Name

fit_dat — Parameter identification based on measured data

Calling Sequence

[p,err]=fit_dat(G,p0,Z [,W] [,pmin,pmax] [,DG])

Parameters

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

optim, datafit