How to limit my x=[]; to a range of values between 0<=x<=1.

V=1000; Q=50; Fa0=1;  k=1; E=-1; x=[]; fval=[];
for a=0:0.05:1
    f=@(x) [Fa0*x(1)-k*a*V*(Fa0*(1-x(1)))/(Q*(1+E*x(1))); Fa0*(x(2)-x(1))-k*(1-a)*V*(Fa0*(1-x(2)))/(Q*(1+E*x(2)))];
    [x(:,end+1),fval(:,end+1)] = fsolve(f,[0.5,0.5]);
end 
x(2,:)
b=linspace(0,1,21)
plot(b,x(2,:))
ylabel('x2') 
xlabel('Alpha') 

%%The reason I ask is bc when E=-1 fsolve will give me values of x outside of 0-1 which I don't want to have. Thanks guys.

Answer 1

[Walter Roberson]

V=1000; Q=50; Fa0=1;  k=1; E=-1; x=[]; fval=[];
syms x [1 2] real
syms a positive
f = [Fa0*x(1)-k*a*V*(Fa0*(1-x(1)))/(Q*(1+E*x(1))); Fa0*(x(2)-x(1))-k*(1-a)*V*(Fa0*(1-x(2)))/(Q*(1+E*x(2)))];
f

f = 

sol = solve(f, x)

sol = struct with fields:
    x1: 20*a
    x2: 20

sol.x1

ans = 

sol.x2

ans = 

20

so x(2) will always be exactly 20 no matter what the a value is, and 20 is outside of the range 0 to 1.

meanwhile, you have a=0:0.05:1 which is a = 0:1/20:1 and since x1 = 20*a then the only two a values that can fit in the 0<=x<=1 range are 0 and 1/20, and nothing from 1/10 onward

[Victor Jimenez Carrillo]

Thanks for the answer. This makes sense. I have no idea why my professor was swearing up and down by limiting the values of x would fix this issue. I just used a value of E=-0.92 and it works. Close enough to one imo.

Answer 2

[Harikrishnan Balachandran Nair]

Hi,

I understand that you are trying to use fsolve, and you want to have the output only within your range of interest.

You can refer to a similar question here :https://www.mathworks.com/matlabcentral/answers/59567-use-fsolve-with-boundaries.