# R – Get Cumulative Maximum in a Vector

In this tutorial, we will look at how to get the cumulative maximum in a vector in R with the help of some examples.

## What is the cumulative maximum?

The cumulative max in a series of values is the maximum value up to that value in our series. For example, for a vector of three values (a1, a2, and a3), the cumulative maximum would be a1, max(a1,a2), and max(a1,a2,a3). The following image illustrates this with an example.

In the above image, we have five values 1, 3, 2, 6, and 4. The cumulative max for these values is 1, max(1, 3), max(1, 3, 2), max(1, 3, 2, 6), and max(1, 3, 2, 6, 4) respectively. Note that the order in which these values appear is important when computing the cumulative max.

## How to calculate the cumulative max of a vector in R?

You can use the `cummax()` function in R to compute the cumulative maximum of the values in a vector. Pass the vector as an argument to the function. The following is the syntax –

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```# cumulative max of vector x
cummax(x)```

It returns a vector containing the cumulative maximum of the values in the passed vector.

## Examples

Let’s now look at some examples of using the above syntax.

### Cumulative max of a vector of numbers

Let’s create a vector of some numbers and use the `cummax()` function to calculate its cumulative maximum. For example, let’s compute the cumulative max for the vector `c(1, 3, 2, 6, 4, 5)`.

```# create a vector
vec <- c(1, 3, 2, 6, 4, 5)
# cumulative max of vector
print(cummax(vec))```

Output:

` 1 3 3 6 6 6`

We print the resulting vector. You can see that each value in the resulting vector is the maximum of all values till that particular index from the original vector.

Let’s look at another example. What if the values in the vector are in ascending order?

Let’s find out.

```# create a vector
vec <- c(1, 2, 3, 4, 5, 6)
# cumulative max of vector
print(cummax(vec))```

Output:

` 1 2 3 4 5 6`

We get the same vector as the cumulative max. This is because the values in the original vector are in ascending order thus each new value is greater than all the previous values.

What if the values are in descending order?

Let’s find out.

```# create a vector
vec <- c(6, 5, 4, 3, 2, 1)
# cumulative max of vector
print(cummax(vec))```

Output:

` 6 6 6 6 6 6`

You can see that the cumulative maximum contains only 6 as all its values. This is because the first element itself is the maximum value in the entire vector and thus we get the first element, 6 as the cumulative maximum for all the values.

### Cumulative max of a vector with `NA` values

What would happen if you apply the `cummax()` function to a vector containing some `NA` values?

Let’s find out.

For this, we will create a vector with some `NA` values and then apply the `cummax()` function.

```# create a vector
vec <- c(1, 3, 2, NA, 4, NA, 5)
# cumulative max of vector
print(cummax(vec))```

Output:

`  1  3  3 NA NA NA NA`

You can see that we get the cumulative max till we encounter the first `NA` in our vector. From this point onwards, the resulting cumulative max for all the values is `NA`. This happens because performing any arithmetic operation with `NA` results in an `NA` in R.

If you want to compute the cumulative max irrespective of the `NA` values, you can first remove the `NA` values from the vector and then apply the `cummax()` function.

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