clear; fname = 'ABC'; par = [0.08 0.02];
% [0.0629595 0.0211523]
myfile = strcat(fname, '.dat'); fname = load (myfile);
tvec = fname(:,1); ymat = fname(:,2:4);
x0 = [1 0 0]; %initial values, ODE's
[t, x] = ode45(@mysystem, tvec, x0, [], par);
plot (t, x, tvec, ymat, 'Marker', 'o', 'MarkerSize', 6)
title ('Preliminary: concentrations vs. time'); xlabel ('\it t'); ylabel ('mole')
new = fminsearch(@mydiff, par, [], tvec, ymat, x0)
[t, x] = ode45(@mysystem, tvec, x0, [], new);
figure
plot (t, x, tvec, ymat, 'Marker', 'o', 'MarkerSize', 8)
title ('(Optimised) Concentrations vs. time'); xlabel ('\it t'); ylabel ('mole')

function xprime = mysystem(t,x,par) % ODE's
k1 = par(1); k2 = par(2);
xprime = [-k1*x(1); -k2*x(2) + k1*x(1); k2*x(2)];
end
function d = mydiff(par, tvec, ymat, x0)
     [t, x] = ode45(@mysystem, tvec, x0, [], par);
     d = sum((x-ymat).^2, 'all')
end