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TakeSmallestBy
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TakeSmallestBy

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TakeSmallestBy[data,f,n]

gives the n elements ei in data for which f[ei] is smallest, sorted in ascending order.

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TakeSmallestBy[dataprop,f,n]

gives the property prop for the n elements in data for which f[ei] is smallest.

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TakeSmallestBy[data,f,n,p]

uses the ordering function p for sorting.

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represents an operator form of TakeSmallestBy that can be applied to an expression.

Details and Options

  • TakeSmallestBy gives the elements ei in the first level of the input data corresponding to the smallest f[ei] values.
  • By default, TakeSmallestBy uses NumericalOrder to sort f[ei] values that are numeric expressions, Quantity objects and DateObject expressions. For other types of objects, TakeSmallestBy sorts the f[ei] values by canonical Order.
  • The data can have the following forms:
  • {e1,e2,…}list of values, including numbers, quantities, dates, ...
    Association[…]association of values »
    QuantityArray[…]quantity array or other structured array
    Tabular[…]type-consistent tabular data »
    TabularColumn[…]type-consistent column data »
    Dataset[…]general hierarchical data »
  • TakeSmallestBy[assoc,f,n] gives an association of length n by taking the values in assoc that are smallest according to f, preserving their keys.
  • For tabular data tab, TakeSmallestBy[tab,f,…] applies the function f to individual rows of tab, with the row being an association <|col1val1,…|> if tab has column keys or a list {val1,…} if tab does not have column keys.
  • In TakeSmallestBy[dataprop,f,n], possible forms for prop include:
  • "Element"gives each element itself »
    "Index"gives the index for each element »
    "Value"gives the value f[x] for each element x »
    {prop1,prop2,…}a list of multiple forms »
    Allgives an association with element, index and f value »
  • TakeSmallestBy[data,f,UpTo[n]] takes n elements or as many as are available. »
  • TakeSmallestBy[f,n][data] is equivalent to TakeSmallestBy[data,f,n].
  • TakeSmallestBy has option ExcludedForms. With the default setting ExcludedForms->Automatic, TakeSmallestBy excludes from its final results elements for which f[ei] is None, Null or Indeterminate or has head Missing. »
  • The setting ExcludedForms->{patt1,patt2,…} specifies that expressions for which f[ei] matches any of the patti should be excluded from results generated by TakeSmallestBy. »

Examples

open allclose all

Basic Examples  (5)Summary of the most common use cases

Give the four numbers closest to zero:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-quxmyv
Out[1]=1

Take the two shortest strings in a list:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-xh63mx
Out[1]=1

Do the same using the operator form of TakeSmallestBy:

In[2]:=2
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https://wolfram.com/xid/0cpr7b0syb67il-cvc29l
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0cpr7b0syb67il-vm8bxx
Out[3]=3

Take three smallest Quantity lengths according to their distance to :

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-6t1czq
Out[1]=1

Take the three DateObject expressions with the smallest day of the month:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-rfaq8r
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cpr7b0syb67il-3oy020
Out[2]=2

Take the two shortest strings in an association:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-jgfph4
Out[1]=1

Scope  (8)Survey of the scope of standard use cases

Give the four numbers closest to zero or as many as are available if fewer:

In[2]:=2
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https://wolfram.com/xid/0cpr7b0syb67il-0pcpdc
Out[2]=2

The discovery date value for some planets is missing:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-il3p2i
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cpr7b0syb67il-oh3twu
Out[2]=2

By default, Missing[] and several other symbolic expressions are excluded if returned by the selection function:

In[3]:=3
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https://wolfram.com/xid/0cpr7b0syb67il-c91uu4
Out[3]=3

Get the two smallest elements by magnitude in a list:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-1p39n0
In[2]:=2
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https://wolfram.com/xid/0cpr7b0syb67il-5yfcey
Out[2]=2

Get the positions of the two smallest elements by magnitude in a list:

In[3]:=3
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https://wolfram.com/xid/0cpr7b0syb67il-cr2dko
Out[3]=3

Get the two smallest magnitudes in a list:

In[4]:=4
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https://wolfram.com/xid/0cpr7b0syb67il-gpmais
Out[4]=4

Get the two smallest elements by magnitude in a list along with their positions:

In[5]:=5
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https://wolfram.com/xid/0cpr7b0syb67il-i70n6a
Out[5]=5

Get the two smallest elements by magnitude in a list with their positions given first:

In[6]:=6
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https://wolfram.com/xid/0cpr7b0syb67il-dw04qo
Out[6]=6

Get associations containing the element, position and Abs value of the two smallest elements by magnitude in a list:

In[7]:=7
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https://wolfram.com/xid/0cpr7b0syb67il-21mfoi
Out[7]=7

