In R, a global variable is declared by assigning a value to a variable outside of any function. By assigning a value to a variable in the global environment, it becomes a global variable that can be accessed from anywhere in the program.

The vapply() function in R is a faster alternative to a for loop for repetitive computations. It applies a function to each element of a vector or a list and returns a vector of the desired type and length. It is particularly useful when the result of the function is known in advance.

In R, the mean of a numeric vector is calculated using the mean() function. The mean() function calculates the arithmetic average of the values in the vector.

To use a nested function in R to calculate the mean of a vector and subtract the mean from each element, you can use the following code: subtract_mean <- function(vector) { mean_value <- mean(vector); subtracted <- function(x) { x - mean_value }; subtracted(vector) }. The nested function subtracted is defined within the main function subtract_mean. It captures the mean_value from the outer function's environment and subtracts it from each element of the vector. Finally, the nested function is called with the vector as the argument.

In R, the is.array() function can be used to check if an object is an array. It returns TRUE if the object is an array and FALSE otherwise. This function is useful for verifying the type of an object before applying operations specific to arrays.

R provides a wide array of tools for data handling and storage. This makes it ideal for processing and analyzing data.

A list in R is a data type that can contain elements of different types - like strings, numbers, vectors and another list inside it.

When optimizing code that operates on large arrays, you can use strategies such as vectorization to perform operations on entire arrays at once, leveraging the efficiency of R's internal operations. Additionally, you can utilize parallel processing techniques to distribute the calculations across multiple cores or machines, which can significantly speed up computations. Implementing efficient algorithms specific to the problem domain can also help improve performance. By combining these strategies, you can optimize the code and enhance the performance of complex calculations on large arrays.

To find the index of the maximum value in a vector in R, you would use the which.max() function. The which.max() function returns the index of the first occurrence of the maximum value in the vector.

When handling missing values in a vector while finding the maximum or minimum value in R, you can use the na.rm = TRUE parameter in the max() or min() function. Setting na.rm = TRUE instructs R to ignore missing values and calculate the maximum or minimum based on the available non-missing values. This ensures that missing values do not impact the calculation.

When a matrix is created in R with elements of different data types, R coerces the elements to the most flexible type within the matrix. This means that if the matrix contains elements of different data types, R will automatically convert them to a common type that can accommodate all the values in the matrix.

To add a title to a plot in R, you would use the main parameter. It allows you to provide a descriptive title that summarizes the content or purpose of the plot.