diff --git a/group__complex_gad70670d8278d34dc0f0faf883a48eab8.html b/group__complex_gad70670d8278d34dc0f0faf883a48eab8.html index 3da801dc..7ef555ad 100644 --- a/group__complex_gad70670d8278d34dc0f0faf883a48eab8.html +++ b/group__complex_gad70670d8278d34dc0f0faf883a48eab8.html @@ -164,7 +164,7 @@

Callable Signatures

  • 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>
    diff --git a/group__functions.html b/group__functions.html index 773666d2..556d47ad 100644 --- a/group__functions.html +++ b/group__functions.html @@ -210,6 +210,21 @@ constexpr auto kyosu::average = eve::functor<average_t>  Computes the average of the parameters.
      +constexpr auto kyosu::bessel_h = eve::functor<bessel_h_t> + Computes the spherical or cylindrical Hankel functions, extended to the complex plane and cayley_dickson algebras.
    +  +constexpr auto kyosu::bessel_i = eve::functor<bessel_i_t> + Computes the spherical or cylindrical modified Bessel functions of the second kind, extended to the complex plane and cayley_dickson algebras.
    +  +constexpr auto kyosu::bessel_j = eve::functor<bessel_j_t> + Computes the spherical or cylindrical Bessel functions of the first kind, extended to the complex plane and cayley_dickson algebras.
    +  +constexpr auto kyosu::bessel_k = eve::functor<bessel_k_t> + Computes the spherical or cylindrical modified Bessel functions of the second kind, extended to the complex plane and cayley_dickson algebras.
    +  +constexpr auto kyosu::bessel_y = eve::functor<bessel_y_t> + Computes the spherical or cylindrical Bessel functions of the second kind, extended to the complex plane and cayley_dickson algebras.
    +  constexpr auto kyosu::beta = eve::functor<beta_t>  Computes the beta function: \(\displaystyle \mathbf{B}(x, y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\) for real or complex entries.
      @@ -258,103 +273,6 @@ constexpr auto kyosu::cscpi = eve::functor<cscpi_t>  Computes the cosecant from the argument in \(\pi\) multiples.
      -constexpr auto kyosu::cyl_bessel_h1 = eve::functor<cyl_bessel_h1_t> - Computes the Bessel functions of the third kind (Hankel functions) \(H_{\nu}^{(1)}\).
    -  -constexpr auto kyosu::cyl_bessel_h12 = eve::functor<cyl_bessel_h12_t> - Computes the Hankel functions of the first and second kind,.
    -  -constexpr auto kyosu::cyl_bessel_h12n = eve::functor<cyl_bessel_h12n_t> - Computes the Hankel functions of the first and second kind,.
    -  -constexpr auto kyosu::cyl_bessel_h12r = eve::functor<cyl_bessel_h12r_t> - Computes the Hankel functions of the first and second kind,.
    -  -constexpr auto kyosu::cyl_bessel_h1_0 = eve::functor<cyl_bessel_h1_0_t> - Computes the Bessel function of the third kind, \( H^{(1)}_0(x)\),.
    -  -constexpr auto kyosu::cyl_bessel_h1_1 = eve::functor<cyl_bessel_h1_1_t> - Computes the Bessel function of the third kind, \( H^{(1)}_1(x)\),.
    -  -constexpr auto kyosu::cyl_bessel_h1n = eve::functor<cyl_bessel_h1n_t> - Computes the Bessel/Hankel functions of the third kind, \( H_n^{(1)}(z) = J_n(z)+iY_n(z)\).
    -  -constexpr auto kyosu::cyl_bessel_h2 = eve::functor<cyl_bessel_h2_t> - Computes the Bessel functions of the third kind (Hankel functions) \(H_{\nu}^{(2)}\).
    -  -constexpr auto kyosu::cyl_bessel_h2_0 = eve::functor<cyl_bessel_h2_0_t> - Computes the Bessel function of the third kind, \( H^{(2)}_0(x)\).
    -  -constexpr auto kyosu::cyl_bessel_h2_1 = eve::functor<cyl_bessel_h2_1_t> - Computes the Bessel function of the third kind, \( H^{(2)}_1(x)\),.
    -  -constexpr auto kyosu::cyl_bessel_h2n = eve::functor<cyl_bessel_h2n_t> - Computes the Bessel/Hankel functions of the third kind , \( H_n^{(2)} = J_n(z)-iY_n(z)\).
    -  -constexpr auto kyosu::cyl_bessel_i = eve::functor<cyl_bessel_i_t> - Computes the modified Bessel functions of the first kind,.
    -  -constexpr auto kyosu::cyl_bessel_i0 = eve::functor<cyl_bessel_i0_t> - Computes the modified Bessel function of the first kind \(I_{0}(x)=J_{0}(ix)\) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::cyl_bessel_i1 = eve::functor<cyl_bessel_i1_t> - Computes the modified Bessel function of the first kind, \( I_1(x)= iJ_1(ix) \) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::cyl_bessel_ik = eve::functor<cyl_bessel_ik_t> - Computes the simultaneous Bessel functions of the first and second kind,.
    -  -constexpr auto kyosu::cyl_bessel_ikn = eve::functor<cyl_bessel_ikn_t> - Computes simultaneously the modified Bessel functions of the first and second kind of integer orders,.
    -  -constexpr auto kyosu::cyl_bessel_in = eve::functor<cyl_bessel_in_t> - Computes the modified Bessel functions of the first kind \(I_{n}(x)=i^{-n}J_{n }(ix)\), extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::cyl_bessel_j = eve::functor<cyl_bessel_j_t> - Computes the Bessel functions of the first kind, \( J_{\nu}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+\nu +1)}} - {\left({x \over 2}\right)}^{2p+\nu }\) extended to the complex plane and cayley_dickson values.
    -  -constexpr auto kyosu::cyl_bessel_j0 = eve::functor<cyl_bessel_j0_t> - Computes the Bessel function of the first kind, \( J_0(x)=\frac1{\pi }\int _{0}^{\pi}\cos(x\sin \tau) - \,\mathrm {d} \tau \) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::cyl_bessel_j1 = eve::functor<cyl_bessel_j1_t> - Computes the Bessel function of the first kind, \( J_1\).
    -  -constexpr auto kyosu::cyl_bessel_jn = eve::functor<cyl_bessel_jn_t> - Computes the Bessel functions of the first kind, \( J_{n}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+n +1)}} - {\left({x \over 2}\right)}^{2p+n }\) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::cyl_bessel_jy = eve::functor<cyl_bessel_jy_t> - Computes the simultaneous Bessel functions of the first and second kind,.
    -  -constexpr auto kyosu::cyl_bessel_jyn = eve::functor<cyl_bessel_jyn_t> - Computes the simultaneous Bessel functions of the first and second kind,.
    -  -constexpr auto kyosu::cyl_bessel_k = eve::functor<cyl_bessel_k_t> - Computes the Modified Bessel functions of the second kind.
    -  -constexpr auto kyosu::cyl_bessel_k0 = eve::functor<cyl_bessel_k0_t> - Computes the modified Bessel function of the second kind, \( K_0(x)=\lim_{\alpha\to 0}{\frac {\pi }{2}}{\frac {I_{-\alpha }(x)-I_{\alpha }(x)}{\sin \alpha \pi }}\). extended to the complex plane and cayley_dickson values.
