diff --git a/group__functions.html b/group__functions.html index b6705245..77f3cfbe 100644 --- a/group__functions.html +++ b/group__functions.html @@ -254,7 +254,7 @@  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 tags::callable_cyl_bessel_i1 kyosu::cyl_bessel_i1 = {} - Computes the modified Bessel function of the first kind, \( I_1(x)= _iJ_1(ix) \) extended to the complex plane and cayley_dickson algebras.
+ 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 tags::callable_cyl_bessel_in kyosu::cyl_bessel_in = {}  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.
@@ -597,6 +597,9 @@ constexpr tags::callable_sinh kyosu::sinh = {}  Computes the hyperbolic sine of the argument.
  +constexpr tags::callable_sinhc kyosu::sinhc = {} + Computes the hyperbolic sine cardinal of the argument.
+  constexpr tags::callable_sinhcosh kyosu::sinhcosh = {}  Computes simultaneously the hyperbolic sine and cosine of the argument.
  @@ -609,6 +612,63 @@ constexpr tags::callable_slerp kyosu::slerp = {}  Computes the spherical interpolation between unitary quaternions.
  +constexpr tags::callable_sph_bessel_h1_0 kyosu::sph_bessel_h1_0 = {} + Computes the spherical Bessel/hankel functions of the third kind, \( h_0^{(1)}(z) = j_1(z)+iy_1(z)\).
+  +constexpr tags::callable_sph_bessel_h1_1 kyosu::sph_bessel_h1_1 = {} + Computes the spherical Bessel/hankel functions of the third kind, \( h_1^{(1)}(z) = j_1(z)+iy_1(z)\).
+  +constexpr tags::callable_sph_bessel_h1n kyosu::sph_bessel_h1n = {} + Computes the spherical Bessel/hankel functions of the third kind, \( h_n^{(1)}(z) = j_n(z)+iy_n(z)\).
+  +constexpr tags::callable_sph_bessel_h2_0 kyosu::sph_bessel_h2_0 = {} + Computes the spherical Bessel/hankel functions of the third kind, \( h_0^{(2)}(z) = j_0(z)-iy_0(z)\).
+  +constexpr tags::callable_sph_bessel_h2_1 kyosu::sph_bessel_h2_1 = {} + Computes the spherical Bessel/hankel functions of the third kind, \( h_1^{(2)}(z) = j_1(z)-iy_1(z)\).
+  +constexpr tags::callable_sph_bessel_h2n kyosu::sph_bessel_h2n = {} + Computes the spherical Bessel/hankel functions of the third kind, \( h_n^{(2)}(z) = j_n(z)-iy_n(z)\).
+  +constexpr tags::callable_sph_bessel_i1_0 kyosu::sph_bessel_i1_0 = {} + Computes the Bessel function, \( i_0^{(1)}(z) = j_n(iz)\) extended to the complex plane and cayley_dickson algebras.
+  +constexpr tags::callable_sph_bessel_i1_1 kyosu::sph_bessel_i1_1 = {} + Computes the Bessel function, \( i_1^{(1)}(z) = -i j_1(iz)\) extended to the complex plane and cayley_dickson algebras.
+  +constexpr tags::callable_sph_bessel_i1n kyosu::sph_bessel_i1n = {} + Computes the spherical Bessel functions \( i_n^{(1)}(z) = i^{-n}j_n(iz)\).
+  +constexpr tags::callable_sph_bessel_i2_0 kyosu::sph_bessel_i2_0 = {} + Computes the Bessel function, \( i_0^{(2)}(z) = -i y_n(iz)\) extended to the complex plane and cayley_dickson algebras.
+  +constexpr tags::callable_sph_bessel_i2_1 kyosu::sph_bessel_i2_1 = {} + Computes the Bessel function, \( i_1^{(2)}(z) = -y_1(iz)\) extended to the complex plane and cayley_dickson algebras.
+  +constexpr tags::callable_sph_bessel_i2n kyosu::sph_bessel_i2n = {} + Computes the spherical Bessel functions \( i_n^{(2)}(z) = i^{-n-1}y_n(iz)\).
+  +constexpr tags::callable_sph_bessel_j0 kyosu::sph_bessel_j0 = {} + Computes the Bessel function of the first kind, \( j_0(x)=\sin z/z \) extended to the complex plane and cayley_dickson algebras.
+  +constexpr tags::callable_sph_bessel_jn kyosu::sph_bessel_jn = {} + Computes the spherical Bessel functions of the first kind \(j_{n}(x)\), extended to the complex plane and cayley_dickson algebras.
+  +constexpr tags::callable_sph_bessel_k0 kyosu::sph_bessel_k0 = {} + Computes the spherical Bessel function of the first kind, \( k_0(x)= \pi e^{-z}/(2z) \) extended to the complex plane and cayley_dickson algebras.
+  +constexpr tags::callable_sph_bessel_k1 kyosu::sph_bessel_k1 = {} + Computes the spherical Bessel function of the first kind, \( k_1(x)= (\pi/2) e^{-z}(1/z+1/z^2)\) extended to the complex plane and cayley_dickson algebras.
+  +constexpr tags::callable_sph_bessel_kn kyosu::sph_bessel_kn = {} + Computes the spherical Bessel functions \(k_{n}(x)\), extended to the complex plane and cayley_dickson algebras.
+  +constexpr tags::callable_sph_bessel_y0 kyosu::sph_bessel_y0 = {} + 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 tags::callable_sph_bessel_yn kyosu::sph_bessel_yn = {} + Computes the spherical Bessel functions of the first kind \(y_{n}(x)\), extended to the complex plane and cayley_dickson algebras.
+  constexpr tags::callable_sqr kyosu::sqr = {}  Computes the square value.
  diff --git a/group__functions_ga062b5b6068ed042bb0dd5fde1b159f67.html b/group__functions_ga062b5b6068ed042bb0dd5fde1b159f67.html new file mode 100644 index 00000000..1f2e5a8e --- /dev/null +++ b/group__functions_ga062b5b6068ed042bb0dd5fde1b159f67.html @@ -0,0 +1,226 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_kn + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
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+
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+
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+
+
+
+
+ +
+ +

◆ sph_bessel_kn

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_kn = {}
+ 		+inlineconstexpr
+
+ +

Computes the spherical Bessel functions \(k_{n}(x)\), extended to the complex plane and cayley_dickson algebras.

