cumsum

Cumulative sum

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 is greater than 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 is greater than 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.

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.

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.

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.

Examples

Cumulative Sum of Vector

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

Cumulative Sum in Matrix Columns

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

Cumulative Sum in Matrix Rows

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

Cumulative Sum of Logical Input

Create an array of logical values.

A = [true false true; true true false]

A = 2x3 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'

Reverse Cumulative Sum

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

Cumulative Sum Excluding Missing Values

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

A — Input array

vector | matrix | multidimensional array | table | timetable

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

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.

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

direction — Direction of cumulation

"forward" (default) | "reverse"

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.

nanflag — Missing value condition

"includemissing" (default) | "includenan" | "omitmissing" | "omitnan"

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

Tall Arrays

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

This function supports tall arrays with the limitations:

The "reverse" direction is not supported.

For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Logical inputs are not supported. Cast input to double first.

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

GPU Code Generation

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

Usage notes and limitations:

• Logical inputs are not supported. Cast input to double first.

• 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™.

Usage notes and limitations:

• The nanflag argument is not supported.

• The order of the additions within the cumsum operation is not defined. Therefore, the cumsum operation on a gpuArray might not return exactly the same answer as the cumsum operation on the corresponding numeric array. The differences might be significant when A is a signed integer type.

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™.

Usage notes and limitations:

• The order of the additions within the cumsum operation is not defined. Therefore, the cumsum operation on a distributed array might not return exactly the same answer as the cumsum operation on the corresponding numeric array. The differences might be significant when A is a signed integer type.

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

Version History

Introduced before R2006a

R2023a: Specify missing value condition

Include or omit missing values in the input array when computing cumulative sums by using the "includemissing" or "omitmissing" options. These options have the same behavior as the "includenan" and "omitnan" options, respectively.

R2023a: Perform calculations directly on tables and timetables

The cumsum function can calculate on all variables within a table or timetable without indexing to access those variables. All variables must have data types that support the calculation. For more information, see Direct Calculations on Tables and Timetables.