function [V,G_inv] = soliton2(V,z,eigs,c,x,t)

% eigs = [1i; 2 + 3i]; c = [2.3; 5.7];
c = c.*exp(2i*eigs*x);
N = numel(eigs);

A = 1./(eigs - eigs'); B = -A.';

u = (eye(N) - B*A)\(-conj(c));
v = (eye(N) - B*A)\(B*c);
s = (eye(N) - A*B)\c;
r = (eye(N) - A*B)\(-A*conj(c));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% z0 = 2-3i;
%
% R = .01;
% N = 100; h = 2*pi/N;
%
% t = (0:h:2*pi-h).';
%
% z = z0 + R*exp(1i*t);
% dz = R*1i*exp(1i*t);
%
% f = zeros(N,1);

G = zeros(numel(z),2,2); G_inv = zeros(numel(z),2,2);

for i = 1:numel(z)
    z1 = 1./(z(i)-eigs); z2 = 1./(z(i)-conj(eigs));
    G(i,1,1) = 1 + dot(r,z1);
    G(i,2,1) = dot(s,z1);
    G(i,1,2) = dot(u,z2);
    G(i,2,2) = 1 + dot(v,z2);
    G_inv(i,:,:) = inv(squeeze(G(i,:,:)));
end

% compute f = G * V
f11 = G(:,1,1).*V(:,1,1) + G(:,1,2).*V(:,2,1);
f12 = G(:,1,1).*V(:,1,2) + G(:,1,2).*V(:,2,2);
f21 = G(:,2,1).*V(:,1,1) + G(:,2,2).*V(:,2,1);
f22 = G(:,2,1).*V(:,1,2) + G(:,2,2).*V(:,2,2);

% compute f * G^-1 = G*V*G^-1
V(:,1,1) = f11.*G_inv(:,1,1) + f12.*G_inv(:,2,1);
V(:,1,2) = f11.*G_inv(:,1,2) + f12.*G_inv(:,2,2);
V(:,2,1) = f21.*G_inv(:,1,1) + f22.*G_inv(:,2,1);
V(:,2,2) = f21.*G_inv(:,1,2) + f22.*G_inv(:,2,2);
%
% residue = 1/(2i*pi)*sum(f.*dz*h)

end