ldivide, .\

Left array division

Syntax

x = B.\A

x = ldivide(B,A)

Description

x = B.\A divides each element of A by the corresponding element of B. The sizes of A and B must be the same or be compatible.

If the sizes of A and B are compatible, then the two arrays implicitly expand to match each other. For example, if one of A or B is 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 divide A by B, but is rarely used. It enables operator overloading for classes.

Examples

Divide Two Numeric Arrays

Create two numeric arrays, A and B, 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 = 2×3

    1.0000    0.5000    0.3333
    0.2500    0.2000    0.1667

Divide Scalar by Numeric Array

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 = 2×3

    2.0000    1.0000    0.6667
    0.5000    0.4000    0.3333

Divide Row and Column Vectors

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 = 3×2

    1.0000    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 to b(i) .\ a(j):

$$\mathit{a}=\left[{\mathit{a}}_1{\mathit{a}}_2\right],\mathit{b}=\left[\begin{array}{c}{\mathit{b}}_1\\ {\mathit{b}}_2\\ {\mathit{b}}_3\end{array}\right],\mathit{b}.\backslash \mathit{a}=\left[\begin{array}{cc}{\mathit{b}}_1.\backslash {\mathit{a}}_1& {\mathit{b}}_1.\backslash {\mathit{a}}_2\\ {\mathit{b}}_2.\backslash {\mathit{a}}_1& {\mathit{b}}_2.\backslash {\mathit{a}}_2\\ {\mathit{b}}_3.\backslash {\mathit{a}}_1& {\mathit{b}}_3.\backslash {\mathit{a}}_2\end{array}\right].$$

Input Arguments

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.

• If A or B is 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.

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

Tips

• The element-wise operators ./ and .\ are related to each other by the equation A./B = B.\A.

• When dividing integers, use idivide for more rounding options.

• MATLAB^® does not support complex integer division.

Compatibility Considerations

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 duration arrays

Behavior changed in R2020b

Starting in R2020b, ldivide supports implicit expansion when the arguments are duration arrays. Between R2020a and R2016b, implicit expansion was supported only for numeric 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™.

Usage notes and limitations:

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

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

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, 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).