Re: Re: 'NonlinearFit` confusion

```Yas,

skipping some of the data will not eliminate the potential
multi-extremality of a nonlinear model-fitting problem (but can make the
solution less stable). As Paul Abbott noted, either one needs a
'sufficiently good' starting point for successful local
fitting/optimization, or needs to apply global optimization methods to find
the best numerical fit.

Regards,
Janos Pinter

At 10:21 AM 8/5/2004, you wrote:
>Hi,
>
>Why not take less points, rather than more??
>
>In[480]:=
>Clear[datay,datax,data1]
>datay = Table [6 + 2Sin[3 + x], {x, -10Pi, 10Pi, 0.05}];
>datax = Table [x, {x, -10Pi, 10Pi, 0.05}];
>data1 = Table[{datax[[i]], datay[[i]]}, {i, 1, Length[datay]}];
>Length[data1]
>First[data1]
>
>Out[484]=
>1257
>
>Out[485]=
>{-31.4159,6.28224}
>
>In[511]:=
>Clear[a,b,c,d,e]
>sinFit1=NonlinearFit[Take[data1,40], c + a *Sin[d + e *x], x, {a, c,
>d,e}]
>
>Out[512]=
>6.\[InvisibleSpace]+2. Sin[3.\[InvisibleSpace]+1. x]
>
>
>In[513]:=
>Clear[y,datay,datax,a,b,c,d,e]
>datay = Table [6 + 2Sin[3 + 5 x], {x, -10Pi, 10Pi, 0.05}];
>datax = Table [x, {x, -10Pi, 10Pi, 0.05}];
>data2 = Table[{datax[[i]], datay[[i]]}, {i, 1, Length[datay]}];
>Length[data2]
>First[data2]
>
>Out[517]=
>1257
>
>Out[518]=
>{-31.4159,6.28224}
>
>In[519]:=
>y=a*Sin[d+e x]+c;
>sinFit2=NonlinearFit[Take[data2,40],y, x, {a,c, d,e}]
>
>Out[520]=
>6.\[InvisibleSpace]+2. Sin[122.381\[InvisibleSpace]+5. x]
>
>
>DisplayTogether[
>    Plot[sinFit1, {x, -10Pi, -8 Pi}, PlotStyle -> Blue],
>    Plot[sinFit2, {x, -10Pi, -8 Pi}, PlotStyle -> Red],
>
>    ListPlot[Take[data1, 40], PlotStyle -> {Blue, PointSize[0.011]}],
>    ListPlot[Take[data2, 30], PlotStyle -> {Red, PointSize[0.011]}],
>    Prolog -> {
>        {
>          Blue,
>          Text["sinFit1", {-27.5, 7}, {-1, 0},
>            TextStyle -> {FontFamily -> "Times",
>                FontWeight -> "Bold",
>                FontSize -> 18
>                }
>            ]
>          },
>
>        {
>          Red,
>          Text["sinFit2", {-26.9, 6}, {-1, 0},
>            TextStyle -> {FontFamily -> "Times",
>                FontWeight -> "Bold",
>                FontSize -> 18
>                }
>            ]
>          }
>        },
>    ImageSize -> 800,
>    Frame -> False,
>    AxesOrigin -> {-31.5, 4.0}
>
>    ]
>
>Cheers
>Yas
>
>
>
>On Aug 4, 2004, at 9:46 AM, Klingot wrote:
>
> > I'm trying to fit a sinusoidal function to my data using
> > 'NonlinearFit' but it's exhibiting rather odd behaviour. Please see my
> > examples below:
> >
> > EXAMPLE (1).
> >
> > **** As a test, I created a list of data from a function of the form y
> > = 6 + 2Sin[3 + x] with:
> >
> > datay = Table [6 + 2Sin[3 + x], {x, -10Pi, 10Pi, 0.05}];
> > datax = Table [x, {x, -10Pi, 10Pi, 0.05}];
> > data = Table[{datax[[i]], datay[[i]]}, {i, 1, Length[datay]}];
> >
> > **** Then tested to see whether NonlinearFit would correctly deduce
> > the equations parameters with:
> >
> > NonlinearFit[data, c + a Sin[d + e x], x, {a, c, d,e}]
> >
> > **** As expected, it gave me '6.+ 2. Sin[3. + 1. x]' ... exactly as
> > one would expect :)
> >
> >
> > EXAMPLE (2).
> >
> > **** Second test, I modified the equation by multiplying x by 5, ie.
> > y = 6 + 2Sin[3 + 5x]:
> >
> > datay = Table [6 + 2Sin[3 + 5 x], {x, -10Pi, 10Pi, 0.05}];
> > datax = Table [x, {x, -10Pi, 10Pi, 0.05}];
> > data = Table[{datax[[i]], datay[[i]]}, {i, 1, Length[datay]}];
> >
> > ***** and applied the NonlinearFit as before:
> >
> > NonlinearFit[data, c + a Sin[d + e x], x, {a, c, d,e}]
> >
> > ***** but this time I get a wildly innacurate result:    6.000165 +
> > 0.025086 Sin[0.0080308 - 0.247967 x]
> >
> > Specifically, the parameters 'a', 'd' and 'e' are all completely in
> > error by orders of magnitude.
> >
> > I tried extending the range of the data to include more cycles of the
> > sinusoid, thereby making it more continuous/monotonic but that made no
> > difference.
> >
> > Am I missing something fundamental here?
> >
> > Any assistance would be greatly appreciated.
> >
> > PS: I'm using Mathematica 5.0 on a MAC.
> >
>Dr. Yasvir A. Tesiram
>Associate Research Scientist
>Oklahoma Medical Research Foundation
>Free Radical Biology and Ageing Research Program
>825 NE 13th Street, OKC, OK, 73104
>
>P: (405) 271 7126
>F: (405) 271 1795
>E: yat at omrf.ouhsc.edu

```

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