Why is Matlab's unifrnd(a,b) so slow? - matlab

Question

I was doing a simple speed comparison between Matlab and Julia (using the tic, toc command) running a Gibbs sampler with rejection sampling. For Matlab I ran two different versions of the code. One was using the built-in unifrnd(a,b) while the other was drawing uniform random numbers in the interval (a,b) by calling the following function:
% Draw a uniform random sample in the interval (a,b)
function f = rand_uniform(a,b)
f = a + rand*(b - a);
end
I used the same function as above in the Julia code.
The results from running the code with 1000000 iterations were the following:
Case 1: Matlab using unifrnd(a,b):
x_bar = 1.0944
y_bar = 1.1426
Elapsed time is 255.201619 seconds.
Case 2: Matlab calling rand_uniform(a,b) (function above):
x_bar =1.0947
y_bar =1.1429
Elapsed time is 38.704601 seconds.
Case 3: Julia calling rand_uniform(a,b) (function above):
x_bar = 1.0951446303536603
y_bar = 1.142634615899686
Elapsed time: 3.563854193 seconds
Clearly using unifrnd(a,b) slowed the Matlab code down a lot but the question is why? The density is taken from one of the examples in Introduction to Applied Bayesian Statistics and Estimation for Social Scientists and if anyone is interested the theoretical mean, mu_x = 1.095 while mu_y = 1.143.
Case 1: The Matlab code using the built-in unifrnd(a,b) is:
clear;
clc;
tic
% == Setting up matrices and preliminaries == %
d = 1000000; % No. of iterations
b = d*0.25; % Burn-in length. We discard 25% of the sample (not used here)
x = zeros(1,d);
x(1) = -1;
y = zeros(1,d);
y(1) = -1;
m = 25; % The constant multiplied on g(x)
count = 0; % Counting no. of iterations
% == The Gibbs sampler using rejection sampling == %
for i = 2:d
% Sample from x|y
z = 0;
while z == 0
u = unifrnd(0,2);
if ((2*u+3*y(i-1)+2) > unifrnd(0,2)*m) % Height is (1/(b-a))*m = 0.5*25 = 12.5
x(i) = u;
z = 1;
end
end
% Sample from y|x
z = 0;
while z == 0
u = unifrnd(0,2);
if ((2*x(i)+3*u+2) > unifrnd(0,2)*m)
y(i) = u;
z = 1;
end
end
%count = count+1 % For counting no. of total draws from m*g(x)
end
x_bar = mean(x)
y_bar = mean(y)
toc
Case 2: The Matlab code calling rand_uniform(a,b) (function above):
clear;
clc;
tic
% == Setting up matrices and preliminaries == %
d = 1000000; % No. of iterations
b = d*0.25; % Burn-in length. We discard 25% of the sample (not used here)
x = zeros(1,d);
x(1) = -1;
y = zeros(1,d);
y(1) = -1;
m = 25; % The constant multiplied on g(x)
count = 0; % Counting no. of iterations
% == The Gibbs sampler using rejection sampling == %
for i = 2:d
% Sample from x|y
z = 0;
while z == 0
u = rand_uniform(0,2);
if ((2*u+3*y(i-1)+2) > rand_uniform(0,2)*m) % Height is (1/(b-a))*m = 0.5*25 = 12.5
x(i) = u;
z = 1;
end
end
% Sample from y|x
z = 0;
while z == 0
u = rand_uniform(0,2);
if ((2*x(i)+3*u+2) > rand_uniform(0,2)*m)
y(i) = u;
z = 1;
end
end
%count = count+1 % For counting no. of total draws from m*g(x)
end
x_bar = mean(x)
y_bar = mean(y)
toc
Case 3: The Julia code calling rand_uniform(a,b) (function above):
# Gibbs sampling with rejection sampling
tic()
# == Return a uniform random sample from the interval (a, b) == #
function rand_uniform(a, b)
a + rand()*(b - a)
end
# == Setup and preliminaries == #
d = 1000000 # No. of iterations
b = d*0.25 # Burn-in length. We discard 25% of the sample (not used here)
x = zeros(d)
x[1] = -1
y = zeros(d)
y[1] = -1
m = 25
# == The Gibbs sampler using rejection sampling == #
for i in 2:d
#Sample from y|x
z = 0
while z==0
u = rand_uniform(0,2)
if ((2*u+3*y[i-1]+2) > rand_uniform(0,2)*m) #Height is (1/(b-a))*m = 0.5*25 = 12.5
x[i] = u
z = 1
end
end
#Sample from x|y
z = 0
while z == 0
u = rand_uniform(0,2)
if ((2*x[i]+3*u+2) > rand_uniform(0,2)*m)
y[i] = u
z = 1
end
end
end
println("x_bar = ", mean(x))
println("y_bar = ", mean(y))
toc()