Nonlinear fit of segmented curve
7 ビュー (過去 30 日間)
古いコメントを表示
How would I go about getting a nonlinear least-squares fit of a segmented curve? In this case, I have a short, linear, lag period followed by a logistic growth phase (typical of bacterial growth in culture).
Thus, for x < T0, y = Y0; for x >= T0, y = Y0 + (Plateau-Y0)*(1 - exp(-K*(X-X0)).
I need least squares estimates for each of the parameters: T0, Y0, Plateau, and K
I've attempted to use a custom function in the curve fitting toolbox, but cannot figure out how to allow for the two curves.
Thanks!
0 件のコメント
採用された回答
Teja Muppirala
2012 年 12 月 5 日
It is no problem to fit piecewise curves in MATLAB using the Curve Fitting Toolbox. You can deal with piecewise functions by multiplying each piece by its respective domain. For example:
rng(0); %Just fixing the random number generator for initial conditions
X = (0:0.01:10)';
% True Values
Y0_true = 3;
PLATEAU_true = 5;
K_true = 1;
X0_true = 4;
Y = [Y0_true] * (X <= X0_true) + [Y0_true + (PLATEAU_true-Y0_true)*(1 - exp(-K_true*(X-X0_true)))].* (X > X0_true);
Y = Y + 0.1*randn(size(Y));
plot(X,Y);
ftobj = fittype('[Y0] * (x <= X0) + [Y0 + (PLATEAU-Y0)*(1 - exp(-K*(x-X0)))].* (x > X0)');
cfobj = fit(X,Y,ftobj,'startpoint',rand(4,1))
hold on;
plot(X,cfobj(X),'r','linewidth',2);
5 件のコメント
Jonathan Gößwein
2022 年 10 月 14 日
The problem are the startpoints, rand(4,1) does not work indeed, but with an appropriate selection the method works (e.g. the true values).
その他の回答 (2 件)
John Petersen
2012 年 12 月 4 日
Not sure how you would do that, but you could try using a sigmoid function which will get you close, relatively speaking. Something like, for example,
y2 = Y0 + (Plateau-Y0)./(1 + exp(-K*(X-X0)));
laoya
2013 年 5 月 14 日
Hi Teja Muppirala,
I am also interested in this topic. Now my problem is: if the express of curves are not expressed explicitly, but should be calculated by functions, how to use this function?
Thanks, Tang Laoya
0 件のコメント
参考
カテゴリ
Help Center および File Exchange で Get Started with Curve Fitting Toolbox についてさらに検索
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!