    -  -constexpr auto kyosu::cyl_bessel_k1 = eve::functor<cyl_bessel_k1_t> - Computes the Bessel function of the second kind, \( K_1(x)\lim_{\alpha\to 1}{\frac {\pi }{2}}{\frac {I_{-\alpha }(x)-I_{\alpha }(x)}{\sin \alpha \pi }}\) extended to the complex plane and cayley_dickson values.
    -  -constexpr auto kyosu::cyl_bessel_kn = eve::functor<cyl_bessel_kn_t> - Computes the modified Bessel functions of the second kind, \( Y_n(x)=\lim_{\alpha\to n}{{\frac {J_{\alpha }(x)\cos(\alpha\pi)-J_{-\alpha }(x)}{\sin(\alpha\pi)}}}\), extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::cyl_bessel_y = eve::functor<cyl_bessel_y_t> - Computes the Bessel functions of the first kind, \( J_{\nu}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+\nu +1)}} - {\left({x \over 2}\right)}^{2p+\nu }\) extended to the complex plane and cayley_dickson values.
    -  -constexpr auto kyosu::cyl_bessel_y0 = eve::functor<cyl_bessel_y0_t> - Computes the Bessel function of the second kind, \( Y_0(x)=\lim_{\alpha\to 0}{{\frac {J_{\alpha }(x)\cos(\alpha\pi)-J_{-\alpha }(x)}{\sin(\alpha\pi)}}}\), extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::cyl_bessel_y1 = eve::functor<cyl_bessel_y1_t> - Computes the Bessel function of the second kind, \( Y_1(x)=\lim_{\alpha\to 1}{{\frac {J_{\alpha }(x)\cos(\alpha\pi)-J_{-\alpha }(x)}{\sin(\alpha\pi)}}}\), extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::cyl_bessel_yn = eve::functor<cyl_bessel_yn_t> - Computes the modified Bessel functions of the second kind, \( Y_n(x)=\lim_{\alpha\to n}{{\frac {J_{\alpha }(x)\cos(\alpha\pi)-J_{-\alpha }(x)}{\sin(\alpha\pi)}}}\), extended to the complex plane and cayley_dickson algebras.
    -  constexpr auto kyosu::dec = eve::functor<dec_t>  decrements the argument by 1.
      @@ -685,69 +603,6 @@ constexpr auto kyosu::slerp = eve::functor<slerp_t>  Computes the spherical interpolation between unitary quaternions.
      -constexpr auto kyosu::sph_bessel_h1_0 = eve::functor<sph_bessel_h1_0_t> - Computes the spherical Bessel/hankel functions of the third kind, \( h_0^{(1)}(z) = j_1(z)+iy_1(z)\).
    -  -constexpr auto kyosu::sph_bessel_h1_1 = eve::functor<sph_bessel_h1_1_t> - Computes the spherical Bessel/hankel functions of the third kind, \( h_1^{(1)}(z) = j_1(z)+iy_1(z)\).
    -  -constexpr auto kyosu::sph_bessel_h1n = eve::functor<sph_bessel_h1n_t> - Computes the spherical Bessel/hankel functions of the third kind, \( h_n^{(1)}(z) = j_n(z)+iy_n(z)\).
    -  -constexpr auto kyosu::sph_bessel_h2_0 = eve::functor<sph_bessel_h2_0_t> - Computes the spherical Bessel/hankel functions of the third kind, \( h_0^{(2)}(z) = j_0(z)-iy_0(z)\).
    -  -constexpr auto kyosu::sph_bessel_h2_1 = eve::functor<sph_bessel_h2_1_t> - Computes the spherical Bessel/hankel functions of the third kind, \( h_1^{(2)}(z) = j_1(z)-iy_1(z)\).
    -  -constexpr auto kyosu::sph_bessel_h2n = eve::functor<sph_bessel_h2n_t> - Computes the spherical Bessel/hankel functions of the third kind, \( h_n^{(2)}(z) = j_n(z)-iy_n(z)\).
    -  -constexpr auto kyosu::sph_bessel_i1_0 = eve::functor<sph_bessel_i1_0_t> - Computes the Bessel function, \( i_0^{(1)}(z) = j_0(iz)\) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::sph_bessel_i1_1 = eve::functor<sph_bessel_i1_1_t> - Computes the Bessel function, \( i_1^{(1)}(z) = -i j_1(iz)\) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::sph_bessel_i1n = eve::functor<sph_bessel_i1n_t> - Computes the spherical Bessel functions of the first kind, extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::sph_bessel_i2_0 = eve::functor<sph_bessel_i2_0_t> - Computes the Bessel function, \( i_0^{(2)}(z) = -i y_0(iz)\) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::sph_bessel_i2_1 = eve::functor<sph_bessel_i2_1_t> - Computes the Bessel function, \( i_1^{(2)}(z) = -y_1(iz)\) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::sph_bessel_i2n = eve::functor<sph_bessel_i2n_t> - Computes the spherical Bessel functions of the first kind, extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::sph_bessel_j0 = eve::functor<sph_bessel_j0_t> - Computes the Bessel function of the first kind, \( j_0(z)=\sin z/z \) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::sph_bessel_j1 = eve::functor<sph_bessel_j1_t> - Computes the Spherical Bessel function of the first kind, \( j_1(z)= \sin z/z^2 -\cos z/z\) extended to the complex plane and cayley_dickson values.
    -  -constexpr auto kyosu::sph_bessel_jn = eve::functor<sph_bessel_jn_t> - Computes the spherical Bessel functions of the first kind, extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::sph_bessel_k0 = eve::functor<sph_bessel_k0_t> - Computes the spherical Bessel function of the first kind, \( k_0(z)= \pi e^{-z}/(2z) \) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::sph_bessel_k1 = eve::functor<sph_bessel_k1_t> - Computes the spherical Bessel function of the first kind, \( k_1(z)= (\pi/2) e^{-z}(1/z+1/z^2)\) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::sph_bessel_kn = eve::functor<sph_bessel_kn_t> - Computes the spherical Bessel functions of the first kind, extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::sph_bessel_y0 = eve::functor<sph_bessel_y0_t> - Computes the spherical Bessel function of the first kind, \( y_0(x)=\cos z/z \) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto kyosu::sph_bessel_y1 = eve::functor<sph_bessel_y1_t> - Computes the spherical Bessel function of the first kind, \( y_1(x)= -\coz z/z^2 -\sin z/z\) extended to the complex plane and cayley_dickson values.
    -  -constexpr auto kyosu::sph_bessel_yn = eve::functor<sph_bessel_yn_t> - Computes the spherical Bessel functions of the second kind, extended to the complex plane and cayley_dickson algebras.
    -  constexpr auto kyosu::sqr = eve::functor<sqr_t>  Computes the square value.
      diff --git a/group__functions_gad889d1c4424dc0752a3d939b7a32de05.html b/group__functions_ga0153dc797fee1fd05255e729f21ce789.html similarity index 56% rename from group__functions_gad889d1c4424dc0752a3d939b7a32de05.html rename to group__functions_ga0153dc797fee1fd05255e729f21ce789.html index 7394835b..240ec552 100644 --- a/group__functions_gad889d1c4424dc0752a3d939b7a32de05.html +++ b/group__functions_ga0153dc797fee1fd05255e729f21ce789.html @@ -6,7 +6,7 @@ -kyosu: kyosu::cyl_bessel_h2 +kyosu: kyosu::bessel_k @@ -95,7 +95,7 @@
    @@ -121,8 +121,8 @@
    - -

