Skip to main content

Plotting piecewise function with distinct colors in each section


I have a piecewise function that I would like to plot but I was wondering if it is possible that each part of the function that is plotted when its corresponding condition is true be plotted with a different color from the other parts. That is, if I have a Piecewise function Piecewise[{{val1, cond1},{val2,cond2},{val3,cond3}}] then I want val1, val2, and val3 to be plotted with different colors so that I can differentiate each case in the plot.



Answer



Here's an alternative approach than Spartacus' answer. What he did is splitting up the piecewise function into many different functions valid in only a small domain; what I am doing here is directly plotting the piecewise function as given, while the coloring is done using ColorFunction.


I'll use the same function as Spartacus,


f = Piecewise[{{#^2, # <= 0}, {#, 0 < # <= 2}, {Log[#], 2 < #}}] &


Now let's create a ColorFunction that does the desired thing out of this. I'll do this using Part, i.e. double brackets [[ ]], which is not limited to lists only.


First, create a copy of f.



colorFunction = f;

Now we need to find out how many pieces there are in this function; for this we have to extract those into a list we can allpy Length to. Step by step:


colorFunction[[1]]


Piecewise[{{#1^2, #1 <= 0}, {#1, Inequality[0, Less, #1, LessEqual, 2]}, {Log[#1], 2 < #1}}, 0]

That's the full function body. By applying another [[1]], we can get the first argument of Piecewise:


colorFunction[[1, 1]]



{{#1^2, #1 <= 0}, {#1, 0 < #1 <= 2}, {Log[#1], 2 < #1}}

From this matrix-shaped list, we'd like to get the length, leaving us with


piecewiseParts = Length@colorFunction[[1,1]]

Alright! Now make some colors out of that. The default plot colors are stored in ColorData[1][x], where x=1,2,3,4... is the usual blue/magenta/yellowish/green and so on.


colors = ColorData[1][#] & /@ Range@piecewiseParts



{RGBColor[0.2472, 0.24, 0.6], RGBColor[0.6, 0.24, 0.442893], RGBColor[0.6, 0.547014, 0.24]}

Now we need to take these color directives and inject them into the original function (that is, the colorFunction copy I've made in the beginning), so that it replaces squares and logarithms by reds and blues. This is some more Part acrobatics:


colorFunction[[1, 1, All, 1]] = colors

Done! colorFunction is now identical to the original function f, only that the actual functions have been replaced by colors. It looks like this:


Piecewise[{{RGBColor[...], # <= 0}, {RGBColor[...], 0 < # <= 2}, {RGBColor[...], 2 < #}}] &

Now it's time to plot, see the completed code below.




f = Piecewise[{{#^2, # <= 0}, {#, 0 < # <= 2}, {Log[#], 2 < #}}] &;

colorFunction = f;
piecewiseParts = Length@colorFunction[[1, 1]];
colors = ColorData[1][#] & /@ Range@piecewiseParts;
colorFunction[[1, 1, All, 1]] = colors;

Plot[
    f[x],

    {x, -2, 4},
    ColorFunction -> colorFunction, 
    ColorFunctionScaling -> False
]

final plot


(The option ColorFunctionScaling determines whether Mathematica scales the domain for the color function to $[0,1]$. Handy in some cases, not so much here, since our self-made colorFunction is constant in this domain.)


Comments

Post a Comment

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}]
Post a Comment
Read more

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}]
Post a Comment
Read more

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.
Post a Comment
Read more