std::norm(std::complex)
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
#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
returns the magnitude of a complex number (function template) |
|
returns the complex conjugate (function template) |
|
constructs a complex number from magnitude and phase angle (function template) |
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