E.V.E
v2022.09.01

◆ lambda

eve::lambda = {}
inlineconstexpr

Callable object computing The Dirichlet \( \displaystyle \lambda(z) = \sum_0^\infty \frac{1}{(2n+1)^z}\).

This function can be extended to the whole complex plane as \(\lambda(z) = \zeta(z)(1-2^{-x})\) (where \(\zeta\) is the Riemann zeta function). It coincides with the serie where the serie converges. However for z = 1 the result is \(\infty\).

Defined in Header

#include <eve/module/complex.hpp>

Callable Signatures

namespace eve
{
template< like<complex> T >
T lambda(T z) noexcept;
}
constexpr callable_lambda_ lambda
Callable object computing The Dirichlet .
Definition: lambda.hpp:64
Definition: all_of.hpp:22

Parameters

Return value

Returns the Dirichlet sum \( \displaystyle \sum_0^\infty \frac{1}{(2n+1)^z}\)

Example

Real version

#include <eve/module/complex.hpp>
#include <eve/wide.hpp>
#include <iostream>
int main()
{
wide_ft xf = { 3.0f, 2.0f, 1.0f, 0.5f};
std::cout
<< "---- simd" << std::endl
<< "<- xf = " << xf << std::endl
<< "-> lambda(xf) = " << eve::lambda(xf) << std::endl;
return 0;
}
Wrapper for SIMD registers.
Definition: wide.hpp:65

Complex version

#include <eve/module/complex.hpp>
#include <eve/wide.hpp>
#include <iostream>
int main()
{
wide_ft ref1 = { 3.0f, 2.0f, 1.0f, 0.5f};
wide_ft imf1 = { 2.0f , -1.0, -5.0, 0.0};
auto zc = eve::as_complex_t<wide_ft>(ref1, imf1);
std::cout
<< "---- simd" << std::endl
<< "<- zc = " << zc << std::endl
<< "-> lambda(zc) = " << eve::lambda(zc)<< std::endl;
return 0;
}