exponential curve fit coefficients

Is there a way to calculate exponential curve fit coefficients without using the curvefit toolbox??

Answer 1

[Star Strider]

Linearising it by log-transforming the data is not appropriate, because that distorts the errors, making them multiplicative rather than additive.

It is straightforward to do a nonlinear parameter estimation using fminsearch, which is a core-MATLAB function, requiring no toolboxes.

EDIT — (8 Sep 2021 at 15:30)

To illustrate —

x = linspace(0, 5, 25);
y = x.^2 + randn(size(x));
y = abs(y);

objfcn = @(b,x) b(1).*exp(b(2).*x);                                     % Objective Function
B0 = rand(3,1);
[B1,Fval] = fminsearch(@(b) norm(y - objfcn(b,x)), B0)                  % Nonlinear Iterative Solution

B1 = 3×1

1.4102 0.5850 -1.0206

Fval = 7.3191

Fit1 = objfcn(B1,x);

B2 = polyfit(x, log(y), 1)

B2 = 1×2

0.9478 -0.9879

Fit2 = polyval(B2, x);
Fit2 = exp(Fit2);

figure
subplot(2,1,1)
    plot(x, y, '.b')
    hold on
    plot(x, Fit1, '-r')
    hold off
    grid
    title('Nonlinear Fit')
subplot(2,1,2)
    plot(x, y, '.b')
    hold on
    plot(x, Fit2, '-r')
    hold off
    grid
    title('Linearised Fit')

.

[Ravi Narasimhan]

Very interesting. I didn't know this was available in core Matlab. I thought (probably incorrectly) that the OP was looking for a quick and dirty solution where the linearization wasn't a big concern.

Answer 2

[Ravi Narasimhan]

See the answer to a similar question in:

https://www.mathworks.com/matlabcentral/answers/1448569-queston-for-school-linearize-an-equation?s_tid=srchtitle

(corrected link)