From e6ae8bde9f817c330489da996b7b008bd9658c10 Mon Sep 17 00:00:00 2001 From: jfalcou Date: Fri, 15 Dec 2023 18:22:00 +0000 Subject: [PATCH] deploy: 914acca186103358cd18594c423431613b5f9abf --- dir_12c6a5b07df34aef879622d954c76196.html | 4 + dir_177876519b6c2fe776705e228d283fc7.html | 143 ++++++++++++ dir_603762341fae708cb1fd302d853e09e1.html | 143 ++++++++++++ group__functions.html | 42 +++- ...ns_ga0155afce8a03c6d97c771e0b764cc9a8.html | 196 ++++++++++++++++ ...ns_ga25d1d487644b360a20917f1ef7176fb9.html | 217 +++++++++++++++++ ...ns_ga270b8ac2d250b8abc40eb9198c8ba2ac.html | 212 +++++++++++++++++ ...ns_ga307f7bf98b0a57927aefe945a1addc35.html | 206 +++++++++++++++++ ...ns_ga5a48ea11c00ce56c6ead01f9fd2990f4.html | 4 +- ...ns_ga5b438623b13a87948a9e9a36922b39d6.html | 207 +++++++++++++++++ ...ns_ga5cba68185585e3a3df8cbf73736e6c81.html | 45 +++- ...ns_ga639104aa250364e553c61cfb0754358c.html | 196 ++++++++++++++++ ...ns_ga658858c9e724f37a163126c8e24b80e5.html | 6 + ...ns_ga73b9c389e1b28c1c5c1d414768ca3adf.html | 196 ++++++++++++++++ ...ns_ga82af5f221c47d5769a5619d14baf2998.html | 196 ++++++++++++++++ ...ns_ga96400e65eaf1b63c5ab88ba5aff6d818.html | 15 +- ...ns_ga9987b97d382dd2cffa30b1b196c161f4.html | 45 +++- ...ns_ga9b7a275aff934ab54c1bc52599cf5371.html | 212 +++++++++++++++++ ...ns_ga9d8707d3de321182b50e9bee1728a3c6.html | 216 +++++++++++++++++ ...ns_gaa200851cb18a56a131469203b3b5f9fa.html | 218 ++++++++++++++++++ ...ns_gaaad895e7ba266d0e4d531d43ea44e273.html | 4 +- ...ns_gab07b0b22e10bac659c95fd81ea819086.html | 13 +- ...ns_gab8e5dcb27d3ca0fce7ed2f7e69218f88.html | 6 +- ...ns_gad889d1c4424dc0752a3d939b7a32de05.html | 218 ++++++++++++++++++ ...ns_gaf7b3924df2aa81781473dfc547daf604.html | 2 +- ...ns_gafc9416d5a0fb124785d4f67369ce665a.html | 208 +++++++++++++++++ index.html | 10 +- namespacekyosu.html | 42 +++- navtreedata.js | 10 +- navtreeindex0.js | 10 +- search/all_2.js | 41 ++-- search/variables_2.js | 41 ++-- 32 files changed, 3255 insertions(+), 69 deletions(-) create mode 100644 dir_177876519b6c2fe776705e228d283fc7.html create mode 100644 dir_603762341fae708cb1fd302d853e09e1.html create mode 100644 group__functions_ga0155afce8a03c6d97c771e0b764cc9a8.html create mode 100644 group__functions_ga25d1d487644b360a20917f1ef7176fb9.html create mode 100644 group__functions_ga270b8ac2d250b8abc40eb9198c8ba2ac.html create mode 100644 group__functions_ga307f7bf98b0a57927aefe945a1addc35.html create mode 100644 group__functions_ga5b438623b13a87948a9e9a36922b39d6.html create mode 100644 group__functions_ga639104aa250364e553c61cfb0754358c.html create mode 100644 group__functions_ga73b9c389e1b28c1c5c1d414768ca3adf.html create mode 100644 group__functions_ga82af5f221c47d5769a5619d14baf2998.html create mode 100644 group__functions_ga9b7a275aff934ab54c1bc52599cf5371.html create mode 100644 group__functions_ga9d8707d3de321182b50e9bee1728a3c6.html create mode 100644 group__functions_gaa200851cb18a56a131469203b3b5f9fa.html create mode 100644 group__functions_gad889d1c4424dc0752a3d939b7a32de05.html create mode 100644 group__functions_gafc9416d5a0fb124785d4f67369ce665a.html diff --git a/dir_12c6a5b07df34aef879622d954c76196.html b/dir_12c6a5b07df34aef879622d954c76196.html index ee477d0c..907563da 100644 --- a/dir_12c6a5b07df34aef879622d954c76196.html +++ b/dir_12c6a5b07df34aef879622d954c76196.html @@ -128,6 +128,10 @@ + + + + diff --git a/dir_177876519b6c2fe776705e228d283fc7.html b/dir_177876519b6c2fe776705e228d283fc7.html new file mode 100644 index 00000000..9f9d4ca0 --- /dev/null +++ b/dir_177876519b6c2fe776705e228d283fc7.html @@ -0,0 +1,143 @@ + + + + + + + + +kyosu: kyosu/types/impl/besselr Directory Reference + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+

Directories

directory  bessel
 
directory  besselr
 
directory  detail
 
directory  quaternion
+ + + + + + + +
+
kyosu v0.1.0 +
+
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besselr Directory Reference
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+
kyosu v0.1.0 +
+
Complex Without Complexes
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+ + + + + + + + + + diff --git a/group__functions.html b/group__functions.html index c2296d98..2db09875 100644 --- a/group__functions.html +++ b/group__functions.html @@ -244,32 +244,69 @@ constexpr tags::callable_cscpi kyosu::cscpi = {}  Computes the cosecant from the argument in \(\pi\) multiples.
  +constexpr tags::callable_cyl_bessel_h1 kyosu::cyl_bessel_h1 = {} + Computes the Bessel functions of the third kind \(H^{(1)}\),.
+  +constexpr tags::callable_cyl_bessel_h12 kyosu::cyl_bessel_h12 = {} + Computes the Bessel functions of the third kind \( H^{(1)} \) and \( H^{(2)} \),.
+  +constexpr tags::callable_cyl_bessel_h1_0 kyosu::cyl_bessel_h1_0 = {} + Computes the Bessel function of the third kind, \( H^{(1)}_0(x)\),.
+  +constexpr tags::callable_cyl_bessel_h1_1 kyosu::cyl_bessel_h1_1 = {} + Computes the Bessel function of the third kind, \( H^{(1)}_1(x)\),.
+  constexpr tags::callable_cyl_bessel_h1n kyosu::cyl_bessel_h1n = {}  Computes the Bessel/Hankel functions of the third kind, \( H_n^{(1)}(z) = J_n(z)+iY_n(z)\).
  +constexpr tags::callable_cyl_bessel_h2 kyosu::cyl_bessel_h2 = {} + Computes the Bessel functions of the third kind \( H^{(2)}_\nu \),.
+  +constexpr tags::callable_cyl_bessel_h2_0 kyosu::cyl_bessel_h2_0 = {} + Computes the Bessel function of the third kind, \( H^{(2)}_0(x)\).
+  +constexpr tags::callable_cyl_bessel_h2_1 kyosu::cyl_bessel_h2_1 = {} + Computes the Bessel function of the third kind, \( H^{(2)}_1(x)\),.
+  constexpr tags::callable_cyl_bessel_h2n kyosu::cyl_bessel_h2n = {}  Computes the Bessel/Hankel functions of the third kind , \( H_n^{(2)} = J_n(z)-iY_n(z)\).
  +constexpr tags::callable_cyl_bessel_i kyosu::cyl_bessel_i = {} + Computes the Modified Bessel functions of the first kind.
+  constexpr tags::callable_cyl_bessel_i0 kyosu::cyl_bessel_i0 = {}  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.
  +constexpr tags::callable_cyl_bessel_ik kyosu::cyl_bessel_ik = {} + Computes the modified Bessel functions \(I\) and \(K\),.
+  +constexpr tags::callable_cyl_bessel_ikn kyosu::cyl_bessel_ikn = {} + Computes the Bessel functions of the second kind \(I\) and \(K \)of integral order,.
+  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.
  +constexpr tags::callable_cyl_bessel_j kyosu::cyl_bessel_j = {} + 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 tags::callable_cyl_bessel_j0 kyosu::cyl_bessel_j0 = {}  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 tags::callable_cyl_bessel_j1 kyosu::cyl_bessel_j1 = {} - Computes the Bessel function of the first kind, \( J_1(x)=\frac1{\pi }\int _{0}^{\pi}\cos(\tau-x\sin \tau )\,\mathrm {d} \tau \) extended to the complex plane and cayley_dickson values. It is the solution of \( x^{2}y''+xy'+x^2y=0\) for which \( y(0) = 1\).
+ Computes the Bessel function of the first kind, \( J_1\).
  constexpr tags::callable_cyl_bessel_jn kyosu::cyl_bessel_jn = {}  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 values.
  +constexpr tags::callable_cyl_bessel_k kyosu::cyl_bessel_k = {} + Computes the Modified Bessel functions of the second kind.
+  constexpr tags::callable_cyl_bessel_k0 kyosu::cyl_bessel_k0 = {}  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.
  @@ -279,6 +316,9 @@ constexpr tags::callable_cyl_bessel_kn kyosu::cyl_bessel_kn = {}  Computes the modified Bessel functions of the second kind, \( K_{n}(x)=\lim_{\alpha\to n}{\frac {\pi }{2}}{\frac {I_{-\alpha }(x)-I_{\alpha }(x)}{\sin \alpha \pi }}\). extended to the complex plane and cayley_dickson algebras.
  +constexpr tags::callable_cyl_bessel_y kyosu::cyl_bessel_y = {} + Computes the Bessel functions of the second kind,.
+  constexpr tags::callable_cyl_bessel_y0 kyosu::cyl_bessel_y0 = {}  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.
  diff --git a/group__functions_ga0155afce8a03c6d97c771e0b764cc9a8.html b/group__functions_ga0155afce8a03c6d97c771e0b764cc9a8.html new file mode 100644 index 00000000..cbc84c68 --- /dev/null +++ b/group__functions_ga0155afce8a03c6d97c771e0b764cc9a8.html @@ -0,0 +1,196 @@ + + + + + + + + +kyosu: kyosu::cyl_bessel_h1_1 + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
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+
kyosu v0.1.0 +
+
Complex Without Complexes
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◆ cyl_bessel_h1_1

