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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) INRIA
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
//
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)
//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]=datafit(G,DG,Z,[3;5;10])
//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')
//
[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(msprintf(gettext("%s: Jacobian cannot be a list, parameters must be set in G."),"datafit"));
else
GR=%f
end
Z=varargin(1);
varargin(1)=null()
if type(Z)<>1 then
error(msprintf(gettext("%s: Wrong measurement matrix."),"datafit"));
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
if size(W,1)==1 then
error(msprintf(gettext("%s: Initial guess must be a column vector."),"datafit"));
else
error(msprintf(gettext("%s: Weighting matrix must be square."),"datafit"));
end
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(msprintf(gettext("%s: With hard coded function, user must give output size of G."),"datafit"));
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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