Is there a way to compound functions in C++? - c++

Question

General question :
If there are two objects A and B with respective functions f_A(arg list) and f_B(arg list).
What's the best way to create an object C with a function compounded of f_A(...) and f_B(...) ?
for example : f_C() = f_A() + f_B() or f_C() = f_A(f_B())
Is it possible to overload the "+" operator such that we can create the object C doing something like that ?
auto object_c = object_a + object_b
Here is a sample of my code :
class GaussianKernel : public Kernel {
public:
GaussianKernel(double sigma) : m_sigma(sigma), m_scale(1) {}
double covarianceFunction(
double X,
double Y
)
{
double result;
result = m_scale * exp(-norm(X - Y) / (m_sigma*m_sigma));
return result;
}
GaussianKernel operator+(const GaussianKernel& b) {
/*Here I would like to overload the + operator such that
I can create a kernel from two others kernels,
I mean with a covariance function compound of the previous ones
*/
}
private:
double m_sigma;
double m_scale;
};
Thanks you.

Answer 1

Given two methods f_A and f_B you can get f_C returning the sum of the others by using for example a lambda:
auto f_C = [](/*param*/){ return f_A(/*param*/) + f_B(/*param*/); };
auto sum_result = f_C(param);
To get the compound method it would be this:
auto f_C = [](/*param*/){ return f_B( f_A(/*param*/)); };
auto compound_result = f_C(param);
PS: I know that this is not directly applicable to your example, still trying to find out what exactly you want to do.

Answer 2

I would start with prototype solution like this:
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){
return this->covarianceFunction(X, Y) + b.covarianceFunction(X, Y);
});
}
private:
std::function<double(double, double)> fun_;
};
class GaussianKernel : public Kernel {
public:
GaussianKernel(double sigma) : m_sigma(sigma), m_scale(1) {}
double covarianceFunction(
double X,
double Y
) const
{
double result;
result = m_scale * exp(-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){
return this->covarianceFunction(X, Y) + b.covarianceFunction(X, Y);
});
}
private:
double m_sigma;
double m_scale;
};
No longer lambdas are used, but now uses Your function as You wished.
Later on I would try to remove the std::function as it may have quite big performance impact. Instead I would make the FooKernel a class template, that stores callable by value.

Answer 3

I would suggest another subclass of Kernel:
class CompoundGaussianKernel : public Kernel {
public:
CompoundGaussianKernel(GaussianKernel const& kernel1, GaussianKernel const& kernel2)
: m_kernel1(kernel1), m_kernel2(kernel2)
{}
double covarianceFunction(double X, double Y)
{
return m_kernel1.covarianceFunction(X, Y) + m_kernel2.covarianceFunction(X, Y);
// or any other composition than "+"
}
private:
GaussianKernel m_kernel1;
GaussianKernel m_kernel2;
};
I recommend not to define operator+ inside of a class but as a free function.
CompoundGaussianKernel operator+(GaussianKernel const& kernel1, GaussianKernel const& kernel2)
{
return CompoundGaussianKernel(kernel1, kernel2);
}