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# le, <=

Determine less than or equal to

## 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, it returns 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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### Test Vector Elements

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 =

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    12     7     9    11     2
```

The result is a subset of the elements in A.

### Replace Elements of Matrix

Create a matrix.

`A = magic(4)`
```A =

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 =

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.

### Compare Values in Categorical Array

Create an ordinal categorical array.

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

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 =

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 =

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.

### Test Complex Numbers

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 =

1.0000 + 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 =

1.0000 + 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.

## Input Arguments

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### A — Left arraynumeric array | logical array | character array | ordinal categorical array

Left array, specified as a numeric array, logical array, character array, or categorical array. Inputs A and B must be the same size unless one is a scalar. A scalar input expands into an array of the same size as the other input.

If one input is an ordinal categorical array, the other input can be an ordinal categorical array, a cell array of strings, or a single string. A single string expands into a cell array of strings 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.

### B — Right arraynumeric array | logical array | character array | ordinal categorical array

Right array, specified as a numeric array, logical array, character array, or categorical array. Inputs A and B must be the same size unless one is a scalar. A scalar input expands into an array of the same size as the other input.

If one input is an ordinal categorical array, the other input can be an ordinal categorical array, a cell array of strings, or a single string. A single string expands into a cell array of strings 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.

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