我写的代码:
const double PI = 3.141592653589793;
namespace
{
const int N = 8;
const double points[8] = {-0.9602898564975363, -0.7966664774136267, -0.5255324099163290, -0.1834346424956498,
0.1834346424956498, 0.5255324099163290, 0.7966664774136267, 0.9602898564975363};
const double weights[8] = {0.1012285362903706, 0.2223810344533744, 0.3137066458778874, 0.3626837833783621, 0.3626837833783621,
0.3137066458778874, 0.2223810344533744, 0.1012285362903706};
const double error = 1e-10;
template <class TFunction, class TNumber>
class ChangeOfVariables
{
TFunction f;
public:
ChangeOfVariables(TFunction f) : f(f){}
TNumber operator() (TNumber x) { TNumber c=std::cos(x); return f(std::tan(x))/(c*c); }
};
}
class Quadrature
{
public:
Quadrature(void) {};
~Quadrature(void) {};
template <class TFunction, class TNumber>
TNumber integrate(TFunction f, TNumber a, TNumber b)
{
TNumber result = 0.0;
for(int i=0; i<N; i++)
{
result+= weights[i]*f(0.5*((b-a)*points[i]+(a+b)));
}
return 0.5*(b-a)*result;
}
template <class TFunction, class TNumber>
TNumber integrateToInfty(TFunction f, TNumber a)
{
using std::atan;
return integrate<ChangeOfVariables<TFunction,TNumber>, TNumber>(ChangeOfVariables<TFunction,TNumber>(f), atan(a), PI/2);
}
};
这里用到:
double dampendedExp(double x) {return std::exp(-2.0*x);}
int main()
{
Quadrature quadrature;
cout<<"e^(-2x)="<<quadrature.integrateToInfty(dampendedExp, 0)<<endl;
}
但是编译器提示:
Error 1 error C2668: 'atan' : ambiguous call to overloaded function c:\users\ga1009\documents\dev\fouriertransform\fouriertransform\quadrature.h 48
我们的想法是让它适用于不同的数字类型,例如double
和 complex<double>
,其中定义了 atan。我该如何解决?
最佳答案
Visual Studio 将解释 0
作为一个整数,在调用 std::atan
时失败因为它不知道应该将整数转换为哪种浮点类型(float
、double
、long double
):
~\documents\visual studio 2010\projects\so-atan\so-atan\quadrature.h(44): error C2668: 'atan': ambiguous call to overloaded function c:\program files (x86)\microsoft visual studio 10.0\vc\include\math.h(553): can be 'long double atan(long double)' c:\program files (x86)\microsoft visual studio 10.0\vc\include\math.h(505): or "float atan(float)" c:\program files (x86)\microsoft visual studio 10.0\vc\include\math.h(108): or "double atan(double)" ~\documents\visual studio 2010\projects\so-atan\so-atan\main.cpp(12): in [...] "TNumber Quadrature::integrateToInfty(TFunction,TNumber)". with [ TNumber=int, TFunction=double (__cdecl *)(double) ]
You can recreate this behavior yourself very easily:
#include <iostream>
float f(float x){return x;}
double f(double x){return x;}
long double f(long double x){return x;}
int main()
{
std::cout << f(0) << std::endl;
}
这将产生完全相同的错误。要摆脱这种情况,您应该使用特定版本的 std::atan
, std::cos
和 std::tan
通过使用 static_cast<double>
或 static_cast<long double>
在你的正交中,
template <class TFunction, class TNumber>
TNumber integrateToInfty(TFunction f, TNumber a)
{
using std::atan;
return integrate<ChangeOfVariables<TFunction,TNumber>, TNumber>
(ChangeOfVariables<TFunction,TNumber>(f),
atan(static_cast<long double>(a)), PI/2);
/* ^^^^^^^^^^^^^^^^^^^^^^^^^^^ */
}
或者在调用中使用 float 而不是整数(这样更容易):
cout<<"e^(-2x)="<<quadrature.integrateToInfty(dampendedExp, 0.0)<<endl;
// cout<<"e^(-2x)="<<quadrature.integrateToInfty(dampendedExp, static_cast<double>(x))<<endl;
关于c++ - 在 C++ 中使用带有模板参数的标准数学函数,我们在Stack Overflow上找到一个类似的问题: https://stackoverflow.com/questions/10933936/