Skip to main content

plotting - ListContourPlot interpolation fails if x and y axes have different scales


To summarize what is below:



ListContourPlot doesn't work when the domain has different x and y scales (fails when x/y~10^4, which seems surprisingly small).




  • Is it possible to call ListContourPlot on a pre-defined Interpolation[] object, while also restricting the domain of the interpolated solution to the domain of the data (the way ListContourPlot usually does automatically)?




  • Is it possible to set the numerical precision of the interpolation algorithm inside ListContourPlot?




and/or




  • (Thanks to @SimonWoods) Is there an alternative to the undocumented ListContourPlot option Method -> {"DelaunayDomainScaling" -> True} that is implemented in v10?


Related: @SimonWoods's solution for v7+ although note that my kernel is not crashing.


--


Consider a regular but unstructured array of points on a rectangular domain of arbitrary aspect ratio. In this example, the domain can be scaled along the x and y axes by the input arguments:


dataZ = RandomReal[{1, 10}, {10, 10}];
scaleTheDomainBy10To[bx_, by_] := Module[{},
    data = Flatten[Table[{x*10^(bx - 1), y*10^(by - 1), dataZ[[x, y]]}
                         , {x, 1, 10}, {y, 1, 10}],  1];

    Show[
        ListContourPlot[data, ImageSize -> 250, PlotLabel -> {bx, by}],
        ListPlot@Map[#[[{1, 2}]] &, data]
        ]
];

In v10 on Win7, When the aspect ratio of the domain approaches ~10^4, the interpolation methods inside ListContourPlot start to break down:


Grid[{{scaleTheDomainBy10To[3, 0], scaleTheDomainBy10To[3.5, 0], scaleTheDomainBy10To[4, 0]},
      {scaleTheDomainBy10To[0, -3], scaleTheDomainBy10To[0, -3.5], scaleTheDomainBy10To[0, -4]}}]


grid of different domain sizes


I tried scaling the domain and then applying DataRange inside ListContourPlot, but apparently ListContourPlot scales the data before doing its thing, which seems rather counterproductive.


My current workaround is to scale the domain, construct an Interpolation object of order 1, then call ContourPlot on that object using explicitly scaled input arguments.


However, I am not happy with that solution because the domain of my actual data is slightly ragged, which means to prevent Mathematica from showing the regions where the interpolation object is garbage, I have to set explicit boundaries for the plot region, either using plot limits such as


ContourPlot[..., {x,1.1,9.9},{y,1100,9900}]

which misses some of the solution, or using RegionFunction, which is slow and requires manual tweaking for each dataset. One nice feature of ListContourPlot is that it usually seems to truncate the plot region to the non-garbage regions (something like the Delaunay "hull" of the input data?), which is a feature I'd like to keep using.


I am not really interested in trying to regularize or smooth my data, as some of the raggedness is crucial for interpretation.


--


Thanks to @Kuba (removed comment), using Standardize[] with DataRange seems to create a slightly different problem? grid of different domain sizes using Kuba's code





Comments

Post a Comment

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...
Post a Comment
Read more

equation solving - Invert and fit implicitly defined curve

I need to fit an implicitly defined curve. I thought I could get some data out of Solve , and then using FindFit . Therefore, I would like to find the relation the parametric curve defined by $F(x,y)=0$: Solve[-(1/2) + 1/2 (0.41202 BesselK[0, 0.1 Sqrt[x^2 + y^2]] + (0.101483 x BesselK[1, 0.1 Sqrt[x^2 + y^2]])/Sqrt[x^2 + y^2]) == 0, y] But I can't get an output: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >> Edit: In particular, I would like to fit the data coming from the curve with the expression of another curve, and not with a function $f(x)$. In particular, since this clearly looks like a cardioid , I would like it to fit to something like it. What other strategies could I try?
Post a Comment
Read more

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...
Post a Comment
Read more