Octave Programming Tutorial/Vectorization
Writing routines in terms of vector operations can be orders of magnitudes more efficient than using built-in interpretted loops because Octave can make use of highly optimized FORTRAN and C numerical linear algebra libraries instead. Even if a routine or function is not written in a vectorized form, it is possible to take advantage of vectorization by using arrayfun or a similar structure.
 vectorizing a regular function with arrayfun
Consider an anonymous function
octave:1> f = @(x) sin(x)*x
Octave output :
f = @(x) sin (x)*x
and assume that we want to calculate this function for every element of a given vector of integers from 1 to 7 :
y = 1 2 3 4 5 6 7
then passing y as an argument for f will give error
octave:3> f(y) error: operator *: nonconformant arguments (op1 is 1x7, op2 is 1x7) error: called from: error: at line -1, column -1
this is because f is not defined for a vector input. But this is not a problem as we can do:
and output is :
ans = 0.84147 1.81859 0.42336 -3.02721 -4.79462 -1.67649 4.59891
This is an order of magnitude faster than calculating f for many y values by using a loop which has a big overhead.