# cumprod

Cumulative product

## Syntax

``B = cumprod(A)``
``B = cumprod(A,dim)``
``B = cumprod(___,direction)``
``B = cumprod(___,nanflag)``

## 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.```

example

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

## Examples

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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 = 1×5 1 2 6 24 120 ```

Define 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 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 = 3×3 1 4 7 2 20 56 6 120 504 ```

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 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 = 2×3 1 3 15 2 8 48 ```

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 product of the rows of `A`.

`B = cumprod(A,2)`
```B = 2×3 1 0 0 1 1 0 ```

The output has type `double`.

`class(B)`
```ans = 'double' ```

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 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 = 3×3 180 70 180 20 7 60 2 1 10 ```

Create a vector containing `NaN` values and compute the cumulative products. By default, `cumprod` includes `NaN` values. When you include `NaN` values in the calculation, the cumulative product becomes `NaN` as soon as the first `NaN` value in `A` is encountered.

```A = [1 3 NaN 2 4 NaN]; B = cumprod(A)```
```B = 1×6 1 3 NaN NaN NaN NaN ```

Ignore `NaN` values in the cumulative product calculation using the `'omitnan'` option.

`B = cumprod(A,'omitnan')`
```B = 1×6 1 3 3 6 24 24 ```

## 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 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`.

• `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.

`NaN` condition, specified as one of these values:

• `'includenan'` — Include `NaN` values from the input when computing each product, resulting in `NaN` values in the output.

• `'omitnan'` — Ignore `NaN` values in the input. The product of elements containing `NaN` values is the product of all non-`NaN` elements. If all elements are `NaN`, then `cumprod` returns 1.

## 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`.

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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.

## Version History

Introduced before R2006a