Skip to main content

plotting - Can I use a custom (Frame)Ticks specification to define the PlotRange?


The documentation for Ticks and FrameTicks shows how one can define a function for custom ticks or frame ticks, for example:


niceTicks[min_, max_, n_: 7] := FindDivisions[{min, max}, n]

After creating some example data


fakedata1 = FoldList[0.99 #1 + #2 &, 1., 
RandomVariate[NormalDistribution[0, 1], {100}]];

We can see that FrameTicks specifications will allow for functions, and will automatically pass the minimum and maximum of the data set as arguments.



ListLinePlot[fakedata1, Frame -> True, PlotRange -> All, PlotRangePadding -> 0, 
FrameTicks -> {{niceTicks, None}, {Automatic, None}}]

enter image description here


Similarly one could use:


ListLinePlot[fakedata1, Frame -> True, PlotRange -> All, PlotRangePadding -> 0, 
FrameTicks -> {{niceTicks[##, 10] &, None}, {Automatic, None}}]

enter image description here


As an aside, when using data points specified in terms of ${x,y}$ coordinates, as in DateListPlot and related functions, the FrameTicks specification will correctly pass the minimum and maximum of the x or y coordinates as appropriate, which is pretty cool.



My question is how one can link the PlotRange of the plot to the ticks determined by such a custom function. In this particular instance, the FindDivisions function called by niceTicks ranges from -2 to 10, but the plot only takes up as much space as the data require, plus any PlotRangePadding.


niceTicks[Min@fakedata1, Max@fakedata1]
(* {-2, 0, 2, 4, 6, 8, 10} *)

If I want the plot to have ticks effectively at the very top and bottom of the frame like this, using all the ticks output by my niceTicks function, I need to specify the PlotRange explicitly using the same niceTicks function:


ListLinePlot[fakedata1, Frame -> True, 
PlotRange -> niceTicks[Min@fakedata1, Max@fakedata1][[{1, -1}]],
PlotRangePadding -> 0, FrameTicks -> {{niceTicks, None}, {Automatic, None}}]

enter image description here



I'm sure that calling an auxiliary function twice like this doesn't add a lot of overhead, but it does require getting explicit minima and maxima from the data, which is a bit clunky when you consider multiple series, dated data for DateListPlots etc.


Is there a way to pass the maximum and minimum tick values determined in the Ticks or FrameTicks option expression to the PlotRange option automatically? It would be more elegant code with fewer special cases to code for. I'm building this into a suite of custom plotting functions, where a tick specification like the last picture shown is a requirement.


It would also be nice to pass the same tickmarks to GridLines somehow, so that Automatic gridlines automatically matched up with the specified ticks.



Answer



I thought something like what @Mr Wizard suggested might work but it seems that PlotRange is called earlier in the evaluation sequence. You can however match the GridLines ok:


niceTicks[min_, max_, n_: 7] := (yRange = {min, max}; 
FindDivisions[{min, max}, n, Method -> "ExtendRange"])

Dynamic@ListLinePlot[fakedata1,
FrameTicks -> {{niceTicks[##, 3] &, None}, {Automatic, None}},

GridLines -> {None, niceTicks[##, 3] &}, Frame -> True,
PlotRangePadding -> 0, PlotLabel -> yRange]

Unfortunately using PlotRange->{Automatic,yRange} doesn't work.


Comments

Popular posts from this blog

plotting - Filling between two spheres in SphericalPlot3D

Manipulate[ SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, Mesh -> None, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], {n, 0, 1}] I cant' seem to be able to make a filling between two spheres. I've already tried the obvious Filling -> {1 -> {2}} but Mathematica doesn't seem to like that option. Is there any easy way around this or ... Answer There is no built-in filling in SphericalPlot3D . One option is to use ParametricPlot3D to draw the surfaces between the two shells: Manipulate[ Show[SphericalPlot3D[{1, 2 - n}, {θ, 0, Pi}, {ϕ, 0, 1.5 Pi}, PlotPoints -> 15, PlotRange -> {-2.2, 2.2}], ParametricPlot3D[{ r {Sin[t] Cos[1.5 Pi], Sin[t] Sin[1.5 Pi], Cos[t]}, r {Sin[t] Cos[0 Pi], Sin[t] Sin[0 Pi], Cos[t]}}, {r, 1, 2 - n}, {t, 0, Pi}, PlotStyle -> Yellow, Mesh -> {2, 15}]], {n, 0, 1}]

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

plotting - Mathematica: 3D plot based on combined 2D graphs

I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data. I would now like to show these different 2D plots projected in 3D as in but then using proper perspective. In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes. Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage). (* some test data *) data = Table[Null, {i, 4}]; data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5, 1.0}, {1, -6.8}, {2, -4.7}, {3, -1.