c++ - 使用用户定义的随机生成器运行 std::normal_distribution

Question

我要生成一组正态分布的伪随机数。据我所知，std 库为此提供了以下代码:

std::random_device rd;
std::mt19937 gen(rd());
std::normal_distribution<> d(mean,std);
...
double number = d(gen);

问题是我想使用 Sobol 的准随机序列而不是 Mersenne Twister 伪随机生成器。所以，我的问题是: 是否可以使用用户定义的随机生成器(在我的例子中使用 Sobol 的准随机序列生成器)来运行 std::normal_distribution？

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更多细节:我有一个名为 RandomGenerators 的类，用于生成 Sobol 的准随机数:

RandomGenerator randgen;
double number = randgen.sobol(0,1);

Answer 1

是的，这是可能的。只需使其符合统一随机数生成器的要求即可(§26.5.1.3 第 2 和第 3 段):

2 A class G satisfies the requirements of a uniform random number generator if the expressions shown in Table 116 are valid and have the indicated semantics, and if G also satisfies all other requirements of this section. In that Table and throughout this section:

a) T is the type named by G’s associatedresult_type`, and

b) g is a value of G.

Table 116 — Uniform random number generator requirements

Expression     | Return type | Pre/post-condition         | Complexity
----------------------------------------------------------------------
G::result_type |    T        | T is an unsigned integer   | compile-time
               |             | type (§3.9.1).             |
----------------------------------------------------------------------
g()            |    T        | Returns a value in the     | amortized constant
               |             | closed interval            |
               |             | [G::min(), G::max()].      |
----------------------------------------------------------------------
G::min()       |    T        | Denotes the least value    | compile-time
               |             | potentially returned by    |
               |             | operator().                |
----------------------------------------------------------------------
G::max()       |    T        | Denotes the greatest value | compile-time
               |             | potentially returned by    |
               |             | operator().                |

3 The following relation shall hold: G::min() < G::max().