sum

Sum of array elements

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Syntax

S = sum(A)

S = sum(A,'all')

S = sum(A,dim)

S = sum(A,vecdim)

S = sum(___,outtype)

S = sum(___,nanflag)

Description

example

S = sum(A)returns the sum of the elements of A along the first array dimension whose size does not equal 1.

IfAis a vector, thensum(A)returns the sum of the elements.
IfAis a matrix, thensum(A)returns a row vector containing the sum of each column.
IfAis a multidimensional array, thensum(A)operates along the first array dimension whose size does not equal 1, treating the elements as vectors. This dimension becomes1while the sizes of all other dimensions remain the same.

example

S = sum(A,'all')computes the sum of all elements ofA. This syntax is valid for MATLAB^®versions R2018b and later.

example

S = sum(A,dim)returns the sum along dimensiondim. For example, ifAis a matrix, thensum(A,2)is a column vector containing the sum of each row.

example

S = sum(A,vecdim)sums the elements ofAbased on the dimensions specified in the vectorvecdim. For example, ifAis a matrix, thensum(A,[1 2])is the sum of all elements inA, since every element of a matrix is contained in the array slice defined by dimensions 1 and 2.

example

S = sum(___,outtype)returns the sum with a specified data type, using any of the input arguments in the previous syntaxes.outtypecan be'default','double', or'native'.

example

S = sum(___,nanflag)specifies whether to include or omitNaNvalues from the calculation for any of the previous syntaxes.sum(A,'includenan')includes allNaNvalues in the calculation whilesum(A,'omitnan')ignores them.

Examples

collapse all

Sum of Vector Elements

Open Live Script

Create a vector and compute the sum of its elements.

A = 1:10; S = sum(A)

S = 55

Sum of Matrix Columns

Open Live Script

Create a matrix and compute the sum of the elements in each column.

A = [1 3 2; 4 2 5; 6 1 4]

A =3×31 3 2 4 2 5 6 1 4

S = sum(A)

S =1×311 6 11

Sum of Matrix Rows

Open Live Script

Create a matrix and compute the sum of the elements in each row.

A = [1 3 2; 4 2 5; 6 1 4]

A =3×31 3 2 4 2 5 6 1 4

S = sum(A,2)

S =3×16 11 11

Sum of Array Slices

Open Live Script

Use a vector dimension argument to operate on specific slices of an array.

Create a 3-D array whose elements are 1.

A = ones(4,3,2);

To sum all elements in each page ofA, specify the dimensions in which to sum (row and column) using a vector dimension argument. Since both pages are a 4-by-3 matrix of ones, the sum of each page is 12.

S1 = sum(A,[1 2])

S1 = S1(:,:,1) = 12 S1(:,:,2) = 12

If you sliceAalong the first dimension, you can sum the elements of the resulting 4 pages, which are each 3-by-2 matrices.

S2 = sum(A,[2 3])

S2 =4×16 6 6 6

Slicing along the second dimension, each page sum is over a 4-by-2 matrix.

S3 = sum(A,[1 3])

S3 =1×38 8 8

Starting in R2018b, to sum over all dimensions of an array, you can either specify each dimension in the vector dimension argument, or use the'all'option.

S4 = sum(A,[1 2 3])

S4 = 24

Sall = sum(A,'all')

Sall = 24

Sum of 3-D Array

Open Live Script

Create a 4-by-2-by-3 array of ones and compute the sum along the third dimension.

A = ones(4,2,3); S = sum(A,3)

S =4×23 3 3 3 3 3 3 3

Sum of 32-bit Integers

Open Live Script

Create a vector of 32-bit integers and compute theint32sum of its elements by specifying the output type asnative.

A = int32(1:10); S = sum(A,'native')

S =int3255

Sum Excluding`NaN`

Open Live Script

Create a vector and compute its sum, excludingNaNvalues.

A = [1.77 -0.005 3.98 -2.95 NaN 0.34 NaN 0.19]; S = sum(A,'omitnan')

S = 3.3250

If you do not specify'omitnan', thensum(A)returnsNaN.