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_kn(int n, T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr T sph_bessel_kn(int n, T z) noexcept;
+
}
+
kyosu::sph_bessel_kn
constexpr tags::callable_sph_bessel_kn sph_bessel_kn
Computes the spherical Bessel functions , extended to the complex plane and cayley_dickson algebras.
Definition: sph_bessel_kn.hpp:78
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(k_n(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
+
size_t n = 12;
+
using kyosu::sph_bessel_kn;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_kn(n,1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_kn(n,kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_kn(n,15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_kn(n,kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_kn(n,40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_kn(n,kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_kn(n,60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_kn(n,kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_kn(n,z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_kn(n,zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_kn(n,1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_kn(n,kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_kn(n,kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_kn(n,z0) << "\n";
+
+
+
for(int i=75; i < 100; ++i)
+
std::cout << "i " << i << " -> " << kyosu::sph_bessel_kn(i,kyosu::complex(1.0, 1.0)) << "\n";
+
+
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_ga19db4b9fc67ce7a017c8404a96b54d3b.html b/group__functions_ga19db4b9fc67ce7a017c8404a96b54d3b.html new file mode 100644 index 00000000..2e9eb6f0 --- /dev/null +++ b/group__functions_ga19db4b9fc67ce7a017c8404a96b54d3b.html @@ -0,0 +1,218 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_i1_1 + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
Loading...
+
Searching...
+
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+
+
+
+
+ +
+ +

◆ sph_bessel_i1_1

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_i1_1 = {}
+ 		+inlineconstexpr
+
+ +

Computes the Bessel function, \( i_1^{(1)}(z) = -i j_1(iz)\) extended to the complex plane and cayley_dickson algebras.

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_i1_1(T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr T sph_bessel_i1_1(T z) noexcept;
+
}
+
kyosu::sph_bessel_i1_1
constexpr tags::callable_sph_bessel_i1_1 sph_bessel_i1_1
Computes the Bessel function, extended to the complex plane and cayley_dickson algebras.
Definition: sph_bessel_i1_1.hpp:77
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(i_1^{(1)}(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
using kyosu::sph_bessel_i1_1;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_i1_1(1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_i1_1(kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_i1_1(15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_i1_1(kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_i1_1(40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_i1_1(kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_i1_1(60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_i1_1(kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_i1_1(z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_i1_1(zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_i1_1(1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_i1_1(kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_i1_1(kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_i1_1(z0) << "\n";
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_ga19f41db61477aab9133f69fec5e2b278.html b/group__functions_ga19f41db61477aab9133f69fec5e2b278.html new file mode 100644 index 00000000..e03ecb09 --- /dev/null +++ b/group__functions_ga19f41db61477aab9133f69fec5e2b278.html @@ -0,0 +1,218 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_y0 + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
Loading...
+
Searching...
+
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+
+
+
+
+ +
+ +

◆ sph_bessel_y0

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_y0 = {}
+ 		+inlineconstexpr
+
+ +

Computes the spherical Bessel function of the first kind, \( y_0(x)=\cos z/z \) extended to the complex plane and cayley_dickson algebras.

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_y0(T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr T sph_bessel_y0(T z) noexcept;
+
}
+
kyosu::sph_bessel_y0
constexpr tags::callable_sph_bessel_y0 sph_bessel_y0
Computes the spherical Bessel function of the first kind, extended to the complex plane and cayley_d...
Definition: sph_bessel_y0.hpp:72
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(y_0(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
using kyosu::sph_bessel_y0;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_y0(1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_y0(kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_y0(15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_y0(kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_y0(40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_y0(kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_y0(60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_y0(kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_y0(z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_y0(zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_y0(1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_y0(kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_y0(kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_y0(z0) << "\n";
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_ga27aede1e1a07bc45152336019f674a4f.html b/group__functions_ga27aede1e1a07bc45152336019f674a4f.html new file mode 100644 index 00000000..03896a46 --- /dev/null +++ b/group__functions_ga27aede1e1a07bc45152336019f674a4f.html @@ -0,0 +1,218 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_i2_0 + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
Loading...
+
Searching...
+
No Matches
+
+
+
+
+ +
+ +

◆ sph_bessel_i2_0

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_i2_0 = {}
+ 		+inlineconstexpr
+
+ +

Computes the Bessel function, \( i_0^{(2)}(z) = -i y_n(iz)\) extended to the complex plane and cayley_dickson algebras.

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_i2_0(T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr T sph_bessel_i2_0(T z) noexcept;
+
}
+
kyosu::sph_bessel_i2_0
constexpr tags::callable_sph_bessel_i2_0 sph_bessel_i2_0
Computes the Bessel function, extended to the complex plane and cayley_dickson algebras.
Definition: sph_bessel_i2_0.hpp:74
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(i_0^{(2)}(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
using kyosu::sph_bessel_i2_0;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_i2_0(1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_i2_0(kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_i2_0(15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_i2_0(kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_i2_0(40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_i2_0(kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_i2_0(60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_i2_0(kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_i2_0(z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_i2_0(zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_i2_0(1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_i2_0(kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_i2_0(kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_i2_0(z0) << "\n";
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_ga3bb27dafa9d5251251038abd2493d396.html b/group__functions_ga3bb27dafa9d5251251038abd2493d396.html new file mode 100644 index 00000000..144b1084 --- /dev/null +++ b/group__functions_ga3bb27dafa9d5251251038abd2493d396.html @@ -0,0 +1,225 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_i1n + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
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+
Searching...
+
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+
+
+
+
+ +
+ +

◆ sph_bessel_i1n

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_i1n = {}
+ 		+inlineconstexpr
+
+ +

Computes the spherical Bessel functions \( i_n^{(1)}(z) = i^{-n}j_n(iz)\).

