Complex arithmetics in the openMHA

Collaboration diagram for Complex arithmetics in the openMHA:

Classes
struct	mha_complex_t
	Type for complex floating point values. More...

Functions
mha_complex_t &	set (mha_complex_t &self, mha_real_t real, mha_real_t imag=0)
	Assign real and imaginary parts to a mha_complex_t variable. More...
mha_complex_t	mha_complex (mha_real_t real, mha_real_t imag=0)
	Create a new mha_complex_t with specified real and imaginary parts. More...
mha_complex_t &	set (mha_complex_t &self, const std::complex< mha_real_t > &stdcomplex)
	Assign a mha_complex_t variable from a std::complex. More...
std::complex< mha_real_t >	stdcomplex (const mha_complex_t &self)
	Create a std::complex from mha_complex_t. More...
mha_complex_t &	expi (mha_complex_t &self, mha_real_t angle)
	replaces the value of the given mha_complex_t with exp(i*b). More...
double	angle (const mha_complex_t &self)
	Computes the angle of a complex number in the complex plane. More...
mha_complex_t &	operator+= (mha_complex_t &self, const mha_complex_t &other)
	Addition of two complex numbers, overwriting the first. More...
mha_complex_t	operator+ (const mha_complex_t &self, const mha_complex_t &other)
	Addition of two complex numbers, result is a temporary object. More...
mha_complex_t &	operator+= (mha_complex_t &self, mha_real_t other_real)
	Addition of a complex and a real number, overwriting the complex. More...
mha_complex_t	operator+ (const mha_complex_t &self, mha_real_t other_real)
	Addition of a complex and a real number, result is a temporary object. More...
mha_complex_t &	operator-= (mha_complex_t &self, const mha_complex_t &other)
	Subtraction of two complex numbers, overwriting the first. More...
mha_complex_t	operator- (const mha_complex_t &self, const mha_complex_t &other)
	Subtraction of two complex numbers, result is a temporary object. More...
mha_complex_t &	operator-= (mha_complex_t &self, mha_real_t other_real)
	Subtraction of a complex and a real number, overwriting the complex. More...
mha_complex_t	operator- (const mha_complex_t &self, mha_real_t other_real)
	Subtraction of a complex and a real number, result is a temporary object. More...
mha_complex_t &	operator*= (mha_complex_t &self, const mha_complex_t &other)
	Multiplication of two complex numbers, overwriting the first. More...
mha_complex_t	operator* (const mha_complex_t &self, const mha_complex_t &other)
	Multiplication of two complex numbers, result is a temporary object. More...
mha_complex_t &	operator*= (mha_complex_t &self, mha_real_t other_real)
	Multiplication of a complex and a real number, overwriting the complex. More...
mha_complex_t &	expi (mha_complex_t &self, mha_real_t angle, mha_real_t factor)
	replaces (!) the value of the given mha_complex_t with a * exp(i*b) More...
mha_complex_t	operator* (const mha_complex_t &self, mha_real_t other_real)
	Multiplication of a complex and a real number, result is a temporary object. More...
mha_real_t	abs2 (const mha_complex_t &self)
	Compute the square of the absolute value of a complex value. More...
mha_real_t	abs (const mha_complex_t &self)
	Compute the absolute value of a complex value. More...
mha_complex_t &	operator/= (mha_complex_t &self, mha_real_t other_real)
	Division of a complex and a real number, overwriting the complex. More...
mha_complex_t	operator/ (const mha_complex_t &self, mha_real_t other_real)
	Division of a complex and a real number, result is a temporary object. More...
mha_complex_t &	safe_div (mha_complex_t &self, const mha_complex_t &other, mha_real_t eps, mha_real_t eps2)
	Safe division of two complex numbers, overwriting the first. More...
mha_complex_t &	operator/= (mha_complex_t &self, const mha_complex_t &other)
	Division of two complex numbers, overwriting the first. More...
mha_complex_t	operator/ (const mha_complex_t &self, const mha_complex_t &other)
	Division of two complex numbers, result is a temporary object. More...
mha_complex_t	operator- (const mha_complex_t &self)
	Unary minus on a complex results in a negative temporary object. More...
bool	operator== (const mha_complex_t &x, const mha_complex_t &y)
	Compare two complex numbers for equality. More...
bool	operator!= (const mha_complex_t &x, const mha_complex_t &y)
	Compare two complex numbers for inequality. More...
void	conjugate (mha_complex_t &self)
	Replace (!) the value of this mha_complex_t with its conjugate. More...
mha_complex_t	_conjugate (const mha_complex_t &self)
	Compute the cojugate of this complex value. More...
void	reciprocal (mha_complex_t &self)
	Replace the value of this complex with its reciprocal. More...
mha_complex_t	_reciprocal (const mha_complex_t &self)
	compute the reciprocal of this complex value. More...
void	normalize (mha_complex_t &self)
	Divide a complex by its absolute value, thereby normalizing it (projecting onto the unit circle). More...
void	normalize (mha_complex_t &self, mha_real_t margin)
	Divide a complex by its absolute value, thereby normalizing it (projecting onto the unit circle), with a safety margin. More...
bool	almost (const mha_complex_t &self, const mha_complex_t &other, mha_real_t times_epsilon=1e2)
	Compare two complex numbers for equality except for a small relative error. More...
bool	operator< (const mha_complex_t &x, const mha_complex_t &y)
	Compares the absolute values of two complex numbers. More...

