chore: import upstream snapshot with attribution

2026-07-13 13:30:25 +08:00
commit f19b2512d7
562 changed files with 38082 additions and 0 deletions
@@ -0,0 +1,58 @@
+import numpy as np
+from prml.kernel.kernel import Kernel
+
+
+class RBF(Kernel):
+
+    def __init__(self, params):
+        """
+        construct Radial basis kernel function
+
+        Parameters
+        ----------
+        params : (ndim + 1,) ndarray
+            parameters of radial basis function
+
+        Attributes
+        ----------
+        ndim : int
+            dimension of expected input data
+        """
+        assert params.ndim == 1
+        self.params = params
+        self.ndim = len(params) - 1
+
+    def __call__(self, x, y, pairwise=True):
+        """
+        calculate radial basis function
+        k(x, y) = c0 * exp(-0.5 * c1 * (x1 - y1) ** 2 ...)
+
+        Parameters
+        ----------
+        x : ndarray [..., ndim]
+            input of this kernel function
+        y : ndarray [..., ndim]
+            another input
+
+        Returns
+        -------
+        output : ndarray
+            output of this radial basis function
+        """
+        assert x.shape[-1] == self.ndim
+        assert y.shape[-1] == self.ndim
+        if pairwise:
+            x, y = self._pairwise(x, y)
+        d = self.params[1:] * (x - y) ** 2
+        return self.params[0] * np.exp(-0.5 * np.sum(d, axis=-1))
+
+    def derivatives(self, x, y, pairwise=True):
+        if pairwise:
+            x, y = self._pairwise(x, y)
+        d = self.params[1:] * (x - y) ** 2
+        delta = np.exp(-0.5 * np.sum(d, axis=-1))
+        deltas = -0.5 * (x - y) ** 2 * (delta * self.params[0])[:, :, None]
+        return np.concatenate((np.expand_dims(delta, 0), deltas.T))
+
+    def update_parameters(self, updates):
+        self.params += updates