mink - Find k smallest elements of array - MATLAB (original) (raw)

Find k smallest elements of array

Syntax

Description

[B](#d126e1114494) = mink([A](#d126e1114237),[k](#d126e1114339)) returns the k smallest elements of A.

If A is a vector, then mink returns a vector containing the k smallest elements of A.
If A is a matrix, then mink returns a matrix whose columns contain the k smallest elements of each column of A.
If A is a multidimensional array, thenmink returns the k smallest elements along the first dimension whose size does not equal 1.

[B](#d126e1114494) = mink([A](#d126e1114237),[k](#d126e1114339),[dim](#d126e1114361)) determines the k smallest elements of A along dimension dim.

example

[B](#d126e1114494) = mink(___,'ComparisonMethod',[c](#d126e1114422)) optionally specifies how to compare elements of A for any of the previous syntaxes. For example,mink(A,k,'ComparisonMethod','abs') returns thek smallest elements of A according to their absolute values.

example

[[B](#d126e1114494),[I](#d126e1114524)] = mink(___) finds the indices of the smallest k values ofA and returns them in I.

example

Examples

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Compute the smallest 3 elements of a vector.

Compute the smallest 3 elements of each row of a matrix.

A = 5×5

17    24     1     8    15
23     5     7    14    16
 4     6    13    20    22
10    12    19    21     3
11    18    25     2     9

B = 5×3

 1     8    15
 5     7    14
 4     6    13
 3    10    12
 2     9    11

Compute the 2 smallest elements of a complex vector according to their magnitude, and return the indices where they are located in the input vector.

A = [2-2i 5+i -7-3i -1+i]

A = 1×4 complex

2.0000 - 2.0000i 5.0000 + 1.0000i -7.0000 - 3.0000i -1.0000 + 1.0000i

[B,I] = mink(A,2,'ComparisonMethod','abs')

B = 1×2 complex

-1.0000 + 1.0000i 2.0000 - 2.0000i

Input Arguments

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Input array, specified as a vector, matrix, or multidimensional array.

If A is a vector, thenmink returns a vector containing thek smallest elements ofA.
If A is a matrix, thenmink returns a matrix whose columns contain the k smallest elements of each column of A.
If A is a multidimensional array, thenmink returns the k smallest elements along the first dimension whose size does not equal 1.

If A has type categorical, then it must be ordinal.

Number of minima to return, specified as a positive integer scalar. Ifk is greater than or equal to the number of elements in the operating dimension, then mink sorts the input array along that dimension.

Operating dimension, specified as a positive integer scalar. If no value is specified, then the default is the first array dimension whose size does not equal 1.

Consider an m-by-n input matrix,A:

mink(A,k,1) computes thek smallest values in each column ofA and returns ak-by-n matrix.
mink(A,k,2) computes thek smallest values in each row ofA and returns anm-by-k matrix.

Comparison method, specified as one of the following:

'auto' — Compare elements of inputA by real(A) whenA is real, and byabs(A) when A is complex.
'real' — Compare elements of inputA by real(A) whenA is real or complex. IfA has elements with equal real parts, then use imag(A) to break ties.
'abs' — Compare elements of inputA by abs(A) whenA is real or complex. IfA has elements with equal magnitude, then use angle(A) in the interval (-π,π] to break ties.

Output Arguments

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Output array, returned as a scalar, vector, matrix, or multidimensional array. mink returns the k elements in order from smallest to largest.

Index array, returned as a vector, matrix, or multidimensional array.I is the same size as B. If the output array B contains repeated elements, then the order of their indices in I matches the order in which they appear in the input array.

Extended Capabilities

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Themink function fully supports tall arrays. For more information, see Tall Arrays.

Usage notes and limitations:

For input argument A:
- If you do not specify a dimension, the code generator operates along the first dimension of the input array that is variable size or whose size does not equal 1. If this dimension is variable size at code generation time and is 1 at run time, a run-time error can occur. To avoid this error, specify the dimension.
- In the generated code, the input array remains complex, even if all of its elements have zero-valued imaginary parts. Under these circumstances, the results produced by the generated code might differ from those produced by MATLAB. See Code Generation for Complex Data with Zero-Valued Imaginary Parts (MATLAB Coder).

Version History

Introduced in R2017b

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The mink function shows improved performance for numeric data, including complex data, and logical data when_k_ is at least 512 and is at least 8% of the operating dimension length.

For example, this code returns the smallest 5000 elements of each column in a numeric matrix containing 10,000 rows. The code is about 3.75x faster than in the previous release.

function timingTest A = rand(1e4,10); for i = 1:120 M = mink(A,5000); end end

The approximate execution times are:

R2024b: 1.05 s

R2025a: 0.28 s

The code was timed on a Windows® 11, AMD EPYC™ 74F3 24-Core Processor @ 3.19 GHz test system using thetimeit function.