Copying non-sequential columns from an array into another array C++ and removing duplicates based on 1 column

I would use std::transform.

It could look like this:

#include <algorithm> // transform
#include <vector>
#include <iostream>
#include <iterator>  // back_inserter

int main() {
    std::vector<std::vector<double>> orig{
        {1,2,3,4,5,6,7,8},
        {11,12,13,14,15,16,17,18},
    };

    std::vector<std::vector<double>> result;
    result.reserve(orig.size());

    std::transform(orig.begin(), orig.end(), std::back_inserter(result),
        [](auto& iv) -> std::vector<double> {
            return {iv[3], iv[4], iv[5], iv[7]};
        });

    // print the result:
    for(auto& inner : result) {
        for(auto val : inner) std::cout << val << ' ';
        std::cout << '\n';
    }
}

Output:

4 5 6 8 
14 15 16 18 

Note: If any of the inner vector<double>s in orig has fewer elements than 8, the transformation will access that array out of bounds (with undefined behavior as a result) - so, make sure they all have the required amount of elements.

Or using C++20 ranges to create the resulting vector from a transformation view:

#include <iostream>
#include <ranges>  // views::transform
#include <vector>

int main() {
    std::vector<std::vector<double>> orig{
        {1, 2, 3, 4, 5, 6, 7, 8},
        {11, 12, 13, 14, 15, 16, 17, 18},
    };

    auto trans = [](auto&& iv) -> std::vector<double> {
        return {iv[3], iv[4], iv[5], iv[7]};
    };

    auto tview = orig | std::views::transform(trans);
    
    std::vector<std::vector<double>> result(tview.begin(), tview.end());

    // print the result:
    for (auto& inner : result) {
        for (auto val : inner) std::cout << val << ' ';
        std::cout << '\n';
    }
}