# sort

Sort array elements

## Description

sorts the elements
of `B`

= sort(`A`

)`A`

. By default, `sort`

uses ascending sorted
order.

If

`A`

is a vector, then`sort(A)`

sorts the vector elements.If

`A`

is a matrix, then`sort(A)`

treats the columns of`A`

as vectors and sorts each column.If

`A`

is a multidimensional array, then`sort(A)`

operates along the first array dimension whose size does not equal 1, treating the elements as vectors.

specifies
additional parameters for sorting. For example, `B`

= sort(___,`Name,Value`

)`sort(A,'ComparisonMethod','abs')`

sorts
the elements of `A`

by magnitude.

## Examples

### Sort Vector in Ascending Order

Create a row vector and sort its elements in ascending order.

A = [9 0 -7 5 3 8 -10 4 2]; B = sort(A)

`B = `*1×9*
-10 -7 0 2 3 4 5 8 9

### Sort Matrix Rows in Ascending Order

Create a matrix and sort each of its rows in ascending order.

A = [3 6 5; 7 -2 4; 1 0 -9]

`A = `*3×3*
3 6 5
7 -2 4
1 0 -9

B = sort(A,2)

`B = `*3×3*
3 5 6
-2 4 7
-9 0 1

### Sort Matrix Columns in Descending Order

Create a matrix and sort its columns in descending order.

A = [10 -12 4 8; 6 -9 8 0; 2 3 11 -2; 1 1 9 3]

`A = `*4×4*
10 -12 4 8
6 -9 8 0
2 3 11 -2
1 1 9 3

`B = sort(A,'descend')`

`B = `*4×4*
10 3 11 8
6 1 9 3
2 -9 8 0
1 -12 4 -2

### Sort String Array

Starting in R2017a, you can create string arrays using double quotes, and sort them using the `sort`

function. Sort strings in each column of a string array according to Unicode® dictionary order.

A = ["Santos","Burns"; ... "Jones","Morita"; ... "Petrov","Adams"]; B = sort(A)

`B = `*3x2 string*
"Jones" "Adams"
"Petrov" "Burns"
"Santos" "Morita"

Sort the strings in each row.

B = sort(A,2)

`B = `*3x2 string*
"Burns" "Santos"
"Jones" "Morita"
"Adams" "Petrov"

### Sort and Index `datetime`

Array

Create an array of `datetime`

values and sort them in ascending order, that is, from the earliest to the latest calendar date.

ds = {'2012-12-22';'2063-04-05';'1992-01-12'}; A = datetime(ds,'Format','yyyy-MM-dd')

`A = `*3x1 datetime*
2012-12-22
2063-04-05
1992-01-12

[B,I] = sort(A)

`B = `*3x1 datetime*
1992-01-12
2012-12-22
2063-04-05

`I = `*3×1*
3
1
2

`B`

lists the sorted dates and `I`

contains the corresponding indices of `A`

.

Access the sorted elements from the original array directly by using the index array `I`

.

A(I)

`ans = `*3x1 datetime*
1992-01-12
2012-12-22
2063-04-05

### Sort Vectors in Same Order

Create two row vectors that contain related data in the corresponding elements.

X = [3 6 4 2 1 5]; Y = ["yellow" "purple" "green" "orange" "red" "blue"];

First sort the vector `X`

, then sort the vector `Y`

in the same order as `X`

.

[Xsorted,I] = sort(X)

`Xsorted = `*1×6*
1 2 3 4 5 6

`I = `*1×6*
5 4 1 3 6 2

Ysorted = Y(I)

`Ysorted = `*1x6 string*
"red" "orange" "yellow" "green" "blue" "purple"

### Sort 3-D Array

Create a 2-by-2-by-2 array and sort its elements in ascending order along the third dimension.

A(:,:,1) = [2 3; 1 6]; A(:,:,2) = [-1 9; 0 12]; A

A = A(:,:,1) = 2 3 1 6 A(:,:,2) = -1 9 0 12

B = sort(A,3)

B = B(:,:,1) = -1 3 0 6 B(:,:,2) = 2 9 1 12

Use `A(:)`

, the column representation of `A`

, to sort all of the elements of `A`

.

B = sort(A(:))

`B = `*8×1*
-1
0
1
2
3
6
9
12

### Complex Vector

Sort the elements of a complex vector by their real parts. By default, the `sort`

function sorts complex values by their magnitude, and breaks ties using phase angles. Specify the value of `'ComparisonMethod'`

as `'real'`

to instead sort complex values by their real parts. For elements with equal real parts, `sort`

breaks the tie based on their imaginary parts.

A = [1+2i 3+1i 1i 0 -1i]; B = sort(A,'ComparisonMethod','real')

`B = `*1×5 complex*
0.0000 - 1.0000i 0.0000 + 0.0000i 0.0000 + 1.0000i 1.0000 + 2.0000i 3.0000 + 1.0000i

## Input Arguments

`A`

— Input array

vector | matrix | multidimensional array

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

If

`A`

is a scalar, then`sort(A)`

returns`A`

.If

`A`

is complex, then by default,`sort`

sorts the elements by magnitude. If more than one element has equal magnitude, then the elements are sorted by phase angle on the interval (−π, π].If

`A`

is a cell array of character vectors or a string array, then`sort(A)`

sorts the elements according to the code order for the UTF-16 character encoding scheme. The sort is case-sensitive. For more information on sorting character and string arrays, see Sort Order for Character and String Arrays.If

`A`

is a string array, then`sort`

reorders the elements of the array, but does not reorder characters within the strings.If

`A`

is a categorical array, then the sorting order is based on the category order returned by`categories(A)`

.

