How do i make an exponential curve graph from a vector?

3 views (last 30 days)
How do i make a graph that looks like this from the following code
I tried fitnlm or polyval or polyfit but i don't know if i'm not using the right functions or i just don't understand how to use them.
Teta1 = [0 19.727 25.705 28.796 30.154 31.375 31.787 31.961 31.164 32.504 32.285];
Teta2 = [0 11.356 17.764 21.162 22.806 23.712 24.292 24.573 24.765 24.826 24.753];
Teta3 = [0 10.239 15.604 18.588 20.312 21.164 21.579 21.671 21.896 21.820 21.750];
Teta4 = [0 20.346 28.186 32.687 35.272 26.975 37.823 38.785 38.794 39.194 39.240];
Teta5 = [0 11.957 20.023 24.820 27.567 29.355 30.386 31.244 31.458 31.830 31.772];
Teta6 = [0 10.803 17.642 22.031 24.655 26.389 27.414 27.884 28.064 28.299 28.152];

Accepted Answer

John D'Errico
John D'Errico on 30 Nov 2023
Edited: John D'Errico on 30 Nov 2023
You can't have a polynomial that will fit that curve shape. They simply do not have that characteristic form. So using polyfit (and polyval) is therefore a waste of time.
t = (0:5:50)';
Teta1 = [0 19.727 25.705 28.796 30.154 31.375 31.787 31.961 31.164 32.504 32.285];
plot(t,Teta1,'o')
We see one of your curves above.As a first guess, a negative expoential model tht rises to a constant asymptote seems a good start.
mdl = fittype('a-b*exp(-t/c)','indep','t')
mdl =
General model: mdl(a,b,c,t) = a-b*exp(-t/c)
fittedmdl = fit(t,Teta1',mdl,'start',[30 30 10])
fittedmdl =
General model: fittedmdl(t) = a-b*exp(-t/c) Coefficients (with 95% confidence bounds): a = 31.76 (31.12, 32.39) b = 31.5 (29.85, 33.15) c = 5.688 (4.991, 6.385)
plot(fittedmdl,'b-')
hold on
plot(t,Teta1,'ro')
hold off
And we see at least a reasonable fit. Do the same for each of your curves.
Is that the correct choice of model? Well, probably not perfect. I would note that it is not constrained to pass exactly through zero at t==0. mdl2 does that.
mdl2 = fittype('a*(1-exp(-t/b))','indep','t')
mdl2 =
General model: mdl2(a,b,t) = a*(1-exp(-t/b))
fittedmdl2 = fit(t,Teta1',mdl2,'start',[30 10])
fittedmdl2 =
General model: fittedmdl2(t) = a*(1-exp(-t/b)) Coefficients (with 95% confidence bounds): a = 31.75 (31.15, 32.34) b = 5.643 (5.044, 6.241)
plot(fittedmdl2,'b-')
hold on
plot(t,Teta1,'ro')
The fit is similar in quality, but now it passes exactly through 0 at t==0. My guess is that would be your goal.

More Answers (0)

Products


Release

R2022a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!