+ +
+
+ + + + + +
+ + + + +
kyosu::cyl_bessel_h1_1 = {}
+ 		+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 tags::callable_cyl_bessel_h1_1 cyl_bessel_h1_1
Computes the Bessel function of the third kind, ,.
Definition: cyl_bessel_h1_1.hpp:75
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

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 tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
+
+
+
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+ + + + + + + + + + diff --git a/group__functions_ga25d1d487644b360a20917f1ef7176fb9.html b/group__functions_ga25d1d487644b360a20917f1ef7176fb9.html new file mode 100644 index 00000000..333918ba --- /dev/null +++ b/group__functions_ga25d1d487644b360a20917f1ef7176fb9.html @@ -0,0 +1,217 @@ + + + + + + + + +kyosu: kyosu::cyl_bessel_i + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
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◆ cyl_bessel_i

+ +
+
+ + + + + +
+ + + + +
kyosu::cyl_bessel_i = {}
+ 		+inlineconstexpr
+
+ +

Computes the Modified Bessel functions of the first kind.

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<eve::floating_ordered_value, kyosu::concepts::cayley_dickson T>
+
constexpr auto cyl_bessel_i(N nu, T z) noexcept;
+
+
template<eve::floating_ordered_value, eve::floating_ordered_value T>
+
constexpr T cyl_bessel_i(N nu, T z) noexcept;
+
+
template<eve::floating_ordered_value, kyosu::concepts::cayley_dickson T, Range R>
+
constexpr auto cyl_bessel_i(N nu, T z, R & is) noexcept;
+
+
template<eve::floating_ordered_value, eve::floating_ordered_value T, Range R>
+
constexpr T cyl_bessel_i(N nu, T z, R& is) noexcept;
+
}
+
kyosu::cyl_bessel_i
constexpr tags::callable_cyl_bessel_i cyl_bessel_i
Computes the Modified Bessel functions of the first kind.
Definition: cyl_bessel_i.hpp:106
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • nu: order of the function.
    • +
  • z: Value to process.
    • +
  • is: Ouput range able to contain n = int(abs(nu))+1 complex values (of type complex_t<T> or Z respectively)
    • +
+

Return value

+
    +
  • returns \(I_\nu(z)\).
    • +
+

*Ouput values

+
    +
  • on output (if present) 1s contains the values of \( (I^{(1)}_{\nu_0+\epsilon i})_{i = 0 \cdots n} \); where \( \nu_0 \) is the fractional part of \(\nu\) and \(\epsilon\) is the sign of \( \nu\).
    • +
+

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));
+
auto v = 3.3;
+
std::cout << "z " << z << std::endl;
+
std::vector<decltype(z)> is(4);
+
kyosu::cyl_bessel_i(v, z, is);
+
for(int n=0; n <= 3; ++n)
+
{
+
std::cout << "is[" << n << "] = " << is[n] << std::endl;
+
}
+
return 0;
+
}
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
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+
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+ + + + + + + + + + diff --git a/group__functions_ga270b8ac2d250b8abc40eb9198c8ba2ac.html b/group__functions_ga270b8ac2d250b8abc40eb9198c8ba2ac.html new file mode 100644 index 00000000..1e4b2239 --- /dev/null +++ b/group__functions_ga270b8ac2d250b8abc40eb9198c8ba2ac.html @@ -0,0 +1,212 @@ + + + + + + + + +kyosu: kyosu::cyl_bessel_h12 + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
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◆ cyl_bessel_h12

+ +
+
+ + + + + +
+ + + + +
kyosu::cyl_bessel_h12 = {}
+ 		+inlineconstexpr
+
+ +

Computes the Bessel functions of the third kind \( H^{(1)} \) and \( H^{(2)} \),.

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<eve::floating_scalar_value N, eve::floating_ordered_value T, complexRange R1, complexRange R2>
+
constexpr auto cyl_bessel_h12(N nu, T z, R1& h1s, R2& h2s) noexcept;
+
+
template<eve::floating_scalar_value N, conceots::kyosu::complex Z, complexRange R1, complexRange R2>
+
constexpr T cyl_bessel_h12(N nu, Z z, R1& h1s, R2& h2s) noexcept;
+
}
+
kyosu::cyl_bessel_h12
constexpr tags::callable_cyl_bessel_h12 cyl_bessel_h12
Computes the Bessel functions of the third kind and ,.
Definition: cyl_bessel_h12.hpp:87
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • n: scalar floating order of the function.
    • +
  • z: Value to process.
    • +
  • h1s: range able to containn = int(abs(nu))+1complex values (of type complex_t<T> or Z respectively) *h2s: range able to contain n = int(abs(nu))+1 complex values (of type complex_t<T> or Z respectively)
    • +
+

Return value

+
    +
  • returns the kumi pair \( \{ H^{(1)}_\nu(z). H^{(2)}_\nu(z) \} \).
    • +
+

*Ouput values

+
    +
  • on output (if present) h1s and h2s contains the values of \( (H^{(1\|2)}_{\nu_0+\epsilon i})_{i = 0 \cdots n} \) respectively, where \( \nu_0 \) is the fractional part of \(\nu\) and \(\epsilon\) is the sign of \( \nu\).
    • +
+

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));
+
auto v = 3.3;
+
std::cout << "z " << z << std::endl;
+
std::vector<decltype(z)> h1(4), h2(4);
+
kyosu::cyl_bessel_h12(v, z, h1, h2);
+
for(int n=0; n <= 3; ++n)
+
{
+
std::cout << "h1[" << n << "] = " << h1[n] << std::endl;
+
std::cout << "h2[" << n << "] = " << h2[n] << std::endl;
+
}
+
return 0;
+
}
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_ga307f7bf98b0a57927aefe945a1addc35.html b/group__functions_ga307f7bf98b0a57927aefe945a1addc35.html new file mode 100644 index 00000000..82858046 --- /dev/null +++ b/group__functions_ga307f7bf98b0a57927aefe945a1addc35.html @@ -0,0 +1,206 @@ + + + + + + + + +kyosu: kyosu::cyl_bessel_k + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
+ + + + + + + + +
+
kyosu v0.1.0 +
+
Complex Without Complexes
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◆ cyl_bessel_k

+ +
+
+ + + + + +
+ + + + +
kyosu::cyl_bessel_k = {}
+ 		+inlineconstexpr
+
+ +

Computes the Modified Bessel functions of the second kind.

