Hello Heinz,
You can have a look at pages 45-49 of my slides on least Squares :
http://www.utc.fr/~mottelet/mt94/leastSquares.pdf
Page 48 you have an example where the Covariance matrix is
approximated for a fitting problem with an ode defined page 42.
S.
Quoting Heinz Nabielek <[email protected]>:
Scilab friends: the power of Scilab is amazing and I have used it
recently for non-linear least-squares fitting, below example from
Scilab help function for "datafit". On occasions, I have also used
"leastsq".
Question: how do I derive the 1sigma standard error in the three
parameters p(1), p(2), and p(3)? And, if it is not too complicated,
covariances?
I know this is written in dozens of textbooks, but I am always
getting lost.
Please provide a simple recipe written in Scilab.
Best greetings
Heinz
// -- 04/04/2020 14:57:30 -- ////generate the datafunction y=FF(x,
p) y=p(1)*(x-p(2))+p(3)*x.*xendfunctionX=[]; Y=[]; pg=[34;12;14]
//parameter used to generate datafor x=0:.1:3
Y=[Y,FF(x,pg)+100*(rand()-.5)]; X=[X,x]; endZ=[Y;X]; //The
criterion functionfunction e=G(p, z), y=z(1),x=z(2);
e=y-FF(x,p), endfunction//Solve the
problemp0=[3;5;10][p,err]=datafit(G,Z,p0);
scf(0);clf()plot2d(X,FF(X,pg),5) //the curve without
noiseplot2d(X,Y,-1) // the noisy dataplot2d(X,FF(X,p),12) //the
solutionxgrid();legend("the curve without noise"," the noisy data",
"THE FINAL SOLUTION.....",4); title("solution set 39.868419
10.312053 11.482521","fontsize",4);
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