Rename num_eigenfunctions to num_eigenlevels in MaternKarhunenLoeveKe…

…rnel to avoid confusion

Signed-off-by: Viacheslav Borovitskiy <vabor112@users.noreply.github.com>

geometric_kernels/kernels/geometric_kernels.py

@@ -38,19 +38,23 @@ class MaternKarhunenLoeveKernel(BaseGeometricKernel):
     def __init__(
         self,
         space: DiscreteSpectrumSpace,
-        num_eigenfunctions: int,
+        num_eigenlevels: int,
     ):
         r"""
         :param space: Space providing the eigenvalues and eigenfunctions of
             the Laplace-Beltrami operator.
         :param nu: Determines continuity of the Mat\'ern kernel. Typical values
             include 1/2 (i.e., the Exponential kernel), 3/2, 5/2 and +\infty
             `np.inf` which corresponds to the Squared Exponential kernel.
-        :param num_eigenfunctions: number of eigenvalues and functions to include
-            in the summation.
+        :param num_eigenlevels: determines the number of eigenvalues and
+            functions to include in the summation but does not have to be
+            equal to the exact number. For example, thanks to the addition
+            theorem, for spheres this is the number of unique eigenvalues
+            to use (which is much less than the number of eigenvalues counted
+            with multiplicity).
         """
         super().__init__(space)
-        self.num_eigenfunctions = num_eigenfunctions  # in code referred to as `M`.
+        self.num_eigenlevels = num_eigenlevels  # in code referred to as `M`.
 
     def init_params_and_state(self):
         """
@@ -63,8 +67,8 @@ def init_params_and_state(self):
         """
         params = dict(lengthscale=np.array(1.0), nu=np.array(np.inf))
 
-        eigenvalues_laplacian = self.space.get_eigenvalues(self.num_eigenfunctions)
-        eigenfunctions = self.space.get_eigenfunctions(self.num_eigenfunctions)
+        eigenvalues_laplacian = self.space.get_eigenvalues(self.num_eigenlevels)
+        eigenfunctions = self.space.get_eigenfunctions(self.num_eigenlevels)
 
         state = dict(
             eigenvalues_laplacian=eigenvalues_laplacian, eigenfunctions=eigenfunctions
@@ -94,7 +98,7 @@ def eigenfunctions(self) -> Eigenfunctions:
         """
         Eigenfunctions of the kernel, may depend on parameters.
         """
-        eigenfunctions = self.space.get_eigenfunctions(self.num_eigenfunctions)
+        eigenfunctions = self.space.get_eigenfunctions(self.num_eigenlevels)
         return eigenfunctions
 
     def eigenvalues(self, params, state) -> B.Numeric: