I am trying to translate my Matlab code to Julia code, so I can use Julia as my main tool in teaching. I ran into an issue that I could not solve.

Below is my Matlab code:

clear all
m = 0; % mean
sd= 1; %std deviation
charfunc = @(v) exp(1i*m*v-0.5.*(sd^2).*(v.^2));
M=1/(2*pi);
X=3;
a=-100;
b=100;
func2 = @(v) exp(-1i.*v*X).*charfunc(v);
res1 = M*real(quad(func2,a,b))
res2 = normpdf(X,m,sd)

Below is my Julia code:

using QuantEcon, Distributions
m = 0 #mean
sd = 1 #standard deviation
function charfunc(v)
exp(im*m*v-0.5.*(sd^2).*(v.^2))
end
M = 1/(2*pi)
X = 3
a = -100
b = 100
function func2(v)
exp(-im.*v*X).*charfunc(v)
end
nodes, weights = qnwlege(65, a, b)
integral = do_quad(func2, nodes, weights) #integration between a and b
res1 = real(integral)*M
d = Normal(0,1)
res2 = pdf(d, X)

I expect res1 to be equal to res2. In my Julia code, I could not get the correct answer, but I am not sure where the bug is.

Not sure what the qnwlege and do_quad function are, but using the basic quadrature function in base (quadgk, which returns a tuple of the result and the error), I do get similar values. Do you need lower error bounds?

Note also that you don’t need the .* in your integrand. Unlike in Matlab, the integrand is called on scalar arguments—it doesn’t need to be vectorized for performance.

(What will hurt performance in Julia is your use of a global variable in the integrand.)