From ba2b84c5203b4f1f5c8f3360db4745f9f0eaae22 Mon Sep 17 00:00:00 2001
From: SIKAI ZHANG <34108862+MatthewSZhang@users.noreply.github.com>
Date: Fri, 3 Jan 2025 16:51:56 +0800
Subject: [PATCH] DOC add example for basic of NARX

---
 examples/plot_narx.py | 151 +++++++
 fastcan/narx.py       |  48 +--
 pixi.lock             | 943 +++++++++++++++++++++---------------------
 tests/test_narx.py    |  14 +-
 4 files changed, 649 insertions(+), 507 deletions(-)
 create mode 100644 examples/plot_narx.py

diff --git a/examples/plot_narx.py b/examples/plot_narx.py
new file mode 100644
index 0000000..d056962
--- /dev/null
+++ b/examples/plot_narx.py
@@ -0,0 +1,151 @@
+"""
+===============================================
+Nonlinear AutoRegressive eXogenous (NARX) model
+===============================================
+
+.. currentmodule:: fastcan
+
+In this example, we illustrate how to build a polynomial
+NARX model for time series prediction.
+"""
+
+# Authors: Sikai Zhang
+# SPDX-License-Identifier: MIT
+
+# %%
+# Prepare data
+# ------------
+#
+# First, a simulated time series dataset is generated from the following nonlinear
+# system.
+#
+# .. 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.
+
+
+import numpy as np
+
+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)
+u1 = rng.normal(0, 0.1, n_samples+max_delay)
+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-3]+1
+y = y[max_delay:]+e
+X = np.c_[u0[max_delay:], u1[max_delay:]]
+
+# %%
+# Build term libriary
+# -------------------
+#
+# To build a polynomial NARX model, it is normally have two steps:
+#
+# 1. 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.
+# 2. Learn the coefficients before the terms.
+#
+# To search the structure of the model, the candidate term libriary should be
+# constructed.
+#
+# 1. Time-shifted variables: the raw input-output data, i.e., :math:`u0(k)`,
+# :math:`u1(k)`, and :math:`y(k)`, are converted into :math:`u0(k-1)`, :math:`u1(k-2)`,
+# etc.
+# 2. Nonlinear terms: the time-shifted variables are onverted to nonlinear terms
+# via polynomial basis functions, e.g., :math:`u_0(k-1)^2`, :math:`u_0(k-1)u_0(k-3)`,
+# etc.
+#
+#   .. rubric:: References
+#
+#   * `"Nonlinear system identification: NARMAX methods in the time, frequency,
+#     and spatio-temporal domains" <https://doi.org/10.1002/9781118535561>`_
+#     Billings, S. A. John Wiley & Sons, (2013).
+#
+#
+# Make time-shifted variables
+# ^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+from fastcan.narx import make_time_shift_features, make_time_shift_ids
+
+time_shift_ids = make_time_shift_ids(
+    n_features=3, # Number of inputs (2) and output (1) signals
+    max_delay=3, # Maximum time delays
+    include_zero_delay = [True, True, False], # Whether to include zero delay
+    # for each signal. The output signal should not have zero delay.
+)
+
+time_shift_vars = make_time_shift_features(np.c_[X, y], time_shift_ids)
+
+# %%
+# Make nonlinear terms
+# ^^^^^^^^^^^^^^^^^^^^
+
+from fastcan.narx import make_poly_features, make_poly_ids
+
+poly_ids = make_poly_ids(
+    n_features=time_shift_vars.shape[1], # Number of time-shifted variables
+    degree=2, # Maximum polynomial degree
+)
+
+poly_terms = make_poly_features(time_shift_vars, poly_ids)
+
+# %%
+# Term selection
+# --------------
+# After the term library is constructed, the terms can be selected by :class:`FastCan`,
+# whose :math:`X` is the nonlinear terms and :math:`y` is the output signal.
+
+from fastcan import FastCan
+
+selector = FastCan(
+    n_features_to_select=4, # 4 terms should be selected
+).fit(poly_terms, y)
+
+support = selector.get_support()
+selected_poly_ids = poly_ids[support]
+
+
+# %%
+# Build NARX model
+# ----------------
+# As the polynomical NARX is a linear function of the nonlinear tems,
+# the coefficient of each term can be easily estimated by oridnary least squares.
+
+from fastcan.narx import NARX, print_narx
+
+narx_model = NARX(
+    time_shift_ids=time_shift_ids,
+    poly_ids = selected_poly_ids,
+)
+
+narx_model.fit(X, y)
+
+# In the printed NARX model, it is found that :class:`FastCan` selects the correct
+# terms and the coefficients are close to the true values.
+print_narx(narx_model)
+
+# %%
+# Plot NARX prediction performance
+# --------------------------------
+
+import matplotlib.pyplot as plt
+from sklearn.metrics import r2_score
+
+y_pred = narx_model.predict(
+    X[:100],
+    y_init=y[:narx_model.max_delay_] # Set the initial values of the prediction to
+    # the true values
+)
+
+plt.plot(y[:100], label="True")
+plt.plot(y_pred, label="Predicted")
+plt.xlabel("Time index k")
+plt.legend()
+plt.title(f"NARX prediction R-squared: {r2_score(y[:100], y_pred):.5f}")
+plt.show()
diff --git a/fastcan/narx.py b/fastcan/narx.py
index 879483e..d815b3c 100644
--- a/fastcan/narx.py
+++ b/fastcan/narx.py
@@ -274,9 +274,9 @@ def _mask_missing_value(*arr):
     return tuple([x[mask_nomissing] for x in arr])
 
