GatherBy

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`GatherBy`

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GatherBy[list,f]

gathers into sublists each set of elements in list that gives the same value when f is applied.

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GatherBy[list,{f₁,f₂,…}]

gathers list into nested sublists using f_i at level i.

Details

GatherBy[{e₁,e₂,e₃,…},f] evaluates f[e_i] for each i to determine how to gather the e_i.
GatherBy[list,…] gives results that follow the ordering of elements in list.
Within each sublist generated by GatherBy[list,…], elements appear in the same order as in list; the complete sublists are ordered so that their first elements appear in the same order as in list.
GatherBy effectively produces an equivalence partition.
GatherBy[list,{f₁,f₂}] is equivalent to Map[GatherBy[#,f₂]&,GatherBy[list,f₁]].

Examples

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Basic Examples (2)Summary of the most common use cases

Gather data in odd and even lists:

In[1]:=1

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https://wolfram.com/xid/0btn96qzowjx-l8dnlt

Out[1]=1

Gather by the first part:

In[1]:=1

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https://wolfram.com/xid/0btn96qzowjx-dmyv5c

Out[1]=1

Applications (6)Sample problems that can be solved with this function

Sort and then gather strings by their first letters:

In[1]:=1

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https://wolfram.com/xid/0btn96qzowjx-ddfp0t

In[2]:=2

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https://wolfram.com/xid/0btn96qzowjx-fnd0dn

In[4]:=4

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https://wolfram.com/xid/0btn96qzowjx-ezcoz3

Gather by the first component, and within that group, gather by the last component:

In[1]:=1

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https://wolfram.com/xid/0btn96qzowjx-i2ebc6

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0btn96qzowjx-ess4m1

Out[2]=2

Use Framed to display grouping:

In[3]:=3

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https://wolfram.com/xid/0btn96qzowjx-jb5a2m

Out[3]=3

Gather by remainder:

In[1]:=1

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https://wolfram.com/xid/0btn96qzowjx-g8y2tg

Out[1]=1

Gather by the first component in a vector:

In[1]:=1

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https://wolfram.com/xid/0btn96qzowjx-pd3dn

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0btn96qzowjx-pj6s1l

Out[2]=2

Gather dates by year:

In[1]:=1

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https://wolfram.com/xid/0btn96qzowjx-iw5ib

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0btn96qzowjx-cg3l96

Out[2]=2

Simulate some data:

In[3]:=3

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https://wolfram.com/xid/0btn96qzowjx-x1zngv

Out[3]=3

Group elements based on the value of the second element:

In[4]:=4

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https://wolfram.com/xid/0btn96qzowjx-ojjuc0

Out[4]=4

Count the number of data points in each group:

In[5]:=5

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https://wolfram.com/xid/0btn96qzowjx-biw2ln

Out[5]=5

Compute the means of the third element by group:

In[6]:=6

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https://wolfram.com/xid/0btn96qzowjx-q4muwn

Out[6]=6

Group machine numbers by equivalence class based on rounding off the last tol bits:

In[1]:=1

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https://wolfram.com/xid/0btn96qzowjx-xj2b34

Generate an unordered sample of distinct machine numbers close to 1:

In[2]:=2

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https://wolfram.com/xid/0btn96qzowjx-4mx5q8

Out[2]=2

Gather by equivalence class:

In[3]:=3

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https://wolfram.com/xid/0btn96qzowjx-xqs7nz

Out[3]=3

See how the factors in were grouped:

In[4]:=4

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https://wolfram.com/xid/0btn96qzowjx-wvgkl9

Out[4]=4

Here are the equivalence representatives and the values such that :

In[5]:=5

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https://wolfram.com/xid/0btn96qzowjx-bmjigr

Out[5]=5

Properties & Relations (1)Properties of the function, and connections to other functions

GatherBy[list,f] is equivalent to Gather[list,(f[#1]===f[#2])&]:

In[1]:=1

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https://wolfram.com/xid/0btn96qzowjx-glc9v8

Gather the rows by Norm and display with the common norm of each group:

In[2]:=2

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https://wolfram.com/xid/0btn96qzowjx-k9tylk

Out[2]=2

Compare to the result of Gather:

In[3]:=3

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https://wolfram.com/xid/0btn96qzowjx-p5iq4

Out[3]=3

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