Directories
+
+
+
+
+
+
+
+
+
+
+
+
+
+ |
+
+ kyosu v0.1.0
+
+ Complex Without Complexes
+ |
+
|
+
+
+
+
+
+
+
+ | |
+
+
+
+
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+
diff --git a/dir_603762341fae708cb1fd302d853e09e1.html b/dir_603762341fae708cb1fd302d853e09e1.html
new file mode 100644
index 00000000..5c37e4eb
--- /dev/null
+++ b/dir_603762341fae708cb1fd302d853e09e1.html
@@ -0,0 +1,143 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
+
+
+
+
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+
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+Loading...
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+
+
+besselr Directory Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ |
+
+ 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 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+bessel Directory Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ |
+
+ kyosu v0.1.0
+
+ Complex Without Complexes
+ |
+
|
+
+
+
+
+
+
+
+ | |
+
+
+
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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 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+◆ 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
+{
+
+
+}
+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
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;
+}
+constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
+
+
+
+
+
+
+
+
+
+
+
+
+ |
+
+ kyosu v0.1.0
+
+ Complex Without Complexes
+ |
+
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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 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+◆ 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>
+
+ template<eve::floating_ordered_value, eve::floating_ordered_value T>
+
+ template<eve::floating_ordered_value, kyosu::concepts::cayley_dickson T, Range R>
+
+ template<eve::floating_ordered_value, eve::floating_ordered_value T, Range R>
+
+}
+constexpr tags::callable_cyl_bessel_i cyl_bessel_i
Computes the Modified Bessel functions of the first kind.
Definition: cyl_bessel_i.hpp:106
Parameters
+-
+
nu: order of the function.
+z: Value to process.
+is: Ouput range able to containn = int(abs(nu))+1complex 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;
+}
+constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
+
+
+
+
+
+
+
+
+
+
+
+
+ |
+
+ kyosu v0.1.0
+
+ Complex Without Complexes
+ |
+
|
+
+
+
+
+
+
+
+ | |
+
+
+
+
+
+
+
+
+
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+
+
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 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+◆ 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>
+
+ template<eve::floating_scalar_value N, conceots::kyosu::complex Z, complexRange R1, complexRange R2>
+
+}
+constexpr tags::callable_cyl_bessel_h12 cyl_bessel_h12
Computes the Bessel functions of the third kind and ,.
Definition: cyl_bessel_h12.hpp:87
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 containn = int(abs(nu))+1complex 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;
+}
+constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
+
+
+
+
+
+
+
+
+
+
+
+
+ |
+
+ kyosu v0.1.0
+
+ Complex Without Complexes
+ |
+
|
+
+
+
+
+
+
+
+ | |
+
+
+
+
+
+
+
+
+
+
+
+
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 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+◆ 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>
+
+ template<eve::floating_ordered_value, eve::floating_ordered_value T>
+
+}
+constexpr tags::callable_cyl_bessel_k cyl_bessel_k
Computes the Modified Bessel functions of the second kind.
Definition: cyl_bessel_k.hpp:95
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;
+}
+constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_jn(int n, T z) noexcept;
}
-constexpr tags::callable_sph_bessel_jn sph_bessel_jnComputes the spherical Bessel functions of the first kind , extended to the complex plane and cayley_...Definition: sph_bessel_jn.hpp:73
+constexpr tags::callable_sph_bessel_jn sph_bessel_jnComputes the spherical Bessel functions of the first kind , extended to the complex plane and cayley_...Definition: sph_bessel_jn.hpp:87
Parameters
@@ -196,7 +196,7 @@ Example
-
+
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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+
+
+
+
+◆ 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>
+
+
+ template<eve::floating_ordered_value, eve::floating_ordered_value T>
+
+}
+constexpr tags::callable_cyl_bessel_y cyl_bessel_yComputes the Bessel functions of the second kind,.Definition: cyl_bessel_y.hpp:80
+
+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;
+}
+constexpr tags::callable_cyl_bessel_i cyl_bessel_iComputes the Modified Bessel functions of the first kind.Definition: cyl_bessel_i.hpp:106
+constexpr tags::callable_complex complexConstructs 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);
+
+
+
+
+
+
+
+
+
+
+ eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+ auto zz = kyosu::complex(z);
+
+
+
+
+
+ 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);
+
+
+ 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);
+
+
+ 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;
+}
+constexpr tags::callable_complex complexConstructs a kyosu::complex.Definition: to_complex.hpp:70
+constexpr tags::callable_quaternion quaternionConstructs 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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+
+
+
+
+◆ 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
+{
+
+
+}
+constexpr tags::callable_cyl_bessel_h2_0 cyl_bessel_h2_0Computes the Bessel function of the third kind, .Definition: cyl_bessel_h2_0.hpp:74
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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);
+
+ 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);
+
+
+
return 0;
}
constexpr tags::callable_complex complexConstructs 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...
