std::norm(std::complex)

 

C++

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Symbols index

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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 C++20) operator<<operator>>	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
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>
	(1)
template< class T > T norm( const std::complex<T>& z );			(until C++20)
template< class T > constexpr T norm( const std::complex<T>& z );			(since C++20)
		(2)
float norm( float z ); template< class DoubleOrInteger > double norm( DoubleOrInteger z ); long double norm( long double z );				(since C++11) (until C++20)
constexpr float norm( float z ); template< class DoubleOrInteger > constexpr double norm( DoubleOrInteger z ); constexpr long double norm( long double z );				(since C++20)

1) Returns the squared magnitude of the complex number z.

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

(since C++11)

Parameters

z

-

complex value

Return value

the squared magnitude of z

Notes

The norm calculated by this function is also known as field norm or absolute square.

The Euclidean norm of a complex number is provided by std::abs, which is more costly to compute. In some situations, it may be replaced by std::norm, for example, if abs(z1) > abs(z2) then norm(z1) > norm(z2).

Example

Run this code

#include <cassert>
#include <complex>
#include <iostream>
 
int main()
{
    constexpr std::complex<double> z{3, 4};
    static_assert(std::norm(z) == (z.real() * z.real() + z.imag() * z.imag()));
    static_assert(std::norm(z) == (z * std::conj(z)));
           assert(std::norm(z) == (std::abs(z) * std::abs(z)));
    std::cout << "std::norm(" << z << ") = " << std::norm(z) << '\n';
}

Output:

std::norm((3,4)) = 25

See also

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