From 0b38856319ce003ac3a12396241caf0f9f1d9fb9 Mon Sep 17 00:00:00 2001 From: SIKAI ZHANG <34108862+MatthewSZhang@users.noreply.github.com> Date: Tue, 14 Jan 2025 13:42:33 +0800 Subject: [PATCH] MNT fix same y_init used for different sessions (#37) * MNT fix same y_init used for different sessions * DOC add example of msa NARX --- doc/multioutput.rst | 4 +- doc/narx.rst | 142 +++ doc/user_guide.rst | 3 +- examples/plot_narx.py | 4 +- examples/plot_narx_msa.py | 182 ++++ fastcan/narx.py | 16 +- meson.build | 2 +- pixi.lock | 1832 ++++++++++++++----------------------- pyproject.toml | 31 +- tests/test_narx.py | 48 +- 10 files changed, 1082 insertions(+), 1182 deletions(-) create mode 100644 doc/narx.rst create mode 100644 examples/plot_narx_msa.py diff --git a/doc/multioutput.rst b/doc/multioutput.rst index 776b7bc..26a1220 100644 --- a/doc/multioutput.rst +++ b/doc/multioutput.rst @@ -19,7 +19,7 @@ multioutput data may result in better accuracy in the following classification t than applying it directly to the original single-label data. See Figure 5 in [2]_. Relationship on multiclass data -------------------------------- +=============================== Assume the feature matrix is :math:`X \in \mathbb{R}^{N\times n}`, the multiclass target vector is :math:`y \in \mathbb{R}^{N\times 1}`, and the one-hot encoded target matrix is :math:`Y \in \mathbb{R}^{N\times m}`. Then, the Fisher's criterion for @@ -54,4 +54,4 @@ coefficient is one-to-one correspondence to each Fisher's criterion. .. rubric:: Examples * See :ref:`sphx_glr_auto_examples_plot_fisher.py` for an example of - the equivalent relationship between CCA and LDA on multiclass data. \ No newline at end of file + the equivalent relationship between CCA and LDA on multiclass data. diff --git a/doc/narx.rst b/doc/narx.rst new file mode 100644 index 0000000..773572d --- /dev/null +++ b/doc/narx.rst @@ -0,0 +1,142 @@ +.. currentmodule:: fastcan.narx + +.. _narx: + +======================================================= +Reduced polynomial NARX model for system identification +======================================================= + +:class:`NARX` is a class to build a reduced polynomial NARX (Nonlinear AutoRegressive eXogenous) model for system identification. +The structure of a polynomial NARX model is shown below: + +.. math:: + y(k) = 0.5y(k-1) + 0.3u_0(k)^2 + 2u_0(k-1)u_0(k-3) + 1.5u_0(k-2)u_1(k-3) + 1 + +where :math:`k` is the time index, :math:`u_0` and :math:`u_1` are input signals, and :math:`y` is the output signal. + + +The NARX model is composed of three parts: + +#. Terms: :math:`y(k-1)`, :math:`u_0(k)^2`, :math:`u_0(k-1)u_0(k-3)`, and :math:`u_0(k-2)u_1(k-3)` +#. Coefficients: 0.5, 0.3, 2, and 1.5 +#. Intercept: 1 + + +To build a reduced polynomial NARX model, we normally need the following steps: + +#. Build term library + #. Get time shifted variables: e.g., :math:`u(t-2)` and :math:`y(t-1)` + #. Get terms by nonlinearising the time shifted variables with polynomial basis, e.g., :math:`u_0(k-1)u_0(k-3)` and :math:`u_0(k-2)u_1(k-3)` +#. Search useful terms by feature selection, i.e., `Reduced Order Modelling (ROM) `_ +#. Learn the coefficients by least-squares + +.. rubric:: Examples + +* See :ref:`sphx_glr_auto_examples_plot_narx.py` for an example of the basic usage of the NARX model. + +Multiple time series and missing values +======================================= + +For time series modelling, the continuity of the data is important. +The continuity means all neighbouring samples have the same time interval. +A discontinuous time series can be treated as multiple pieces of continuous time series. +The discontinuity can be caused