SysIdentPy

https://sysidentpy.org
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Open-source Python library for nonlinear system identification, time series forecasting, and dynamic...
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### Install Required Packages

Source: https://sysidentpy.org/book/10-Case-Studies?q=

Create a requirements.txt file with the specified package versions to install all necessary dependencies for the case study.

```text
sysidentpy==0.4.0
datasetsforecast==0.0.8
pandas==2.2.2
numpy==1.26.0
matplotlib==3.8.4
s3fs==2024.6.1

```

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

### Install Required Packages

Source: https://sysidentpy.org/book/10-Case-Studies

Create a requirements.txt file with the specified package versions and install them using pip.

```text
sysidentpy==0.4.0
datasetsforecast==0.0.8
pandas==2.2.2
numpy==1.26.0
matplotlib==3.8.4
s3fs==2024.6.1

```

```bash
pip install -r requirements.txt

```

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

### Install Required Packages

Source: https://sysidentpy.org/book/10-Case-Studies

Installs necessary packages for the case study using a requirements file. Ensure you are using a virtual environment.

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

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

### Install Docs Extras

Source: https://sysidentpy.org/developer-guide/how-to-add-a-translation?q=

Installs the necessary extras for working with the documentation, including translation tools.

```bash
pip install -e ".[docs]"

```

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

### Install Required Packages

Source: https://sysidentpy.org/book/10-Case-Studies

Create a requirements.txt file with the specified package versions and install them using pip. Ensure you are using a virtual environment.

```text
sysidentpy==0.4.0
pystan==2.19.1.1
holidays==0.11.2
fbprophet==0.7.1
neuralprophet==0.2.7
pandas==1.3.2
numpy==1.23.3
matplotlib==3.8.4
pmdarima==1.8.3
scikit-learn==0.24.2
scipy==1.9.1
sktime==0.8.0
statsmodels==0.12.2
tbats==1.1.0
torch==1.12.1

```

```bash
pip install -r requirements.txt

```

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

### Install Required Packages

Source: https://sysidentpy.org/book/10-Case-Studies

Create a requirements.txt file with the specified package versions and install them using pip. Ensure you are using a virtual environment.

```text
sysidentpy==0.4.0
pandas==2.2.2
numpy==1.26.0
matplotlib==3.8.4
scikit-learn==1.4.2
```

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

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

### Install SysIdentPy

Source: https://sysidentpy.org/user-guide/how-to/create-a-narx-neural-network

Install the SysIdentPy library using pip. This is the first step before importing any modules.

```bash
pip install sysidentpy

```

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

### Install Development and Docs Dependencies

Source: https://sysidentpy.org/developer-guide/contribute

Install SysIdentPy along with all necessary dependencies for development and documentation. This ensures you have the tools needed for testing and building docs.

```bash
pip install "sysidentpy[dev, docs]"

```

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

### System Equation Simulation Example

Source: https://sysidentpy.org/book/2-NARMAX-Model-Representation?q=

This example defines a system equation for simulation purposes, illustrating a basic ARMAX-like structure. It is intended for conceptual understanding and replication of examples.

```python
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d

random_samples = 50
n = np.arange(random_samples)
def system_equation(y, u, nu):
    yk = 0.9*y[0] - 0.24*y[1] + 0.92*u[0] + 0.92*nu[0] + nu[1]
    return yk

```

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

### NonNegativeLeastSquares Solver Example

Source: https://sysidentpy.org/user-guide/API/parameter-estimation

Demonstrates the usage of the NonNegativeLeastSquares solver to estimate parameters. This example shows how to initialize the solver and call the optimize method with sample data.

```python
>>> b = np.array([-1, -1, -1])
>>> x = nnls_solver.optimize(A, b)
>>> print(x)
[[0.]
 [0.]]
```

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

### Example R and qit Matrices

Source: https://sysidentpy.org/user-guide/tutorials/multiobjective-parameter-estimation-overview