+
#include <kyosu/functions.hpp>
+

Callable Signatures

+
namespace kyosu
+
{
+
template<eve::floating_ordered_value, kyosu::concepts::cayley_dickson T>
+
constexpr auto cyl_bessel_k(N nu, T z) noexcept;
+
+
template<eve::floating_ordered_value, eve::floating_ordered_value T>
+
constexpr T cyl_bessel_k(N n, T z) noexcept;
+
}
+
kyosu::cyl_bessel_k
constexpr tags::callable_cyl_bessel_k cyl_bessel_k
Computes the Modified Bessel functions of the second kind.
Definition: cyl_bessel_k.hpp:95
+
kyosu
Main KYOSU namespace.
Definition: types.hpp:14
+

Parameters

+
    +
  • nu: order of the function.
    • +
  • z: Value to process.
    • +
+

Return value

+
    +
  • returns \(K_\nu(z)\).
    • +
+

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));
+
auto v = 3.3;
+
std::cout << "z " << z << std::endl;
+
std::vector<decltype(z)> ks(4);
+
kyosu::cyl_bessel_k(v, z, ks);
+
for(int n=0; n <= 3; ++n)
+
{
+
std::cout << "ks[" << n << "] = " << ks[n] << std::endl;
+
}
+
return 0;
+
}
+
kyosu::complex
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
+
+
+
+
+ + + + + + + + + + diff --git a/group__functions_ga5a48ea11c00ce56c6ead01f9fd2990f4.html b/group__functions_ga5a48ea11c00ce56c6ead01f9fd2990f4.html index 8be6cb1d..b294ee29 100644 --- a/group__functions_ga5a48ea11c00ce56c6ead01f9fd2990f4.html +++ b/group__functions_ga5a48ea11c00ce56c6ead01f9fd2990f4.html @@ -150,7 +150,7 @@

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::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:87
kyosu
Main KYOSU namespace.
Definition: types.hpp:14

Parameters

    @@ -196,7 +196,7 @@

    Example

    std::cout << z0 << " \n-> " << sph_bessel_jn(n,z0) << "\n";
    -
    for(int i=75; i < 100; ++i)
    +
    for(int i = 0; i < 10; ++i)
    std::cout << "i " << i << " -> " << kyosu::sph_bessel_jn(i,kyosu::complex(1.0, 1.0)) << "\n";
    diff --git a/group__functions_ga5b438623b13a87948a9e9a36922b39d6.html b/group__functions_ga5b438623b13a87948a9e9a36922b39d6.html new file mode 100644 index 00000000..afa3edb0 --- /dev/null +++ b/group__functions_ga5b438623b13a87948a9e9a36922b39d6.html @@ -0,0 +1,207 @@ + + + + + + + + +kyosu: kyosu::cyl_bessel_y + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + +
    + + + + + + + + +
    +
    kyosu v0.1.0 +
    +
    Complex Without Complexes
    +
    + +   + + + + +
    +
    +
    + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    +
    +
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    +
    +
    Loading...
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    +
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    +
    + +
    + +

    ◆ cyl_bessel_y

    + +
    +
    + + + + + +
    + + + + +
    kyosu::cyl_bessel_y = {}
    +     		+inlineconstexpr
    +
    + +

    Computes the Bessel functions of the second kind,.

    +
    #include <kyosu/functions.hpp>
    +

    Callable Signatures

    +
    namespace kyosu
    +
    {
    +
    template<eve::floating_ordered_value, kyosu::concepts::cayley_dickson T>
    +
    constexpr auto cyl_bessel_y(N nu, T z) noexcept;
    +
    +
    template<eve::floating_ordered_value, eve::floating_ordered_value T>
    +
    constexpr T cyl_bessel_y(N n, T z) noexcept;
    +
    }
    +
    kyosu::cyl_bessel_y
    constexpr tags::callable_cyl_bessel_y cyl_bessel_y
    Computes the Bessel functions of the second kind,.
    Definition: cyl_bessel_y.hpp:80
    +
    kyosu
    Main KYOSU namespace.
    Definition: types.hpp:14
    +

    Parameters

    +
      +
    • nu: order of the function.
      • +
    • z: Value to process.
      • +
    +

    Return value

    +
      +
    • returns \(Y_\nu(z)\).
      • +
    +

    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));
    +
    auto v = 3.3;
    +
    std::cout << "z " << z << std::endl;
    +
    std::vector<decltype(z)> is(4);
    +
    kyosu::cyl_bessel_i(v, z, is);
    +
    for(int n=0; n <= 3; ++n)
    +
    {
    +
    std::cout << "is[" << n << "] = " << is[n] << std::endl;
    +
    }
    +
    return 0;
    +
    }
    +
    kyosu::cyl_bessel_i
    constexpr tags::callable_cyl_bessel_i cyl_bessel_i
    Computes the Modified Bessel functions of the first kind.
    Definition: cyl_bessel_i.hpp:106
    +
    kyosu::complex
    constexpr tags::callable_complex complex
    Constructs a kyosu::complex.
    Definition: to_complex.hpp:70
    +
    +
    +
    +
    +
    + + + + + + + + + + diff --git a/group__functions_ga5cba68185585e3a3df8cbf73736e6c81.html b/group__functions_ga5cba68185585e3a3df8cbf73736e6c81.html index 32f20a34..a91b6344 100644 --- a/group__functions_ga5cba68185585e3a3df8cbf73736e6c81.html +++ b/group__functions_ga5cba68185585e3a3df8cbf73736e6c81.html @@ -161,7 +161,50 @@

