MATLAB: How to force a exponential fit to go through a preestablish point (x,y)

exponential fitfitting

Hi, I have some data X and Y and I want to fit it to an exponential function but giving it an initial point (Xo,Yo):

f = fit(x,y,'exp1','StartPoint',[0 2])

Is there any way to do it? I think I've tried everything I could.

Best Answer

x0 = ...;  % x coordinate of preestablished point
y0 = ...;  % y coordinate of preestablished point 
g = @(p,x)y0*exp(-p*(x-x0));
f = fit(x,y,g)
plot(f,x,y)

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MATLAB: Solving an ODE with best-fit adjustment to empirical observations

If I understood correctly, you want to find the parameters for an ODE such that the ODE fits some experimental data. If you have the Optimization Toolbox this is easy to program. You basically put the ODE solver inside the cost function for your optimization

Say your ODE is :

y' = A*y*(B-y)

And you want to find A, B, and y(0). This is some sample code that shows how it's done. Save it and run it.

function xout = do_optimization
% The true parameters
y0_true = 1;
A_true = 2;
B_true = 3;
T = (0:.01:1)';
ytrue =3./(1 + 2*exp(-6*T)) + 0.1*randn(size(T));
hold on;
plot(T,ytrue);
h = plot(T,nan*ytrue,'r');
set(h,'tag','solution');
x0 = [0.4 3.9 1.2];   % Just some Initial Condition
ub = [5 5 5];         % Upper bounds
lb = [0 0 0];         % Lower bounds
F = @(x) COST(x,T,ytrue);
xout = fmincon(F,x0,[],[],[],[],lb,ub); %<-- FMINCON is the optimizer
legend({'Experimental Data','Fitted Data'});
function COST = COST(x,T,ytrue)
y0 = x(1);
A = x(2);
B = x(3);
% The cost function calls the ODE solver.
[tout,yout] = ode45(@dydt,T,y0,[],A,B);
COST = sum((yout - ytrue).^2);
h = findobj('tag','solution');
set(h,'ydata',yout);
title(['y0 = ' num2str(y0) '   ' 'A = ' num2str(A) '    B = ' num2str(B)]);
drawnow;
function yprime = dydt(t,y,A,B)
yprime = A*y*(B-y);

MATLAB: How to do “Cosine wave approximation“ for random plot data

easy peasy. Though I have no clue what it means to "forcef\ully approximate".

x0 = [mean(y),max(y) - min(y)/2,0,3];
ft = fittype('a + b*cos((x-c)*d)')
ft = 
     General model:
     ft(a,b,c,d,x) = a + b*cos((x-c)*d)
mdl = fit(x',y',ft,'startpoint',x0)
mdl = 
     General model:
     mdl(x) = a + b*cos((x-c)*d)
     Coefficients (with 95% confidence bounds):
       a =       11.96  (7.416, 16.51)
       b =       10.43  (4.97, 15.88)
       c =    -0.02594  (-0.8867, 0.8348)
       d =       2.079  (0.141, 4.017)
plot(x,y,'o'),hold on,plot(mdl)

Best Answer

Related Solutions

MATLAB: Solving an ODE with best-fit adjustment to empirical observations

MATLAB: How to do “Cosine wave approximation“ for random plot data

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