# Welcome to SysIdentPy’s documentation!¶

SysIdentPy is a Python module for System Identification using NARMAX models built on top of numpy and is distributed under the 3-Clause BSD license.

The project was started in by Wilson R. L. Junior, Luan Pascoal C. Andrade and Samir A. M. Martins as a project for System Identification discipline. Samuel joined early in 2019 and since then have contributed.

The examples directory has several Jupyter notebooks presenting basic tutorials of how to use the package and some specific applications of SysIdentPy. Try it out!

Tip

SysIdentPy now support NARX Neural Network and General estimators, e.g., sklearn estimators and Catboost. Check it out!

```import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sysidentpy.metrics import mean_squared_error
from sysidentpy.utils.generate_data import get_siso_data

# Generate a dataset of a simulated dynamical system
x_train, x_valid, y_train, y_valid = get_siso_data(
n=1000,
colored_noise=False,
sigma=0.001,
train_percentage=80
)
```

## Polynomial NARX¶

```from sysidentpy.polynomial_basis import PolynomialNarmax

model = PolynomialNarmax(
non_degree=2,
order_selection=True,
n_info_values=10,
extended_least_squares=False,
ylag=2,
xlag=2,
info_criteria='aic',
estimator='least_squares'
)
model.fit(x_train, y_train)
yhat = model.predict(x_valid, y_valid)
results = pd.DataFrame(model.results(err_precision=8,
dtype='dec'),
columns=['Regressors', 'Parameters', 'ERR'])

print(results)

Regressors     Parameters        ERR
0        x1(k-2)     0.9000  0.95556574
1         y(k-1)     0.1999  0.04107943
2  x1(k-1)y(k-1)     0.1000  0.00335113

ee, ex, extras, lam = model.residuals(x_valid, y_valid, yhat)
model.plot_result(y_valid, yhat, ee, ex)
```

## NARX Neural Network¶

```from torch import nn
from sysidentpy.neural_network import NARXNN

class NARX(nn.Module):
def __init__(self):
super().__init__()
self.lin = nn.Linear(4, 10)
self.lin2 = nn.Linear(10, 10)
self.lin3 = nn.Linear(10, 1)
self.tanh = nn.Tanh()

def forward(self, xb):
z = self.lin(xb)
z = self.tanh(z)
z = self.lin2(z)
z = self.tanh(z)
z = self.lin3(z)
return z

narx_net = NARXNN(
net=NARX(),
ylag=2,
xlag=2,
loss_func='mse_loss',
epochs=200,
verbose=False,
optim_params={'betas': (0.9, 0.999), 'eps': 1e-05} # optional parameters of the optimizer
)

train_dl = narx_net.data_transform(x_train, y_train)
valid_dl = narx_net.data_transform(x_valid, y_valid)
narx_net.fit(train_dl, valid_dl)
yhat = narx_net.predict(x_valid, y_valid)
ee, ex, extras, lam = narx_net.residuals(x_valid, y_valid, yhat)
narx_net.plot_result(y_valid, yhat, ee, ex)
```

## Catboost-narx¶

```from sysidentpy.general_estimators import NARX
from catboost import CatBoostRegressor

catboost_narx = NARX(
base_estimator=CatBoostRegressor(
iterations=300,
learning_rate=0.1,
depth=6),
xlag=2,
ylag=2,
fit_params={'verbose': False}
)

catboost_narx.fit(x_train, y_train)
yhat = catboost_narx.predict(x_valid, y_valid)
ee, ex, extras, lam = catboost_narx.residuals(x_valid, y_valid, yhat)
catboost_narx.plot_result(y_valid, yhat, ee, ex)
```

## Catboost without NARX configuration¶

The following is the Catboost performance without the NARX configuration.

```def plot_results(yvalid, yhat):
_, ax = plt.subplots(figsize=(14, 8))
ax.plot(y_valid[:200], label='Data', marker='o')
ax.plot(yhat[:200], label='Prediction', marker='*')
ax.set_xlabel("\$n\$", fontsize=18)
ax.set_ylabel("\$y[n]\$", fontsize=18)
ax.grid()
ax.legend(fontsize=18)
plt.show()

catboost = CatBoostRegressor(
iterations=300,
learning_rate=0.1,
depth=6
)

catboost.fit(x_train, y_train, verbose=False)
plot_results(y_valid, catboost.predict(x_valid))
```

### Changelog¶

See the changelog for a history of notable changes to SysIdentPy.

### Development¶

We welcome new contributors of all experience levels. The SysIdentPy community goals are to be helpful, welcoming, and effective.

Note

We use the pytest package for testing. The test functions are located in tests subdirectories at each folder inside SysIdentPy, which check the validity of the algorithms.

Run the pytest in the respective folder to perform all the tests of the corresponding sub-packages.

Currently, we have around 81% of code coverage.

You can install pytest using

```pip install -U pytest
```

### Example of how to run the tests:¶

Open a terminal emulator of your choice and go to a subdirectory, e.g,

```\sysidentpy\metrics\
```

Just type `pytest` and you get a result like

```========== 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 ==================
```

You can also see the code coverage using the `pytest-cov` package. First, install `pytest-cov` using

```pip install pytest-cov
```

Run the command below in the SysIdentPy root directory, to generate the report.

```pytest --cov=.
```

### Source code¶

You can check the latest sources with the command:

```git clone https://github.com/wilsonrljr/sysidentpy.git
```

### Project History¶

The project was started by Wilson R. L. Junior, Luan Pascoal and Samir A. M. Martins as a project for System Identification discipline. Samuel joined early in 2019 and since then have contributed.

The initial purpose was to learn the python language. Over time, the project has matured to the state it is in today.

The project is currently maintained by its creators and looking for contributors.

### Citation¶

If you use SysIdentPy on your project, please drop me a line.

If you use SysIdentPy on your scientific publication, we would appreciate citations to the following paper:

• Lacerda et al., (2020). SysIdentPy: A Python package for System Identification using NARMAX models. Journal of Open Source Software, 5(54), 2384, https://doi.org/10.21105/joss.02384

```@article{Lacerda2020,
doi = {10.21105/joss.02384},
url = {https://doi.org/10.21105/joss.02384},
year = {2020},
publisher = {The Open Journal},
volume = {5},
number = {54},
pages = {2384},
author = {Wilson Rocha Lacerda Junior and Luan Pascoal Costa da Andrade and Samuel Carlos Pessoa Oliveira and Samir Angelo Milani Martins},
title = {SysIdentPy: A Python package for System Identification using NARMAX models},
journal = {Journal of Open Source Software}
}
```

### Inspiration¶

The documentation and structure (even this section) is openly inspired by sklearn, einsteinpy, and many others as we used (and keep using) them to learn.