# cumprod

Symbolic 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. The output `B` has the same size as `A`.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 of 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)` specifies the direction using any of the previous syntaxes. 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 all `NaN` values in the calculation while `cumprod(A,'omitnan')` ignores them.```

## Examples

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Create a symbolic vector. Find the cumulative product of its elements.

```syms x A = (1:5)*x```
`A = $\left(\begin{array}{ccccc}x& 2 x& 3 x& 4 x& 5 x\end{array}\right)$`

In the vector of cumulative products, 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)`.

`B = cumprod(A)`
`B = $\left(\begin{array}{ccccc}x& 2 {x}^{2}& 6 {x}^{3}& 24 {x}^{4}& 120 {x}^{5}\end{array}\right)$`

Create a 3-by-3 symbolic matrix `A` whose all elements are `x`.

```syms x A = ones(3)*x```
```A =  $\left(\begin{array}{ccc}x& x& x\\ x& x& x\\ x& x& x\end{array}\right)$```

Compute the cumulative product of elements of `A`. By default, `cumprod` returns the cumulative product of each column.

`B = cumprod(A)`
```B =  $\left(\begin{array}{ccc}x& x& x\\ {x}^{2}& {x}^{2}& {x}^{2}\\ {x}^{3}& {x}^{3}& {x}^{3}\end{array}\right)$```

To compute the cumulative product of each row, set the value of the `dim` option to `2`.

`B = cumprod(A,2)`
```B =  $\left(\begin{array}{ccc}x& {x}^{2}& {x}^{3}\\ x& {x}^{2}& {x}^{3}\\ x& {x}^{2}& {x}^{3}\end{array}\right)$```

Create a 3-by-3-by-2 symbolic array.

```syms x y A(:,:,1) = [x y 0; x 3 x*y; x 1/3 y]; A(:,:,2) = [x y 3; 3 x y; y 3 x]; A```
```A(:,:,1) =  $\left(\begin{array}{ccc}x& y& 0\\ x& 3& x y\\ x& \frac{1}{3}& y\end{array}\right)$```
```A(:,:,2) =  $\left(\begin{array}{ccc}x& y& 3\\ 3& x& y\\ y& 3& x\end{array}\right)$```

Compute the cumulative product along the rows by specifying `dim` as `2`. Specify the `'reverse'` option to work from right to left in each row. The result is the same size as `A`.

`B = cumprod(A,2,'reverse')`
```B(:,:,1) =  $\left(\begin{array}{ccc}0& 0& 0\\ 3 {x}^{2} y& 3 x y& x y\\ \frac{x y}{3}& \frac{y}{3}& y\end{array}\right)$```
```B(:,:,2) =  $\left(\begin{array}{ccc}3 x y& 3 y& 3\\ 3 x y& x y& y\\ 3 x y& 3 x& x\end{array}\right)$```

To compute the cumulative product along the third (page) dimension, specify `dim` as `3`. Specify the `'reverse'` option to work from the largest page index to the smallest page index.

`B = cumprod(A,3,'reverse')`
```B(:,:,1) =  $\left(\begin{array}{ccc}{x}^{2}& {y}^{2}& 0\\ 3 x& 3 x& x {y}^{2}\\ x y& 1& x y\end{array}\right)$```
```B(:,:,2) =  $\left(\begin{array}{ccc}x& y& 3\\ 3& x& y\\ y& 3& x\end{array}\right)$```

Create a symbolic vector containing `NaN` values. Compute the cumulative products.

`A = [sym('a') sym('b') 1 NaN 2]`
`A = $\left(\begin{array}{ccccc}a& b& 1& \mathrm{NaN}& 2\end{array}\right)$`
`B = cumprod(A)`
`B = $\left(\begin{array}{ccccc}a& a b& a b& \mathrm{NaN}& \mathrm{NaN}\end{array}\right)$`

You can ignore `NaN` values in the cumulative product calculation using the `'omitnan'` option.

`B = cumprod(A,'omitnan')`
`B = $\left(\begin{array}{ccccc}a& a b& a b& a b& 2 a b\end{array}\right)$`

## Input Arguments

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

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 product of each column.

• `cumprod(A,2)` works on successive elements in the rows of `A` and returns the cumulative product 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`

`NaN` condition, specified as:

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

• `'omitnan'` — Ignore all `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.

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 `A`.

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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`.