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MathGroup Archive 2000

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Re: Fitting a function to a list (newbie)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg21869] Re: Fitting a function to a list (newbie)
  • From: "Kevin J. McCann" <kevin.mccann at jhuapl.edu>
  • Date: Wed, 2 Feb 2000 22:54:25 -0500 (EST)
  • Organization: Johns Hopkins University Applied Physics Lab, Laurel, MD, USA
  • References: <872jej$civ@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I believe that what you want is a least squares fit to your data.

I have attached a NB at the bottom. Let me know if it helps.

Kevin
--

Kevin J. McCann
Johns Hopkins University APL


<mathprof at bigfoot.com> wrote in message news:872jej$civ at smc.vnet.net...
> I'm new to Mathematica 4.0, so I apologize if this question is overly
> trivial (and please let me know if there's a place for trivial
> question).
>
> I have a list that I'd like to fit to the function:
>
> A + B*Sin[C*x+D]
>
> In other words, I'd like to find the (approximate numeric) values of
> A,B,C,D that yield the best fit to my data.
>
> I tried using Fit[], but it only applies to linear combinations of
> functions, and couldn't optomize the values of C and D.
>
> For this specific problem, I'm guessing some sort of Fourier transform
> might work, but I'm interested in a more general solution -- for example
> if Sin[] were replaced with a more complicated function.
>
> Any help appreciated!
>
>
> Sent via Deja.com http://www.deja.com/
> Before you buy.
>
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Notebook[{

Cell[CellGroupData[{
Cell["Multivariate LSQ fit", "Title"],

Cell["\<\
by Kevin McCann
kevinmccann at Home.com\
\>", "Author"],

Cell["Here is a \"data\" function", "Text"],

Cell[BoxData[
    \(\(g[x_] = 4 + 3\ Sin[2 + x];\)\)], "Input",
  CellLabel->"In[91]:="],

Cell["Generate a random list of x-values", "Text"],

Cell[BoxData[
    \(\(xlist = Table[Random[Real, {0, 4  \[Pi]}], {100}];\)\)], "Input",
  CellLabel->"In[92]:="],

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Cell[BoxData[
    \(\(dataList = \(({#, g[#] + Random[Real, {\(-1.5\), 1.5}]} &)\)\  /@ \
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Cell["and here is a plot of the data", "Text"],

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          PlotStyle \[Rule] {RGBColor[0, 0, 1],
              AbsolutePointSize[5]}];\)\)], "Input",
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Cell["Here is the function we wish to fit to.", "Text"],

Cell[BoxData[
    \(f[x_, a_, b_, c_, d_] := a\  + \ b\ Sin[c + d\ x]\)], "Input",
  CellLabel->"In[97]:="],

Cell["\<\
and a Module to do a least-squares sum for a given set of a,b,c,d.\
\>", "Text"],

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            dataList, {1}]\[IndentingNewLine]]\)], "Input",
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Now just find the minimum of that. I have given each of the parameters an \
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