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# 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 does not equal 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 does not equal 1, treating the elements as vectors. This dimension becomes 1 while the sizes of all other dimensions remain the same.

example

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

example

S = sum(A,dim) returns the sum along dimension dim. For example, if A is a matrix, then sum(A,2) is 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]) is the sum of all elements in A, 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. outtype can be 'default', 'double', or 'native'.

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S = sum(___,nanflag) specifies whether to include or omit NaN values from the calculation for any of the previous syntaxes. sum(A,'includenan') includes all NaN values in the calculation while sum(A,'omitnan') ignores them.

## Examples

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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

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

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 vector and compute its sum, excluding NaN values.

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', then sum(A) returns NaN.

## Input Arguments

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

• 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
Complex Number Support: Yes

Dimension to operate along, specified as a positive integer scalar. If no value is specified, then the default is the first array dimension whose size does not equal 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 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

NaN condition, specified as one of these values:

• 'includenan' — Include NaN values when computing the sum, resulting in NaN.

• 'omitnan' — Ignore all NaN values in the input.

Data Types: char

## See Also

Introduced before R2006a

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