+Searching...
+No Matches
+
+
+
+
+
+
+
+◆ 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
+{
+
+
+}
+constexpr tags::callable_cyl_bessel_h2_1 cyl_bessel_h2_1Computes the Bessel function of the third kind, ,.Definition: cyl_bessel_h2_1.hpp:75
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+
+
+
+
+◆ 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
+{
+
+
+}
+constexpr tags::callable_cyl_bessel_h1_0 cyl_bessel_h1_0Computes the Bessel function of the third kind, ,.Definition: cyl_bessel_h1_0.hpp:75
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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;
}
-constexpr tags::callable_cyl_bessel_yn cyl_bessel_ynComputes the modified Bessel functions of the second kind, , extended to the complex plane and cayley...Definition: cyl_bessel_yn.hpp:74
+constexpr tags::callable_cyl_bessel_yn cyl_bessel_ynComputes the modified Bessel functions of the second kind, , extended to the complex plane and cayley...Definition: cyl_bessel_yn.hpp:89
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;
-
-
+
+
@@ -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);
-
-
-
-
-
-
return 0;
}
constexpr tags::callable_real realExtracts the real part of a value.Definition: real.hpp:83
constexpr tags::callable_complex complexConstructs a kyosu::complex.Definition: to_complex.hpp:70
constexpr tags::callable_quaternion quaternionConstructs a kyosu::quaternion.Definition: to_quaternion.hpp:72
-constexpr tags::callable_i iComputes 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);
+
+
+
+
+
+
+
+
+
+
+ eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+ auto zz = kyosu::complex(z);
+
+
+
+
+
+ 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);
+
+
+ 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);
+
+
+ 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;
+}
+constexpr tags::callable_complex complexConstructs a kyosu::complex.Definition: to_complex.hpp:70
+constexpr tags::callable_quaternion quaternionConstructs 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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+
+
+
+
+◆ 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>
+
+
+ template<eve::integral_scalar_value N, conceots::kyosu::complex Z, complexRange R>
+
+}
+constexpr tags::callable_cyl_bessel_ikn cyl_bessel_iknComputes the Bessel functions of the second kind and of integral order,.Definition: cyl_bessel_ikn.hpp:87
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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...
+Searching...
+No Matches
+
+
+
+
+
+
+
+◆ 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>
+
+
+ template<eve::floating_scalar_ordered_value N, conceots::kyosu::complex Z, complexRange R>
+
+}
+constexpr tags::callable_cyl_bessel_ik cyl_bessel_ikComputes the modified Bessel functions and ,.Definition: cyl_bessel_ik.hpp:91
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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...
+Searching...