Displays example R and qit matrices generated during the multiobjective parameter estimation process. These matrices are crucial for analyzing the model structure and parameter dependencies.

```text
R matrix:
[[1 0 0 0 0 0 0 0]
 [0 1 1 0 0 0 0 0]
 [0 0 0 1 1 0 0 0]
 [0 0 0 0 0 1 1 1]]
qit matrix:
[[0 0]
 [1 0]
 [0 1]
 [0 2]]
```

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

### Full SysIdentPy Workflow Example

Source: https://sysidentpy.org/getting-started/quickstart-guide

A comprehensive example demonstrating data generation, model building, fitting, prediction, evaluation, result display, and residual analysis in SysIdentPy.

```python
import pandas as pd

from sysidentpy.utils.generate_data import get_siso_data
from sysidentpy.model_structure_selection import FROLS
from sysidentpy.basis_function import Polynomial
from sysidentpy.metrics import root_relative_squared_error
from sysidentpy.utils.display_results import results
from sysidentpy.utils.plotting import plot_results
from sysidentpy.utils.plotting import plot_residues_correlation
from sysidentpy.residues.residues_correlation import (
    compute_residues_autocorrelation,
    compute_cross_correlation,
)

# Generate a dataset from a simulated dynamic system.
x_train, x_valid, y_train, y_valid = get_siso_data(
    n=300,
    colored_noise=False,
    sigma=0.0001,
    train_percentage=80
)


basis_function = Polynomial(degree=2)
model = FROLS(
    ylag=2,
    xlag=2,
    basis_function=basis_function,
)
model.fit(X=x_train, y=y_train)
yhat = model.predict(X=x_valid, y=y_valid)

rrse = root_relative_squared_error(y_valid, yhat)
print(rrse)

r = pd.DataFrame(
    results(
        model.final_model, model.theta, model.err,
        model.n_terms, err_precision=8, dtype='sci'
        ),
    columns=['Regressors', 'Parameters', 'ERR'])
print(r)

plot_results(y=y_valid, yhat=yhat, n=1000, figsize=(15, 4))
# Compute and plot autocorrelation of the residuals
ee = compute_residues_autocorrelation(y_valid, yhat)
plot_residues_correlation(data=ee, title="Residues", ylabel="$e^2$")
# Compute and plot cross-correlation between residuals and an input
x1e = compute_cross_correlation(y_valid, yhat, x_valid)
plot_residues_correlation(data=x1e, title="Residues", ylabel="$x_1e$")

```

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

### Install Required Packages for SysIdentPy

Source: https://sysidentpy.org/book/10-Case-Studies

Lists the required packages and their versions for the F-16 benchmark case study. Use this content to create a requirements.txt file for installation.

```text
sysidentpy==0.4.0
pandas==2.2.2
numpy==1.26.0
matplotlib==3.8.4

```

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

### Python Requirements for Case Study

Source: https://sysidentpy.org/book/10-Case-Studies?q=

Lists the specific versions of Python packages required to replicate the case study. Install using 'pip install -r requirements.txt'.

```text
sysidentpy==0.4.0
pandas==2.2.2
numpy==1.26.0
matplotlib==3.8.4
scikit-learn==1.4.2
```

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

### Matrix Q Example

Source: https://sysidentpy.org/user-guide/tutorials/multiobjective-parameter-estimation-overview?q=

An example of the Q matrix, representing static function information. This matrix is typically derived from input (Uo) and output (Yo) data.

```python
array([[   50.        ,   800.        ,   800.        ,   100.        ,
          100.        ,   269.3877551 ,   269.3877551 ,   269.3877551 ],
       [  800.        , 17240.81632653, 17240.81632653,  1044.89795918,
         1044.89795918,  2089.79591837,  2089.79591837,  2089.79591837],
       [  800.        , 17240.81632653, 17240.81632653,  1044.89795918,
         1044.89795918,  2089.79591837,  2089.79591837,  2089.79591837],
       [  100.        ,  1044.89795918,  1044.89795918,   269.3877551 ,
          269.3877551 ,   816.32653061,   816.32653061,   816.32653061],
       [  100.        ,  1044.89795918,  1044.89795918,   269.3877551 ,
          269.3877551 ,   816.32653061,   816.32653061,   816.32653061],
       [  269.3877551 ,  2089.79591837,  2089.79591837,   816.32653061,
          816.32653061,  2638.54142407,  2638.54142407,  2638.54142407],
       [  269.3877551 ,  2089.79591837,  2089.79591837,   816.32653061,
          816.32653061,  2638.54142407,  2638.54142407,  2638.54142407],
       [  269.3877551 ,  2089.79591837,  2089.79591837,   816.32653061,
          816.32653061,  2638.54142407,  2638.54142407,  2638.54142407]])
```

