I want to know why MATLAB says "Equation solved at initial point"

Hi everybody,

I have a code that gives the following answer from MATLAB:

"Equation solved at initial point.

fsolve completed because the vector of function values at the initial

point is near zero as measured by the selected value of the function tolerance,

and the problem appears regular as measured by the gradient. "

What is wrong ?

Thanks a lot to everybody!!

Here the code:

function main

x0 = rand(5,1);

options = optimoptions(@fsolve, 'Algorithm', 'levenberg-marquardt', 'MaxFunctionEvaluations', 1000000, 'MaxIterations', 1000000,'OptimalityTolerance', 1e-10, 'FunctionTolerance', 1e-08);

x = fsolve(@fun,x0,options)

res = fun(x)

k1 = x(1)^2;

k2 = x(2)^2;

k3 = x(3)^2;

k4 = x(4)^2;

k7 = x(5)^2;

%K1 = k3/(k4+k7)

end

function res = fun(x)

k1 = x(1)^2; %because I need positive k's

k2 = x(2)^2;

k3 = x(3)^2;

k4 = x(4)^2;

k7 = x(5)^2;

ET=0.5

i1=0.009621821;

i2=0.030538822;

i3=0.054802544;

i4=0.068189424;

i5=0.084504685;

i6=0.091198126;

i7=0.094544846;

i8=0.110441767;

i9=0.112951807;

i10=0.125502008;

x1=0;

x2=30;

x3=50;

x4=75;

x5=100;

x6=130;

x7=160;

x8=200;

x9=280;

x10=380;

%h correspond à E au niveau de la branche "Dimerization" (eq. 82)

h1 = (-(k2+k1*x1-k7*k3/(k4+k7)*ET)+sqrt((k2+k1*x1-k7*k3/(k4+k7)*ET)^2+4*k2*ET*(2*k1*k3/(k4+k7)*x1+k7*k3/(k4+k7))))/(2*k3/(k4+k7)*(k7+2*k1*x1));

h2 = (-(k2+k1*x2-k7*k3/(k4+k7)*ET)+sqrt((k2+k1*x2-k7*k3/(k4+k7)*ET)^2+4*k2*ET*(2*k1*k3/(k4+k7)*x2+k7*k3/(k4+k7))))/(2*k3/(k4+k7)*(k7+2*k1*x2));

h3 = (-(k2+k1*x3-k7*k3/(k4+k7)*ET)+sqrt((k2+k1*x3-k7*k3/(k4+k7)*ET)^2+4*k2*ET*(2*k1*k3/(k4+k7)*x3+k7*k3/(k4+k7))))/(2*k3/(k4+k7)*(k7+2*k1*x3));

h4 = (-(k2+k1*x4-k7*k3/(k4+k7)*ET)+sqrt((k2+k1*x4-k7*k3/(k4+k7)*ET)^2+4*k2*ET*(2*k1*k3/(k4+k7)*x4+k7*k3/(k4+k7))))/(2*k3/(k4+k7)*(k7+2*k1*x4));

h5 = (-(k2+k1*x5-k7*k3/(k4+k7)*ET)+sqrt((k2+k1*x5-k7*k3/(k4+k7)*ET)^2+4*k2*ET*(2*k1*k3/(k4+k7)*x5+k7*k3/(k4+k7))))/(2*k3/(k4+k7)*(k7+2*k1*x5));

h6 = (-(k2+k1*x6-k7*k3/(k4+k7)*ET)+sqrt((k2+k1*x6-k7*k3/(k4+k7)*ET)^2+4*k2*ET*(2*k1*k3/(k4+k7)*x6+k7*k3/(k4+k7))))/(2*k3/(k4+k7)*(k7+2*k1*x6));

