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[英]`numpy.empty()` and `numpy.random.rand()` same or different
[英]Same random numbers in C++ as computed by Python3 numpy.random.rand
我想在 C++ 中复制一些已经在 Python3 中实现的代码的测试,这些代码依赖于numpy.random.rand
和randn
值以及特定的种子(例如, seed = 1
)。
我知道 Python 的随机实现是基于 Mersenne twister 的。 C++ 标准库也在std::mersenne_twister_engine
中提供了这个。
C++ 版本返回一个无符号整数,而 Python rand 是一个浮点值。
有没有办法在 C++ 中获得与在 Python 中生成的值相同的值,并确保它们相同? randn
生成的数组也是如此?
对于 integer 值,您可以这样做:
import numpy as np
np.random.seed(12345)
print(np.random.randint(256**4, dtype='<u4', size=1)[0])
#include <iostream>
#include <random>
int main()
{
std::mt19937 e2(12345);
std::cout << e2() << std::endl;
}
两个片段的结果都是 3992670690
通过查看rand
的源代码,您可以通过这种方式在 C++ 代码中实现它:
import numpy as np
np.random.seed(12345)
print(np.random.rand())
#include <iostream>
#include <iomanip>
#include <random>
int main()
{
std::mt19937 e2(12345);
int a = e2() >> 5;
int b = e2() >> 6;
double value = (a * 67108864.0 + b) / 9007199254740992.0;
std::cout << std::fixed << std::setprecision(16) << value << std::endl;
}
两个随机值都是 0.9296160928171479
使用std::generate_canonical
会很方便,但它使用另一种方法将 Mersenne twister 的 output 转换为双倍。 它们不同的原因可能是generate_canonical
比 NumPy 中使用的随机生成器更优化,因为它避免了昂贵的浮点运算,尤其是乘法和除法,如源代码所示。 然而,它似乎依赖于实现,而 NumPy 在所有平台上产生相同的结果。
double value = std::generate_canonical<double, std::numeric_limits<double>::digits>(e2);
这不起作用并产生结果 0.8901547132827379,这与 Python 代码的 output 不同。
为了完整性和避免重新发明轮子,这里是 C++ 中 numpy.rand 和 numpy.randn 的实现
header 文件:
#ifndef RANDOMNUMGEN_NUMPYCOMPATIBLE_H
#define RANDOMNUMGEN_NUMPYCOMPATIBLE_H
#include "RandomNumGenerator.h"
//Uniform distribution - numpy.rand
class RandomNumGen_NumpyCompatible {
public:
RandomNumGen_NumpyCompatible();
RandomNumGen_NumpyCompatible(std::uint_fast32_t newSeed);
std::uint_fast32_t min() const { return m_mersenneEngine.min(); }
std::uint_fast32_t max() const { return m_mersenneEngine.max(); }
void seed(std::uint_fast32_t seed);
void discard(unsigned long long); // NOTE!! Advances and discards twice as many values as passed in to keep tracking with Numpy order
uint_fast32_t operator()(); //Simply returns the next Mersenne value from the engine
double getDouble(); //Calculates the next uniformly random double as numpy.rand does
std::string getGeneratorType() const { return "RandomNumGen_NumpyCompatible"; }
private:
std::mt19937 m_mersenneEngine;
};
///////////////////
//Gaussian distribution - numpy.randn
class GaussianRandomNumGen_NumpyCompatible {
public:
GaussianRandomNumGen_NumpyCompatible();
GaussianRandomNumGen_NumpyCompatible(std::uint_fast32_t newSeed);
std::uint_fast32_t min() const { return m_mersenneEngine.min(); }
std::uint_fast32_t max() const { return m_mersenneEngine.max(); }
void seed(std::uint_fast32_t seed);
void discard(unsigned long long); // NOTE!! Advances and discards twice as many values as passed in to keep tracking with Numpy order
uint_fast32_t operator()(); //Simply returns the next Mersenne value from the engine
double getDouble(); //Calculates the next normally (Gaussian) distrubuted random double as numpy.randn does
std::string getGeneratorType() const { return "GaussianRandomNumGen_NumpyCompatible"; }
private:
bool m_haveNextVal;
double m_nextVal;
std::mt19937 m_mersenneEngine;
};
#endif
和实施:
#include "RandomNumGen_NumpyCompatible.h"
RandomNumGen_NumpyCompatible::RandomNumGen_NumpyCompatible()
{
}
RandomNumGen_NumpyCompatible::RandomNumGen_NumpyCompatible(std::uint_fast32_t seed)
