Chapter 32: R Arrays

Part 1: What is an Array?

An array is a multi-dimensional data structure where all elements must be of the same type (like matrices). It’s essentially a generalization of matrices to any number of dimensions.

Key Characteristics of Arrays

1. Multi-dimensional – Can have 1, 2, 3, or more dimensions

2. Homogeneous – All elements must be the same type

3. Rectangular – All dimensions have fixed sizes

4. Indexed – Elements accessed by indices in each dimension

Part 2: Creating Arrays

Using array() Function

The primary way to create arrays is with the array() function:

Let’s break down what this means:

• dim = c(2, 3, 4) means:

  • Dimension 1: 2 rows

  • Dimension 2: 3 columns

  • Dimension 3: 4 layers (or “slices”)

• Total elements: 2 × 3 × 4 = 24

Visualizing the Array

To better understand, let’s look at each layer separately:

Arrays with Named Dimensions

Creating from Vectors

Part 3: Array Properties

Basic Information

Dimension Names

Part 4: Accessing Array Elements

By Index Positions

By Dimension Names

By Logical Conditions

Part 5: Manipulating Arrays

Applying Functions Across Dimensions

Adding and Removing Dimensions

Combining Arrays

Part 6: Practical Examples

Example 1: Weather Data Analysis

Example 2: Image Data (RGB)

Example 3: Stock Portfolio Analysis

Example 4: Scientific Data – 3D Chemical Concentration

Part 7: Higher-Dimensional Arrays

4D Arrays and Beyond

Reshaping Arrays

Part 8: Arrays vs Other Structures

Arrays vs Matrices

Arrays vs Lists

Part 9: Common Operations with Arrays

Marginal Sums and Means

Cumulative Operations

Sorting and Ordering

Part 10: Common Mistakes and How to Avoid Them

Mistake 1: Confusing Dimension Order

Mistake 2: Forgetting that apply Returns Different Structures

Mistake 3: Indexing Out of Bounds

Mistake 4: Not Using drop = FALSE

Mistake 5: Assuming Arrays are Always Numeric

Summary: The Array Philosophy

Arrays are your tool for multi-dimensional homogeneous data. Master these concepts:

Creating arrays:

• array() with dim parameter

• Setting dim attribute on vectors

• Named dimensions with dimnames

Accessing elements:

• [dim1, dim2, dim3, ...] notation

• Dimension names for readability

• Logical indexing

Key functions:

• dim(), length(), dimnames()

• apply() for operations across dimensions

• aperm() for permuting dimensions

• abind() for combining arrays

• drop() for removing singleton dimensions

Best practices:

• Document your dimension order

• Use drop = FALSE to preserve structure

• Check dimensions before indexing

• Understand what apply() returns

• Use meaningful dimension names

When to use arrays:

• Image data (height × width × channels)

• Scientific data (x × y × z × time)

• Multi-dimensional measurements

• Any data with >2 dimensions

Arrays extend the power of matrices to higher dimensions. They’re essential for scientific computing, image processing, and any domain where data naturally lives in more than two dimensions. Master arrays, and you’ll be able to handle complex multi-dimensional data with ease!

Would you like me to elaborate on any specific aspect of arrays or explore more advanced array operations?