le, <=

Determine less than or equal to

Syntax

A <= B

le(A,B)

Description

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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Test Vector Elements

Open Live Script

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

Open Live Script

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

Open Live Script

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

Open Live Script

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

Open Live Script

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

Input Arguments

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`A`, `B` — Operands
scalars | vectors | matrices | multidimensional arrays

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

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 Avoiding Common Problems with Floating-Point Arithmetic.

Compatibility Considerations

expand all

Implicit expansion change affects arguments for operators

Behavior changed in R2016b

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.

Implicit expansion change affects ordinal `categorical` arrays, `datetime` arrays, and `duration` arrays

Behavior changed in R2020b

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.

Extended Capabilities

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

This 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 Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

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

This function fully supports GPU arrays. 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).

Documentation

le, <=

Syntax

Description

Examples

Test Vector Elements

Replace Elements of Matrix

Compare Values in Categorical Array

Test Complex Numbers

Test Duration Values

Input Arguments

`A`, `B` — Operands
scalars | vectors | matrices | multidimensional arrays

Tips

Compatibility Considerations

Implicit expansion change affects arguments for operators

Implicit expansion change affects ordinal `categorical` arrays, `datetime` arrays, and `duration` arrays

Extended Capabilities

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

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 Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

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

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

See Also

Topics

MATLAB Documentation

Support

Documentation

le, <=

Syntax

Description

Examples

Test Vector Elements

Replace Elements of Matrix

Compare Values in Categorical Array

Test Complex Numbers

Test Duration Values

Input Arguments

A, B — Operands scalars | vectors | matrices | multidimensional arrays

Tips

Compatibility Considerations

Implicit expansion change affects arguments for operators

Implicit expansion change affects ordinal categorical arrays, datetime arrays, and duration arrays

Extended Capabilities

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

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 Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

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

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

See Also

Topics

MATLAB Documentation

Support

`A`, `B` — Operands
scalars | vectors | matrices | multidimensional arrays

Implicit expansion change affects ordinal `categorical` arrays, `datetime` arrays, and `duration` arrays

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

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 Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

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

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