h7 = (-(k2+k1*x7-k7*k3/(k4+k7)*ET)+sqrt((k2+k1*x7-k7*k3/(k4+k7)*ET)^2+4*k2*ET*(2*k1*k3/(k4+k7)*x7+k7*k3/(k4+k7))))/(2*k3/(k4+k7)*(k7+2*k1*x7));

h8 = (-(k2+k1*x8-k7*k3/(k4+k7)*ET)+sqrt((k2+k1*x8-k7*k3/(k4+k7)*ET)^2+4*k2*ET*(2*k1*k3/(k4+k7)*x8+k7*k3/(k4+k7))))/(2*k3/(k4+k7)*(k7+2*k1*x8));

h9 = (-(k2+k1*x9-k7*k3/(k4+k7)*ET)+sqrt((k2+k1*x9-k7*k3/(k4+k7)*ET)^2+4*k2*ET*(2*k1*k3/(k4+k7)*x9+k7*k3/(k4+k7))))/(2*k3/(k4+k7)*(k7+2*k1*x9));

h10 = (-(k2+k1*x10-k7*k3/(k4+k7)*ET)+sqrt((k2+k1*x10-k7*k3/(k4+k7)*ET)^2+4*k2*ET*(2*k1*k3/(k4+k7)*x10+k7*k3/(k4+k7))))/(2*k3/(k4+k7)*(k7+2*k1*x10));

%i est la vitesse de catalyse au niveau de la branche "Dimerization" (eq. 86)

i1=k7*k3/(k4+k7)*h1*(ET-h1)/(1+2*k3/(k4+k7)*h1);

i2=k7*k3/(k4+k7)*h2*(ET-h2)/(1+2*k3/(k4+k7)*h2);

i3=k7*k3/(k4+k7)*h3*(ET-h3)/(1+2*k3/(k4+k7)*h3);

i4=k7*k3/(k4+k7)*h4*(ET-h4)/(1+2*k3/(k4+k7)*h4);

i5=k7*k3/(k4+k7)*h5*(ET-h5)/(1+2*k3/(k4+k7)*h5);

i6=k7*k3/(k4+k7)*h6*(ET-h6)/(1+2*k3/(k4+k7)*h6);

i7=k7*k3/(k4+k7)*h7*(ET-h7)/(1+2*k3/(k4+k7)*h7);

i8=k7*k3/(k4+k7)*h8*(ET-h8)/(1+2*k3/(k4+k7)*h8);

i9=k7*k3/(k4+k7)*h9*(ET-h9)/(1+2*k3/(k4+k7)*h9);

i10=k7*k3/(k4+k7)*h10*(ET-h10)/(1+2*k3/(k4+k7)*h10);

res(1) = -i1+k7*k3/(k4+k7)*h1*(ET-h1)/(1+2*k3/(k4+k7)*h1);

res(2) = -i2+k7*k3/(k4+k7)*h2*(ET-h2)/(1+2*k3/(k4+k7)*h2);

res(3) = -i3+k7*k3/(k4+k7)*h3*(ET-h3)/(1+2*k3/(k4+k7)*h3);

res(4) = -i4+k7*k3/(k4+k7)*h4*(ET-h4)/(1+2*k3/(k4+k7)*h4);

res(5) = -i5+k7*k3/(k4+k7)*h5*(ET-h5)/(1+2*k3/(k4+k7)*h5);

res(6) = -i6+k7*k3/(k4+k7)*h6*(ET-h6)/(1+2*k3/(k4+k7)*h6);

res(7) = -i7+k7*k3/(k4+k7)*h7*(ET-h7)/(1+2*k3/(k4+k7)*h7);

res(8) = -i8+k7*k3/(k4+k7)*h8*(ET-h8)/(1+2*k3/(k4+k7)*h8);

res(9) = -i9+k7*k3/(k4+k7)*h9*(ET-h9)/(1+2*k3/(k4+k7)*h9);

res(10) = -i10+k7*k3/(k4+k7)*h10*(ET-h10)/(1+2*k3/(k4+k7)*h10);

end