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Arrays are also objects in R, and R can create one-dimensional or multi-dimensional arrays. An R array is a collection of the same type. The matrix we learned earlier is actually a two-dimensional array. The relationship between vectors, matrices, and arrays can be seen in the following diagram: !(#) R arrays are created using the `array()` function. This function takes a vector as input and can use `dim` to set the array dimensions. The syntax for the `array()` function is as follows: `array(data = NA, dim = length(data), dimnames = NULL)` **Parameter Description:** * **data** - Specifies the data source for the array. It can be a vector, matrix, or list. * **dim** - Specifies the dimensions of the array. It can be an integer vector or a tuple representing dimensions. The default is a one-dimensional array. For example, `dim = c(2, 3, 4)` creates a **2x3x4** three-dimensional array. * **dimnames** - An optional parameter used to specify the names for each dimension of the array. It can be a list containing dimension names. In R, array indexing starts from 1, which differs from the convention in other programming languages. Additionally, R provides a rich set of functions and operators for handling array data, such as indexing, slicing, reshaping, aggregation, etc. In R, you can use (#) or (#) to represent multi-dimensional arrays. **Matrix:** The matrix is the most common form of representing arrays in R. It is a two-dimensional structure with a fixed number of rows and columns. You can use the `matrix()` function to create a matrix, specifying the data elements and dimensions. ## Example # Create a 3x3 matrix my_matrix <-matrix(c(1, 2, 3, 4, 5, 6, 7, 8, 9), nrow=3, ncol=3) print(my_matrix) **List:** A list is a more general form of multi-dimensional array in R. It can contain elements of different types, and each element can be a matrix, vector, or other data structure. ## Example # Create a list containing a matrix and a vector my_list <-list(matrix(c(1, 2, 3, 4), nrow=2), c(5, 6, 7)) print(my_list) ## Example # Create a list containing a matrix and a vector my_list <-list(matrix(c(1, 2, 3, 4), nrow=2), c(5, 6, 7)) print(my_list) Besides matrices and lists, R also provides other data structures to represent multi-dimensional arrays, such as Array and Data Frame. ### Example Here are some examples demonstrating the use of the **`array()`** function: Create a one-dimensional array using a vector: ## Example my_vector <-c(1, 2, 3, 4) my_array <-array(my_vector, dim=c(4)) print(my_array) In the following example, we create a two-dimensional array with 3 rows and 3 columns: ## Example # Create two vectors of different lengths vector1 <-c(5,9,3) vector2 <-c(10,11,12,13,14,15) # Create the array result <-array(c(vector1,vector2),dim=c(3,3,2)) print(result) Executing the above code produces the following output: , , 1 [,1] [,2] [,3] [1,] 5 10 13 [2,] 9 11 14 [3,] 3 12 15 , , 2 [,1] [,2] [,3] [1,] 5 10 13 [2,] 9 11 14 [3,] 3 12 15 Use the `dimnames` parameter to set the names for each dimension: ## Example # Create two vectors of different lengths vector1 <-c(5,9,3) vector2 <-c(10,11,12,13,14,15) column.names<-c("COL1","COL2","COL3") row.names<-c("ROW1","ROW2","ROW3") matrix.names<-c("Matrix1","Matrix2") # Create the array and set the names for each dimension result <-array(c(vector1,vector2),dim=c(3,3,2),dimnames=list(row.names,column.names,matrix.names)) print(result) Executing the above code produces the following output: , , Matrix1 COL1 COL2 COL3 ROW1 5 10 13 ROW2 9 11 14 ROW3 3 12 15 , , Matrix2 COL1 COL2 COL3 ROW1 5 10 13 ROW2 9 11 14 ROW3 3 12 15 ### Accessing Array Elements In R, you can use the indexing operator `` to access elements of a multi-dimensional array. The indexing operator allows you to retrieve specific elements from the array based on specified index positions. To access an array element, you can use the column index and row index of the element, similar to a coordinate format. Access a single element: ## Example my_array <-array(1:12, dim=c(2, 3, 2))# Create a 3D array element <- my_array[1, 2, 1]# Access the element where the first dimension is 1, the second dimension