Detailed Description

Function Documentation

set() [1/2]

mha_complex_t& set ( mha_complex_t &  self, mha_real_t  real, mha_real_t  imag = 0  )

inline

Assign real and imaginary parts to a mha_complex_t variable.

Parameters

self	The mha_complex_t variable whose value is about to change.
real	The new real part.
imag	The new imaginary part.

Returns

A reference to the changed variable.

mha_complex()

mha_complex_t mha_complex ( mha_real_t  real, mha_real_t  imag = 0  )

inline

Create a new mha_complex_t with specified real and imaginary parts.

Parameters

real	The real part.
imag	The imaginary part.

Returns

The new value.

set() [2/2]

mha_complex_t& set ( mha_complex_t &  self, const std::complex< mha_real_t > &  stdcomplex  )

inline

Assign a mha_complex_t variable from a std::complex.

Parameters

self	The mha_complex_t variable whose value is about to change.
stdcomplex	The new complex value.

Returns

A reference to the changed variable.

stdcomplex()

std::complex<mha_real_t> stdcomplex ( const mha_complex_t &  self )

inline

Create a std::complex from mha_complex_t.

expi() [1/2]

mha_complex_t& expi ( mha_complex_t &  self, mha_real_t  angle  )

inline

replaces the value of the given mha_complex_t with exp(i*b).

Parameters

self	The mha_complex_t variable whose value is about to change.
angle	The angle in the complex plane [rad].

Returns

A reference to the changed variable.

angle()

double angle ( const mha_complex_t &  self )

inline

Computes the angle of a complex number in the complex plane.

Parameters

self	The complex number whose angle is needed.

Returns

The angle of a complex number in the complex plane.

operator+=() [1/2]

mha_complex_t& operator+= ( mha_complex_t &  self, const mha_complex_t &  other  )

inline

Addition of two complex numbers, overwriting the first.

operator+() [1/2]

mha_complex_t operator+ ( const mha_complex_t &  self, const mha_complex_t &  other  )

inline

Addition of two complex numbers, result is a temporary object.

operator+=() [2/2]

mha_complex_t& operator+= ( mha_complex_t &  self, mha_real_t  other_real  )

inline

Addition of a complex and a real number, overwriting the complex.

operator+() [2/2]

mha_complex_t operator+ ( const mha_complex_t &  self, mha_real_t  other_real  )

inline

Addition of a complex and a real number, result is a temporary object.

operator-=() [1/2]

mha_complex_t& operator-= ( mha_complex_t &  self, const mha_complex_t &  other  )

inline

Subtraction of two complex numbers, overwriting the first.

operator-() [1/3]

mha_complex_t operator- ( const mha_complex_t &  self, const mha_complex_t &  other  )

inline

Subtraction of two complex numbers, result is a temporary object.

operator-=() [2/2]

mha_complex_t& operator-= ( mha_complex_t &  self, mha_real_t  other_real  )

inline

Subtraction of a complex and a real number, overwriting the complex.

operator-() [2/3]

mha_complex_t operator- ( const mha_complex_t &  self, mha_real_t  other_real  )

inline

Subtraction of a complex and a real number, result is a temporary object.

operator*=() [1/2]

mha_complex_t& operator*= ( mha_complex_t &  self, const mha_complex_t &  other  )

inline

Multiplication of two complex numbers, overwriting the first.

