generating random array in c++11

I want to create an MxN array (M particles in N dimensional space) filled with random numbers within an upper and lower boundary. I have a working python code that looks something like this:

# upper_bound/lower_bound are arrays of shape (dim,)
positions = np.random.rand(num_particle,dim)*(upper_bound-lower_bound)+lower_bound

Each row represents a particle, and each column represents a dimension in the problem space. So the upper_bound and lower_bound applies to each column. Now I want to translate the above code to c++, and I have something like this:

#include <iostream>
#include <vector>
#include <random>
#include <algorithm>
#include <ctime>

typedef std::vector<double> vect1d;

std::vector<vect1d> positions;

for (int i=0; i<num_particle; i++){
    std::mt19937_64 generator(static_cast<std::mt19937::result_type>(time(0)));
    std::uniform_real_distribution<double> distribution(0,1);
    vect1d pos(dimension);
    std::generate(pos.begin(),pos.end(),distribution(generator));
    positions[i] = pos;
    }

My problems:

1. It gives error regarding the generator, so I'm not sure if I set it properly. I'm also not sure how to use the std::generator. I'm trying it as I've looked at other similar posts and it seems that it allows me to generate more than one random number at a time, so I don't have to run it MxN times for each element. Is this true and how to correctly use it?

2. In python I can just vectorization and broadcasting to manipulate the numpy array. What's the most 'vectorized' way to do it in c++?

3. The above (incorrect) code only creates random number between 0 and 1, but how to incorporate the lower_bound and upper_bound as in the python version? I understand that I can change the values inside distribution(0,1), but the problem is the limits can be different for each dimension (so each column can have different valid range), so what's the most efficient way to generate random number, taking into account the range for each dimension?

Thanks