Logarithmic and exponential curve fitting

Hello,

I have two sets of data and I would like to fit a logarithmic function (base 10) to the first dataset and an exponential function (also base 10) to the second dataset. Could you please tell me how to do this? I am unexperienced in curve fitting (details are welcome)...

Thanks

Answer 1

[TED MOSBY]

Hi,

You can use MATLAB's "fit" and "polyfit" functions to fit the data after preprocessing it. For the logarithmic function you can fit it like below:

% Assuming your datasets are stored in MATLAB arrays
% Here x1 is your independent variable and y1 is your dependent variable

log10_x1 = log10(x1); % transform x-values with log10
coeffs_log = polyfit(log10_x1, y1, 1); % Linear fit on transformed data

% Coefficients
a_log = coeffs_log(1);
b_log = coeffs_log(2);

% Fitted function
y1_fit = a_log * log10(x1) + b_log;

Likewise you can fit for the exponential function:

log10_y2 = log10(y2); % transform y-values with log10
coeffs_exp = polyfit(x2, log10_y2, 1); % Linear fit on transformed data

% Coefficients
b_exp = coeffs_exp(1);
log10_a_exp = coeffs_exp(2);
a_exp = 10^(log10_a_exp);

% Fitted function
y2_fit = a_exp * 10.^(b_exp * x2);

You can then proceed to plot the results to visualize them.

For more information on the fitting functions please refer to the documentation below:

https://www.mathworks.com/help/matlab/ref/polyfit.html?s_tid=srchtitle_support_results_1_polyfit

https://www.mathworks.com/help/curvefit/fit.html?s_tid=srchtitle_support_results_1_fit

Hope this helps!