.array(init_support_set, dtype="int32")
            if init_support_set.ndim > 1:
                raise ValueError(
                    "The initial active set should be an 1D array of integers."
                )
            if init_support_set.min() < 0 or init_support_set.max() >= p:
                raise ValueError("init_support_set contains wrong index.")

        # init_params
        if init_params is None:
            random_init = False
            if len(layers) > 0:
                random_init = np.any(
                    np.array([layer.random_initilization for layer in layers])
                )
            if random_init:
                init_params = np.random.RandomState(self.random_state).randn(p)
```

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

### GET /api/v1/scope

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/LinearModelAndVariants/isotonic-regression.ipynb

Retrieves the scope data for the specified project identifier.

```APIDOC
## GET /api/v1/scope

### Description
Retrieves the scope data for the specified project identifier.

### Method
GET

### Endpoint
/api/v1/scope

### Parameters
#### Query Parameters
- **project_id** (string) - Required - The unique identifier for the project.

### Request Example
GET /api/v1/scope?project_id=skscope_readthedocs_io_en

### Response
#### Success Response (200)
- **data** (object) - The scope information for the project.

#### Response Example
{
  "project_id": "skscope_readthedocs_io_en",
  "status": "active",
  "data": {}
}
```

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

### Initialize and Solve with ScopeSolver using Sparse Matrix

Source: https://skscope.readthedocs.io/en/latest/feature/ComputationalTips.html

Initialize ScopeSolver with the problem dimensions and sparsity level, then solve the OLS loss function using JIT compilation.

```python
solver = ScopeSolver(p, sparsity=3)
params_skscope = solver.solve(ols_loss, jit=True)

```

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

### GET /get_estimated_params

Source: https://skscope.readthedocs.io/en/latest/_modules/skscope/base_solver.html

Retrieves only the optimal parameters calculated by the objective function.

```APIDOC
## GET /get_estimated_params

### Description
Returns the optimal solution parameters.

### Method
GET

### Response
#### Success Response (200)
- **parameters** (array) - The optimal solution of shape (dimensionality,)

#### Response Example
{
  "parameters": [0.1, 0.0, 0.5]
}
```

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

### Initialize HTPSolver

Source: https://skscope.readthedocs.io/en/latest/_modules/skscope/solver.html

Initializes the HTPSolver with various parameters controlling sparsity, optimization, and cross-validation. Ensure 'convex_solver_LBFGS' is available if not providing a custom solver.

```python
def __init__(
        self,
        dimensionality,
        sparsity=None,
        sample_size=1,
        *,
        preselect=[],
        step_size=0.005,
        numeric_solver=convex_solver_LBFGS,
        max_iter=100,
        group=None,
        ic_method=None,
        cv=1,
        cv_fold_id=None,
        split_method=None,
        random_state=None,
    ):
        super().__init__(
            dimensionality=dimensionality,
            sparsity=sparsity,
            sample_size=sample_size,
            preselect=preselect,
            numeric_solver=numeric_solver,
            max_iter=max_iter,
            group=group,
            ic_method=ic_method,
            cv=cv,
            cv_fold_id=cv_fold_id,
            split_method=split_method,
            random_state=random_state,
        )
        self.step_size = step_size
```

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

### PortfolioSelection Class Initialization

Source: https://skscope.readthedocs.io/en/latest/_modules/skscope/skmodel.html

Initializes a sparse portfolio selection model. Configure sparsity, objective function (MinVar/MeanVar), alpha for mean-variance, covariance matrix estimator, and random state.

```python
class PortfolioSelection(BaseEstimator):
    r"""
    Construct a sparse portfolio using ``skscope`` with ``MinVar`` or ``MeanVar`` measure.

    Parameters
    ------------
    sparsity : int, default=10
        The number of stocks to be chosen, i.e., the sparsity level

    obj : {"MinVar", "MeanVar"}, default="MinVar"
            The objective of the portfolio optimization

    alpha: float, default=0
        The penalty coefficient of the return

    cov_matrix : {"empirical", "lw"}, default="lw"
        Specify the estimator of covariance matrix.
        If ``empirical``, it will be the empirical estimator. If ``lw``, it will be the LedoitWolf estimator.

    random_state : {None, int, array_like[ints], SeedSequence, BitGenerator, Generator}, default=None
        The seed to initialize the parameter ``init_params`` in ``ScopeSolver``
    """

    def __init__(
        self,
        sparsity=1,
        obj="MinVar",
        alpha=0,
        cov_matrix="lw",
        random_state=None,
    ):
        self.sparsity = sparsity
        self.obj = obj
        self.alpha = alpha
        self.cov_matrix = cov_matrix
        self.random_state = random_state

    _parameter_constraints: dict = {
        "sparsity": [Interval(Integral, 1, None, closed="left")],
        "obj": [StrOptions({"MinVar", "MeanVar"})],
        "alpha": [Interval(Real, 0, None, closed="left")],
        "cov_matrix": [StrOptions({"empirical", "lw"})],
        "random_state": ["random_state"],
    }

    # def _more_tags(self):
    #     return {'non_deterministic': True}

```

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

### Initialize ScopeSolver

Source: https://skscope.readthedocs.io/en/latest/_modules/skscope/solver.html

Instantiate the ScopeSolver with specified parameters. Ensure 'dimensionality' is provided. Other parameters like 'sparsity', 'sample_size', and 'numeric_solver' can be customized.

