Bug in VectorFieldPlot[] with InterpolatingFunction[]?

What is happening is that x and y are being set equal to numeric values. (One might notice that the color for x and y changes from blue to black, but my eyes have trouble seeing that for single-letter variables.) For some reason, these values are outside the domain specified in the plot. I think this must be a bug and have reported it to WRI.

Clear[x, y]
{x, y}
field = {Interpolation[Range[4]^2/4][y], x};
VectorDensityPlot[field, {x, 1, 4}, {y, 1, 4}]
{x, y}

enter image description here

One possible workaround is to clear the variables after plotting with Clear[x, y]. Another is to use Block:

Block[{x, y}, VectorDensityPlot[field, {x, 1, 4}, {y, 1, 4}]]

Further, it does not seem restricted only to InterpolatingFunction. The following has the same issue, and, further, VectorStyle is ignored:

Clear[x, y, ff]
{x, y}
ff[xx_, yy_] := {yy^2/4, xx};
VectorDensityPlot[ff[x, y], {x, 1, 4}, {y, 1, 4}, VectorStyle -> Red]
{x, y}
(*  output is the same as above, same coloring  *)

Pre-evaluating ff[x, y] gives the desired plot:

VectorDensityPlot[Evaluate@ff[x, y], {x, 1, 4}, {y, 1, 4}, VectorStyle -> Red]

This works...once you have potdistr, run this to get a Function

pdg = Evaluate[Grad[potdistr[#1, #2], {#1, #2}]] &

You can then run the plot function repeatedly, no problem, and go back and run previous statements (you couldn't when x, y were getting set).

VectorDensityPlot[pdg[x,y], {x, 0, 0.1}, {y, 0, 0.05}]
VectorDensityPlot[pdg[x,y], {x, 0, 0.1}, {y, 0, 0.05}]
VectorDensityPlot[pdg[x,y], {x, 0, 0.1}, {y, 0, 0.05}]

enter image description here

You can also run this kludgy version, but it is slow.

VectorDensityPlot[Evaluate[Grad[potdistr[#1, #2], {#1, #2}]] &[x, y], 
                  {x, 0, 0.1}, {y, 0, 0.05}]

I was interested in the not very useful looking StreamPlot I was getting.

StreamPlot[pdg[x, y], {x, 0, 0.1}, {y, 0, 0.05}]

enter image description here

One thing I found odd is that if you look at the domain for potdistr versus the plot ranges people are using, there should be some extrapolation going on. Shouldn't we get warnings for that?

Tags:

Interpolation

Evaluation

Plotting

Bugs

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