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_i1n(int n, T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr auto sph_bessel_i1n(int n, T z) noexcept;
+
}
+
kyosu::sph_bessel_i1n
constexpr tags::callable_sph_bessel_i1n sph_bessel_i1n
Computes the spherical Bessel functions .
Definition: sph_bessel_i1n.hpp:77
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(i_n^{(1)}(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
size_t n = 12;
+
using kyosu::sph_bessel_i1n;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_i1n(n,1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_i1n(n,kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_i1n(n,15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_i1n(n,kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_i1n(n,40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_i1n(n,kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_i1n(n,60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_i1n(n,kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_i1n(n,z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_i1n(n,zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_i1n(n,1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_i1n(n,kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_i1n(n,kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_i1n(n,z0) << "\n";
+
+
+
for(int i=75; i < 100; ++i)
+
std::cout << "i " << i << " -> " << kyosu::sph_bessel_i1n(i,kyosu::complex(1.0, 1.0)) << "\n";
+
+
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_ga5a48ea11c00ce56c6ead01f9fd2990f4.html b/group__functions_ga5a48ea11c00ce56c6ead01f9fd2990f4.html new file mode 100644 index 00000000..a8a9a3db --- /dev/null +++ b/group__functions_ga5a48ea11c00ce56c6ead01f9fd2990f4.html @@ -0,0 +1,226 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_jn + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
Loading...
+
Searching...
+
No Matches
+
+
+
+
+ +
+ +

◆ sph_bessel_jn

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_jn = {}
+ 		+inlineconstexpr
+
+ +

Computes the spherical Bessel functions of the first kind \(j_{n}(x)\), extended to the complex plane and cayley_dickson algebras.

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_jn(int n, T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr T sph_bessel_jn(int n, T z) noexcept;
+
}
+
kyosu::sph_bessel_jn
constexpr tags::callable_sph_bessel_jn sph_bessel_jn
Computes the spherical Bessel functions of the first kind , extended to the complex plane and cayley_...
Definition: sph_bessel_jn.hpp:73
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(j_n(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
+
size_t n = 12;
+
using kyosu::sph_bessel_jn;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_jn(n,1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_jn(n,kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_jn(n,15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_jn(n,kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_jn(n,40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_jn(n,kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_jn(n,60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_jn(n,kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_jn(n,z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_jn(n,zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_jn(n,1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_jn(n,kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_jn(n,kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_jn(n,z0) << "\n";
+
+
+
for(int i=75; i < 100; ++i)
+
std::cout << "i " << i << " -> " << kyosu::sph_bessel_jn(i,kyosu::complex(1.0, 1.0)) << "\n";
+
+
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_ga641bd70cc5d8305d074ed733e477178a.html b/group__functions_ga641bd70cc5d8305d074ed733e477178a.html new file mode 100644 index 00000000..a3a45876 --- /dev/null +++ b/group__functions_ga641bd70cc5d8305d074ed733e477178a.html @@ -0,0 +1,218 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_i1_0 + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
Loading...
+
Searching...
+
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+
+
+
+
+ +
+ +

◆ sph_bessel_i1_0

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_i1_0 = {}
+ 		+inlineconstexpr
+
+ +

Computes the Bessel function, \( i_0^{(1)}(z) = j_n(iz)\) extended to the complex plane and cayley_dickson algebras.

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_i1_0(T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr T sph_bessel_i1_0(T z) noexcept;
+
}
+
kyosu::sph_bessel_i1_0
constexpr tags::callable_sph_bessel_i1_0 sph_bessel_i1_0
Computes the Bessel function, extended to the complex plane and cayley_dickson algebras.
Definition: sph_bessel_i1_0.hpp:75
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(i_0^{(1)}(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
using kyosu::sph_bessel_i1_0;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_i1_0(1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_i1_0(kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_i1_0(15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_i1_0(kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_i1_0(40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_i1_0(kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_i1_0(60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_i1_0(kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_i1_0(z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_i1_0(zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_i1_0(1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_i1_0(kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_i1_0(kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_i1_0(z0) << "\n";
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_ga6955189373673f4c2228b8b18d72b66c.html b/group__functions_ga6955189373673f4c2228b8b18d72b66c.html new file mode 100644 index 00000000..d4826c12 --- /dev/null +++ b/group__functions_ga6955189373673f4c2228b8b18d72b66c.html @@ -0,0 +1,218 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_h2_0 + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
Loading...
+
Searching...
+
No Matches
+
+
+
+
+ +
+ +

◆ sph_bessel_h2_0

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_h2_0 = {}
+ 		+inlineconstexpr
+
+ +

Computes the spherical Bessel/hankel functions of the third kind, \( h_0^{(2)}(z) = j_0(z)-iy_0(z)\).

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_h2_1(int n, T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr auto sph_bessel_h2_1(int n, T z) noexcept;
+
}
+
kyosu::sph_bessel_h2_1
constexpr tags::callable_sph_bessel_h2_1 sph_bessel_h2_1
Computes the spherical Bessel/hankel functions of the third kind, .
Definition: sph_bessel_h2_1.hpp:76
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(h_1^{(2)}(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
using kyosu::sph_bessel_h2_1;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_h2_1(1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_h2_1(kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_h2_1(15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_h2_1(kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_h2_1(40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_h2_1(kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_h2_1(60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_h2_1(kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_h2_1(z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_h2_1(zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_h2_1(1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_h2_1(kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_h2_1(kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_h2_1(z0) << "\n";
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_ga6a219f9cacecb5ba52b049519820ef08.html b/group__functions_ga6a219f9cacecb5ba52b049519820ef08.html new file mode 100644 index 00000000..85b69935 --- /dev/null +++ b/group__functions_ga6a219f9cacecb5ba52b049519820ef08.html @@ -0,0 +1,218 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_k0 + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
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+
Searching...
+
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+
+
+
+
+ +
+ +

◆ sph_bessel_k0

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_k0 = {}
+ 		+inlineconstexpr
+
+ +

Computes the spherical Bessel function of the first kind, \( k_0(x)= \pi e^{-z}/(2z) \) extended to the complex plane and cayley_dickson algebras.