    ◆ cyl_bessel_h2

    + +

    ◆ bessel_k

    @@ -131,7 +131,7 @@

    - +
    kyosu::cyl_bessel_h2 = eve::functor<cyl_bessel_h2_t>kyosu::bessel_k = eve::functor<bessel_k_t>
    @@ -141,63 +141,75 @@

    -

    Computes the Bessel functions of the third kind (Hankel functions) \(H_{\nu}^{(2)}\).

    +

    Computes the spherical or cylindrical modified Bessel functions of the second kind, extended to the complex plane and cayley_dickson algebras.

    #include <kyosu/functions.hpp>

    Callable Signatures

    namespace kyosu
    {
    -
    template<eve::floating_scalar_value N, eve::floating_ordered_value T,>
    -
    constexpr auto cyl_bessel_h2(N nu, T z) noexcept;
    -
    -
    template<eve::floating_scalar_value N, concepts::kyosu::complex Z>
    -
    constexpr T cyl_bessel_h2(N nu, Z z) noexcept;
    -
    -
    template<eve::floating_scalar_value N, eve::floating_ordered_value T, complexRange R>
    -
    constexpr auto cyl_bessel_h2(N nu, T z, R& h1s) noexcept;
    -
    -
    template<eve::floating_scalar_value N, concepts::kyosu::complex Z, complexRange R>
    -
    constexpr T cyl_bessel_h2(N nu, Z z, R& h1s) noexcept;
    +
    template<eve;scalar_value N, kyosu::concepts::cayley_dickson T> constexpr auto bessel_k(N n, T z) noexcept; //1
    +
    template<eve;scalar_value N, kyosu::concepts::real T> constexpr T bessel_k(N n, T z) noexcept; //1
    +
    template<eve;scalar_value N, kyosu::concepts::complex T, size_t S> constexpr auto bessel_k(N n, T z, std::span<Z, S> cis) noexcept; //2
    +
    template<eve;scalar_value N, kyosu::concepts::real T, size_t S> constexpr T bessel_k(N n, T z, std::span<Z, S> cis) noexcept; //2
    +
    template<eve;scalar_value N, kyosu::concepts::cayley_dickson T> constexpr auto bessel_k[spherical](N n, T z) noexcept; //3
    +
    template<eve;scalar_value N, kyosu::concepts::real T> constexpr T bessel_k[spherical](N n, T z) noexcept; //3
    +
    template<eve;scalar_value N, kyosu::concepts::complex T, size_t S> constexpr auto bessel_k[spherical](N n, T z, std::span<Z, S> sis) noexcept; //4
    +
    template<eve;scalar_value N, kyosu::concepts::real T, size_t S> constexpr T bessel_k[spherical](N n, T z, std::span<Z, S> sis) noexcept; //4
    }
    -
    kyosu::cyl_bessel_h2
    constexpr auto cyl_bessel_h2
    Computes the Bessel functions of the third kind (Hankel functions) .
    Definition: cyl_bessel_h2.hpp:86
    +
    kyosu::bessel_k
    constexpr auto bessel_k
    Computes the spherical or cylindrical modified Bessel functions of the second kind,...
    Definition: bessel_k.hpp:141
    kyosu
    Main KYOSU namespace.
    Definition: cinf.hpp:13

