commGSP/commGSP_spectral2poly.m
234a68af8299master

commGSP_spectral2poly.m
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			function p = commGSP_spectral2poly(A, H, order, type, plotbool)
			% Given a spectrally defined graph filter, find the best
			% approximative filter in the polynomial form
			% INPUT:
			% A - (symmetric) adjacency matrix
			% H - diagonal filter matrix with weights atributed ot each
			% of the spectral components (eigenvectors of the shift);
			% assumed ordering: increasing eigenvalue for laplacian
			% decreasing eigenvalue for modularity
			% order - scalar order of the polynomial aproximation
			% type - string defining what shift operator to use when filtering
			% 'laplacian' - Laplacian matrix
			% 'modularity' - modularity matrix
			% plotbool - if equal to 1, plot polynomial approximation
			% OUTPUT
			% p - vector of polynomial coefficients of the filter
			% approximating the one defined by the H matrix
			% (first entry of p corresponds to the highest order term, i.e.
			% to ?^order and last entry corresponds to ?^0)

			[~, D] = commGSP_eig_implicit(A, type);
			eigval=diag(D);
			coeffs=diag(H);

			p = polyfit(eigval,coeffs,order);

			if plotbool==1
			figure('Name','Polynomial approximation')
			plot(eigval,coeffs,'k','LineWidth',2)
			hold on
			plot(eigval,polyval(p,eigval),'*r','LineWidth',2)
			hold off
			legend({'desired spectral coefficients','polynomial evaluation at eigenvalues'})
			xlabel('eigenvalue range')
			set(gca,'FontSize',14)
			end

			end