Skip to main content

gathering - Collecting lists using Reap/Sow


I have a list like {{a,x},{b,y},{c,x},{d,z},{e,y}} and would like to produce from it a list formed by collecting all top-level elements whose second components are the same into a single list. For the list above, the desired output would be { {{a,c},x}, {{b,e},y}, {d, z}}. Here x, y, and z could also be lists, if that matters. This seems like an application of Reap and Sow. But the on-line documentation of these functions is pretty poor, and the examples don't add much. Shifrin's book keeps referring to a discussion of Reap and Sow in Part II, but I can't actually find a part II. Is there a resource somewhere that I can look at to understand the ins and outs of these functions, and see some real examples of how to use them?



The simple Reap[Map[Sow[#, #[[2]]] &, r]], where r is the list above, produces almost what I want, but instead of {{a,c},x} above, it produces {{a,x},{c,x}}.


(I'm sure that someone will post a solution to my programming problem; for that I would be grateful. But I really would like to understand these functions better.)


EDIT: The code Reap[Map[Sow[#[[1]], #[[2]]] &, r], _, {#2, #1} &] // Rest does the trick. Perhaps there's a better way. In any case, my question about documentation still stands.



Answer



This question may be deemed a duplicate, as the specific operation has been addressed before (actually quite a few times as I recall). Nevertheless I shall attempt to provide a useful answer regarding Sow and Reap. First, I there are many examples of the use of these functions on this site, and I encourage you to search for them, as they will provide a broader application than is practical in a single answer.


For your given example you could write:


data = {{a, x}, {b, y}, {c, x}, {d, z}, {e, y}};

Reap[Sow @@@ data, _, {#2, #} &][[2]]



{{{a, c}, x}, {{b, e}, y}, {{d}, z}}

This doesn't quite match your desired output but it is a more consistent format.


However, you mention: "Here x, y, and z could also be lists, if that matters." Yes, it does matter, because if the second argument of Sow is a list it is not treated as a single tag but a list of tags. Therefore you need to wrap the list itself in {} to have it treated as a single tag. First an example of the failure:


x = {1, 2, 3};

Reap[Sow @@@ data, _, {#2, #} &][[2]]



{{{a, c}, 1}, {{a, c}, 2}, {{a, c}, 3}, {{b, e}, y}, {{d}, z}}

And then the correction:


Reap[Sow[#, {#2}] & @@@ data, _, {#2, #} &][[2]]


{{{a, c}, {1, 2, 3}}, {{b, e}, y}, {{d}, z}}


A few posts you should read:




Perhaps also of interest:




Version 10 update: although specifically Reap and Sow were requested I think it is worth noting that this can be done with Associations as well, e.g.:


{#2, #} & @@@ Normal @ GroupBy[data, Last -> First]


{{{a, c}, x}, {{b, e}, y}, {{d}, z}}


Comments

Post a Comment

Popular posts from this blog

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 - 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 - 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