Why does my for-loop substitute only one value throughout 31 iterations?

Hi all, on the attached file, I am trying to use the for-loop to substitute values for every iteration. However, it seems like the for-loop only substitute one value. What could be the cause of that?

Kind Regards Dursman

[Adam]

Why are you redefining G, H, I, J, K inside the for loop. They are constants so should be defined outside the for loop unless you are expecting them to change. You seem to be telling it to do the same thing every time round the loop. What is supposed to change? You refer to x(i) so I assume you intended to assign something to x(i) rather than just x every time round the loop.

[Dursman Mchabe]

Thanks for the response Adam. I was not sure where to define G, H, I, J and K. I expect x to change. When I change line 38 to

x(i) = fsolve(@(x) x(i) + 2.* G - ((H.* A.*x(i))/(x(i).^2 + A.*x(i) ...

I get an error message:

Unable to perform assignment because the indices on the left side are not compatible with the size of the right side.

Error in my_fsolve2 (line 38)
  x(i) = fsolve(@(x) x(i) + 2.* G - ((H.* A.*x(i))/(x(i).^2 + A.*x(i)...

I'm so grateful of your help.

[Dursman Mchabe]

The current state of the code is:

function my_fsolve3()
% Constant Parameters
A       = 6.24;
B       = 5.68e-5;
C       = 1.7e-3;
D       = 6.55e-8;
E       = 5.3e-8;
F       = 9.46e-1;

t       = [0;600;1200;1800;2400;3000;10200;17400;24600;31800;...
    39000;46200;53400;60600;67800;75000;82200;89400;96600;103800;...
    111000;118200;125400;132600;139800;147000;154200;161400;168600;175800;183000];

G       = [0.00;4.88E-06;4.88E-06;5.11E-06;5.11E-06;5.35E-06;5.35E-06;5.36E-06;5.36E-06;5.07E-06;....
    5.07E-06;4.93E-06;5.30E-06;5.30E-06;5.30E-06;9.46E-06;9.46E-06;1.13E-05;1.15E-05;1.10E-05;...
    1.10E-05;1.04E-05;1.04E-05;1.04E-05;1.03E-05;1.04E-05;1.06E-05;1.13E-05;1.13E-05;1.13E-05;1.03E-05];

H     = [0.00;3.34E-01;6.79E-01;1.04E+00;1.41E+00;6.00E+00;1.07E+01;1.56E+01;2.07E+01;2.59E+01;...
    3.14E+01;3.67E+01;4.18E+01;4.66E+01;5.09E+01;5.51E+01;5.90E+01;6.23E+01;6.56E+01;6.87E+01;...
    7.12E+01;7.36E+01;7.59E+01;7.78E+01;7.95E+01;8.11E+01;8.24E+01;8.24E+01;8.23E+01;8.21E+01;8.20E+01];

I     = [0.00;4.88E-06;4.88E-06;5.11E-06;5.11E-06;5.35E-06;5.35E-06;5.36E-06;5.36E-06;5.07E-06;...
    5.07E-06;4.93E-06;5.30E-06;5.30E-06;5.30E-06;9.46E-06;9.46E-06;1.13E-05;1.15E-05;1.10E-05;...
    1.10E-05;1.04E-05;1.04E-05;1.04E-05;1.03E-05;1.04E-05;1.06E-05;1.13E-05;1.13E-05;1.13E-05;1.03E-05];

J       = [1.78E-07;7.41E-06;9.33E-06;1.20E-05;1.05E-05;1.74E-05;3.72E-05;3.55E-05;1.00E-04;4.07E-02;...
    2.45E-01;6.17E-01;1.32E+00;2.29E+00;2.34E+00;2.40E+00;1.82E+00;1.38E+00;2.09E+00;1.82E+00;...
    1.58E+00;2.29E+00;1.62E+00;1.12E+00;8.91E-01;8.51E-01;7.59E-01;8.71E-01;1.12E+00;1.00E+00;8.51E-01];