    Example

    -
    +
    #include <kyosu/kyosu.hpp>
    +
    #include <eve/wide.hpp>
    +
    #include <iostream>
    +
    +
    int main()
    +
    {
    +
    using kyosu::cyl_bessel_k0;
    +
    std::cout.precision(16);
    +
    +
    std::cout << "1.0 " << " -> " << cyl_bessel_k0(1.0) << "\n";
    +
    std::cout << "1+0i " << " -> " << cyl_bessel_k0(kyosu::complex(1.0, 0.0)) << "\n";
    +
    std::cout << "15.0 " << " -> " << cyl_bessel_k0(15.0) << "\n";
    +
    std::cout << "15+0i " << " -> " << cyl_bessel_k0(kyosu::complex(15.0, 0.0)) << "\n";
    +
    std::cout << "40.0 " << " -> " << cyl_bessel_k0(40.0) << "\n";
    +
    std::cout << "40+0i " << " -> " << cyl_bessel_k0(kyosu::complex(40.0, 0.0)) << "\n";
    +
    std::cout << "60.0 " << " -> " << cyl_bessel_k0(60.0) << "\n";
    +
    std::cout << "60+0i " << " -> " << cyl_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" << cyl_bessel_k0(z) << "\n";
    +
    std::cout << zz << " -> \n" << cyl_bessel_k0(zz) << "\n";
    +
    +
    std::cout << "1.0 " << " -> " << cyl_bessel_k0(1.0) << "\n";
    +
    std::cout << "1.0+36.0i " << " -> " << cyl_bessel_k0(kyosu::complex(1.0, 36.0)) << "\n";
    +
    std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << cyl_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 -> " << cyl_bessel_k0(z0) << "\n";
    +
    +
    eve::wide<double, eve::fixed<8>> l(1.0, 15.0, 40.0, 60.0, eve::inf(eve::as<double>()),eve::minf(eve::as<double>()), eve::nan(eve::as<double>()), 0.0);
    +
    auto lims = kyosu::complex(l);
    +
    std::cout << lims << " -> \n" << cyl_bessel_k0(lims) << "\n";
    +
    std::cout << l << " -> \n" << cyl_bessel_k0(l) << "\n";
    +
    auto nanan = kyosu::complex(eve::nan(eve::as<double>()), eve::nan(eve::as<double>()));
    +
    std::cout << nanan << " -> \n" << cyl_bessel_k0(nanan) << std::endl;
    +
    +
    return 0;
    +
    }
    +
    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_ga639104aa250364e553c61cfb0754358c.html b/group__functions_ga639104aa250364e553c61cfb0754358c.html new file mode 100644 index 00000000..61885993 --- /dev/null +++ b/group__functions_ga639104aa250364e553c61cfb0754358c.html @@ -0,0 +1,196 @@ + + + + + + + + +kyosu: kyosu::cyl_bessel_h2_0 + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + +
    + + + + + + + + +
    +
    kyosu v0.1.0 +
    +
    Complex Without Complexes
    +
    + +   + + + + +
    +
    +
    + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +
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    +
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    +
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    +
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    + +

    ◆ cyl_bessel_h2_0

    + +
    +
    + + + + + +
    + + + + +
    kyosu::cyl_bessel_h2_0 = {}
    +     		+inlineconstexpr
    +
    + +

    Computes the Bessel function of the third kind, \( H^{(2)}_0(x)\).

    +
    #include <kyosu/functions.hpp>
    +

    Callable Signatures

    +
    namespace kyosu
    +
    {
    +
    template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_h2_0(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T cyl_bessel_h2_0(T z) noexcept;
    +
    }
    +
    kyosu::cyl_bessel_h2_0
    constexpr tags::callable_cyl_bessel_h2_0 cyl_bessel_h2_0
    Computes the Bessel function of the third kind, .
    Definition: cyl_bessel_h2_0.hpp:74
    +
    kyosu
    Main KYOSU namespace.
    Definition: types.hpp:14
    +

    Parameters

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

    Return value

    +
      +
    • returns \( H^{(2)}_0(x)\).
      • +
    +

    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_h2_0(z) " << kyosu::cyl_bessel_h2_0(z) << std::endl;
    +
    return 0;
    +
    }
    +
    kyosu::complex
    constexpr tags::callable_complex complex
    Constructs a kyosu::complex.
    Definition: to_complex.hpp:70
    +
    +
    +
    +
    +
    + + + + + + + + + + diff --git a/group__functions_ga658858c9e724f37a163126c8e24b80e5.html b/group__functions_ga658858c9e724f37a163126c8e24b80e5.html index f08a4b79..06eeffdb 100644 --- a/group__functions_ga658858c9e724f37a163126c8e24b80e5.html +++ b/group__functions_ga658858c9e724f37a163126c8e24b80e5.html @@ -192,6 +192,12 @@

    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_y1(z0) << "\n";
    +
    +
    eve::wide<double, eve::fixed<8>> l(1.0, 15.0, 40.0, 60.0, eve::inf(eve::as<double>()),eve::minf(eve::as<double>()), eve::nan(eve::as<double>()), 0.0);
    +
    auto lims = kyosu::complex(l);
    +
    std::cout << lims << " \n -> \n" << kyosu::cyl_bessel_y1(lims) << "\n";
    +
    std::cout << l << " \n -> \n" << cyl_bessel_y1(l) << "\n";
    +
    return 0;
    }
    kyosu::complex
    constexpr tags::callable_complex complex
    Constructs a kyosu::complex.
    Definition: to_complex.hpp:70
    diff --git a/group__functions_ga73b9c389e1b28c1c5c1d414768ca3adf.html b/group__functions_ga73b9c389e1b28c1c5c1d414768ca3adf.html new file mode 100644 index 00000000..7f33eeed --- /dev/null +++ b/group__functions_ga73b9c389e1b28c1c5c1d414768ca3adf.html @@ -0,0 +1,196 @@ + + + + + + + + +kyosu: kyosu::cyl_bessel_h2_1 + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + +
    + + + + + + + + +
    +
    kyosu v0.1.0 +
    +
    Complex Without Complexes
    +
    + +   + + + + +
    +
    +
    + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    +
    +
    +
    +
    +
    Loading...
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    +
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    + +

    ◆ cyl_bessel_h2_1

    + +
    +
    + + + + + +
    + + + + +
    kyosu::cyl_bessel_h2_1 = {}
    +     		+inlineconstexpr
    +
    + +

    Computes the Bessel function of the third kind, \( H^{(2)}_1(x)\),.

    +
    #include <kyosu/functions.hpp>
    +

    Callable Signatures

    +
    namespace kyosu
    +
    {
    +
    template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_h2_1(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr T cyl_bessel_h2_1(T z) noexcept;
    +
    }
    +
    kyosu::cyl_bessel_h2_1
    constexpr tags::callable_cyl_bessel_h2_1 cyl_bessel_h2_1
    Computes the Bessel function of the third kind, ,.
    Definition: cyl_bessel_h2_1.hpp:75
    +
    kyosu
    Main KYOSU namespace.
    Definition: types.hpp:14
    +

    Parameters

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

    Return value

    +
      +
    • returns \( H^{(2)}_1(x)\).
      • +
    +

    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_h2_1(z) " << kyosu::cyl_bessel_h2_1(z) << std::endl;
    +
    return 0;
    +
    }
    +
    kyosu::complex
    constexpr tags::callable_complex complex
    Constructs a kyosu::complex.
    Definition: to_complex.hpp:70
    +
    +
    +
    +
    +
    + + + + + + + + + + diff --git a/group__functions_ga82af5f221c47d5769a5619d14baf2998.html b/group__functions_ga82af5f221c47d5769a5619d14baf2998.html new file mode 100644 index 00000000..15a2994c --- /dev/null +++ b/group__functions_ga82af5f221c47d5769a5619d14baf2998.html @@ -0,0 +1,196 @@ + + + + + + + + +kyosu: kyosu::cyl_bessel_h1_0 + + + + + + + + + + + + + + + + + + + + + + + + + + +
    + +
    + + + + + + + + +
    +
    kyosu v0.1.0 +
    +
    Complex Without Complexes
    +
    + +   + + + + +
    +
    +
    + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    +
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    +
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    + +

    ◆ cyl_bessel_h1_0

    + +
    +
    + + + + + +
    + + + + +
    kyosu::cyl_bessel_h1_0 = {}
    +     		+inlineconstexpr
    +
    + +

    Computes the Bessel function of the third kind, \( H^{(1)}_0(x)\),.