+No Matches
+
+
+
+
+
+
+
+◆ 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,>
+
+
+ template<eve::floating_scalar_value N, concepts::kyosu::complex Z>
+
+
+ template<eve::floating_scalar_value N, eve::floating_ordered_value T, complexRange R>
+
+
+ template<eve::floating_scalar_value N, concepts::kyosu::complex Z, complexRange R>
+
+}
+constexpr tags::callable_cyl_bessel_h1 cyl_bessel_h1Computes the Bessel functions of the third kind ,.Definition: cyl_bessel_h1.hpp:106
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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;
}
-constexpr tags::callable_cyl_bessel_in cyl_bessel_inComputes the modified Bessel functions of the first kind , extended to the complex plane and cayley_d...Definition: cyl_bessel_in.hpp:76
+constexpr tags::callable_cyl_bessel_in cyl_bessel_inComputes the modified Bessel functions of the first kind , extended to the complex plane and cayley_d...Definition: cyl_bessel_in.hpp:79
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;
}
-constexpr tags::callable_cyl_bessel_j1 cyl_bessel_j1Computes the Bessel function of the first kind, extended to the complex plane and cayley_dickson val...Definition: cyl_bessel_j1.hpp:74
+constexpr tags::callable_cyl_bessel_j1 cyl_bessel_j1Computes the Bessel function of the first kind, .Definition: cyl_bessel_j1.hpp:71
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);
+
+ 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;
+
+
+
return 0;
}
constexpr tags::callable_real realExtracts 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;
}
-constexpr tags::callable_sph_bessel_yn sph_bessel_ynComputes the spherical Bessel functions of the first kind , extended to the complex plane and cayley_...Definition: sph_bessel_yn.hpp:73
+constexpr tags::callable_sph_bessel_yn sph_bessel_ynComputes the spherical Bessel functions of the first kind , extended to the complex plane and cayley_...Definition: sph_bessel_yn.hpp:88
Parameters
@@ -195,13 +195,13 @@ Example
-
+
return 0;
}
-constexpr tags::callable_cyl_bessel_yn cyl_bessel_ynComputes the modified Bessel functions of the second kind, , extended to the complex plane and cayley...Definition: cyl_bessel_yn.hpp:74
+constexpr tags::callable_cyl_bessel_yn cyl_bessel_ynComputes the modified Bessel functions of the second kind, , extended to the complex plane and cayley...Definition: cyl_bessel_yn.hpp:89
constexpr tags::callable_real realExtracts the real part of a value.Definition: real.hpp:83
constexpr tags::callable_complex complexConstructs a kyosu::complex.Definition: to_complex.hpp:70
constexpr tags::callable_quaternion quaternionConstructs 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...
+No Matches
+
+
+
+
+
+
+
+◆ 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,>
+
+
+ template<eve::floating_scalar_value N, concepts::kyosu::complex Z>
+
+
+ template<eve::floating_scalar_value N, eve::floating_ordered_value T, complexRange R>
+
+
+ template<eve::floating_scalar_value N, concepts::kyosu::complex Z, complexRange R>
+
+}
+constexpr tags::callable_cyl_bessel_h2 cyl_bessel_h2Computes the Bessel functions of the third kind ,.Definition: cyl_bessel_h2.hpp:106
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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;
}
-constexpr tags::callable_cyl_bessel_jn cyl_bessel_jnComputes the Bessel functions of the first kind, extended to the complex plane and cayley_dickson v...Definition: cyl_bessel_jn.hpp:78
+constexpr tags::callable_cyl_bessel_jn cyl_bessel_jnComputes the Bessel functions of the first kind, extended to the complex plane and cayley_dickson v...Definition: cyl_bessel_jn.hpp:95
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>
+
+
+ template<eve::floating_ordered_value, eve::floating_ordered_value T>
+
+}
+constexpr tags::callable_cyl_bessel_j cyl_bessel_jComputes the Bessel functions of the first kind, extended to the complex plane and cayley_dickson v...Definition: cyl_bessel_j.hpp:100
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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 @@
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
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
Example
+
+
+
+
+
+
+
+
+
+
+
+
+
+ |
+
+ kyosu v0.1.0
+
+ Complex Without Complexes
+ |
+
|
+
+
+
+
+
+
+
+ | |
+
+
+
+
+
+
+
+
+
+
+
+
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 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+◆ 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>
+
+ template<eve::floating_ordered_value, eve::floating_ordered_value T>
+
+}
+constexpr tags::callable_cyl_bessel_y cyl_bessel_y
Computes the Bessel functions of the second kind,.
Definition: cyl_bessel_y.hpp:80
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;
+}
+constexpr tags::callable_cyl_bessel_i cyl_bessel_i
Computes the Modified Bessel functions of the first kind.