: m_mersenneEngine(seed)
{
}
void RandomNumGen_NumpyCompatible::seed(std::uint_fast32_t newSeed)
{
m_mersenneEngine.seed(newSeed);
}
void RandomNumGen_NumpyCompatible::discard(unsigned long long z)
{
//Advances and discards TWICE as many values to keep with Numpy order
m_mersenneEngine.discard(2*z);
}
std::uint_fast32_t RandomNumGen_NumpyCompatible::operator()()
{
return m_mersenneEngine();
}
double RandomNumGen_NumpyCompatible::getDouble()
{
int a = m_mersenneEngine() >> 5;
int b = m_mersenneEngine() >> 6;
return (a * 67108864.0 + b) / 9007199254740992.0;
}
///////////////////
GaussianRandomNumGen_NumpyCompatible::GaussianRandomNumGen_NumpyCompatible()
: m_haveNextVal(false)
{
}
GaussianRandomNumGen_NumpyCompatible::GaussianRandomNumGen_NumpyCompatible(std::uint_fast32_t seed)
: m_haveNextVal(false), m_mersenneEngine(seed)
{
}
void GaussianRandomNumGen_NumpyCompatible::seed(std::uint_fast32_t newSeed)
{
m_mersenneEngine.seed(newSeed);
}
void GaussianRandomNumGen_NumpyCompatible::discard(unsigned long long z)
{
//Burn some CPU cyles here
for (unsigned i = 0; i < z; ++i)
getDouble();
}
std::uint_fast32_t GaussianRandomNumGen_NumpyCompatible::operator()()
{
return m_mersenneEngine();
}
double GaussianRandomNumGen_NumpyCompatible::getDouble()
{
if (m_haveNextVal) {
m_haveNextVal = false;
return m_nextVal;
}
double f, x1, x2, r2;
do {
int a1 = m_mersenneEngine() >> 5;
int b1 = m_mersenneEngine() >> 6;
int a2 = m_mersenneEngine() >> 5;
int b2 = m_mersenneEngine() >> 6;
x1 = 2.0 * ((a1 * 67108864.0 + b1) / 9007199254740992.0) - 1.0;
x2 = 2.0 * ((a2 * 67108864.0 + b2) / 9007199254740992.0) - 1.0;
r2 = x1 * x1 + x2 * x2;
} while (r2 >= 1.0 || r2 == 0.0);
/* Box-Muller transform */
f = sqrt(-2.0 * log(r2) / r2);
m_haveNextVal = true;
m_nextVal = f * x1;
return f * x2;
}
经过一些测试后,当 C++ 无符号整数除以无unsigned int
整数的最大值时,这些值似乎在公差范围内(参见下面的@fdermishin 评论),如下所示:
#include <limits>
...
std::mt19937 generator1(seed); // mt19937 is a standard mersenne_twister_engine
unsigned val1 = generator1();
std::cout << "Gen 1 random value: " << val1 << std::endl;
std::cout << "Normalized Gen 1: " << static_cast<double>(val1) / std::numeric_limits<std::uint32_t>::max() << std::endl;
但是,Python 的版本似乎跳过了所有其他值。 给定以下两个程序:
#!/usr/bin/env python3
import numpy as np
def main():
np.random.seed(1)
for i in range(0, 10):
print(np.random.rand())
###########
# Call main and exit success
if __name__ == "__main__":
main()
sys.exit()
和
#include <cstdlib>
#include <iostream>
#include <random>
#include <limits>
int main()
{
unsigned seed = 1;
std::mt19937 generator1(seed); // mt19937 is a standard mersenne_twister_engine
for (unsigned i = 0; i < 10; ++i) {
unsigned val1 = generator1();
std::cout << "Normalized, #" << i << ": " << (static_cast<double>(val1) / std::numeric_limits<std::uint32_t>::max()) << std::endl;
}
return EXIT_SUCCESS;
}
Python 程序打印:
0.417022004702574
0.7203244934421581
0.00011437481734488664
0.30233257263183977
0.14675589081711304
0.0923385947687978
0.1862602113776709
0.34556072704304774
0.39676747423066994
0.538816734003357
而 C++ 程序打印:
Normalized, #0: 0.417022
Normalized, #1: 0.997185
Normalized, #2: 0.720324
Normalized, #3: 0.932557
Normalized, #4: 0.000114381
Normalized, #5: 0.128124
Normalized, #6: 0.302333
Normalized, #7: 0.999041
Normalized, #8: 0.146756
Normalized, #9: 0.236089
我可以轻松跳过 C++ 版本中的所有其他值,它应该给我与 Python 版本匹配的数字(在公差范围内)。 但是为什么 Python 的实现似乎会跳过所有其他值,或者 C++ 版本中的这些额外值来自哪里?
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