Project: s41467-024-44757-7 | Function: __call__ (python)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** RBF kernel computation that calculates cell-cell similarity using radial basis function with Euclidean distance

**KEY TERMS:** {
  "x": "left argument of kernel k(X, Y)",
  "y": "right argument of kernel k(X, Y)",
  "length_scale": "length scale parameter l",
  "d(x_i, x_j)": "Euclidean distance"
}

**CONTEXT CODE:**     "LaplacianKernel",
]
torch = bu._safe_import("torch", raise_exc=False)


def _num_samples(x):
    """Return number of samples in array-like x."""
    message = "Expected sequence or array-like, got %s" % type(x)

    if not hasattr(x, "__len__") and not hasattr(x, "shape"):
        if hasattr(x, "__array__"):
            x = np.asarray(x)
        else:
            raise TypeError(message)

    if hasattr(x, "shape") and x.shape is not None:
        if len(x.shape) == 0:
            raise TypeError(
                "Singleton array %r cannot be considered a valid collection." % x
            )
        # Check that shape is returning an integer or default to len
        # Dask dataframes may not return numeric shape[0] value
        if isinstance(x.shape[0], numbers.Integral):
            return x.shape[0]

    try:
        return len(x)
    except TypeError as type_error:
        raise TypeError(message) from type_error


class Kernel(ABC):
    """Base kernel class."""

    def __init__(
        self,
        kernel: Optional[st.ArrayLike] = None,
        dtype: Optional[st.DtypeLike] = None,
        device: Optional[st.Device_t] = None,
        backend: Optional[Backend] = None,
    ):
        self._k = kernel
        self._dtype = dtype
        self._backend = bu.get_backend(backend)
        self._device = bu.get_device(self._backend) if device is None else device

    def __repr__(self):
        return f"{self.__class__.__name__}"

    @abstractmethod
    def __call__(
        self,
        x: st.ArrayLike,
        y: Optional[st.ArrayLike] = None,
        materialize: bool = False,
    ) -> st.KernelLike:
        """Evaluate the kernel on a pair of inputs.

        Parameters
        ----------
        x
            Left argument of the returned kernel :math:`k(X, Y)`, array of shape ``[n_samples, n_features]``.
        y
            Right argument of the returned kernel :math:`k(X, Y)`, array of shape ``[n_samples, n_features]``.
            If `None`, :math:`k(X, X)` is evaluated instead.
        materialize
            Whether to materialize the kernel.

        Returns
        -------
        LazyTensor resembling the kernel.
        """

    @classmethod
    def _create(cls, kernel_type: st.Kernel_t, **kwargs: Any) -> "Kernel":
        # MASKED: Kernel factory method implementation
        raise NotImplementedError("This function is masked for testing purposes.")

    @property
    def dtype(self) -> st.DtypeLike:
        """The kernel's data type."""
        return self._dtype

    @dtype.setter
    def dtype(self, dtype: st.DtypeLike) -> None:
        self._dtype = dtype

    @property
    def device(self) -> Optional[st.Device_t]:
        """The kernel's device."""
        return self._device

    @device.setter
    def device(self, device: Optional[st.Device_t]) -> None:
        self._device = device

    @property
    def backend(self) -> Backend:
        """The kernel's :mod:`pykeops` backend.

        Can be either :mod:`torch` or :mod:`numpy`."""
        return self._backend

    @backend.setter
    def backend(self, backend: Union[str, Backend]) -> None:
        self._backend = Backend(backend)

    @property
    def k(self) -> st.KernelLike:
        """The instantiated kernel object."""
        if self._k is None:
            raise RuntimeError(
                "Must instantiate a kernel object or supply a valid basis"
            )
        return self._k

    @k.setter
    def k(self, kernel: st.KernelLike) -> None:
        self._k = kernel

    def _materialize_kernel(self):
        if isinstance(self.k, GenericLazyTensor):
            if self.backend == Backend.TORCH:
                return self.k @ torch.diag(
                    torch.ones(self.k.shape[1], dtype=self.dtype, device=self.device)
                )
            elif self.backend == Backend.NUMPY:
                return self.k @ np.diag(np.ones(self.k.shape[1]))
        else:
            return self.k

    def _LazyTensor(self, x, axis=0):
        if self._backend == Backend.TORCH:
            if not torch.is_tensor(x):
                x = torch.tensor(x, dtype=self.dtype, device=self.device).contiguous()
            if axis == 0:
                return pykeops.torch.LazyTensor(x[:, None, None])
            return pykeops.torch.LazyTensor(x[None, :, None])
        elif self._backend == Backend.NUMPY:
            return pykeops.numpy.LazyTensor(x)

    def _Vi(self, x):
        if self._backend == Backend.TORCH:
            if not torch.is_tensor(x):
                x = torch.tensor(x, dtype=self.dtype, device=self.device).contiguous()
            return pykeops.torch.Vi(x)
        elif self._backend == Backend.NUMPY:
            return pykeops.numpy.Vi(x)

    def _Vj(self, x):


Complete the function implementation replacing "raise NotImplementedError".