mink

Find k smallest elements of array

Syntax

B = mink(A,k)

B = mink(A,k,dim)

B = mink(___,'ComparisonMethod',c)

[B,I] = mink(___)

Description

B = mink(A,k) 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, then mink returns the k smallest elements along the first dimension whose size does not equal 1.

B = mink(A,k,dim) determines the k smallest elements of A along dimension dim.

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

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

Examples

Smallest Vector Elements

Compute the smallest 3 elements of a vector.

A = 1:10;
B = mink(A,3)

B = 1×3

     1     2     3

Smallest Elements of Matrix Rows

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

A = magic(5)

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 = mink(A,3,2)

B = 5×3

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

Complex Vector

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

I = 1×2

     4     1

Input Arguments

A — Input array

vector | matrix | multidimensional array

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

• 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, then mink 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.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char | categorical | datetime | duration
Complex Number Support: Yes

k — Number of minima

nonnegative integer scalar

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

dim — Operating dimension

positive integer scalar

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 the k smallest values in each column of A and returns a k-by-n matrix.

  

• mink(A,k,2) computes the k smallest values in each row of A and returns an m-by-k matrix.

  

c — Comparison method

'auto' (default) | 'real' | 'abs'

Comparison method, specified as one of the following:

• 'auto' — Compare elements of input A by real(A) when A is real, and by abs(A) when A is complex.

• 'real' — Compare elements of input A by real(A) when A is real or complex. If A has elements with equal real parts, then use imag(A) to break ties.

• 'abs' — Compare elements of input A by abs(A) when A is real or complex. If A has elements with equal magnitude, then use angle(A) in the interval (-π,π] to break ties.

Output Arguments

B — Output array

scalar | vector | matrix | multidimensional array

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

I — Index array

scalar | vector | matrix | multidimensional array

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

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

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

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

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).

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced in R2017b

R2025a: Improved performance when returning a large number of rows for numeric or logical data

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 the timeit function.

timeit(@timingTest)