    +
    #include <kyosu/functions.hpp>
    +

    Callable Signatures

    +
    namespace kyosu
    +
    {
    +
    template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_h1_0(T z) noexcept;
    +
    template<eve::floating_ordered_value T> constexpr auto cyl_bessel_h1_0(T z) noexcept;
    +
    }
    +
    kyosu::cyl_bessel_h1_0
    constexpr tags::callable_cyl_bessel_h1_0 cyl_bessel_h1_0
    Computes the Bessel function of the third kind, ,.
    Definition: cyl_bessel_h1_0.hpp:75
    +
    kyosu
    Main KYOSU namespace.
    Definition: types.hpp:14
    +

    Parameters

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

    Return value

    +
      +
    • returns \( H^{(1)}_0(x)\).
      • +
    +

    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_0(z) " << kyosu::cyl_bessel_h1_0(z) << std::endl;
    +
    return 0;
    +
    }
    +
    kyosu::complex
    constexpr tags::callable_complex complex
    Constructs a kyosu::complex.
    Definition: to_complex.hpp:70
    +
    +
    +
    +
    +
    + + + + + + + + + + diff --git a/group__functions_ga96400e65eaf1b63c5ab88ba5aff6d818.html b/group__functions_ga96400e65eaf1b63c5ab88ba5aff6d818.html index 16e83595..a4b1debb 100644 --- a/group__functions_ga96400e65eaf1b63c5ab88ba5aff6d818.html +++ b/group__functions_ga96400e65eaf1b63c5ab88ba5aff6d818.html @@ -150,7 +150,7 @@

    template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_yn(int n, T z) noexcept;
    template<eve::floating_ordered_value N, eve::floating_ordered_value T> constexpr T cyl_bessel_yn(N n, T z) noexcept;
    }
    -
    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::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:89
    kyosu
    Main KYOSU namespace.
    Definition: types.hpp:14

    Parameters

      @@ -167,12 +167,12 @@

      Example

      int main()
      {
      -
      size_t n = 12;
      +
      size_t n = 3;
      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 << "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";
      @@ -193,18 +193,11 @@

      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
      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
      -
      kyosu::i
      constexpr tags::callable_i i
      Computes the complex number cinf i.e. complex(nan, inf) in the chosen type.
      Definition: i.hpp:77
      diff --git a/group__functions_ga9987b97d382dd2cffa30b1b196c161f4.html b/group__functions_ga9987b97d382dd2cffa30b1b196c161f4.html index becc83be..fbf519b4 100644 --- a/group__functions_ga9987b97d382dd2cffa30b1b196c161f4.html +++ b/group__functions_ga9987b97d382dd2cffa30b1b196c161f4.html @@ -161,7 +161,50 @@

      Example

      -
      +
      #include <kyosu/kyosu.hpp>
      +
      #include <eve/wide.hpp>
      +
      #include <iostream>
      +
      +
      int main()
      +
      {
      +
      using kyosu::cyl_bessel_k1;
      +
      std::cout.precision(16);
      +
      +
      std::cout << "1.0 " << " -> " << cyl_bessel_k1(1.0) << "\n";
      +
      std::cout << "1+0i " << " -> " << cyl_bessel_k1(kyosu::complex(1.0, 0.0)) << "\n";
      +
      std::cout << "15.0 " << " -> " << cyl_bessel_k1(15.0) << "\n";
      +
      std::cout << "15+0i " << " -> " << cyl_bessel_k1(kyosu::complex(15.0, 0.0)) << "\n";
      +
      std::cout << "40.0 " << " -> " << cyl_bessel_k1(40.0) << "\n";
      +
      std::cout << "40+0i " << " -> " << cyl_bessel_k1(kyosu::complex(40.0, 0.0)) << "\n";
      +
      std::cout << "60.0 " << " -> " << cyl_bessel_k1(60.0) << "\n";
      +
      std::cout << "60+0i " << " -> " << cyl_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" << cyl_bessel_k1(z) << "\n";
      +
      std::cout << zz << " -> \n" << cyl_bessel_k1(zz) << "\n";
      +
      +
      std::cout << "1.0 " << " -> " << cyl_bessel_k1(1.0) << "\n";
      +
      std::cout << "1.0+36.0i " << " -> " << cyl_bessel_k1(kyosu::complex(1.0, 36.0)) << "\n";
      +
      std::cout << "1.0+36.0i+2.0j+1.5k " << " -> " << cyl_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 -> " << cyl_bessel_k1(z0) << "\n";
      +
      +
      eve::wide<double, eve::fixed<8>> l(1.0, 15.0, 40.0, 60.0, eve::inf(eve::as<double>()),eve::minf(eve::as<double>()), eve::nan(eve::as<double>()), 0.0);
      +
      auto lims = kyosu::complex(l);
      +
      std::cout << lims << " -> \n" << cyl_bessel_k1(lims) << "\n";
      +
      std::cout << l << " -> \n" << cyl_bessel_k1(l) << "\n";
      +
      auto nanan = kyosu::complex(eve::nan(eve::as<double>()), eve::nan(eve::as<double>()));
      +
      std::cout << nanan << " -> \n" << cyl_bessel_k1(nanan) << std::endl;
      +
      +
      return 0;
      +
      }
      +
      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_ga9b7a275aff934ab54c1bc52599cf5371.html b/group__functions_ga9b7a275aff934ab54c1bc52599cf5371.html new file mode 100644 index 00000000..c8e0836a --- /dev/null +++ b/group__functions_ga9b7a275aff934ab54c1bc52599cf5371.html @@ -0,0 +1,212 @@ + + + + + + + + +kyosu: kyosu::cyl_bessel_ikn + + + + + + + + + + + + + + + + + + + + + + + + + + +
      + +
      + + + + + + + + +
      +
      kyosu v0.1.0 +
      +
      Complex Without Complexes
      +
      + +   + + + + +
      +
      +
      + + + + +
      +
      + +
      +
      +
      + +
      + +
      +
      + + +
      +
      +
      +
      +
      +
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      +
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      +
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      +
      +
      +
      +
      + +
      + +

      ◆ cyl_bessel_ikn

      + +
      +
      + + + + + +
      + + + + +
      kyosu::cyl_bessel_ikn = {}
      +       		+inlineconstexpr
      +
      + +

      Computes the Bessel functions of the second kind \(I\) and \(K \)of integral order,.

      +
      #include <kyosu/functions.hpp>
      +

      Callable Signatures

      +
      namespace kyosu
      +
      {
      +
      template<eve::integral_scalar_value N, eve::floating_ordered_value T, complexRange R>
      +
      constexpr auto cyl_bessel_ikn(N n, T z, R& js, R& ys) noexcept;
      +
      +
      template<eve::integral_scalar_value N, conceots::kyosu::complex Z, complexRange R>
      +
      constexpr T cyl_bessel_ikn(N n, Z z, R& js, R& ys) noexcept;
      +
      }
      +
      kyosu::cyl_bessel_ikn
      constexpr tags::callable_cyl_bessel_ikn cyl_bessel_ikn
      Computes the Bessel functions of the second kind and of integral order,.
      Definition: cyl_bessel_ikn.hpp:87
      +
      kyosu
      Main KYOSU namespace.
      Definition: types.hpp:14
      +

      Parameters

      +
        +
      • n: scalar integral order of the function.
        • +
      • z: Value to process.
        • +
      • is: range able to contain int(nu)+1 complex values (of type complex_t<T> or Z respectively) *ks: range able to contain int(nu)+1 complex values (of type complex_t<T> or Z respectively)
        • +
      +

      Return value

      +
        +
      • returns the kumi pair \(\{I_\nu(z), K_\nu(z)\}\).
        • +
      +

      *Ouput values

      +
        +
      • on output is contains the values of \(((I_{0+i})_{i = 0\cdot n}\)
        • +
      • on output ks contains the values of \(((K_{0+i})_{i = 0\cdot n}\)
        • +
      +

      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::vector<decltype(z)> is(4), ks(4);
      +
      kyosu::cyl_bessel_ikn(3, z, is, ks);
      +
      for(int n=0; n <= 3; ++n)
      +
      {
      +
      std::cout << "is[" << n << "] = " << is[n] << std::endl;
      +
      std::cout << "ks[" << n << "] = " << ks[n] << std::endl;
      +
      }
      +
      return 0;
      +
      }
      +
      kyosu::complex
      constexpr tags::callable_complex complex
      Constructs a kyosu::complex.
      Definition: to_complex.hpp:70
      +
      +
      +
      +
      +
      + + + + + + + + + + diff --git a/group__functions_ga9d8707d3de321182b50e9bee1728a3c6.html b/group__functions_ga9d8707d3de321182b50e9bee1728a3c6.html new file mode 100644 index 00000000..7c597d7d --- /dev/null +++ b/group__functions_ga9d8707d3de321182b50e9bee1728a3c6.html @@ -0,0 +1,216 @@ + + + + + + + + +kyosu: kyosu::cyl_bessel_ik + + + + + + + + + + + + + + + + + + + + + + + + + + +
      + +
      + + + + + + + + +
      +
      kyosu v0.1.0 +
      +
      Complex Without Complexes
      +
      + +   + + + + +
      +
      +
      + + + + +
      +
      + +
      +
      +
      + +
      + +
      +
      + + +
      +
      +
      +
      +
      +
      Loading...
      +
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      +
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      +
      +
      +
      +
      + +
      + +

      ◆ cyl_bessel_ik

      + +
      +
      + + + + + +
      + + + + +
      kyosu::cyl_bessel_ik = {}
      +       		+inlineconstexpr
      +
      + +

      Computes the modified Bessel functions \(I\) and \(K\),.

