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%% Eigenvalues and Singular Values of Sparse Matrix % Copyright 2015 The MathWorks, Inc. %% Section 1 % This example shows how to find the smallest eigenvalue and eigenvector of % a sparse matrix. %% % Set up the five-point Laplacian difference operator on a 65-by-65 grid in % an _L_-shaped, two-dimensional domain. L = numgrid('L',65); A = delsq(L); %% % Determine the order and number of nonzero elements. size(A) nnz(A) %% % |A| is a matrix of order 2945 with 14,473 nonzero elements. %% % Compute the smallest eigenvalue and eigenvector. [v,d] = eigs(A,1,0); %% % Distribute the components of the eigenvector over the appropriate grid % points and produce a contour plot of the result. L(L>0) = full(v(L(L>0))); x = -1:1/32:1; contour(x,x,L,15) axis square