# sum

Sum of array elements

## Description

example

S = sum(A) returns the sum of the elements of A along the first array dimension whose size is greater than 1.

• If A is a vector, then sum(A) returns the sum of the elements.

• If A is a matrix, then sum(A) returns a row vector containing the sum of each column.

• If A is a multidimensional array, then sum(A) operates along the first array dimension whose size is greater than 1, treating the elements as vectors. The size of S in this dimension becomes 1 while the sizes of all other dimensions remain the same as in A.

• If A is a table or timetable, then sum(A) returns a one-row table containing the sum of each variable. (since R2023a)

example

S = sum(A,"all") returns the sum of all elements of A.

example

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

example

S = sum(A,vecdim) sums the elements of A based on the dimensions specified in the vector vecdim. For example, if A is a matrix, then sum(A,[1 2]) returns the sum of all elements in A because 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 the specified data type, using any of the input arguments in the previous syntaxes. outtype can be "default", "double", or "native".

example

S = sum(___,nanflag) specifies whether to include or omit NaN values in A. For example, sum(A,"omitnan") ignores NaN values when computing the sum. By default, sum includes NaN values.

## Examples

collapse all

Create a vector and compute the sum of its elements.

A = 1:10;
S = sum(A)
S = 55

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

A = [1 3 2; 4 2 5; 6 1 4]
A = 3×3

1     3     2
4     2     5
6     1     4

S = sum(A)
S = 1×3

11     6    11

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

A = [1 3 2; 4 2 5; 6 1 4]
A = 3×3

1     3     2
4     2     5
6     1     4

S = sum(A,2)
S = 3×1

6
11
11

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 of A, 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 slice A along 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 = 4×1

6
6
6
6

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

S3 = sum(A,[1 3])
S3 = 1×3

8     8     8

To compute the 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

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 = 4×2

3     3
3     3
3     3
3     3

Create a vector of 32-bit integers and compute the int32 sum of its elements by specifying the output type as native.

A = int32(1:10);
S = sum(A,"native")
S = int32
55

Create a matrix containing NaN values.

A = [1.77 -0.005 NaN -2.95; NaN 0.34 NaN 0.19]
A = 2×4

1.7700   -0.0050       NaN   -2.9500
NaN    0.3400       NaN    0.1900

Compute the sum of the matrix, excluding NaN values. For matrix columns that contain any NaN value, sum computes with the non-NaN elements. For matrix columns that contain all NaN values, the sum is 0.

S = sum(A,"omitnan")
S = 1×4

1.7700    0.3350         0   -2.7600

## Input Arguments

collapse all

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

• If A is a scalar, then sum(A) returns A.

• If A is an empty 0-by-0 matrix, then sum(A) returns 0.

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

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.

Dimension dim indicates the dimension whose length reduces to 1. The size(S,dim) is 1, 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 of A and returns a row vector of the sums of each column.

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

sum returns A when dim is greater than ndims(A) or when size(A,dim) is 1.

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

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. Then sum(A,[1 2]) returns a 1-by-1-by-3 array whose elements are the sums of each page of A.

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

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

outtypeOutput data type
"default"double, unless the input data type is single, duration, table, or timetable, in which case, the output is "native"
"double"double, unless the data type is duration, table, or timetable, 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; or unless the input data type is timetable, in which case the output data type is table

Missing value condition, specified as one of these values:

• "includemissing" or "includenan" — Include NaN values in A when computing the sum. If any element in the operating dimension is NaN, then the corresponding element in S is NaN. "includemissing" and "includenan" have the same behavior.

• "omitmissing" or "omitnan" — Ignore NaN values in A, and compute the sum over fewer points. If all elements in the operating dimension are NaN, then the corresponding element in S is 0. "omitmissing" and "omitnan" have the same behavior.

## Version History

Introduced before R2006a

expand all