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Author: lambdacdm

core.h

@@ -0,0 +1,150 @@
+#ifndef CORE_H
+#define CORE_H
+#include<iostream>
+#include<iomanip>
+#include<cmath>
+#include<functional>
+#include<vector>
+using std::cerr;
+using std::cout;
+using std::function;
+using std::vector;
+
+namespace cor{
+
+//-----常量部分-----
+const double Machine_Epsilon = pow(2, -52);
+
+//-----声明部分-----
+
+//杂例I
+template <class DM>
+double Norm(const vector<DM> &, double);
+template<class DJ> DJ Abs(DJ);
+template <class DJ> DJ Sign(DJ);
+template <class DJ> vector<DJ> Range(DJ, DJ,DJ);
+template <class DJ> vector<DJ> Range(DJ, DJ);
+template <class DJ> vector<DJ> Rand(int);
+template <class DJ> DJ Limit(std::function<DJ(DJ)>, DJ);
+template <class DJ> DJ N(DJ,int);
+inline int Sig(){return rand()%2?1:-1;}//random Sign(+/-)
+
+template <class DD> DD Iteration(std::function<DD(DD)>, DD);
+template <class DD> DD Sqrt(DD);
+template <> double Sqrt(double);
+
+
+//-----定义部分-----
+
+
+//杂例I
+template<class DM> double Norm(const vector<DM> &a, double p)
+{
+    if(p==INFINITY)
+    {
+        double max = 0;
+        for (long long unsigned int i = 0; i < a.size();++i)
+        {
+            if(Abs(a[i])>max)
+                max = Abs(a[i]);
+        }
+        return max;
+    }
+    double s = 0;
+    for (long long unsigned int i = 0; i < a.size();++i)
+    {
+        s += pow(Abs(a[i]), p);
+    }
+    s = pow(s, 1 / p);
+    return s;
+}
+template<class DJ> DJ Abs(DJ a)
+{
+    if(a>0)
+        return a;
+    return -a;
+}
+template<class DJ> DJ Sign(DJ a)
+{
+    if(a>0)
+        return 1;
+    if(a<0)
+        return -1;
+    return 0;
+}
+template <class DJ> vector<DJ> Range(DJ a, DJ b,DJ c)
+{
+    vector<DJ> r;
+    DJ s = a;
+    while(s<=b)
+    {
+        r.emplace_back(s);
+        s = s + DJ(c);
+    }
+    return r;
+}
+template <class DJ> vector<DJ> Range(DJ a, DJ b)
+{
+    return Range(a, b, DJ(1));
+}
+template <class DJ> vector<DJ> Rand(int a)
+{
+    vector<DJ> r(a);
+    for (int i = 0;i<a;++i)
+        r[i]=std::rand()*Sig();
+    return r;
+}
+template <class DJ> DJ Limit(std::function<DJ(DJ)> f, DJ x0)
+{
+    const DJ h = 1e-7;
+    return 0.5 * (f(x0+h)+f(x0-h));
+}
+template <class DJ> DJ N(DJ a,int n)
+{
+    cout << std::setprecision(n) << a << '\n';
+    return a;
+}
+
+template <class DD> DD Iteration(std::function<DD(DD)> phi, DD a)
+{
+    int times = 100;//迭代次数
+    int k = 0;
+    DD pre=a;
+    DD x = phi(a);
+    while (Abs(x-pre)>1e-14 && k < times)
+    {
+        pre = x;
+        x = phi(x);
+        ++k;
+    } 
+    if(k>=times)
+    {
+        cerr<<"警告：未在指定次数内达到预期精度。"<<'\n';
+        cerr << "可能是初值的选择使迭代法不收敛，或者迭代函数的选择使收敛速度很慢。" << '\n';
+    }
+    return x;
+}
+template<class DD> DD Sqrt(DD c)
+{
+    std::function<DD(DD)> phi = [&](DD x) { return (x + c / x) / 2; };
+    return Iteration(phi,c);
+}
+template<> double Sqrt<double>(double c)
+{
+    if(c<0)
+    {
+        cerr << "错误：根号下不能是负数。" << '\n';
+        return NAN;
+    }
+    double pre=0;
+    double x = 0.5*c;
+    while (fabs(pre-x)>1e-14)
+    {
+        pre = x;
+        x = 0.5 * (x + c / x);
+    }
+    return x;
+}
+
+}
+#endif