lbeta

auto kyosu::lbeta = eve::functor<lbeta_t>

inlineconstexpr

Computes the principal branch of the natural logarithm of the beta function.

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
  //  regular call
  auto lbeta(auto z0,auto z1) noexcept;
  auto log(auto z0,  auto z1, eve::value n) noexcept;
 
  // semantic modifyers
  auto lbeta[real_only](auto z0, auto z1) noexcept;
}

Parameters

• x,y : Values to process.

Return value

• Real typed input z0 and z1 is treated as if complex(z0) and complex(z1) were entered, unless the option real_only is used in which case the result will the same as to an eve::lbeta call
• Real typed entries are treated as complex ones. unless the option real_only is used in which case the parameter must be a floating_value, implying a Nan result if the theoretical result is not real.
• Returns log(beta(x, y)).

Note

lΒ (l followed by upper case greek letter) can be used as an alias in code.

External references

• Wolfram MathWorld: Beta Function

Example

#include <eve/wide.hpp>
#include <iostream>
#include <kyosu/kyosu.hpp>
 
int main()
{
  using kyosu::complex_t;
  using kyosu::lbeta;
  using e_t = float;
  using c_t = kyosu::complex_t<float>;
  using we_t = eve::wide<float, eve::fixed<2>>;
  using wc_t = eve::wide<kyosu::complex_t<float>, eve::fixed<2>>;
 
  std::cout << "Real:        " << "\n";
  e_t e0(1);
  e_t e1(2);
  std::cout << e0 << ", " << e1 << " -> " << lbeta(e0, e1) << "\n";
  std::cout << e0 << ", " << e0 << " -> " << lbeta(e0, e0) << "\n";
  we_t we0(e0);
  we_t we1(e1);
  std::cout << we0 << ", " << we1 << " -> " << lbeta(we0, we1) << "\n";
 
  std::cout << "Complex:     " << "\n";
  c_t c0(1, 5);
  c_t c1(5, 9);
  std::cout << c0 << ", " << c1 << " -> " << lbeta(c0, c1) << "\n";
  std::cout << c0 << ", " << c0 << " -> " << lbeta(c0, c0) << "\n";
  wc_t wc0(c0, c1);
  wc_t wc1(c1, c1);
  std::cout << wc0 << ", " << wc1 << " -> " << lbeta(wc0, wc1) << "\n";
 
  double a = 1.5;
  double b = -2.6;
  auto lbetab = kyosu::lbeta(a, b);
  auto lrbetab = eve::lbeta(a, b);
  auto lrrbetab = kyosu::lbeta[kyosu::real_only](a, b);
  std::cout << "kyosu::lbeta(a, b)                   "<< lbetab << std::endl;
  std::cout << "eve::lbeta(a, b)                     "<< lrbetab << std::endl;
  std::cout << "kyosu::lbeta[kyosu::real_only](a, b) "<< lrrbetab << std::endl;
  return 0;
}