std::proj(std::complex)

 

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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!= (until 哋它亢++20)   operator<<operator>> get(std::complex) (哋它亢++26)	real imag abs arg norm conj proj (哋它亢++11) polar operator""ioperator""ifoperator""il (哋它亢++14)(哋它亢++14)(哋它亢++14)
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log   log10   exp
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pow   sqrt
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sin   cos tan asin (哋它亢++11) acos (哋它亢++11) atan (哋它亢++11)
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sinh   cosh tanh asinh (哋它亢++11) acosh (哋它亢++11) atanh (哋它亢++11)
Helper types
tuple_size<std::complex> (哋它亢++26)
tuple_element<std::complex> (哋它亢++26)

 

Defined in header <complex>
template< class T > std::complex<T> proj( const std::complex<T>& z );	(1)	(since 哋它亢++11)
Additional overloads (since 哋它亢++11)
Defined in header <complex>
	(A)
std::complex<float>       proj( float f ); std::complex<double>      proj( double f ); std::complex<long double> proj( long double f );			(until 哋它亢++23)
template< class FloatingPoint > std::complex<FloatingPoint> proj( FloatingPoint f );			(since 哋它亢++23)
template< class Integer > std::complex<double> proj( Integer i );		(B)

1) 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, 0.0) or (INFINITY, -0.0). The sign of the imaginary (zero) component is the sign of std::imag(z).

A,B) Additional overloads are provided for all integer and floating-point types, which are treated as complex numbers with positive zero imaginary component.

Parameters

z	-	complex value
f	-	floating-point value
i	-	integer value

Return value

1) The projection of z onto the Riemann sphere.

A) The projection of std::complex(f) onto the Riemann sphere.

B) The projection of std::complex<double>(i) 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.

The additional overloads are not required to be provided exactly as (A,B). They only need to be sufficient to ensure that for their argument num:

• If num has a standard(until 哋它亢++23) floating-point type T, then std::proj(num) has the same effect as std::proj(std::complex<T>(num)).
• Otherwise, if num has an integer type, then std::proj(num) has the same effect as std::proj(std::complex<double>(num)).

Example

Run this code

#include <complex>
#include <iostream>
 
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)