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 operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
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exp
log
log10
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pow
sqrt
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sin cos tan	asin (C++11) acos (C++11) atan (C++11)
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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 DoubleOrInteger > 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).

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

Notes

The proj function helps model the Riemann sphere by mapping all infinities to one (give or take the sign of the imaginary zero), and should be used just before any operation, especially comparisons, that might give spurious results for any of the other infinities.

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)