# le, <=

Determine less than or equal to

## Description

returns a logical
array or a table of logical values with elements set to logical `A`

<= `B`

`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.

## Examples

### 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 = `*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`

.

### Replace Elements of Matrix

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`

.

### Compare Values in Categorical Array

Create an ordinal categorical array.

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

`A = `*2x3 categorical*
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.

### 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 = `*1×4 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.

### Test Duration Values

Create a `duration`

array.

d = hours(21:25) + minutes(75)

`d = `*1x5 duration*
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

### Compare Tables

*Since R2023a*

Create two tables and compare them. The row names (if present in both) and variable names must be the same, but do not need to be in the same orders. Rows and variables of the output are in the same orders as the first input.

A = table([1;2],[3;4],VariableNames=["V1","V2"],RowNames=["R1","R2"])

`A=`*2×2 table*
V1 V2
__ __
R1 1 3
R2 2 4

B = table([4;2],[3;1],VariableNames=["V2","V1"],RowNames=["R2","R1"])

`B=`*2×2 table*
V2 V1
__ __
R2 4 3
R1 2 1

A <= B

`ans=`*2×2 table*
V1 V2
_____ _____
R1 true false
R2 true true

## Input Arguments

`A`

, `B`

— Operands

scalars | vectors | matrices | multidimensional arrays | tables | timetables

Operands, specified as scalars, vectors, matrices, multidimensional arrays, tables, or
timetables. 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.

You can compare numeric inputs of any type, and the comparison does not suffer loss of precision due to type conversion.

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.

Inputs that are tables or timetables must meet the
following conditions:* (since R2023a)*

If an input is a table or timetable, then all its variables must have data types that support the operation.

If only one input is a table or timetable, then the other input must be a numeric or logical array.

If both inputs are tables or timetables, then:

Both inputs must have the same size, or one of them must be a one-row table.

Both inputs must have variables with the same names. However, the variables in each input can be in a different order.

If both inputs are tables and they both have row names, then their row names must be the same. However, the row names in each input can be in a different order.

If both inputs are timetables, then their row times must be the same. However, the row times in each input can be in a different order.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `logical`

| `char`

| `string`

| `categorical`

| `datetime`

| `duration`

| `table`

| `timetable`

**Complex Number Support: **Yes

## Tips

Some floating-point numbers cannot be represented exactly in binary form. This leads to small differences in results that the

`<=`

operator reflects. For more information, see Floating-Point Numbers.

## Extended Capabilities

### Tall Arrays

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

The
`le`

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

### C/C++ Code Generation

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

### GPU Code Generation

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

### HDL Code Generation

Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL 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.

### GPU Arrays

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

The `le`

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™.

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

## Version History

**Introduced before R2006a**

### R2023a: Perform operations directly on tables and timetables

The `le`

operator supports operations directly on tables and
timetables without indexing to access their variables. All variables must have data types
that support the operation. For more information, see Direct Calculations on Tables and Timetables.

### R2020b: Implicit expansion change affects ordinal `categorical`

arrays, `datetime`

arrays, and `duration`

arrays

Starting in R2020b, `le`

supports implicit expansion when the
arguments are ordinal `categorical`

arrays, `datetime`

arrays, or `duration`

arrays. Between R2020a and R2016b, implicit expansion
was supported only for numeric and string data types.

### R2016b: Implicit expansion change affects arguments for operators

Starting in R2016b with the addition of implicit expansion, some combinations of arguments for basic operations that previously returned errors now produce results. For example, you previously could not add a row and a column vector, but those operands are now valid for addition. In other words, an expression like `[1 2] + [1; 2]`

previously returned a size mismatch error, but now it executes.

If your code uses element-wise operators and relies on the errors that MATLAB^{®} previously returned for mismatched sizes, particularly within a `try`

/`catch`

block, then your code might no longer catch those errors.

For more information on the required input sizes for basic array operations, see Compatible Array Sizes for Basic Operations.

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