manhattan

kyosu::manhattan = eve::functor<manhattan_t>

inlineconstexpr

Computes the sum of the absolute values of all terms of all the parameters.

Header file

#include <kyosu/functions.hpp>

Callable Signatures

namespace kyosu
{
  constexpr auto manhattan(auto z0, auto ...zs) noexcept;
}

Parameters

• z0, ...zs: Value to process.

Return value

The value of the sum of the values (the \(l_1\) norm) of the \(l_1\) norm of its arguments is returned.

Note

This is NOT lpnorm(1, x0, xs...) which is the \(l_1\) norm of \(l_2\) norm of its arguments.

External references

• Wolfram MathWorld: L1 norm

Example

#include <kyosu/kyosu.hpp>
#include <eve/wide.hpp>
#include <iostream>
 
int main()
{
  using kyosu::manhattan;
  using kyosu::complex_t;
  using kyosu::quaternion_t;
  using e_t = float;
  using c_t = kyosu::complex_t<float>;
  using q_t = kyosu::quaternion_t<float>;
  using we_t = eve::wide<float, eve::fixed<2>>;
  using wc_t = eve::wide<kyosu::complex_t<float>, eve::fixed<2>>;
  using wq_t = eve::wide<kyosu::quaternion_t<float>, eve::fixed<2>>;
 
  std::cout << "Real:        "<< "\n";
  e_t e0(1);
  e_t e1(2);
  std::cout << e0 << ", " << e1 << " -> " << manhattan(e0, e1) << "\n";
  we_t we0(e0);
  we_t we1(e1);
  std::cout << we0 << ", " << we1 << " -> " << manhattan(we0, we1) << "\n";
 
  std::cout << "Complex:     "<< "\n";
  c_t c0(5);
  c_t c1(5, 9);
  std::cout << c0 << ", " << c1 << " -> " << manhattan(c0, c1) << "\n";
  wc_t wc0(c0);
  wc_t wc1(c1);
  std::cout << wc0 << ", " << wc1 << " -> " << manhattan(wc0, wc1) << "\n";
 
  std::cout << "Quaternion:  "<< "\n";
  q_t q0(5, 2, 3);
  q_t q1(5, 9, 6, 7);
  std::cout << q0 << ", " << q1 << " -> " << manhattan(q0, q1) << "\n";
  wq_t wq0(q0);
  wq_t wq1(q1);
  std::cout << wq0 << ", " << wq1 << " -> " << manhattan(wq0, wq1) << "\n";
 
  return 0;
}