To find exponent in power law equation of the form y = ax^m + b
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Faisal
el 19 de En. de 2023
Comentada: Matt J
el 19 de En. de 2023
I have X and Y points for a curve to be of the form Y = ax^m + b.
I want to find the exponent m, lets just say that m could be inbetween 1.2 - 2.5.
How can I find exact value for m?
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Respuesta aceptada
Matt J
el 19 de En. de 2023
Editada: Matt J
el 19 de En. de 2023
fminspleas downloadable from
is especially appropriate for power law fits.
a = 0.55;
m = 1.3;
b = -0.78;
% dummy data
x = (1:25)';
y = a*x.^m + b + randn(size(x));
m=fminspleas( {@(m,x)x.^m , 1}, 2,x,y, 1.2,2.5 )
2 comentarios
Matt J
el 19 de En. de 2023
Probably similar, but with 3 unknowns fminsearch is not guaranteed to converge, so no rigorous predictions are possible.
Más respuestas (2)
Mathieu NOE
el 19 de En. de 2023
hello
try this
may need some refinement for the initial guess for the parameters depending of your data
a = 0.55;
m = 1.3;
b = -0.78;
% dummy data
x = (1:25);
y = a*x.^m + b + randn(size(x));
% equation model y = a*x^m + b
f = @(a,m,b,x) (a*x.^m + b);
obj_fun = @(params) norm(f(params(1), params(2), params(3),x)-y);
% IC guessed
sol = fminsearch(obj_fun, rand(3,1));
a_sol = sol(1)
m_sol = sol(2)
b_sol = sol(3)
y_fit = f(a_sol, m_sol, b_sol, x);
Rsquared = my_Rsquared_coeff(y,y_fit); % correlation coefficient
figure(1)
plot(x,y,'rd',x,y_fit,'b-');
title(['Power Fit / R² = ' num2str(Rsquared) ], 'FontSize', 15)
ylabel('Intensity (arb. unit)', 'FontSize', 14)
xlabel('x(nm)', 'FontSize', 14)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function Rsquared = my_Rsquared_coeff(data,data_fit)
% R² correlation coefficient computation
% The total sum of squares
sum_of_squares = sum((data-mean(data)).^2);
% The sum of squares of residuals, also called the residual sum of squares:
sum_of_squares_of_residuals = sum((data-data_fit).^2);
% definition of the coefficient of correlation is
Rsquared = 1 - sum_of_squares_of_residuals/sum_of_squares;
end
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Matt J
el 19 de En. de 2023
If you have the Curve Fitting Toolbox,
a = 0.55;
m = 1.3;
b = -0.78;
% dummy data
x = (1:25)';
y = a*x.^m + b + randn(size(x));
fobj=fit(x,y,'power2','Lower',[-inf,1.2,-inf],'Upper',[+inf,2.5,+inf])
plot(fobj,x,y)
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