Definition: cyl_bessel_i.hpp:106
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
Example
- +#include <kyosu/kyosu.hpp>
+#include <eve/wide.hpp>
+#include <iostream>
+int main()
+{
+ using kyosu::cyl_bessel_k0;
+ std::cout.precision(16);
+ eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+ auto zz = kyosu::complex(z);
+
+
+ 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);
+
+ 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);
+
+
+ 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;
+}
+constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+
+
+
+
+
+
+
+
+ |
+
+ kyosu v0.1.0
+
+ Complex Without Complexes
+ |
+
|
+
+
+
+
+
+
+
+ | |
+
+
+
+
+
+
+
+
+
+
+
+
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 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+◆ 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
+{
+
+
+}
+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
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;
+}
+constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
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);
+ 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);
+
+
+ return 0;
}
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
+
+
+
+
+
+
+
+
+
+
+
+
+ |
+
+ kyosu v0.1.0
+
+ Complex Without Complexes
+ |
+
|
+
+
+
+
+
+
+
+ | |
+
+
+
+
+
+
+
+
+
+
+
+
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 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+◆ 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
+{
+
+
+}
+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
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;
+}
+constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
+
+
+
+
+
+
+
+
+
+
+
+
+ |
+
+ kyosu v0.1.0
+
+ Complex Without Complexes
+ |
+
|
+
+
+
+
+
+
+
+ | |
+
+
+
+
+
+
+
+
+
+
+
+
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 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+◆ 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
+{
+
+
+}
+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
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;
+}
+constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
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;
}
-constexpr tags::callable_cyl_bessel_yn cyl_bessel_ynComputes the modified Bessel functions of the second kind, , extended to the complex plane and cayley...Definition: cyl_bessel_yn.hpp:74
+constexpr tags::callable_cyl_bessel_yn cyl_bessel_ynComputes the modified Bessel functions of the second kind, , extended to the complex plane and cayley...Definition: cyl_bessel_yn.hpp:89
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;
-
-
+
+
@@ -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);
-
-
-
-
-
-
return 0;
}
constexpr tags::callable_real realExtracts the real part of a value.Definition: real.hpp:83
constexpr tags::callable_complex complexConstructs a kyosu::complex.Definition: to_complex.hpp:70
constexpr tags::callable_quaternion quaternionConstructs a kyosu::quaternion.Definition: to_quaternion.hpp:72
-constexpr tags::callable_i iComputes 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);
+
+
+
+
+
+
+
+
+
+
+ eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+ auto zz = kyosu::complex(z);
+
+
+
+
+
+ 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);
+
+
+ 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);
+
+
+ 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;
+}
+constexpr tags::callable_complex complexConstructs a kyosu::complex.Definition: to_complex.hpp:70
+constexpr tags::callable_quaternion quaternionConstructs 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
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+
+
+
+
+◆ 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>
+
+
+ template<eve::integral_scalar_value N, conceots::kyosu::complex Z, complexRange R>
+
+}
+constexpr tags::callable_cyl_bessel_ikn cyl_bessel_iknComputes the Bessel functions of the second kind and of integral order,.Definition: cyl_bessel_ikn.hpp:87
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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...
+Searching...
+No Matches
+
+
+
+
+
+
+
+◆ 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>
+
+
+ template<eve::floating_scalar_ordered_value N, conceots::kyosu::complex Z, complexRange R>
+
+}
+constexpr tags::callable_cyl_bessel_ik cyl_bessel_ikComputes the modified Bessel functions and ,.Definition: cyl_bessel_ik.hpp:91
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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...
+Searching...
+No Matches
+
+
+
+
+
+
+
+◆ 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,>
+
+
+ template<eve::floating_scalar_value N, concepts::kyosu::complex Z>
+
+
+ template<eve::floating_scalar_value N, eve::floating_ordered_value T, complexRange R>
+
+
+ template<eve::floating_scalar_value N, concepts::kyosu::complex Z, complexRange R>
+
+}
+constexpr tags::callable_cyl_bessel_h1 cyl_bessel_h1Computes the Bessel functions of the third kind ,.Definition: cyl_bessel_h1.hpp:106
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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;
}
-constexpr tags::callable_cyl_bessel_in cyl_bessel_inComputes the modified Bessel functions of the first kind , extended to the complex plane and cayley_d...Definition: cyl_bessel_in.hpp:76
