DOC add multi-output narx example

examples/plot_narx_multi.py

@@ -0,0 +1,105 @@
+"""
+=======================
+Mulit-output NARX model
+=======================
+
+.. currentmodule:: fastcan
+
+In this example, we illustrate how to build a multi-output polynomial
+NARX model for time series prediction.
+"""
+
+# Authors: The fastcan developers
+# SPDX-License-Identifier: MIT
+
+# %%
+# Prepare data
+# ------------
+#
+# First, a simulated time series dataset is generated from the following nonlinear
+# system.
+#
+# .. math::
+#     y_0(k) &=\\
+#     &0.5y_0(k-1) + 0.8y_1(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\\
+#     y_1(k) &=\\
+#     &0.6y_1(k-1) - 0.2y_0(k-1)y_1(k-2) + 0.3u_1(k)^2 + 1.5u_1(k-2)u_0(k-3)
+#     + 0.5
+#
+#
+# where :math:`k` is the time index,
+# :math:`u_0` and :math:`u_1` are input signals,
+# and :math:`y_0` and :math:`y_1` are output signals.
+
+import numpy as np
+
+rng = np.random.default_rng(12345)
+n_samples = 1000
+max_delay = 3
+e0 = rng.normal(0, 0.1, n_samples)
+e1 = rng.normal(0, 0.02, n_samples)
+u0 = rng.uniform(0, 1, n_samples + max_delay)
+u1 = rng.normal(0, 0.1, n_samples + max_delay)
+y0 = np.zeros(n_samples + max_delay)
+y1 = np.zeros(n_samples + max_delay)
+for i in range(max_delay, n_samples + max_delay):
+    y0[i] = (
+        0.5 * y0[i - 1]
+        + 0.8 * y1[i - 1]
+        + 0.3 * u0[i] ** 2
+        + 2 * u0[i - 1] * u0[i - 3]
+        + 1.5 * u0[i - 2] * u1[i - 3]
+        + 1
+    )
+    y1[i] = (
+        0.6 * y1[i - 1]
+        - 0.2 * y0[i - 1] * y1[i - 2]
+        + 0.3 * u1[i] ** 2
+        + 1.5 * u1[i - 2] * u0[i - 3]
+        + 0.5
+    )
+y = np.c_[y0[max_delay:] + e0, y1[max_delay:] + e1]
+X = np.c_[u0[max_delay:], u1[max_delay:]]
+
+
+# %%
+# Identify the mulit-output NARX model
+# ------------------------------------
+# We provide :meth:`narx.make_narx` to automatically find the model
+# structure. `n_terms_to_select` can be a list to indicate the number
+# of terms (excluding intercept) for each output.
+
+from fastcan.narx import make_narx, print_narx
+
+narx_model = make_narx(
+    X=X,
+    y=y,
+    n_terms_to_select=[5, 4],
+    max_delay=3,
+    poly_degree=2,
+    verbose=0,
+).fit(X, y)
+
+print_narx(narx_model, term_space=30)
+
+
+# %%
+# 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(["y0 True", "y1 True", "y0 Pred", "y1 Pred"], loc="right")
+plt.title(f"NARX prediction R-squared: {r2_score(y[:100], y_pred):.5f}")
+plt.show()