Multidimensional Array in R

In R, arrays can be used to represent multi-dimensional datasets. While matrices in R are limited to two dimensions (rows and columns), arrays can have two or more dimensions. This tutorial will guide you through the creation, indexing, and manipulation of multidimensional arrays in R.

1. Creating a Multidimensional Array:

You can create an array in R using the array() function:

# Create a 3x3x2 array
data <- 1:18  # Data from 1 to 18
array_dims <- c(3, 3, 2)
my_array <- array(data, dim = array_dims)
print(my_array)

Here, my_array is a 3x3 matrix repeated in 2 layers.

2. Indexing a Multidimensional Array:

Indexing an array is similar to indexing a matrix, but you have additional dimensions to consider:

# Accessing an element
element <- my_array[2, 3, 1]  # Fetches the element in the 2nd row, 3rd column, and 1st layer

# Accessing a whole layer
layer1 <- my_array[, , 1]

# Accessing a specific row across layers
row1_across_layers <- my_array[1, , ]

3. Manipulating Multidimensional Arrays:

You can perform operations on arrays just like you would with matrices:

# Create another 3x3x2 array
data2 <- 19:36
array2 <- array(data2, dim = array_dims)

# Sum of two arrays
sum_array <- my_array + array2

# Element-wise multiplication
product_array <- my_array * array2

4. Applying Functions Across Margins:

The apply() function allows you to apply a function (like sum, mean) across the margins of an array:

# Sum across the 1st margin (rows)
row_sums <- apply(my_array, MARGIN = 1, FUN = sum)

# Average across the 2nd margin (columns)
col_means <- apply(my_array, MARGIN = 2, FUN = mean)

5. Combining Arrays:

You can combine multidimensional arrays using functions like abind from the abind package:

install.packages("abind")
library(abind)

# Combining arrays along the third dimension
combined_array <- abind(my_array, array2, along = 3)

Conclusion:

Multidimensional arrays in R are a flexible data structure that allows you to represent and manipulate complex datasets. While they are powerful, they can also become challenging to visualize and conceptualize as the number of dimensions increases. In such cases, alternative data structures or specialized packages may be more appropriate.

Creating multidimensional arrays in R:
- Overview: Introduce the concept of multidimensional arrays in R and how to create them.
- Code:
```
# Creating a 3D array in R
arr <- array(1:27, dim = c(3, 3, 3))
print("3D Array:")
print(arr)
```

Indexing and slicing multidimensional arrays in R:

Overview: Explain how to index and slice multidimensional arrays to access specific elements or subsets.

Code:

# Indexing and slicing a 3D array in R
arr <- array(1:27, dim = c(3, 3, 3))

# Accessing an element
print("Element at (2, 2, 2):")
print(arr[2, 2, 2])

# Slicing along dimensions
print("Slicing along the third dimension:")
print(arr[,, 3])

R apply function on multidimensional arrays:

Overview: Demonstrate how to use the apply() function on multidimensional arrays for applying a function along specific dimensions.

Code:

# Applying a function along a dimension in a 3D array
arr <- array(1:27, dim = c(3, 3, 3))

# Applying sum along the third dimension
summed_array <- apply(arr, 3, sum)

print("Original 3D Array:")
print(arr)
print("Summed along the third dimension:")
print(summed_array)