2. Groups of Data - Vectors, Matrices & Lists.Rmd

---
title: "Groups of Data - Vectors, Matrices & Lists"
author: Mark Edward M. Gonzales^[De La Salle University, Manila, Philippines, gonzales.markedward@gmail.com]
output: html_notebook
---

In this notebook, we will learn how to handle groups of data --- or, in R terminology, groups of _objects_. 

R provides several ways for grouping objects: <br>
- **Vector**: Collection of objects with the same data type <br>
- **Matrix**: Table consisting of objects with the same data type <br>
- **List**: Collection of objects with possibly different data types


## Vector
A vector is a collection of objects with the same data type.

To create a vector, use the `c()` function:

```{r}
amino_acids <- c("methionine", "leucine", "alanine", "valine", "glutamine", "threonine")
```

Accessing items in a vector can be done like so:

```{r}
amino_acids[1] # Access the first element
amino_acids[2] # Access the second element
```

We can also combine two vectors into a single vector using the `c()` function:

```{r}
addl_amino_acids <- c("glycine", "cysteine", "serine")
many_amino_acids <- c(amino_acids, addl_amino_acids)
many_amino_acids
```

## Matrix
A matrix is a table consisting of objects with the same data type.

To create a matrix, use the `matrix()` function:

```{r}
amino_acids_matrix <- matrix(c("methionine", "leucine", "alanine", "valine", "glutamine", "threonine"), nrow=3, ncol=2)
amino_acids_matrix
```
We can add rows and columns using `rbind()` and `cbind()`, respectively:

```{r}
amino_acids_matrix <-  rbind(amino_acids_matrix, c("proline", "arginine"))
amino_acids_matrix
```
```{r}
amino_acids_matrix <-  cbind(amino_acids_matrix, c("histidine", "phenylalanine", "tryptophan", "selenocysteine"))
amino_acids_matrix
```

Accessing items in a matrix can be done like so:

```{r}
amino_acids_matrix[1, 2] # Accesses the first row, second column
amino_acids_matrix[4, 3] # Accesses the fourth row, third column
```

We can also check if the items in a matrix satisfies a given condition:
- `any()` checks if at least one of the items satisfies the condition
- `all()` checks if all of the items satisfy the condition

```{r}
numbers <- matrix(c(2, 4, 6, 8, 10, 12, 14, 16, 18), nrow=3, ncol=3)
any(numbers < 6)
any(numbers < 1)
all(numbers < 20)
all(numbers < 5)
```
It is possible to name the rows and columns (also called the _dimensions_) of a matrix using `colnames()` and `rownames()`, respectively.

This can greatly aid in making our matrix more descriptive, especially when we perform some analysis.

```{r}
colnames(numbers) <- c("Treatment 1", "Treatment 2", "Treatment 3")
rownames(numbers) <- c("Patient 1", "Patient 2", "Patient 3")
numbers
```

Finally, we demonstrate some matrix operations:

```{r}
numbers1 <- matrix(c(2, 4, 6, 8, 10, 12, 14, 16, 18), nrow=3, ncol=3)
numbers2 <- matrix(c(12, 14, 16, 18, 20, 22, 24, 26, 28), nrow=3, ncol=3)

numbers1 + numbers2
numbers1 - numbers2
numbers1 * numbers2
numbers1 / numbers2

100 * numbers1 # Scalar multiplication
t(numbers1) # Matrix transpose
```

## List

A list is a collection of objects with possibly different data types.

To create a list, use the `list()` function:

```{r}
assorted_list <- list("proline", "methionine", 1, 2)
assorted_list
```

Accessing list items can be a bit tricky though.

Observe how `assorted_list[1]` does not return the item `proline` per se. It actually returns a list containing `proline`.

```{r}
assorted_list[1]
```

If we want the item `proline` to be returned, we have to use double brackets:

```{r}
assorted_list[[1]]
```

If we want a summary of the list elements, we can use the `summary()` function.

```{r}
summary(assorted_list)
```