 
-class Narx(RegressorMixin, BaseEstimator):
+class NARX(RegressorMixin, BaseEstimator):
     """The Nonlinear Autoregressive eXogenous (NARX) model class.
-    For example, a (polynomial) Narx model is like
+    For example, a (polynomial) NARX model is like
     y(t) = y(t-1)*u(t-1) + u(t-1)^2 + u(t-2) + 1.5
     where y(t) is the system output at time t,
     u(t) is the system input at time t,
@@ -333,7 +333,7 @@ class Narx(RegressorMixin, BaseEstimator):
     Examples
     --------
     >>> import numpy as np
-    >>> from fastcan.narx import Narx, print_narx
+    >>> from fastcan.narx import NARX, print_narx
     >>> rng = np.random.default_rng(12345)
     >>> n_samples = 1000
     >>> max_delay = 3
@@ -351,7 +351,7 @@ class Narx(RegressorMixin, BaseEstimator):
     >>> poly_ids = [[0, 2], # 1*u(k-1)
     ...             [0, 4], # 1*y(k-1)
     ...             [1, 3]] # u(k-1)*u(k-3)
-    >>> narx = Narx(time_shift_ids=time_shift_ids,
+    >>> narx = NARX(time_shift_ids=time_shift_ids,
     ...             poly_ids=poly_ids).fit(X, y, coef_init="one_step_ahead")
     >>> print_narx(narx)
     |        Term        |   Coef   |
@@ -397,16 +397,16 @@ def fit(self, X, y, sample_weight=None, coef_init=None, **params):
 
         sample_weight : array-like of shape (n_samples,), default=None
             Individual weights for each sample, which are used for a One-Step-Ahead
-            Narx.
+            NARX.
 
         coef_init : array-like of shape (n_terms,), default=None
             The initial values of coefficients and intercept for optimization.
-            When `coef_init` is None, the model will be a One-Step-Ahead Narx.
+            When `coef_init` is None, the model will be a One-Step-Ahead NARX.
             When `coef_init` is `one_step_ahead`, the model will be a Multi-Step-Ahead
-            Narx whose coefficients and intercept are initialized by the a
-            One-Step-Ahead Narx.
+            NARX whose coefficients and intercept are initialized by the a
+            One-Step-Ahead NARX.
             When `coef_init` is an array, the model will be a Multi-Step-Ahead
-            Narx whose coefficients and intercept are initialized by the array.
+            NARX whose coefficients and intercept are initialized by the array.
 
             .. note::
                 When coef_init is None, missing values (i.e., np.nan) are allowed.
@@ -477,7 +477,7 @@ def fit(self, X, y, sample_weight=None, coef_init=None, **params):
         n_terms = self.poly_ids_.shape[0] + 1
 
         if isinstance(coef_init, (type(None), str)):
-            # fit a one-step-ahead Narx model
+            # fit a one-step-ahead NARX model
             xy_hstack = np.c_[X, y]
             osa_narx = LinearRegression()
             time_shift_vars = make_time_shift_features(xy_hstack, self.time_shift_ids_)
@@ -508,7 +508,7 @@ def fit(self, X, y, sample_weight=None, coef_init=None, **params):
                 )
 
         lsq = least_squares(
-            Narx._residual,
+            NARX._residual,
             x0=coef_init,
             args=(
                 self._expression,
@@ -578,7 +578,7 @@ 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[:max_delay], coef, intercept, max_delay)
 
         y_masked, y_hat_masked = _mask_missing_value(y, y_hat)
 
@@ -622,7 +622,7 @@ def predict(self, X, y_init=None):
                     f"but got {y_init.shape}."
                 )
 
-        return Narx._predict(
+        return NARX._predict(
             self._expression,
             X,
             y_init,
@@ -639,7 +639,7 @@ def __sklearn_tags__(self):
 
 @validate_params(
     {
-        "narx": [Narx],
+        "narx": [NARX],
         "term_space": [Interval(Integral, 1, None, closed="left")],
         "coef_space": [Interval(Integral, 1, None, closed="left")],
         "float_precision": [Interval(Integral, 0, None, closed="left")],
@@ -652,12 +652,12 @@ def print_narx(
     coef_space=10,
     float_precision=3,
 ):
-    """Print a Narx model as a Table which contains Term and Coef.
+    """Print a NARX model as a Table which contains Term and Coef.
 
     Parameters
     ----------
-    narx : Narx model
-        The Narx model to be printed.
+    narx : NARX model
+        The NARX model to be printed.
 
     term_space: int, default=20
         The space for the column of Term.
@@ -671,14 +671,14 @@ def print_narx(
     Returns
     -------
     table : str
-        The table of terms and coefficients of the Narx model.
+        The table of terms and coefficients of the NARX model.
 
