variance

eve::variance = functor<variance_t>

inlineconstexpr

Header file

#include <eve/module/core.hpp>

Callable Signatures

namespace eve
{
   // Regular overloads
   constexpr auto variance(eve::floating_value auto ... xs)                                    noexcept; // 1
   constexpr auto variance(kumi::non_empty_product_type auto const& xs)                        noexcept; // 2
 
   // Lanes masking
   constexpr auto variance[conditional_expr auto c](/* any of the above overloads */)          noexcept; // 3
   constexpr auto variance[logical_value auto m](/* any of the above overloads */)             noexcept; // 3
 
   // Semantic options
   constexpr auto variance[raw] (/* any of the above overloads */)                             noexcept; // 4
   constexpr auto variance[widen](/* any of the above overloads */)                            noexcept; // 5
   constexpr auto variance[kahan](/* any of the above overloads */)                            noexcept; // 6
   constexpr auto variance[unbiased](/* any of the above overloads */)                         noexcept; // 7
 
}

Parameters

• xs...: floating value arguments or tuple of floating values.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

The value of the variance of the arguments is returned.

1. the computation of the variance of its arguments.
2. the computation is made on the tuple values.
3. The operation is performed conditionnaly
4. No provision is made to avoid inaccuracies.
5. The variance is computed in the double sized element type (if available).
6. Compensated algorithm for better precision.
7. the normalizing factor N-1 instead of N to get the best unbiased estimate.

See also

`welford_variance` for incremental or parallel variance and average computations.

External references

• Wikipedia Variance

Example

// revision 0
#include <eve/module/core.hpp>
#include <iostream>
#include <iomanip>
 
int main()
{
  eve::wide wf0{0.0, 1.0, 2.0, 3.0, -1.0, -2.0, -3.0, 1.0};
  eve::wide wf1{0.0, -4.0, 1.0, -1.0, 2.0, -2.0, -eve::smallestposval(eve::as(1.0)), eve::smallestposval(eve::as(1.0))};
  eve::wide wi0{0, 1, 2, 3, -1, -2, -3, -4};
  eve::wide wi1{0, -4, 1, -1, 2, -2, 3, -3};
 
  std::cout << "<- wf0                                        = " << wf0 << "\n";
  std::cout << "<- wf1                                        = " << wf1 << "\n";
  std::cout << "<- wi0                                        = " << wi0 << "\n";
  std::cout << "<- wi1                                        = " << wi1 << "\n";
  std::cout << std::setprecision(15);
 
  std::cout << "-> variance(wf0, wf1)                          = " << eve::variance(wf0, wf1) << "\n";
  std::cout << "-> variance(wi0, wi1)                          = " << eve::variance(wi0, wi1) << "\n";
  std::cout << "-> variance[ignore_last(2)](wi0, wi1)          = " << eve::variance[eve::ignore_last(2)](wi0, wi1) << "\n";
  std::cout << "-> variance[wi0 != 0](wi0, wi1)                = " << eve::variance[wi0 != 0](wi0, wi1) << "\n";
  std::cout << "-> variance[raw](wi0, wi1)                     = " << eve::variance[eve::raw](wi0, wi1) << "\n";
  auto eps_2 = eve::eps(eve::as<float>())/2;
  std::cout << "-> variance(1.0f, eps_2, eps_2, eps_2)         = " << eve::variance(1.0f, eps_2, eps_2, eps_2) << "\n";
  std::cout << "-> variance[kahan](1.0f, eps_2, eps_2, eps_2)  = " << eve::variance[eve::kahan](1.0f, eps_2, eps_2, eps_2) << " // float computation\n";
  std::cout << "-> variance[raw](1.0f, eps_2, eps_2, eps_2)    = " << eve::variance[eve::raw](1.0f, eps_2, eps_2, eps_2) << "\n";
  auto deps_2 = double(eps_2);
  std::cout << "-> variance(1.0, deps_2, deps_2, eps_2)        = " << float(eve::variance[eve::kahan](1.0, deps_2, deps_2, deps_2)) << " // double computation converted to float\n";
  auto tup = kumi::tuple{1.0f, eps_2, eps_2, eps_2};
  std::cout << "-> variance[kahan](tup)   = " << eve::variance[eve::kahan](tup) << "\n";
  std::cout <<eve::variance(1.0f, 2.0f, 3.0f, 4.0f) << "\n";
  std::cout <<eve::variance[eve::raw](1.0f, 2.0f, 3.0f, 4.0f) << "\n";
  std::cout <<eve::variance[eve::unbiased](1.0f, 2.0f, 3.0f, 4.0f) << "\n";
  std::cout <<eve::variance[eve::unbiased][eve::raw](1.0f, 2.0f, 3.0f, 4.0f) << "\n";
  std::cout <<eve::variance[eve::unbiased][eve::raw][eve::widen](1.0f, 2.0f, 3.0f, 4.0f) << "\n";
 
}