```python
from sklearn.model_selection import KFold
from .base_solver import BaseSolver
from sklearn.base import BaseEstimator
import numpy as np
import jax
from jax import numpy as jnp
from . import _scope, utilities
from .numeric_solver import convex_solver_LBFGS



[docs]
class ScopeSolver(BaseEstimator):
    r"""
    Get sparse optimal solution of convex objective function by Sparse-Constrained Optimization via Splicing Iteration (SCOPE) algorithm, which also can be used for variables selection.
    Specifically, ``ScopeSolver`` aims to tackle this problem: :math:`\min_{x \in R^p} f(x) \text{ s.t. } ||x||_0 \leq s`, where :math:`f(x)` is a convex objective function and :math:`s` is the sparsity level. Each element of :math:`x` can be seen as a variable, and the nonzero elements of :math:`x` are the selected variables.

    Parameters
    ----------
    dimensionality : int
        Dimension of the optimization problem, which is also the total number of variables that will be considered to select or not, denoted as :math:`p`.
    sparsity : int or array of int, optional
        The sparsity level, which is the number of nonzero elements of the optimal solution, denoted as :math:`s`.
        default is ``range(int(p/log(log(p))/log(p)))``.
        Used only when ``path_type`` is "seq".
    sample_size : int, default=1
        Sample size, denoted as :math:`n`.
    preselect : array of int, default=[]
        An array contains the indexes of variables which must be selected.
    numeric_solver : callable, optional
        A solver for the convex optimization problem. ``ScopeSolver`` will call this function to solve the convex optimization problem in each iteration.
        It should have the same interface as ``skscope.convex_solver_LBFGS``.
    max_iter : int, default=20
        Maximum number of iterations taken for converging.
    ic_method : callable, optional
        A function to calculate the information criterion for choosing the sparsity level.
        ``ic(loss, p, s, n) -> ic_value``, where ``loss`` is the value of the objective function, ``p`` is the dimensionality, ``s`` is the sparsity level and ``n`` is the sample size.
        Used only when ``sparsity`` is array and ``cv`` is 1.
        Note that ``sample_size`` must be given when using ``ic_method``.
    cv : int, default=1
        The folds number when use the cross-validation method. If ``cv`` = 1, the sparsity level will be chosen by the information criterion. If ``cv`` > 1, the sparsity level will be chosen by the cross-validation method.
    split_method: callable, optional
        A function to get the part of data used in each fold of cross-validation.
        Its interface should be ``(data, index) -> part_data`` where ``index`` is an array of int.
    cv_fold_id: array of shape (sample_size,), optional
        An array indicates different folds in CV, which samples in the same fold should be given the same number.
        The number of different elements should be equal to ``cv``.
        Used only when `cv` > 1.
    group : array of shape (dimensionality,), default=range(dimensionality)
        The group index for each variable, and it must be an incremental integer array starting from 0 without gap.
        The variables in the same group must be adjacent, and they will be selected together or not.
        Here are wrong examples: ``[0,2,1,2]`` (not incremental), ``[1,2,3,3]`` (not start from 0), ``[0,2,2,3]`` (there is a gap).
        It's worth mentioning that the concept "a variable" means "a group of variables" in fact. For example,``sparsity=[3]`` means there will be 3 groups of variables selected rather than 3 variables,
        and ``always_include=[0,3]`` means the 0-th and 3-th groups must be selected.
    important_search : int, default=128
        The number of important variables which need be splicing.
        This is used to reduce the computational cost. If it's too large, it would greatly increase runtime.
    screening_size : int, default=-1
        The number of variables remaining after the screening before variables select. Screening is used to reduce the computational cost.
        ``screening_size`` should be a non-negative number smaller than p, but larger than any value in sparsity. If ``screening_size`` is -1, screening will not be used. If ``screening_size`` is 0, ``screening_size`` will be set as ``int(p/log(log(p))/log(p))``.
    max_exchange_num : int, optional, default=5
        Maximum exchange number when splicing.
    is_dynamic_max_exchange_num : bool, default=True
        If ``is_dynamic_max_exchange_num`` is True, ``max_exchange_num`` will be decreased dynamically according to the number of variables exchanged in the last iteration.
    greedy : bool, default=True,
        If ``greedy`` is True, the first exchange-number which can reduce the objective function value will be selected.
    """
    pass
```

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

### Data Visualization with Matplotlib

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/LinearModelAndVariants/isotonic-regression.ipynb

Shows a simple scatter plot using matplotlib. Requires matplotlib to be installed.