      +
      #include <kyosu/functions.hpp>
      +

      Callable Signatures

      +
      namespace kyosu
      +
      {
      +
      template<eve::floating_scalar_ordered_value N, eve::floating_ordered_value T, complexRange R>
      +
      constexpr auto cyl_bessel_ik(N nu, T z, R& js, R& ys) noexcept;
      +
      +
      template<eve::floating_scalar_ordered_value N, conceots::kyosu::complex Z, complexRange R>
      +
      constexpr T cyl_bessel_ik(N n, Z z, R& js, R& ys) noexcept;
      +
      }
      +
      kyosu::cyl_bessel_ik
      constexpr tags::callable_cyl_bessel_ik cyl_bessel_ik
      Computes the modified Bessel functions and ,.
      Definition: cyl_bessel_ik.hpp:91
      +
      kyosu
      Main KYOSU namespace.
      Definition: types.hpp:14
      +

      Parameters

      +
        +
      • nu: scalar order of the function not necessarily integral.
        • +
      • z: Value to process.
        • +
      • js: range able to contain int(nu)+1 complex values (of type complex_t<T> or Z respectively) *ys: range able to contain int(nu)+1 complex values (of type complex_t<T> or Z respectively)
        • +
      +

      Return value

      +
        +
      • returns the kumi pair \(\{I_\nu(z), K_\nu(z)\}\) of complex values.
        • +
      +

      *Ouput values

      +
        +
      • on output js contains the values of \(((I_{\nu_0+\epsilon i})_{i = 0\cdot n}\)
        • +

      • on output ys contains the values of \(((K_{\nu_0+\epsilon i})_{i = 0\cdot n}\)

        +

        where \(\nu_0\) is the fractional part of \(\nu\), \(\nu = \nu_0+\epsilon n\) and \(\epsilon\) is the sign of \(\nu\) .

        +
        • +
      +

      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));
      +
      auto v = 3.3;
      +
      std::cout << "z " << z << std::endl;
      +
      std::vector<kyosu::complex_t<w_t>> is(4), ks(4);
      +
      kyosu::cyl_bessel_ik(v, z, is, ks);
      +
      for(int n=0; n <= 3; ++n)
      +
      {
      +
      std::cout << "is[" << n << "] = " << is[n] << std::endl;
      +
      std::cout << "ks[" << n << "] = " << ks[n] << std::endl;
      +
      }
      +
      return 0;
      +
      }
      +
      kyosu::complex
      constexpr tags::callable_complex complex
      Constructs a kyosu::complex.
      Definition: to_complex.hpp:70
      +
      +
      +
      +
      +
      + + + + + + + + + + diff --git a/group__functions_gaa200851cb18a56a131469203b3b5f9fa.html b/group__functions_gaa200851cb18a56a131469203b3b5f9fa.html new file mode 100644 index 00000000..226fff10 --- /dev/null +++ b/group__functions_gaa200851cb18a56a131469203b3b5f9fa.html @@ -0,0 +1,218 @@ + + + + + + + + +kyosu: kyosu::cyl_bessel_h1 + + + + + + + + + + + + + + + + + + + + + + + + + + +
      + +
      + + + + + + + + +
      +
      kyosu v0.1.0 +
      +
      Complex Without Complexes
      +
      + +   + + + + +
      +
      +
      + + + + +
      +
      + +
      +
      +
      + +
      + +
      +
      + + +
      +
      +
      +
      +
      +
      Loading...
      +
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      +
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      +
      +
      +
      +
      + +
      + +

      ◆ cyl_bessel_h1

      + +
      +
      + + + + + +
      + + + + +
      kyosu::cyl_bessel_h1 = {}
      +       		+inlineconstexpr
      +
      + +

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

      +
      #include <kyosu/functions.hpp>
      +

      Callable Signatures

      +
      namespace kyosu
      +
      {
      +
      template<eve::floating_scalar_value N, eve::floating_ordered_value T,>
      +
      constexpr auto cyl_bessel_h1(N nu, T z) noexcept;
      +
      +
      template<eve::floating_scalar_value N, concepts::kyosu::complex Z>
      +
      constexpr T cyl_bessel_h1(N nu, Z z) noexcept;
      +
      +
      template<eve::floating_scalar_value N, eve::floating_ordered_value T, complexRange R>
      +
      constexpr auto cyl_bessel_h1(N nu, T z, R& h1s) noexcept;
      +
      +
      template<eve::floating_scalar_value N, concepts::kyosu::complex Z, complexRange R>
      +
      constexpr T cyl_bessel_h1(N nu, Z z, R& h1s) noexcept;
      +
      }
      +
      kyosu::cyl_bessel_h1
      constexpr tags::callable_cyl_bessel_h1 cyl_bessel_h1
      Computes the Bessel functions of the third kind ,.
      Definition: cyl_bessel_h1.hpp:106
      +
      kyosu
      Main KYOSU namespace.
      Definition: types.hpp:14
      +

      Parameters

      +
        +
      • nu: scalar floating order of the function.
        • +
      • z: Value to process.
        • +
      • h1s: range able to containn = int(abs(nu))+1` complex values (of type complex_t<T> or Z respectively)
        • +
      +

      Return value

      +
        +
      • returns \(H^{(1)}_\nu(z)\).
        • +
      +

      *Ouput values

      +
        +
      • on output (if present) h1s contains the values of \( (H^{(1)}_{\nu_0+\epsilon i})_{i = 0 \cdots n} \); where \( \nu_0 \) is the fractional part of \(\nu\) and \(\epsilon\) is the sign of \( \nu\).
        • +
      +

      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));
      +
      auto v = 0.0;
      +
      std::cout << "z " << z << std::endl;
      +
      for(int n=0; n <= 3; ++n)
      +
      {
      +
      auto h1 = kyosu::cyl_bessel_h1(v, z);
      +
      std::cout << "v " << v << std::endl;
      +
      std::cout << "yl_bessel_h1(v, z) " << h1 << std::endl;
      +
      v = v+0.25;
      +
      }
      +
      return 0;
      +
      }
      +
      kyosu::complex
      constexpr tags::callable_complex complex
      Constructs a kyosu::complex.
      Definition: to_complex.hpp:70
      +
      +
      +
      +
      +
      + + + + + + + + + + diff --git a/group__functions_gaaad895e7ba266d0e4d531d43ea44e273.html b/group__functions_gaaad895e7ba266d0e4d531d43ea44e273.html index 769e3612..928a2786 100644 --- a/group__functions_gaaad895e7ba266d0e4d531d43ea44e273.html +++ b/group__functions_gaaad895e7ba266d0e4d531d43ea44e273.html @@ -151,7 +151,7 @@

      template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_in(int n, T z) noexcept;
      template<eve::floating_ordered_value T> constexpr T cyl_bessel_in(int n, T z) noexcept;
      }
      -
      kyosu::cyl_bessel_in
      constexpr tags::callable_cyl_bessel_in cyl_bessel_in
      Computes the modified Bessel functions of the first kind , extended to the complex plane and cayley_d...
      Definition: cyl_bessel_in.hpp:76
      +
      kyosu::cyl_bessel_in
      constexpr tags::callable_cyl_bessel_in cyl_bessel_in
      Computes the modified Bessel functions of the first kind , extended to the complex plane and cayley_d...
      Definition: cyl_bessel_in.hpp:79
      kyosu
      Main KYOSU namespace.
      Definition: types.hpp:14

      Parameters

        @@ -159,7 +159,7 @@

        Example

        #include <kyosu/kyosu.hpp>
        diff --git a/group__functions_gab07b0b22e10bac659c95fd81ea819086.html b/group__functions_gab07b0b22e10bac659c95fd81ea819086.html index 75f5e507..90b19e58 100644 --- a/group__functions_gab07b0b22e10bac659c95fd81ea819086.html +++ b/group__functions_gab07b0b22e10bac659c95fd81ea819086.html @@ -142,7 +142,7 @@

        -

        Computes the Bessel function of the first kind, \( J_1(x)=\frac1{\pi }\int _{0}^{\pi}\cos(\tau-x\sin \tau )\,\mathrm {d} \tau \) extended to the complex plane and cayley_dickson values. It is the solution of \( x^{2}y''+xy'+x^2y=0\) for which \( y(0) = 1\).

