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From: Piter_ on 16 Nov 2009 13:29
Hi all.
I have one question about CurveFitting toolbox.

Lest say I have 3 datasets.
D1= A1_1exp(k1*t)+A2_1*exp(k2*t)+A3_1*exp(k3*t)+C1
D2= A1_2exp(k1*t)+A2_2*exp(k2*t)+A3_2*exp(k3*t)+C2
D3= A1_3exp(k1*t)+A2_3*exp(k2*t)+A3_3*exp(k3*t)+C3
Is there any way to fit it using curve fitting toolbox.

Thanks
Petro

P.S. So far I did it using matrix based fit and fminsearch but I
wanted to apply curve fitting toolbox there:
function [ssq par] = exp_mb_ls(par,t,v,s)
[ro co]=size(t);
len=ro;
[ro co]=size(par);
F=ones(len, co+1);
F(:,1:co)=(ones(size(t))*par(1,:).*exp(-ones(size(t))*par(2,:).*(t*ones
(1,co))));
Ht=pinv(F)*v;
v_star=F*Ht;
resid=v-v_star;
pinv(F);
ssq=norm(resid*s);


And fitfing using exp_mb_ls function
par0=[0.5 0.5 0.2 0.1;...
10000 5000 80 50;]...
%matrix based fit of v vectors
par_svd=fminsearch('exp_mb_ls',par0,[],t,v(:,1:3),s(1:3,1:3));
%generating fitted v vectors
[ro co]=size(par_svd);
F=ones(21,co+1);
for i=1:co
F(:,i)=exp(-t*par_svd(2,i))*par_svd(1,i);
end
Ht=pinv(F)*v(:,1:3);
vfit=F*Ht;
figure
plot(t,[v(:,1:3)],'o',t,vfit,'*')
%legend('v','v fit')
grid on
title('svd based fit of v(:,1:3)')
set(gca,'xscale','log')
grid on

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