operator*() [1/2]

mha_complex_t operator* ( const mha_complex_t &  self, const mha_complex_t &  other  )

inline

Multiplication of two complex numbers, result is a temporary object.

operator*=() [2/2]

mha_complex_t& operator*= ( mha_complex_t &  self, mha_real_t  other_real  )

inline

Multiplication of a complex and a real number, overwriting the complex.

expi() [2/2]

mha_complex_t& expi ( mha_complex_t &  self, mha_real_t  angle, mha_real_t  factor  )

inline

replaces (!) the value of the given mha_complex_t with a * exp(i*b)

Parameters

self	The mha_complex_t variable whose value is about to change.
angle	The imaginary exponent.
factor	The absolute value of the result.

Returns

A reference to the changed variable.

operator*() [2/2]

mha_complex_t operator* ( const mha_complex_t &  self, mha_real_t  other_real  )

inline

Multiplication of a complex and a real number, result is a temporary object.

abs2()

mha_real_t abs2 ( const mha_complex_t &  self )

inline

Compute the square of the absolute value of a complex value.

Returns

The square of the absolute value of self.

abs()

mha_real_t abs ( const mha_complex_t &  self )

inline

Compute the absolute value of a complex value.

Returns

The absolute value of self.

operator/=() [1/2]

mha_complex_t& operator/= ( mha_complex_t &  self, mha_real_t  other_real  )

inline

Division of a complex and a real number, overwriting the complex.

operator/() [1/2]

mha_complex_t operator/ ( const mha_complex_t &  self, mha_real_t  other_real  )

inline

Division of a complex and a real number, result is a temporary object.

safe_div()

mha_complex_t& safe_div ( mha_complex_t &  self, const mha_complex_t &  other, mha_real_t  eps, mha_real_t  eps2  )

inline

Safe division of two complex numbers, overwriting the first.

If abs(divisor) < eps, then divisor is replaced by eps. eps2 = eps*eps.

operator/=() [2/2]

mha_complex_t& operator/= ( mha_complex_t &  self, const mha_complex_t &  other  )

inline

Division of two complex numbers, overwriting the first.

operator/() [2/2]

mha_complex_t operator/ ( const mha_complex_t &  self, const mha_complex_t &  other  )

inline

Division of two complex numbers, result is a temporary object.

operator-() [3/3]

mha_complex_t operator- ( const mha_complex_t &  self )

inline

Unary minus on a complex results in a negative temporary object.

operator==()

bool operator== ( const mha_complex_t &  x, const mha_complex_t &  y  )

inline

Compare two complex numbers for equality.

operator!=()

bool operator!= ( const mha_complex_t &  x, const mha_complex_t &  y  )

inline

Compare two complex numbers for inequality.

conjugate()

void conjugate ( mha_complex_t &  self )

inline

Replace (!) the value of this mha_complex_t with its conjugate.

_conjugate()

mha_complex_t _conjugate ( const mha_complex_t &  self )

inline

Compute the cojugate of this complex value.

Returns

A temporary object holding the conjugate value.

reciprocal()

void reciprocal ( mha_complex_t &  self )

inline

Replace the value of this complex with its reciprocal.

_reciprocal()

mha_complex_t _reciprocal ( const mha_complex_t &  self )

inline

compute the reciprocal of this complex value.

Returns

A temporary object holding the reciprocal value.

normalize() [1/2]

void normalize ( mha_complex_t &  self )

inline

Divide a complex by its absolute value, thereby normalizing it (projecting onto the unit circle).

normalize() [2/2]

void normalize ( mha_complex_t &  self, mha_real_t  margin  )

inline

Divide a complex by its absolute value, thereby normalizing it (projecting onto the unit circle), with a safety margin.

almost()

bool almost ( const mha_complex_t &  self, const mha_complex_t &  other, mha_real_t  times_epsilon = 1e2  )

inline

Compare two complex numbers for equality except for a small relative error.

Parameters

self	The first complex number.
other	The second complex number.
times_epsilon	Permitted relative error is this number multiplied with the machine accuracy for this Floating point format (std::numeric_limits<mha_real_t>::epsilon)

Returns

true if the relative difference is below times_epsilon * std::numeric_limits<mha_real_t>::epsilon

operator<()

bool operator< ( const mha_complex_t &  x, const mha_complex_t &  y  )

inline

Compares the absolute values of two complex numbers.