    Parameters

      -
    • nu: scalar floating order of the function.
      • +
    • n: scalar order (integral or floating)
    • z: Value to process.
      • -
    • h1s: range able to contain n = int(abs(nu))+1 complex values (of type complex_t<T> or Z respectively)
      • +
    • sis, cis : std::span of T

    Return value

    -
      -
    • returns \(H^{(2)}_\nu(z)\).
      • +
        +
      1. returns \(K_n\)(z) (cylindrical).
        2. +
      2. Same as 1, but cis is filled by the lesser orders.
        3. +
      3. returns \(k_n\)(z) (spherical).
        4. +
      4. Same as 3, but sis is filled by the lesser orders.
        5. +
      +
      Note
        +
      • Let \( i = \lfloor |n| \rfloor \) and \( j=|n|-i\). If \(n\) is positive the lesser order are \((\pm j, \pm(j+1), \dots, \pm(j+i)) \) with \(+\) sign if \(n\) is positive and \(-\) sign if \(n\) is negative.
        • +
      • The span parameters are filled according the minimum of their allocated size and \(i\).
        • +
      • cylindical option can be used and its result is identical to the regular call (no option).
      +

      External references

      Example

      #include <kyosu/kyosu.hpp>
      #include <eve/wide.hpp>
      #include <iostream>
      +
      #include <iomanip>
      int main()
      {
      -
      std::cout.precision(16);
      +
      std::cout<< std::setprecision(16) << std::endl;
      using w_t = eve::wide<double, eve::fixed<2>>;
      auto z = kyosu::complex(w_t(20.0, 1.5), w_t(0.0, 1.5));
      -
      auto v = 0.0;
      +
      auto v = -(2+1/3.0);
      +
      int nb = int(eve::abs(v)+1);
      std::cout << "z " << z << std::endl;
      -
      for(int n=0; n <= 3; ++n)
      +
      std::vector<decltype(z)> ks(nb);
      +
      kyosu::bessel_k(v, z, std::span(ks));
      +
      auto inc = eve::sign(v);
      +
      auto v0 = eve::frac(v);
      +
      for(int n=0; n < nb; ++n)
      {
      -
      auto h2 = kyosu::cyl_bessel_h2(v, z);
      -
      std::cout << "v " << v << std::endl;
      -
      std::cout << "yl_bessel_h2(v, z) " << h2 << std::endl;
      -
      v = v+0.25;
      +
      std::cout << "ks[" << n << "] = " << ks[n] << std::endl;
      +
      std::cout << "bessel_k[cylindrical](v0, z) = " << kyosu::bessel_k(v0, z) << std::endl;
      +
      v0 += inc;
      }
      return 0;
      }
      +
      kyosu::inc
      constexpr auto inc
      Increments the argument.
      Definition: inc.hpp:64
      kyosu::complex
      constexpr auto complex
      Constructs a kyosu::complex_t instance.
      Definition: to_complex.hpp:75

    diff --git a/group__functions_ga0155afce8a03c6d97c771e0b764cc9a8.html b/group__functions_ga0155afce8a03c6d97c771e0b764cc9a8.html deleted file mode 100644 index 1b78d566..00000000 --- a/group__functions_ga0155afce8a03c6d97c771e0b764cc9a8.html +++ /dev/null @@ -1,195 +0,0 @@ - - - - - - - - -kyosu: kyosu::cyl_bessel_h1_1 - - - - - - - - - - - - - - - - - - - - - - - - - - -
    - -
    - - - - - - - - -
    -
    kyosu v0.1.0 -
    -
    Complex Without Complexes
    -
    - -   - - - - -
    -
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    - - - -
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    - -
    -
    -
    - -
    - -
    -
    - - -
    -
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    -
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    Loading...
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    Searching...
    -
    No Matches
    -
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    - -
    - -

    ◆ cyl_bessel_h1_1

    - -
    -
    - - - - - -
    - - - - -
    kyosu::cyl_bessel_h1_1 = eve::functor<cyl_bessel_h1_1_t>
    -     		-inlineconstexpr
    -
    - -

    Computes the Bessel function of the third kind, \( H^{(1)}_1(x)\),.