K      = [9.75;8.13;8.03;7.92;7.98;7.76;7.43;7.45;7.00;4.39;...
    3.61;3.21;2.88;2.64;2.63;2.62;2.74;2.86;2.68;2.74;...
    2.8;2.64;2.79;2.95;3.05;3.07;3.12;3.06;2.95;3.00;3.07];

for i = 1:length(t)

      s(i)    = fsolve(@(x) x(i) + 2.* G(i) - ((H(i).* A.*x(i))/(x(i).^2 + A.*x(i) + A.*B))- 2.*((H(i).*A.*B)/(x(i).^2 ...
              + A.*x(i) + A.*B))-((I(i).*C.*x(i))/(x(i).^2 + C.*x(i) + C.*D))- 2.*((I(i).*C.*D)/(x(i).^2 ...
              + C.*x(i) + C.*D))- E/x(i), F);

end
L = 6 - log10(s);   
plot(t,L)
hold on
plot (t,K,'v')
xlabel('Time (sec)')
ylabel('pH')
hold off
legend('pH-Mod','pH-Exp')
end
Which gives an error message of

Index exceeds the number of array elements (1).

Error in
my_fsolve3>@(x)x(i)+2.*G(i)-((H(i).*A.*x(i))/(x(i).^2+A.*x(i)+A.*B))-2.*((H(i).*A.*B)/(x(i).^2+A.*x(i)+A.*B))-((I(i).*C.*x(i))/(x(i).^2+C.*x(i)+C.*D))-2.*((I(i).*C.*D)/(x(i).^2+C.*x(i)+C.*D))-E/x(i)
(line 36)
    s(i)    = fsolve(@(x) x(i) + 2.* G(i) - ((H(i).* A.*x(i))/(x(i).^2 + A.*x(i) + A.*B))- 2.*((H(i).*A.*B)/(x(i).^2 ...

Error in fsolve (line 242)
            fuser = feval(funfcn{3},x,varargin{:});

Error in my_fsolve3 (line 36)
    s(i)    = fsolve(@(x) x(i) + 2.* G(i) - ((H(i).* A.*x(i))/(x(i).^2 + A.*x(i) + A.*B))- 2.*((H(i).*A.*B)/(x(i).^2 ...

Caused by:
    Failure in initial objective function evaluation. FSOLVE cannot continue.

>>

I trust that I should be able to resolve it in the next few days.

Answer 1

[dpb]

function my_fsolve2()
% Constant Parameters
A       = 6.24;
B       = 5.68e-5;
C       = 1.7e-3;
D       = 6.55e-8;
E       = 5.3e-8;
F       = 9.46e-1;
t           = [0;600;1200;1800;2400;3000;10200;17400;24600;31800;...
            39000;46200;53400;60600;67800;75000;82200;89400;96600;103800;
            111000;118200;125400;132600;139800;147000;154200;161400;168600;175800;183000];
G    = [0.00;4.88E-06;4.88E-06;5.11E-06;5.11E-06;5.35E-06;5.35E-06;5.36E-06;5.36E-06;5.07E-06;....
            5.07E-06;4.93E-06;5.30E-06;5.30E-06;5.30E-06;9.46E-06;9.46E-06;1.13E-05;1.15E-05;1.10E-05;...
            1.10E-05;1.04E-05;1.04E-05;1.04E-05;1.03E-05;1.04E-05;1.06E-05;1.13E-05;1.13E-05;1.13E-05;1.03E-05];
H     = [0.00;3.34E-01;6.79E-01;1.04E+00;1.41E+00;6.00E+00;1.07E+01;1.56E+01;2.07E+01;2.59E+01;...
            3.14E+01;3.67E+01;4.18E+01;4.66E+01;5.09E+01;5.51E+01;5.90E+01;6.23E+01;6.56E+01;6.87E+01;...
            7.12E+01;7.36E+01;7.59E+01;7.78E+01;7.95E+01;8.11E+01;8.24E+01;8.24E+01;8.23E+01;8.21E+01;8.20E+01];
I     = [0.00;4.88E-06;4.88E-06;5.11E-06;5.11E-06;5.35E-06;5.35E-06;5.36E-06;5.36E-06;5.07E-06;...
            5.07E-06;4.93E-06;5.30E-06;5.30E-06;5.30E-06;9.46E-06;9.46E-06;1.13E-05;1.15E-05;1.10E-05;
            1.10E-05;1.04E-05;1.04E-05;1.04E-05;1.03E-05;1.04E-05;1.06E-05;1.13E-05;1.13E-05;1.13E-05;1.03E-05];
J         = [1.78E-07;7.41E-06;9.33E-06;1.20E-05;1.05E-05;1.74E-05;3.72E-05;3.55E-05;1.00E-04;4.07E-02;...
            2.45E-01;6.17E-01;1.32E+00;2.29E+00;2.34E+00;2.40E+00;1.82E+00;1.38E+00;2.09E+00;1.82E+00;...
            1.58E+00;2.29E+00;1.62E+00;1.12E+00;8.91E-01;8.51E-01;7.59E-01;8.71E-01;1.12E+00;1.00E+00;8.51E-01];
K      = [9.75;8.13;8.03;7.92;7.98;7.76;7.43;7.45;7.00;4.39;...
            3.61;3.21;2.88;2.64;2.63;2.62;2.74;2.86;2.68;2.74;...
            2.8;2.64;2.79;2.95;3.05;3.07;3.12;3.06;2.95;3.00;3.07];
for i = 1:length(t)

