waveblocks::math::ContinuousSqrt< T > Class Template Reference

This class deals with the issue, that the square root of complex numbers is not unique. More...

#include <continuous_sqrt.hpp>

Public Member Functions
	ContinuousSqrt ()
	Delayes initialization of the stored reference solution. More...
	ContinuousSqrt (std::complex< T > sqrt)
	Initializes the stored reference solution to a chosen value. More...
std::complex< T >	operator() (std::complex< T > input)
	Solves the quadratic equation \( z^2 = c \). More...
std::complex< T >	operator() () const
	Retrieve the stored reference solution. More...
T	get_state (void) const
	getter for state state More...

Static Public Member Functions
static T	continuate (T ref, T arg)

Private Attributes
std::complex< T >	sqrt_
T	state_
bool	empty_

Detailed Description

template<class T>
class waveblocks::math::ContinuousSqrt< T >

This class deals with the issue, that the square root of complex numbers is not unique.

The equation \( z^2 = r \exp{(i\phi)} \) has two solutions, namely \( z_1=\sqrt{r} \exp{\left(i\frac{\phi}{2}\right)} \) and \( z_2=\sqrt{r} \exp{\left(i(\frac{\phi}{2}+\pi)\right)} \).

This class chooses the solution, that is nearest to the solution of the previous computation ( = reference solution). Then this class overrides the stored reference solution with the current solution.

The distance between the two complex numbers is determined by the angle-distance.

Template Parameters

T	Type of both the real and imaginary components of the complex number.

Constructor & Destructor Documentation

template<class T>

waveblocks::math::ContinuousSqrt< T >::ContinuousSqrt ( )

inline

Delayes initialization of the stored reference solution.

The next call to operator()() yields the principal square root.

template<class T>

waveblocks::math::ContinuousSqrt< T >::ContinuousSqrt ( std::complex< T >  sqrt )

inline

Initializes the stored reference solution to a chosen value.

Parameters

sqrt	The initial reference solution.

Member Function Documentation

template<class T>

static T waveblocks::math::ContinuousSqrt< T >::continuate ( T  ref, T  arg  )

inlinestatic

Chooses the square root angle (argument) that continuates the reference angle the best. Throws an exception if the deviation above an accepted value (by default > pi/4).

Parameters

[in]	ref	The angle of the reference square root. domain = \( [-\pi;\pi] \)
[in]	arg	The angle of the computed square root. domain = \( [-\pi;\pi] \)

Returns

The angle of the continuating square root. domain = \( [-\pi;\pi] \)

template<class T>

T waveblocks::math::ContinuousSqrt< T >::get_state ( void  ) const

inline

getter for state state

Returns

state_[-pi,pi]

template<class T>

std::complex<T> waveblocks::math::ContinuousSqrt< T >::operator() ( std::complex< T >  input )

inline

Solves the quadratic equation \( z^2 = c \).

Chooses the solution \( \hat{z} \) that best continuates the prior result \( z_0 \) and updates the reference solution ( \( z_0 \gets \hat{z} \)).

Parameters

input

The right-hand-side \( c \).

Returns

The best solution \( \hat{z} \).

template<class T>

std::complex<T> waveblocks::math::ContinuousSqrt< T >::operator() ( ) const

inline

Retrieve the stored reference solution.

Member Data Documentation

template<class T>

bool waveblocks::math::ContinuousSqrt< T >::empty_

private

false iff a reference solution is stored

template<class T>

std::complex<T> waveblocks::math::ContinuousSqrt< T >::sqrt_

private

stored reference solution

template<class T>

T waveblocks::math::ContinuousSqrt< T >::state_

private

argument (angle) of reference solution domain = [-pi;pi]

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

• /userdata/raoulb/LWB/libwaveblocks/waveblocks/math/continuous_sqrt.hpp