How do I fit a function to data using LSQNONLIN or LSQCURVEFIT?

I would like to fit the following function to data I have using LSQNONLIN or LSQCURVEFIT.

My function is described in the code.

However, it always gives error.

a = 0.800; 
b = 0.150; 
c = 0.200;

x0 = 0.300;
x = 0.500;

y0 = 0.150;
y = 0.150;

z0 = 0.100;
z = 0.100;

tempodados = [ 0.0000755000
0.0000790000
0.0000825000
0.0000860000
0.0000895000
0.0000930000
0.0000965000
0.0001000000
0.0001035000
0.0001070000
0.0001105000
0.0001140000
0.0001175000
0.0001210000
0.0001245000];

energiadados = [-2.998561136
-2.047288671
-1.423256844
-0.555726195
0.877699417
2.200575773
3.082059591
3.558854247
3.711599564
3.666770625
3.676198031
3.880316305
4.303658902
4.80742401
5.157829146];

E = @(e,tempodados)[

log(e(3).*exp(-e(2).*tempodados).*(1+(2.*GA.*2.*GB.*2.*GC)+(2.*GA+2.*GB+2.*GC)+((2.*GA.*2.*GB)+(2.*GA.*2.*GC)+(2.*GB.*2.*GC))));

GA = 0;
for n = 1:1:500
    ga = cos((n.*pi.*x)./a).*cos((n.*pi.*x0)./a).*exp(-e(1).*((n*pi/a).^2).*tempodados);
    GA = GA + ga;
end

GB = 0;
for n = 1:1:500
    gb = cos((n.*pi.*y)./b).*cos((n.*pi.*y0)./b).*exp(-e(1).*((n.*pi./b).^2).*tempodados);
    GB = GB + gb;
end

GC = 0;
for n = 1:1:500
    gc = cos((n.*pi.*z)./c).*cos((n.*pi.*z0)./c).*exp(-e(1).*((n.*pi./c).^2).*tempodados);
    GC = GC + gc;
end
];

e0 = [1,1,1];

e = lsqnonlin(fun,e0,tempodados,energiadados)

[Vaclav Rimal]

What error it actually produces?

Answer 1

[Torsten]

function main

  tempodados = [ 0.0000755000
  0.0000790000
  0.0000825000
  0.0000860000
  0.0000895000
  0.0000930000
  0.0000965000
  0.0001000000
  0.0001035000  
  0.0001070000
  0.0001105000
  0.0001140000
  0.0001175000
  0.0001210000
  0.0001245000];

  energiadados = [-2.998561136
  -2.047288671
  -1.423256844
  -0.555726195
  0.877699417
  2.200575773
  3.082059591
  3.558854247
  3.711599564
  3.666770625
  3.676198031
  3.880316305
  4.303658902
  4.80742401
  5.157829146];

  e0 = [1,1,1];

  e = lsqcurvefit(@fun,e0,tempodados,energiadados)

end

function E = fun(e,tempodados)

a = 0.800; 
b = 0.150; 
c = 0.200;

x0 = 0.300;
x = 0.500;

y0 = 0.150;
y = 0.150;

z0 = 0.100;
z = 0.100;

GA = 0;
for n = 1:1:500
    ga = cos((n.*pi.*x)./a).*cos((n.*pi.*x0)./a).*exp(-e(1).*((n*pi/a).^2).*tempodados);
    GA = GA + ga;
end

GB = 0;
for n = 1:1:500
    gb = cos((n.*pi.*y)./b).*cos((n.*pi.*y0)./b).*exp(-e(1).*((n.*pi./b).^2).*tempodados);
    GB = GB + gb;
end

GC = 0;
for n = 1:1:500
    gc = cos((n.*pi.*z)./c).*cos((n.*pi.*z0)./c).*exp(-e(1).*((n.*pi./c).^2).*tempodados);
    GC = GC + gc;
end 

E = log(e(3).*exp(-e(2).*tempodados).*(1+(2.*GA.*2.*GB.*2.*GC)+(2.*GA+2.*GB+2.*GC)+((2.*GA.*2.*GB)+(2.*GA.*2.*GC)+(2.*GB.*2.*GC))));

end