LSQcurvefit does not yield same result for comparable data sets
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I have used the following code to fit my data. Key is that the fit captures the peak at the start of the curve.
For a lot of data sets, the method works (example are x_good,y_good).
For two sets this method does not work adequate enough (x5, y5 and x10, y10)
Anyone who can see if I am doing something wrong? Or give a different method which works better?
clear all
clc
close all
% Working data set
x_good = [0 0.0025 0.020666667 0.0915 0.129 0.169916667 0.204 0.2415 0.299833333 0.359833333 0.409833333 0.459833333 0.589833333 0.674833333];
y_good = [0.000001 -1.791689626 -2.085814283 -1.254192484 -1.130978553 -0.852663995 -0.650156083 -0.605732792 -0.552092535 -0.466707459 -0.381595899 -0.341840176 -0.112360934 -0.107089368];
%Not working data set
x5 = [0 0.0025 0.020666667 0.0915 0.129 0.169916667 0.204 0.299833333 0.359833333 0.509833333 0.589833333 0.674833333];
y5 = [0.000001 -1.512917459 -1.397221246 -0.861543826 -0.678138048 -0.538930943 -0.440640054 -0.253865251 -0.192352332 0.001791084 0.078138742 0.156925367];
%Not working data set
x10 = [0 0.0025 0.020666667 0.0915 0.129 0.169916667 0.204 0.2415 0.299833333 0.359833333 0.409833333 0.459833333 0.589833333 0.674833333];
y10 = [0.000001 -0.909146404 -1.389416499 -0.736431181 -0.767464076 -0.430784784 -0.298350016 -0.477736703 -0.174485909 -0.10975744 -0.038531763 0.009471926 0.133414928 0.178482903];
% LSQ
t = x5;
y =y10;
xspace = linspace(t(1), t(end), 1000);
options = optimoptions('lsqcurvefit', 'MaxFunctionEvaluations', 100e3)
% fit function y = c(1)*exp(-lam(1)*t) + c(2)*exp(-lam(2)*t)
F = @(x,t)(x(1)*exp(-x(2)*t) + x(3)*exp(-x(4)*t));
x4 = [1 1 1 0];
[x,resnorm,~,~,output] = lsqcurvefit(F,x4,t,y, [], [], options)
figure
plot(t,y,'ro')
title("Least squared method ")
hold on
plot(t,F(x,t), 'r')
hold on
plot(xspace, F(x, xspace), '--r')
set(gca, 'YDir','reverse')
legend("data points", "LSQ, resnorm: " + resnorm, "LSQ continous")
0 Comments
Accepted Answer
Torsten
on 29 Sep 2022
Use
x4 = [-2.1782 5.0283 2.1782 720.8491];
instead of
x4 = [1 1 1 0];
as initial guess for the parameters.
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