**Data Types: **`double`

| `single`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `logical`

| `char`

| `string`

| `cell`

| `categorical`

| `datetime`

| `duration`

**Complex Number Support: **Yes

`dim`

— Dimension to operate along

positive integer scalar

Dimension to operate along, 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 a matrix

`A`

.`sort(A,1)`

sorts the elements in the columns of`A`

.`sort(A,2)`

sorts the elements in the rows of`A`

.

`sort`

returns `A`

if `dim`

is
greater than `ndims(A)`

. `dim`

is
not supported when `A`

is a cell array, that is, `sort`

only
operates along the first array dimension whose size does not equal
1.

**Data Types: **`double`

| `single`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`direction`

— Sorting direction

`'ascend'`

(default) | `'descend'`

Sorting direction, specified as `'ascend'`

or `'descend'`

. `direction`

is
not supported when `A`

is a cell array, that is, `sort`

only
sorts in ascending order.

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

**Example: **`sort(A,'MissingPlacement','last')`

`MissingPlacement`

— Placement of missing values

`'auto'`

(default) | `'first'`

| `'last'`

Placement of missing values (`NaN`

, `NaT`

, `<undefined>`

,
and `missing`

) specified as the comma-separated pair
consisting of `'MissingPlacement'`

and one of the
following:

`'auto'`

— Missing elements are placed last for ascending order and first for descending order.`'first'`

— Missing elements are placed first.`'last'`

— Missing elements are placed last.

`ComparisonMethod`

— Element comparison method

`'auto'`

(default) | `'real'`

| `'abs'`

Element comparison method for numeric input, specified as the comma-separated pair consisting
of `'ComparisonMethod'`

and one of the following:

`'auto'`

— Sort`A`

by`real(A)`

when`A`

is real, and sort by`abs(A)`

when`A`

is complex.`'real'`

— Sort`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'`

— Sort`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`

— Sorted array

vector | matrix | multidimensional array

Sorted array, returned as a vector, matrix, or multidimensional array. `B`

is
the same size and type as `A`

.

**Data Types: **`double`

| `single`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `logical`

| `char`

| `string`

| `cell`

| `categorical`

| `datetime`

| `duration`

`I`

— Sort index

vector | matrix | multidimensional array

Sort index, returned as a vector, matrix, or multidimensional
array. `I`

is the same size as `A`

.
The index vectors are oriented along the same dimension that `sort`

operates
on. For example, if `A`

is a 2-by-3 matrix, then ```
[B,I]
= sort(A,2)
```

sorts the elements in each row of `A`

.
The output `I`

is a collection of 1-by-3 row index
vectors describing the rearrangement of each row of `A`

.

The `sort`

function uses a stable sorting algorithm. So,
when the input contains repeated values, the sort index preserves the
original order from the input, regardless of sorting direction. For example,
if `A = [1 2 1 2]`

, then ```
[Ba,Ia] =
sort(A,'ascend')
```

returns the sort index ```
Ia = [1 3 2
4]
```

and `[Bd,Id] = sort(A,'descend')`

returns
the sort index `Id = [2 4 1 3]`

.

## More About

### Sort Order for Character and String Arrays

MATLAB^{®} stores characters as Unicode^{®} using
the UTF-16 character encoding scheme. Character and string arrays
are sorted according to the UTF-16 code point order. For the characters
that are also the ASCII characters, this order means that uppercase
letters come before lowercase letters. Digits and some punctuation
also come before letters.

## Tips

The

`sortrows`

function provides additional flexibility for subsorting over multiple columns of matrix or table inputs.The

`sort`

function and the relational operators use different orderings for complex numbers. For more information, see Relational Operations.

## Extended Capabilities

### Tall Arrays

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

This function supports tall arrays with the limitations:

You must specify the dimension to sort, as in

`sort(X,dim)`

.Sorting the tall dimension, as in

`sort(X,1)`

, is only supported for column vectors.

For more information, see Tall Arrays.

### C/C++ Code Generation

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

Usage notes and limitations:

If

`A`

is complex with all zero imaginary parts, then MATLAB might convert`A`

to`real(A)`

before calling`sort(A)`

. In this case, MATLAB sorts`A`

by`real(A)`

, but the generated code sorts`A`

by`abs(A)`

. To make the generated code match MATLAB, use`sort(real(A))`

or`sort(A,'ComparisonMethod','real')`

. See Code Generation for Complex Data with Zero-Valued Imaginary Parts (MATLAB Coder).If you supply

`dim`

, then it must be constant.Variable-sizing support must be enabled when input cell array is heterogeneous.

For limitations related to variable-size inputs, see Variable-Sizing Restrictions for Code Generation of Toolbox Functions (MATLAB Coder).

### GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Refer to the usage notes and limitations in the C/C++ Code Generation section. The same limitations apply to GPU code generation.

### 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.

### GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The `sort`

function
fully supports GPU arrays. To run the function on a GPU, specify the input data as a `gpuArray`

(Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

### Distributed Arrays

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

Usage notes and limitations:

Table, timetable, and datetime inputs are not supported.

For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

## Version History

**Introduced before R2006a**

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