Motivation: a little tour of CLEF

As usual, the best is to start with a few examples, to show the library in action.

#include <triqs/clef.hpp>
#include <triqs/arrays.hpp>
#include <iostream>
#include <algorithm>
int main() {
  // Declaring some placeholders (i.e. dummy variables).
  triqs::clef::placeholder<0> i_;
  triqs::clef::placeholder<1> j_;

  // Declaring a 3x3 matrix
  triqs::arrays::matrix<double> A(3, 3);

  // Automatically filling the matrix
  // -> forget about the bounds, it is automatic
  // -> forget about the best order to order the for loops for performance, it is also automatic
  A(i_, j_) << i_ + 2 * j_;

  // Cheking the result
  std::cout << A << std::endl;

  // It also works for std container: we just have to add a call clef::make_expr function
  std::vector<double> V(10);
  double pi = std::acos(-1);

  // Automatically filling the vector with the evaluation of the expression in i_
  triqs::clef::make_expr(V)[i_] << cos(2 * pi / 5.0 * i_);

  // -> by the way, the constant calculation is precomputed
  // (expressions are partially evaluated as soon as possible)
  // illustration :
  // the time_consuming_function will be called only once in the loop, while cos is called 10 times
  auto time_consuming_function = [](double x) {
    std::cout << "call time_consuming_function" << std::endl;
    return 2 * x;
  };
  triqs::clef::make_expr(V)[i_] << cos(time_consuming_function(10) * i_);

  // If you insist using on more complex containers...
  std::vector<std::vector<double>> W(3, std::vector<double>(5));
  triqs::clef::make_expr(W)[i_][j_] << i_ + cos(time_consuming_function(10) * j_ + i_);

  // You can also put a CLEF expression in a std::function
  // a function i -> 2*i +1
  std::function<int(int)> f = i_ >> 2 * i_ + 1;
  // a function (i,j)  -> 2*i +j
  std::function<double(int, int)> g = var(i_, j_) >> 2 * i_ + j_;
  // checking ...
  std::cout << "f(10) =" << f(10) << "  g(1,2) =" << g(1, 2) << std::endl;

  // You can also use a Curry form : h is a function i-> j -> 2*i+ j
  auto h = i_ >> (j_ >> 2 * i_ + j_);
  std::cout << "h(1)(2) = " << h(1)(2) << std::endl;

  // You an also use this to quickly write some lambda, as an alternative syntax to the C++ lambda
  // with e.g. STL algorithms (with the advantage that the function is polymorphic!).
  std::vector<int> v = {0, -1, 2, -3, 4, 5, -6};
  // replace all negative elements (i.e. those for which i -> (i<0) return true), by 0
  std::replace_if(begin(v), end(v), i_ >> (i_ < 0), 0);
  // for non believer, it really worked ...
  for (auto const &x : v) std::cout << x << " ";
  std::cout << std::endl;
}