cumsum

Cumulative sum

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Syntax

B = cumsum(A)
B = cumsum(A,dim)
B = cumsum(___,direction)
B = cumsum(___,nanflag)

Description

B = cumsum(A) returns the cumulative sum of A starting at the beginning of the first array dimension in A whose size does not equal 1.

  • If A is a vector, then B is a vector of the same size containing the cumulative sum of A.

  • If A is a matrix, then B is a matrix of the same size containing the cumulative sum in each column of A.

  • If A is a multidimensional array, then B is an array of the same size containing the cumulative sum along the first array dimension of A whose size does not equal 1.

  • If A is a table or timetable, then M is a table or timetable of the same size containing the cumulative sum in each variable of A. (since R2023a)

The class of B is the same as the class of A except if A is logical, in which case B is double.

example

B = cumsum(A,dim) returns the cumulative sum of the elements along dimension dim. For example, if A is a matrix, then cumsum(A,2) returns the cumulative sum along the rows of A.

example

B = cumsum(___,direction) specifies the direction for any of the previous syntaxes. For example, cumsum(A,2,"reverse") returns the cumulative sum within the rows of A by working from end to beginning of the second dimension.

example

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

example

Examples

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Open Live Script

Find the cumulative sum of the integers from 1 to 5. The element B(2) is the sum of A(1) and A(2), while B(5) is the sum of elements A(1) through A(5). 

A = 1:5;
B = cumsum(A)
B = 1×5

     1     3     6    10    15
Open Live Script

Create a 3-by-3 matrix whose elements correspond to their linear indices. 

A = [1 4 7; 2 5 8; 3 6 9]
A = 3×3

     1     4     7
     2     5     8
     3     6     9

Find the cumulative sum of the columns of A. The element B(5) is the sum of A(4) and A(5), while B(9) is the sum of A(7), A(8), and A(9).

B = cumsum(A)
B = 3×3

     1     4     7
     3     9    15
     6    15    24
Open Live Script

Define a 2-by-3 matrix whose elements correspond to their linear indices. 

A = [1 3 5; 2 4 6]
A = 2×3

     1     3     5
     2     4     6

Find the cumulative sum of the rows of A. The element B(3) is the sum of A(1) and A(3), while B(5) is the sum of A(1), A(3), and A(5).

B = cumsum(A,2)
B = 2×3

     1     4     9
     2     6    12
Open Live Script

Create an array of logical values. 

A = [true false true; true true false]
A = 2×3 logical array

   1   0   1
   1   1   0

Find the cumulative sum of the rows of A. 

B = cumsum(A,2)
B = 2×3

     1     1     2
     1     2     2

The output has type double. 

class(B)
ans = 
'double'
Open Live Script

Create a 3-by-3 matrix of random integers between 1 and 10. 

rng default;
A = randi([1,10],3)
A = 3×3

     9    10     3
    10     7     6
     2     1    10

Calculate the cumulative sum along the rows. Specify the "reverse" option to work from right to left in each row. The result is the same size as A. 

B = cumsum(A,2,"reverse")
B = 3×3

    22    13     3
    23    13     6
    13    11    10
Open Live Script

Create a matrix containing NaN values.

A = [3 5 NaN 4; 2 6 NaN 9; 1 3 5 NaN]
A = 3×4

     3     5   NaN     4
     2     6   NaN     9
     1     3     5   NaN

Compute the cumulative sums of the matrix, excluding NaN values. For matrix columns that contain leading NaN values, the cumulative sum is 0 until a non-NaN value is encountered.

B = cumsum(A,"omitnan")
B = 3×4

     3     5     0     4
     5    11     0    13
     6    14     5    13

Input Arguments

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

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | 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 whose size does not equal 1.

Consider a two-dimensional input array, A:

  • cumsum(A,1) works on successive elements in the columns of A and returns the cumulative sums of each column.

  • cumsum(A,2) works on successive elements in the rows of A and returns the cumulative sums of each row.

cumsum(A,1) column-wise operation and cumsum(A,2) row-wise operation

cumsum returns A if dim is greater than ndims(A).

Direction of cumulation, specified as one of these values:

  • "forward" — Work from 1 to end of the operating dimension.

  • "reverse" — Work from end to 1 of the operating dimension.

Missing value condition, specified as one of these values:

  • "includemissing" or "includenan" — Include NaN values in A when computing the cumulative sums. Elements in B are NaN as soon as the first NaN value in A is encountered. "includemissing" and "includenan" have the same behavior.

  • "omitmissing" or "omitnan" — Ignore NaN values in A when computing the cumulative sums. If A has consecutive leading NaN values, then the corresponding elements in B are 0. "omitmissing" and "omitnan" have the same behavior.

Tips

  • The "reverse" option in many cumulative functions allows quick directional calculations without requiring a flip or reflection of the input array.

Extended Capabilities

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Version History

Introduced before R2006a

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See Also

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