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Re: Controling the color of line segments in a Log plot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90157] Re: Controling the color of line segments in a Log plot
  • From: "David Park" <djmpark at comcast.net>
  • Date: Tue, 1 Jul 2008 06:57:53 -0400 (EDT)
  • References: <g4a6r8$8s5$1@smc.vnet.net>

Using your sample point list:

yValues = Table[10^n, {n, 10}]
xy = Transpose[{Range[Length[yValues]], yValues}]

One might have hoped that the following construction would work:

ListLogPlot[xy, Joined -> True,
 ColorFunction -> Function[{x, y}, If[3 <= x <= 6, Red, Black]]]

But it doesn't. Perhaps someone will know how to make that approach work.

So I go to a more detailed approach using the Presentations package. This 
parallels your second approach but without all the level jumping. First, we 
need a format function for the y tick labels.

Needs["Presentations`Master`"]

nformat[n_] := Switch[n,
  1, 1,
  10, 10,
  _, Superscript[10, Log[10, n]]]

Then we construct custom ticks and grids. I'm going to use a Frame plot with 
a light grid.

yticks = CustomTicks[Log, {1, 10, {1}, {2, 3, 4, 5, 6, 7, 8, 9}},
   CTNumberFunction -> (nformat[#] &)];
ygrid = CustomGridLines[Log, {1, 10, Range[9]}, {LightGray}];
xgrid = CustomGridLines[Identity, {1, 10, 1}, {LightGray}];

Then we can draw the custom plot, using separate draw statements for the 
regions of the curve:

Draw2D[
 {ListLogDraw[Take[xy, {1, 3}], Joined -> True],
  ListLogDraw[Take[xy, {6, 10}], Joined -> True],
  Red,
  ListLogDraw[Take[xy, {3, 6}], Joined -> True]},

 AspectRatio -> 1,
 PlotRange -> {{1, 10}, {Log[10], Log[10^10]}},
 Frame -> True,
 FrameTicks -> {{yticks, yticks // NoTickLabels}, {Automatic,
    Automatic}},
 GridLines -> {xgrid, ygrid},
 ImageSize -> 500]

I could have used PlotRange -> {{1, 10}, All} but I gave explicit values to 
the y plot range just to show that, in fact, Mathematica DOES use the 
natural log for the underlying plot values. Also notice that I used natural 
log in the CustomTicks and CustomGrid functions as the routine to get from 
the label value to the underlying plot value.

-- 
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/


"Donald DuBois" <donabc at comcast.net> wrote in message 
news:g4a6r8$8s5$1 at smc.vnet.net...
>I would like to control the color of line segments in a Log plot. I have 
>three Questions (A,B,C) regarding this problem.
>
> A simple example:  I start with the data yValues = Table[10^n, {n,10}] - 
> which should also be the Y-axis tick values - and use ListLogPlot to graph 
> it.
>
> yValues = Table[10^n, {n, 10}]
> xy = Transpose[{Range[Length[yValues]], yValues}]
> ListLogPlot[xy, Joined -> True]
>
>
> Question A . Does anyone find it peculiar that ListLogPlot seems to be 
> taking
> Log to base 10 as a default as in the above plot when Log by itself 
> defaults to base E?  This is FINE for me, as I want it to be to the base 
> 10. But still,
> does anyone know why this is so or am I misconstruing something?
>
>
> Question B.
> I would like to change the color to Red of the line segment with X values 
> going from
> 3 to 6. (In general, I would like to change the segment color to Red for 
> any number of segments of the same Log plot.) Is there a way to do this at 
> the  ListLogPlot level (i.e.giving directives directly to ListLogPlot)?
> That would be the simplest solution.
>
> I can change the color of this part of the graph by going down to the 
> Graphics element level using Line as in the following, but this is 
> tedious.
>
> logY = Map[N[ Log[10, #]] &, yValues]
> xyLog = Transpose[{Range[Length[logY]], logY}]
> l2 = Graphics[{Red, Thick, Line[Take[xyLog, {3, 6}]]}];
> l1 =  Graphics[{Line[Take[xyLog, {1, 3}]]}];
> l3 =   Graphics[{Line[Take[xyLog, {6, 10}]]}];
> Show[l1, l2, l3, Axes -> True, AxesOrigin -> {0, 0}]
>
> Question C.  The above graph loses the original Y axis tick values which 
> are contained in the yValues list defined above.  Is there any way to 
> solve this?  I want the graph to look like the first graph above  with the 
> same Y tick values (using ListLogPlot) except the Line segment with X 
> values from 3 to 6 should be Red.
>
> Thank you in advance for any help you can give me.
>
> Don
> 



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