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Difference between revisions of "cpp/numeric/complex/abs"

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< cpp‎ | numeric‎ | complex
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{{cpp/title|abs{{small|(std::complex)}}}}
 
{{cpp/title|abs{{small|(std::complex)}}}}
 
{{cpp/numeric/complex/navbar}}
 
{{cpp/numeric/complex/navbar}}
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{{ddcl | header=complex | 1=
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{{ddcl|header=complex|1=
 
template< class T >  
 
template< class T >  
 
T abs( const complex<T>& z );
 
T abs( const complex<T>& z );
 
}}
 
}}
  
−
Returns the magnitude of the complex number {{tt|z}}.
+
Returns the magnitude of the complex number {{c|z}}.
  
 
===Parameters===
 
===Parameters===
−
{{param list begin}}
+
{{par begin}}
−
{{param list item | z | complex value}}
+
{{par|z|complex value}}
−
{{param list end}}
+
{{par end}}
  
 
===Return value===
 
===Return value===
 +
If no errors occur, returns the absolute value (also known as norm, modulus, or magnitude) of {{c|z}}.
  
−
the magnitude of {{tt|z}}
+
Errors and special cases are handled as if the function is implemented as {{c|std::hypot(std::real(z), std::imag(z))}}.
 +
 
 +
===Example===
 +
{{example|
 +
|code=
 +
#include <complex>
 +
#include <iostream>
 +
 
 +
int main()
 +
{
 +
    std::complex<double> z(1, 1);
 +
    std::cout << z << " cartesian is rho = " << std::abs(z)
 +
              << " theta = " << std::arg(z) << " polar\n";
 +
}
 +
|output=
 +
(1,1) cartesian is rho = 1.41421 theta = 0.785398 polar
 +
}}
  
 
===See also===
 
===See also===
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{{dcl list begin}}
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{{dsc begin}}
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{{dcl list template | cpp/numeric/complex/dcl list arg}}
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{{dsc inc|cpp/numeric/complex/dsc arg}}
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{{dcl list end}}
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{{dsc inc|cpp/numeric/complex/dsc polar}}
 +
{{dsc inc|cpp/numeric/math/dsc abs}}
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{{dsc inc|cpp/numeric/math/dsc fabs}}
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{{dsc inc|cpp/numeric/math/dsc hypot}}
 +
{{dsc inc|cpp/numeric/valarray/dsc abs}}
 +
{{dsc see c|c/numeric/complex/cabs}}
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{{dsc end}}
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 +
{{langlinks|de|es|fr|it|ja|pt|ru|zh}}

Latest revision as of 12:31, 20 April 2023

 
C++
 
Numerics library
Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
Factor operations
(C++17)
(C++17)
Interpolations
(C++20)
(C++20)
Saturation arithmetic
(C++26)
(C++26)
(C++26)
(C++26)
(C++26)

Generic numeric operations
Bit operations
(C++20)    
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++23)
(C++20)
 
std::complex
 
Defined in header <complex>
template< class T >
T abs( const complex<T>& z );

Returns the magnitude of the complex number z.

Contents

[edit] Parameters

z - complex value

[edit] Return value

If no errors occur, returns the absolute value (also known as norm, modulus, or magnitude) of z.

Errors and special cases are handled as if the function is implemented as std::hypot(std::real(z), std::imag(z)).

[edit] Example

Run this code
#include <complex>
#include <iostream>
 
int main()
{
    std::complex<double> z(1, 1);
    std::cout << z << " cartesian is rho = " << std::abs(z)
              << " theta = " << std::arg(z) << " polar\n";
}

Output: 

(1,1) cartesian is rho = 1.41421 theta = 0.785398 polar

[edit] See also

 returns the phase angle
(function template) [edit]
constructs a complex number from magnitude and phase angle
(function template) [edit]
(C++11)
 computes absolute value of an integral value (|x|)
(function) [edit]
(C++11)(C++11)
 absolute value of a floating point value (|x|)
(function) [edit]
(C++11)(C++11)(C++11)
 computes square root of the sum of the squares of two or three(since C++17) given numbers (√x2+y2), (√x2+y2+z2)(since C++17)
(function) [edit]
applies the function abs to each element of valarray
(function template) [edit]
C documentation for cabs
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