CDPL::Math::ComplexTraits< T > Struct Template Reference

Common operations and type aliases for complex arithmetic types. More...

#include <TypeTraits.hpp>

Inheritance diagram for CDPL::Math::ComplexTraits< T >:

Public Types
typedef T	ValueType
	The complex value type (a std::complex specialization). More...
typedef T::value_type	RealType
	The underlying real-valued type. More...
typedef const T &	ConstReference
	Constant-reference type to a value. More...
typedef ComplexTraits< T >	SelfType
	Convenience alias for this traits instantiation. More...

Static Public Member Functions
static RealType	real (ConstReference t)
	Returns the real part of the complex value t. More...
static RealType	imag (ConstReference t)
	Returns the imaginary part of the complex value t. More...
static ValueType	conj (ConstReference t)
	Returns the complex conjugate of t. More...
static RealType	abs (ConstReference t)
	Returns the modulus (absolute value) of the complex value t. More...
static ValueType	sqrt (ConstReference t)
	Returns the principal complex square root of t. More...
static RealType	norm1 (ConstReference t)
	Returns the L1 norm of the complex value t ( \( |\mathrm{Re}(t)| + |\mathrm{Im}(t)| \)). More...
static RealType	norm2 (ConstReference t)
	Returns the L2 norm of the complex value t (identical to its modulus). More...
static RealType	normInf (ConstReference t)
	Returns the L∞ norm of the complex value t ( \( \max(|\mathrm{Re}(t)|, |\mathrm{Im}(t)|) \)). More...

Detailed Description

template<typename T>
struct CDPL::Math::ComplexTraits< T >

Common operations and type aliases for complex arithmetic types.

Template Parameters

T	A std::complex specialization.

Member Typedef Documentation

ValueType

template<typename T >

typedef T CDPL::Math::ComplexTraits< T >::ValueType

The complex value type (a std::complex specialization).

RealType

template<typename T >

typedef T::value_type CDPL::Math::ComplexTraits< T >::RealType

The underlying real-valued type.

ConstReference

template<typename T >

typedef const T& CDPL::Math::ComplexTraits< T >::ConstReference

Constant-reference type to a value.

SelfType

template<typename T >

typedef ComplexTraits<T> CDPL::Math::ComplexTraits< T >::SelfType

Convenience alias for this traits instantiation.

Member Function Documentation

real()

template<typename T >

static RealType CDPL::Math::ComplexTraits< T >::real ( ConstReference  t )

inlinestatic

Returns the real part of the complex value t.

Parameters

t	The complex value.

Returns

The real part \( \mathrm{Re}(t) \).

imag()

template<typename T >

static RealType CDPL::Math::ComplexTraits< T >::imag ( ConstReference  t )

inlinestatic

Returns the imaginary part of the complex value t.

Parameters

t	The complex value.

Returns

The imaginary part \( \mathrm{Im}(t) \).

conj()

template<typename T >

static ValueType CDPL::Math::ComplexTraits< T >::conj ( ConstReference  t )

inlinestatic

Returns the complex conjugate of t.

Parameters

t	The complex value.

Returns

The conjugate \( \overline{t} \).

abs()

template<typename T >

static RealType CDPL::Math::ComplexTraits< T >::abs ( ConstReference  t )

inlinestatic

Returns the modulus (absolute value) of the complex value t.

Parameters

t	The complex value.

Returns

The modulus \( |t| \).

sqrt()

template<typename T >

static ValueType CDPL::Math::ComplexTraits< T >::sqrt ( ConstReference  t )

inlinestatic

Returns the principal complex square root of t.

Parameters

t	The complex value.

Returns

\( \sqrt{t} \) as a complex value.

norm1()

template<typename T >

static RealType CDPL::Math::ComplexTraits< T >::norm1 ( ConstReference  t )

inlinestatic

Returns the L1 norm of the complex value t ( \( |\mathrm{Re}(t)| + |\mathrm{Im}(t)| \)).

Parameters

t	The complex value.

Returns

The L1 norm of t.

norm2()

template<typename T >

static RealType CDPL::Math::ComplexTraits< T >::norm2 ( ConstReference  t )

inlinestatic

Returns the L2 norm of the complex value t (identical to its modulus).

Parameters

t	The complex value.

Returns

The L2 norm of t.

normInf()

template<typename T >

static RealType CDPL::Math::ComplexTraits< T >::normInf ( ConstReference  t )

inlinestatic

Returns the L∞ norm of the complex value t ( \( \max(|\mathrm{Re}(t)|, |\mathrm{Im}(t)|) \)).

Parameters

t	The complex value.

Returns

The L∞ norm of t.

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The documentation for this struct was generated from the following file:

• TypeTraits.hpp