Apply array function such as fft to nested array

When working with nested arrays in Julia, it can sometimes be challenging to apply array functions to them. One common example is applying the Fast Fourier Transform (FFT) to a nested array. In this article, we will explore three different ways to solve this problem.

Option 1: Using a Recursive Function

One way to apply array functions to nested arrays is by using a recursive function. We can define a function that checks if an element is an array, and if so, applies the desired array function to it. If the element is not an array, we can simply return it. Here’s an example:

function apply_fft(arr)
    if typeof(arr) == Array
        return fft.(arr)
    else
        return arr
    end
end

We can then use this function to apply the FFT to a nested array:

nested_array = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
result = apply_fft(nested_array)

This approach works well for small nested arrays, but it can be inefficient for large arrays due to the recursive nature of the function.

Option 2: Using a Nested Loop

Another way to apply array functions to nested arrays is by using a nested loop. We can iterate over each element of the nested array and apply the desired array function to it. Here’s an example:

nested_array = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
result = copy(nested_array)

for i in 1:length(nested_array)
    for j in 1:length(nested_array[i])
        result[i][j] = fft(nested_array[i][j])
    end
end

This approach is more efficient than the recursive function since it avoids the overhead of function calls. However, it can be cumbersome to write and maintain, especially for deeply nested arrays.

Option 3: Using the `map` Function

The third option is to use the `map` function in Julia. The `map` function applies a given function to each element of an array and returns a new array with the results. We can use this function to apply the FFT to each element of the nested array. Here’s an example:

nested_array = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
result = map(x -> fft(x), nested_array)

This approach is concise and efficient, as it leverages the built-in `map` function in Julia. It also allows for easy customization by using anonymous functions.

After considering the three options, the best approach for applying array functions to nested arrays in Julia is using the `map` function. It provides a concise and efficient solution, while also allowing for customization. However, the choice ultimately depends on the specific requirements and constraints of your project.