by + +#. Different measurement sessions, e.g., one measurement session is carried out at Monday and + lasts for one hour at 1 Hz, and another measurement is carried out at Tuesday and lasts for two hours at 1 Hz +#. Missing values + +No matter how the discontinuity is caused, :class:`NARX` treats the discontinuous time series as multiple pieces of continuous time series in the same way. + +.. note:: + It is easy to notify :class:`NARX` that the time series data are from different measurement sessions by inserting np.nan to break the data. For example, + + >>> import numpy as np + >>> x0 = np.zeros((3, 2)) # First measurement session has 3 samples with 2 features + >>> x1 = np.ones((5, 2)) # Second measurement session has 5 samples with 2 features + >>> u = np.r_[x0, [[np.nan, np.nan]], x1] # Insert np.nan to break the two measurement sessions + + It is important to break the different measurement sessions by np.nan, because otherwise, + the model will assume the time interval between the two measurement sessions is the same as the time interval within a session. + + +One-step-ahead and multiple-step-ahead prediction +================================================= + +In system identification, two types of predictions can be made by NARX models: + +#. One-step-ahead prediction: predict the output at the next time step given the measured input and the measured output at the past time steps, e.g., :math:`\hat{y}(k) = 0.5y(k-1) + 0.3u_0(k-1)^2`, where :math:`\hat{y}(k)` is the predicted output at time step :math:`k` +#. Multiple-step-ahead prediction: predict the output at the next time step given the measured input and the predicted output at the past time steps, e.g., :math:`\hat{y}(k) = 0.5\hat{y}(k-1) + 0.3u_0(k-1)^2` + +Obviously, the multiple-step-ahead prediction is more challenging, because the predicted output is used as the input to predict the output at the next step, which may accumulate the error. +The `prediction` method of :class:`NARX` gives the multiple-step-ahead prediction. + +It should also be noted the different types of predictions in model training. + +#. If assume the NARX model is one-step-ahead prediction structure, we know all input data for training in advance, + and the model can be trained by the simple ordinary least-squares (OLS) method +#. If assume the NARX model is a multiple-step-ahead prediction structure, the input data, like :math:`\hat{y}(k-1)` is + unknown in advance. Therefore, the training data must first be generated by the multiple-step-ahead prediction with + the initial model coefficients, and then the coefficients can be updated recursively. + +ARX and OE model +---------------- + +To better understant the two types of training, it is helpful to know two linear time series model structures, +i.e., `ARX (AutoRegressive eXogenous) model `_ and +`OE (output error) model `_. + +The ARX model structure is + +.. math:: + (1-A(z))y(t) = B(z)u(t) + e(t) + +where :math:`A(z)` and :math:`B(z)` are polynomials of :math:`z`, e.g., +:math:`A(z) = 1.5 z^{-1} - 0.7 z^{-2}`, :math:`z` is a complex number from `Z-transformation `_ +and :math:`z^{-1}` can be view as a time-shift operator, and :math:`e(t)` is the white noise. + +The OE model structure is + +.. math:: + y(t) = \frac{B(z)}{(1-A(z))} u(t) + e(t) + + +The ARX model and OE model is very similar. If we rewrite ARX model to :math:`y(t) = \frac{B(z)}{(1-A(z))} u(t) + \frac{1}{(1-A(z))} e(t)`, +we can see that both the ARX model and the OE model have the same transfer function :math:`\frac{B(z)}{(1-A(z))}`. +The two key differences are: + +#. noise assumption +#. `best linear unbiased estimator (BLUE) `_ + +For noise