我有一些类，可以用来组合协方差函数（也称为核函数，请见 https://stats.stackexchange.com/questions/228552/covariance-functions-or-kernels-what-exactly-are-they），然后根据新的核函数计算协方差，例如：
auto C = GaussianKernel(50,60) + GaussianKernel(100,200);auto result = C.covarianceFunction(30.0,40.0);但问题是我在计算协方差时调用了 std::function，有没有简单的方法来避免它？
请注意，我需要计算一个大的协方差矩阵（大约50K*50K），这意味着性能非常重要。
以下是代码
class Kernel {public: /* Covariance function : return the covariance between two R.V. for the entire kernel's domain definition. */ virtual double covarianceFunction( double X, double Y )const = 0 ; ~Kernel() = default;};class FooKernel : public Kernel {public: FooKernel(std::function<double(double, double)> fun) : fun_(fun) {} double covarianceFunction( double X, double Y ) const { return fun_(X, Y); } template<class T> auto operator+(const T b) const { return FooKernel([b, this](double X, double Y) -> double { return this->covarianceFunction(X, Y) + b.covarianceFunction(X, Y); }); } FooKernel operator=(const FooKernel other) const { return other; }private: std::function<double(double, double)> fun_;};class GaussianKernel : public Kernel {public: GaussianKernel(double sigma, double scale) : m_sigma(sigma), m_scale(scale) {} GaussianKernel(double sigma) : m_sigma(sigma), m_scale(1) {} /* A well known covariance function that enforces smooth deformations Ref : Shape modeling using Gaussian process Morphable Models, Luethi et al. */ double covarianceFunction( double X, double Y ) const { //use diagonal matrix doulbe result; result = m_scale * exp(-std::norm(X - Y) / (m_sigma*m_sigma)); return result; } template<class T> auto operator+(const T b) const { return FooKernel([b, this](double X, double Y) -> double { auto debugBval = b.covarianceFunction(X, Y); auto debugAval = this->covarianceFunction(X, Y); auto test = debugBval + debugAval; return test; }); }private: double m_sigma; double m_scale;};回答：
通过对 FooKernel 使用模板化，你可以避免使用 std::function 的需要。
#include <iostream>#include <complex>#include <functional>class Kernel {public: /* Covariance function : return the covariance between two R.V. for the entire kernel's domain definition. */ virtual double covarianceFunction( double X, double Y )const = 0 ; ~Kernel() = default;};template <typename Func>class FooKernel : public Kernel {public: FooKernel(Func&& fun) : fun_(std::forward<Func>(fun)) {} double covarianceFunction( double X, double Y ) const { return fun_(X, Y); } template<class T> auto operator+(const T b) const { return make_foo_kernel([b, this](double X, double Y) -> double { return this->covarianceFunction(X, Y) + b.covarianceFunction(X, Y); }); } FooKernel operator=(const FooKernel other) const { return other; }private: Func fun_;};template <typename Func>auto make_foo_kernel(Func&& fun){ return FooKernel<Func>(std::forward<Func>(fun));}class GaussianKernel : public Kernel {public: GaussianKernel(double sigma, double scale) : m_sigma(sigma), m_scale(scale) {} GaussianKernel(double sigma) : m_sigma(sigma), m_scale(1) {} /* A well known covariance function that enforces smooth deformations Ref : Shape modeling using Gaussian process Morphable Models, Luethi et al. */ double covarianceFunction( double X, double Y ) const { //use diagonal matrix double result; result = m_scale * exp(-std::norm(X - Y) / (m_sigma*m_sigma)); return result; } template<class T> auto operator+(const T b) const { return make_foo_kernel([b, this](double X, double Y) -> double { auto debugBval = b.covarianceFunction(X, Y); auto debugAval = this->covarianceFunction(X, Y); auto test = debugBval + debugAval; return test; }); }private: double m_sigma; double m_scale;};int main(){ auto C = GaussianKernel(50,60) + GaussianKernel(100,200); auto result = C.covarianceFunction(30.0,40.0); return 0;}