digamma

auto kyosu::digamma = eve::functor<digamma_t>

inlineconstexpr

Computes the Digamma function i.e. the logarithmic derivative of the \(\Gamma\) function.

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
  template<concepts::cayley_dickson_like Z> constexpr complexify_t<Z> digamma(Z z) noexcept;
}

Parameters

• z : value to process.

Return value

The value of the Digamma function: \(\psi(z) = \frac{\Gamma'(z)}{\Gamma(z)}\) is returned. psi or ψ can be used as an alias.

External references

• Wikipedia: Digamma function

Example

#include <eve/wide.hpp>
#include <iostream>
#include <kyosu/kyosu.hpp>
 
int main()
{
 
  using wide_ft = eve::wide<float, eve::fixed<4>>;
  wide_ft ref1 = {3.0f, 2.0f, 1.0f, 0.5f};
  wide_ft imf1 = {2.0f, -1.0, -5.0, 0.0};
  wide_ft ref2 = {0.0, 1.0, 2.0, 3.0};
  auto zc = kyosu::complex_t<wide_ft>(ref1, imf1);
 
  std::cout << "---- simd" << std::endl
            << "<- zc               = " << zc << std::endl
            << "<- ref2             = " << ref2 << std::endl
            << "-> digamma(zc)      = " << kyosu::digamma(zc) << std::endl
            << "-> digamma(ref2)    = " << kyosu::digamma(ref2) << std::endl;
 
  return 0;
}