am

auto eve::am = functor<am_t>

inlineconstexpr

External references

• C++ standard reference: am
• DLMF: Jacobi zeta
• Wolfram MathWorld: Jacobi Zeta Function
• Boost: jacobi_zeta

Example

// revision 1
#include <eve/module/elliptic.hpp>
#include <iostream>
 
eve::wide wf{1.0, 0.0, 0.75, 0.5};
eve::wide wphi{1.0, 1.0e-30, 0.5, 0.0};
 
int main(){
   std::cout << "<- wf   = " << wf << "\n";
   std::cout << "<- wphi = " << wphi << "\n";
 
   std::cout << "-> am(wphi, wf)               = " << eve::am(wphi, wf) << "\n";
   std::cout << "-> am[ignore_last(2)](wphi,wf)= " << eve::am[eve::ignore_last(2)](wphi, wf) << "\n";
   std::cout << "-> am[wf != 1.0](wphi,wf)     = " << eve::am[wf != -1.0f](wphi, wf) << "\n";
   std::cout << "-> am(pio_2[lower], wf)       = " << eve::am(eve::pio_2[eve::lower](eve::as(wphi)), wf) << '\n';
   std::cout << "-> am(pio_2[upper], wf)       = " << eve::am(eve::pio_2[eve::upper](eve::as(wphi)), wf) << '\n';
}

Header file

#include <eve/module/elliptic.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto am(floating_value auto u, floating_value auto x)                 noexcept; // 1
 
   //Semantic modifiers
   constexpr auto am[modular](floating_value auto u, floating_value auto alpha)    noexcept; // 1
   constexpr auto am[eccentric(floating_value auto u, floating_value auto k)       noexcept; // 1
   constexpr auto am[threshold = tol](floating_value auto u, floating_value auto x) noexcept;// 3
 
   // Lanes masking
   constexpr auto am[conditional_expr auto c](/*any of the above overloads*/)       noexcept; // 2
   constexpr auto am[logical_value autolm](/*any of the above overloads*/)          noexcept; // 2
}

Parameters

• u: argument.
• x: amplitude parameter ( \(0\le m\le 1\)).
• alpha: modular angle given in radian (modular option).
• m : elliptic modulus or eccentricity (eccentric option).
• c: Conditional expression masking the operation.
• l: Logical value masking the operation.

Return value

1. return the jacobian amplitude function. Take care that the meaning of the second parameters depends on the option used (see note below).
2. The operation is performed conditionally
3. a threshold can be given controlling the needed accuracy.

Note

• \(\alpha\) is named the modular angle given in radian (modular option).
• \( k = \sin\alpha \) is named the elliptic modulus or eccentricity (eccentric option).
• \( m = k^2 = \sin^2\alpha\) is named the parameter (no option). Each of the above three quantities is completely determined by any of the others (given that they are non-negative). Thus, they can be used interchangeably (give the right option).