        +

        Computes the Bessel function of the first kind, \( J_1\).

        #include <kyosu/functions.hpp>

        Callable Signatures

        namespace kyosu
        @@ -150,7 +150,7 @@

        template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_j1(T z) noexcept;

        template<eve::floating_ordered_value T> constexpr T cyl_bessel_j1(T z) noexcept;
        }
        -
        kyosu::cyl_bessel_j1
        constexpr tags::callable_cyl_bessel_j1 cyl_bessel_j1
        Computes the Bessel function of the first kind, extended to the complex plane and cayley_dickson val...
        Definition: cyl_bessel_j1.hpp:74
        +
        kyosu::cyl_bessel_j1
        constexpr tags::callable_cyl_bessel_j1 cyl_bessel_j1
        Computes the Bessel function of the first kind, .
        Definition: cyl_bessel_j1.hpp:71
        kyosu
        Main KYOSU namespace.
        Definition: types.hpp:14

        Parameters

          @@ -158,7 +158,7 @@

          Example

          #include <kyosu/kyosu.hpp>
          @@ -192,6 +192,13 @@

          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_j1(z0) << "\n";
          +
          +
          eve::wide<double, eve::fixed<8>> l(1.0, 15.0, 40.0, 60.0, eve::inf(eve::as<double>()),eve::minf(eve::as<double>()), eve::nan(eve::as<double>()), 0.0);
          +
          auto lims = kyosu::complex(l);
          +
          std::cout << " ==================== " << std::endl;
          +
          std::cout << lims << " \n -> \n" << cyl_bessel_j1(lims) << "\n";
          +
          std::cout << l << " \n -> \n" << cyl_bessel_j1(l) << "\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_gab8e5dcb27d3ca0fce7ed2f7e69218f88.html b/group__functions_gab8e5dcb27d3ca0fce7ed2f7e69218f88.html index 2f7b1147..bd024887 100644 --- a/group__functions_gab8e5dcb27d3ca0fce7ed2f7e69218f88.html +++ b/group__functions_gab8e5dcb27d3ca0fce7ed2f7e69218f88.html @@ -150,7 +150,7 @@

          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::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:88
          kyosu
          Main KYOSU namespace.
          Definition: types.hpp:14

          Parameters

            @@ -195,13 +195,13 @@

            Example

            std::cout << z0 << " \n-> " << cyl_bessel_yn(n,z0) << "\n";
            -
            for(int i=75; i < 100; ++i)
            +
            for(int i=0; i <= 10; ++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::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:89
            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_gad889d1c4424dc0752a3d939b7a32de05.html b/group__functions_gad889d1c4424dc0752a3d939b7a32de05.html new file mode 100644 index 00000000..777270b4 --- /dev/null +++ b/group__functions_gad889d1c4424dc0752a3d939b7a32de05.html @@ -0,0 +1,218 @@ + + + + + + + + +kyosu: kyosu::cyl_bessel_h2 + + + + + + + + + + + + + + + + + + + + + + + + + + +
            + +
            + + + + + + + + +
            +
            kyosu v0.1.0 +
            +
            Complex Without Complexes
            +
            + +   + + + + +
            +
            +
            + + + + +
            +
            + +
            +
            +
            + +
            + +
            +
            + + +
            +
            +
            +
            +
            +
            Loading...
            +
            Searching...
            +
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            +
            +
            +
            +
            + +
            + +

            ◆ cyl_bessel_h2

            + +
            +
            + + + + + +
            + + + + +
            kyosu::cyl_bessel_h2 = {}
            +             		+inlineconstexpr
            +
            + +

            Computes the Bessel functions of the third kind \( H^{(2)}_\nu \),.

            +
            #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& h2s) noexcept;
            +
            +
            template<eve::floating_scalar_value N, concepts::kyosu::complex Z, complexRange R>
            +
            constexpr T cyl_bessel_h2(N nu, Z z, R& h2s) noexcept;
            +
            }
            +
            kyosu::cyl_bessel_h2
            constexpr tags::callable_cyl_bessel_h2 cyl_bessel_h2
            Computes the Bessel functions of the third kind ,.
            Definition: cyl_bessel_h2.hpp:106
            +
            kyosu
            Main KYOSU namespace.
            Definition: types.hpp:14
            +

            Parameters

            +
              +
            • nu: scalar floating order of the function.
              • +
            • z: Value to process.
              • +
            • h2s: range able to containn = int(abs(nu))+1` complex values (of type complex_t<T> or Z respectively)
              • +
            +

            Return value

            +
              +
            • returns \(H^{(2)}_\nu(z)\).
              • +
            +

            *Ouput values

            +
              +
            • on output (if present) h2s contains the values of \( (H^{(2)}_{\nu_0+\epsilon i})_{i = 0 \cdots n} \), where \( \nu_0 \) is the fractional part of \(\nu\) and \(\epsilon\) is the sign of \( \nu\).
              • +
            +

            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));
            +
            auto v = 0.0;
            +
            std::cout << "z " << z << std::endl;
            +
            for(int n=0; n <= 3; ++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;
            +
            }
            +
            return 0;
            +
            }
            +
            kyosu::complex
            constexpr tags::callable_complex complex
            Constructs a kyosu::complex.
            Definition: to_complex.hpp:70
            +
            +
            +
            +
            +
            + + + + + + + + + + diff --git a/group__functions_gaf7b3924df2aa81781473dfc547daf604.html b/group__functions_gaf7b3924df2aa81781473dfc547daf604.html index 87153100..4afdafe4 100644 --- a/group__functions_gaf7b3924df2aa81781473dfc547daf604.html +++ b/group__functions_gaf7b3924df2aa81781473dfc547daf604.html @@ -152,7 +152,7 @@

            template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_jn(int n, T z) noexcept;
            template<eve::floating_ordered_value T> constexpr T cyl_bessel_jn(int n, T z) noexcept;
            }
            -
            kyosu::cyl_bessel_jn
            constexpr tags::callable_cyl_bessel_jn cyl_bessel_jn
            Computes the Bessel functions of the first kind, extended to the complex plane and cayley_dickson v...
            Definition: cyl_bessel_jn.hpp:78
            +
            kyosu::cyl_bessel_jn
            constexpr tags::callable_cyl_bessel_jn cyl_bessel_jn
            Computes the Bessel functions of the first kind, extended to the complex plane and cayley_dickson v...
            Definition: cyl_bessel_jn.hpp:95
            kyosu
            Main KYOSU namespace.
            Definition: types.hpp:14

            Parameters

              diff --git a/group__functions_gafc9416d5a0fb124785d4f67369ce665a.html b/group__functions_gafc9416d5a0fb124785d4f67369ce665a.html new file mode 100644 index 00000000..e85aa96c --- /dev/null +++ b/group__functions_gafc9416d5a0fb124785d4f67369ce665a.html @@ -0,0 +1,208 @@ + + + + + + + + +kyosu: kyosu::cyl_bessel_j + + + + + + + + + + + + + + + + + + + + + + + + + + +
              + +
              + + + + + + + + +
              +
              kyosu v0.1.0 +
              +
              Complex Without Complexes
              +
              + +   + + + + +
              +
              +
              + + + + +
              +
              + +
              +
              +
              + +
              + +
              +
              + + +
              +
              +
              +
              +
              +
              Loading...
              +
              Searching...
              +
              No Matches
              +
              +
              +
              +
              + +
              + +

              ◆ cyl_bessel_j

              + +
              +
              + + + + + +
              + + + + +
              kyosu::cyl_bessel_j = {}
              +               		+inlineconstexpr
              +
              + +

              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.

