vectorized.Rmd

# Vectorized Operations

[Watch a video of this chapter](https://youtu.be/YH3qtw7mTyA)

```{r,echo=FALSE}
knitr::opts_chunk$set(comment = NA, prompt = TRUE, collapse = TRUE)
```

Many operations in R are _vectorized_, meaning that operations occur
in parallel in certain R objects. This allows you to write code that
is efficient, concise, and easier to read than in non-vectorized
languages.

The simplest example is when adding two vectors together.

```{r}
x <- 1:4
y <- 6:9 
z <- x + y
z
```

Natural, right? Without vectorization, you'd have to do something like

```{r,prompt=FALSE}
z <- numeric(length(x))
for(i in seq_along(x)) {
      z[i] <- x[i] + y[i]
}
z
```

If you had to do that every time you wanted to add two vectors, your
hands would get very tired from all the typing.

Another operation you can do in a vectorized manner is logical
comparisons. So suppose you wanted to know which elements of a vector
were greater than 2. You could do he following.

```{r}
x
x > 2
```

Here are other vectorized logical operations.

```{r}
x >= 2
x < 3
y == 8
```

Notice that these logical operations return a logical vector of `TRUE`
and `FALSE`.


Of course, subtraction, multiplication and division are also vectorized.

```{r}
x - y
x * y
x / y
```

## Vectorized Matrix Operations

Matrix operations are also vectorized, making for nicly compact
notation. This way, we can do element-by-element operations on
matrices without having to loop over every element.

```{r}
x <- matrix(1:4, 2, 2)
y <- matrix(rep(10, 4), 2, 2)

## element-wise multiplication
x * y       

## element-wise division
x / y       

## true matrix multiplication
x %*% y     
```