cumprod

Cumulative product

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Syntax

Description

example

B = cumprod(A) returns the cumulative product 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 cumprod(A) returns a vector containing the cumulative product of the elements of A.

  • If A is a matrix, then cumprod(A) returns a matrix containing the cumulative products for each column of A.

  • If A is a multidimensional array, then cumprod(A) acts along the first nonsingleton dimension.

example

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

example

B = cumprod(___,direction) optionally specifies the direction using any of the previous syntaxes. You must specify A, and optionally can specify dim. For instance, cumprod(A,2,'reverse') returns the cumulative product within the rows of A by working from end to beginning of the second dimension.

Examples

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Open Script

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

A = 1:5;
B = cumprod(A)

B =

     1     2     6    24   120
Open Script

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

A = [1 4 7; 2 5 8; 3 6 9]

A =

     1     4     7
     2     5     8
     3     6     9

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

B = cumprod(A)

B =

     1     4     7
     2    20    56
     6   120   504
Open Script

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

A = [1 3 5; 2 4 6]

A =

     1     3     5
     2     4     6

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

B = cumprod(A,2)

B =

     1     3    15
     2     8    48
Open 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 product of the rows of A.

B = cumprod(A,2)

B =

     1     0     0
     1     1     0

The output has type double.

class(B)

ans =

double
Open Script

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

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

A =

     9    10     3
    10     7     6
     2     1    10

Calculate the cumulative product along the columns. Specify the 'reverse' option to work from bottom to top in each column. The result is the same size as A.

B = cumprod(A,'reverse')

B =

   180    70   180
    20     7    60
     2     1    10

Input Arguments

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

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

Consider a two-dimensional input array, A.

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

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

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

Direction of cumulation, specified as 'forward' (default) or 'reverse'.

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

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

Data Types: char

Output Arguments

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

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

More About

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First Nonsingleton Dimension

The first nonsingleton dimension is the first dimension of an array whose size is not equal to 1.

For example:

  • If X is a 1-by-n row vector, then the second dimension is the first nonsingleton dimension of X.

  • If X is a 1-by-0-by-n empty array, then the second dimension is the first nonsingleton dimension of X.

  • If X is a 1-by-1-by-3 array, then the third dimension is the first nonsingleton dimension of X.

Tips

  • Many cumulative functions in MATLAB® support the 'reverse' option. This option allows quick directional calculations without needing a flip or reflection of the input array.

See Also

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Introduced before R2006a

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