# R – Get Cumulative Minimum in a Vector in R

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

## What is the cumulative minimum?

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

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

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

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

```# cumulative min of vector x
cummin(x)```

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

## Examples

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

### Cumulative min of a vector of numbers

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

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

Output:

` 6 3 3 1 1 1`

We print the resulting vector. You can see that each value in the resulting vector is the minimum 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 min of vector
print(cummin(vec))```

Output:

` 1 1 1 1 1 1`

You can see that the cumulative minimum vector contains only 1 as all its values. This is because the first element itself is the minimum value in the entire vector and thus we get the first element, 1 as the cumulative minimum for all the 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 min of vector
print(cummin(vec))```

Output:

` 6 5 4 3 2 1`

We get the same vector as the cumulative min vector. This is because the values in the original vector are in descending order thus each new value is smaller than all the previous values.

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

What would happen if you apply the `cummin()` 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 `cummin()` function.

```# create a vector
vec <- c(6, 3, 4, NA, 2, NA, 5)
# cumulative min of vector
print(cummin(vec))```

Output:

`  6  3  3 NA NA NA NA`

You can see that we get the cumulative min till we encounter the first `NA` in our vector. From this point onwards, the resulting cumulative min 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 min irrespective of the `NA` values, you can first remove the `NA` values from the vector and then apply the `cummin()` function.

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