assumption, the noise of the ARX model passes through a filter :math:`\frac{1}{(1-A(z))}` while the noise of the OE model not. +The structure of ARX models implies that the measurement noise is a very special colored noise, which is not common in practice. + +For difference in BLUE, to get BLUE of models, we need to rewrite models to the form of + +.. math:: + e(t) = y(t) - \hat{y}(t) + +where :math:`\hat{y}(t)` is a predictor, which describes how to compute the predicted output to make the error white. +It is easy to find that for a ARX model + +.. math:: + \hat{y}(t) = A(z)y(t) + B(z)u(t) + +while for an OE model + +.. math:: + \hat{y}(t) = \frac{B(z)}{(1-A(z))} u(t) = A(z)\hat{y}(t) + B(z)u(t) + +The difference between the two predictors is the one for ARX models uses both measured input and output to make prediction, +while the one for OE models only uses measured input to make prediction. +In other words, the predictor of the BLUE for ARX computes one-step-ahead prediction, +while the predictor of the BLUE for OE computes multiple-step-ahead prediction. + +In summary, using multiple-step-ahead prediction in model training is more aligned with the real noise condition, but harder to train. +However, using one-step-ahead prediction in model training is easier to train, but the noise assumption is too strong to be true. +The `fit` method of :class:`NARX` uses the one-step-ahead prediction for training by default, +but the multiple-step-ahead prediction can be used by setting the parameter `coef_init`. + +.. rubric:: Examples + +* See :ref:`sphx_glr_auto_examples_plot_narx_msa.py` for an illustration of the multiple-step-ahead NARX model. diff --git a/doc/user_guide.rst b/doc/user_guide.rst index c5e32e2..fd4ecba 100644 --- a/doc/user_guide.rst +++ b/doc/user_guide.rst @@ -11,4 +11,5 @@ User Guide unsupervised.rst multioutput.rst redundancy.rst - ols_and_omp.rst \ No newline at end of file + ols_and_omp.rst + narx.rst diff --git a/examples/plot_narx.py b/examples/plot_narx.py index f739528..720bbcb 100644 --- a/examples/plot_narx.py +++ b/examples/plot_narx.py @@ -44,7 +44,7 @@ # %% # Build term libriary # ------------------- -# To build a polynomial NARX model, it is normally have two steps: +# To build a reduced polynomial NARX model, it is normally have two steps: # # #. Search the structure of the model, i.e., the terms in the model, e.g., # :math:`u_0(k-1)u_0(k-3)`, :math:`u_0(k-2)u_1(k-3)`, etc. @@ -115,7 +115,7 @@ # %% # Build NARX model # ---------------- -# As the polynomical NARX is a linear function of the nonlinear tems, +# As the reduced polynomial NARX is a linear function of the nonlinear tems, # the coefficient of each term can be easily estimated by oridnary least squares. # In the printed NARX model, it is found that :class:`FastCan` selects the correct # terms and the coefficients are close to the true values. diff --git a/examples/plot_narx_msa.py b/examples/plot_narx_msa.py new file mode 100644 index 0000000..a7cc04a --- /dev/null +++ b/examples/plot_narx_msa.py @@ -0,0 +1,182 @@ +""" +=========================== +Multi-step-ahead NARX model +=========================== + +.. currentmodule:: fastcan + +In this example, we will compare one-step-ahead NARX and multi-step-ahead NARX. +""" + +# Authors: Sikai Zhang +# SPDX-License-Identifier: MIT + +# %% +# Nonlinear system +# ---------------- +# +# `Duffing equation ` is used to +# generate simulated data. The mathematical model is given by +# +# .. math:: +# \ddot{y} + 0.1\dot{y} - y + 0.25y^3 = u +# +# where :math:`y` is the output signal and :math:`u` is the input signal, which is +# :math:`u(t) = 2.5\cos(2\pi t)`. +# +# The phase