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_k0(T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr T sph_bessel_k0(T z) noexcept;
+
}
+
kyosu::sph_bessel_k0
constexpr tags::callable_sph_bessel_k0 sph_bessel_k0
Computes the spherical Bessel function of the first kind, extended to the complex plane and cayley_d...
Definition: sph_bessel_k0.hpp:75
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(k_0(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
using kyosu::sph_bessel_k0;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_k0(1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_k0(kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_k0(15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_k0(kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_k0(40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_k0(kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_k0(60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_k0(kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_k0(z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_k0(zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_k0(1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_k0(kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_k0(kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_k0(z0) << "\n";
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_ga82a411040c89aa8ef180d0d36bc86df5.html b/group__functions_ga82a411040c89aa8ef180d0d36bc86df5.html new file mode 100644 index 00000000..26b5def6 --- /dev/null +++ b/group__functions_ga82a411040c89aa8ef180d0d36bc86df5.html @@ -0,0 +1,225 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_i2n + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
Loading...
+
Searching...
+
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+
+
+
+
+ +
+ +

◆ sph_bessel_i2n

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_i2n = {}
+ 		+inlineconstexpr
+
+ +

Computes the spherical Bessel functions \( i_n^{(2)}(z) = i^{-n-1}y_n(iz)\).

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_i2n(int n, T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr auto sph_bessel_i2n(int n, T z) noexcept;
+
}
+
kyosu::sph_bessel_i2n
constexpr tags::callable_sph_bessel_i2n sph_bessel_i2n
Computes the spherical Bessel functions .
Definition: sph_bessel_i2n.hpp:77
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(i_n^{(2)}(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
size_t n = 12;
+
using kyosu::sph_bessel_i2n;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_i2n(n,1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_i2n(n,kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_i2n(n,15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_i2n(n,kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_i2n(n,40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_i2n(n,kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_i2n(n,60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_i2n(n,kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_i2n(n,z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_i2n(n,zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_i2n(n,1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_i2n(n,kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_i2n(n,kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_i2n(n,z0) << "\n";
+
+
+
for(int i=75; i < 100; ++i)
+
std::cout << "i " << i << " -> " << kyosu::sph_bessel_i2n(i,kyosu::complex(1.0, 1.0)) << "\n";
+
+
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_ga873a430b7d76aa66b2038248c3213aca.html b/group__functions_ga873a430b7d76aa66b2038248c3213aca.html new file mode 100644 index 00000000..c9a89534 --- /dev/null +++ b/group__functions_ga873a430b7d76aa66b2038248c3213aca.html @@ -0,0 +1,218 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_h1_1 + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
Loading...
+
Searching...
+
No Matches
+
+
+
+
+ +
+ +

◆ sph_bessel_h1_1

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_h1_1 = {}
+ 		+inlineconstexpr
+
+ +

Computes the spherical Bessel/hankel functions of the third kind, \( h_1^{(1)}(z) = j_1(z)+iy_1(z)\).

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_h1_1(int n, T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr auto sph_bessel_h1_1(int n, T z) noexcept;
+
}
+
kyosu::sph_bessel_h1_1
constexpr tags::callable_sph_bessel_h1_1 sph_bessel_h1_1
Computes the spherical Bessel/hankel functions of the third kind, .
Definition: sph_bessel_h1_1.hpp:76
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(h_1^{(1)}(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
using kyosu::sph_bessel_h1_1;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_h1_1(1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_h1_1(kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_h1_1(15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_h1_1(kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_h1_1(40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_h1_1(kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_h1_1(60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_h1_1(kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_h1_1(z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_h1_1(zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_h1_1(1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_h1_1(kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_h1_1(kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_h1_1(z0) << "\n";
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_ga9022cd9a81d5057a6f3356c16c76c940.html b/group__functions_ga9022cd9a81d5057a6f3356c16c76c940.html index c1ce23c9..f1c06c0a 100644 --- a/group__functions_ga9022cd9a81d5057a6f3356c16c76c940.html +++ b/group__functions_ga9022cd9a81d5057a6f3356c16c76c940.html @@ -142,7 +142,7 @@

-

Computes the modified Bessel function of the first kind, \( I_1(x)= _iJ_1(ix) \) extended to the complex plane and cayley_dickson algebras.

+

Computes the modified Bessel function of the first kind, \( I_1(x)= iJ_1(ix) \) extended to the complex plane and cayley_dickson algebras.

It is the solution of \( x^{2}y''+xy'+x^2y=0\) for which \( y(0) = 0\).

#include <kyosu/functions.hpp>

Callable Signatures

diff --git a/group__functions_ga96400e65eaf1b63c5ab88ba5aff6d818.html b/group__functions_ga96400e65eaf1b63c5ab88ba5aff6d818.html index 9b36b5c4..b553e74f 100644 --- a/group__functions_ga96400e65eaf1b63c5ab88ba5aff6d818.html +++ b/group__functions_ga96400e65eaf1b63c5ab88ba5aff6d818.html @@ -193,6 +193,12 @@

Example

eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
auto z0 = kyosu::complex(z1, z2);
std::cout << z0 << " \n-> " << cyl_bessel_yn(n,z0) << "\n";
+
+
+
for(int i=75; i < 100; ++i)
+
std::cout << "i " << i << " -> " << cyl_bessel_yn(i,kyosu::complex(1.0, 1.0)) << "\n";
+
+
return 0;
}
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
diff --git a/group__functions_ga98914c0086476e35b5c083d3f6c469e6.html b/group__functions_ga98914c0086476e35b5c083d3f6c469e6.html new file mode 100644 index 00000000..f6d31e7c --- /dev/null +++ b/group__functions_ga98914c0086476e35b5c083d3f6c469e6.html @@ -0,0 +1,225 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_h2n + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
Loading...
+
Searching...
+
No Matches
+
+
+
+
+ +
+ +

◆ sph_bessel_h2n

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_h2n = {}
+ 		+inlineconstexpr
+
+ +

Computes the spherical Bessel/hankel functions of the third kind, \( h_n^{(2)}(z) = j_n(z)-iy_n(z)\).

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_h2n(int n, T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr auto sph_bessel_h2n(int n, T z) noexcept;
+
}
+
kyosu::sph_bessel_h2n
constexpr tags::callable_sph_bessel_h2n sph_bessel_h2n
Computes the spherical Bessel/hankel functions of the third kind, .
Definition: sph_bessel_h2n.hpp:76
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(h_n^{(2)}(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
size_t n = 12;
+
using kyosu::sph_bessel_h2n;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_h2n(n,1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_h2n(n,kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_h2n(n,15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_h2n(n,kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_h2n(n,40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_h2n(n,kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_h2n(n,60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_h2n(n,kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_h2n(n,z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_h2n(n,zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_h2n(n,1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_h2n(n,kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_h2n(n,kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_h2n(n,z0) << "\n";
+
+
+
for(int i=75; i < 100; ++i)
+
std::cout << "i " << i << " -> " << kyosu::sph_bessel_h2n(i,kyosu::complex(1.0, 1.0)) << "\n";
+
+
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_gaa76644cdbfade2b6b239955cf9d418b0.html b/group__functions_gaa76644cdbfade2b6b239955cf9d418b0.html new file mode 100644 index 00000000..c4c8c104 --- /dev/null +++ b/group__functions_gaa76644cdbfade2b6b239955cf9d418b0.html @@ -0,0 +1,218 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_h2_1 + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
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+
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+ +
+ +

◆ sph_bessel_h2_1

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_h2_1 = {}
+ 		+inlineconstexpr
+
+ +

Computes the spherical Bessel/hankel functions of the third kind, \( h_1^{(2)}(z) = j_1(z)-iy_1(z)\).

