GNU Octave

Time for action – vectorizing the Monte Carlo integrator

Using the method above, the vectorized version of mcintgr is:

Code Listing 5.8
function I = mcintgrv(fun, a, b, mcloops)				#1
  									#2
  # Find maximum value of f						#3
  x = linspace(a,b);							#4
  f = feval(fun,x);							#5
  maxf = max(f);							#6
  									#7
  # Generating random arrays						#8
  r1 = rand(mcloops,1);							#9
  r2 = rand(mcloops,1);							#10
  									#11
  # Get random x and y values						#12
  l = b - a;								#13
  x = a + l.*r1;							#14
  y = maxf.*r2;								#15
  fx = feval(fun, x);							#16
  									#17
  # Counts the number of points that lie under the graph		#18
  counter = length(find(y<fx));					#19
  									#20
  # The integral							#21
  I = counter/mcloops*maxf*l;						#22
									#23
endfunction								#24

What just happened?

The vectorized function is called with the exact same inputs and outputs as mcintgr. The code ...