```python
import matplotlib.pyplot as plt

plt.scatter(df['x'], df['y'])
plt.xlabel('X-axis')
plt.ylabel('Y-axis')
plt.title('Scatter Plot')
plt.show()
```

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

### PDASSolver Initialization

Source: https://skscope.readthedocs.io/en/latest/autoapi/solver.html

Initializes the PDASSolver to solve min β ∈ Rp l(β) s.t. ||β||0=k.

```APIDOC
## PDASSolver

### Description
Solve the best subset selection problem with the subset size k by Primal-dual active set (PDAS) algorithm.

### Parameters
- **dimensionality** (int) - Required - Dimension of the optimization problem (p).
- **sparsity** (int or array of int) - Optional - The number of nonzero elements of the optimal solution (s).
- **sample_size** (int) - Optional - Sample size (n).
- **preselect** (array of int) - Optional - Indexes of variables which must be selected.
- **step_size** (float) - Optional - Step size of gradient descent.
- **numeric_solver** (callable) - Optional - A solver for the convex optimization problem.
- **max_iter** (int) - Optional - Maximum number of iterations.
- **group** (array) - Optional - The group index for each variable.
- **cv** (int) - Optional - The folds number for cross-validation.
- **cv_fold_id** (array) - Optional - Indicates different folds in CV.
- **split_method** (callable) - Optional - Function to get data for each fold.
- **random_state** (int) - Optional - Random seed for cross-validation.
- **ic_method** (callable) - Optional - Function to calculate information criterion.
```

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

### Setup regression model with intercept

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/LinearModelAndVariants/linear-regression.ipynb

Generates synthetic data for a regression model including an intercept term.

```python
n, p = 150, 30
rng = np.random.default_rng(0)
X = rng.normal(0, 1, (n, p))
beta = np.zeros(p)
beta[:3] = [1, 2, 3]
y = X @ beta + rng.normal(1, 0.1, n)
```

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

### Import Libraries and Set Up

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/Miscellaneous/compositional-data-correlation-inference.ipynb

Imports necessary libraries including numpy, jax, matplotlib, seaborn, and skscope. It also sets a random seed for reproducibility and suppresses warnings.

```python
import numpy as np
np.random.seed(123)
import jax.numpy as jnp
import matplotlib.pyplot as plt
import seaborn as sns
from skscope import ScopeSolver

import warnings
warnings.filterwarnings('ignore')
```

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

### Initialize BaseSolver with various parameters

Source: https://skscope.readthedocs.io/en/latest/_modules/skscope/solver.html

Initializes the BaseSolver with parameters for dimensionality, sparsity, sample size, and advanced options like numeric solver, max iterations, group constraints, and cross-validation settings.

```python
def __init__(
        self,
        dimensionality,
        sparsity=None,
        sample_size=1,
        *,
        threshold=0.0,
        strict_sparsity=True,
        preselect=[],
        numeric_solver=convex_solver_LBFGS,
        max_iter=100,
        group=None,
        ic_method=None,
        cv=1,
        cv_fold_id=None,
        split_method=None,
        random_state=None,
    ):
        super().__init__(
            dimensionality=dimensionality,
            sparsity=sparsity,
            sample_size=sample_size,
            threshold=threshold,
            strict_sparsity=strict_sparsity,
            preselect=preselect,
            numeric_solver=numeric_solver,
            max_iter=max_iter,
            group=group,
            ic_method=ic_method,
            cv=cv,
            cv_fold_id=cv_fold_id,
            split_method=split_method,
            random_state=random_state,
        )
        self.use_gradient = True
```

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

### Use LinearSIC for Sparsity Selection

Source: https://skscope.readthedocs.io/en/latest/feature/DataScienceTool.html

Example demonstrating the use of LinearSIC to evaluate sparsity levels in a regression task.

```python
import jax.numpy as jnp
import numpy as np
from sklearn.datasets import make_regression
from skscope.utilities import LinearSIC

n, p, k = 100, 10, 3
X, y = make_regression(n_samples=n, n_features=p, n_informative=k)
solver = ScopeSolver(
    dimensionality=p,
    sparsity=[1, 2, 3, 4, 5] ## we want to select 1-5 variables
    sample_size=n,           ## the number of samples
    ic_method=LinearSIC,     ## use SIC to evaluate sparsity levels
)
solver.solve(
    lambda params: jnp.sum((X @ params - y)**2),
    jit = True,
)
print(solver.get_result())
```

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

### HTML/JavaScript: Interactive Element

Source: https://skscope.readthedocs.io/en/latest/_sources/gallery/FusionModels/depth-first-search-graph-trend-filtering.ipynb

An example of an interactive HTML element with embedded JavaScript. This can be used for dynamic user interfaces.

```html
<!DOCTYPE html>
<html>
<head>
<title>Page Title</title>
</head>
<body>

<h1>This is a Heading</h1>
<p>This is a paragraph.</p>

</body>
</html>
```