portraits of the Duffing equation are shown below. + +import matplotlib.pyplot as plt +import numpy as np +from scipy.integrate import odeint + + +def duffing_equation(y, t): + """Non-autonomous system""" + y1, y2 = y + u = 2.5 * np.cos(2 * np.pi * t) + dydt = [y2, -0.1 * y2 + y1 - 0.25 * y1**3 + u] + return dydt + + +def auto_duffing_equation(y, t): + """Autonomous system""" + y1, y2 = y + dydt = [y2, -0.1 * y2 + y1 - 0.25 * y1**3] + return dydt + + +dur = 10 +n_samples = 1000 + +y0 = None +if y0 is None: + n_init = 10 + x0 = np.linspace(0, 2, n_init) + y0_y = np.cos(np.pi * x0) + y0_x = np.sin(np.pi * x0) + y0 = np.c_[y0_x, y0_y] +else: + n_init = len(y0) + +t = np.linspace(0, dur, n_samples) +sol = np.zeros((n_init, n_samples, 2)) +for i in range(n_init): + sol[i] = odeint(auto_duffing_equation, y0[i], t) + +for i in range(n_init): + plt.plot(sol[i, :, 0], sol[i, :, 1], c="tab:blue") + +plt.title("Phase portraits of Duffing equation") +plt.xlabel("y(t)") +plt.ylabel("dy/dt(t)") +plt.show() + +# %% +# Generate training-test data +# --------------------------- +# +# In the phase portraits, it is shown that the system has two stable equilibria. +# We use one to generate training data and the other to generate test data. + +dur = 10 +n_samples = 1000 + +t = np.linspace(0, dur, n_samples) + +sol = odeint(duffing_equation, [0.6, 0.8], t) +u_train = 2.5 * np.cos(2 * np.pi * t).reshape(-1, 1) +y_train = sol[:, 0] + +sol = odeint(auto_duffing_equation, [0.6, -0.8], t) +u_test = 2.5 * np.cos(2 * np.pi * t).reshape(-1, 1) +y_test = sol[:, 0] + +# %% +# One-step-head VS. multi-step-ahead NARX +# --------------------------------------- +# +# First, we use :meth:`make_narx` to obtain the reduced NARX model. +# Then, the NARX model will be fitted with one-step-ahead predictor and +# multi-step-ahead predictor, respectively. Generally, the training of one-step-ahead +# (OSA) NARX is faster, while the multi-step-ahead (MSA) NARX is more accurate. + +from sklearn.metrics import r2_score + +from fastcan.narx import make_narx + +max_delay = 2 + +narx_model = make_narx( + X=u_train, + y=y_train, + n_features_to_select=10, + max_delay=max_delay, + poly_degree=3, + verbose=0, +) + + +def plot_prediction(ax, t, y_true, y_pred, title): + ax.plot(t, y_true, label="true") + ax.plot(t, y_pred, label="predicted") + ax.legend() + ax.set_title(f"{title} (R2: {r2_score(y_true, y_pred):.5f})") + ax.set_xlabel("t (s)") + ax.set_ylabel("y(t)") + + +narx_model.fit(u_train, y_train) +y_train_osa_pred = narx_model.predict(u_train, y_init=y_train[:max_delay]) +y_test_osa_pred = narx_model.predict(u_test, y_init=y_test[:max_delay]) + +narx_model.fit(u_train, y_train, coef_init="one_step_ahead") +y_train_msa_pred = narx_model.predict(u_train, y_init=y_train[:max_delay]) +y_test_msa_pred = narx_model.predict(u_test, y_init=y_test[:max_delay]) + +fig, ax = plt.subplots(2, 2, figsize=(8, 6)) +plot_prediction(ax[0, 0], t, y_train, y_train_osa_pred, "OSA NARX on Train") +plot_prediction(ax[0, 1], t, y_train, y_train_msa_pred, "MSA NARX on Train") +plot_prediction(ax[1, 0], t, y_test, y_test_osa_pred, "OSA NARX on Test") +plot_prediction(ax[1, 1], t, y_test, y_test_msa_pred, "MSA NARX on Test") +fig.tight_layout() +plt.show() + + +# %% +# Multiple measurement sessions +# ----------------------------- +# +# The plot above shows that the NARX model cannot capture the dynamics at +# the left equilibrium shown in the phase portraits. To improve the performance, let us +# combine the training and test data for model training to include the dynamics of both +# equilibria. Here, we need to insert `np.nan` to indicate the model that training data +# and