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_h2_1(int n, T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr auto sph_bessel_h2_1(int n, T z) noexcept;
+
}
+
kyosu::sph_bessel_h2_1
constexpr tags::callable_sph_bessel_h2_1 sph_bessel_h2_1
Computes the spherical Bessel/hankel functions of the third kind, .
Definition: sph_bessel_h2_1.hpp:76
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(h_1^{(2)}(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
using kyosu::sph_bessel_h2_1;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_h2_1(1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_h2_1(kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_h2_1(15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_h2_1(kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_h2_1(40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_h2_1(kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_h2_1(60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_h2_1(kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_h2_1(z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_h2_1(zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_h2_1(1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_h2_1(kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_h2_1(kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_h2_1(z0) << "\n";
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_gab8e5dcb27d3ca0fce7ed2f7e69218f88.html b/group__functions_gab8e5dcb27d3ca0fce7ed2f7e69218f88.html new file mode 100644 index 00000000..83c318db --- /dev/null +++ b/group__functions_gab8e5dcb27d3ca0fce7ed2f7e69218f88.html @@ -0,0 +1,226 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_yn + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
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+
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+
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+
+
+
+
+ +
+ +

◆ sph_bessel_yn

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_yn = {}
+ 		+inlineconstexpr
+
+ +

Computes the spherical Bessel functions of the first kind \(y_{n}(x)\), extended to the complex plane and cayley_dickson algebras.

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_yn(int n, T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr T sph_bessel_yn(int n, T z) noexcept;
+
}
+
kyosu::sph_bessel_yn
constexpr tags::callable_sph_bessel_yn sph_bessel_yn
Computes the spherical Bessel functions of the first kind , extended to the complex plane and cayley_...
Definition: sph_bessel_yn.hpp:73
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(y_n(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
size_t n = 12;
+
using kyosu::cyl_bessel_yn;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << cyl_bessel_yn(n,1.0) << "\n";
+
std::cout << "1+0i " << " -> " << cyl_bessel_yn(n,kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << cyl_bessel_yn(n,15.0) << "\n";
+
std::cout << "15+0i " << " -> " << cyl_bessel_yn(n,kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << cyl_bessel_yn(n,40.0) << "\n";
+
std::cout << "40+0i " << " -> " << cyl_bessel_yn(n,kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << cyl_bessel_yn(n,60.0) << "\n";
+
std::cout << "60+0i " << " -> " << cyl_bessel_yn(n,kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << cyl_bessel_yn(n,z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(cyl_bessel_yn(n,zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << cyl_bessel_yn(n,1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << cyl_bessel_yn(n,kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << cyl_bessel_yn(n,kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << cyl_bessel_yn(n,z0) << "\n";
+
+
+
for(int i=75; i < 100; ++i)
+
std::cout << "i " << i << " -> " << kyosu::sph_bessel_yn(i,kyosu::complex(1.0, 1.0)) << "\n";
+
+
+
return 0;
+
}
+
kyosu::cyl_bessel_yn
constexpr tags::callable_cyl_bessel_yn cyl_bessel_yn
Computes the modified Bessel functions of the second kind, , extended to the complex plane and cayley...
Definition: cyl_bessel_yn.hpp:74
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_gabf9e786b1c33a3f38029543a6427c11a.html b/group__functions_gabf9e786b1c33a3f38029543a6427c11a.html new file mode 100644 index 00000000..c63bc694 --- /dev/null +++ b/group__functions_gabf9e786b1c33a3f38029543a6427c11a.html @@ -0,0 +1,226 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_h1n + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
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+
Searching...
+
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+
+
+
+
+ +
+ +

◆ sph_bessel_h1n

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_h1n = {}
+ 		+inlineconstexpr
+
+ +

Computes the spherical Bessel/hankel functions of the third kind, \( h_n^{(1)}(z) = j_n(z)+iy_n(z)\).

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_h1n(int n, T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr auto sph_bessel_h1n(int n, T z) noexcept;
+
}
+
kyosu::sph_bessel_h1n
constexpr tags::callable_sph_bessel_h1n sph_bessel_h1n
Computes the spherical Bessel/hankel functions of the third kind, .
Definition: sph_bessel_h1n.hpp:76
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(h_n^{(1)}(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
+
size_t n = 12;
+
using kyosu::sph_bessel_h1n;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_h1n(n,1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_h1n(n,kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_h1n(n,15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_h1n(n,kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_h1n(n,40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_h1n(n,kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_h1n(n,60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_h1n(n,kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_h1n(n,z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_h1n(n,zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_h1n(n,1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_h1n(n,kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_h1n(n,kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_h1n(n,z0) << "\n";
+
+
+
for(int i=75; i < 100; ++i)
+
std::cout << "i " << i << " -> " << kyosu::sph_bessel_h1n(i,kyosu::complex(1.0, 1.0)) << "\n";
+
+
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_gac15decb6616c1fc56afe415e0b60f5de.html b/group__functions_gac15decb6616c1fc56afe415e0b60f5de.html new file mode 100644 index 00000000..7f3edb70 --- /dev/null +++ b/group__functions_gac15decb6616c1fc56afe415e0b60f5de.html @@ -0,0 +1,218 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_j0 + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
Loading...
+
Searching...
+
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+
+
+
+
+ +
+ +

◆ sph_bessel_j0

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_j0 = {}
+ 		+inlineconstexpr
+
+ +

Computes the Bessel function of the first kind, \( j_0(x)=\sin z/z \) extended to the complex plane and cayley_dickson algebras.