     Examples
     --------
     >>> from sklearn.datasets import load_diabetes
-    >>> from fastcan.narx import print_narx, Narx
+    >>> from fastcan.narx import print_narx, NARX
     >>> X, y = load_diabetes(return_X_y=True)
-    >>> print_narx(Narx().fit(X, y), term_space=10, coef_space=5, float_precision=0)
+    >>> print_narx(NARX().fit(X, y), term_space=10, coef_space=5, float_precision=0)
     |   Term   |Coef |
     ==================
     |Intercept | 152 |
@@ -765,7 +765,7 @@ def make_narx(
     refine_max_iter=None,
     **params,
 ):
-    """Find `time_shift_ids` and `poly_ids` for a Narx model.
+    """Find `time_shift_ids` and `poly_ids` for a NARX model.
 
     Parameters
     ----------
@@ -810,8 +810,8 @@ def make_narx(
 
     Returns
     -------
-    narx : Narx
-        Narx instance.
+    narx : NARX
+        NARX instance.
 
     Examples
     --------
@@ -912,4 +912,4 @@ def make_narx(
         - 1
     )
 
-    return Narx(time_shift_ids=time_shift_ids, poly_ids=poly_ids)
+    return NARX(time_shift_ids=time_shift_ids, poly_ids=poly_ids)
diff --git a/pixi.lock b/pixi.lock
index 51f2613..b3cd3b2 100644
--- a/pixi.lock
+++ b/pixi.lock
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-      - conda: https://conda.anaconda.org/conda-forge/noarch/click-8.1.7-unix_pyh707e725_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/ca-certificates-2024.12.14-hbcca054_0.conda
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/coverage-7.6.9-py313h8060acc_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/coverage-7.6.10-py313h8060acc_0.conda
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/liblapack-3.9.0-25_linux64_openblas.conda
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-      - conda: https://conda.anaconda.org/conda-forge/linux-64/ruff-0.8.3-py313he87ea70_0.conda
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   constrains:
-  - liblapack 3.9.0 25_linux64_openblas
-  - libcblas 3.9.0 25_linux64_openblas
+  - libcblas 3.9.0 26_linux64_openblas
+  - liblapack 3.9.0 26_linux64_openblas
+  - liblapacke 3.9.0 26_linux64_openblas
   - blas * openblas
-  - liblapacke 3.9.0 25_linux64_openblas
   arch: x86_64
   platform: linux
   license: BSD-3-Clause
   license_family: BSD
   purls: []
-  size: 15677
-  timestamp: 1729642900350
-- conda: https://conda.anaconda.org/conda-forge/osx-64/libblas-3.9.0-25_osx64_openblas.conda
-  build_number: 25
-  sha256: 1b22b5322a311a775bca637b26317645cf07e35f125cede9278c6c45db6e7105
-  md5: da0a6f87958893e1d2e2bbc7e7a6541f
+  size: 16393
+  timestamp: 1734432564346
+- conda: https://conda.anaconda.org/conda-forge/osx-64/libblas-3.9.0-26_osx64_openblas.conda
+  build_number: 26
+  sha256: 4e860b60c06be04f2c37c45def870e4ea5268f568547b80a8f69ad6ecddb6f31
+  md5: 2f03da7a6d52d98bbea1f7390d6997bf
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   - libopenblas >=0.3.28,<1.0a0
   constrains:
-  - liblapack 3.9.0 25_osx64_openblas
-  - liblapacke 3.9.0 25_osx64_openblas
+  - libcblas 3.9.0 26_osx64_openblas
+  - liblapack 3.9.0 26_osx64_openblas
   - blas * openblas
-  - libcblas 3.9.0 25_osx64_openblas
+  - liblapacke 3.9.0 26_osx64_openblas
   arch: x86_64
   platform: osx
   license: BSD-3-Clause
   license_family: BSD
   purls: []
-  size: 15952
-  timestamp: 1729643159199
-- conda: https://conda.anaconda.org/conda-forge/osx-arm64/libblas-3.9.0-25_osxarm64_openblas.conda
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-  md5: f8cf4d920ff36ce471619010eff59cac
+  size: 16611
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+- conda: https://conda.anaconda.org/conda-forge/osx-arm64/libblas-3.9.0-26_osxarm64_openblas.conda
+  build_number: 26
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   - libopenblas >=0.3.28,<0.3.29.0a0
   - libopenblas >=0.3.28,<1.0a0
   constrains:
+  - liblapack 3.9.0 26_osxarm64_openblas
+  - liblapacke 3.9.0 26_osxarm64_openblas
+  - libcblas 3.9.0 26_osxarm64_openblas
   - blas * openblas
-  - liblapack 3.9.0 25_osxarm64_openblas
-  - liblapacke 3.9.0 25_osxarm64_openblas
-  - libcblas 3.9.0 25_osxarm64_openblas
   arch: arm64
   platform: osx
   license: BSD-3-Clause
   license_family: BSD
   purls: []
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-- conda: https://conda.anaconda.org/conda-forge/win-64/libblas-3.9.0-25_win64_mkl.conda
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-  md5: 499208e81242efb6e5abc7366c91c816
