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

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vlernest
vlernest 2022-7-16
回答： Star Strider 2022-7-16
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.

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采纳的回答

Star Strider
Star Strider 2022-7-16
Ran in:
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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