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

### Biased Parameter Estimation Setup

Source: https://sysidentpy.org/book/3-Parameter-Estimation?q=

This snippet shows the setup for biased parameter estimation, including plotting vertical lines for real parameter values and displaying Kernel Density Estimates (KDEs).

```python
plt.axvline(x=0.1, color='k', linestyle='--', label='Real Value 0.1')
plt.axvline(x=0.2, color='k', linestyle='--', label='Real Value 0.2')
plt.axvline(x=0.9, color='k', linestyle='--', label='Real Value 0.9')
plt.xlabel('Parameter Value')
plt.ylabel('Density')
plt.title('Kernel Density Estimate of Parameters')
plt.legend()
plt.show()
```

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

### Importing Essential Python Libraries for SysIdentPy

Source: https://sysidentpy.org/book/0-Preface

These are the core libraries required to follow along with the Python examples in the book. Ensure these are installed before proceeding with the examples.

```python
import sysidentpy
import pandas as pd
import numpy as np
import torch
import matplotlib
import scipy
```

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

### Serve Documentation Locally

Source: https://sysidentpy.org/developer-guide/contribute

Build and serve the documentation website locally using MkDocs. This allows you to preview changes in real-time.

```bash
$ mkdocs serve
INFO     -  [13:25:00] Browser connected: http://127.0.0.1:8000

```

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

### Infinity-Step-Ahead Prediction Example

Source: https://sysidentpy.org/book/9-Validation

Illustrates the iterative calculation of predicted values `yhat` for infinity-step-ahead prediction, starting with initial conditions from `y_test`.

```python
y_initial = yhat(0) = 8
yhat(1) = 1*8 + 2*1 = 10
yhat(2) = 1*10 + 2*2 = 14
yhat(3) = 1*14 + 2*3 = 20
yhat(4) = 1*20 + 2*4 = 28

```

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

### Iterate Through Training Data Groups

Source: https://sysidentpy.org/user-guide/tutorials/m4-benchmark?q=

Initializes an empty list 'r' and starts iterating through the training data grouped by 'unique_id'. This is a setup for further processing or analysis of each time series group.

```python
r = []
ds_test = list(range(701, 749))
for u_id, data in train.groupby(by=["unique_id"], observed=True):

```

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

### Run Local Docs Server

Source: https://sysidentpy.org/developer-guide/how-to-add-a-translation?q=

Starts a local development server for previewing documentation changes. Restart the server if new files do not appear.

```bash
mkdocs serve

