std::norm(std::complex) - cppreference.com (original) (raw)
| Defined in header | | | | ---------------------------------------------------------------------------------------------------------------- | | --------------------------- | | (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 | | | | (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) |
- 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) |
|---|
[edit] Parameters
| z | - | complex value |
|---|---|---|
| f | - | floating-point value |
| i | - | integer value |
[edit] Return value
- The squared magnitude of z.
A) The square of f.
B) The square of i.
[edit] 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)).
[edit] Example
#include #include #include int main() { constexpr std::complex 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:
[edit] See also
| | 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] |