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Tuning and simplification complex example

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ckormanyos
2025-07-14 09:47:28 +02:00
parent 3305c6914e
commit 2ad2822bfd
1 changed files with 71 additions and 114 deletions
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example/cpp_complex_examples.cpp
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@@ -11,139 +11,96 @@ In the following, we will show how using the complex_adaptor backend together wi
*/ */
//[cpp_complex_eg //[cpp_complex_eg
#include <iostream>
#include <complex>
#include <boost/multiprecision/cpp_complex.hpp> #include <boost/multiprecision/cpp_complex.hpp>
#include <cmath> template<class Complex>
#include <complex>
#include <iostream>
template<class NumericType>
void elementary_functions(const NumericType z1)
{
std::cout << "\nElementary special functions:\n";
std::cout << "Absolute value : " << abs(z1) << std::endl;
using std::arg;
std::cout << "Argument : " << arg(z1) << std::endl;
using std::norm;
std::cout << "Norm : " << norm(z1) << std::endl;
using std::conj;
std::cout << "Complex conjugate : " << conj(z1) << std::endl;
using std::proj;
std::cout << "Proj on Riemann sphere : " << proj(z1) << std::endl;
using std::exp;
std::cout << "exp(z1) : " << exp(z1) << std::endl;
using std::log;
std::cout << "log(z1) : " << log(z1) << std::endl;
using std::log10;
std::cout << "log10(z1) : " << log10(z1) << std::endl;
using std::pow;
std::cout << "pow(z1, z1) : " << pow(z1, z1) << std::endl;
using std::sqrt;
std::cout << "Take its square root : " << sqrt(z1) << std::endl;
using std::sin;
std::cout << "sin(z1) : " << sin(z1) << std::endl;
using std::cos;
std::cout << "cos(z1) : " << cos(z1) << std::endl;
using std::tan;
std::cout << "tan(z1) : " << tan(z1) << std::endl;
using std::asin;
std::cout << "asin(z1) : " << asin(z1) << std::endl;
using std::acos;
std::cout << "acos(z1) : " << acos(z1) << std::endl;
using std::atan;
std::cout << "atan(z1) : " << atan(z1) << std::endl;
using std::sinh;
std::cout << "sinh(z1) : " << sinh(z1) << std::endl;
using std::cosh;
std::cout << "cosh(z1) : " << cosh(z1) << std::endl;
using std::tanh;
std::cout << "tanh(z1) : " << tanh(z1) << std::endl;
using std::asinh;
std::cout << "asinh(z1) : " << asinh(z1) << std::endl;
using std::acosh;
std::cout << "acosh(z1) : " << acosh(z1) << std::endl;
using std::atanh;
std::cout << "atanh(z1) : " << atanh(z1) << std::endl;
}
template<class ComplexType>
void complex_number_examples() void complex_number_examples()
{ {
using complex_type = ComplexType; Complex z1{0, 1};
using real_type = typename complex_type::value_type; std::cout << std::setprecision(std::numeric_limits<typename Complex::value_type>::digits10);
std::cout << std::scientific << std::fixed;
std::cout << "Print a complex number : " << z1 << std::endl;
std::cout << "Square it : " << z1*z1 << std::endl;
std::cout << "Real part : " << z1.real() << " = " << real(z1) << std::endl;
std::cout << "Imaginary part : " << z1.imag() << " = " << imag(z1) << std::endl;
std::cout << "Absolute value : " << abs(z1) << std::endl;
std::cout << "Argument : " << arg(z1) << std::endl;
std::cout << "Norm : " << norm(z1) << std::endl;
std::cout << "Complex conjugate : " << conj(z1) << std::endl;
std::cout << "Proj onto Riemann sphere : " << proj(z1) << std::endl;
typename Complex::value_type r = 1;
typename Complex::value_type theta = 0.8;
complex_type z1 { real_type(0), real_type(1) }; // We need a using declaration here, since polar is called with a scalar:
std::cout << "Print a complex number : " << z1 << std::endl;
