from_polar

kyosu::from_polar = eve::functor<from_polar_t>

inlineconstexpr

Callable object computing a complex or a general Cayley-Dickson from a polar representation.

This function is the reciprocal of to_polar

Callable Signatures

#include kyosu/quaternion.hpp>`

Callable Signatures

namespace eve
{
 template<eve::floating_ordered_value T0, eve::floating_ordered_value T1>,
  auto from_polar( T0 rho, T1 theta) const noexcept;                   // 1
 template<eve::floating_ordered_value T0, eve::floating_ordered_value T1, kyosu::concepts::cayley_dickson C>,
  auto from_polar( T0 rho, T1 theta, C iz) const noexcept;             // 2
}

Parameters

rho : modulus.

theta: argument.

iz : unitary cayley dickson value.

Return value

1. the complex number rho*exp(i*theta).
2. the cayley_dickson value rho*exp(iz*theta).

Note

the entries constitue a proper polar representation if rho is non-negative and if iz present it must be pure unitary with non-negative jpart. However the formula is used as is.

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
#include <array>
#include <iostream>
 
int main()
{
  using kyosu::from_polar;
  using kyosu::complex_t;
  using kyosu::quaternion_t;
 
 
  auto theta = eve::pio_3(eve::as<double>());
  auto rho   = 3.0;
  auto iz0   = kyosu::sign(kyosu::quaternion(0., 1.));
  auto iz1   = kyosu::sign(kyosu::quaternion(0., 1., 2., 3.));
 
  std::cout << " <- theta = " << theta << std::endl;
  std::cout << " <- rho   = " << rho << std::endl;
  std::cout << " -> " << from_polar(theta, rho) << "\n";
  std::cout << " -> " << from_polar(theta, rho, iz0) << "\n";
  std::cout << " -> " << from_polar(theta, rho, iz1) << "\n";
 
  return 0;
}