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+  - mkl 2024.2.2 h66d3029_15
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+  - liblapack 3.9.0 26_win64_mkl
   - blas * mkl
-  - libcblas 3.9.0 25_win64_mkl
-  - liblapack 3.9.0 25_win64_mkl
-  - liblapacke 3.9.0 25_win64_mkl
+  - libcblas 3.9.0 26_win64_mkl
   arch: x86_64
   platform: win
   license: BSD-3-Clause
   license_family: BSD
   purls: []
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-  md5: 5dbd1b0fc0d01ec5e0e1fbe667281a11
+  size: 3733122
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+- conda: https://conda.anaconda.org/conda-forge/linux-64/libcblas-3.9.0-26_linux64_openblas.conda
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+  - libblas 3.9.0 26_linux64_openblas
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+  - liblapack 3.9.0 26_linux64_openblas
+  - liblapacke 3.9.0 26_linux64_openblas
   - blas * openblas
-  - liblapacke 3.9.0 25_linux64_openblas
   arch: x86_64
   platform: linux
   license: BSD-3-Clause
   license_family: BSD
   purls: []
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-  md5: ab304b75ea67f850cf7adf9156e3f62f
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+  - libblas 3.9.0 26_osx64_openblas
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-  - liblapacke 3.9.0 25_osx64_openblas
+  - liblapack 3.9.0 26_osx64_openblas
   - blas * openblas
+  - liblapacke 3.9.0 26_osx64_openblas
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   platform: osx
   license: BSD-3-Clause
   license_family: BSD
   purls: []
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-  md5: 4df0fae81f0b5bf47d48c882b086da11
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+- conda: https://conda.anaconda.org/conda-forge/osx-arm64/libcblas-3.9.0-26_osxarm64_openblas.conda
+  build_number: 26
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+  md5: a0e9980fe12d42f6d0c0ec009f67e948
   depends:
-  - libblas 3.9.0 25_osxarm64_openblas
+  - libblas 3.9.0 26_osxarm64_openblas
   constrains:
+  - liblapack 3.9.0 26_osxarm64_openblas
+  - liblapacke 3.9.0 26_osxarm64_openblas
   - blas * openblas
-  - liblapack 3.9.0 25_osxarm64_openblas
-  - liblapacke 3.9.0 25_osxarm64_openblas
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+- conda: https://conda.anaconda.org/conda-forge/win-64/libcblas-3.9.0-26_win64_mkl.conda
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-  - libblas 3.9.0 25_win64_mkl
+  - libblas 3.9.0 26_win64_mkl
   constrains:
+  - liblapacke 3.9.0 26_win64_mkl
+  - liblapack 3.9.0 26_win64_mkl
   - blas * mkl
-  - liblapack 3.9.0 25_win64_mkl
-  - liblapacke 3.9.0 25_win64_mkl
   arch: x86_64
   platform: win
   license: BSD-3-Clause
   license_family: BSD
   purls: []
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 - conda: https://conda.anaconda.org/conda-forge/osx-64/libclang-cpp17-17.0.6-default_hb173f14_7.conda
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-- conda: https://conda.anaconda.org/conda-forge/osx-64/libcxx-19.1.5-hf95d169_0.conda
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-  md5: a20d4ea6839510372d1eeb8532b09acf
+- conda: https://conda.anaconda.org/conda-forge/osx-64/libcxx-19.1.6-hf95d169_1.conda
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+  md5: 1bad6c181a0799298aad42fc5a7e98b7
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   license_family: Apache
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-- conda: https://conda.anaconda.org/conda-forge/osx-arm64/libcxx-19.1.5-ha82da77_0.conda
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+- conda: https://conda.anaconda.org/conda-forge/osx-arm64/libcxx-19.1.6-ha82da77_1.conda
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+  md5: ce5252d8db110cdb4ae4173d0a63c7c5
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   - __osx >=11.0
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@@ -2197,8 +2192,8 @@ packages:
   license: Apache-2.0 WITH LLVM-exception
   license_family: Apache
   purls: []
-  size: 519819
-  timestamp: 1733291654212
+  size: 520992
+  timestamp: 1734494699681
 - conda: https://conda.anaconda.org/conda-forge/osx-64/libcxx-devel-17.0.6-h8f8a49f_6.conda
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-  md5: 4dc03a53fc69371a6158d0ed37214cd3
+- conda: https://conda.anaconda.org/conda-forge/linux-64/liblapack-3.9.0-26_linux64_openblas.conda
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   depends:
