.. sysidentpy documentation master file, created by sphinx-quickstart on Sun Mar 15 08:37:08 2020. You can adapt this file completely to your liking, but it should at least contain the root `toctree` directive. 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 NARMAX model is described as: .. math:: y_k= F[y_{k-1}, \dotsc, y_{k-n_y},x_{k-d}, x_{k-d-1}, \dotsc, x_{k-d-n_x} + e_{k-1}, \dotsc, e_{k-n_e}] + e_k where :math:`n_y\in \mathbb{N}^*`, :math:`n_x \in \mathbb{N}`, :math:`n_e \in \mathbb{N}`, are the maximum lags for the system output and input respectively; :math:`x_k \in \mathbb{R}^{n_x}` is the system input and :math:`y_k \in \mathbb{R}^{n_y}` is the system output at discrete time :math:`k \in \mathbb{N}^n`; :math:`e_k \in \mathbb{R}^{n_e}` stands for uncertainties and possible noise at discrete time :math:`k`. In this case, :math:`\mathcal{F}` is some nonlinear function of the input and output regressors and :math:`d` is a time delay typically set to :math:`d=1`. .. note:: The update **v0.2.0** has been released with major changes and additional features. There are several API modifications and you will need to change your code to have the new (and upcoming) features. Check the examples of how to use the new version in the `documentation page `__ For more details, please see the `changelog `__ .. seealso:: 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! .. code-block:: python 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 ~~~~~~~~~~~~~~~ .. code-block:: python from sysidentpy.model_structure_selection import FROLS from sysidentpy.basis_function._basis_function import Polynomial from sysidentpy.utils.display_results import results from sysidentpy.utils.plotting import plot_residues_correlation, plot_results from sysidentpy.residues.residues_correlation import compute_residues_autocorrelation, compute_cross_correlation basis_function = Polynomial(degree=2) model = FROLS( order_selection=True, n_info_values=10, extended_least_squares=False, ylag=2, xlag=2, info_criteria='aic', estimator='least_squares', 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) 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 plot_results(y=y_valid, yhat=yhat, n=1000) ee = compute_residues_autocorrelation(y_valid, yhat) plot_residues_correlation(data=ee, title="Residues", ylabel="$e^2$") x1e = compute_cross_correlation(y_valid, yhat, x2_val) plot_residues_correlation(data=x1e, title="Residues", ylabel="$x_1e$") .. image:: ../../examples/figures/polynomial_narmax.png NARX Neural Network ~~~~~~~~~~~~~~~~~~~ .. code-block:: python from torch import nn from sysidentpy.neural_network import NARXNN from sysidentpy.basis_function._basis_function import Polynomial from sysidentpy.utils.plotting import plot_residues_correlation, plot_results from sysidentpy.residues.residues_correlation import compute_residues_autocorrelation, compute_cross_correlation 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 basis_function=Polynomial(degree=1) narx_net = NARXNN( net=NARX(), ylag=2, xlag=2, basis_function=basis_function, model_type="NARMAX", loss_func='mse_loss', optimizer='Adam', epochs=200, verbose=False, optim_params={'betas': (0.9, 0.999), 'eps': 1e-05} # optional parameters of the optimizer ) narx_net.fit(X=x_train, y=y_train) yhat = narx_net.predict(X=x_valid, y=y_valid) plot_results(y=y_valid, yhat=yhat, n=200) ee = compute_residues_autocorrelation(y_valid, yhat) plot_residues_correlation(data=ee, title="Residues", ylabel="$e^2$") x1e = compute_cross_correlation(y_valid, yhat, x_valid) plot_residues_correlation(data=x1e, title="Residues", ylabel="$x_1e$") .. image:: ../../examples/figures/narx_network.png Catboost-narx ~~~~~~~~~~~~~ .. code-block:: python from sysidentpy.general_estimators import NARX from catboost import CatBoostRegressor from sysidentpy.basis_function._basis_function import Polynomial from sysidentpy.utils.plotting import plot_residues_correlation, plot_results from sysidentpy.residues.residues_correlation import compute_residues_autocorrelation, compute_cross_correlation catboost_narx = NARX( base_estimator=CatBoostRegressor( iterations=300, learning_rate=0.1, depth=6), xlag=2, ylag=2, basis_function=basis_function, model_type="NARMAX", fit_params={'verbose': False} ) catboost_narx.fit(X=x_train, y=y_train) yhat = catboost_narx.predict(X=x_valid, y=y_valid) plot_results(y=y_valid, yhat=yhat, n=200) ee = compute_residues_autocorrelation(y_valid, yhat) plot_residues_correlation(data=ee, title="Residues", ylabel="$e^2$") x1e = compute_cross_correlation(y_valid, yhat, x_valid) plot_residues_correlation(data=x1e, title="Residues", ylabel="$x_1e$") .. image:: ../../examples/figures/catboost_narx.png Catboost without NARX configuration ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The following is the Catboost performance *without* the NARX configuration. .. code-block:: python def plot_results_tmp(y_valid, 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)) .. image:: ../../examples/figures/catboost.png 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 :code:`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 :code:`pytest-cov` package. First, install :code:`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. The project is actively maintained by Wilson R. L. Junior and looking for contributors. Communication ------------- - Discord server: https://discord.gg/8eGE3PQ - Website(soon): http://sysidentpy.org 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. Contents -------- .. toctree:: :maxdepth: 1 installation introduction_to_narmax user_guide dev_guide notebooks changelog/v0.2.0 code