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MathGroup Archive 1996

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Functional programming; Outer; NonlinearFit

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4147] Functional programming; Outer; NonlinearFit
  • From: vvs124 at rsphy1.anu.edu.au (vvs124)
  • Date: Fri, 7 Jun 1996 02:08:43 -0400
  • Organization: Optical Sciences Centre, ANU
  • Sender: owner-wri-mathgroup at wolfram.com

Dear MathGroup,

Here is the kind of thing that is giving me trouble: 

¥ First - I want to renormalize the list d 

d := {1, 2, 3, 4}               

according to the rule

Renorm[{S_, P_, N0_}] = d/b    

where
b := (1+S)^(P/2)/(Sqrt[N0]). 

Parameters S, P and N0 are defined in the 

ParamList := {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12}}

each set {S, P, N0} corresponding to the respective value of d in the
list.

I can do it for a d = const this way:        

Vectors   := Table[f[i], {i, Length[ParamList]}]
ToNumbers := Thread[Vectors -> ParamList]
RenormArray := Outer[Renorm, Vectors]
RenormNbrs  := RenormArray /. ToNumbers

But it obviously doesn't work if d has more than one element. In this
case 
I end up with a whole matrix, but I only need the diagonal elements. I
am 
REALLY tempted to do 

RenormD = Table[RenormNbrs[[i,i]], {i, Length[[ParamList]}],

but there_should_be a more elegant way of doing this. 
Can someone help me out here?

¥ Second question - does anybody have a hint for getting closer to the
global 
minimum of ChiSquared in NonlinearFit (Method -> FindMinimum)? With
3-parameter 
models it gets out of hand.  

THANKS!

Vicki

________________________________________________________________________

 Victoria Steblina                      Email: vvs124 at rsphy1.anu.edu.au
 
                                                                      
 Optical Sciences Centre                Tel:   61 6 249 5129           
                                                              
 Research School of Physical            Fax:   61 6 249 5184         
 Sciences and Engineering                                              
 Australian National University                 
 Canberra, ACT 0200, Australia                                         
________________________________________________________________________

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