Octave Programming Tutorial/Vectorization

Writing routines in terms of vector operations can be orders of magnitudes more efficient than using built-in interpreted 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 :

octave:2> y=1:7

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:

octave:4> arrayfun(f,y)

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.