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# le, <=

Determine less than or equal to

## Syntax

``A <= B``
``le(A,B)``

## Description

example

````A <= B` returns a logical array with elements set to logical 1 (`true`) where `A` is less than or equal to `B`; otherwise, the element is logical `0` (`false`). The test compares only the real part of numeric arrays. `le` returns logical `0` (`false`) where `A` or `B` have NaN or undefined categorical elements.```
````le(A,B)` is an alternate way to execute `A <= B`, but is rarely used. It enables operator overloading for classes.```

## Examples

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Find which vector elements are less than or equal to a given value.

Create a numeric vector.

`A = [1 12 18 7 9 11 2 15];`

Test the vector for elements that are less than or equal to `12`.

`A <= 12`
```ans = 1x8 logical array 1 1 0 1 1 1 1 0 ```

The result is a vector with values of logical `1` (`true`) where the elements of `A` satisfy the expression.

Use the vector of logical values as an index to view the values in `A` that are less than or equal to `12`.

`A(A <= 12)`
```ans = 1×6 1 12 7 9 11 2 ```

The result is a subset of the elements in `A`.

Create a matrix.

`A = magic(4)`
```A = 4×4 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 ```

Replace all values less than or equal to `9` with the value `10`.

`A(A <= 9) = 10`
```A = 4×4 16 10 10 13 10 11 10 10 10 10 10 12 10 14 15 10 ```

The result is a new matrix whose smallest element is `10`.

Create an ordinal categorical array.

```A = categorical({'large' 'medium' 'small'; 'medium' ... 'small' 'large'},{'small' 'medium' 'large'},'Ordinal',1)```
```A = 2x3 categorical array large medium small medium small large ```

The array has three categories: `'small'`, `'medium'`, and `'large'`.

Find all values less than or equal to the category `'medium'`.

`A <= 'medium'`
```ans = 2x3 logical array 0 1 1 1 1 0 ```

A value of logical `1` (`true`) indicates a value less than or equal to the category `'medium'`.

Compare the rows of `A`.

`A(1,:) <= A(2,:)`
```ans = 1x3 logical array 0 0 1 ```

The function returns logical `1` (`true`) where the first row has a category value less than or equal to the second row.

Create a vector of complex numbers.

`A = [1+i 2-2i 1+3i 1-2i 5-i];`

Find the values that are less than or equal to `3`.

`A(A <= 3)`
```ans = 1×4 complex 1.0000 + 1.0000i 2.0000 - 2.0000i 1.0000 + 3.0000i 1.0000 - 2.0000i ```

`le` compares only the real part of the elements in `A`.

Use `abs` to find which elements are within a radius of `3` from the origin.

`A(abs(A) <= 3)`
```ans = 1×3 complex 1.0000 + 1.0000i 2.0000 - 2.0000i 1.0000 - 2.0000i ```

The result has one less element. The element `1.0000 + 3.0000i` is not within a radius of `3` from the origin.

Create a `duration` array.

`d = hours(21:25) + minutes(75)`
```d = 1x5 duration array 22.25 hr 23.25 hr 24.25 hr 25.25 hr 26.25 hr ```

Test the array for elements that are less than or equal to one standard day.

`d <= 1`
```ans = 1x5 logical array 1 1 0 0 0 ```

## Input Arguments

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Left array, specified as a scalar, vector, matrix, or multidimensional array. Numeric or string inputs `A` and `B` must either be the same size or have sizes that are compatible (for example, `A` is an `M`-by-`N` matrix and `B` is a scalar or `1`-by-`N` row vector). For more information, see Compatible Array Sizes for Basic Operations.

If `A` and `B` are categorical, datetime, or duration arrays, then they must be the same size unless one is a scalar.

• If one input is an ordinal categorical array, the other input can be an ordinal categorical array, a cell array of character vectors, or a single character vector. A single character vector expands into a cell array of character vectors of the same size as the other input. If both inputs are ordinal categorical arrays, they must have the same sets of categories, including their order. See Compare Categorical Array Elements for more details.

• If one input is a datetime array, the other input can be a datetime array, a character vector, or a cell array of character vectors.

• If one input is a duration array, the other input can be a duration array or a numeric array. The operator treats each numeric value as a number of standard 24-hour days.

• If one input is a string array, the other input can be a string array, a character vector, or a cell array of character vectors. The corresponding elements of `A` and `B` are compared lexicographically.

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

Right array, specified as a scalar, vector, matrix, or multidimensional array. Numeric or string inputs `A` and `B` must either be the same size or have sizes that are compatible (for example, `A` is an `M`-by-`N` matrix and `B` is a scalar or `1`-by-`N` row vector). For more information, see Compatible Array Sizes for Basic Operations.

If `A` and `B` are categorical, datetime, or duration arrays, then they must be the same size unless one is a scalar.

• If one input is an ordinal categorical array, the other input can be an ordinal categorical array, a cell array of character vectors, or a single character vector. A single character vector expands into a cell array of character vectors of the same size as the other input. If both inputs are ordinal categorical arrays, they must have the same sets of categories, including their order. See Compare Categorical Array Elements for more details.

• If one input is a datetime array, the other input can be a datetime array, a character vector, or a cell array of character vectors.

• If one input is a duration array, the other input can be a duration array or a numeric array. The operator treats each numeric value as a number of standard 24-hour days.

• If one input is a string array, the other input can be a string array, a character vector, or a cell array of character vectors. The corresponding elements of `A` and `B` are compared lexicographically.

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

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