fitting data with exponential + linear form

I want to fit my data into

y= a*exp(-x/b)+cx+d (exponential linear form).

I got number of data set of about 600.

If I put it in

y= a*exp(-x)+cx+d, it works although it doesn't fit 'best'

explinearfit = fittype({'exp(-x)','x','1'})

fo = fitoptions(explinearfit);
fo.normalize = 'on';

myFit = fit(t2,n,explinearfit);
 
plot(myFit,t2,n)

xlabel('time(t2)')
ylabel('electrons(n)')
legend('Data','Fitted graph')
title('Data and Fitted Curve')


 
clear opts

However, if I put 'b' inside the exponential, it goes way wrong.

explinearfit = fittype('a*exp(-x/b)+c*x+d')

fo = fitoptions(explinearfit);
fo.normalize = 'on';

myFit = fit(t2,n,explinearfit);
 
plot(myFit,t2,n)

xlabel('time(t2)')
ylabel('electrons(n)')
legend('Data','Fitted graph')
title('Data and Fitted Curve')


 
clear opts

How can I fix this?

The warning sign says that there are no starting points so they were randomly chosen.

Answer 1

[Alan Stevens]

Try starting with the following guesses: a = 6E10, b = 4E-4, c = 0, d = -1.57E12.

with

explinearfit = fittype( @(a,b,c,d,x) a*exp(-x/b)+c*x+d );

(I'm guessing at the fittype as I don't have the Curve fitting toolbox myself!).

[Alex Sha]

Hi, Alan, refer to the results below:

Root of Mean Square Error (RMSE): 1390205473.08086
Sum of Squared Residual: 1.16926611071731E21
Correlation Coef. (R): 0.992002295260181
R-Square: 0.984068553801468
Adjusted R-Square: 0.984015625408781

Parameter	Best Estimate
----------	-------------
a	50867056286.6369
b	0.000427936677731703
c	-1152953437385.39
d	-1565359446337.44

[Alan Stevens]

Looks like a good fit!

[찬 소]

Yeap! I got the reasonable fit as well.

But how did you guess the initial values?

I think I might also have other sets of data.

[Alan Stevens]

First I looked at x = 0 and set a+d to a value near the top of the points. Then at the other end it looked as if the curve might be asymptotically horizontal, so, with x set at infinity, I set c = 0, and d to a value near the bottom of the points (thus allowing me to get a as well). I then just plotted the resulting curve against the points, starting with b = 1, and adjusted b until I got what looked like a reasonable fit by eye (it took about four guesses) . The constants were never going to be perfect, but were likely to provide a decent initial guess.

Answer 2

[Md Shariful Islam]

Hi,

In this code, do we just need to declare the initial guesses(a = 6E10, b = 4E-4, c = 0, d = -1.57E12) before following code?

I was trying to reproduce the plot with best fit as I encounter similar issues. However, I could not get a good fit rather I am getting a fit like 2nd image.

May I get a working code for this problem?

"

explinearfit = fittype('a*exp(-x/b)+c*x+d')

fo = fitoptions(explinearfit);

fo.normalize = 'on';

myFit = fit(t2,n,explinearfit);

plot(myFit,t2,n)

xlabel('time(t2)')

ylabel('electrons(n)')

legend('Data','Fitted graph')

title('Data and Fitted Curve')

"