How do I fit a curve with a custom equation and a loop?

I want to make a loop for a scatterplot and for each loop I want to do the fit curving to the plot with a custom equation. The equation for the scatterplot looks like this:

i_vals = [1 8 9 10]
j_vals = 1:10

for i = 1:length(i_vals)
    for j = 1:length(j_vals)
    scatter(eave(j, i_vals(i)), epsilonacc(j,i_vals(i)) ./ f_ampl(i_vals(i)), "sk")
    hold on
    end
end

hold off
title("Alle Proben bei N = 100")
xlabel("Porenzahl e")
 ylabel("\epsilon^{acc} / f_{ampl}")
%legend
clear ('i_vals')

[1 8 9 10] - these are four samples

1:10 - ten rows per sample (representing N=10, N=100, N=500 ... N=100.000)

The scatter plot that you get from my code looks like this:

Each loop creates four points in a horizontal way. It should create something similar to this one (source: T. Wichtmann, A. Niemunis, Th. Triantafyllidis):

The function I want to use for the curve fitting ist the following:

f = kn .* ( (Ce - e).^2 ./ '(1 + e) )

Ce being a constant, e being a variable and kn being a constant which won't be used later.

If it doesn't work for this big amount of loops, than individual takes are also possible. At the end I need to get an average value of all the fitting curves to determine a constant.

Answer 1

[Star Strider]

The posted code needs the required variables and functions necessary to run it.

That aside, trysoimething like this —

a = linspace(0, atan(0.75/0.62), 7);                % Create Missing Data
r = [0.52; 0.56; 0.62; 0.66]+0.1;                   % Create Missing Data
r = logspace(log10(0.52), log10(0.66), 7).';        % Create Missing Data
emx = r*cos(a);                                     % Create Missing Data
emy = r*sin(a)+0.1;                                 % Create Missing Data

f = @(kn,Ce,e) kn .* ( (Ce - e).^2 ./ (1 + e) );

b0 = randi(9,2,1)                                   % Choose Appropriate Initial Parameter Estimates

b0 = 2×1

5 6

for k = 1:numel(a)
    B(:,k) = fminsearch(@(b)norm(emy(:,k) - f(b(1),b(2),emx(:,k))), b0);
end

 
Exiting: Maximum number of function evaluations has been exceeded
         - increase MaxFunEvals option.
         Current function value: 0.000812 

figure
plot(emx, emy, 's')
hold on
emxv = linspace(min(emx(:)), max(emx(:)), 50);
emxv = linspace(0, max(emx(:)), 50);
for k = 1:numel(a)
    plot(emxv, f(B(1,k),B(2,k),emxv))
end
hold off
grid

There appears to be more to this than was posted, however this should get you started.

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