-  - libblas 3.9.0 25_linux64_openblas
+  - libblas 3.9.0 26_linux64_openblas
   constrains:
-  - liblapacke 3.9.0 25_linux64_openblas
-  - libcblas 3.9.0 25_linux64_openblas
+  - libcblas 3.9.0 26_linux64_openblas
+  - liblapacke 3.9.0 26_linux64_openblas
   - blas * openblas
   arch: x86_64
   platform: linux
   license: BSD-3-Clause
   license_family: BSD
   purls: []
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-- conda: https://conda.anaconda.org/conda-forge/osx-64/liblapack-3.9.0-25_osx64_openblas.conda
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-  md5: dda0e24b4605ebbd381e48606a107bed
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+- conda: https://conda.anaconda.org/conda-forge/osx-64/liblapack-3.9.0-26_osx64_openblas.conda
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-  - libblas 3.9.0 25_osx64_openblas
+  - libblas 3.9.0 26_osx64_openblas
   constrains:
-  - liblapacke 3.9.0 25_osx64_openblas
+  - libcblas 3.9.0 26_osx64_openblas
   - blas * openblas
-  - libcblas 3.9.0 25_osx64_openblas
+  - liblapacke 3.9.0 26_osx64_openblas
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   platform: osx
   license: BSD-3-Clause
   license_family: BSD
   purls: []
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-- conda: https://conda.anaconda.org/conda-forge/osx-arm64/liblapack-3.9.0-25_osxarm64_openblas.conda
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+- conda: https://conda.anaconda.org/conda-forge/osx-arm64/liblapack-3.9.0-26_osxarm64_openblas.conda
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-  - libblas 3.9.0 25_osxarm64_openblas
+  - libblas 3.9.0 26_osxarm64_openblas
   constrains:
+  - liblapacke 3.9.0 26_osxarm64_openblas
+  - libcblas 3.9.0 26_osxarm64_openblas
   - blas * openblas
-  - liblapacke 3.9.0 25_osxarm64_openblas
-  - libcblas 3.9.0 25_osxarm64_openblas
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-  - libblas 3.9.0 25_win64_mkl
+  - libblas 3.9.0 26_win64_mkl
   constrains:
+  - liblapacke 3.9.0 26_win64_mkl
   - blas * mkl
-  - libcblas 3.9.0 25_win64_mkl
-  - liblapacke 3.9.0 25_win64_mkl
+  - libcblas 3.9.0 26_win64_mkl
   arch: x86_64
   platform: win
   license: BSD-3-Clause
   license_family: BSD
   purls: []
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+- conda: https://conda.anaconda.org/conda-forge/osx-64/llvm-openmp-19.1.6-ha54dae1_0.conda
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+  md5: 4fe4d62071f8a3322ffb6588b49ccbb8
   depends:
   - __osx >=10.13
   constrains:
-  - openmp 19.1.5|19.1.5.*
+  - openmp 19.1.6|19.1.6.*
   arch: x86_64
   platform: osx
   license: Apache-2.0 WITH LLVM-exception
   license_family: APACHE
   purls: []
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-- conda: https://conda.anaconda.org/conda-forge/osx-arm64/llvm-openmp-19.1.5-hdb05f8b_0.conda
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-  md5: f2c2e187a1d2637d282e34dc92021a70
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+  timestamp: 1734520356844
+- conda: https://conda.anaconda.org/conda-forge/osx-arm64/llvm-openmp-19.1.6-hdb05f8b_0.conda
+  sha256: a0f3e9139ab16f0a67b9d2bbabc15b78977168f4a5b5503fed4962dcb9a96102
+  md5: 34fdeffa0555a1a56f38839415cc066c
   depends:
   - __osx >=11.0
   constrains:
-  - openmp 19.1.5|19.1.5.*
+  - openmp 19.1.6|19.1.6.*
   arch: arm64
   platform: osx
   license: Apache-2.0 WITH LLVM-exception
   license_family: APACHE
   purls: []
-  size: 281120
-  timestamp: 1733376089600
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 - conda: https://conda.anaconda.org/conda-forge/osx-64/llvm-tools-17.0.6-hbedff68_1.conda
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@@ -3055,10 +3050,10 @@ packages:
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   requires_python: '>=3.9'
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+- pypi: https://files.pythonhosted.org/packages/0d/c4/87b6ad2723070511a411ea719f9c70fde64605423b184face4e94986de9d/matplotlib-3.10.0-cp313-cp313-macosx_11_0_arm64.whl
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+- pypi: https://files.pythonhosted.org/packages/de/7c/7433122d1cfadc740f577cb55526fdc39129a648ac65ce64db2eb7209277/pillow-11.1.0-cp313-cp313-manylinux_2_28_x86_64.whl
   name: pillow
-  version: 11.0.0
-  sha256: 8ba470552b48e5835f1d23ecb936bb7f71d206f9dfeee64245f30c3270b994de
+  version: 11.1.0
+  sha256: 3764d53e09cdedd91bee65c2527815d315c6b90d7b8b79759cc48d7bf5d4f114
   requires_dist:
