ldivide,.\

Left array division

Syntax

x = B.\A

x = ldivide(B,A)

Description

x =B.\Adivides each element ofAby the corresponding element ofB. The sizes ofAandBmust be the same or becompatible.

If the sizes ofAandBare compatible, then the two arrays implicitly expand to match each other. For example, if one ofAorBis a scalar, then the scalar is combined with each element of the other array. Also, vectors with different orientations (one row vector and one column vector) implicitly expand to form a matrix.

x = ldivide(B,A)is an alternative way to divideAbyB, but is rarely used. It enables operator overloading for classes.

Examples

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Divide Two Numeric Arrays

Open Live Script

Create two numeric arrays,AandB, and divide the second array,B, into the first,A.

A = ones(2,3); B = [1 2 3; 4 5 6]; x = B.\A

x =2×31.0000 0.5000 0.3333 0.2500 0.2000 0.1667

Divide Scalar by Numeric Array

Open Live Script

Create a scalar,c, and divide it by a numeric array. The result is the same size as the array.

c = 2; D = [1 2 3; 4 5 6]; x = D.\c

x =2×32.0000 1.0000 0.6667 0.5000 0.4000 0.3333

Divide Row and Column Vectors

Open Live Script

Create a 1-by-2 row vector and 3-by-1 column vector and divide them.

a = 1:2; b = (1:3)'; b .\ a

ans =3×21.0000 2.0000 0.5000 1.0000 0.3333 0.6667

The result is a 3-by-2 matrix, where each (i,j) element in the matrix is equal tob(i) .\ a(j):

$a = [a_{1} a_{2}], b = [\begin{matrix} b_{1} \\ b_{2} \\ b_{3} \end{matrix}], b . \ a = [\begin{matrix} b_{1} . \ a_{1} & b_{1} . \ a_{2} \\ b_{2} . \ a_{1} & b_{2} . \ a_{2} \\ b_{3} . \ a_{1} & b_{3} . \ a_{2} \end{matrix}] .$

Input Arguments

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

Operands, specified as scalars, vectors, matrices, or multidimensional arrays. InputsAandBmust either be the same size or have sizes that are compatible (for example,Ais anM-by-Nmatrix andBis a scalar or1-by-Nrow vector). For more information, seeCompatible Array Sizes for Basic Operations.

IfAorBis an integer data type, then the other input must be the same integer type or be a scalar double. Operands with an integer data type cannot be complex.

Tips

The element-wise operators./and.\are related to each other by the equationA./B = B.\A.
When dividing integers, useidividefor more rounding options.
MATLAB^®does not support complex integer division.

Extended Capabilities

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

This function fully supports tall arrays. For more information, seeTall Arrays.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

If you useldividewith single type and double type operands, the generated code might not produce the same result as MATLAB. SeeBinary Element-Wise Operations with Single and Double Operands(MATLAB Coder).

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU 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, seeRun MATLAB Functions in Thread-Based Environment.

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

Usage notes and limitations:

64-bit integers are not supported.

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

Version History

Introduced before R2006a

expand all

R2020b: Implicit expansion change affects`duration`arrays

Behavior changed in R2020b

Starting in R2020b,ldividesupports implicit expansion when the arguments areduration数组。R2020a和R2016b之间隐式依斯攀ion was supported only for numeric data types.

R2016b: Implicit expansion change affects arguments for operators

Behavior changed in R2016b

与一个R2016b开始ddition 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 atry/catchblock, then your code might no longer catch those errors.

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

ldivide,.\

Syntax

Description

Examples

Divide Two Numeric Arrays

Divide Scalar by Numeric Array

Divide Row and Column Vectors

Input Arguments

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

Tips

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™.

Thread-Based Environment
Run code in the background using MATLAB®`backgroundPool`or accelerate code with Parallel Computing Toolbox™`ThreadPool`.

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™.

Version History

R2020b: Implicit expansion change affects`duration`arrays

R2016b: Implicit expansion change affects arguments for operators

See Also

Topics

ldivide,.\

Syntax

Description

Examples

Divide Two Numeric Arrays

Divide Scalar by Numeric Array

Divide Row and Column Vectors

Input Arguments

A,B—Operandsscalars|vectors|matrices|multidimensional arrays

Tips

Extended Capabilities

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

C/C++ Code GenerationGenerate C and C++ code using MATLAB® Coder™.

GPU Code GenerationGenerate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Thread-Based EnvironmentRun code in the background using MATLAB®backgroundPoolor accelerate code with Parallel Computing Toolbox™ThreadPool.

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

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

Version History

R2020b: Implicit expansion change affectsdurationarrays

R2016b: Implicit expansion change affects arguments for operators

See Also

Topics

`A`,`B`—Operands
scalars|vectors|matrices|multidimensional 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™.

Thread-Based Environment
Run code in the background using MATLAB®`backgroundPool`or accelerate code with Parallel Computing Toolbox™`ThreadPool`.

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™.

R2020b: Implicit expansion change affects`duration`arrays