syntax - Parentheses in pure functions: # & vs. ( # &)

I've been using Mathematica for years, and over time I have developed the habit of using:

Select[data, (# == 1 &)]

instead of

Select[data, # == 1 &]

I learned this by mimicking the style of more experienced users. I'm pretty sure that there are reasons for flanking the function with parentheses, but I'm not sure that I have seen a reason for why this is necessary or a good habit to get into. Would someone be able to comment?

Answer

It is a good habit to get into because you can often get tripped up by precedence rules (no one remembers everything!). For instance, PatternTest binds very tightly. See the difference between these two definitions:

Clear@f
f[_?(# == 2 &)] := Print@"foo"
f[_] := Print@"bar"

f[2]
(* "foo" *)

Clear@g
g[_?# == 2 &] := Print@"foo"
g[_] := Print@"bar"
g[2]
(* "bar" *)

You can see that the second function does not behave as expected. Further inspection of the patterns will show that the function is not being defined as expected:

_?#1 == 2 & // FullForm
(* Function[Equal[PatternTest[Blank[],Slot[1]],2]] *)

_?(#1 == 2 &) // FullForm
(* PatternTest[Blank[],Function[Equal[Slot[1],2]]] *)

A similar situation arises when you're supplying a pure function to options such as ColorFunction, Mesh, etc.

Comments

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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....

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