   - furo ; extra == 'docs'
   - olefile ; extra == 'docs'
@@ -3752,7 +3742,7 @@ packages:
   - olefile ; extra == 'fpx'
   - olefile ; extra == 'mic'
   - check-manifest ; extra == 'tests'
-  - coverage ; extra == 'tests'
+  - coverage>=7.4.2 ; extra == 'tests'
   - defusedxml ; extra == 'tests'
   - markdown2 ; extra == 'tests'
   - olefile ; extra == 'tests'
@@ -3761,6 +3751,7 @@ packages:
   - pytest ; extra == 'tests'
   - pytest-cov ; extra == 'tests'
   - pytest-timeout ; extra == 'tests'
+  - trove-classifiers>=2024.10.12 ; extra == 'tests'
   - typing-extensions ; python_full_version < '3.10' and extra == 'typing'
   - defusedxml ; extra == 'xmp'
   requires_python: '>=3.9'
@@ -3786,9 +3777,9 @@ packages:
   - pkg:pypi/pluggy?source=hash-mapping
   size: 23595
   timestamp: 1733222855563
-- conda: https://conda.anaconda.org/conda-forge/linux-64/psutil-6.1.0-py313h536fd9c_0.conda
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-  md5: b50a00ebd2fda55306b8a095363ce27f
+- conda: https://conda.anaconda.org/conda-forge/linux-64/psutil-6.1.1-py313h536fd9c_0.conda
+  sha256: c235557ce853c2e986c014d1eb2bd9a97103a3129db9da055c6b767d404e0713
+  md5: 79969031e331ecd8036a7c1992b64f9b
   depends:
   - __glibc >=2.17,<3.0.a0
   - libgcc >=13
@@ -3800,11 +3791,11 @@ packages:
   license_family: BSD
   purls:
   - pkg:pypi/psutil?source=hash-mapping
-  size: 494158
-  timestamp: 1729847232458
-- conda: https://conda.anaconda.org/conda-forge/osx-64/psutil-6.1.0-py313hb558fbc_0.conda
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-  md5: 6b9bcae4917442ec9054a5b6a859452b
+  size: 495006
+  timestamp: 1735327440037
+- conda: https://conda.anaconda.org/conda-forge/osx-64/psutil-6.1.1-py313h63b0ddb_0.conda
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+  md5: 8538f25c72edf35a53a7281bb7501209
   depends:
   - __osx >=10.13
   - python >=3.13,<3.14.0a0
@@ -3815,11 +3806,11 @@ packages:
   license_family: BSD
   purls:
   - pkg:pypi/psutil?source=hash-mapping
-  size: 501944
-  timestamp: 1729847219864
-- conda: https://conda.anaconda.org/conda-forge/osx-arm64/psutil-6.1.0-py313h63a2874_0.conda
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-  md5: 6f4dae78857fd194485497ed0a6762ab
+  size: 501460
+  timestamp: 1735327516357
+- conda: https://conda.anaconda.org/conda-forge/osx-arm64/psutil-6.1.1-py313h90d716c_0.conda
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+  md5: e5ac5c32237fa39e3f3e682857346366
   depends:
   - __osx >=11.0
   - python >=3.13,<3.14.0a0
@@ -3831,11 +3822,11 @@ packages:
   license_family: BSD
   purls:
   - pkg:pypi/psutil?source=hash-mapping
-  size: 501427
-  timestamp: 1729847280285
-- conda: https://conda.anaconda.org/conda-forge/win-64/psutil-6.1.0-py313ha7868ed_0.conda
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-  md5: d13841485f9159f317a4e8bb974e9c8e
+  size: 502858
+  timestamp: 1735327598235
+- conda: https://conda.anaconda.org/conda-forge/win-64/psutil-6.1.1-py313ha7868ed_0.conda
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   depends:
   - python >=3.13,<3.14.0a0
   - python_abi 3.13.* *_cp313
@@ -3848,8 +3839,8 @@ packages:
   license_family: BSD
   purls:
   - pkg:pypi/psutil?source=hash-mapping
-  size: 508489
-  timestamp: 1729847497486
+  size: 511743
+  timestamp: 1735327885260
 - conda: https://conda.anaconda.org/conda-forge/noarch/pycodestyle-2.12.1-pyhd8ed1ab_1.conda
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   md5: e895db5e6cee923018cbb1656c8ca7fa
@@ -3868,10 +3859,10 @@ packages:
   requires_dist:
   - colorama>=0.4.6 ; extra == 'windows-terminal'
   requires_python: '>=3.8'
-- pypi: https://files.pythonhosted.org/packages/be/ec/2eb3cd785efd67806c46c13a17339708ddc346cbb684eade7a6e6f79536a/pyparsing-3.2.0-py3-none-any.whl
+- pypi: https://files.pythonhosted.org/packages/1c/a7/c8a2d361bf89c0d9577c934ebb7421b25dc84bf3a8e3ac0a40aed9acc547/pyparsing-3.2.1-py3-none-any.whl
   name: pyparsing
-  version: 3.2.0
-  sha256: 93d9577b88da0bbea8cc8334ee8b918ed014968fd2ec383e868fb8afb1ccef84
+  version: 3.2.1
+  sha256: 506ff4f4386c4cec0590ec19e6302d3aedb992fdc02c761e90416f158dacf8e1
   requires_dist:
   - railroad-diagrams ; extra == 'diagrams'
   - jinja2 ; extra == 'diagrams'
@@ -4189,9 +4180,9 @@ packages:
   - pysocks>=1.5.6,!=1.5.7 ; extra == 'socks'
   - chardet>=3.0.2,<6 ; extra == 'use-chardet-on-py3'
   requires_python: '>=3.8'
-- conda: https://conda.anaconda.org/conda-forge/linux-64/ruff-0.8.3-py313he87ea70_0.conda
