Exponential Curve Fitting in Matlab

0

votes

I have a data-set which is loaded into matlab. I need to do exponential fitting for the plotted curve without using the curve fitting tool cftool.

I want to do this manually through executing a code/function that will output the values of a and b corresponding to the equation:

 y = a*exp(b*x)

Then be using those values, I will do error optimization and create the best fit for the data I have.

Any help please?

Thanks in advance.

matlabcurve-fitting

Hi, is your curve a graph of a function, namely (x,a*exp(b*x))? In this case I would suggest standard methods, minimizing the least-square error by Levenberg-Marquardt, Gradient Descent, Gauß-Newton. If you want to save time and if it is available use the optimization toolbox's function lsqnonlin. Example:

data_x = [0,1,2,3]; data_y = [0.5,1.5,4.5,13.5]; residua = @(x) x(1) * exp(data_x * x(2)) - data_y; lsqnonlin(residua,[1,1])

– matheburg

1

votes

Try this...

f = fit(x,y,'exp1');

0

votes

I think the typical objective in this type of assignment is to recognize that by taking the log of both sides, various methods of polynomial fit approaches can be used.

    ln(y) = ln(a) + ln( exp(x).^b ) 
    ln(y) = ln(a) + b * ln( exp(x) )

There can be difficulties with this approach when errors such as noise are involved due to the behavior of ln as it approaches zero.

0

votes

In this exercise I have a set of data that present an exponential curve and I want to fit them exponentially and get the values of a and b. I used the following code and it worked with the data I have.

"trail.m" file: 
 %defining the data used 
 load trialforfitting.txt;
 xdata= trialforfitting(:,1); 
 ydata= trialforfitting(:,2); 

 %calling the "fitcurvedemo" function
 [estimates, model] = fitcurvedemo(xdata,ydata)
 disp(sse); 

 plot(xdata, ydata, 'o'); %Data curve

 hold on
 [sse, FittedCurve] = model(estimates);

 plot(xdata, FittedCurve, 'r')%Fitted curve
xlabel('Voltage (V)')
ylabel('Current (A)')
title('Exponential Fitting to IV curves');
legend('data', ['Fitting'])
hold off

"fitcurvedemo.m" file: 
function [estimates, model] = fitcurvedemo(xdata, ydata)
%Call fminsearch with a random starting point.
start_point = rand(1, 2);
model = @expfun;
estimates = fminsearch(model, start_point);
%"expfun" accepts curve parameters as inputs, and outputs 
%the sum of squares error [sse] expfun is a function handle;
%a value that contains a matlab object methods and the constructor
%"FMINSEARCH" only needs sse
%estimate returns the value of A and lambda
%model computes the exponential function 
    function [sse, FittedCurve] = expfun(params)
        A = params(1);
        lambda = params(2);
        %exponential function model to fit
        FittedCurve = A .* exp(lambda * xdata); 
        ErrorVector = FittedCurve - ydata;
        %output of the expfun function [sum of squares of error]
        sse = sum(ErrorVector .^ 2);

     end
 end

I have a new set of data that doesn't work with this code and give the appropriate exponential fit for the data curve plotted.

Exponential Curve Fitting in Matlab

3 Answers