Vectorizing loops in MATLAB

In MATLAB one should try to avoid loops. This can be done by vectorizing your code. The idea is that MATLAB is very fast on vector and matrix operations and correspondingly slow with loops. We illustrate this by an example.

EXAMPLE 1

Given a_n=n, and b_n=1000−n for n=1,...,1000. Calculate

1000

∑

n=1

(a_nb_n), and store in the variable ssum.

Solution: It might be tempting to implement the above calculation as

 a = 1:1000; b = 1000 - a; ssum=0; for n=1:1000 %poor style...    ssum = ssum +a(n)*b(n); end 

Recognizing that the sum is the inner product of the vectors a and b, ab^T, we can do better:

 ssum = a*b' %Vectorized, better! 

For more detailed information on vectorization, please take a look at MathWorks' Code Vectorization Guide.