              +

              It is the solution of \( x^{2}y''+xy'+(x^2-\nu^2)y=0\) for which \( y(0) = 0\) if \(\nu \ne 0\) else \(1\).

              +
              #include <kyosu/functions.hpp>
              +

              Callable Signatures

              +
              namespace kyosu
              +
              {
              +
              template<eve::floating_ordered_value, kyosu::concepts::cayley_dickson T>
              +
              constexpr auto cyl_bessel_j(N nu, T z) noexcept;
              +
              +
              template<eve::floating_ordered_value, eve::floating_ordered_value T>
              +
              constexpr T cyl_bessel_j(N n, T z) noexcept;
              +
              }
              +
              kyosu::cyl_bessel_j
              constexpr tags::callable_cyl_bessel_j cyl_bessel_j
              Computes the Bessel functions of the first kind, extended to the complex plane and cayley_dickson v...
              Definition: cyl_bessel_j.hpp:100
              +
              kyosu
              Main KYOSU namespace.
              Definition: types.hpp:14
              +

              Parameters

              +
                +
              • nu: order of the function.
                • +
              • z: Value to process.
                • +
              +

              Return value

              +
                +
              • returns \(J_\nu(z)\).
                • +
              +

              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));
              +
              auto v = 3.3;
              +
              std::cout << "z " << z << std::endl;
              +
              std::vector<decltype(z)> js(4);
              +
              kyosu::cyl_bessel_j(v, z, js);
              +
              for(int n=0; n <= 3; ++n)
              +
              {
              +
              std::cout << "js[" << n << "] = " << js[n] << std::endl;
              +
              }
              +
              return 0;
              +
              }
              +
              kyosu::complex
              constexpr tags::callable_complex complex
              Constructs a kyosu::complex.
              Definition: to_complex.hpp:70
              +
              +
              +
              +
              +
              + + + + + + + + + + diff --git a/index.html b/index.html index dc2c03da..2a7782e0 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 cbeac211..68eb6db1 100644 --- a/namespacekyosu.html +++ b/namespacekyosu.html @@ -386,32 +386,69 @@ constexpr tags::callable_cscpi cscpi = {}  Computes the cosecant from the argument in \(\pi\) multiples.
                +constexpr tags::callable_cyl_bessel_h1 cyl_bessel_h1 = {} + Computes the Bessel functions of the third kind \(H^{(1)}\),.
              +  +constexpr tags::callable_cyl_bessel_h12 cyl_bessel_h12 = {} + Computes the Bessel functions of the third kind \( H^{(1)} \) and \( H^{(2)} \),.
              +  +constexpr tags::callable_cyl_bessel_h1_0 cyl_bessel_h1_0 = {} + Computes the Bessel function of the third kind, \( H^{(1)}_0(x)\),.
              +  +constexpr tags::callable_cyl_bessel_h1_1 cyl_bessel_h1_1 = {} + Computes the Bessel function of the third kind, \( H^{(1)}_1(x)\),.
              +  constexpr tags::callable_cyl_bessel_h1n cyl_bessel_h1n = {}  Computes the Bessel/Hankel functions of the third kind, \( H_n^{(1)}(z) = J_n(z)+iY_n(z)\).
                +constexpr tags::callable_cyl_bessel_h2 cyl_bessel_h2 = {} + Computes the Bessel functions of the third kind \( H^{(2)}_\nu \),.
              +  +constexpr tags::callable_cyl_bessel_h2_0 cyl_bessel_h2_0 = {} + Computes the Bessel function of the third kind, \( H^{(2)}_0(x)\).
              +  +constexpr tags::callable_cyl_bessel_h2_1 cyl_bessel_h2_1 = {} + Computes the Bessel function of the third kind, \( H^{(2)}_1(x)\),.
              +  constexpr tags::callable_cyl_bessel_h2n cyl_bessel_h2n = {}  Computes the Bessel/Hankel functions of the third kind , \( H_n^{(2)} = J_n(z)-iY_n(z)\).
                +constexpr tags::callable_cyl_bessel_i cyl_bessel_i = {} + Computes the Modified Bessel functions of the first kind.
              +  constexpr tags::callable_cyl_bessel_i0 cyl_bessel_i0 = {}  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.
                +constexpr tags::callable_cyl_bessel_ik cyl_bessel_ik = {} + Computes the modified Bessel functions \(I\) and \(K\),.
              +  +constexpr tags::callable_cyl_bessel_ikn cyl_bessel_ikn = {} + Computes the Bessel functions of the second kind \(I\) and \(K \)of integral order,.
              +  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.
                +constexpr tags::callable_cyl_bessel_j cyl_bessel_j = {} + 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 tags::callable_cyl_bessel_j0 cyl_bessel_j0 = {}  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 tags::callable_cyl_bessel_j1 cyl_bessel_j1 = {} - Computes the Bessel function of the first kind, \( J_1(x)=\frac1{\pi }\int _{0}^{\pi}\cos(\tau-x\sin \tau )\,\mathrm {d} \tau \) extended to the complex plane and cayley_dickson values. It is the solution of \( x^{2}y''+xy'+x^2y=0\) for which \( y(0) = 1\).
              + Computes the Bessel function of the first kind, \( J_1\).
                constexpr tags::callable_cyl_bessel_jn cyl_bessel_jn = {}  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 values.
                +constexpr tags::callable_cyl_bessel_k cyl_bessel_k = {} + Computes the Modified Bessel functions of the second kind.
              +  constexpr tags::callable_cyl_bessel_k0 cyl_bessel_k0 = {}  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.
                @@ -421,6 +458,9 @@ constexpr tags::callable_cyl_bessel_kn cyl_bessel_kn = {}  Computes the modified Bessel functions of the second kind, \( K_{n}(x)=\lim_{\alpha\to n}{\frac {\pi }{2}}{\frac {I_{-\alpha }(x)-I_{\alpha }(x)}{\sin \alpha \pi }}\). extended to the complex plane and cayley_dickson algebras.
                +constexpr tags::callable_cyl_bessel_y cyl_bessel_y = {} + Computes the Bessel functions of the second kind,.
              +  constexpr tags::callable_cyl_bessel_y0 cyl_bessel_y0 = {}  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.
                diff --git a/navtreedata.js b/navtreedata.js index e61e4e9b..5f45b4e5 100644 --- a/navtreedata.js +++ b/navtreedata.js @@ -25,11 +25,11 @@ var NAVTREE = [ [ "kyosu", "index.html", [ - [ "Cayley-Dickson algebras", "index.html#autotoc_md29", null ], - [ "What does this implementation provide", "index.html#autotoc_md30", [ - [ "Constructors", "index.html#autotoc_md31", null ], - [ "Operators", "index.html#autotoc_md32", null ], - [ "Functions", "index.html#autotoc_md33", null ] + [ "Cayley-Dickson algebras", "index.html#autotoc_md31", null ], + [ "What does this implementation provide", "index.html#autotoc_md32", [ + [ "Constructors", "index.html#autotoc_md33", null ], + [ "Operators", "index.html#autotoc_md34", null ], + [ "Functions", "index.html#autotoc_md35", null ] ] ], [ "How-Tos", "usergroup0.html", null ], [ "Reference Documentation", "usergroup1.html", [ diff --git a/navtreeindex0.js b/navtreeindex0.js index a27ecba0..5d2ed020 100644 --- a/navtreeindex0.js +++ 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