neville

auto eve::neville = functor<neville_t>

inlineconstexpr

Header file

#include <eve/module/core.hpp>

Callable Signatures

namespace eve
{
   // Regular overloads
   constexpr auto neville(auto x, auto const& xs..., auto const& ys...)                                                    noexcept; // 1
   constexpr auto neville(auto x, eve::non_empty_product_type auto const& xx,  eve::non_empty_product_type auto const& yy) noexcept; // 2
}

Parameters

• xs ..., ys ...: real values arguments
• xx, yy : kumi::tuple of arguments

Return value

• 1. Return the value at x of the polynomial \(p\) of degree n, satisfying \(p(x_i) = y_i\) for \(i = 0..n\), where n+1 is the common number of xs, ys.
• 2. Same as 1., using the tuple elements.

External references

• Wikipedia neville's algorithm

  Example

// revision 1 TODO
#include <eve/module/math.hpp>
#include <iostream>
#include <iomanip>
 
int main()
{
  {
    kumi::tuple xd{1.0, 2.0};
    kumi::tuple yd = kumi::map([](auto x){return 2*x+1; }, xd);
    eve::wide<double, eve::fixed<4>> x(0.5, 2.0, -2.5, 5.0);
 
    std::cout << "<- xd                                   = " << xd << '\n';
    std::cout << "<- yd                                   = " << yd  << '\n';
    std::cout << "<- x                                    = " << x  << '\n';
 
    std::cout << "-> neville(x, xd, yd)                   = " << eve::neville(x, 1.0, 2.0, 3.0, 5.0)<< '\n';
    std::cout << "-> neville(x, xd, yd)                   = " << eve::neville(x, kumi::cat(xd, yd)) << '\n';
    std::cout << "-> neville(x, xd, yd)                   = " << eve::neville(x, xd, yd) << '\n';
  }
   {
    kumi::tuple xd{1.0, 2.0, 3.0, 4.0};
    kumi::tuple yd = kumi::map([](auto x){return x*x; }, xd);
    eve::wide<double, eve::fixed<8>> x(0.5, 2.0, -2.5, 5.0,0.5, 2.0, -2.5, 5.0 );
 
    std::cout << "<- xd                                   = " << xd << '\n';
    std::cout << "<- yd                                   = " << yd  << '\n';
    std::cout << "<- x                                    = " << x  << '\n';
 
    std::cout << "-> neville(x, xd, yd)                   = " << eve::neville(x, 1.0, 2.0, 3.0, 4.0, 1.0, 4.0, 9.0, 16.0) << '\n';
    std::cout << "-> neville(x, xd, yd)                   = " << eve::neville(x, kumi::cat(xd, yd)) << '\n';
    std::cout << "-> neville(x, xd, yd)                   = " << eve::neville(x, xd, yd) << '\n';
  }
}