MATLAB: How to fit an exponential curve fit function using fminsearch. Program runs, but result is incorrect.

fminsearch

Attached is my code
yfirst=[.8967e07 1.6294e07 2.6587e07 3.2537e07 3.6136e07 3.8419e07 3.9706e07]'; 
xfirst=[1,2,4,6,8,10,15];
[estimates, model] = myfun(xfirst,yfirst);
[sse, FittedCurve] = model(estimates);
semilogx(xfirst,FittedCurve,'-g*'); hold on;
semilogx(xfirst,yfirst,'-rd');hold off;
 xlim([ 0 50 ]);
%%%%FUNCTION FILE 
function [estimates, model] = myfun(xdata, ydata)
% Call fminsearch with guessed starting point.
% start_point =[2.23e7;.005];
model = @expfun;
estimates = fminsearch(model,start_point);
    function [sse, FittedCurve] = expfun(params)
        A=params(1)
        lambda=params(2)
        FittedCurve =(A .* exp(lambda * xdata));
        ErrorVector = FittedCurve - ydata;
        sse = sum(ErrorVector .^ 2);
    end
end
I get a large error and the curve does not match when plotted together. Thanks

Best Answer

There are several problems with your code.
This works:
yfirst=[.8967e07 1.6294e07 2.6587e07 3.2537e07 3.6136e07 3.8419e07 3.9706e07]'; 
xfirst=[1,2,4,6,8,10,15]';
expfun = @(b,xdata) b(1) -b(2) .* exp(b(3) .* xdata);             % Objective Funciton
SSECF = @(b) sum((yfirst - expfun(b,xfirst)).^2);           % Sum-Squared-Error Cost Function
start_point =[4E+7; 2.23e7; -.005];
[B, SSE] = fminsearch(SSECF, start_point);
figure(1)
plot(xfirst, yfirst, 'bp')
hold on
plot(xfirst, expfun(B,xfirst), '-r')
hold off
grid
text(5.2, 1.75E+7, sprintf('f(x) = %9.2E - %9.2E\\cdote^{%9.2E\\cdotx}', B))
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