std::cout << "Square it : " << z1*z1 << std::endl;
std::cout << "Real part : " << z1.real() << " = " << real(z1) << std::endl;
std::cout << "Imaginary part : " << z1.imag() << " = " << imag(z1) << std::endl;
real_type r { 1 };
real_type theta { 0.75 };
using std::polar; using std::polar;
std::cout << "Polar coord phase = 0 : " << polar(r) << std::endl;
std::cout << "Polar coord phase != 0 : " << polar(r, theta) << std::endl;
elementary_functions(z1); std::cout << "Polar coord phase = 0 : " << polar(r) << std::endl;
std::cout << "Polar coord phase != 0 : " << polar(r, theta) << std::endl;
std::cout << "\nElementary special functions:\n";
std::cout << "exp(z1) : " << exp(z1) << std::endl;
std::cout << "log(z1) : " << log(z1) << std::endl;
std::cout << "log10(z1) : " << log10(z1) << std::endl;
std::cout << "pow(z1, z1) : " << pow(z1, z1) << std::endl;
std::cout << "Take its square root : " << sqrt(z1) << std::endl;
std::cout << "sin(z1) : " << sin(z1) << std::endl;
std::cout << "cos(z1) : " << cos(z1) << std::endl;
std::cout << "tan(z1) : " << tan(z1) << std::endl;
std::cout << "asin(z1) : " << asin(z1) << std::endl;
std::cout << "acos(z1) : " << acos(z1) << std::endl;
std::cout << "atan(z1) : " << atan(z1) << std::endl;
std::cout << "sinh(z1) : " << sinh(z1) << std::endl;
std::cout << "cosh(z1) : " << cosh(z1) << std::endl;
std::cout << "tanh(z1) : " << tanh(z1) << std::endl;
std::cout << "asinh(z1) : " << asinh(z1) << std::endl;
std::cout << "acosh(z1) : " << acosh(z1) << std::endl;
std::cout << "atanh(z1) : " << atanh(z1) << std::endl;
} }
int main() int main()
{ {
const auto flags_orig = std::cout.flags(); std::cout << "First, some operations performed with std::complex:\n";
std::cout << std::scientific << std::fixed;
std::cout << "First, some operations we usually perform with std::complex:\n";
std::cout << std::setprecision(std::numeric_limits<typename std::complex<double>::value_type>::digits10);
complex_number_examples<std::complex<double>>(); complex_number_examples<std::complex<double>>();
std::cout << "\nNow the same operations performed using quad precision complex numbers:\n"; std::cout << "\nNow the same operations performed with quad precision complex numbers:\n";
std::cout << std::setprecision(std::numeric_limits<typename boost::multiprecision::cpp_complex_quad::value_type>::digits10);
complex_number_examples<boost::multiprecision::cpp_complex_quad>(); complex_number_examples<boost::multiprecision::cpp_complex_quad>();
}//]
std::cout << "\nNow the elementary functions performed using built-in, real-valued long double numbers:\n";
std::cout << std::setprecision(std::numeric_limits<long double>::digits10);
const long double ld_arg { 0.125L };
elementary_functions(ld_arg);
std::cout.flags(flags_orig);
}
//]
/* /*
//[cpp_complex_out //[cpp_complex_out
Now the same operations performed using quad precision complex numbers:
Print a complex number : (0.000000000000000000000000000000000,1.000000000000000000000000000000000) Print a complex number : (0.000000000000000000000000000000000,1.000000000000000000000000000000000)
Square it : -1.000000000000000000000000000000000 Square it : -1.000000000000000000000000000000000
Real part : 0.000000000000000000000000000000000 = 0.000000000000000000000000000000000 Real part : 0.000000000000000000000000000000000 = 0.000000000000000000000000000000000
Imaginary part : 1.000000000000000000000000000000000 = 1.000000000000000000000000000000000 Imaginary part : 1.000000000000000000000000000000000 = 1.000000000000000000000000000000000
Polar coord phase = 0 : 1.000000000000000000000000000000000 Absolute value : 1.000000000000000000000000000000000
