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Re: NonlinearFit + Sums
*To*: mathgroup at smc.vnet.net
*Subject*: [mg68806] Re: [mg68760] NonlinearFit + Sums
*From*: Darren Glosemeyer <darreng at wolfram.com>
*Date*: Sat, 19 Aug 2006 00:41:10 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
I would suggest assigning the list of variable names to a symbol and using
Total to do the summation in the model. A shortened example using 5 x_i
variables follows.
In[1]:= << Statistics`
In[2]:= xvect = Table[ToExpression[StringJoin["x", ToString[i]]], {i, 1, 5}]
Out[2]= {x1, x2, x3, x4, x5}
In[3]:= model=E^(mu)*Total[xvect]
mu
Out[3]= E (x1 + x2 + x3 + x4 + x5)
In[4]:= data = Table[Random[], {100}, {6}];
In[5]:= NonlinearFit[data, model, xvect, {mu}]
Out[5]= 0.19181 (x1 + x2 + x3 + x4 + x5)
Since E^(mu) was just a constant multiplier in the model sent, I factored
it out in model above. In general, if you have a model that is a sum of a
function f of the individual variables, you could do something like the
following.
In[6]:= Total[ Map[f, xvect]]
Out[6]= f[x1] + f[x2] + f[x3] + f[x4] + f[x5]
For the example model sent, this would work like the following.
In[7]:= Total[ Map[E^(mu)*#&, xvect]]//InputForm
Out[7]//InputForm= E^mu*x1 + E^mu*x2 + E^mu*x3 + E^mu*x4 + E^mu*x5
Darren Glosemeyer
Wolfram Research
At 03:12 AM 8/18/2006 -0400, Lyta wrote:
>Hi,
>
>I want to do a mulitdimensional nonlinear fitting and I'm not sure how to
>define the mathematica statement for that.
>
>I have a matrix "data" of dimensions 140x37 that contains 36 samples of
>140 functions. The 37th column contains the resulting value of a mapping
>of the type R36->R1. I want to calculate the parameter mu of a function
>that integrates over the samples - i posted a simplified version of the
>function below. My problem is, that I don't know what to write instead of
>x_i. For the second x_ it should be something like {x1, x2, x3, x4, ...,
>x36}. But the first x_i should be something like x[[i]] (this doesn't work
>ofc). How do i assign the data to the sum?
>
>NonlinearFit[data, Sum[E^(mu)*x_i, {i, 1, 36}], x_i, {mu}]
>
>I hope you can help :-)
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