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_j0(T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr T sph_bessel_j0(T z) noexcept;
+
}
+
kyosu::sph_bessel_j0
constexpr tags::callable_sph_bessel_j0 sph_bessel_j0
Computes the Bessel function of the first kind, extended to the complex plane and cayley_dickson alg...
Definition: sph_bessel_j0.hpp:72
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(j_0(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
using kyosu::sph_bessel_j0;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_j0(1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_j0(kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_j0(15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_j0(kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_j0(40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_j0(kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_j0(60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_j0(kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_j0(z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_j0(zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_j0(1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_j0(kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_j0(kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_j0(z0) << "\n";
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_gac5db660b955ba1f13a2a24d5b0489c3f.html b/group__functions_gac5db660b955ba1f13a2a24d5b0489c3f.html new file mode 100644 index 00000000..112fe66b --- /dev/null +++ b/group__functions_gac5db660b955ba1f13a2a24d5b0489c3f.html @@ -0,0 +1,219 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_k1 + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
Loading...
+
Searching...
+
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+
+
+
+
+ +
+ +

◆ sph_bessel_k1

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_k1 = {}
+ 		+inlineconstexpr
+
+ +

Computes the spherical Bessel function of the first kind, \( k_1(x)= (\pi/2) e^{-z}(1/z+1/z^2)\) extended to the complex plane and cayley_dickson algebras.

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_k1(T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr T sph_bessel_k1(T z) noexcept;
+
}
+
kyosu::sph_bessel_k1
constexpr tags::callable_sph_bessel_k1 sph_bessel_k1
Computes the spherical Bessel function of the first kind, extended to the complex plane and cayley_d...
Definition: sph_bessel_k1.hpp:76
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(k_1(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
using kyosu::sph_bessel_k1;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_k1(1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_k1(kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_k1(15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_k1(kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_k1(40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_k1(kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_k1(60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_k1(kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_k1(z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_k1(zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_k1(1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_k1(kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0j " << " -> " << sph_bessel_k1(kyosu::quaternion(1.0, 0.0, 36.0, 0.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_k1(kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_k1(z0) << "\n";
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_gad09488c0c7ff98bd6a299014fb40fd9e.html b/group__functions_gad09488c0c7ff98bd6a299014fb40fd9e.html new file mode 100644 index 00000000..51f09739 --- /dev/null +++ b/group__functions_gad09488c0c7ff98bd6a299014fb40fd9e.html @@ -0,0 +1,218 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_i2_1 + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
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+
Searching...
+
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+
+
+
+
+ +
+ +

◆ sph_bessel_i2_1

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_i2_1 = {}
+ 		+inlineconstexpr
+
+ +

Computes the Bessel function, \( i_1^{(2)}(z) = -y_1(iz)\) extended to the complex plane and cayley_dickson algebras.

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_i2_1(T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr T sph_bessel_i2_1(T z) noexcept;
+
}
+
kyosu::sph_bessel_i2_1
constexpr tags::callable_sph_bessel_i2_1 sph_bessel_i2_1
Computes the Bessel function, extended to the complex plane and cayley_dickson algebras.
Definition: sph_bessel_i2_1.hpp:77
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(i_1^{(2)}(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
using kyosu::sph_bessel_i2_1;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_i2_1(1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_i2_1(kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_i2_1(15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_i2_1(kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_i2_1(40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_i2_1(kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_i2_1(60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_i2_1(kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_i2_1(z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_i2_1(zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_i2_1(1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_i2_1(kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_i2_1(kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_i2_1(z0) << "\n";
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_gad70c0ed719461813ec9e9cda14c5751c.html b/group__functions_gad70c0ed719461813ec9e9cda14c5751c.html new file mode 100644 index 00000000..b72e8a86 --- /dev/null +++ b/group__functions_gad70c0ed719461813ec9e9cda14c5751c.html @@ -0,0 +1,218 @@ + + + + + + + + +kyosu: kyosu::sph_bessel_h1_0 + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
Loading...
+
Searching...
+
No Matches
+
+
+
+
+ +
+ +

◆ sph_bessel_h1_0

+ +
+
+ + + + + +
+ + + + +
kyosu::sph_bessel_h1_0 = {}
+ 		+inlineconstexpr
+
+ +

Computes the spherical Bessel/hankel functions of the third kind, \( h_0^{(1)}(z) = j_1(z)+iy_1(z)\).

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_h1_0(int n, T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr auto sph_bessel_h1_0(int n, T z) noexcept;
+
}
+
kyosu::sph_bessel_h1_0
constexpr tags::callable_sph_bessel_h1_0 sph_bessel_h1_0
Computes the spherical Bessel/hankel functions of the third kind, .
Definition: sph_bessel_h1_0.hpp:76
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(h_0^{(1)}(z)\).
    • +
+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
using kyosu::sph_bessel_h1_0;
+
std::cout.precision(16);
+
std::cout << std::scientific << std::endl;
+
std::cout << "1.0 " << " -> " << sph_bessel_h1_0(1.0) << "\n";
+
std::cout << "1+0i " << " -> " << sph_bessel_h1_0(kyosu::complex(1.0, 0.0)) << "\n";
+
std::cout << "15.0 " << " -> " << sph_bessel_h1_0(15.0) << "\n";
+
std::cout << "15+0i " << " -> " << sph_bessel_h1_0(kyosu::complex(15.0, 0.0)) << "\n";
+
std::cout << "40.0 " << " -> " << sph_bessel_h1_0(40.0) << "\n";
+
std::cout << "40+0i " << " -> " << sph_bessel_h1_0(kyosu::complex(40.0, 0.0)) << "\n";
+
std::cout << "60.0 " << " -> " << sph_bessel_h1_0(60.0) << "\n";
+
std::cout << "60+0i " << " -> " << sph_bessel_h1_0(kyosu::complex(60.0, 0.0)) << "\n";
+
+
eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+
auto zz = kyosu::complex(z);
+
std::cout << z << "\n -> " << sph_bessel_h1_0(z) << "\n";
+
std::cout << zz << "\n -> " << kyosu::real(sph_bessel_h1_0(zz)) << "\n";
+
+
std::cout << "1.0 " << " -> " << sph_bessel_h1_0(1.0) << "\n";
+
std::cout << "1.0+36.0i " << " -> " << sph_bessel_h1_0(kyosu::complex(1.0, 36.0)) << "\n";
+
std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << sph_bessel_h1_0(kyosu::quaternion(1.0, 36.0, 2.0, 1.5)) << "\n";
+
+
+
eve::wide<double, eve::fixed<4>> z1(1.0, 2.0, 40.0, 0.0), z2(36.0, 0.5, 0.0, 40.0);
+
auto z0 = kyosu::complex(z1, z2);
+
std::cout << z0 << " \n-> " << sph_bessel_h1_0(z0) << "\n";
+
return 0;
+
}
+
kyosu::real
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
kyosu::quaternion
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_gae0bcc9ef41c3390b4dd85f9f3f8cd457.html b/group__functions_gae0bcc9ef41c3390b4dd85f9f3f8cd457.html new file mode 100644 index 00000000..cd503210 --- /dev/null +++ b/group__functions_gae0bcc9ef41c3390b4dd85f9f3f8cd457.html @@ -0,0 +1,208 @@ + + + + + + + + +kyosu: kyosu::sinhc + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
+
+ +   + + + + +
+
+
+ + + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+
+
+
+
+
Loading...
+
Searching...
+
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+
+
+
+
+ +
+ +

