feat: add Fourier and vectorized Polynomial basis functions with accompanying tests.

sysidentpy/basis_function/_fourier.py

@@ -39,6 +39,9 @@ class Fourier(BaseBasisFunction):
     degree : int (max_degree), default=2
         The maximum degree of the polynomial features.
 
+    include_bias : bool, default=True
+        Whether to include the bias (constant) term in the output feature matrix.
+
     Notes
     -----
     Be aware that the number of features in the output array scales
@@ -47,11 +50,12 @@ class Fourier(BaseBasisFunction):
     """
 
     def __init__(
-        self, n: int = 1, p: float = 2 * np.pi, degree: int = 1, ensemble: bool = True
+        self, n: int = 1, p: float = 2 * np.pi, degree: int = 1, include_bias: bool = True, ensemble: bool = True
     ):
         self.n = n
         self.p = p
         self.degree = degree
+        self.include_bias = include_bias
         self.ensemble = ensemble
 
     def _fourier_expansion(self, data: np.ndarray, n: int):
@@ -125,6 +129,10 @@ def fit(
         else:
             psi = psi[:, 1:]
 
+        if self.include_bias:
+            bias_column = np.ones((psi.shape[0], 1))
+            psi = np.hstack((bias_column, psi))
+
         if predefined_regressors is None:
             return psi
 

sysidentpy/basis_function/_polynomial.py

@@ -28,6 +28,9 @@ class Polynomial(BaseBasisFunction):
     degree : int (max_degree), default=2
         The maximum degree of the polynomial features.
 
+    include_bias : bool, default=True
+        Whether to include the bias (constant) term in the output feature matrix.
+
     Notes
     -----
     Be aware that the number of features in the output array scales
@@ -38,9 +41,10 @@ class Polynomial(BaseBasisFunction):
     def __init__(
         self,
         degree: int = 2,
+        include_bias: bool = True,
     ):
         self.degree = degree
-        # Cache combination indices per (n_features, degree) to avoid rebuilding
+        self.include_bias = include_bias
         self._combination_cache: Dict[Tuple[int, int], np.ndarray] = {}
 
     def _get_combination_indices(self, n_features: int) -> np.ndarray:
@@ -115,9 +119,12 @@ def fit(
             The lagged matrix built in respect with each lag and column.
 
         """
-        # Create combinations of all columns based on its index
         psi = self._evaluate_terms(data, predefined_regressors)
-        return psi[max_lag:, :]
+        psi = psi[max_lag:, :]
+        if self.include_bias:
+            bias_column = np.ones((psi.shape[0], 1))
+            psi = np.hstack((bias_column, psi))
+        return psi
 
     def transform(
         self,

sysidentpy/basis_function/tests/test_basis_functions.py

@@ -9,7 +9,7 @@ def test_fit_polynomial():
     basis_function = Polynomial(degree=2)
     data = np.array(([1, 1, 1], [2, 3, 4], [3, 3, 3]))
     max_lag = 1
-    output = np.array([[4, 6, 8, 9, 12, 16], [9, 9, 9, 9, 9, 9]])
+    output = np.array([[1, 4, 6, 8, 9, 12, 16], [1, 9, 9, 9, 9, 9, 9]])
 
     r = basis_function.fit(data=data, max_lag=max_lag)
 
@@ -21,7 +21,7 @@ def test_fit_polynomial_predefined():
     data = np.array(([1, 1, 1], [2, 3, 4], [3, 3, 3]))
     max_lag = 1
     predefined_regressors = np.array([0, 2, 4])
-    output = np.array([[4, 8, 12], [9, 9, 9]])
+    output = np.array([[1, 6, 9], [1, 9, 9]])
 
     r = basis_function.fit(
         data=data, max_lag=max_lag, predefined_regressors=predefined_regressors
@@ -34,13 +34,31 @@ def test_transform_polynomial():
     basis_function = Polynomial(degree=2)
     data = np.array(([1, 1, 1], [2, 3, 4], [3, 3, 3]))
     max_lag = 1
-    output = np.array([[4, 6, 8, 9, 12, 16], [9, 9, 9, 9, 9, 9]])
+    output = np.array([[1, 4, 6, 8, 9, 12, 16], [1, 9, 9, 9, 9, 9, 9]])
 
     r = basis_function.transform(data=data, max_lag=max_lag)
 
     assert_array_equal(output, r)
 
 
+def test_polynomial_include_bias():
+    basis_function = Polynomial(degree=2, include_bias=True)
+    data = np.array(([1, 1, 1], [2, 3, 4], [3, 3, 3]))
+    max_lag = 1
+
+    r = basis_function.fit(data=data, max_lag=max_lag)
+    assert np.all(r[:, 0] == 1)
+
+
+def test_polynomial_no_bias():
+    basis_function = Polynomial(degree=2, include_bias=False)
+    data = np.array(([1, 1, 1], [2, 3, 4], [3, 3, 3]))
+    max_lag = 1
+
+    r = basis_function.fit(data=data, max_lag=max_lag)
+    assert not np.all(r[:, 0] == 1)
+
+
 def test_fit_fourier():
     basis_function = Fourier(n=5, ensemble=False)
     data = np.array(([1, 1, 1], [2, 3, 4], [3, 3, 3]))
@@ -173,6 +191,24 @@ def test_transform_fourier():
     assert_almost_equal(output, r, decimal=7)
 
 
+def test_fourier_include_bias():
+    basis_function = Fourier(n=5, ensemble=False, include_bias=True)
+    data = np.array(([1, 1, 1], [2, 3, 4], [3, 3, 3]))
+    max_lag = 1
+
+    r = basis_function.fit(data=data, max_lag=max_lag)
+    assert np.all(r[:, 0] == 1)
+
+
+def test_fourier_no_bias():
+    basis_function = Fourier(n=5, ensemble=False, include_bias=False)
+    data = np.array(([1, 1, 1], [2, 3, 4], [3, 3, 3]))
+    max_lag = 1
+
+    r = basis_function.fit(data=data, max_lag=max_lag)
+    assert not np.all(r[:, 0] == 1)
+
+
 class _DummyBasis(BaseBasisFunction):
     def __init__(self, degree=3):
         super().__init__(degree=degree)