Skip to main content

function construction - Pattern that matches colors


Suppose I'm writing a function that takes a color as a parameter; for example:



drawShape[color_] := Graphics[{Style[Disk[], color]}];

But if the caller inputs an invalid color, bad things happen:


Bad


So I want to use a pattern to define drawShape only for values that are actually colors. Conceptually,


drawShape[color_Color] := ...

The problem is that unlike (say) Lists, Integers, Reals, Complexes, or Graphicses, color objects do not share a Color head. That is,


In[1]:= Red // Head
Out[1]= RGBColor

In[2]:= Hue[0.5] // Head
Out[2]= Hue
In[3]:= GrayLevel[0.5] // Head
Out[3]= GrayLevel
In[4]:= CMYKColor[0, 1, 1, 1/2] // Head
Out[4]= CMYKColor
In[4]:= Opacity[0.5, Purple] // Head
Out[4]= Opacity
In[5]:= Transparent // Head
Out[5]= GrayLevel


So that won't work. I also don't see any ColorQ function, with which I could write drawShape[color_ ? ColorQ] := ....


How can I write a pattern that matches any valid color object? Is there a more robust way than just testing for each of these heads?



Answer



Original method


colorQ = Quiet @ Check[Blend @ {#, Red}; True, False] &;

colorQ /@ {Red, Hue[0.5], GrayLevel[0.5], CMYKColor[0, 1, 1, 1/2], Opacity[0.5, Purple]}



{True, True, True, True, True}

colorQ /@ {17, 1.3, Pi, "not a color", {1, 2, 3}, Hue["bad arg"]}


{False, False, False, False, False, False}

You would use: drawShape[color_?colorQ] := . . .



Inspired by kguler's comment this might also be formulated as:



colorQ = Quiet[Head @ Darker @ # =!= Darker] &;

Or:


colorQ = FreeQ[Quiet @ Darker @ #, Darker] &;

Edit: Darker works on entire Image and Graphics objects and therefore the two forms immediately above will incorrectly return True in these cases. Blend solution is still valid.



Version 10 update and analysis


In version 10 there is a built-in function for this: ColorQ




ColorQ[color] yields True if color is a valid color directive and False otherwise.



A bit of spelunking reveals that the inner definition of this function is (contexts stripped for clarity):


iColorQ[args_?(ColorDirectiveQ[Head[#1[[1]]]] &), opts_] := 
  NumberQ[Quiet[ToColor[args[[1]], XYZColor][[1]]]]

This is very similar to my own method, however the inner definition of ColorDirectiveQ omits Opacity:


iColorDirectiveQ[args_, opts_] := 
 TrueQ[Quiet[
   MatchQ[args[[1]], 

    GrayLevel | RGBColor | CMYKColor | Hue | XYZColor | LUVColor | LABColor | LCHColor]]]

This means that the function will return False for e.g. Opacity[0.5, Purple] where mine returns True.


Comments

Post a Comment

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more