Nonlinear equation solver issue

I am trying to solve a system of nonlinear equations for two variables, in which some of the variables in the equations are vectors. When I run fsolve, I get the following error:

My function is defined as:

function F = root2d(x,m,g,L0,Kleg,u,T)
K_vert = x(1);
v = x(2);
F(:,1) = T - ((4.*sqrt(m./x(1))).*(pi-atan((x(2)./g).*sqrt(x(1)./m)))+(4.*x(2)./g));
F(:,2) = (x(1)./Kleg) - (1 + ((L0.*x(1)-sqrt(L0.^2.*x(1).^2-m.*x(1).*u.^2.*(pi-atan((x(2)./g).*sqrt(x(1)./m))).^2))./(m.*g+sqrt(m.^2.*g.^2+m.*x(1).*x(2).^2))));
end

Where the original equations are:

And, my code is:

g = 9.81;
m = 90.72;
uL = 0.364; % length of upper leg (m)
lL = 0.543; % length of lower leg (m)
L0 = uL+lL;
K_leg1 = 15;
K_leg2 = 0.715*m^0.67;
K_leg = (K_leg1+K_leg2)/2;
u = linspace(1.42,2.7,150);
f = 0.65 + 0.2.*u;
T = 1./f;
x0 = [18;3]';
for i = 1:150
    x = fsolve(@(x)root2d(x,m,g,L0,K_leg,u(i),T(i)),x0);
    K_vert(i) = x(1);
    v(i) = x(2);
end

The value for K_vert has to be greater than 15, and the value for v should be in between 0 and 5, so I know that my starting values should not be the cause.

Any help would be appreciated! I've been trying to figure this out for hours.

[Walter Roberson]

Volunteers have an easier time answering when they are able to copy and paste code instead of having to type it in from a picture of the code.

[Michael ODonnell]

Sorry, this is my first time posting. It is fixed now

Answer 1

[Walter Roberson]

With those constants, solutions appear to be imaginary. The starting point becomes important.

g = 9.81;
m = 90.72;
uL = 0.364; % length of upper leg (m)
lL = 0.543; % length of lower leg (m)
L0 = uL+lL;
K_leg1 = 15;
K_leg2 = 0.715*m^0.67;
K_leg = (K_leg1+K_leg2)/2;
N = 150;
u = linspace(1.42,2.7,N);
f = 0.65 + 0.2.*u;
T = 1./f;
%x0 = [18;3]';
x0 = [10-1i, -1-1i];
K_vert = zeros(1,N);
v = zeros(1,N);
fval = zeros(N,2);
options = optimoptions('fsolve','Display','none');

for i = 1:N
    [x, fval(i,:)] = fsolve(@(x)root2d(x,m,g,L0,K_leg,u(i),T(i)), x0, options);
    K_vert(i) = x(1);
    v(i) = x(2);
    x0 = x;
end

Question: is your m^0.67 intended to represent m^(2/3) ?

Answer 2

[Mohamed Amin Ibrahim]

function ret=Code(lenchrom,bound)
%本函数将变量编码成染色体，用于随机初始化一个种群
% lenchrom   input : 染色体长度
% bound      input : 变量的取值范围
% ret        output: 染色体的编码值

flag=0;
while flag==0
    pick=rand(1,length(lenchrom));
    ret=bound(:,1)'+(bound(:,2)-bound(:,1))'.*pick; %线性插值
    flag=test(lenchrom,bound,ret);             %检验染色体的可行性
end

[Mohamed Amin Ibrahim]

hello am new to matlab but when i try to run this code i usually got error, please show me where there is error

[Walter Roberson]

What error message are you seeing?

MATLAB does not have a function named test so unless you have your own function test() then test(lenchrom,bound,ret) will fail.