    s(i)=fsolve(@(x) x+2*G(i)-((H(i)*A*x)/(x^2+A*x+A*B))-2*((H(i)*A*B)/(x^2 ...
              + A*x+A*B))-((I(i)*C.*x)/(x^2+C*x+C*D))-2.*((I(i)*C*D)/(x^2 ...
              + C*x+C*D))-E/x, x(i));
end
L = 6 - log10(s);   

plot(t,L)
hold on
plot (t,K,'v')
xlabel('Time (sec)')
ylabel('pH')
hold off
legend('pH-Mod','pH-Exp')
end

Just taking a stab at what you may have intended... fsolve only solves for a single equation solution at a time, not an array of solutions.

You were overwriting x with the result each pass, not saving a solution and passing the array of time-dependent values instead of solving for each solution ("s") each iteration.

[Dursman Mchabe]

Thanks a lot for the answer. I believe that I should be able to solve it from here. The current error is

Index exceeds the number of array elements (1).

Error in
my_fsolve3>@(x)x(i)+2.*G(i)-((H(i).*A.*x(i))/(x(i).^2+A.*x(i)+A.*B))-2.*((H(i).*A.*B)/(x(i).^2+A.*x(i)+A.*B))-((I(i).*C.*x(i))/(x(i).^2+C.*x(i)+C.*D))-2.*((I(i).*C.*D)/(x(i).^2+C.*x(i)+C.*D))-E/x(i)
(line 36)
    s(i)    = fsolve(@(x) x(i) + 2.* G(i) - ((H(i).* A.*x(i))/(x(i).^2 + A.*x(i) + A.*B))- 2.*((H(i).*A.*B)/(x(i).^2 ...

Error in fsolve (line 242)
            fuser = feval(funfcn{3},x,varargin{:});

Error in my_fsolve3 (line 36)
    s(i)    = fsolve(@(x) x(i) + 2.* G(i) - ((H(i).* A.*x(i))/(x(i).^2 + A.*x(i) + A.*B))- 2.*((H(i).*A.*B)/(x(i).^2 ...

Caused by:
    Failure in initial objective function evaluation. FSOLVE cannot continue.
>>

I will go through previous answers to find a way of solving it. Thanks a lot for the answer once again.

[dpb]

...
for i=1:numel(G)
  fnS=@(x)x+2.*G(i)-((H(i).*A.*x)./(x.^2+A.*x+A.*B))-2.*((H(i).*A.*B)./(x.^2+C.*x+C.*D))-E./x;
  x(i)=fsolve(fnS,1);
end
L=6-log10(x);

seems to work ok...presuming, of course, that the intent is to solve the equation for each set of coefficients as given in the arrays.

There's an apparent discontinuity in the solution plotted vs the t array; don't know if that's expected, indicative of a typo in one of the coefficient arrays, or just experimental noise/uncertainty/error...

Not sure what I, J, K are for as they don't show up in the solution anywhere; maybe they're some other part of the problem past this point?

[Dursman Mchabe]

Thanks a lot dpb. I have since found the solution from your previous answer, the code works perfectly. Thanks once again.