ArrayPlot and non-integer PlotRange

Question

There seems to weird bug regarding non-integer PlotRange in ArrayPlot. For example...

ArrayPlot[
   Table[Sin[x/50 π] Tanh[y/50 π], {y, 100}, {x, 100}],
   DataRange -> {{0, 1}, {0, 1}},
   PlotRange -> {{0, 1}, {0.5, .9}}
]

gives an error:

Value of option PlotRange -> {{0,1},{0.5,0.9}} is not All, Full, Automatic, a positive machine number, or an appropriate list of range specifications.

The same code works, if one of the plot range parameters for y-axes is turned into an integer.

Did I do smth wrong? Is there a workaround?

I need to use array plot as ListContourPlot is too slow for large datasets and MatrixPlot has the same problem.

I am using Mathematica 8 64 bit version on linux.

Edit

After some more testing I see, that it works whenever PlotRange includes at least one integer. For example PlotRange -> {{0, 1}, {0.5, 1.2}} works as it includes 1. So one possible workaround is just to scale the range, such that max-min would be larger than 1.

But I am still looking forward, if anyone finds a way to have shorter than 1 range on the axes. Dirty way would be just using manual 'Ticks'.

Edit 2

Possible workaround.

As I wrote in the previous edit, it works, then the range includes at least one integer. So one could just scale the range. Here is a naive hard-coded example how it might be done.

ArrayPlot[
   Table[Sin[x/50 π] Tanh[y/50 π], {y, 100}, {x, 100}],
   DataRange -> {{0, 1}, {0, 1} 10}, 
   PlotRange -> {{0, 1}, {0.1, 0.8} 10}, 
   FrameTicks -> {Table[{y, ToString[y/10 // N]}, {y, 1, 8, 1}], 
   Table[{x, ToString[x // N]}, {x, 0, 1, 0.25}]}, 
   AspectRatio -> 1
]

This means that I have bypassed the only side-effect of scaling the range, which is messing up the tick labels.

I would submit it as a solution, when I have waited my 8 hours and there is no nicer one proposed.

Answer 1

Here is a workaround that works in V7,8,9,10 (the underlying problem persists):

Show[
 ArrayPlot[
  Table[Sin[x/50 π] Tanh[y/50 π], {y, 100}, {x, 100}], 
  DataRange -> {{0, 1}, {0, 1}}],
 PlotRange -> {{0, 1}, {0.5, .9}}, FrameTicks -> All]

Answer 2

All observations that follow were made using Mathematica 7.

---

The problem is that deep in the option processing of ArrayPlot, Floor and Ceiling are used on the numeric values in the PlotRange option value. This is evidenced by Blocking these function while calling ArrayPlot:

Block[{Floor = Identity, Ceiling = Identity},
 ArrayPlot[
  Table[Sin[x/50 π] Tanh[y/50 π], {y, 100}, {x, 100}],
  DataRange -> {{0, 1}, {0, 1}}, PlotRange -> {{0, 1}, {0.5, .9}},
  FrameTicks -> All
 ]
]

This actually works just fine here and we get the desired plot, but this fix is hardly "safe" as it's impossible to guess what other steps in the plot creation are altered by this.

I am continuing to dig through internal code but even if I find a fix for version 7 there is no guarantee that it will be easily ported to later versions.

---

In version 7 the two functions that need to be modified are:

• Graphics`ArrayPlotDump`Private`ArrayTicks

• Graphics`ArrayPlotDump`Private`getRange

Answer 3

From help

PlotRange -> {{ imin,imax }, {jmin ,jmax }} shows only elements 
with and in the specified ranges. The top-left element has , 
increases down the page; increases to the right. 

So these are index values. You can't use .5 and .9 or even zero.

ArrayPlot[
 N@Table[Sin[x/50 π] Tanh[y/50 π], {y, 100}, {x, 100}], 
 PlotRange -> {{30, 50}, {30, 100}}]

You said : The same code works, if one of the plot range parameters for y-axes is turned into an integer

Can you should the code you used for this? I am not following.

http://reference.wolfram.com/mathematica/ref/ArrayPlot.html