Solve is not returnig solution - matlab

Hi,

I'm trying to find the vector x=[x1 ; x2 ; x3 ; x4 ; x5] by solving:

 Valorantigo(1,1)=3441/(1-0.00302+x1) + 3441/(1-0.00261+x1)^2 + 301720.5/(1-0.00208+x1)^3
 Valorantigo(2,1)=68750/(1-0.00302+x2) + 1068750/(1-0.00261+x2)^2 + 0/(1-0.00208+x2)^3
 Valorantigo(3,1)=170040/(1-0.00302+x3) + 13085020/(1-0.00261+x3)^2 + 0/(1-0.00208+x3)^3
 Valorantigo(4,1)=229350/(1-0.00302+x4) + 229350/(1-0.00261+x4)^2 + 5729350/(1-0.00208+x4)^3
 Valorantigo(5,1)=34194000/(1-0.00302+x5) + 0/(1-0.00261+x5)^2 + 0/(1-0.00208+x5)^3

My code is:

    A=[99.23;100.05;91;107.71;104.1];
    B=[3441 3441 301720.5;68750 1068750 0;170040 13085020 0;229350 229350 5729350;34194000 0 0];
    N=[300000;1000000;13000000;5500000;32800000];
    E=[-0.00302;-0.00261;-0.00208];

    [c3,r3]=size(A);
    [c4,r4]=size(B);

    Valorantigo(1:c3,1)=A(1:c3,1).* N(1:c3,1) ./100;

    x=sym ('x',[1 c3]);
    x=transpose(x);

     for i=1:c3
        Valor(i,1)=symfun(0,x);
        for j=1:r4
            Valor(i,1)=symfun((Valor(i,1)/(1+E(j,1)+x(i,1))^j)+((B(i,j)/((1+E(j,1)+x(i,1))^j))),x);
        end
     end

    eqn=Valor(1:c3,1)==Valorantigo(1:c3,1);

    [x1,x2,x3,x4, x5, param, cond] = solve(eqn, x, 'ReturnConditions', true);

But the solve don't return any value, can you understand why?

[Jan]

The more threads you open for a specific question, the higher is the level of confusion for the ones, who want to assist you.

Answer 1

[Torsten]

function main
x0=ones(5,1);
sol=fsolve(@myfun,x0)

function F=myfun(x)
A=[99.23;100.05;91;107.71;104.1];
B=[3441 3441 301720.5;68750 1068750 0;170040 13085020 0;229350 229350 5729350;34194000 0 0];
N=[300000;1000000;13000000;5500000;32800000];
E=[-0.00302;-0.00261;-0.00208];
[c3,r3]=size(A);
[c4,r4]=size(B);
Valorantigo(1:c3)=A(1:c3).*N(1:c3)./100;
for i=1:c3
   Valor(i)=0.0;
   for j=1:r4
      Valor(i)=Valor(i)+B(i,j)/(1+E(j)+x(i)^j);
   end
   F(i)=Valor(i)-Valorantigo(i); 
end

Note that your 5th equation does not have a zero - so you will have to exclude it from the above calculation.

Best wishes

Torsten.

[Mariana Ferreira]

Thanks. Could u explain better that about the 5th equation? I'm not understanding.

[John D'Errico]

Valorantigo(5,1)=34194000/(1-0.00302+x5) + 0/(1-0.00261+x5)^2 + 0/(1-0.00208+x5)^3

But see that TWO of the terms are zero ALWAYS. They are 0/stuff. So the 5th equation reduces to trying to solve for x5, such that

34194000/(1-0.00302+x5) == 0

Under what circumstances with that EVER be zero? NONE. There is no real or complex value for x5 that makes the left hand side zero.

[Mariana Ferreira]

But

Valorantigo(5,1)==34144800

so it will be

34194000/(1-0.00302+x5) == 34144800

[Torsten]

You are right.

Best wishes

Torsten.

[Mariana Ferreira]

Now that I checked the solution obtained is not right, for the first should be 1,4299, for the second 7,1098 and so on. I tried to include optimset but didnt work.

[Torsten]

If you insert the above values in the first and second equation, you will see that they don't solve them.

But - as Jan pointed out - there is an error in the code: a parenthesis is set incorrectly.

Use

Valor(i)=Valor(i)+B(i,j)/(1+E(j)+x(i))^j;

instead of

Valor(i)=Valor(i)+B(i,j)/(1+E(j)+x(i)^j);

Best wishes

Torsten.