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Author: lambdacdm

ODE.h

@@ -16,6 +16,8 @@ std::function<DO(DS)> DSolve(std::function<DO(DS, DO)>, const pair<DS, DO> &, st
 template <class DS, class DO>
 std::function<DO(DS)> DSolve(std::function<DO(DS, DO)>, const pair<DS, DO> &);
 
+//-----定义部分-----
+
 //常微分方程
 template<class DS,class DO,class DP> DO Iteration(const DP &phi,const pair<DS,DO> &initial,DS x,int n)
 {

probability.h

@@ -0,0 +1,101 @@
+#ifndef PROBABILITY_H
+#define PROBABILITY_H
+#include "numerical.h"
+using namespace nmr;
+
+namespace prb{
+
+//-----声明部分-----
+
+//随机变量
+class DiscreteRandomVariable
+{
+    public:
+        DiscreteRandomVariable(const Matrix<double>&);
+        friend Matrix<double> Distribution(const DiscreteRandomVariable &);
+    private:
+        Matrix<double> _distribution;
+};
+Matrix<double> Distribution(const DiscreteRandomVariable &);
+double Expectation(Matrix<double> );
+double Expectation(DiscreteRandomVariable X);
+
+//分布
+class NormalDistribution
+{
+    public:
+        NormalDistribution(double, double);
+        friend double Expectation(const NormalDistribution&);
+        friend double StandardDeviation(const NormalDistribution&);
+
+    private:
+        double _mu;
+        double _sigma;
+};
+double Expectation(const NormalDistribution &);
+double StandardDeviation(const NormalDistribution &);
+double PDF(const NormalDistribution &, double );
+double CDF(const NormalDistribution &, double );
+
+//-----定义部分-----
+
+//随机变量
+DiscreteRandomVariable::DiscreteRandomVariable(const Matrix<double> &M)
+{
+    _distribution = M;
+}
+Matrix<double> Distribution(const DiscreteRandomVariable &X)
+{
+    return X._distribution;
+}
+double Expectation(Matrix<double> A)
+{
+    if(RowSize(A)!=2)
+    {
+        cerr << "错误：输入的矩阵不是分布列" << '\n';
+        return 0;
+    }
+    double s = 0;
+    for (int j= 0; j< ColumnSize(A);++j)
+    {
+        s = s + A[0][j] * A[1][j];
+    }
+    return s;
+}
+double Expectation(DiscreteRandomVariable X)
+{
+    return Expectation(Distribution(X));
+}
+
+//分布
+NormalDistribution::NormalDistribution(double mu,double sigma)
+{
+    _mu = mu;
+    _sigma = sigma;
+}
+double Expectation(const NormalDistribution &N)
+{
+    return N._mu;
+}
+double StandardDeviation(const NormalDistribution &N)
+{
+    return N._sigma;
+}
+double PDF(const NormalDistribution &N,double x)
+{
+    const double mu = Expectation(N);
+    const double sigma = StandardDeviation(N);
+    return 1 / (sqrt(2 * Pi<double>)*sigma)*exp(-pow(x-mu,2)/(2*sigma*sigma));
+}
+double CDF(const NormalDistribution &N,double x)
+{
+    double leftend = Expectation(N) - 6 * StandardDeviation(N);
+    if(x<=leftend)
+        return 0;
+    auto p = [&](double t) { return PDF(N, t); };
+    return Integrate<double>(p, leftend, x);
+}
+
+}
+
+#endif