How can I avoid nested for loops when varying multiple array elements?
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I am trying to do a fit to 9 sets of data at once. They all have the same fit parameters with the exception of tau and n(k) which are different for each set. I am trying to find the best values for A, which is an array of four numbers. However, the only way I can think of to do this is to loop through the four values using nested loops (as I don't know which combinations of numbers will give the best fit). This is taking a very long time, so I would like to avoid the for loops (or at least the nested loops). I don't have much experience programming so this is proving to be a challenge. Any suggestions would be great!
The parts of the code I think are relevant are below:
% initialize parameters used in fitting
dbstop if error
tau = [4E-5 5E-5 7.5E-5 1E-4 1.5E-4 2E-4 3E-4 4E-4 5E-4];
tc = [2E-5 3E-4 6E-3 1E-1];
delM2 = 1E8*[.9 1 .2 .3];
n = [41 41 41 31 21 16 11 8 7];
chisqr_B = [999 999 999 999 999 999 999 999 999];
A_fit = zeros(1,4);
comp_fit = zeros(41,9);
T2eAve = (T2elow + T2ehigh)/2;
impr = 0;
for T2eInv = T2eAve:1:T2ehigh
% test fit for different population amplitudes A
for w = 0.06:0.01:0.40
for x = 0.06:0.01:0.40
for y = 0.06:0.01:0.40
for z = 0.06:0.01:0.40
A = [w x y z];
amp0 = A(1)+A(2)+A(3)+A(4); % fit amplitude for n=0
chisqr = zeros(1,9);
amp = zeros(9,41);
comp = zeros(41,9);
chi = zeros(9,41);
for k = 1:9
amp(k,1) = amp0;
% sum ampl contributions from 4 motions (i)
for m = 2:n(k)
amp1 = A(1)*something;
amp2 = A(2)*something;
amp3 = A(3)*something;
amp4 = A(4)*something;
amp(k,m) = amp1 + amp2 + amp3 + amp4;
comp(m,k) = log(amp(k,m)/amp(1,2));
if m>2
chi(k,m) = abs(comp(m,k)-dat(m,2*k))^2/abs(comp(m,k));
chisqr(1,k) = chisqr(1,k) + chi(k,m);
end
end
end
% store fit and population ampl for smallest chi-squared
if (sum(chisqr) <= sum(chisqr_B))
chisqr_B = chisqr;
A_fit = A;
T2e_fit = T2eInv;
comp_fit = comp;
impr = 1;
end
end
end
end
end
Note: I don't want to get rid of the k = 1:9 or the m = 1:n(k) loops, so I say A(i)*something as the 'something' is quite long and not really relevant. Also T2e values are input to the function.
Cheers, Lauren
采纳的回答
Bjorn Gustavsson
2012-7-31
You should have a look at:
fminsearch
that is the first optimization function to use for problems like this. That way you'd have to write the contenst in the 2 inner-most loops in a function returning the chi-2 value for a given combination of parameters and data set:
your_chi2fcn(par,data_set)
Then you call fminsearch with that function:
bestPars = fminsearch(@(par) your_chi2fcn(par,data_setNr1),par0);
Where par0 is some start-guess you have.
HTH,
3 个评论
Lauren
2012-7-31
Bjorn Gustavsson
2012-7-31
The way I thought you'd want to go about it was to sum up all the chisqr like you did in the if-condition in the loopy version above. I think that is what's causing you problems, fminsearch needs a scalar output from the objective function.
Lauren
2012-7-31
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