Take a few English words:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-gd1pkd

They can be translated to Spanish with WordTranslation, which gives a list of possibilities:

In[2]:=2
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https://wolfram.com/xid/0cpr7b0syb67il-ufmytu
In[3]:=3
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https://wolfram.com/xid/0cpr7b0syb67il-z63mfq
Out[3]=3

These are the smallest two words according to canonical order:

In[4]:=4
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https://wolfram.com/xid/0cpr7b0syb67il-6zdtb7
Out[4]=4

These are the smallest two English words according to canonical order of their Spanish translations:

In[5]:=5
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https://wolfram.com/xid/0cpr7b0syb67il-4utuab
Out[5]=5

Use properties to show simultaneously the English word and its translation to Spanish:

In[6]:=6
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https://wolfram.com/xid/0cpr7b0syb67il-gkizxz
Out[6]=6

Construct a TabularColumn object with 100 words:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-ss77bg
Out[1]=1

Select the five shortest words:

In[2]:=2
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https://wolfram.com/xid/0cpr7b0syb67il-ije4w6
Out[2]=2

Normalize the result to a list:

In[3]:=3
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https://wolfram.com/xid/0cpr7b0syb67il-5kepgn
Out[3]=3

Find the four rows in a Tabular object with smallest values in a given column:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-jpfbrr
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0cpr7b0syb67il-y5poc
Out[2]=2

Use general functional notation instead of the column name:

In[3]:=3
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https://wolfram.com/xid/0cpr7b0syb67il-2shaqt
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0cpr7b0syb67il-r1yvkm
Out[4]=4

Take a dataset of the solar system planets:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-2sxsoh
Out[1]=1

Find the three planets with the smallest number of moons:

In[2]:=2
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https://wolfram.com/xid/0cpr7b0syb67il-3981jc
Out[2]=2

Take a list of integer 3-vectors:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-pyk5yx
Out[1]=1

These are their norms:

In[2]:=2
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https://wolfram.com/xid/0cpr7b0syb67il-uzhb9e
Out[2]=2

Select the three vectors with smallest norms, by default sorting numerically those norms:

In[3]:=3
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https://wolfram.com/xid/0cpr7b0syb67il-9chmoz
Out[3]=3

Sorting the norms by canonical order can give a different result:

In[4]:=4
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https://wolfram.com/xid/0cpr7b0syb67il-266zb3
Out[4]=4

Options  (2)Common values & functionality for each option

ExcludedForms  (2)

Take the list of all planets in the solar system:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-o9kj4i
Out[1]=1

Find the four planets that are currently closest to your location, with a lower limit of .1 au in distance (to exclude the location planet):

In[14]:=14
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https://wolfram.com/xid/0cpr7b0syb67il-o1c69u
Out[14]=14

Plot the evolution of the distances during a two-year period centered at the current moment:

In[15]:=15
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https://wolfram.com/xid/0cpr7b0syb67il-ejty5f
In[17]:=17
✖
https://wolfram.com/xid/0cpr7b0syb67il-bb1ah6
Out[17]=17

Take an association:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-gg93zh
Out[1]=1

Not all these keys have values in the association:

In[2]:=2
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https://wolfram.com/xid/0cpr7b0syb67il-wkaz6w
In[3]:=3
✖
https://wolfram.com/xid/0cpr7b0syb67il-wna32b
Out[3]=3

Find the keys corresponding up to the four smallest values in the association:

In[4]:=4
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https://wolfram.com/xid/0cpr7b0syb67il-bonkqh
Out[4]=4

By default, some symbolic objects like Missing[] or None are excluded as results of the selection function, so the previous result is equivalent to this:

In[5]:=5
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https://wolfram.com/xid/0cpr7b0syb67il-9kqzz5
Out[5]=5

Specify that no value should be excluded:

In[6]:=6
✖
https://wolfram.com/xid/0cpr7b0syb67il-rjnsp0
Out[6]=6

Specify that only values None should be excluded:

In[7]:=7
✖
https://wolfram.com/xid/0cpr7b0syb67il-fy7rmm
Out[7]=7

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

Find the eight capitals of continental US states that are closest to Kansas City:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-et8buy
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0cpr7b0syb67il-66q9wg
Out[2]=2

Find the five oldest James Bond movies:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-lgvrjt
Out[1]=1

Find the 10 countries with the shortest names:

In[1]:=1
✖
https://wolfram.com/xid/0cpr7b0syb67il-fcthyl
Out[1]=1

From the BRICS group of countries, give the country that is closest to the current location:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-wfok81
Out[1]=1

Find the seven US states with the smallest number of neighboring states and show them:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-f0nqbi
Out[1]=1