+constexpr tags::callable_cyl_bessel_in cyl_bessel_inComputes the modified Bessel functions of the first kind , extended to the complex plane and cayley_d...Definition: cyl_bessel_in.hpp:79
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;
}
-constexpr tags::callable_cyl_bessel_j1 cyl_bessel_j1Computes the Bessel function of the first kind, extended to the complex plane and cayley_dickson val...Definition: cyl_bessel_j1.hpp:74
+constexpr tags::callable_cyl_bessel_j1 cyl_bessel_j1Computes the Bessel function of the first kind, .Definition: cyl_bessel_j1.hpp:71
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);
+
+ 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;
+
+
+
return 0;
}
constexpr tags::callable_real realExtracts 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;
}
-constexpr tags::callable_sph_bessel_yn sph_bessel_ynComputes the spherical Bessel functions of the first kind , extended to the complex plane and cayley_...Definition: sph_bessel_yn.hpp:73
+constexpr tags::callable_sph_bessel_yn sph_bessel_ynComputes the spherical Bessel functions of the first kind , extended to the complex plane and cayley_...Definition: sph_bessel_yn.hpp:88
Parameters
@@ -195,13 +195,13 @@ Example
-
+
return 0;
}
-constexpr tags::callable_cyl_bessel_yn cyl_bessel_ynComputes the modified Bessel functions of the second kind, , extended to the complex plane and cayley...Definition: cyl_bessel_yn.hpp:74
+constexpr tags::callable_cyl_bessel_yn cyl_bessel_ynComputes the modified Bessel functions of the second kind, , extended to the complex plane and cayley...Definition: cyl_bessel_yn.hpp:89
constexpr tags::callable_real realExtracts the real part of a value.Definition: real.hpp:83
constexpr tags::callable_complex complexConstructs a kyosu::complex.Definition: to_complex.hpp:70
constexpr tags::callable_quaternion quaternionConstructs 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...
+No Matches
+
+
+
+
+
+
+
+◆ 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,>
+
+
+ template<eve::floating_scalar_value N, concepts::kyosu::complex Z>
+
+
+ template<eve::floating_scalar_value N, eve::floating_ordered_value T, complexRange R>
+
+
+ template<eve::floating_scalar_value N, concepts::kyosu::complex Z, complexRange R>
+
+}
+constexpr tags::callable_cyl_bessel_h2 cyl_bessel_h2Computes the Bessel functions of the third kind ,.Definition: cyl_bessel_h2.hpp:106
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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;
}
-constexpr tags::callable_cyl_bessel_jn cyl_bessel_jnComputes the Bessel functions of the first kind, extended to the complex plane and cayley_dickson v...Definition: cyl_bessel_jn.hpp:78
+constexpr tags::callable_cyl_bessel_jn cyl_bessel_jnComputes the Bessel functions of the first kind, extended to the complex plane and cayley_dickson v...Definition: cyl_bessel_jn.hpp:95
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
+
+
+
+
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+
+
+
+
+
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+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+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>
+
+
+ template<eve::floating_ordered_value, eve::floating_ordered_value T>
+
+}
+constexpr tags::callable_cyl_bessel_j cyl_bessel_jComputes the Bessel functions of the first kind, extended to the complex plane and cayley_dickson v...Definition: cyl_bessel_j.hpp:100
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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 @@
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
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
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;
-
-
+
+
@@ -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);
- return 0;
}
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
constexpr tags::callable_i i
Computes the complex number cinf i.e. complex(nan, inf) in the chosen type.
Definition: i.hpp:77
Example
- +#include <kyosu/kyosu.hpp>
+#include <eve/wide.hpp>
+#include <iostream>
+int main()
+{
+ using kyosu::cyl_bessel_k1;
+ std::cout.precision(16);
+ eve::wide<double, eve::fixed<4>> z(1.0, 15.0, 40.0, 60.0);
+ auto zz = kyosu::complex(z);
+
+
+ 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);
+
+ 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);
+
+
+ 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;
+}
+constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+
+
+
+
+
+
+
+
+ |
+
+ kyosu v0.1.0
+
+ Complex Without Complexes
+ |
+
|
+
+
+
+
+
+
+
+ | |
+
+
+
+
+
+
+
+
+
+
+
+
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 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+◆ 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>
+
+ template<eve::integral_scalar_value N, conceots::kyosu::complex Z, complexRange R>
+
+}
+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
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;
+}
+constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
+
+
+
+
+
+
+
+
+
+
+
+
+ |
+
+ kyosu v0.1.0
+
+ Complex Without Complexes
+ |
+
|
+
+
+
+
+
+
+
+ | |
+
+
+
+
+
+
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+
+
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 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+◆ 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>
+
+ template<eve::floating_scalar_ordered_value N, conceots::kyosu::complex Z, complexRange R>
+
+}
+constexpr tags::callable_cyl_bessel_ik cyl_bessel_ik
Computes the modified Bessel functions and ,.