◆ sinhc

+ +
+
+ + + + + +
+ + + + +
kyosu::sinhc = {}
+ 		+inlineconstexpr
+
+ +

Computes the hyperbolic sine cardinal of the argument.

+

Defined in Header

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<kyosu::concepts::cayley_dickson T> constexpr auto sinhc(T z) noexcept;
+
template<eve::floating_ordered_value T> constexpr auto sinhc(T z) noexcept;
+
}
+
kyosu::sinhc
constexpr tags::callable_sinhc sinhc
Computes the hyperbolic sine cardinal of the argument.
Definition: sinhc.hpp:73
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • z: Value to process.
    • +
+

Return value

+

Returns the hyperbolic sine cardinal of the argument.

+

Example

+
#include <kyosu/kyosu.hpp>
+
#include <eve/wide.hpp>
+
#include <iostream>
+
+
int main()
+
{
+
using kyosu::sinhc;
+
using kyosu::complex_t;
+
using kyosu::quaternion_t;
+
+
std::cout << "Real: ";
+
std::cout << 12.9f << " -> " << sinhc(12.9f) << "\n";
+
+
std::cout << "Complex: ";
+
std::cout << kyosu::complex_t<float>(3.5f,-2.9f) << " -> " << sinhc(kyosu::complex_t<float>(3.5f,-2.9f)) << "\n";
+
+
std::cout << "Quaternion: ";
+
std::cout << kyosu::quaternion_t<double>(1.,2.,3.,4.) << " -> " << sinhc(kyosu::quaternion_t<double>(1.,2.,3.,4.)) << "\n";
+
+
std::cout << "SIMD: ";
+
using wc_t = eve::wide<kyosu::complex_t<double>, eve::fixed<2>>;
+
std::cout << wc_t(kyosu::complex_t<double>(1.3,-3.7)) << " -> " << sinhc(wc_t(kyosu::complex_t<double>(1.3,-3.7))) << "\n";
+
+
return 0;
+
}
+
kyosu::quaternion_t
as_cayley_dickson_n_t< 4, T > quaternion_t
Type alias for quaternion numbers.
Definition: quaternion.hpp:27
+
kyosu::complex_t
as_cayley_dickson_n_t< 2, T > complex_t
Type alias for complex numbers.
Definition: complex.hpp:27
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_gaeb24f578562330d825ff8f68da4b9252.html b/group__functions_gaeb24f578562330d825ff8f68da4b9252.html index 6e73930a..0374183c 100644 --- a/group__functions_gaeb24f578562330d825ff8f68da4b9252.html +++ b/group__functions_gaeb24f578562330d825ff8f68da4b9252.html @@ -150,7 +150,7 @@

{
auto from_angle_axis(auto angle, auto axis, auto norming = normalize) const noexcept;
}
-
kyosu::from_angle_axis
constexpr tags::callable_from_angle_axis from_angle_axis
Callable object computing an an unitary quaternion from an angle value and a 3 dimensionnal axis vect...
Definition: from_angle_axis.hpp:119
+
kyosu::from_angle_axis
constexpr tags::callable_from_angle_axis from_angle_axis
Callable object computing an an unitary quaternion from an angle value and a 3 dimensionnal axis vect...
Definition: from_angle_axis.hpp:115
kyosu
Main KYOSU namespace.
Definition: types.hpp:14

Parameters

    diff --git a/group__quaternion_gafb8e2e7cadea72110b134c4df850ee3a.html b/group__quaternion_gafb8e2e7cadea72110b134c4df850ee3a.html index 163b842f..b27927f7 100644 --- a/group__quaternion_gafb8e2e7cadea72110b134c4df850ee3a.html +++ b/group__quaternion_gafb8e2e7cadea72110b134c4df850ee3a.html @@ -178,7 +178,7 @@

    return 0;
    }
    -
    kyosu::from_angle_axis
    constexpr tags::callable_from_angle_axis from_angle_axis
    Callable object computing an an unitary quaternion from an angle value and a 3 dimensionnal axis vect...
    Definition: from_angle_axis.hpp:119
    +
    kyosu::from_angle_axis
    constexpr tags::callable_from_angle_axis from_angle_axis
    Callable object computing an an unitary quaternion from an angle value and a 3 dimensionnal axis vect...
    Definition: from_angle_axis.hpp:115
    diff --git a/index.html b/index.html index 7c89e3da..a932afd7 100644 --- a/index.html +++ b/index.html @@ -197,13 +197,13 @@

    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 dimensinalities. Of course the biggest dimensionlity is recovered in the output.

    +

    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.

    Functions

    -

    Most KYOSU callables are usable with all cayley_dickson types. The exception being mainly special complex functions and 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.
    +

    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.

    eve::acos(2.0) wil returns a NaN value, but kyosu::acos(2.0) will return the pure imaginary complex number \(i\;\log(2+\sqrt{3})\)

    All these kinds of functions called with a floating value in the kyosu namespace will return a complex value.