Input Arguments

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`A`—Input array
vector|matrix|multidimensional array

Input array, specified as a vector, matrix, or multidimensional array.

IfAis a scalar, thensum(A)returnsA.
IfAis an empty 0-by-0 matrix, thensum(A)returns0.

`dim`—Dimension to operate along
positive integer scalar

Dimension to operate along, specified as a positive integer scalar. If you do not specify the dimension, then the default is the first array dimension of size greater than 1.

Dimensiondimindicates the dimension whose length reduces to 1. Thesize(S,dim)is1, while the sizes of all other dimensions remain the same.

Consider a two-dimensional input array,A:

sum(A,1)operates on successive elements in the columns ofAand returns a row vector of the sums of each column.
sum(A,2)operates on successive elements in the rows ofAand returns a column vector of the sums of each row.

sumreturnsAwhendimis greater thanndims(A)or whensize(A,dim)is1.

`vecdim`—Vector of dimensions
vector of positive integers

Vector of dimensions, specified as a vector of positive integers. Each element represents a dimension of the input array. The lengths of the output in the specified operating dimensions are 1, while the others remain the same.

Consider a 2-by-3-by-3 input array,A. Thensum(A,[1 2])returns a 1-by-1-by-3 array whose elements are the sums of each page ofA.

`outtype`—Output data type
`'default'`(default) |`'double'`|`'native'`

Output data type, specified as'default','double', or'native'. These options also specify the data type in which the operation is performed.

`outtype`	Output data type
`'default'`	`double`, unless the input data type is`single`or`duration`, in which case, the output is`'native'`
`'double'`	`double`, unless the data type is`duration`, in which case,`'double'`is not supported
`'native'`	same data type as the input, unless the input data type is`char`, in which case,`'native'`is not supported

Data Types:char

`nanflag`—`NaN`condition
‘`includenan`’(default) |‘`omitnan`’

NaNcondition, specified as one of these values:

'includenan'— IncludeNaNvalues when computing the sum, resulting inNaN.
'omitnan'— Ignore allNaNvalues in the input.

Data Types:char

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 specifydim, then it must be a constant.
Theouttypeandnanflagoptions must be constant character vectors.
SeeVariable-Sizing Restrictions for Code Generation of Toolbox Functions(MATLAB Coder).

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

Usage notes and limitations:

If you specifydim, then it must be a constant.
Theouttypeandnanflagoptions must be constant character vectors.

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:

The order of the additions in thesumoperation is not defined. Therefore, thesumoperation on a GPU array might not return exactly the same answer as thesum操作相应的MATLAB数值array. The difference might be significant whenAis a signed integer type and its product is accumulated natively.

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™.

Usage notes and limitations:

The order of the additions insumoperation is not defined. Therefore, thesumoperation on a distributed array might not return exactly the same answer as thesum操作相应的MATLAB数值array. The difference might be significant whenAis a signed integer type and its product is accumulated natively.

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

Version History

Introduced before R2006a

sum

Syntax

Description

Examples

Sum of Vector Elements

Sum of Matrix Columns

Sum of Matrix Rows

Sum of Array Slices

Sum of 3-D Array

Sum of 32-bit Integers

Sum ExcludingNaN

Input Arguments

A—Input arrayvector|matrix|multidimensional array

dim—Dimension to operate alongpositive integer scalar

vecdim—Vector of dimensionsvector of positive integers

outtype—Output data type'default'(default) |'double'|'native'

nanflag—NaNcondition‘includenan’(default) |‘omitnan’

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

See Also

Sum Excluding`NaN`

`A`—Input array
vector|matrix|multidimensional array

`dim`—Dimension to operate along
positive integer scalar

`vecdim`—Vector of dimensions
vector of positive integers

`outtype`—Output data type
`'default'`(default) |`'double'`|`'native'`

`nanflag`—`NaN`condition
‘`includenan`’(default) |‘`omitnan`’

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™.