%csv file containing edges and weights e = csvread('edge.csv'); %finds number of edges ne = length(e);

%makes sure vertices are in order for i = 1:ne if e(i,1) > e(i,2) A = e(i,1); e(i,1) = e(i,2); e(i,2) = A; e(i,3) = -e(i,3); end end

%creates vertex matrix %finds number of vertices nv = max(max([e(:,1), e(:,2)]));

V = zeros(1,nv);

for i = 1:ne A = e(i,1); B = e(i,2); V(A) = V(A)+1; V(B) = V(B)+1; end

valence = max(V); V = zeros(1,nv); v = zeros(nv,valence);

for i = 1:ne A = e(i,1); B = e(i,2); V(A) = V(A)+1; V(B) = V(B)+1; v(A,V(A)) = i; v(B,V(B)) = i; end

w = e(:,3);

%calculates edge weight %w = zeros(ne,1); %for p = 1:ne % sum = 0; % for i = 1:ne % if e(i,1) == p || e(i,2) == p % if e(i,1) == p % sum = sum + e(i,3); % end % if e(i,2) == p % sum = sum - e(i,3); % end

% w(p,1) = sum; % end % end %end

% Creates face matrix by searcing for shared edges of a triangle. % Faces are stored as triples of vertices.

nf = 0; for i = 1:ne A = e(i,1); %end points of the selected min edge B = e(i,2); %end points of the selected min edge for j = v(A,:) %Edge number search for k = v(B,:) %Edge number search if j > i && k > i %------------------- if e(j,1) == A % This area determines the 'other' va = e(j,2); % vertex for each edge (j and k) else % The goal is that these two match. va = e(j,1); % end % if e(k,1) == B % vb = e(k,2); % else % vb = e(k,1); % end %------------------- if va == vb && va ~= A && va ~= B %---------------- nf = nf +1; % This area checks v1 = min([A,B,va]); % that the verts v3 = max([A,B,va]); % are appropriate for vert = [A,B,va] % then adds them if v1 ~= vert && v3 ~= vert % to the faces v2 = vert; % in the correct end % orientation. end % f(nf,1) = v1; % f(nf,2) = v2; % f(nf,3) = v3; % end %---------------- end end end end

%initialize delta_0 and delta_1 delta_0 = zeros(ne,nv); delta_1 = zeros(nf,ne); temp = zeros(1,2);

%creates delta_0 %recall that delta_0(f)[v_1,v_2] = f(v_2) - f(v_1) for i = 1:ne delta_0(i,e(i,1))=-1; delta_0(i,e(i,2))=1; end delta_0 = delta_0';

delta_0f = delta_0*w;

%creates delta_1 %recall that delta_1(f)[v_1,v_2,v_3] = f(v_2,v_3) - f(v_1,v_3) + f(v_1,v_2) for i = 1:nf %Computes f(v_2,v_3) temp(1,1) = f(i,2); temp(1,2) = f(i,3); %Finds the corresponding edge for k = 1:ne if temp(1,1) == e(k,1) if temp(1,2) == e(k,2) j = k; end else k=k+1; end end delta_1(i,j) = 1;

%Computes f(v_1,v_3) temp(1,1) = f(i,1); temp(1,2) = f(i,3); %Finds corresponding edge for k = 1:ne if temp(1,1) == e(k,1) if temp(1,2) == e(k,2) j = k; end else k=k+1; end end %-1 because ...-f(v_1,v_3)+... delta_1(i,j) = -1;

%Computes f(v_1,v_2) temp(1,1) = f(i,1); temp(1,2) = f(i,2); %Finds corresponding edge for k = 1:ne if temp(1,1) == e(k,1) if temp(1,2) == e(k,2) j = k; end else k=k+1; end end delta_1(i,j) = 1; end delta_1 = delta_1';

lap_0 = delta_0'*delta_0;

ONB = null(lap_0);

temp = size(ONB); N = temp(2); imvec = zeros(1,ne); for i = 1:N ort = ONB(:,i); imvec = imvec + (w'*ort)*ort'; end

ee = zeros(ne,3);

for i = 1:ne %------------------- ee(i,1) = e(i,1); % Assigns a new ee(i,2) = e(i,2); % edge flow in ee(i,3) = imvec(i); % Ker(Lapl). end %-------------------

csvwrite('loops.csv',ee); %display(imvec) %display(w')