    -
    #include <kyosu/functions.hpp>
    -

    Callable Signatures

    -
    namespace kyosu
    -
    {
    -
    template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_h1_1(T z) noexcept;
    -
    template<eve::floating_ordered_value T> constexpr auto cyl_bessel_h1_1(T z) noexcept;
    -
    }
    -
    kyosu::cyl_bessel_h1_1
    constexpr auto cyl_bessel_h1_1
    Computes the Bessel function of the third kind, ,.
    Definition: cyl_bessel_h1_1.hpp:64
    -
    kyosu
    Main KYOSU namespace.
    Definition: cinf.hpp:13
    -

    Parameters

    -
      -
    • z: Value to process.
      • -
    -

    Return value

    -
      -
    • returns \( H^{(1)}_1(x)\).
      • -
    -

    Example

    -
    #include <kyosu/kyosu.hpp>
    -
    #include <eve/wide.hpp>
    -
    #include <iostream>
    -
    -
    int main()
    -
    {
    -
    std::cout.precision(16);
    -
    using w_t = eve::wide<double, eve::fixed<2>>;
    -
    auto z = kyosu::complex(w_t(20.0, 1.5), w_t(0.0, 1.5));
    -
    std::cout << "z " << z << std::endl;
    -
    std::cout << "cyl_bessel_h1_1(z) " << kyosu::cyl_bessel_h1_1(z) << std::endl;
    -
    return 0;
    -
    }
    -
    kyosu::complex
    constexpr auto complex
    Constructs a kyosu::complex_t instance.
    Definition: to_complex.hpp:75
    -
    -
    -
    -
    -
    - - - -
    -
    - - - - - diff --git a/group__functions_ga042a2f799b04de5311c4614c1101d949.html b/group__functions_ga042a2f799b04de5311c4614c1101d949.html index 29911bf2..3545bb0c 100644 --- a/group__functions_ga042a2f799b04de5311c4614c1101d949.html +++ b/group__functions_ga042a2f799b04de5311c4614c1101d949.html @@ -150,7 +150,7 @@

    Header file

    template<eve::floating_ordered_value T> constexpr auto airy(T z) noexcept;
    template<kyosu::concepts::cayley_dickson T> constexpr auto airy(T z) noexcept;
    }
    -
    kyosu::airy
    constexpr auto airy
    Computes simultaneously the airy functions and .
    Definition: airy.hpp:86
    +
    kyosu::airy
    constexpr auto airy
    Computes simultaneously the airy functions and .
    Definition: airy.hpp:87
    kyosu
    Main KYOSU namespace.
    Definition: cinf.hpp:13

    Parameters

    Return value

    the quaternion value

    -

    +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__quaternion_gaa5964ee08fa64046a80d3908056a09c4.html b/group__quaternion_gaa5964ee08fa64046a80d3908056a09c4.html index 05f3f605..e50195ab 100644 --- a/group__quaternion_gaa5964ee08fa64046a80d3908056a09c4.html +++ b/group__quaternion_gaa5964ee08fa64046a80d3908056a09c4.html @@ -155,7 +155,7 @@

    Header file

    Return value

    a span containing the three coordinates of the axis if the quaternion is zero {1, 0, 0} is returned

    -

    +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__quaternion_gad7e50e38859bb508a816fdd9d63d7b0a.html b/group__quaternion_gad7e50e38859bb508a816fdd9d63d7b0a.html index b9a1ec83..52968662 100644 --- a/group__quaternion_gad7e50e38859bb508a816fdd9d63d7b0a.html +++ b/group__quaternion_gad7e50e38859bb508a816fdd9d63d7b0a.html @@ -156,7 +156,7 @@

    Header file

    Return value

    a tuple containing in this order rho, theta, ph1 ph2: the components of the spherical parametrisation of \(\mathbb{R}^4\) coordinates

    -

    +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__quaternion_gadc8b483ae153b0e6d1eb4d7ece78660d.html b/group__quaternion_gadc8b483ae153b0e6d1eb4d7ece78660d.html index 40397ce7..b1b5ecfe 100644 --- a/group__quaternion_gadc8b483ae153b0e6d1eb4d7ece78660d.html +++ b/group__quaternion_gadc8b483ae153b0e6d1eb4d7ece78660d.html @@ -156,7 +156,7 @@

    Header file

    Return value

    a tuple containing in this order t, radius, longitude latitude: the components of the cylindrospherical parametrisation of \(\mathbb{R}^4\) coordinates

    -

    +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/group__quaternion_gafb8e2e7cadea72110b134c4df850ee3a.html b/group__quaternion_gafb8e2e7cadea72110b134c4df850ee3a.html index cefa4905..4b08e727 100644 --- a/group__quaternion_gafb8e2e7cadea72110b134c4df850ee3a.html +++ b/group__quaternion_gafb8e2e7cadea72110b134c4df850ee3a.html @@ -158,7 +158,7 @@

    Header file

  • the span rotated by q
  • with assume_unitary, assumes that q is already normalized
    • -

    +

    Example

    #include <kyosu/kyosu.hpp>
    #include <eve/wide.hpp>
    diff --git a/index.html b/index.html index b24454db..399680c1 100644 --- a/index.html +++ b/index.html @@ -130,7 +130,7 @@

    The Cayley-Dickson construction scheme defines a new algebra as a Cartesian product of an algebra with itself, with multiplication defined in a specific way (different from the componentwise multiplication) and an involution known as conjugation.

    We currently only implement the Cayley-Dickson algebras based on the IEEE float and double representations of real numbers.

    Kyosu proper usable objects are all in the namespace kyosu.

    -

    +

    Cayley-Dickson algebras

    These are algebras over the real numbers with an involution named conjugation. The product of an element by its conjugate is 'real' and its positive square root is a norm on the vector space defined by the algebra.

    Starting from the real numbers (supported by type T float or double) we define:

    @@ -162,11 +162,11 @@

    The functions commutator (resp. associator) can be used to see if two (resp. three) Cayley-Dickson value commute (resp. associate).

