路由器 东莞网站建设/建站流程主要有哪些
以下帖子解决,问题是因为
http://www.cplusplus.com/reference/random/piecewise_constant_distribution/错过了公式的解释,强烈建议读者考虑页面：
http://en.cppreference.com/w/cpp/numeric/random/piecewise_constant_distribution
我有以下奇怪的现象让我感到困惑！：
我有一个分段常数概率密度
using RandomGenType = std::mt19937_64;
RandomGenType gen(51651651651);
using PREC = long double;
std::array intervals {0.59, 0.7, 0.85, 1, 1.18};
std::array weights {1.36814, 1.99139, 0.29116, 0.039562};
// integral over the pdf to normalize:
PREC normalization =0;
for(unsigned int i=0;i<4;i++){
normalization += weights[i]*(intervals[i+1]-intervals[i]);
}
std::cout << std::setprecision(30) << "Normalization: " << normalization << std::endl;
// normalize all weights (such that the integral gives 1)!
for(auto & w : weights){
w /= normalization;
}
std::piecewise_constant_distribution
distribution (intervals.begin(),intervals.end(),weights.begin());
当我从这个分布中绘制n个随机数(以毫米为单位的球体半径)并计算球体的质量并将它们总结为：
unsigned int n = 1000000;
double density = 2400;
double mass = 0;
for(int i=0;i
auto d = 2* distribution(gen) * 1e-3;
mass += d*d*d/3.0*M_PI_2*density;
}
我得到质量= 4.3283千克(见LIVE here)
在Mathematica中做完全相同的事情,如：
提供4.5287千克的正确值. (见mathematica)
哪个不一样,也有不同的种子,C和Mathematica从不匹配！ ？是数字不准确,我怀疑它是什么……？
问题：C中的采样有什么问题？
简单Mathematica代码：
pdf[r_] = 2*Piecewise[{{0, r < 0.59}, {1.36814, 0.59 <= r <= 0.7},
{1.99139, Inequality[0.7, Less, r, LessEqual, 0.85]},
{0.29116, Inequality[0.85, Less, r, LessEqual, 1]},
{0.039562, Inequality[1, Less, r, LessEqual, 1.18]},
{0, r > 1.18}}];
pdfr[r_] = pdf[r] / Integrate[pdf[r], {r, 0, 3}];(*normalize*)
Plot[pdf[r], {r, 0.4, 1.3}, Filling -> Axis]
PDFr = ProbabilityDistribution[pdfr[r], {r, 0, 1.18}];
(*if you put 1.18=2 then we dont get 4.52??*)
SeedRandom[100, Method -> "MersenneTwister"]
dataR = RandomVariate[PDFr, 1000000, WorkingPrecision -> MachinePrecision];
Fold[#1 + (2*#2*10^-3)^3 Pi/6 2400 &, 0, dataR]
(*Analytical Solution*)
PDFr = ProbabilityDistribution[pdfr[r], {r, 0, 3}];
1000000 Integrate[ 2400 (2 InverseCDF[PDFr, p] 10^-3)^3 Pi/6, {p, 0, 1}]
更新：
我做了一些分析：
>读入Mathematica生成的数字(64位双打)
C – >计算总和,它与Mathematica相同
通过还原计算的质量：4.52528010260687096888432279229
>将从C(64位双倍)生成的数字读入Mathematica – >计算总和,它给出相同的4.32402
>我几乎得出结论,使用std :: piecewise_constant_distribution的采样是不准确的(或者像64bit浮点数那样准确)或者有一个错误……或者我的权重有问题？
>在http://coliru.stacked-crooked.com/a/ca171bf600b5148f中错误地计算密度std :: piecewise_constant_distribution ===>这似乎是一个错误！
CPP的直方图生成值与所需分布相比较：
file = NotebookDirectory[] <> "numbersCpp.bin";
dataCPP = BinaryReadList[file, "Real64"];
Hpdf = HistogramDistribution[dataCPP];
h = DiscretePlot[ PDF[ Hpdf, x], {x, 0.4, 1.2, 0.001},
PlotStyle -> Red];
Show[h, p, PlotRange -> All]