```

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

### Get Minimum Info Value

Source: https://sysidentpy.org/user-guide/API/ofr-base?q=

Finds the index of the first element where values start to increase monotonically. Assumes a 1-dimensional array-like structure and uses np.diff to check for increases.

```python
def get_min_info_value(info_values):
    """Find the index of the first increasing value in an array.

    Parameters
    ----------
    info_values : array-like
        A sequence of numeric values to be analyzed.

    Returns
    -------
    int
        The index of the first element where the values start to increase
        monotonically. If no such element exists, the length of
        `info_values` is returned.

    Notes
    -----
    - The function assumes that `info_values` is a 1-dimensional array-like
    structure.
    - The function uses `np.diff` to compute the difference between consecutive
    elements in the sequence.
    - The function checks if any differences are positive, indicating an increase
    in value.

    Examples
    --------
    >>> class MyClass:
    ...     def __init__(self, values):
    ...         self.info_values = values
    ...     def get_min_info_value(self):
    ...         is_monotonique = np.diff(self.info_values) > 0
    ...         if any(is_monotonique):
    ...             return np.where(is_monotonique)[0][0] + 1
    ...         return len(self.info_values)
    >>> instance = MyClass([3, 2, 1, 4, 5])
    >>> instance.get_min_info_value()
    3
    """
    xp = get_namespace(info_values)

    if _is_numpy_namespace(xp):
        is_monotonique = np.diff(info_values) > 0
        if any(is_monotonique):
            return np.where(is_monotonique)[0][0] + 1
        return info_values.shape[0]

    is_monotonique = info_values[1:] > info_values[:-1]
    if bool(_to_numpy(xp.any(is_monotonique))):
        first_increase = xp.nonzero(is_monotonique)[0][0]
        return int(_to_numpy(first_increase)) + 1
    return info_values.shape[0]
```

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

### Install Latest SysIdentPy

Source: https://sysidentpy.org/getting-started/getting-started

Install the latest stable version of SysIdentPy using pip. This is the recommended installation method for most users.

```bash
pip install sysidentpy
```

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

### Install SysIdentPy from Git

Source: https://sysidentpy.org/getting-started/getting-started

Install SysIdentPy directly from its GitHub repository using pip. This is useful for installing the latest development version.

```bash
pip install git+https://github.com/wilsonrljr/sysidentpy.git
```

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

### Initialize and Run BoundedVariableLeastSquares

Source: https://sysidentpy.org/user-guide/API/parameter-estimation

Demonstrates initializing BoundedVariableLeastSquares with a sparse matrix A, vector b, and bounds for the variables. It also shows the output indicating the optimization process.

```python
from sysidentpy.parameter_estimation import BoundedVariableLeastSquares
import numpy as np
from scipy.sparse import rand


rng = np.random.default_rng()

m = 20000
n = 10000

A = rand(m, n, density=1e-4, random_state=rng)
b = rng.standard_normal(m)

lb = rng.standard_normal(n)
ub = lb + 1

res = BoundedVariableLeastSquares(A, b, bounds=(lb, ub), lsmr_tol='auto',
verbose=1)
The relative change of the cost function is less than `tol`.
Number of iterations 16, initial cost 1.5039e+04, final cost 1.1112e+04,
first-order optimality 4.66e-08.

```

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

### Install SysIdentPy and Dependencies

Source: https://sysidentpy.org/getting-started/quickstart-guide

Install the core SysIdentPy library along with pandas for data manipulation. Optionally, install all features including those for neural networks.

```bash
pip install sysidentpy pandas
# Optional: For neural networks and advanced features
pip install sysidentpy["all"]
```

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

### Import Libraries and Setup Environment

Source: https://sysidentpy.org/book/10-Case-Studies

Import necessary libraries from sysidentpy, neuralprophet, and other common data science packages. Sets up plotting and error handling.

```python
from warnings import simplefilter
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from sysidentpy.model_structure_selection import FROLS
from sysidentpy.model_structure_selection import AOLS
from sysidentpy.model_structure_selection import MetaMSS
from sysidentpy.basis_function import Polynomial
from sysidentpy.utils.plotting import plot_results
from sysidentpy.neural_network import NARXNN
from sysidentpy.metrics import mean_squared_error
from neuralprophet import NeuralProphet
from neuralprophet import set_random_seed

simplefilter("ignore", FutureWarning)
np.seterr(all="ignore")
%matplotlib inline

loss = mean_squared_error
data_location = r".\datasets"

```

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

### Serve Documentation Locally

Source: https://sysidentpy.org/developer-guide/contribute?q=

Serve the SysIdentPy documentation locally to preview changes. This command uses MkDocs to build and serve the documentation website.

```bash
$ mkdocs serve

