       Re: Plot3D precision limits?

• To: mathgroup at smc.vnet.net
• Subject: [mg6588] Re: [mg6504] Plot3D precision limits?
• From: "Preferred Customer" <sherman.reed at worldnet.att.net>
• Date: Fri, 4 Apr 1997 02:11:37 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Jim,
ContourPlot was useful in looking at the shape of the solution.

DensityPlot was not as useful.

I did not find a way to have the entire x or y scale printed out, but did
verify that the input xmax, xmin, etc. were observed.

sherman reed

----------
> From: Jim Hicks <jim at cern36.ce.uiuc.edu>
> To: mathgroup at smc.vnet.net
> Subject: [mg6588] [mg6504] Plot3D precision limits?
> Date: Thursday, March 27, 1997 1:42 AM
>
> I have two questions regarding the statements listed below that find the
> numerical solution to a system of two equations and two unknowns (x and
> y).  This solution happens to be a maximum likelihood solution to the
> problem of estimating two unknown parameters, x and y.  The solution
> provided by FindRoot using Mathematica 3.0 under Solaris 2.5 for SPARC
> is the following:
>
> 	{x-> -0.237575444848816, y-> -0.0531098274657849}
>
> I am interested in visualizing the surface of the log-likelihood
> function in the immediate vicinity of the optimal solution.  As you can
> see, I have used Plot3D to plot this function near the solution.
>
> Question 1:
> As I increase the number of digits specified for the ranges of x and y
> to zoom in closer to the actual solution, Plot3D produces a non-smooth
> surface.  Plot3D produces a smooth surface if fewer digits are specified
> following the decimal for the plot ranges.  I assume that I am crossing
> some machine precision threshold.  Is this true and is there anyway to
> overcome it so that I can see an accurate representation of the surface
> near the solution given by x and y above?
>
> Question 2:
> If you reproduce the plot that I am considering, you will notice that
> all the axis labels are printed with up to 6 digits after the decimal.
> Is it possible to change this by some option such that for example, as
> many as 15 digits would be displayed?
>
> Thank you very much for your consideration of my questions.
>
> Jim
> je-hicks at uiuc.edu
>
>
>
>
a={52.9,4.1,4.1,56.2,51.8,0.2,27.6,89.9,41.5,95.,99.1,18.5,82.,8.6,22.5,51.4
,81.,51.,62.2,95.1,41.6}
>
>
b={4.4,28.5,86.9,31.6,20.2,91.2,79.7,2.2,24.5,43.5,8.4,84.,38.,1.6,74.1,83.8
,19.2,85.,90.1,22.2,91.5}
>
> c={0,0,1,0,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,1}
>
> p=1/(1+Exp[-x+y(b-a)])
>
> FindRoot[{Sum[c[[i]]-p[[i]],{i,1,21}],
>           Sum[(c[[i]]-p[[i]])(a[[i]]-b[[i]]),{i,1,21}]},{x,0},{y,0}]
>
> Plot3D[Sum[c[[i]]Log[p[[i]]]+(1-c[[i]])Log[1-p[[i]]],{i,1,21}],
>           {x,-.23757544485,-.23757544484},{y,-.05310983,-.05310982},
>           PlotPoints->15, BoxRatios->{1.0,1.0,0.4}]

```

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