Polar coord phase != 0 : (0.731688868873820886311838753000085,0.681638760023334166733241952779894) Argument : 1.570796326794896619231321691639751
Norm : 1.000000000000000000000000000000000
Complex conjugate : (0.000000000000000000000000000000000,-1.000000000000000000000000000000000)
Proj onto Riemann sphere : (0.000000000000000000000000000000000,1.000000000000000000000000000000000)
Polar coord phase = 0 : 1.000000000000000000000000000000000
Polar coord phase != 0 : (0.696706709347165389063740022772448,0.717356090899522792567167815703377)
Elementary special functions: Elementary special functions:
Absolute value : 1.000000000000000000000000000000000 exp(z1) : (0.540302305868139717400936607442977,0.841470984807896506652502321630299)
Argument : 1.570796326794896619231321691639751 log(z1) : (0.000000000000000000000000000000000,1.570796326794896619231321691639751)
Norm : 1.000000000000000000000000000000000 log10(z1) : (0.000000000000000000000000000000000,0.682188176920920673742891812715678)
Complex conjugate : (0.000000000000000000000000000000000,-1.000000000000000000000000000000000) pow(z1, z1) : 0.207879576350761908546955619834979
Proj on Riemann sphere : (0.000000000000000000000000000000000,1.000000000000000000000000000000000) Take its square root : (0.707106781186547524400844362104849,0.707106781186547524400844362104849)
exp(z1) : (0.540302305868139717400936607442977,0.841470984807896506652502321630299) sin(z1) : (0.000000000000000000000000000000000,1.175201193643801456882381850595601)
log(z1) : (0.000000000000000000000000000000000,1.570796326794896619231321691639751) cos(z1) : 1.543080634815243778477905620757062
log10(z1) : (0.000000000000000000000000000000000,0.682188176920920673742891812715678) tan(z1) : (0.000000000000000000000000000000000,0.761594155955764888119458282604794)
pow(z1, z1) : 0.207879576350761908546955619834979 asin(z1) : (0.000000000000000000000000000000000,0.881373587019543025232609324979792)
Take its square root : (0.707106781186547524400844362104849,0.707106781186547524400844362104849) acos(z1) : (1.570796326794896619231321691639751,-0.881373587019543025232609324979792)
sin(z1) : (0.000000000000000000000000000000000,1.175201193643801456882381850595601) atan(z1) : (0.000000000000000000000000000000000,inf)
cos(z1) : 1.543080634815243778477905620757062 sinh(z1) : (0.000000000000000000000000000000000,0.841470984807896506652502321630299)
tan(z1) : (0.000000000000000000000000000000000,0.761594155955764888119458282604794) cosh(z1) : 0.540302305868139717400936607442977
asin(z1) : (0.000000000000000000000000000000000,0.881373587019543025232609324979792) tanh(z1) : (0.000000000000000000000000000000000,1.557407724654902230506974807458360)
acos(z1) : (1.570796326794896619231321691639751,-0.881373587019543025232609324979792) asinh(z1) : (0.000000000000000000000000000000000,1.570796326794896619231321691639751)
atan(z1) : (0.000000000000000000000000000000000,inf) acosh(z1) : (0.881373587019543025232609324979792,1.570796326794896619231321691639751)
sinh(z1) : (0.000000000000000000000000000000000,0.841470984807896506652502321630299) atanh(z1) : (0.000000000000000000000000000000000,0.785398163397448309615660845819876)
cosh(z1) : 0.540302305868139717400936607442977
tanh(z1) : (0.000000000000000000000000000000000,1.557407724654902230506974807458360)
asinh(z1) : (0.000000000000000000000000000000000,1.570796326794896619231321691639751)
acosh(z1) : (0.881373587019543025232609324979792,1.570796326794896619231321691639751)
atanh(z1) : (0.000000000000000000000000000000000,0.785398163397448309615660845819876)
//] //]
*/ */