```

```bash
INFO     -  [13:25:00] Browser connected: http://127.0.0.1:8000

```

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

### Initialize and Run BoundedVariableLeastSquares

Source: https://sysidentpy.org/user-guide/API/parameter-estimation?q=

Demonstrates initializing BoundedVariableLeastSquares with a sparse matrix A, vector b, and bounds for the variables. It also shows the output indicating convergence.

```python
from sysidentpy.parameter_estimation import BoundedVariableLeastSquares
import numpy as np
from scipy.sparse import rand


rng = np.random.default_rng()

m = 20000
n = 10000

A = rand(m, n, density=1e-4, random_state=rng)
b = rng.standard_normal(m)

lb = rng.standard_normal(n)
ub = lb + 1

res = BoundedVariableLeastSquares(A, b, bounds=(lb, ub), lsmr_tol='auto',
verbose=1)
The relative change of the cost function is less than `tol`.
Number of iterations 16, initial cost 1.5039e+04, final cost 1.1112e+04,
first-order optimality 4.66e-08.
```

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

### Example Pytest Output

Source: https://sysidentpy.org/developer-guide/contribute

This is an example of the output you can expect after successfully running the pytest command, indicating all tests have passed.

```text
========== test session starts ==========

platform linux -- Python 3.7.6, pytest-5.4.2, py-1.8.1, pluggy-0.13.1

rootdir: ~/sysidentpy

plugins: cov-2.8.1

collected 12 items

tests/test_regression.py ............ [100%]

========== 12 passed in 2.45s ==================
```

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

### Relative Path Mirroring Example

Source: https://sysidentpy.org/developer-guide/how-to-add-a-translation

Shows how file paths in different languages should correspond to the English source.

```text
```
English: docs/en/developer-guide/how-to-add-a-translation.md
Spanish: docs/es/developer-guide/how-to-add-a-translation.md
French:  docs/fr/developer-guide/how-to-add-a-translation.md

```
```

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

### UOFR Parameter Estimation Example

Source: https://sysidentpy.org/user-guide/API/uofr?q=

Demonstrates how to estimate parameters for a non-linear system using UOFR with polynomial basis functions. Includes data generation, model fitting, prediction, and result visualization.

```python
import numpy as np
import matplotlib.pyplot as plt
from sysidentpy.model_structure_selection import UOFR
from sysidentpy.basis_function import Polynomial
from sysidentpy.utils.display_results import results
from sysidentpy.metrics import root_relative_squared_error
from sysidentpy.utils.generate_data import get_siso_data
import pandas as pd
x_train, x_valid, y_train, y_valid = get_siso_data(n=1000,
                                                    colored_noise=True,
                                                    sigma=0.2,
                                                    train_percentage=90)
basis_function = Polynomial(degree=2)
model = UOFR(basis_function=basis_function,
             order_selection=True,
             n_info_values=10,
             extended_least_squares=False,
             ylag=2,
             xlag=2,
             info_criteria='aic',
             sobolev_order=2,  # Use 1st and 2nd derivatives
             )
model.fit(x_train, y_train)
yhat = model.predict(x_valid, y_valid)
rrse = root_relative_squared_error(y_valid, yhat)
print(rrse)
r = pd.DataFrame(
    results(
        model.final_model, model.theta, model.err,
        model.n_terms, err_precision=8, dtype='sci'
        ),
    columns=['Regressors', 'Parameters', 'ERR'])
print(r)
```

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

### Install Specific Version of SysIdentPy

Source: https://sysidentpy.org/getting-started/getting-started

Install a specific version of SysIdentPy using pip. Replace '0.5.3' with the desired version number.

```bash
pip install sysidentpy=="0.5.3"
```

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

### Translator Note Example

Source: https://sysidentpy.org/developer-guide/how-to-add-a-translation?q=

Provides an example of an HTML comment used to give specific instructions to translators regarding terms or phrases.

```html
<!-- Translator note: keep the term "NARMAX" in English. -->