    Greater dimensions are not even alternative but keep power-associativity which allows to define most elementary functions.

    Note
    Let us recall that alternative means that every subalgrebra generated by two elements is associative.
    -

    +

    What does this implementation provide

    All operators and functions implemented can receive a mix of scalar or simd of cayley-dickson and reals of various dimensionnality and are defined in the namespace kyosu.

    Of course the algebra operation +, -, * and / are provided, but as \ is not an usable C++ character as an operator, the left division a \ b is provided as the call ldiv(a,b).

    -

    +

    Constructors

    complex and quaternion can be constructed using callables facilities complex and quaternion.

    complex can also be constructed from their polar representation
    @@ -195,13 +195,13 @@

    The third column references to the corresponding to_xxx version that gives back the chosen representation from a quaternion input.

    TODO cayley_dickson<N> construction by a function.

    -

    +

    Operators

    Operators (as said before) +, -, * and / can be used in infix form and can mix cayley-dickson values of different dimensionalities. Of course the biggest dimensionlity is recovered in the output.

    Prefix forms are also provided as add, sub, multiply and div. Also plus and minus for unary versions.

    The left division sometimes necessary if the dimensionality is greater than 2 is given as ldiv.

    The left multiplication to the left by i or -i (i*i=-1) can be done calling respectively muli and mulmi

    -

    +

    Functions

    Most KYOSU callables are usable with all cayley_dickson types. The exceptions mainly being rotation related quaternion usage.

