second order data fitting using least squares
29 views (last 30 days)
Show older comments
hi
I am trying to fitting the data
I want to fitting the data 1 by least square fitting it to a quadratic function around the position of maximum data2(*)
f(x) = a(x-x0)^2 + b(x-x0) + c
where C is an additive constant C = f(x0) = 1.
I used several method (ex data fitting tool...) but failed
If you konw how to solve, pleast let me know
2 Comments
Answers (2)
Torsten
on 18 Jan 2019
Edited: Torsten
on 18 Jan 2019
x = [0.81 0.85 0.91 1.00 1.17 1.33 1.36 1.37 1.39 1.40 1.42];
y = [0.58 0.69 0.81 0.93 1 0.91 0.84 0.80 0.74 0.67 0.59];
x0 = x(5);
y0 = y(5);
xtrans = x - x0;
ytrans = y - y0;
xtrans = xtrans.';
ytrans = ytrans.';
%mat = [sum(xtrans.^4) sum(xtrans.^3);sum(xtrans.^3) sum(xtrans.^2)];
%rhs = [sum(xtrans.^2.*ytrans); sum(xtrans.*ytrans)];
mat = [xtrans.^2 xtrans];
rhs = ytrans;
sol = mat\rhs;
a = sol(1);
b = sol(2);
fun = @(x)a*(x-x0).^2+b*(x-x0)+y0;
yfit = fun(x);
plot(x,y,x,yfit)
0 Comments
Akira Agata
on 18 Jan 2019
Another possible solution:
x = [0.81 0.85 0.91 1.00 1.17 1.33 1.36 1.37 1.39 1.40 1.42]';
y = [0.58 0.69 0.81 0.93 1 0.91 0.84 0.80 0.74 0.67 0.59]';
x0 = x(5);
y0 = y(5);
modelfun = @(a,x) a(1)*(x - x0).^2 + a(2)*(x - x0) + y0;
beta0 = [-1 1]; % Initial guess
mdl = fitnlm(x,y,modelfun,beta0);
xq = linspace(min(x),max(x))';
figure
scatter(x,y)
hold on
plot(xq,predict(mdl,xq))
0 Comments
See Also
Categories
Find more on Least Squares in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!