kolmmean

eve::kolmmean = functor<kolmmean_t>

inlineconstexpr

Header file

#include <eve/module/math.hpp>

Callable Signatures

namespace eve
{
   // Regular overloads
   constexpr auto kolmmean(floating_value auto ... xs)                               noexcept; // 1
   constexpr auto kolmmean(kumi::non_empty_product_type auto const& tup)             noexcept; // 2
 
   // Semantic options
   constexpr auto kolmmean[kahan](/*any of the above overloads*/)                    noexcept; // 4
}

Parameters

• f, g: two functions that will be used to compute the mean.
• xs: real arguments.
• tup: non empty tuple of arguments.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. The kolmogorov mean of the inputs is returned
2. equivalent to the call on the elements of the tuple.
3. The operation is performed conditionnaly
4. uses kahan like compensated algorithm for better accuracy.

Note

For the result to be a proper kolmogorov mean, f must be mathematically continuous and injective and g be its inverse. and EVE need them to be defined for a floating_value input, and returning the same type. However \( \mathbf{g}(\sum \mathbf{f}(x_s)) \) is returned if computable.

External references

• wikipedia quasi-arithmetic mean

  Example

// revision 1
#include <eve/module/math.hpp>
#include <iostream>
 
int main()
{
  eve::wide pf = {3.0, -1.0, -3.0, 10.0};
  eve::wide qf = {4.0, 1.0, 1.0, 15.0};
  eve::wide rf = {-1.0, 2.0, 3.0, 1.5};
  kumi::tuple wt{pf, qf, rf};
  auto f0 = eve::abs; //l1 mean
  auto rf0 = f0;
  auto f1 = eve::rec[eve::pedantic]; //harmonic
  auto rf1 = f1;
  auto f2 = [](auto x){ return eve::sqr(x); }; // quadratic
  auto rf2 =  [](auto x){ return eve::sqrt(x); };
  std::cout << "<- pf                              = " << pf << "\n";
  std::cout << "<- qf                              = " << qf << "\n";
  std::cout << "<- rf                              = " << rf << "\n";
  std::cout << "<- wt                              = " << wt << "\n";
 
  std::cout << "-> kolmmean(f0, rf0, pf, qf, rf)   = " << eve::kolmmean(f0, rf0, pf, qf, rf) << " //l1 mean\n";
  std::cout << "-> kolmmean(f0, rf0, wt)           = " << eve::kolmmean(f0, rf0, wt) << "\n";
  std::cout << "-> kolmmean(f1, rf1, pf, qf, rf)   = " << eve::kolmmean(f1, rf1, pf, qf, rf) << " //harmonic mean\n";
  std::cout << "-> kolmmean(f1, rf1, wt)           = " << eve::kolmmean(f1, rf1, wt) << "\n";
  std::cout << "-> kolmmean(f2, rf2, pf, qf, rf)   = " << eve::kolmmean(f2, rf2, pf, qf, rf) << " // quadratic mean\n";
  std::cout << "-> kolmmean(f2, rf2, wt)           = " << eve::kolmmean(f2, rf2, wt) << "\n\n";
}