    Warning
    EVE callables that correspond to mathematical functions that are only defined on a proper part of the real axis as, for example, acos DOES NOT ever provide the same result if called in EVE or KYOSU context.
    diff --git a/namespacekyosu.html b/namespacekyosu.html index fbf9bf8e..fed4e8c6 100644 --- a/namespacekyosu.html +++ b/namespacekyosu.html @@ -276,6 +276,21 @@ constexpr auto average = eve::functor<average_t>  Computes the average of the parameters.
      +constexpr auto bessel_h = eve::functor<bessel_h_t> + Computes the spherical or cylindrical Hankel functions, extended to the complex plane and cayley_dickson algebras.
    +  +constexpr auto bessel_i = eve::functor<bessel_i_t> + Computes the spherical or cylindrical modified Bessel functions of the second kind, extended to the complex plane and cayley_dickson algebras.
    +  +constexpr auto bessel_j = eve::functor<bessel_j_t> + Computes the spherical or cylindrical Bessel functions of the first kind, extended to the complex plane and cayley_dickson algebras.
    +  +constexpr auto bessel_k = eve::functor<bessel_k_t> + Computes the spherical or cylindrical modified Bessel functions of the second kind, extended to the complex plane and cayley_dickson algebras.
    +  +constexpr auto bessel_y = eve::functor<bessel_y_t> + Computes the spherical or cylindrical Bessel functions of the second kind, extended to the complex plane and cayley_dickson algebras.
    +  constexpr auto beta = eve::functor<beta_t>  Computes the beta function: \(\displaystyle \mathbf{B}(x, y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\) for real or complex entries.
      @@ -327,103 +342,6 @@ constexpr auto cscpi = eve::functor<cscpi_t>  Computes the cosecant from the argument in \(\pi\) multiples.
      -constexpr auto cyl_bessel_h1 = eve::functor<cyl_bessel_h1_t> - Computes the Bessel functions of the third kind (Hankel functions) \(H_{\nu}^{(1)}\).
    -  -constexpr auto cyl_bessel_h12 = eve::functor<cyl_bessel_h12_t> - Computes the Hankel functions of the first and second kind,.
    -  -constexpr auto cyl_bessel_h12n = eve::functor<cyl_bessel_h12n_t> - Computes the Hankel functions of the first and second kind,.
    -  -constexpr auto cyl_bessel_h12r = eve::functor<cyl_bessel_h12r_t> - Computes the Hankel functions of the first and second kind,.
    -  -constexpr auto cyl_bessel_h1_0 = eve::functor<cyl_bessel_h1_0_t> - Computes the Bessel function of the third kind, \( H^{(1)}_0(x)\),.
    -  -constexpr auto cyl_bessel_h1_1 = eve::functor<cyl_bessel_h1_1_t> - Computes the Bessel function of the third kind, \( H^{(1)}_1(x)\),.
    -  -constexpr auto cyl_bessel_h1n = eve::functor<cyl_bessel_h1n_t> - Computes the Bessel/Hankel functions of the third kind, \( H_n^{(1)}(z) = J_n(z)+iY_n(z)\).
    -  -constexpr auto cyl_bessel_h2 = eve::functor<cyl_bessel_h2_t> - Computes the Bessel functions of the third kind (Hankel functions) \(H_{\nu}^{(2)}\).
    -  -constexpr auto cyl_bessel_h2_0 = eve::functor<cyl_bessel_h2_0_t> - Computes the Bessel function of the third kind, \( H^{(2)}_0(x)\).
    -  -constexpr auto cyl_bessel_h2_1 = eve::functor<cyl_bessel_h2_1_t> - Computes the Bessel function of the third kind, \( H^{(2)}_1(x)\),.
    -  -constexpr auto cyl_bessel_h2n = eve::functor<cyl_bessel_h2n_t> - Computes the Bessel/Hankel functions of the third kind , \( H_n^{(2)} = J_n(z)-iY_n(z)\).
    -  -constexpr auto cyl_bessel_i = eve::functor<cyl_bessel_i_t> - Computes the modified Bessel functions of the first kind,.
    -  -constexpr auto cyl_bessel_i0 = eve::functor<cyl_bessel_i0_t> - Computes the modified Bessel function of the first kind \(I_{0}(x)=J_{0}(ix)\) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto cyl_bessel_i1 = eve::functor<cyl_bessel_i1_t> - Computes the modified Bessel function of the first kind, \( I_1(x)= iJ_1(ix) \) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto cyl_bessel_ik = eve::functor<cyl_bessel_ik_t> - Computes the simultaneous Bessel functions of the first and second kind,.
    -  -constexpr auto cyl_bessel_ikn = eve::functor<cyl_bessel_ikn_t> - Computes simultaneously the modified Bessel functions of the first and second kind of integer orders,.
    -  -constexpr auto cyl_bessel_in = eve::functor<cyl_bessel_in_t> - Computes the modified Bessel functions of the first kind \(I_{n}(x)=i^{-n}J_{n }(ix)\), extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto cyl_bessel_j = eve::functor<cyl_bessel_j_t> - Computes the Bessel functions of the first kind, \( J_{\nu}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+\nu +1)}} - {\left({x \over 2}\right)}^{2p+\nu }\) extended to the complex plane and cayley_dickson values.
    -  -constexpr auto cyl_bessel_j0 = eve::functor<cyl_bessel_j0_t> - Computes the Bessel function of the first kind, \( J_0(x)=\frac1{\pi }\int _{0}^{\pi}\cos(x\sin \tau) - \,\mathrm {d} \tau \) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto cyl_bessel_j1 = eve::functor<cyl_bessel_j1_t> - Computes the Bessel function of the first kind, \( J_1\).
    -  -constexpr auto cyl_bessel_jn = eve::functor<cyl_bessel_jn_t> - Computes the Bessel functions of the first kind, \( J_{n}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+n +1)}} - {\left({x \over 2}\right)}^{2p+n }\) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto cyl_bessel_jy = eve::functor<cyl_bessel_jy_t> - Computes the simultaneous Bessel functions of the first and second kind,.
    -  -constexpr auto cyl_bessel_jyn = eve::functor<cyl_bessel_jyn_t> - Computes the simultaneous Bessel functions of the first and second kind,.
    -  -constexpr auto cyl_bessel_k = eve::functor<cyl_bessel_k_t> - Computes the Modified Bessel functions of the second kind.
    -  -constexpr auto cyl_bessel_k0 = eve::functor<cyl_bessel_k0_t> - Computes the modified Bessel function of the second kind, \( K_0(x)=\lim_{\alpha\to 0}{\frac {\pi }{2}}{\frac {I_{-\alpha }(x)-I_{\alpha }(x)}{\sin \alpha \pi }}\). extended to the complex plane and cayley_dickson values.
    -  -constexpr auto cyl_bessel_k1 = eve::functor<cyl_bessel_k1_t> - Computes the Bessel function of the second kind, \( K_1(x)\lim_{\alpha\to 1}{\frac {\pi }{2}}{\frac {I_{-\alpha }(x)-I_{\alpha }(x)}{\sin \alpha \pi }}\) extended to the complex plane and cayley_dickson values.
    -  -constexpr auto cyl_bessel_kn = eve::functor<cyl_bessel_kn_t> - Computes the modified Bessel functions of the second kind, \( Y_n(x)=\lim_{\alpha\to n}{{\frac {J_{\alpha }(x)\cos(\alpha\pi)-J_{-\alpha }(x)}{\sin(\alpha\pi)}}}\), extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto cyl_bessel_y = eve::functor<cyl_bessel_y_t> - Computes the Bessel functions of the first kind, \( J_{\nu}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+\nu +1)}} - {\left({x \over 2}\right)}^{2p+\nu }\) extended to the complex plane and cayley_dickson values.