is 2, and the third dimension is 1 print(element) Access multiple elements: ## Example my_array <-array(1:12, dim=c(2, 3, 2))# Create a 3D array elements <- my_array[c(1, 2), c(2, 3), c(1, 2)]# Access multiple elements, with indices 1 and 2 for each dimension print(elements) Access elements of a two-dimensional array: ## Example # Create two vectors of different lengths vector1 <-c(5,9,3) vector2 <-c(10,11,12,13,14,15) column.names<-c("COL1","COL2","COL3") row.names<-c("ROW1","ROW2","ROW3") matrix.names<-c("Matrix1","Matrix2") # Create the array result <-array(c(vector1,vector2),dim=c(3,3,2),dimnames=list(row.names, column.names, matrix.names)) # Display the elements of the third row in the second matrix of the array print(result[3,,2]) # Display the element in the first row and third column of the first matrix of the array print(result[1,3,1]) # Output the second matrix print(result[,,2]) Executing the above code produces the following output: COL1 COL2 COL3 3 12 15 13 COL1 COL2 COL3 ROW1 5 10 13 ROW2 9 11 14 ROW3 3 12 15 Filter using logical conditions: ## Example my_array <-array(1:12, dim=c(2, 3, 2))# Create a 3D array filtered_elements 5]# Select elements greater than 5 print(filtered_elements)# Output: 6 7 8 9 10 11 12 ### Manipulating Array Elements Since an array is composed of matrices across multiple dimensions, we can access array elements by accessing the elements of the matrices. ## Example # Create two vectors of different lengths vector1 <-c(5,9,3) vector2 <-c(10,11,12,13,14,15) # Create the first array array1 <-array(c(vector1,vector2),dim=c(3,3,2)) # Create two vectors of different lengths vector3 <-c(9,1,0) vector4 <-c(6,0,11,3,14,1,2,6,9) array2 <-array(c(vector3,vector4),dim=c(3,3,2)) # Create matrices from the arrays matrix1 <- array1[,,2] matrix2 <- array2[,,2] # Add the matrices result <- matrix1+matrix2 print(result) Executing the above code produces the following output: [,1] [,2] [,3] [1,] 7 19 19 [2,] 15 12 14 [3,] 12 12 26 Additionally, we can use the **`apply()`** function to perform cross-dimensional calculations on array elements. The syntax is as follows: `apply(X, MARGIN, FUN, ...)` Parameter Description: * `X`: The array or matrix to which the function will be applied. * `MARGIN`: Specifies the dimension to which the function will be applied. It can be 1 for rows, 2 for columns, or `c(1, 2)` for both rows and columns simultaneously. * `FUN`: The function to be applied. It can be a built-in function (like `mean`, `sum`, etc.) or a custom function. * `...`: Optional parameters to pass to the function. Below, we use the `apply()` function to calculate the sum of numbers in each row across the two matrices in the array. ## Example # Create two vectors of different lengths vector1 <-c(5,9,3) vector2 <-c(10,11,12,13,14,15) # Create the array new.array<-array(c(vector1,vector2),dim=c(3,3,2)) print(new.array) # Calculate the sum of numbers in the first row of all matrices in the array result <-apply(new.array, c(1), sum) print(result) Executing the above code produces the following output: , , 1 [,1] [,2] [,3] [1,] 5 10 13 [2,] 9 11 14 [3,] 3 12 15 , , 2 [,1] [,2] [,3] [1,] 5 10 13 [2,] 9 11 14 [3,] 3 12 15 56 68 60 Apply a built-in function to the rows or columns of a matrix: ## Example # Create a 3x3 matrix my_matrix <-matrix(1:9, nrow=3) # Apply the sum function to each column col_sums <-apply(my_matrix, 2, sum) print(col_sums) Executing the above code produces the following output: 6 15 24 Apply a custom function to the rows or columns of a matrix: ## Example # Create a 3x3 matrix my_matrix <-matrix(1:9, nrow=3) # Custom function: calculate the mean of each row row_mean <-function(x){ return(mean(x)) } # Apply the row_mean function to each row row_means <-apply(my_matrix, 1, row_mean) print(row_means) Executing the above code produces the following output: 4 5 6 Apply a function to multiple dimensions of an array simultaneously: ## Example # Create a 3D array my_array <-array(1:12, dim=c(2, 3, 2)) # Apply the mean function to the first and third dimensions simultaneously result <-apply(my_array, c(1, 3), mean) print(result) Executing the above code produces the following output: [,1] [,2] [1,] 3 9 [2,] 4 10