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from pytensor import tensor as pt

from pymc.pytensorf import floatX
from pymc.variational.opvi import TestFunction

__all__ = ["rbf"]


class Kernel(TestFunction):
    r"""
    Dummy base class for kernel SVGD in case we implement more.

    .. math::

        f(x) -> (k(x,.), \nabla_x k(x,.))

    """


class RBF(Kernel):
    def __call__(self, X):
        XY = X.dot(X.T)
        x2 = pt.sum(X**2, axis=1).dimshuffle(0, "x")
        X2e = pt.repeat(x2, X.shape[0], axis=1)
        H = X2e + X2e.T - 2.0 * XY

        V = pt.sort(H.flatten())
        length = V.shape[0]
        # median distance
        m = pt.switch(
            pt.eq((length % 2), 0),
            # if even vector
            pt.mean(V[((length // 2) - 1) : ((length // 2) + 1)]),
            # if odd vector
            V[length // 2],
        )

        h = 0.5 * m / pt.log(floatX(H.shape[0]) + floatX(1))

        #  RBF
        Kxy = pt.exp(-H / h / 2.0)

        # Derivative
        dxkxy = -pt.dot(Kxy, X)
        sumkxy = pt.sum(Kxy, axis=-1, keepdims=True)
        dxkxy = pt.add(dxkxy, pt.mul(X, sumkxy)) / h

        return Kxy, dxkxy


rbf = RBF()
