Best fitting curve for variable data

Question

Somnath Kale 2022-4-23

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1703095-best-fitting-curve-for-variable-data

编辑： Matt J 2022-4-23

采纳的回答： Matt J

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!

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Answer 1

Matt J 2022-4-23

1
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1703095-best-fitting-curve-for-variable-data#answer_949100

编辑：Matt J 2022-4-23

在 MATLAB Online 中打开

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)])

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Answer 2

KSSV 2022-4-23

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1703095-best-fitting-curve-for-variable-data#answer_949000

编辑：KSSV 2022-4-23

在 MATLAB Online 中打开

% 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')

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KSSV 2022-4-23

You have the code... Go ahead.

Somnath Kale 2022-4-23

编辑：Somnath Kale 2022-4-23

在 MATLAB Online 中打开

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?

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Best fitting curve for variable data

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Best fitting curve for variable data

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