triqs::stat::mean_and_err_mpi

#include <triqs/stat.hpp>

Synopsis

template<typename V>

auto mean_and_err_mpi (communicator c, V const & data)

Calculate arithmetic mean and standard error [REF] of data spread over multiple MPI threads. Reduces the answer to all threads.

Template parameters

V Iterable type. Pre-conditions: elements must be: addable to each other, have element-wise multiplication, have complex conjugation defined via conj [REF], be MPI reducable.

Parameters

data Container with data

Returns

std::pair with [mean, standard error]; types are deduced from first element of data

Example

#include <triqs/stat/mean_error.hpp>
#include <mpi/mpi.hpp>

using namespace triqs::stat;

int main() {
  mpi::communicator world;
  int rank = world.rank();
  // Define linear data spread over the different mpi threads:
  // thread 0: {1,2,3,4}; thread 1 {5,6,7,8}, etc.
  std::vector<double> data{4. * rank + 1, 4. * rank + 2, 4. * rank + 3, 4. * rank + 4};

  auto [ave, err] = mean_and_err(data);

  std::cout << "Average: " << ave << std::endl;
  // Output: (1.0 + 4.0 * world.size()) / 2.0
  std::cout << "Standard Error: " << err << std::endl;
  // Output: sqrt((world.size() + 1.) / 12.)
}

Output

Average: 2.5
Standard Error: 0.645497