eig_first.m
33bba04159d6master

eig_first.m
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			function [eigval, eigvect] = eig_first(A, n)
			[psi_lower, lower] = eig_ipower(A, 0);
			found = {{lower, psi_lower}};

			while length(found) < n
			[psi_upper, upper] = eig_ipower(A, lower * 2);
			result = eig_between(A, lower, upper);
			found = {found{:} result{:}};
			if abs(upper - lower) > 1e-10
			found = {found{:} {upper, psi_upper}};
			lower = upper;
			else
			lower = lower * 2;
			end
			end

			% rearrange output
			eigval = cell(n,1);
			eigvect = cell(n,1);
			for i = 1:n
			eigval{i} = found{i}{1};
			eigvect{i} = found{i}{2};
			end
			end

			% lower and upper are supposed to be eigenvalues
			function found = eig_between(A, lower, upper)
			found = {};
			if abs(lower - upper) > 1e-10
			mean = (lower + upper) / 2.0;
			[psi, val] = eig_ipower(A, mean);

			if abs(lower - val) > 1e-10 && abs(upper - val) > 1e-10
			flow = eig_between(A, lower, val);
			fhigh = eig_between(A, val, upper);
			found = {flow{:}, {val, psi}, fhigh{:}};
			end
			end
			end