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Defined in header <complex> | ||
| (1) | ||
template<class T> T norm(conststd::complex<T>& z); | (until C++20) | |
template<class T> constexpr T norm(conststd::complex<T>& z); | (since C++20) | |
Additional overloads(since C++11) | ||
Defined in header <complex> | ||
| (A) | ||
float norm(float f); double norm(double f); | (until C++20) | |
constexprfloat norm(float f); constexprdouble norm(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> constexprdouble norm( Integer i); | (since C++20) | |
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) |
Contents |
| z | - | complex value |
| f | - | floating-point value |
| i | - | integer value |
The norm calculated by this function is also known asfield norm orabsolute square.
TheEuclidean norm of a complex number is provided bystd::abs, which is more costly to compute. In some situations, it may be replaced bystd::norm, for example, ifabs(z1)> abs(z2) thennorm(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 argumentnum:
T, thenstd::norm(num) has the same effect asstd::norm(std::complex<T>(num)).#include <cassert>#include <complex>#include <iostream> int main(){constexprstd::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
| returns the magnitude of a complex number (function template)[edit] | |
| returns the complex conjugate (function template)[edit] | |
| constructs a complex number from magnitude and phase angle (function template)[edit] |