    -  -constexpr auto cyl_bessel_y0 = eve::functor<cyl_bessel_y0_t> - Computes the Bessel function of the second kind, \( Y_0(x)=\lim_{\alpha\to 0}{{\frac {J_{\alpha }(x)\cos(\alpha\pi)-J_{-\alpha }(x)}{\sin(\alpha\pi)}}}\), extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto cyl_bessel_y1 = eve::functor<cyl_bessel_y1_t> - Computes the Bessel function of the second kind, \( Y_1(x)=\lim_{\alpha\to 1}{{\frac {J_{\alpha }(x)\cos(\alpha\pi)-J_{-\alpha }(x)}{\sin(\alpha\pi)}}}\), extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto cyl_bessel_yn = eve::functor<cyl_bessel_yn_t> - Computes the modified Bessel functions of the second kind, \( Y_n(x)=\lim_{\alpha\to n}{{\frac {J_{\alpha }(x)\cos(\alpha\pi)-J_{-\alpha }(x)}{\sin(\alpha\pi)}}}\), extended to the complex plane and cayley_dickson algebras.
    -  constexpr auto dec = eve::functor<dec_t>  decrements the argument by 1.
      @@ -803,69 +721,6 @@ constexpr auto slerp = eve::functor<slerp_t>  Computes the spherical interpolation between unitary quaternions.
      -constexpr auto sph_bessel_h1_0 = eve::functor<sph_bessel_h1_0_t> - Computes the spherical Bessel/hankel functions of the third kind, \( h_0^{(1)}(z) = j_1(z)+iy_1(z)\).
    -  -constexpr auto sph_bessel_h1_1 = eve::functor<sph_bessel_h1_1_t> - Computes the spherical Bessel/hankel functions of the third kind, \( h_1^{(1)}(z) = j_1(z)+iy_1(z)\).
    -  -constexpr auto sph_bessel_h1n = eve::functor<sph_bessel_h1n_t> - Computes the spherical Bessel/hankel functions of the third kind, \( h_n^{(1)}(z) = j_n(z)+iy_n(z)\).
    -  -constexpr auto sph_bessel_h2_0 = eve::functor<sph_bessel_h2_0_t> - Computes the spherical Bessel/hankel functions of the third kind, \( h_0^{(2)}(z) = j_0(z)-iy_0(z)\).
    -  -constexpr auto sph_bessel_h2_1 = eve::functor<sph_bessel_h2_1_t> - Computes the spherical Bessel/hankel functions of the third kind, \( h_1^{(2)}(z) = j_1(z)-iy_1(z)\).
    -  -constexpr auto sph_bessel_h2n = eve::functor<sph_bessel_h2n_t> - Computes the spherical Bessel/hankel functions of the third kind, \( h_n^{(2)}(z) = j_n(z)-iy_n(z)\).
    -  -constexpr auto sph_bessel_i1_0 = eve::functor<sph_bessel_i1_0_t> - Computes the Bessel function, \( i_0^{(1)}(z) = j_0(iz)\) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto sph_bessel_i1_1 = eve::functor<sph_bessel_i1_1_t> - Computes the Bessel function, \( i_1^{(1)}(z) = -i j_1(iz)\) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto sph_bessel_i1n = eve::functor<sph_bessel_i1n_t> - Computes the spherical Bessel functions of the first kind, extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto sph_bessel_i2_0 = eve::functor<sph_bessel_i2_0_t> - Computes the Bessel function, \( i_0^{(2)}(z) = -i y_0(iz)\) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto sph_bessel_i2_1 = eve::functor<sph_bessel_i2_1_t> - Computes the Bessel function, \( i_1^{(2)}(z) = -y_1(iz)\) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto sph_bessel_i2n = eve::functor<sph_bessel_i2n_t> - Computes the spherical Bessel functions of the first kind, extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto sph_bessel_j0 = eve::functor<sph_bessel_j0_t> - Computes the Bessel function of the first kind, \( j_0(z)=\sin z/z \) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto sph_bessel_j1 = eve::functor<sph_bessel_j1_t> - Computes the Spherical Bessel function of the first kind, \( j_1(z)= \sin z/z^2 -\cos z/z\) extended to the complex plane and cayley_dickson values.
    -  -constexpr auto sph_bessel_jn = eve::functor<sph_bessel_jn_t> - Computes the spherical Bessel functions of the first kind, extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto sph_bessel_k0 = eve::functor<sph_bessel_k0_t> - Computes the spherical Bessel function of the first kind, \( k_0(z)= \pi e^{-z}/(2z) \) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto sph_bessel_k1 = eve::functor<sph_bessel_k1_t> - Computes the spherical Bessel function of the first kind, \( k_1(z)= (\pi/2) e^{-z}(1/z+1/z^2)\) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto sph_bessel_kn = eve::functor<sph_bessel_kn_t> - Computes the spherical Bessel functions of the first kind, extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto sph_bessel_y0 = eve::functor<sph_bessel_y0_t> - Computes the spherical Bessel function of the first kind, \( y_0(x)=\cos z/z \) extended to the complex plane and cayley_dickson algebras.
    -  -constexpr auto sph_bessel_y1 = eve::functor<sph_bessel_y1_t> - Computes the spherical Bessel function of the first kind, \( y_1(x)= -\coz z/z^2 -\sin z/z\) extended to the complex plane and cayley_dickson values.
    -  -constexpr auto sph_bessel_yn = eve::functor<sph_bessel_yn_t> - Computes the spherical Bessel functions of the second kind, extended to the complex plane and cayley_dickson algebras.
    -  constexpr auto sqr = eve::functor<sqr_t>  Computes the square value.
      diff --git a/navtreedata.js b/navtreedata.js index 0c498387..3baa13bd 100644 --- a/navtreedata.js +++ b/navtreedata.js @@ -25,11 +25,11 @@ var NAVTREE = [ [ "kyosu", "index.html", [ - [ "Cayley-Dickson algebras", "index.html#autotoc_md22", null ], - [ "What does this implementation provide", "index.html#autotoc_md23", [ - [ "Constructors", "index.html#autotoc_md24", null ], - [ "Operators", "index.html#autotoc_md25", null ], - [ "Functions", "index.html#autotoc_md26", null ] + [ "Cayley-Dickson algebras", "index.html#autotoc_md23", null ], + [ "What does this implementation provide", "index.html#autotoc_md24", [ + [ "Constructors", "index.html#autotoc_md25", null ], + [ "Operators", "index.html#autotoc_md26", null ], + [ "Functions", "index.html#autotoc_md27", null ] ] ], [ "How-Tos", "usergroup0.html", null ], [ "Reference Documentation", "usergroup1.html", [ diff --git a/navtreeindex0.js b/navtreeindex0.js index a6d6f578..cd83bd5e 100644 --- a/navtreeindex0.js +++ b/navtreeindex0.js @@ -11,11 +11,11 @@ var NAVTREEINDEX0 = "group__traits.html":[3,3], "group__types.html":[3,0], "index.html":[], -"index.html#autotoc_md22":[0], -"index.html#autotoc_md23":[1], -"index.html#autotoc_md24":[1,0], -"index.html#autotoc_md25":[1,1], -"index.html#autotoc_md26":[1,2], +"index.html#autotoc_md23":[0], +"index.html#autotoc_md24":[1], +"index.html#autotoc_md25":[1,0], +"index.html#autotoc_md26":[1,1], +"index.html#autotoc_md27":[1,2], "licence.html":[4,0], "pages.html":[], "usergroup0.html":[2], diff --git a/search/all_1.js b/search/all_1.js index 27838379..ec2a2c73 100644 --- a/search/all_1.js +++ b/search/all_1.js @@ -1,4 +1,9 @@ var searchData= [ - 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