Definition: cyl_bessel_ik.hpp:91
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;
+}
+constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
+
+
+
+
+
+
+
+
+
+
+
+
+
+ |
+
+ kyosu v0.1.0
+
+ Complex Without Complexes
+ |
+
|
+
+
+
+
+
+
+
+ | |
+
+
+
+
+
+
+
+
+
+
+
+
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 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+◆ 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,>
+
+ template<eve::floating_scalar_value N, concepts::kyosu::complex Z>
+
+ template<eve::floating_scalar_value N, eve::floating_ordered_value T, complexRange R>
+
+ template<eve::floating_scalar_value N, concepts::kyosu::complex Z, complexRange R>
+
+}
+constexpr tags::callable_cyl_bessel_h1 cyl_bessel_h1
Computes the Bessel functions of the third kind ,.
Definition: cyl_bessel_h1.hpp:106
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;
+}
+constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_in(int n, T z) noexcept;
}
-constexpr tags::callable_cyl_bessel_in cyl_bessel_inComputes the modified Bessel functions of the first kind , extended to the complex plane and cayley_d...Definition: cyl_bessel_in.hpp:76
+constexpr tags::callable_cyl_bessel_in cyl_bessel_inComputes the modified Bessel functions of the first kind , extended to the complex plane and cayley_d...Definition: cyl_bessel_in.hpp:79
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;
}
-constexpr tags::callable_cyl_bessel_j1 cyl_bessel_j1Computes the Bessel function of the first kind, extended to the complex plane and cayley_dickson val...Definition: cyl_bessel_j1.hpp:74
+constexpr tags::callable_cyl_bessel_j1 cyl_bessel_j1Computes the Bessel function of the first kind, .Definition: cyl_bessel_j1.hpp:71
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);
+
+ 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;
+
+
+
return 0;
}
constexpr tags::callable_real realExtracts 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;
}
-constexpr tags::callable_sph_bessel_yn sph_bessel_ynComputes the spherical Bessel functions of the first kind , extended to the complex plane and cayley_...Definition: sph_bessel_yn.hpp:73
+constexpr tags::callable_sph_bessel_yn sph_bessel_ynComputes the spherical Bessel functions of the first kind , extended to the complex plane and cayley_...Definition: sph_bessel_yn.hpp:88
Parameters
@@ -195,13 +195,13 @@ Example
-
+
return 0;
}
-constexpr tags::callable_cyl_bessel_yn cyl_bessel_ynComputes the modified Bessel functions of the second kind, , extended to the complex plane and cayley...Definition: cyl_bessel_yn.hpp:74
+constexpr tags::callable_cyl_bessel_yn cyl_bessel_ynComputes the modified Bessel functions of the second kind, , extended to the complex plane and cayley...Definition: cyl_bessel_yn.hpp:89
constexpr tags::callable_real realExtracts the real part of a value.Definition: real.hpp:83
constexpr tags::callable_complex complexConstructs a kyosu::complex.Definition: to_complex.hpp:70
constexpr tags::callable_quaternion quaternionConstructs 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...
+No Matches
+
+
+
+
+
+
+
+◆ 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,>
+
+
+ template<eve::floating_scalar_value N, concepts::kyosu::complex Z>
+
+
+ template<eve::floating_scalar_value N, eve::floating_ordered_value T, complexRange R>
+
+
+ template<eve::floating_scalar_value N, concepts::kyosu::complex Z, complexRange R>
+
+}
+constexpr tags::callable_cyl_bessel_h2 cyl_bessel_h2Computes the Bessel functions of the third kind ,.Definition: cyl_bessel_h2.hpp:106
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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;
}
-constexpr tags::callable_cyl_bessel_jn cyl_bessel_jnComputes the Bessel functions of the first kind, extended to the complex plane and cayley_dickson v...Definition: cyl_bessel_jn.hpp:78
+constexpr tags::callable_cyl_bessel_jn cyl_bessel_jnComputes the Bessel functions of the first kind, extended to the complex plane and cayley_dickson v...Definition: cyl_bessel_jn.hpp:95
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>
+
+
+ template<eve::floating_ordered_value, eve::floating_ordered_value T>
+
+}
+constexpr tags::callable_cyl_bessel_j cyl_bessel_jComputes the Bessel functions of the first kind, extended to the complex plane and cayley_dickson v...Definition: cyl_bessel_j.hpp:100
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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 @@
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
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
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;
}
-constexpr tags::callable_cyl_bessel_j1 cyl_bessel_j1Computes the Bessel function of the first kind, extended to the complex plane and cayley_dickson val...Definition: cyl_bessel_j1.hpp:74
+constexpr tags::callable_cyl_bessel_j1 cyl_bessel_j1Computes the Bessel function of the first kind, .Definition: cyl_bessel_j1.hpp:71
#include <kyosu/functions.hpp>
namespace kyosu
@@ -150,7 +150,7 @@ template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_j1(T z) noexcept;
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
constexpr tags::callable_cyl_bessel_j1 cyl_bessel_j1
Computes the Bessel function of the first kind, .
