std::norm(std::complex)

 

C++

Compiler support

Freestanding and hosted

Language

Standard library

Standard library headers

Named requirements

Feature test macros (C++20)

Language support library

Concepts library (C++20)

Metaprogramming library (C++11)

Diagnostics library

General utilities library

Strings library

Containers library

Iterators library

Ranges library (C++20)

Algorithms library

Numerics library

Localizations library

Input/output library

Filesystem library (C++17)

Regular expressions library (C++11)

Concurrency support library (C++11)

Technical specifications

Symbols index

External libraries

 

Numerics library

Common mathematical functions

Mathematical special functions (C++17)

Mathematical constants (C++20)

Floating-point environment (C++11)

Complex numbers

Numeric arrays

Pseudo-random number generation

Factor operations

gcd (C++17)

lcm (C++17)

Interpolations

midpoint (C++20)

lerp (C++20)

Generic numeric operations

iota (C++11)

ranges::iota (C++23)

accumulate

inner_product

adjacent_difference

partial_sum

reduce (C++17)

transform_reduce (C++17)

inclusive_scan (C++17)

exclusive_scan (C++17)

transform_inclusive_scan (C++17)

transform_exclusive_scan (C++17)

Bit operations

bit_cast (C++20)

byteswap (C++23)

has_single_bit (C++20)

bit_ceil (C++20)

bit_floor (C++20)

bit_width (C++20)

rotl (C++20)

rotr (C++20)

countl_zero (C++20)

countl_one (C++20)

countr_zero (C++20)

countr_one (C++20)

popcount (C++20)

endian (C++20)

 

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)
Additional overloads (since C++11)
Defined in header <complex>
		(A)
float       norm( float f ); double      norm( double f ); long double norm( long double f );				(until C++20)
constexpr float       norm( float f ); constexpr double      norm( double f ); constexpr long double norm( long double f );				(since C++20) (until C++23)
template< class FloatingPoint > constexpr FloatingPoint norm( FloatingPoint f );				(since C++23)
			(B)
template< class Integer > double norm( Integer i );					(until C++20)
template< class Integer > constexpr double norm( Integer i );					(since C++20)

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

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

(since C++11)

Parameters

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

Return value

1) The squared magnitude of z.

A) The square of f.

B) The square of i.

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).

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 C++23) floating-point type T, then std::norm(num) has the same effect as std::norm(std::complex<T>(num)).
• Otherwise, if num has an integer type, then std::norm(num) has the same effect as std::norm(std::complex<double>(num)).

Example

Run this code

#include <cassert>
#include <complex>
#include <iostream>
 
int main()
{
    constexpr std::complex<double> z {3.0, 4.0};
    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)