Dot product - MATLAB dot - MathWorks United Kingdom (2024)

Table of Contents

Syntax Description Examples Dot Product of Real Vectors Dot Product of Complex Vectors Dot Product of Matrices Dot Product of Multidimensional Arrays Input Arguments A,B — Input arrays numeric arrays dim — Dimension to operate along positive integer scalar More About Scalar Dot Product Algorithms 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™. 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 ArraysPartition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™. Version History See Also External Websites MATLAB Command Americas Europe Asia Pacific

Dot product

collapse all in page

Syntax

C = dot(A,B)

C = dot(A,B,dim)

Description

example

C = dot(A,B) returnsthe scalar dotproduct of A and B.

If A and B arevectors, then they must have the same length.
If A and B arematrices or multidimensional arrays, then they must have the samesize. In this case, the dot function treats A and B ascollections of vectors. The function calculates the dot product ofcorresponding vectors along the first array dimension whose size doesnot equal 1.

example

C = dot(A,B,dim) evaluatesthe dot product of A and B alongdimension, dim. The dim inputis a positive integer scalar.

Examples

collapse all

Dot Product of Real Vectors

Open Live Script

Create two simple, three-element vectors.

A = [4 -1 2];B = [2 -2 -1];

Calculate the dot product of A and B.

C = dot(A,B)

C = 8

The result is 8 since

C = A(1)*B(1) + A(2)*B(2) + A(3)*B(3)

Dot Product of Complex Vectors

Open Live Script

Dot Product of Matrices

Open Live Script

Create two matrices.

A = [1 2 3;4 5 6;7 8 9];B = [9 8 7;6 5 4;3 2 1];

Find the dot product of A and B.

C = dot(A,B)

C = 1×3 54 57 54

The result, C, contains three separate dot products. dot treats the columns of A and B as vectors and calculates the dot product of corresponding columns. So, for example, C(1) = 54 is the dot product of A(:,1) with B(:,1).

Find the dot product of A and B, treating the rows as vectors.

D = dot(A,B,2)

D = 3×1 46 73 46

In this case, D(1) = 46 is the dot product of A(1,:) with B(1,:).

Dot Product of Multidimensional Arrays

Open Live Script

Create two multidimensional arrays.

A = cat(3,[1 1;1 1],[2 3;4 5],[6 7;8 9])

A = A(:,:,1) = 1 1 1 1A(:,:,2) = 2 3 4 5A(:,:,3) = 6 7 8 9

B = cat(3,[2 2;2 2],[10 11;12 13],[14 15; 16 17])

B = B(:,:,1) = 2 2 2 2B(:,:,2) = 10 11 12 13B(:,:,3) = 14 15 16 17

Calculate the dot product of A and B along the third dimension (dim = 3).

C = dot(A,B,3)

C = 2×2 106 140 178 220

The result, C, contains four separate dot products. The first dot product, C(1,1) = 106, is equal to the dot product of A(1,1,:) with B(1,1,:).

Input Arguments

collapse all

`A,B` — Input arrays
numeric arrays

Input arrays, specified as numeric arrays.

Data Types: single | double
Complex Number Support: Yes

`dim` — Dimension to operate along
positive integer scalar

Dimension to operate along, specified as a positive integerscalar. If no value is specified, the default is the first array dimensionwhose size does not equal 1.

Consider two 2-D input arrays, A and B:

dot(A,B,1) treats the columnsof A and B as vectors and returnsthe dot products of corresponding columns.
dot(A,B,2) treats the rows of A and B asvectors and returns the dot products of corresponding rows.

dot returns conj(A).*B if dim isgreater than ndims(A).

More About

collapse all

Scalar Dot Product

The scalar dot product of two real vectorsof length n is equal to

$u \cdot v = \sum_{i = 1}^{n} u_{i} v_{i} = u_{1} v_{1} + u_{2} v_{2} + ... + u_{n} v_{n} .$

This relation is commutative for real vectors, such that dot(u,v) equals dot(v,u).If the dot product is equal to zero, then u and v areperpendicular.

For complex vectors, the dot product involves a complex conjugate.This ensures that the inner product of any vector with itself is realand positive definite.

$u \cdot v = \sum_{i = 1}^{n} {\bar{u}}_{i} v_{i} .$

Unlike the relation for real vectors, the complex relation isnot commutative, so dot(u,v) equals conj(dot(v,u)).

Algorithms

When inputs A and B arereal or complex vectors, the dot function treatsthem as column vectors and dot(A,B) is the sameas sum(conj(A).*B).
When the inputs are matrices or multidimensional arrays,the dim argument determines which dimension the sum functionoperates on. In this case, dot(A,B) is the sameas sum(conj(A).*B,dim).

Extended Capabilities

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

This function supports tall arrays with thelimitation:

For the syntax dot(A,B), the arrays A and B musthave the same size, even if they are vectors.

For more information, see Tall Arrays for Out-of-Memory Data.

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

Usage notes and limitations:

Code generation does not support sparse matrix inputs for this function.

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™.

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).

Version History

Introduced before R2006a

MATLAB Command

You clicked a link that corresponds to this MATLAB command:

Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.

Select a Web Site

Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .

You can also select a web site from the following list:

Americas

América Latina (Español)
Canada (English)
United States (English)

Europe

Belgium (English)
Denmark (English)
Deutschland (Deutsch)
España (Español)
Finland (English)
France (Français)
Ireland (English)
Italia (Italiano)
Luxembourg (English)

Netherlands (English)
Norway (English)
Österreich (Deutsch)
Portugal (English)
Sweden (English)
Switzerland
- Deutsch
- English
- Français
United Kingdom (English)

Asia Pacific

Australia (English)
India (English)
New Zealand (English)
中国
- 简体中文
- English
日本 (日本語)
한국 (한국어)

Contact your local office