More about matrices

Previously we looked at simple operations with two-dimensional arrays and two-dimensional matrices.

In this section I will also discuss some further topics to cover multi-dimensional arrays, broadcasting and of handling sparse arrays but first I wish to introduce the concept of vectorized and devectorized code.

Vectorized and devectorized code

Consider the following code to add two vectors:

function vecadd1(a,b,c,N)
  for i = 1:N
    c = a + b 
  end
end

function vecadd2(a,b,c,N)
  for i = 1:N, j = 1:length(c)
    c[j] = a[j] + b[j]
  end
end

julia> A = rand(2); B = rand(2); C = zeros(2);
julia> @elapsed vecadd1(A,B,C,100000000)
@elapsed vecadd1(A,B,C,100000000) # => 18.418755286

julia> @elapsed vecadd2(A,B,C,100000000)
@elapsed vecadd2(A,B,C,100000000) # => 0.524002398

Why the difference in timings? The function vecadd1() uses the array plus operation to perform the calculation whereas vecadd2() explicitly loops through the arrays and performs a series...