-  sha256: 5d4a53cca998fd1d5bb8f3a9487ad60ffdef8a56e04df570a6e785f9edefbaef
-  md5: f140fdf48951ad6bed3181b64deb34c9
+- conda: https://conda.anaconda.org/conda-forge/linux-64/ruff-0.8.5-py313he87ea70_0.conda
+  sha256: dc99a8fa116d11278fcae94a5d3461c9fe7e5c87c587555bee350fd527144568
+  md5: 288d127adebadb240fed28a1ca1964f3
   depends:
   - __glibc >=2.17,<3.0.a0
   - libgcc >=13
@@ -4206,11 +4197,11 @@ packages:
   license_family: MIT
   purls:
   - pkg:pypi/ruff?source=hash-mapping
-  size: 7930518
-  timestamp: 1734067017246
-- conda: https://conda.anaconda.org/conda-forge/osx-64/ruff-0.8.3-py313h2493e73_0.conda
-  sha256: 0d834f7f1f429f082e6b92f157f25998c44b614f14d1dff3cbb2a9acd6c80e2e
-  md5: 0a9c47ed1504bd6bfa58767a60ee4274
+  size: 7957771
+  timestamp: 1735838022549
+- conda: https://conda.anaconda.org/conda-forge/osx-64/ruff-0.8.5-py313h2493e73_0.conda
+  sha256: 6bedda3f7b89bac5eeee7a67fa0c3a1592021a7a34c622b960a320e72bd65024
+  md5: 99cb901fe616e78937339a60e77656dd
   depends:
   - __osx >=10.13
   - libcxx >=18
@@ -4224,11 +4215,11 @@ packages:
   license_family: MIT
   purls:
   - pkg:pypi/ruff?source=hash-mapping
-  size: 7312468
-  timestamp: 1734067136474
-- conda: https://conda.anaconda.org/conda-forge/osx-arm64/ruff-0.8.3-py313heab95af_0.conda
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-  md5: bdb571b33037a1e844df890b0dbcc025
+  size: 7370860
+  timestamp: 1735838179508
+- conda: https://conda.anaconda.org/conda-forge/osx-arm64/ruff-0.8.5-py313heab95af_0.conda
+  sha256: a46cb4be85c0afeb388302fa4b8c716a6c3252e57db73eb5b12f3da4000e4e8a
+  md5: 6d78872cc0b4faa31a202ad098ee3c43
   depends:
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   - libcxx >=18
@@ -4243,11 +4234,11 @@ packages:
   license_family: MIT
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   - pkg:pypi/ruff?source=hash-mapping
-  size: 6970719
-  timestamp: 1734067761445
-- conda: https://conda.anaconda.org/conda-forge/win-64/ruff-0.8.3-py313h331c231_0.conda
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-  md5: 410e3e4201bc0de6b0f9de9b63e4759e
+  size: 7020584
+  timestamp: 1735838228359
+- conda: https://conda.anaconda.org/conda-forge/win-64/ruff-0.8.5-py313h331c231_0.conda
+  sha256: b7fd82e126f951cbc6c569493418a852a6a52ef7af5b3f56948df4fe3362029b
+  md5: 5bc3f5498259a42cf25a2dd023e3a279
   depends:
   - python >=3.13,<3.14.0a0
   - python_abi 3.13.* *_cp313
@@ -4260,8 +4251,8 @@ packages:
   license_family: MIT
   purls:
   - pkg:pypi/ruff?source=hash-mapping
-  size: 6918580
-  timestamp: 1734067315832
+  size: 6948524
+  timestamp: 1735838582723
 - conda: https://conda.anaconda.org/conda-forge/linux-64/scikit-learn-1.6.0-py313h8ef605b_0.conda
   sha256: 8c56beae5f7561617515b230c3f27b3afa4a6de41c4acc5b83b96c12d98cbe81
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@@ -4791,17 +4782,17 @@ packages:
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   size: 11783
   timestamp: 1733251663622
-- conda: https://conda.anaconda.org/conda-forge/noarch/toml-0.10.2-pyhd8ed1ab_0.tar.bz2
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-  md5: f832c45a477c78bebd107098db465095
+- conda: https://conda.anaconda.org/conda-forge/noarch/toml-0.10.2-pyhd8ed1ab_1.conda
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+  md5: b0dd904de08b7db706167240bf37b164
   depends:
-  - python >=2.7
+  - python >=3.9
   license: MIT
   license_family: MIT
   purls:
   - pkg:pypi/toml?source=hash-mapping
-  size: 18433
-  timestamp: 1604308660817
+  size: 22132
+  timestamp: 1734091907682
 - conda: https://conda.anaconda.org/conda-forge/noarch/tomli-2.2.1-pyhd8ed1ab_1.conda
   sha256: 18636339a79656962723077df9a56c0ac7b8a864329eb8f847ee3d38495b863e
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@@ -4842,20 +4833,20 @@ packages:
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-- pypi: https://files.pythonhosted.org/packages/ce/d9/5f4c13cecde62396b0d3fe530a50ccea91e7dfc1ccf0e09c228841bb5ba8/urllib3-2.2.3-py3-none-any.whl
+- pypi: https://files.pythonhosted.org/packages/c8/19/4ec628951a74043532ca2cf5d97b7b14863931476d117c471e8e2b1eb39f/urllib3-2.3.0-py3-none-any.whl
   name: urllib3
-  version: 2.2.3
-  sha256: ca899ca043dcb1bafa3e262d73aa25c465bfb49e0bd9dd5d59f1d0acba2f8fac
+  version: 2.3.0
+  sha256: 1cee9ad369867bfdbbb48b7dd50374c0967a0bb7710050facf0dd6911440e3df
   requires_dist:
   - brotli>=1.0.9 ; platform_python_implementation == 'CPython' and extra == 'brotli'
