Array views

Julia, similarly to most scientific languages, has a very convenient syntax for array slicing. Consider the following example that sums each column of a two-dimensional matrix. First, we will define a function that sums the elements of a vector to produce a scalar. We will then use this function inside a loop to sum the columns of a matrix, passing each column one by one to our vector adder as follows:

function sum_vector(x::Array{Float64, 1}) 
   s = zero(eltype(x))
   for i in 1:length(x) 
      s = s + x[i] 
   end 
   return s 
end 
 
function sum_cols_matrix(x::Array{Float64, 2}) 
   num_cols = size(x, 2) 
   s = zeros(num_cols) 
   for i = 1:num_cols 
     s[i] = sum_vector(x[:, i]) 
   end 
   return s 
end 

The x[:, j] syntax denotes all the row elements of the j^th column. In other words, it slices a matrix into its individual columns. Benchmarking this function, we will...