Updates sum and product kernels example code.

docs/source/utilities/kernels/sum_product_kernels.rst

@@ -15,25 +15,30 @@ example.
 Example sum and product Grassmannian kernels
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
+>>> import numpy as np
+>>> from UQpy.dimension_reduction.grassmann_manifold.projections.SVDProjection import SVDProjection
+>>> from UQpy.utilities.kernels.ProjectionKernel import ProjectionKernel
+>>>
 >>> D1 = 6
 >>> r0 = 2  # rank sample 0
 >>> r1 = 3  # rank sample 1
 >>> r2 = 4  # rank sample 2
 >>> r3 = 3  # rank sample 2
->>>
 >>> Sol0 = np.dot(np.random.rand(D1, r0), np.random.rand(r0, D1))
 >>> Sol1 = np.dot(np.random.rand(D1, r1), np.random.rand(r1, D1))
 >>> Sol2 = np.dot(np.random.rand(D1, r2), np.random.rand(r2, D1))
 >>> Sol3 = np.dot(np.random.rand(D1, r3), np.random.rand(r3, D1))
 >>>
 >>> # Creating a list of solutions.
 >>> Solutions = [Sol0, Sol1, Sol2, Sol3]
->>> from UQpy.dimension_reduction.grassmann_manifold.GrassmannOperations import Grassmann
->>> manifold_projection = SvdProjection(Solutions, p="max")
+>>> manifold_projection = SVDProjection(Solutions, p="max")
 >>> kernel = ProjectionKernel()
 >>>
->>> kernel_psi = kernel.calculate_kernel_matrix(manifold_projection.u)
->>> kernel_phi = kernel.calculate_kernel_matrix(manifold_projection.v)
+>>> kernel.calculate_kernel_matrix(manifold_projection.u)
+>>> kernel_psi = kernel.kernel_matrix
+>>>
+>>> kernel.calculate_kernel_matrix(manifold_projection.v)
+>>> kernel_phi = kernel.kernel_matrix
 >>>
 >>> sum_kernel = kernel_psi + kernel_phi
 >>> product_kernel = kernel_psi * kernel_phi