test data are from different measurement sessions. The plot shows that the +# prediction performance of the NARX on test data has been largely improved. + +u_all = np.r_[u_train, [[np.nan]], u_test] +y_all = np.r_[y_train, [np.nan], y_test] +narx_model = make_narx( + X=u_all, + y=y_all, + n_features_to_select=10, + max_delay=max_delay, + poly_degree=3, + verbose=0, +) + +narx_model.fit(u_all, y_all) +y_train_osa_pred = narx_model.predict(u_train, y_init=y_train[:max_delay]) +y_test_osa_pred = narx_model.predict(u_test, y_init=y_test[:max_delay]) + +narx_model.fit(u_all, y_all, coef_init="one_step_ahead") +y_train_msa_pred = narx_model.predict(u_train, y_init=y_train[:max_delay]) +y_test_msa_pred = narx_model.predict(u_test, y_init=y_test[:max_delay]) + +fig, ax = plt.subplots(2, 2, figsize=(8, 6)) +plot_prediction(ax[0, 0], t, y_train, y_train_osa_pred, "OSA NARX on Train") +plot_prediction(ax[0, 1], t, y_train, y_train_msa_pred, "MSA NARX on Train") +plot_prediction(ax[1, 0], t, y_test, y_test_osa_pred, "OSA NARX on Test") +plot_prediction(ax[1, 1], t, y_test, y_test_msa_pred, "MSA NARX on Test") +fig.tight_layout() +plt.show() diff --git a/fastcan/narx.py b/fastcan/narx.py index d815b3c..37dd8fe 100644 --- a/fastcan/narx.py +++ b/fastcan/narx.py @@ -544,8 +544,9 @@ def _expression(self, X, y_hat, coef, intercept, k): return y_pred @staticmethod - def _predict(expression, X, y_init, coef, intercept, max_delay): + def _predict(expression, X, y_ref, coef, intercept, max_delay): n_samples = X.shape[0] + n_ref = len(y_ref) y_hat = np.zeros(n_samples) at_init = True init_k = 0 @@ -559,7 +560,7 @@ def _predict(expression, X, y_init, coef, intercept, max_delay): at_init = False if at_init: - y_hat[k] = y_init[k - init_k] + y_hat[k] = y_ref[k % n_ref] else: y_hat[k] = expression(X, y_hat, coef, intercept, k) if np.any(y_hat[k] > 1e20): @@ -578,7 +579,7 @@ def _residual( coef = coef_intercept[:-1] intercept = coef_intercept[-1] - y_hat = NARX._predict(expression, X, y[:max_delay], coef, intercept, max_delay) + y_hat = NARX._predict(expression, X, y, coef, intercept, max_delay) y_masked, y_hat_masked = _mask_missing_value(y, y_hat) @@ -599,8 +600,9 @@ def predict(self, X, y_init=None): X : array-like of shape (n_samples, `n_features_in_`) Samples. - y_init : array-like of shape (`max_delay`,), default=None + y_init : array-like of shape (`n_init`,), default=None The initial values for the prediction of y. + It should at least have one sample. Returns ------- @@ -614,11 +616,9 @@ def predict(self, X, y_init=None): y_init = np.zeros(self.max_delay_) else: y_init = column_or_1d(y_init, dtype=float) - if y_init.shape[0] != self.max_delay_: + if y_init.shape[0] < 1: raise ValueError( - "`y_init` should have the shape of " - "(`max_delay`,), i.e., " - f"({self.max_delay_},), " + "`y_init` should at least have one sample " f"but got {y_init.shape}." ) diff --git a/meson.build b/meson.build index 522ef8a..38594de 100644 --- a/meson.build +++ b/meson.build @@ -1,7 +1,7 @@ project( 'fastcan', 'c', 'cython', - version: '0.3.0', + version: '0.3.1', license: 'MIT', meson_version: '>= 1.1.0', default_options: [ diff --git a/pixi.lock b/pixi.lock index 28af7e8..d32dfcd 100644 --- a/pixi.lock +++ b/pixi.lock @@ -34,18 +34,18 @@ environments: - conda: https://conda.anaconda.org/conda-forge/linux-64/libzlib-1.3.1-hb9d3cd8_2.conda - conda: https://conda.anaconda.org/conda-forge/noarch/meson-1.6.1-pyhd8ed1ab_0.conda - conda: https://conda.anaconda.org/conda-forge/noarch/meson-python-0.17.1-pyh70fd9c4_1.conda - 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libzlib 1.3.1 hd23fc13_2 - arch: x86_64 - platform: osx license: Zlib license_family: Other purls: [] @@ -6118,8 +5696,6 @@ packages: depends: - __osx >=11.0 - libzlib 1.3.1 h8359307_2 - arch: arm64 - platform: osx license: Zlib license_family: Other purls: [] @@ -6131,8 +5707,6 @@ packages: depends: - __osx >=10.9 - libzlib >=1.2.13,<2.0.0a0 - arch: x86_64 - platform: osx license: BSD-3-Clause license_family: BSD purls: [] @@ -6144,8 +5718,6 @@ packages: depends: - __osx >=11.0 - libzlib >=1.2.13,<2.0.0a0 - arch: arm64 - platform: osx license: BSD-3-Clause license_family: BSD purls: [] diff --git a/pyproject.toml b/pyproject.toml index 40f5ad2..9b6d9d0 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -1,6 +1,6 @@ [project] name = "fastcan" -version = "0.3.0" +version = "0.3.1" description = "A fast canonical-correlation-based feature selection method" authors = [ { name = "Matthew Sikai Zhang", email = "matthew.szhang91@gmail.com" }, @@ -117,10 +117,10 @@ doc-clean = { cmd = "rm -rf $BUILDDIR generated auto_examples", cwd = "doc", env [tool.pixi.feature.nogil.tasks] nogil-build = { cmd = "uv pip install --editable . --verbose --no-build-isolation --config-settings editable-verbose=true" } -nogil-h = { cmd = "python -Xgil=0 -m timeit -n 5 -s 'import numpy as np; from fastcan import FastCan; X = np.random.rand(3000, 100); y = np.random.rand(3000, 20)' 's = FastCan(100, verbose=0).fit(X, y)'", depends_on = [ +nogil-h = { cmd = "python -Xgil=0 -m timeit -n 5 -s 'import numpy as np; from fastcan import FastCan; X = np.random.rand(3000, 100); y = np.random.rand(3000, 20)' 's = FastCan(100, verbose=0).fit(X, y)'", depends-on = [ "nogil-build", ] } -nogil-eta = { cmd = "python -Xgil=0 -m timeit -n 5 -s 'import numpy as np; from fastcan import FastCan; X = np.random.rand(3000, 100); y = np.random.rand(3000, 20)' 's = FastCan(100, eta=True, verbose=0).fit(X, y)'", depends_on = [ +nogil-eta = { cmd = "python -Xgil=0 -m timeit -n 5 -s 'import numpy as np; from fastcan import FastCan; X = np.random.rand(3000, 100); y = np.random.rand(3000, 20)' 's = FastCan(100, eta=True, verbose=0).fit(X, y)'", depends-on = [ "nogil-build", ] } @@ -148,18 +148,6 @@ exclude = ''' ''' [tool.ruff] -# all rules can be found here: https://beta.ruff.rs/docs/rules/ -lint.select = ["E", "F", "W", "I"] - -lint.ignore = [ - # space before : (needed for how black formats slicing) - "E203", - # do not assign a lambda expression, use a def - "E731", - # do not use variables named 'l', 'O', or 'I' - "E741", -] - # max line length for black line-length = 88 @@ -172,6 +160,19 @@ exclude = [ "build", ] +[tool.ruff.lint] +# all rules can be found here: https://beta.ruff.rs/docs/rules/ +select = ["E", "F", "W", "I"] + +ignore = [ + # space before : (needed for how black formats slicing) + "E203", + # do not assign a lambda expression, use a def + "E731", + # do not use variables named 'l', 'O', or 'I' + "E741", +] + [tool.ruff.lint.per-file-ignores] # It's fine not to put the import at the top of the file in the examples # folder. diff --git a/tests/test_narx.py b/tests/test_narx.py index 122af7f..1137fb6 100644 --- a/tests/test_narx.py +++ b/tests/test_narx.py @@ -11,26 +11,35 @@ def test_narx_is_sklearn_estimator(): check_estimator(NARX()) + def test_poly_ids(): with pytest.raises(ValueError, match=r"The output that would result from the .*"): make_poly_ids(10, 1000) + def test_time_ids(): with pytest.raises(ValueError, match=r"The length of `include_zero_delay`.