std::norm(std::complex)

 

C++

Language

Standard Library Headers

Freestanding and hosted implementations

Named requirements

Language support library

Concepts library (C++20)

Diagnostics library

Utilities library

Strings library

Containers library

Iterators library

Ranges library (C++20)

Algorithms library

Numerics library

Input/output library

Localizations library

Regular expressions library (C++11)

Atomic operations library (C++11)

Thread support library (C++11)

Filesystem library (C++17)

Technical Specifications

 

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

Compile-time rational arithmetic (C++11)

Numeric algorithms

gcd (C++17)

lcm (C++17)

Interpolations

midpoint (C++20)

lerp (C++20)

Generic numeric operations

iota (C++11)

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)

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)
		(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).

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)