Definition: cyl_bessel_j1.hpp:71
Parameters
-
@@ -158,7 +158,7 @@
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)
+- returns \(H^{(2)}_\nu(z)\). +
- 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 \( \nu\). +
nu: order of the function.
+z: Value to process.
+- returns \(J_\nu(z)\). +
- Note
- Let us recall that alternative means that every subalgrebra generated by two elements is associative.
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);
+ 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;
+
+
+ return 0;
}
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
template<kyosu::concepts::cayley_dickson T> constexpr auto sph_bessel_yn(int n, T z) noexcept;
}
-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
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
Parameters
-
@@ -195,13 +195,13 @@
Example
return 0;
}
-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
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
constexpr tags::callable_real real
Extracts the real part of a value.
Definition: real.hpp:83
constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
constexpr tags::callable_quaternion quaternion
Constructs a kyosu::quaternion.
Definition: to_quaternion.hpp:72
+
+
+
+
+
+
+
+
+
+
+
+
+
+ |
+
+ kyosu v0.1.0
+
+ Complex Without Complexes
+ |
+
|
+
+
+
+
+
+
+
+ | |
+
+
+
+
+
+
+
+
+
+
+
+
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 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+◆ 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,>
+
+ template<eve::floating_scalar_value N, concepts::kyosu::complex Z>
+
+ template<eve::floating_scalar_value N, eve::floating_ordered_value T, complexRange R>
+
+ template<eve::floating_scalar_value N, concepts::kyosu::complex Z, complexRange R>
+
+}
+constexpr tags::callable_cyl_bessel_h2 cyl_bessel_h2
Computes the Bessel functions of the third kind ,.
Definition: cyl_bessel_h2.hpp:106
Parameters
+-
+
Return value
+-
+
*Ouput values
+-
+
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;
+}
+constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
template<kyosu::concepts::cayley_dickson T> constexpr auto cyl_bessel_jn(int n, T z) noexcept;
}
-constexpr tags::callable_cyl_bessel_jn cyl_bessel_jnComputes the Bessel functions of the first kind, extended to the complex plane and cayley_dickson v...Definition: cyl_bessel_jn.hpp:78
+constexpr tags::callable_cyl_bessel_jn cyl_bessel_jnComputes the Bessel functions of the first kind, extended to the complex plane and cayley_dickson v...Definition: cyl_bessel_jn.hpp:95
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>
+
+
+ template<eve::floating_ordered_value, eve::floating_ordered_value T>
+
+}
+constexpr tags::callable_cyl_bessel_j cyl_bessel_jComputes the Bessel functions of the first kind, extended to the complex plane and cayley_dickson v...Definition: cyl_bessel_j.hpp:100
+
+Parameters
+
+
+Return value
+
+
+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;
+}
+constexpr tags::callable_complex complexConstructs 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.
-
+
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 @@
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
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 v0.1.0
+
+ Complex Without Complexes
+ |
+
|
+
+
+
+
+
+
+
+ | |
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/index.html b/index.html
index dc2c03da..2a7782e0 100644
--- a/index.html
+++ b/index.html
@@ -130,7 +130,7 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+Loading...
+Searching...
+No Matches
+
+
+
+◆ 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>
+
+ template<eve::floating_ordered_value, eve::floating_ordered_value T>
+
+}
+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
Parameters
+-
+
Return value
+-
+
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;
+}
+constexpr tags::callable_complex complex
Constructs a kyosu::complex.
Definition: to_complex.hpp:70
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.
+
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 @@