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fit_dat
Parameter identification based on measured data
Calling Sequence
[p,err]=fit_dat(G,p0,Z [,W] [,pmin,pmax] [,DG])
Arguments
- G
Scilab function (e=G(p,z), e: nex1, p: npx1, z: nzx1)
- p0
initial guess (size npx1)
- Z
matrix [z_1,z_2,...z_n] where z_i (nzx1) is the ith measurement
- W
weighting matrix of size nexne (optional; default 1)
- pmin
lower bound on p (optional; size npx1)
- pmax
upper bound on p (optional; size npx1)
- DG
partial of G wrt p (optional; S=DG(p,z), S: nexnp)
Description
fit_dat
is used for fitting data to a model. For
a given function G(p,z), this function finds the best vector of parameters
p for approximating G(p,z_i)=0 for a set of measurement vectors z_i.
Vector p is found by minimizing
G(p,z_1)'WG(p,z_1)+G(p,z_2)'WG(p,z_2)+...+G(p,z_n)'WG(p,z_n)
Examples
deff('y=FF(x)','y=a*(x-b)+c*x.*x') X=[];Y=[]; a=34;b=12;c=14;for x=0:.1:3, Y=[Y,FF(x)+100*(rand()-.5)];X=[X,x];end Z=[Y;X]; deff('e=G(p,z)','a=p(1),b=p(2),c=p(3),y=z(1),x=z(2),e=y-FF(x)') [p,err]=fit_dat(G,[3;5;10],Z) xset('window',0) clf(); plot2d(X',Y',-1) plot2d(X',FF(X)',5,'002') a=p(1),b=p(2),c=p(3);plot2d(X',FF(X)',12,'002') a=34;b=12;c=14; deff('s=DG(p,z)','y=z(1),x=z(2),s=-[x-p(2),-p(1),x*x]') [p,err]=fit_dat(G,[3;5;10],Z,DG) xset('window',1) clf(); plot2d(X',Y',-1) plot2d(X',FF(X)',5,'002') a=p(1),b=p(2),c=p(3);plot2d(X',FF(X)',12,'002')
See Also
<< derivative | Optimization and Simulation | fsolve >> |