covariance

auto eve::covariance = functor<covariance_t>

inlineconstexpr

Header file

#include <eve/module/core.hpp>

Callable Signatures

namespace eve
{
   // Regular overloads
   constexpr auto covariance(eve::non_empty_product_type xs, eve::non_empty_product_type ys)            noexcept; // 1
 
   // Semantic options
   constexpr auto covariance[kahan]   (/*any of the above overloads*/)                                    noexcept; // 2
   constexpr auto covariance[unbiased](/*any of the above overloads*/)                                    noexcept; // 3
   constexpr auto covariance[widen]   (/*any of the above overloads*/)                                    noexcept; // 4
}

Parameters

• xs, ys : tuples of floating value arguments.

Return value

1. covariance product. \(\frac1N\sum_s (x_s-\bar{x_s})*(y_s-\bar{y_s})\). where N is the number of x_s (minus 1 if unbiased option is used).
2. Uses a compensated kahan-like algorithm to compute the result more accurately
3. see 1.
4. Uses the upgraded type for computations and result

See also

welford_covariance for incremental or parallel covariance and averages computations.

Example

// revision 0
#include <eve/module/core.hpp>
#include "../../vec3.hpp"
#include <iostream>
#include <iomanip>
#include <tts/tts.hpp>
 
int main()
{
  // scalar covariance vec3<float>
  vec3<float> a(1.0, 2.0, 3.0);
  vec3<float> b(-3.0, -4.0, -6.0);
  std::cout <<  "a " << a << std::endl;
  std::cout <<  "b " << b << std::endl;
  std::cout << "eve::covariance[eve::unbiased](a, b) = "<< eve::covariance[eve::unbiased](a, b) << std::endl;
  std::cout << "eve::covariance[eve::unbiased](a, a) = " << eve::covariance[eve::unbiased](a, a) << std::endl;
  std::cout << "eve::covariance[eve::unbiased](b, a) = " << eve::covariance[eve::unbiased](b, a) << std::endl;
  std::cout << "eve::covariance[eve::unbiased](b, b) = " << eve::covariance[eve::unbiased](b, b) << std::endl;
 
  // simd covariance eve::wide<vec3<float>, eve::fixed<4>>;
  using wv3_t = eve::wide<vec3<float>, eve::fixed<4>>;
  auto wa = wv3_t(a, a, b, b);
  auto wb = wv3_t(b, a, a, b);
  std::cout << "eve::covariance[eve::widen][eve::unbiased](wa, wb) = "<< eve::covariance[eve::widen][eve::unbiased](wa, wb) << std::endl;
  std::cout << "wa " << wa << std::endl;
  std::cout << "wb " << wb << std::endl;
 
 
  kumi::tuple x{4.0f, 3.0f, 2.0f, 1.0f};
  kumi::tuple y{1.0f, 2.0f, 3.0f, 4.0f};
  std::cout << eve::covariance[eve::unbiased](x, x) <<  std::endl;
  std::cout << eve::covariance[eve::unbiased](x, y) <<  std::endl;
  std::cout << eve::covariance[eve::unbiased](y, x) <<  std::endl;
 
}