std::proj(std::complex)

 

C++

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std::complex

Member functions
complex::complex
complex::operator=
complex::real
complex::imag
complex::operator+= complex::operator-= complex::operator*= complex::operator/=
Non-member functions
operator+ operator- operator+ operator- operator* operator/ operator== operator!= operator<< operator>>	real imag abs arg norm conj proj (C++11) polar
Exponential functions
exp
log
log10
Power functions
pow
sqrt
Trigonometric functions
sin cos tan	asin (C++11) acos (C++11) atan (C++11)
Hyperbolic functions
sinh cosh tanh	asinh (C++11) acosh (C++11) atanh (C++11)

 

Defined in header <complex>
template< class T > complex<T> proj( const complex<T>& z );	(1)	(since C++11)
std::complex<long double> proj( long double z );	(2)	(since C++11)
template< class DoubleOrIngeter > std::complex<double> proj( DoubleOrInteger z );	(3)	(since C++11)
std::complex<float> proj( float z );	(4)	(since C++11)

Returns the projection of the complex number z onto the Riemann sphere.

For most z, std::proj(z)==z, but all complex infinities, even the numbers where one component is infinite and the other is NaN, become positive real infinity, (INFINITY, 0) or (INFINITY, -0). The sign of the imaginary (zero) component is the sign of std::imag(z).

(since C++11)Additional overloads are provided for float, double, long double, and all integer types, which are treated as complex numbers with zero imaginary component.

Parameters

z

-

complex value

Return value

the projection of z onto the Riemann sphere

Example

run this code

#include <iostream>
#include <complex>
 
int main()
{
    std::complex<double> c1(1, 2);
    std::cout << "proj" << c1 << " = " << std::proj(c1) << '\n';
 
    std::complex<double> c2(INFINITY, -1);
    std::cout << "proj" << c2 << " = " << std::proj(c2) << '\n';
 
    std::complex<double> c3(0, -INFINITY);
    std::cout << "proj" << c3 << " = " << std::proj(c3) << '\n';
}

Output:

proj(1,2) = (1,2)
proj(inf,-1) = (inf,-0)
proj(0,-inf) = (inf,-0)

See also

abs(std::complex)	returns the magnitude of a complex number (function template)
norm	returns the squared magnitude (function template)
polar	constructs a complex number from magnitude and phase angle (function template)