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Re: fit a complex function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98975] Re: fit a complex function
  • From: dh <dh at metrohm.com>
  • Date: Thu, 23 Apr 2009 06:41:34 -0400 (EDT)
  • References: <gsmn0k$d2r$1@smc.vnet.net>


Hi,

you can not directly fit a complex function. But you may defined an 

error function of the parameters, that returns a real number, specifying 

the error. If you then search the minimum of this function over the 

parameters, you have solved your problem.

here is a simplified version with 1 dim. where we fit Exp[I a x]:

====================================

d = Table[{x, Exp[2 I x]}, {x, 0, Pi, Pi/10}];

err[a_] := Total[Abs[ d[[All, 2]] - ( Exp[a I #] & /@ d[[All, 1]])]^2];

FindMinimum[err[a], a]

====================================

Daniel





Magician wrote:

> I have  data in the following form

> 

> xi  , Fi            (xi is real but Fi is complex)

> 

> i want to determine a fit by using function

> 

> F(x, a , b,c, d)=    a Exp(- x^2/b) + c Sin( d x)

> 

> a, b, c and d are complex numbers to be determined so as to accurately

> represent the data.

> 

> How to do this problem?

> 

> 




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