I'm writing a small library for quantum mechanics and I want to use expression template to form operator expressions. Especially forming the Hamiltonian with expression template.
I basically followed this source to construct the code and overloading the corresponding operators + * -: https://en.wikipedia.org/wiki/Expression_templates
Forming the expression for the Hamiltonian requires a sum
Vec x = u_1 + u_2 + ... + u_N
where N is a (const) integer and u_i are also of type Vec. Writing this expression in the code works but I would like to be able to write
Vec x = Sum_{i=0}^{N} u_i
How would one do this?
------------ EDIT ------------
After some research and with the help of the comments, I came up with an idea of static for loop... After googling I found an article in http://www.drdobbs.com/loops-metaloops-c/184401835?pgno=8 which is exactly what I needed.
There is no way to write a template or function that magically pattern matches variables from the surrounding scope, so your u_i syntax can not work. You could do something similar with a macro, e.g.:
#define SUM_4(x) x ## 1 + x ## 2 + x ## 3 + x ## 4
Usage:
Vec u_1, u_2, u_3, u_4;
...
Vec x = SUM_4(u_);
You'd need to define additional macros for other numbers of source vectors.
The subscript operator in C++ is modeled by array access, e.g. u[1], u[2], .... If you are willing to maintain an array of Vec, you could write a generic function that iterates over the array. In this case the parameter would be the array. Something like:
template<typename T, int N>
T sum(T (&u)[N])
{
// (or your preferred summation procedure)
T x = u[0];
for (int i=1; i < N; ++i)
x += u[i];
return x;
}
Usage:
Vec u[4];
...
Vec x = sum(u);
Even better use a std::vector or fixed size array template.
P.S. Consider using Eigen.
EDIT: Updated sum() template with array size deduction from http://www.cplusplus.com/articles/D4SGz8AR/