```

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

### Folder Structure Example

Source: https://sysidentpy.org/developer-guide/how-to-add-a-translation?q=

Illustrates the directory structure for multilingual documentation, showing the English section and placeholders for translated language sections.

```text
docs/
  en/
    developer-guide/
    getting-started/
    user-guide/
  <locale>/
    (mirrors the structure you translate)

```

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

### Install Required Packages

Source: https://sysidentpy.org/user-guide/tutorials/modeling-a-magneto-rheological-damper-device

Use this code to create a requirements.txt file for installing necessary packages like sysidentpy, pandas, numpy, matplotlib, and scikit-learn.

```text
sysidentpy==0.4.0
pandas==2.2.2
numpy==1.26.0
matplotlib==3.8.4
scikit-learn==1.4.2

```

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

### Import Libraries and Setup

Source: https://sysidentpy.org/user-guide/tutorials/fourier-NARX-overview

Imports necessary libraries for system identification, plotting, and metrics. Sets random seed and suppresses warnings for reproducible results.

```python
import numpy as np
import matplotlib.pyplot as plt

from sysidentpy.model_structure_selection import FROLS
from sysidentpy.basis_function import Polynomial, Fourier
from sysidentpy.parameter_estimation import LeastSquares, RecursiveLeastSquares
from sysidentpy.utils.plotting import plot_results
from sysidentpy.metrics import root_relative_squared_error

np.seterr(all="ignore")
np.random.seed(1)

%matplotlib inline
```

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

### Install Packages using pip

Source: https://sysidentpy.org/book/10-Case-Studies

Command to install all the required Python packages listed in a requirements.txt file. This is a standard method for managing project dependencies.

```bash
pip install -r requirements.txt

```

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

### Import Libraries and Setup

Source: https://sysidentpy.org/user-guide/tutorials/load-forecasting-benchmark

Imports necessary libraries for data manipulation, modeling, plotting, and evaluation. Sets up plotting and error handling.

```python
from warnings import simplefilter
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

from sysidentpy.model_structure_selection import FROLS, AOLS, MetaMSS
from sysidentpy.basis_function import Polynomial
from sysidentpy.parameter_estimation import LeastSquares
from sysidentpy.utils.plotting import plot_results
from sysidentpy.metrics import mean_squared_error

from sktime.datasets import load_airline
from neuralprophet import NeuralProphet
from neuralprophet import set_random_seed

simplefilter("ignore", FutureWarning)
np.seterr(all="ignore")

%matplotlib inline

loss = mean_squared_error
```

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

### Install SysIdentPy with Neural NARX Support

Source: https://sysidentpy.org/getting-started/getting-started

Install SysIdentPy along with all optional dependencies, including support for Neural NARX models, using pip.

```bash
pip install sysidentpy["all"]
```

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

### Import Libraries and Setup

Source: https://sysidentpy.org/user-guide/tutorials/load-forecasting-benchmark?q=

Imports necessary libraries for data manipulation, modeling, and plotting. Sets up plotting and error handling.

```python
from warnings import simplefilter
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

from sysidentpy.model_structure_selection import FROLS, AOLS, MetaMSS
from sysidentpy.basis_function import Polynomial
from sysidentpy.parameter_estimation import LeastSquares
from sysidentpy.utils.plotting import plot_results
from sysidentpy.metrics import mean_squared_error

from sktime.datasets import load_airline
from neuralprophet import NeuralProphet
from neuralprophet import set_random_seed

simplefilter("ignore", FutureWarning)
np.seterr(all="ignore")

%matplotlib inline

loss = mean_squared_error

```

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

### N-Steps Ahead Prediction Example

Source: https://sysidentpy.org/book/9-Validation

Demonstrates the manual calculation for n-steps ahead prediction (with `steps_ahead=2`), showing how predicted values are used in the loop for a defined number of steps before restarting with real values.

```text
y_initial = yhat(0) = 8
yhat(1) = 1*8 + 2*1 = 10
yhat(2) = 1*10 + 2*2 = 14
yhat(3) = 1*10 + 2*3 = 16
yhat(4) = 1*16 + 2*4 = 24
and so on

```
Tokens:
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