Transposing a Matrix in Ruby: Using the Zip Method

Have you ever needed to flip the rows and columns of a matrix in your Ruby code? This process, known as transposing a matrix, can be useful in a variety of situations. In this post, we'll learn how to transpose a matrix safely in Ruby using the zip method.

Asking GPT-3 about the Zip Method

As I was working on some Ruby challenges on Exercism.io, I had the idea to ask GPT-3 about the #zip method. Instead of just Googling it or looking at the documentation, I thought it would be more fun to ask GPT-3. It explained to me that the #zip method combines the elements of two or more arrays into a single array of pairs. For example,

a = [1, 2, 3]
b = ['a', 'b']
c = a.zip(b)
# c is now [[1, 'a'], [2, 'b']]

I asked "What is an interesting use of the #zip method"?. It told me that it was possible to
transpose a matrix using the zip method. The proposed solution was:

matrix.zip.map(&:itself)

It was definitely wrong. So, I decided to come up with my solution to transpose a matrix using zip. Here is what I came up:

matrix = [[1,2],[3,4]]
matrix[0].zip(*matrix[1..]) 
# [[1,3],[2,4]]

But what happens when we try to transpose a matrix with different row sizes?

[[1,2],[3,4,5]].transpose

# transpose': element size differs (3 should be 2) (IndexError)

Safely Transposing a Matrix: The Bass Approach

How do we transpose a matrix safely in Ruby? After some googling, I came across an article by Matthew Bass titled "How to Safely Transpose Ruby Arrays" (http://www.matthewbass.com/2009/05/02/how-to-safely-transpose-ruby-arrays/). In this article, Bass outlines a method for safely transposing a matrix as follows:

def safe_transpose
  result = []
  max_size = self.max { |a,b| a.size <=> b.size }.size
  max_size.times do |i|
    result[i] = Array.new(self.first.size)
    self.each_with_index { |r,j| result[i][j] = r[i] }
  end
  result
end

This method works by first finding the size of the largest row in the matrix. It then iterates over each column in the matrix, creating a new row in the result for each iteration. Finally, it populates each element in the new row by extracting the element at the corresponding position in each row of the original matrix.

Safely Transposing a Matrix: The Zip Method Approach

Inspired by GPT-3's suggestion, I decided to try implementing a safe transpose using the zip method. Here's the result:

def transpose(matrix)
  matrix[0] += [nil] * (matrix.max.size - matrix[0].size)
  matrix[0].zip(*matrix[1..])
end

This method works by first padding the first row of the matrix with nil values until it is as long as the longest row in the matrix. This ensures that all rows have the same number of elements, which is necessary for the zip method to work correctly. Next, it calls the zip method on the first row of the matrix, followed by the rest of the rows (using the splat operator *).

Benchmarking the Bass Approach vs. the Zip Method Approach

Now, let's see how these two methods compare in terms of performance. Here is a simple benchmark that generates a random matrix with 1000 rows and 1000 columns, and measures the time it takes to transpose the matrix using both the blog method and the zip method approach:

require 'benchmark'

# Generate a random matrix with 1000 rows and 1000 columns
matrix = Array.new(1000) { Array.new(1000) { rand(100) } }

# Benchmark the two transpose methods
Benchmark.bm do |x|
  x.report("safe_transpose:") { safe_transpose(matrix) }
  x.report("transpose:") { transpose(matrix) }
end

Here is an example of the output you might see when running this benchmark:

              user     system      total        real
safe_transpose:  0.440000   0.000000   0.440000 (  0.443733)
      transpose:  0.050000   0.000000   0.050000 ( 

Comparison of Approaches

So which approach is better: the blog's method or the zip method approach? Both have their pros and cons.

The first method is relatively simple and easy to understand, but it can be somewhat slow for large matrices due to its nested loops. On the other hand, the zip method approach is faster, but it requires padding the rows of the matrix with nil values, which may not be desirable in all cases.

Conclusion

In this post, we learned how to safely transpose a matrix in Ruby using two approaches. We also compared and contrasted them, considering their pros and cons.

I hope this post has helped you understand how to transpose a matrix in Ruby, and that you feel more confident using either the traditional method or the zip method approach in your own projects. Whether you're a beginner or an experienced programmer, transposing matrices is a useful skill to have in your toolkit.

Thanks for reading!