Matlab VS. C++ in matrix calculation - c++

Question

I am using C++ to do some matrix calculations using Armadillo library.
I tried to make it similar to the Matlab version.
But when I run the code.
While Matlab took about 2 - 3 min, C++ took about 20 min.
I searched a bit and realized that some people also asked why C++ is slower than Matlab in matrix calculations.
But I heard that C++ is way faster than Matlab. So I was wondering whether C++ is not as good as Matlab in terms of Matrix calculations in usual.
Below is just part of my entire code.
Is there any way I can speed up C++ matrix calculations?
Should I use a different library?
while (dif >= tol && it <= itmax) {
it = it + 1;
V = Vnew;
Vfuture = beta * (Ptrans(0) * Vnew.slice(0) + Ptrans(1) * Vnew.slice(1) + Ptrans(2) * Vnew.slice(2));
for (int a = 0; a < Na; a++) {
for (int b = 0; b < Nd; b++) {
for (int c = 0; c < Ny; c++) {
Mat<double> YY(Na, Nd);
YY.fill(Y(c));
Mat<double> AA(Na, Nd);
AA.fill(A(a));
Mat<double> DD(Na, Nd);
DD.fill(D(b));
Mat<double> CC = YY + AA - mg_A_v / R - (mg_D_v - (1 - delta) * DD);
Mat<double> Val = 1 / (1 - 1 / sig) * pow(pow(CC, psi) % pow(mg_D_v, 1 - psi), (1 - 1 / sig)) + Vfuture;
double max_val = Val.max();
uword maxindex_val = Val.index_max();
int index_column = maxindex_val / Na; // column
int index_row = maxindex_val - index_column * Na; // row
Vnew(a, b, c) = max_val;
maxposition_a(a, b, c) = index_row;
maxposition_d(a, b, c) = index_column;
}
}
}
// Howard improvement
for (int h = 0; h < H; h++) {
Vhoward = Vnew;
for (int i = 0; i < Na; i++) {
for (int j = 0; j < Nd; j++) {
for (int k = 0; k < Ny; k++) {
temphoward(i, j) = beta * Vhoward(maxposition_a(i, j, k), maxposition_d(i, j, k), 0) * Ptrans(0) + beta * Vhoward(maxposition_a(i, j, k), maxposition_d(i, j, k), 1) * Ptrans(1) + beta * Vhoward(maxposition_a(i, j, k), maxposition_d(i, j, k), 2) * Ptrans(2);
Vnew(i, j, k) = temphoward(i, j) + utility(Y(k) + A(i) - A(maxposition_a(i, j, k)) / R - D(maxposition_d(i, j, k)) + (1 - delta) * D(j), D(maxposition_d(i, j, k)), sig, psi);
}
}
}
}
tempdiff = abs(V - Vnew);
dif = tempdiff.max();
cout << dif << endl;
cout << it << endl;
}
And this is the part from the matlab.
while dif >= tol && it <= itmax
tic;
it = it + 1;
V = Vnew;
vFuture = beta*reshape(V,Na*Nd,Ny)*P;
for i_a = 1:Na %Loop over state variable a
for i_d = 1:Nd %Loop over state variable d
for i_y = 1:Ny %Loop over state variable y
val = reshape(Utility(Y(i_y) + A(i_a) - mg_A_v/R - (mg_D_v - (1-delta)*D(i_d)),mg_D_v),Na*Nd,1) + vFuture;
[Vnew(i_a,i_d,i_y), indpol(i_a,i_d,i_y)] = max(val);
[indpol_ap(i_a,i_d,i_y),indpol_dp(i_a,i_d,i_y)] = ind2sub([Na,Nd],indpol(i_a,i_d,i_y));
end
end
end
% Howard improvement step
for h = 1:H
Vhoward = Vnew;
for i_a = 1:Na %Loop over state variable a
for i_d = 1:Nd %Loop over state variable d
for i_y = 1:Ny %Loop over state variable y
Vnew(i_a,i_d,i_y) = Utility(Y(i_y) + A(i_a) - A(indpol_ap(i_a,i_d,i_y))/R - ...
(D(indpol_dp(i_a,i_d,i_y)) - (1-delta)*D(i_d)),D(indpol_dp(i_a,i_d,i_y))) ...
+ beta*reshape(Vhoward(indpol_ap(i_a,i_d,i_y),indpol_dp(i_a,i_d,i_y),:),1,Ny)*P;
end
end
end
end
dif = max(max(max(abs(V-Vnew))));
disp([it dif toc])
end