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Re: ArrayPlot coordinates scaling for overlays

• To: mathgroup at smc.vnet.net
• Subject: [mg109256] Re: ArrayPlot coordinates scaling for overlays
• From: Patrick Scheibe <pscheibe at trm.uni-leipzig.de>
• Date: Mon, 19 Apr 2010 05:58:48 -0400 (EDT)
• References: <hq9c3m$qh4$1@smc.vnet.net> <201004190648.CAA06709@smc.vnet.net>

Hi,

what about

ArrayPlot[
  Table[With[{z = x + I y},
    With[{w = (1 + z + z^2 + z^3)/(1 + z + z^2)}, Abs[w]]], {y, -1, 1,
    0.1}, {x, -1, 1, 0.1}],
  ColorFunction -> (Opacity[0.5, ColorData["TemperatureMap"][#]] &),
  DataRange -> {{-1, 1}, {-1, 1}}, Epilog :> {Arrow[{{0, 0}, {1, 1}}]}]

?

Cheers
Patrick

Am Apr 19, 2010 um 8:48 AM schrieb fd:

> All
>
> I've used the DataRange option and it worked quite well. A bit of a
> downside DataRange is not listed in the options of ArrayPlot.
>
> Below is the code with an example of what I'm trying to do. Please let
> me know if any of you would have a neater way of doing it. Many thanks
> for the help.
>
>
> a = ArrayPlot[
>  Table[With[{z = x + I y},
>    With[{w = (1 + z + z^2 + z^3)/(1 + z + z^2)}, Abs[w]]], {y, -1, 1,
>     0.1}, {x, -1, 1, 0.1}], ColorFunction -> "TemperatureMap",
>  DataRange -> {{-1, 1}, {-1, 1}}]
>
>
> b = Graphics[Arrow[{{0, 0}, {1, 1}}]]
>
>
>
> Show[b, Graphics[{Opacity[0.5], First@a}]]
>
>
>
>
>
>
>
>
>
> On Apr 16, 7:53 pm, Patrick Scheibe <psche... at trm.uni-leipzig.de>
> wrote:
>> Hi,
>>
>> use DataRange to tell Mathematica about the rectangle where your
>> ArrayPlot is in
>>
>> img = Import["http://sipi.usc.edu/database/misc/5.1.12.tiff";];
>> Show[{
>>  ArrayPlot[img[[1]], DataRange -> {{0, 2 Pi}, {-1, 1}},
>>   ColorFunction -> GrayLevel],
>>  Plot[Sin[x], {x, 0, 2 Pi}]
>>  }]
>>
>> and you can overlay different plots.
>>
>> Cheers
>> Patrick
>>
>>
>>
>> On Wed, 2010-04-14 at 23:13 -0400, fd wrote:
>>> All
>>
>>> This seems a simple problem I not finding an easy solution.
>>
>>> I have a plot obtained from an ArrayPlot, for which the coordinates
>>> are the indexes of the matrix being plotted; I want to overlay to  
>>> this
>>> plot some other plot, say, from DensityPlot. I have to tell
>>> Mathematica that the bottom left corner of the ArrayPlot is {xi,yi}
>>> and the upper right is {xf,yf}.
>>
>>> It would be nice as well to know how you could do this with a raster
>>> image in general.
>>
>>> I was trying to use ListDensityPlot, but for the specific problem I
>>> dealing with it is excruciatingly slow.
>>
>>> I'm also working to re-scale the FrameTicks by defining a new
>>> ArrayPlot function, with limited success. Below the code I'm working
>>> on.
>>
>>> Would anyone have an idea about this? Thanks in advance for any  
>>> help.
>>> Felipe
>>
>>> arrayPlotScale[array_List, {xmin_, xmax_}, {ymin_, ymax_}] :=
>>> Module[{deltas =
>>>    Reverse[{ymax - ymin, xmax - xmin}/Dimensions[array]],
>>>   n = Dimensions[array] // Reverse},
>>>  ArrayPlot[array,
>>>   FrameTicks ->
>>>    Reverse[{Table[{i, xmin + i deltas[[1]] }, {i, 0, n[[1]], 20}],
>>>      Table[{n[[2]] - i, ymin + i deltas[[2]]}, {i, 0, n[[2]],
>>> 10}]}]]]
>>
>>> test = Table[i j, {i, 1, 100}, {j, 100, 1, -1}];
>>
>>> arrayPlotScale[test, {0, 16}, {0, 100}]
>
>

• References:
  • Re: ArrayPlot coordinates scaling for overlays
    • From: fd <fdimer@gmail.com>