      @@ -272,7 +272,13 @@

      tanh to_polar tgamma trunc zeta
        -

      • callables usable with quaternion complex and real only

        +

      • Bessel functions

        +

        They deserve a separate list to avoid verbosity:

          +
        • cylindrical Bessel functions: cyl_bessel_xxx are all defined for xxx being j0, j1, jn, y0, y1, yn, i0, i1, in, h1_0, h1_1, h1n, h2_0, h2_1, h2n, k1, k0, kn.
          • +
        • spherical Bessel functions: sph_bessel_xxx are all defined for xxx being j0, j1, jn, y0, y1, yn, i1_0, i1_1, i1n, i2_0, i2_1, i2n, h1_0, h1_1, h1n, h2_0, h2_1 h2n, k1, k0, kn.
          • +
        +
        • +

      • Callables usable with quaternion complex and real only

        These functions are related to \(\mathbb{R}^3\) rotations

      diff --git a/namespacekyosu.html b/namespacekyosu.html index 947b11a5..4ac049ee 100644 --- a/namespacekyosu.html +++ b/namespacekyosu.html @@ -396,7 +396,7 @@  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 tags::callable_cyl_bessel_i1 cyl_bessel_i1 = {} - Computes the modified Bessel function of the first kind, \( I_1(x)= _iJ_1(ix) \) extended to the complex plane and cayley_dickson algebras.
      + 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 tags::callable_cyl_bessel_in cyl_bessel_in = {}  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.
      @@ -776,6 +776,9 @@ constexpr tags::callable_sinh sinh = {}  Computes the hyperbolic sine of the argument.
        +constexpr tags::callable_sinhc sinhc = {} + Computes the hyperbolic sine cardinal of the argument.
      +  constexpr tags::callable_sinhcosh sinhcosh = {}  Computes simultaneously the hyperbolic sine and cosine of the argument.
        @@ -788,6 +791,63 @@ constexpr tags::callable_slerp slerp = {}  Computes the spherical interpolation between unitary quaternions.
        +constexpr tags::callable_sph_bessel_h1_0 sph_bessel_h1_0 = {} + Computes the spherical Bessel/hankel functions of the third kind, \( h_0^{(1)}(z) = j_1(z)+iy_1(z)\).
      +  +constexpr tags::callable_sph_bessel_h1_1 sph_bessel_h1_1 = {} + Computes the spherical Bessel/hankel functions of the third kind, \( h_1^{(1)}(z) = j_1(z)+iy_1(z)\).
      +  +constexpr tags::callable_sph_bessel_h1n sph_bessel_h1n = {} + Computes the spherical Bessel/hankel functions of the third kind, \( h_n^{(1)}(z) = j_n(z)+iy_n(z)\).
      +  +constexpr tags::callable_sph_bessel_h2_0 sph_bessel_h2_0 = {} + Computes the spherical Bessel/hankel functions of the third kind, \( h_0^{(2)}(z) = j_0(z)-iy_0(z)\).
      +  +constexpr tags::callable_sph_bessel_h2_1 sph_bessel_h2_1 = {} + Computes the spherical Bessel/hankel functions of the third kind, \( h_1^{(2)}(z) = j_1(z)-iy_1(z)\).
      +  +constexpr tags::callable_sph_bessel_h2n sph_bessel_h2n = {} + Computes the spherical Bessel/hankel functions of the third kind, \( h_n^{(2)}(z) = j_n(z)-iy_n(z)\).
      +  +constexpr tags::callable_sph_bessel_i1_0 sph_bessel_i1_0 = {} + Computes the Bessel function, \( i_0^{(1)}(z) = j_n(iz)\) extended to the complex plane and cayley_dickson algebras.
      +  +constexpr tags::callable_sph_bessel_i1_1 sph_bessel_i1_1 = {} + Computes the Bessel function, \( i_1^{(1)}(z) = -i j_1(iz)\) extended to the complex plane and cayley_dickson algebras.
      +  +constexpr tags::callable_sph_bessel_i1n sph_bessel_i1n = {} + Computes the spherical Bessel functions \( i_n^{(1)}(z) = i^{-n}j_n(iz)\).
      +  +constexpr tags::callable_sph_bessel_i2_0 sph_bessel_i2_0 = {} + Computes the Bessel function, \( i_0^{(2)}(z) = -i y_n(iz)\) extended to the complex plane and cayley_dickson algebras.
      +  +constexpr tags::callable_sph_bessel_i2_1 sph_bessel_i2_1 = {} + Computes the Bessel function, \( i_1^{(2)}(z) = -y_1(iz)\) extended to the complex plane and cayley_dickson algebras.
      +  +constexpr tags::callable_sph_bessel_i2n sph_bessel_i2n = {} + Computes the spherical Bessel functions \( i_n^{(2)}(z) = i^{-n-1}y_n(iz)\).
      +  +constexpr tags::callable_sph_bessel_j0 sph_bessel_j0 = {} + Computes the Bessel function of the first kind, \( j_0(x)=\sin z/z \) extended to the complex plane and cayley_dickson algebras.
      +  +constexpr tags::callable_sph_bessel_jn sph_bessel_jn = {} + Computes the spherical Bessel functions of the first kind \(j_{n}(x)\), extended to the complex plane and cayley_dickson algebras.
      +  +constexpr tags::callable_sph_bessel_k0 sph_bessel_k0 = {} + Computes the spherical Bessel function of the first kind, \( k_0(x)= \pi e^{-z}/(2z) \) extended to the complex plane and cayley_dickson algebras.
      +  +constexpr tags::callable_sph_bessel_k1 sph_bessel_k1 = {} + Computes the spherical Bessel function of the first kind, \( k_1(x)= (\pi/2) e^{-z}(1/z+1/z^2)\) extended to the complex plane and cayley_dickson algebras.
      +  +constexpr tags::callable_sph_bessel_kn sph_bessel_kn = {} + Computes the spherical Bessel functions \(k_{n}(x)\), extended to the complex plane and cayley_dickson algebras.
      +  +constexpr tags::callable_sph_bessel_y0 sph_bessel_y0 = {} + 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 tags::callable_sph_bessel_yn sph_bessel_yn = {} + Computes the spherical Bessel functions of the first kind \(y_{n}(x)\), extended to the complex plane and cayley_dickson algebras.
      +  constexpr tags::callable_sqr sqr = {}  Computes the square value.
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