MinimalBy
MinimalBy[data,f]
returns a list of the elements ei of data for which the value of f is minimal.
MinimalBy[data,f,n]
returns a list of the elements ei of data corresponding to the n smallest f[ei].
MinimalBy[data,f,n,p]
uses the ordering function p for sorting.
Details
- By default, values of f[ei] are compared using Order, the same canonical order as in Sort.
- MinimalBy[data,f] returns the list of minimal elements ei of data in the order they appear in the input.
- MinimalBy[data,f,n] returns the ei sorted in the order of increasing f[ei], with those having the same value of f[ei] being taken in the order they appear in data.
- 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 » - For tabular data tab, MinimalBy[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.
- MinimalBy[data,f, UpTo[n]] gives n elements or as many as are available. »
- MinimalBy[f][data] is equivalent to MinimalBy[data,f]. »
Examples
open allclose allBasic Examples (4)
Find the minimal element by its last part:
Do the same using the operator form of MinimalBy:
All minimal elements are returned, in order of appearance:
Scope (10)
Obtain the first four minimal elements or as many as are available:
MinimalBy works with symbolic expressions, using canonical Order by default:
Find minimal element in a list of comparable quantities with various units:
Comparing by QuantityMagnitude loses the unit information:
Find numerically smallest element:
MinimalBy works on QuantityArray:
MinimalBy will order dates according to canonical order by default:
Convert the dates to absolute times to sort them numerically:
Equivalently, convert the dates to DateObject form and use NumericalOrder instead of Order:
Take the letters of the Polish alphabet:
Transliterate them to the Hiragana script:
These are the five smallest Polish letters according to canonical order:
These are the five smallest Polish letters according to the rules of the Polish alphabet:
These are the five smallest Polish letters according to canonical order of their Hiragana transliteration:
These are the five smallest Polish letters according to alphabetic order in Japanese of their transliteration:
Construct a TabularColumn object with 100 words:
Select the five longest words:
Normalize the result to a list:
Find the four rows in a Tabular object with minimal value in a specified column:
Use general functional notation instead of the column name:
Take a dataset of the solar system planets:
Find the three planets with the minimal number of moons:
When there are common values of f[ei] for different elements ei, the original order will be kept:
Applications (3)
Find the four shortest texts available in ExampleData["Text"]:
Find the five constellations with minimal number of bright stars:
Properties & Relations (3)
MinimalBy[{e1,e2,…},f,n] compares values f[ei] using canonical Order:
TakeSmallestBy[{e1,e2,…},f,n] compares values f[ei] using NumericalOrder:
For a specific ordering function p, MinimalBy[data,f,n,p] is equivalent to TakeSmallestBy[data,f,n,p]:
Possible Issues (1)
By default, the minimal element is determined using canonical Order, not numerical ordering:
Text
Wolfram Research (2014), MinimalBy, Wolfram Language function, https://reference.wolfram.com/language/ref/MinimalBy.html (updated 2025).
CMS
Wolfram Language. 2014. "MinimalBy." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/MinimalBy.html.
APA
Wolfram Language. (2014). MinimalBy. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MinimalBy.html