*"): make_time_shift_ids(3, 2, [False, True, False, True]) + @pytest.mark.parametrize("nan", [False, True]) def test_narx(nan): rng = np.random.default_rng(12345) n_samples = 1000 max_delay = 3 e = rng.normal(0, 0.1, n_samples) - u0 = rng.uniform(0, 1, n_samples+max_delay) + u0 = rng.uniform(0, 1, n_samples + max_delay) u1 = rng.normal(0, 0.1, n_samples) - y = np.zeros(n_samples+max_delay) - for i in range(max_delay, n_samples+max_delay): - y[i] = 0.5*y[i-1]+0.3*u0[i]**2+2*u0[i-1]*u0[i-3]+1.5*u0[i-2]*u1[i-max_delay]+1 - y = y[max_delay:]+e + y = np.zeros(n_samples + max_delay) + for i in range(max_delay, n_samples + max_delay): + y[i] = ( + 0.5 * y[i - 1] + + 0.3 * u0[i] ** 2 + + 2 * u0[i - 1] * u0[i - 3] + + 1.5 * u0[i - 2] * u1[i - max_delay] + + 1 + ) + y = y[max_delay:] + e X = np.c_[u0[max_delay:], u1] if nan: @@ -47,8 +56,7 @@ def test_narx(nan): narx_default = make_narx(X=X, y=y, **params) - assert narx_default.poly_ids.shape[0] ==\ - params["n_features_to_select"] + assert narx_default.poly_ids.shape[0] == params["n_features_to_select"] params["include_zero_delay"] = [False, True] narx_0_delay = make_narx(X=X, y=y, **params) @@ -70,39 +78,34 @@ def test_narx(nan): params["refine_drop"] = 1 params["refine_max_iter"] = 10 narx_drop = make_narx(X=X, y=y, **params) - assert np.any( - narx_drop.poly_ids !=\ - narx_static.poly_ids - ) + assert np.any(narx_drop.poly_ids != narx_static.poly_ids) narx_drop_coef = narx_drop.fit(X, y).coef_ - time_shift_ids = make_time_shift_ids(X.shape[1]+1, 5, include_zero_delay=False) + time_shift_ids = make_time_shift_ids(X.shape[1] + 1, 5, include_zero_delay=False) poly_ids = make_poly_ids(time_shift_ids.shape[0], 2) narx_osa = NARX(time_shift_ids=time_shift_ids, poly_ids=poly_ids).fit(X, y) assert narx_osa.coef_.size == poly_ids.shape[0] - narx_osa_msa = narx_drop.fit( - X, y, coef_init="one_step_ahead" - ) + narx_osa_msa = narx_drop.fit(X, y, coef_init="one_step_ahead") narx_osa_msa_coef = narx_osa_msa.coef_ assert np.any(narx_osa_msa_coef != narx_drop_coef) narx_array_init_msa = narx_osa_msa.fit( - X, y, coef_init=np.zeros(narx_osa_msa_coef.size+1) + X, y, coef_init=np.zeros(narx_osa_msa_coef.size + 1) ) assert np.any(narx_array_init_msa.coef_ != narx_osa_msa_coef) - y_init = [1]*narx_array_init_msa.max_delay_ + y_init = [1] * narx_array_init_msa.max_delay_ y_hat = narx_array_init_msa.predict(X, y_init=y_init) assert_array_equal(y_hat[:3], y_init) print_narx(narx_array_init_msa) - with pytest.raises(ValueError, match=r"`y_init` should have the shape of .*"): - narx_array_init_msa.predict(X, y_init=[1]*(narx_array_init_msa.max_delay_-1)) + with pytest.raises(ValueError, match=r"`y_init` should at least have one .*"): + narx_array_init_msa.predict(X, y_init=[]) with pytest.raises(ValueError, match=r"`coef_init` should have the shape of .*"): narx_array_init_msa.fit(X, y, coef_init=np.zeros(narx_osa_msa_coef.size)) - time_shift_ids = make_time_shift_ids(X.shape[1]+2, 3, include_zero_delay=False) + time_shift_ids = make_time_shift_ids(X.shape[1] + 2, 3, include_zero_delay=False) poly_ids = make_poly_ids(time_shift_ids.shape[0], 2) with pytest.raises(ValueError, match=r"The element x of the first column of tim.*"): narx_osa = NARX(time_shift_ids=time_shift_ids, poly_ids=poly_ids).fit(X, y) @@ -119,8 +122,7 @@ def test_narx(nan): with pytest.raises(ValueError, match=r"The element x of the second column of ti.*"): narx_osa = NARX(time_shift_ids=time_shift_ids, poly_ids=poly_ids).fit(X, y) - - time_shift_ids = make_time_shift_ids(X.shape[1]+1, 3, include_zero_delay=False) - poly_ids = make_poly_ids(time_shift_ids.shape[0]+1, 2) + time_shift_ids = make_time_shift_ids(X.shape[1] + 1, 3, include_zero_delay=False) + poly_ids = make_poly_ids(time_shift_ids.shape[0] + 1, 2) with pytest.raises(ValueError, match=r"The element x of poly_ids should .*"): narx_osa = NARX(time_shift_ids=time_shift_ids, poly_ids=poly_ids).fit(X, y)