Best fitting curve for variable data

Hello

I was trying fitting to fit the following data

x = 1.0779 1.2727 1.4700 1.5766 1.6471 1.7396 1.7828 1.8208 1.8370

y = 7.9511 9.8400 12.8838 15.1925 31.0055 36.0292 62.5528 87.9648 176.4142

for the equation:

y = a exp(b*(1/x)^c)

where a ba nd c are fitting paramters.

I triesd the fiting but unfortinately i was not able to magae it. It will be really helpful experties can guide me in this context.

Thanks in advance!

Answer 1

[Matt J]

Using fminspleas from the File Exchange

https://www.mathworks.com/matlabcentral/fileexchange/10093-fminspleas

% data 
x = [1.0779    1.2727    1.4700  1.5766    1.6471    1.7396   1.7828    1.8208    1.8370]' ; 
y = [7.9511    9.8400   12.8838   15.1925   31.0055   36.0292   62.5528   87.9648  176.4142]' ; ;

      
funlist={1,@(c,xx) (1./xx).^c};
      
[c,ab]= fminspleas(funlist,-3,x,log(y),-inf,0);
a=exp(ab(1));
b=ab(2);

a,b,c

a = 8.6541

b = 0.0088

c = -9.4295

xx=linspace(min(x),max(x),100);
fun=@(x)a*exp(b*(1./x).^c);

plot(x,y,'o',xx,fun(xx))
ylim([0,max(y)])

Answer 2

[KSSV]

% data 
x = [1.0779    1.2727    1.4700  1.5766    1.6471    1.7396   1.7828    1.8208    1.8370]' ; 
y = [7.9511    9.8400   12.8838   15.1925   31.0055   36.0292   62.5528   87.9648  176.4142]' ; ;

eqn = @(a,b,c,x) a*exp(b*(1./x).^c) ; % equation to fit  

% Define Start points
x0 = [1 1 1]; 
% fit-function 
fitfun = fittype(eqn);
% fit curve
[fitted_curve,gof] = fit(x,y,fitfun,'StartPoint',x0)

fitted_curve = 
     General model:
     fitted_curve(x) = a*exp(b*(1./x).^c)
     Coefficients (with 95% confidence bounds):
       a =       15.61  (1.495, 29.73)
       b =    1.14e-06  (-1.433e-05, 1.661e-05)
       c =      -23.93  (-46.14, -1.715)

gof = struct with fields:
           sse: 879.6251
       rsquare: 0.9635
           dfe: 6
    adjrsquare: 0.9513
          rmse: 12.1080

% Save the coeffiecient values for a,b,c 
coeffvals = coeffvalues(fitted_curve);

% Plot results
scatter(x, y, 'bs')
hold on
plot(x,fitted_curve(x),'r')
legend('data','fitted curve')

[Somnath Kale]

Thank you @KSSV for your propmt response!!

Actully im trying to fit the follwing x and y and wanted to plot in following fasion:

x = [0.0970    0.1190    0.1323 0.1419    0.1515    0.1566 0.1605    0.1639    0.1653]';
y = [7.9511    9.8400   12.8838   15.1925   31.0055   36.0292   62.5528   87.9648  176.4142]';

semilogy(1./x,y,'o')

can you pleses help me for this

thanks,

somnath

[KSSV]

You have the code... Go ahead.

[Somnath Kale]

I tried using your code but did not get the expected results for fitting parameters

I have wrote following code uning diffenrt function fminsearch:

% fitting

x = [0.0970    0.1190    0.1323 0.1419    0.1515    0.1566 0.1605    0.1639    0.1653]';
y = [7.9511    9.8400   12.8838   15.1925   31.0055   36.0292   62.5528   87.9648  176.4142]';

semilogy(1./x,y,'o')

f = @(a,b,c,x) a*exp((b./x).^c);
obj_fun = @(params) norm(f(params(1), params(2), params(3), x) -y);
sol = fminsearch(obj_fun, [1,10,1]);

a = sol(1)
b = sol(2)
c = sol(3)

hold on
semilogy(1./x,f(sol(1),sol(2),sol(3),x),'-')
hold off

ylabel('y')
xlabel('1/x')

but im getting following issue:

Exiting: Maximum number of function evaluations has been exceeded

- increase MaxFunEvals option.

Current function value: 103.027992

how take care of this one?