Find the five constellations with the smallest number of bright stars, showing how many each one has:

In[1]:=1
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https://wolfram.com/xid/0cpr7b0syb67il-y9s8ve
Out[1]=1

Properties & Relations  (3)Properties of the function, and connections to other functions

TakeSmallestBy[list,f,n,p] is effectively equivalent to Part[list,TakeSmallest[Map[f,list]"index",n,p]:

In[1]:=1
✖
https://wolfram.com/xid/0cpr7b0syb67il-iezsol
In[2]:=2
✖
https://wolfram.com/xid/0cpr7b0syb67il-dsovx7
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0cpr7b0syb67il-s7dcf5
Out[3]=3

TakeSmallestBy[{e1,e2,…},f,n] compares values f[ei] using NumericalOrder by default:

In[1]:=1
✖
https://wolfram.com/xid/0cpr7b0syb67il-ddbd7p
In[2]:=2
✖
https://wolfram.com/xid/0cpr7b0syb67il-dfljwn
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0cpr7b0syb67il-82pmav
Out[3]=3

MinimalBy[{e1,e2,…},f,n] compares values f[ei] using canonical Order by default:

In[4]:=4
✖
https://wolfram.com/xid/0cpr7b0syb67il-d1gqp2
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/0cpr7b0syb67il-trdyiu
Out[5]=5

Both TakeSmallestBy and MinimalBy take an ordering function as fourth argument, which makes them effectively equivalent:

In[6]:=6
✖
https://wolfram.com/xid/0cpr7b0syb67il-0ihvu1
Out[6]=6
In[7]:=7
✖
https://wolfram.com/xid/0cpr7b0syb67il-mgg1cj
Out[7]=7

When there are common values of f[ei] for different elements ei in TakeSmallestBy[{e1,e2,…},f,n], the original order will be kept:

In[1]:=1
✖
https://wolfram.com/xid/0cpr7b0syb67il-eie171
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0cpr7b0syb67il-7xt8dc
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0cpr7b0syb67il-3qjjjv
Out[3]=3

Possible Issues  (2)Common pitfalls and unexpected behavior

If fewer than the requested number of elements are present, TakeSmallestBy will not evaluate:

In[1]:=1
✖
https://wolfram.com/xid/0cpr7b0syb67il-wv21bw
Out[1]=1

Use UpTo to get as many elements as possible:

In[1]:=1
✖
https://wolfram.com/xid/0cpr7b0syb67il-pu5pzo
Out[1]=1

If the f[ei] are not comparable, TakeSmallestBy will not evaluate:

In[1]:=1
✖
https://wolfram.com/xid/0cpr7b0syb67il-b0vssr
Out[1]=1
Wolfram Research (2015), TakeSmallestBy, Wolfram Language function, https://reference.wolfram.com/language/ref/TakeSmallestBy.html (updated 2025).
✖
Wolfram Research (2015), TakeSmallestBy, Wolfram Language function, https://reference.wolfram.com/language/ref/TakeSmallestBy.html (updated 2025).

Text

Wolfram Research (2015), TakeSmallestBy, Wolfram Language function, https://reference.wolfram.com/language/ref/TakeSmallestBy.html (updated 2025).

✖
Wolfram Research (2015), TakeSmallestBy, Wolfram Language function, https://reference.wolfram.com/language/ref/TakeSmallestBy.html (updated 2025).

CMS

Wolfram Language. 2015. "TakeSmallestBy." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/TakeSmallestBy.html.

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Wolfram Language. 2015. "TakeSmallestBy." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/TakeSmallestBy.html.

APA

Wolfram Language. (2015). TakeSmallestBy. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TakeSmallestBy.html

✖
Wolfram Language. (2015). TakeSmallestBy. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TakeSmallestBy.html

BibTeX

@misc{reference.wolfram_2025_takesmallestby, author="Wolfram Research", title="{TakeSmallestBy}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/TakeSmallestBy.html}", note=[Accessed: 21-June-2025 ]}

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@misc{reference.wolfram_2025_takesmallestby, author="Wolfram Research", title="{TakeSmallestBy}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/TakeSmallestBy.html}", note=[Accessed: 21-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_takesmallestby, organization={Wolfram Research}, title={TakeSmallestBy}, year={2025}, url={https://reference.wolfram.com/language/ref/TakeSmallestBy.html}, note=[Accessed: 21-June-2025 ]}

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@online{reference.wolfram_2025_takesmallestby, organization={Wolfram Research}, title={TakeSmallestBy}, year={2025}, url={https://reference.wolfram.com/language/ref/TakeSmallestBy.html}, note=[Accessed: 21-June-2025 ]}