C++ : Complex numbers library

Complex numbers library

The complex library implements the complex class to contain complex numbers in cartesian form and several functions and overloads to operate with them:

Classes

complex

Complex number class (class template)

Functions

Complex values:

real	Return real part of complex (function template)

imag	Return imaginary part of complex (function template)

abs	Return absolute value of complex (function template)

arg	Return phase angle of complex (function template )

norm	Return norm of complex number (function template)

conj	Return complex conjugate (function template)

polar

Return complex from polar components (function template )

Transcendentals overloads:

cos	Return cosine of complex (function template)

cosh	Return hyperbolic cosine of complex (function template)

exp	Return exponential of complex (function template)

log	Return natural logarithm of complex (function template)

log10

Return common logarithm of complex (function template)

pow	Return complex power (function template)

sin	Return sine of complex (function template)

sinh	Return hyperbolic sine of complex (function template)

sqrt	Return square root of complex (function template)

tan	Return tangent of complex (function template)

tanh	Return hyperbolic tangent of complex (function template)

Operator overloads:

complex operators

Complex number operators (functions)

complex

class template

<complex>

template <class T> class complex;

Complex number class

The complex class is designed to hold two components of the same type, that conform a complex number.

A complex number is formed by adding an imaginary part to a real number:

x + y * i

The imaginary part (y*i) is a factor of i, known as the imaginary unit, and which satisfies that:

i² = -1

In this class, complex numbers have two components: real (corresponding to x in the above example) and imag (corresponding to y). This way of referring to complex numbers by two real components is known and cartesian, because this way they have the ability to be easily representable on a cartesian axis.

The class has been implemented to provide as similar a functionality as the one of a numerical type when this was possible, therefore, complexobjects can be assigned, compared, inserted and extracted, as well as several arithmetical operators have been overloaded to be used on them directly.

Members

(constructor)

Complex number constructor (public member function)

complex::imag

Return imaginary part (public member function)

complex::real

Return real part (public member function)

complex operators

Complex number operators (functions)

The class also includes an alias type of the template argument:

complex::value_type

Value type (public member type)

complex specializations

complex is specialized for the three fundamental floating-point types: float, double and long double.

These specializations have the same members as the template, but optimize its implementation for these fundamental types, as well as they allow operations with other instantiations of complex (complex objects with different template argument).

complex::complex

public member function

 

complex (const T& re = T(), const T& im = T());
complex (const complex& cmplx);
template<class X>
  complex (const complex<X>& cmplx);

Complex number constructor

Constructs a complex object.

It may be constructed from two values (re and im) or from another complex number.

Parameters

re, im

Real and imaginary parts, respectively, of complex number.
T is complex's template type.

cmplx

A complex object.
If constructed from a complex object with a different template parameter (X), the apropriate conversions are performed.

 

Example

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// complex constructor example #include <iostream> #include <complex> using namespace std; int main () { complex<double> first (2.0,2.0); complex<double> second (first); complex<long double> third (second); cout << third; return 0; }

Output:

(2,2)

 

complex::real

public member function

 

T real() const;

Return real part

Returns the real part of the complex number.

A global function exists, real, with the same behavior.

Parameters

none

Return value

Real part.
T is complex's template type.

Example

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// complex::real example #include <iostream> #include <complex> using namespace std; int main () { complex<double> mycomplex (10.0,1.0); cout << "Real part: " << mycomplex.real() << endl; return 0; }

Output:

Real part: 10

 

complex::imag

public member function

 

T imag() const;

Return imaginary part

Returns the imaginary part of the complex number.
The imaginary part is the factor by which the imaginary unit is multiplied.

A global function exists, imag, with the same behavior.

Parameters

none

Return value

Imaginary part.
T is complex's template type.

Example

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// complex::imag example #include <iostream> #include <complex> using namespace std; int main () { complex<double> mycomplex (20.0,2.0); cout << "Imaginary part: " << mycomplex.imag() << endl; return 0; }

Output:

Imaginary part: 2