cumsum

Symbolic cumulative sum

Syntax

B = cumsum(A)

B = cumsum(A,dim)

B = cumsum(___,direction)

Description

B = cumsum(A) returns an array the same size as A containing the cumulative sum.

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

• If A is a matrix, then cumsum(A) returns a matrix containing the cumulative sums of each column of A.

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

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

Examples

Cumulative Sum of Vector

Create a vector and find the cumulative sum of its elements.

V = 1./factorial(sym([1:5]))
sum_V = cumsum(V)

V =
[ 1, 1/2, 1/6, 1/24, 1/120]
 
sum_V =
[ 1, 3/2, 5/3, 41/24, 103/60]

Cumulative Sum of Each Column in Symbolic Matrix

Create matrix a 4-by-4 symbolic matrix A all elements of which equal 1.

A = sym(ones(4,4))

A =
[ 1, 1, 1, 1]
[ 1, 1, 1, 1]
[ 1, 1, 1, 1]
[ 1, 1, 1, 1]

Compute the cumulative sum of elements of A. By default, cumsum returns the cumulative sum of each column.

sumA = cumsum(A)

sumA =
[ 1, 1, 1, 1]
[ 2, 2, 2, 2]
[ 3, 3, 3, 3]
[ 4, 4, 4, 4]

Cumulative Sum of Each Row in Symbolic Matrix

Create matrix a 4-by-4 symbolic matrix A all elements of which equal 1.

A = sym(ones(4,4))

A =
[ 1, 1, 1, 1]
[ 1, 1, 1, 1]
[ 1, 1, 1, 1]
[ 1, 1, 1, 1]

Compute the cumulative sum of each row of the matrix A.

sumA = cumsum(A,2)

sumA =
[ 1, 2, 3, 4]
[ 1, 2, 3, 4]
[ 1, 2, 3, 4]
[ 1, 2, 3, 4]

Reverse Cumulative Sum

Create matrix a 4-by-4 symbolic matrix, all elements of which equal 1.

A = sym(ones(4,4))

A =
[ 1, 1, 1, 1]
[ 1, 1, 1, 1]
[ 1, 1, 1, 1]
[ 1, 1, 1, 1]

Calculate the cumulative sum along the columns in both directions. Specify the 'reverse' option to work from right to left in each row.

columnsDirect = cumsum(A)
columnsReverse = cumsum(A,'reverse')

columnsDirect =
[ 1, 1, 1, 1]
[ 2, 2, 2, 2]
[ 3, 3, 3, 3]
[ 4, 4, 4, 4]
 
columnsReverse =
[ 4, 4, 4, 4]
[ 3, 3, 3, 3]
[ 2, 2, 2, 2]
[ 1, 1, 1, 1]

Calculate the cumulative sum along the rows in both directions. Specify the 'reverse' option to work from right to left in each row.

rowsDirect = cumsum(A,2)
rowsReverse = cumsum(A,2,'reverse')

rowsDirect =
[ 1, 2, 3, 4]
[ 1, 2, 3, 4]
[ 1, 2, 3, 4]
[ 1, 2, 3, 4]
 
rowsReverse =
[ 4, 3, 2, 1]
[ 4, 3, 2, 1]
[ 4, 3, 2, 1]
[ 4, 3, 2, 1]

Input Arguments

A — Input array

symbolic vector | symbolic matrix

Input array, specified as a vector or matrix.

dim — Dimension to operate along

positive integer

Dimension to operate along, specified as a positive integer. The default value is 1.

Consider a two-dimensional input array, A:

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

• cumsum(A,2) works on successive elements in the rows of A and returns the cumulative sum 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 the 'forward' (default) or 'reverse'.

• 'forward' works from 1 to end of the active dimension.

• 'reverse' works from end to 1 of the active dimension.

Output Arguments

B — Cumulative sum array

vector | matrix

Cumulative sum array, returned as a vector or matrix of the same size as the input A.