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function [p,err]=datafit(imp,G,varargin)
//
// [p,err]=datafit([imp,] G [,DG],Z [,W],...)
//
// Function 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)
//
// 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)
// DG: partial of G wrt p (optional; S=DG(p,z), S: nexnp)
//
// 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]=datafit(G,Z,[3;5;10])
//xset('window',0)
//xbasc();
//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]=datafit(G,DG,Z,[3;5;10])
//xset('window',1)
//xbasc();
//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')
//
//
// Copyright INRIA
[lhs,rhs]=argn(0)
if type(imp)<>1 then
varargin(0)=G
G=imp
imp=0
end
if type(G)==15 then
Gparams=G;Gparams(1)=null();
G=G(1)
else
Gparams=list()
end
DG=varargin(1)
if type(DG)==10|type(DG)==11|type(DG)==13 then
GR=%t //Jacobian provided
varargin(1)=null()
elseif type(DG)==15 then
error('Jacobian cannot be a list, parameters must be set in G')
else
GR=%f
end
Z=varargin(1);
varargin(1)=null()
if type(Z)<>1 then
error('datafit : wrong measurement matrix')
end
nv=size(varargin)
if nv>=1 then
if size(varargin(1),2)==1 then // p0 ou 'b'
W=1
else
W=varargin(1);varargin(1)=null()
if size(W,1)~=size(W,2) then
error('Weighting matrix must be square');
end
end
end
if type(varargin(1))==1 then // p0
p0=varargin(1)
else
p0=varargin(4)
end
[mz,nz]=size(Z);np=size(p0,'*');
if type(G)==10 then //form function to call hard coded external
if size(Gparams)==0 then
error('With hard coded function, user must give output size of G'),
end
m=Gparams(1);Gparams(1)=null()
// foo(m,np,p,mz,nz,Z,pars,f)
deff('f=G(p,Z)','f=call('''+G+''','+..
'm,1,''i'',np,2,''i'',p,3,''d'',mz,4,''i'',nz,5,''i'',Z,6,''d'','+..
'pars,7,''out'',['+string(m)+',1],8,''d'')')
pars=[];
for k=1:size(Gparams)
p=Gparams(k)
pars=[pars;p(:)]
end
Gparams=list()
end
if type(DG)==10 then //form function to call hard coded external
// dfoo(m,np,p,mz,nz,Z,pars,f)
deff('f=DG(p,Z)','f=call('''+DG+''','+..
'm,1,''i'',np,2,''i'',p,3,''d'',mz,4,''i'',nz,5,''i'',Z,6,''d'','+..
'pars,7,''out'',['+string(m)+','+string(np)+'],8,''d'')')
end
// form square cost gradient function DGG
if Gparams==list() then
GP = 'G(p,Z(:,i))'
GPPV = 'G(p+v,Z(:,i))'
DGP = 'DG(p,Z(:,i))'
else
GP = 'G(p,Z(:,i),Gparams(:))'
GPPV = 'G(p+v,Z(:,i),Gparams(:))'
DGP = 'DG(p,Z(:,i),Gparams(:))'
end
if ~GR then // finite difference
DGG=['g=0*p';
'pa=sqrt(%eps)*(1+1d-3*abs(p))'
'f=0;'
'for i=1:'+string(nz)
' g1='+GP
' f=f+g1''*W*g1'
'end'
'for j=1:'+string(np)
' v=0*p;v(j)=pa(j),'
' e=0;'
' for i=1:'+string(nz)
' g1='+GPPV
' e=e+g1''*W*g1'
' end'
' g(j)=e-f;'
'end;'
'g=g./pa;']
else // using Jacobian of G
DGG='g=0;for i=1:nz,g=g+2*'+DGP+'''*W*'+GP+',end'
end
// form cost function for optim
deff('[f,g,ind]=costf(p,ind)',[
'if ind==2|ind==4 then '
' f=0;'
' for i=1:'+string(nz)
' g1='+GP
' f=f+g1''*W*g1'
' end'
'else '
' f=0;'
'end';
'if ind==3|ind==4 then'
DGG
'else'
' g=0*p;'
'end'])
[err,p]=optim(costf,varargin(:),imp=imp)
endfunction
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