   - brotlicffi>=0.8.0 ; platform_python_implementation != 'CPython' and extra == 'brotli'
   - h2>=4,<5 ; extra == 'h2'
   - pysocks>=1.5.6,!=1.5.7,<2.0 ; extra == 'socks'
   - zstandard>=0.18.0 ; extra == 'zstd'
-  requires_python: '>=3.8'
-- conda: https://conda.anaconda.org/conda-forge/linux-64/uv-0.5.8-h0f3a69f_0.conda
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-  md5: 405602a1df0c0667d13a7d35a9869e82
+  requires_python: '>=3.9'
+- conda: https://conda.anaconda.org/conda-forge/linux-64/uv-0.5.14-h0f3a69f_0.conda
+  sha256: fb9e6a0b92e2d694afd3f5926de1c631a6f86897494527c0792374d8d96859b3
+  md5: 37aa0d278aeb3a71a2016c7684fc5a6c
   depends:
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   - libgcc >=13
@@ -4866,11 +4857,11 @@ packages:
   platform: linux
   license: Apache-2.0 OR MIT
   purls: []
-  size: 10382046
-  timestamp: 1734058403253
-- conda: https://conda.anaconda.org/conda-forge/osx-64/uv-0.5.8-h8de1528_0.conda
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-  md5: 2451b9242ff261bc90df16e314f6b76e
+  size: 10851448
+  timestamp: 1735852602867
+- conda: https://conda.anaconda.org/conda-forge/osx-64/uv-0.5.14-h8de1528_0.conda
+  sha256: 2cdf69d4bd6eb22429a9b221feabfa5877d9f7ab8e8f05b2d872cf5f9a6f436a
+  md5: 70445b6932c27499d0ddf4b2353a99ca
   depends:
   - __osx >=10.13
   - libcxx >=18
@@ -4880,11 +4871,11 @@ packages:
   platform: osx
   license: Apache-2.0 OR MIT
   purls: []
-  size: 10011460
-  timestamp: 1734058877410
-- conda: https://conda.anaconda.org/conda-forge/osx-arm64/uv-0.5.8-h668ec48_0.conda
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-  md5: 9dd358a8ac3163b892b6866a46b0e99a
+  size: 10382685
+  timestamp: 1735853830567
+- conda: https://conda.anaconda.org/conda-forge/osx-arm64/uv-0.5.14-h668ec48_0.conda
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+  md5: ba74550de2d811d8535f202d403d094d
   depends:
   - __osx >=11.0
   - libcxx >=18
@@ -4894,11 +4885,11 @@ packages:
   platform: osx
   license: Apache-2.0 OR MIT
   purls: []
-  size: 10186932
-  timestamp: 1734058504082
-- conda: https://conda.anaconda.org/conda-forge/win-64/uv-0.5.8-ha08ef0e_0.conda
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-  md5: 2cf91bdb0b7af82c1f36721dfce0ec89
+  size: 10492975
+  timestamp: 1735854336261
+- conda: https://conda.anaconda.org/conda-forge/win-64/uv-0.5.14-ha08ef0e_0.conda
+  sha256: 46be5a5dce7ae00c39211dc216d429266ea53f558dd1a21016fbe6dcb7064c43
+  md5: 0dcc9b2f8fcafee8b458576d8d549182
   depends:
   - ucrt >=10.0.20348.0
   - vc >=14.2,<15
@@ -4907,8 +4898,8 @@ packages:
   platform: win
   license: Apache-2.0 OR MIT
   purls: []
-  size: 11470506
-  timestamp: 1734058988821
+  size: 11283006
+  timestamp: 1735853967653
 - conda: https://conda.anaconda.org/conda-forge/win-64/vc-14.3-ha32ba9b_23.conda
   sha256: 986ddaf8feec2904eac9535a7ddb7acda1a1dfb9482088fdb8129f1595181663
   md5: 7c10ec3158d1eb4ddff7007c9101adb0
diff --git a/tests/test_narx.py b/tests/test_narx.py
index f632cbf..122af7f 100644
--- a/tests/test_narx.py
+++ b/tests/test_narx.py
@@ -1,15 +1,15 @@
-"""Test Narx"""
+"""Test NARX"""
 
 import numpy as np
 import pytest
 from numpy.testing import assert_array_equal
 from sklearn.utils.estimator_checks import check_estimator
 
-from fastcan.narx import Narx, make_narx, make_poly_ids, make_time_shift_ids, print_narx
+from fastcan.narx import NARX, make_narx, make_poly_ids, make_time_shift_ids, print_narx
 
 
 def test_narx_is_sklearn_estimator():
-    check_estimator(Narx())
+    check_estimator(NARX())
 
 def test_poly_ids():
     with pytest.raises(ValueError, match=r"The output that would result from the .*"):
@@ -78,7 +78,7 @@ def test_narx(nan):
 
     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)
+    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"
@@ -105,7 +105,7 @@ def test_narx(nan):
     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)
+        narx_osa = NARX(time_shift_ids=time_shift_ids, poly_ids=poly_ids).fit(X, y)
 
     time_shift_ids = np.array(
         [
@@ -117,10 +117,10 @@ def test_narx(nan):
     )
     poly_ids = make_poly_ids(time_shift_ids.shape[0], 2)
     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)
+        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)
     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)
+        narx_osa = NARX(time_shift_ids=time_shift_ids, poly_ids=poly_ids).fit(X, y)