Imaginary type, used to represent purely imaginary numbers. More...

#include <cmplx.h>

Inheritance diagram for Imaginary_t< T >:

Collaboration diagram for Imaginary_t< T >:

Public Member Functions
T	real () const
	Real part of Complex number.

T	imag () const
	Imaginary part of Complex number.

T	squarenorm () const
	Compute square norm of Complex number.

T	abs () const
	Compute absolute value of Complex number.

T	arg () const
	Compute argument of Complex number.

Complex< T >	conj () const
	Compute conjugate of Complex number.

Complex< T >	dagger () const
	Compute dagger of Complex number.

Complex< T >	polar (const T r, const T theta)
	Stores and returns Complex number given in polar coordinates.

Complex< T > &	random ()
	Assign random values to Complex real and imaginary part.

Complex< T > &	gaussian_random (double width=1.0)
	Produces complex gaussian random values.

template<typename A >
Complex< T > &	operator+= (const Complex< A > &lhs) &
	+= addition assignment operator

template<typename A >
Complex< T > &	operator-= (const Complex< A > &lhs) &
	-= subtraction assignment operator

template<typename A >
Complex< T > &	operator*= (const Complex< A > &lhs) &
	*= multiply assignment operator

template<typename A >
Complex< T > &	operator/= (const Complex< A > &lhs) &
	/= divide assignment operator

Complex< T > &	operator++ ()
	++ increment operator

Complex< T > &	operator-- ()
	– decrement operator

template<typename A >
Complex< T >	conj_mul (const Complex< A > &b) const
	Conjugate multiply method.

template<typename A >
Complex< T >	mul_conj (const Complex< A > &b) const
	Multiply conjugate method.

Detailed Description

template<typename T>
class Imaginary_t< T >

Imaginary type, used to represent purely imaginary numbers.

Useful for reducing multiply operations in im * complex or im * real -ops Derived from Complex class, so generic complex ops should remain valid Defines only operators * and /, others go via Complex class

Note: Imaginary_t should NOT be used in Field variables

Template Parameters

T	type of imaginary (float/double)

Definition at line 1307 of file cmplx.h.

Member Function Documentation

◆ abs()

template<typename T >

T Complex< T >::abs ( ) const

inlineinherited

Compute absolute value of Complex number.

Essentially sqrt(squarenorm(z)):

\begin{align} |z| = \sqrt{\Re(z)^2 + \Im(z)^2}\end{align}

Returns: T

Definition at line 259 of file cmplx.h.

◆ arg()

template<typename T >

T Complex< T >::arg ( ) const

inlineinherited

Compute argument of Complex number.

\begin{align} \arg(z) = \arctan2(\Im(z)),\Re(z)\end{align}

Returns: T

Definition at line 270 of file cmplx.h.

◆ conj()

template<typename T >

Complex< T > Complex< T >::conj ( ) const

inlineinherited

Compute conjugate of Complex number.

\begin{align} z &= x + i\cdot y \\ \Rightarrow z^* &= x - i\cdot y\end{align}

Returns: Complex<T>

Definition at line 282 of file cmplx.h.

◆ conj_mul()

template<typename T >

template<typename A >

Complex< T > Complex< T >::conj_mul ( const Complex< A > & b ) const

inlineinherited

Conjugate multiply method.

Conjugate a (*this) and multiply with give argument b: a.conj_mul(b) \( \equiv a^* \cdot b\)

Template Parameters

A	Type for Complex number b

Parameters

b	number to multiply with

Returns: Complex<T>

Definition at line 611 of file cmplx.h.

◆ dagger()

template<typename T >

Complex< T > Complex< T >::dagger ( ) const

inlineinherited

Compute dagger of Complex number.

Alias to Complex::conj

\begin{align} z^* = z^\dagger \end{align}

Returns: Complex<T>

Definition at line 293 of file cmplx.h.

◆ gaussian_random()

template<typename T >

Complex< T > & Complex< T >::gaussian_random ( double width = 1.0 )

inlineinherited

Produces complex gaussian random values.

Uses hila::gaussrand2 for both real and imaignary part Assigns same random value for both real and imaginary part

Parameters

width gaussian_random

Returns: Complex<T>&

Definition at line 338 of file cmplx.h.

◆ imag()

template<typename T >

T Complex< T >::imag ( ) const

inlineinherited

Imaginary part of Complex number.

Overloads exist for pass by value and pass by reference for when Complex is defined as non-const or const

Returns: T Imaginary part

Definition at line 177 of file cmplx.h.

◆ mul_conj()

template<typename T >

template<typename A >

Complex< T > Complex< T >::mul_conj ( const Complex< A > & b ) const

inlineinherited

Multiply conjugate method.

Multiply a (*this) with conjugate of given argument b: a.mul_conj(b) \( \equiv a \cdot b^*\)

Template Parameters

A	Type for Complex number b

Parameters

b	number to conjugate and multiply withv

Returns: Complex<T>

Definition at line 627 of file cmplx.h.

◆ operator*=()

template<typename T >

template<typename A >

Complex< T > & Complex< T >::operator*= ( const Complex< A > & lhs ) &

inlineinherited

*= multiply assignment operator

Multiply assignment for Complex numbers can be performed in the following ways

Complex multiply assign:

Standard Complex number multiplication

\begin{align}z &= x + iy, w = x' + iy' \\ z w &= (x + iy)(x' + iy') = (xx'-yy') + i(xy' + yx')\end{align}

Complex<double> z,w;
//
// z,w get values
//
z*=w; // z = zw as defined above

Real multiply assign:

Multiply assign by real number to both components of Complex number

Complex<double> z(1,1);

z *= 2; // z.re = 2, z.im = 2

Definition at line 475 of file cmplx.h.

◆ operator++()

template<typename T >

Complex< T > & Complex< T >::operator++ ( )

inlineinherited

++ increment operator

Increments real part of Complex number

Complex<double> z(1,1);

z++; // z.re = 2, z.im = 1

Returns: Complex<T>&

Definition at line 557 of file cmplx.h.

◆ operator+=()

template<typename T >

template<typename A >

Complex< T > & Complex< T >::operator+= ( const Complex< A > & lhs ) &

inlineinherited

+= addition assignment operator

Addition assignment for Complex numbers can be performed in the following ways

Complex addition assignment:

Complex<double> z(0,0);
Complex<double> w(1,1);
z += w; // z.re = 1, z.im = 1

Real addition assignment:

Add assign only to real part of Complex number

Complex<double> z(0,0);

z += 1; // z.re = 1, z.im = 0

Definition at line 391 of file cmplx.h.

◆ operator--()

template<typename T >

Complex< T > & Complex< T >::operator-- ( )

inlineinherited

– decrement operator

Decrement real part of Complex number

Complex<double> z(1,1);

z--; // z.re = 0, z.im = 1

Returns: Complex<T>&

Definition at line 574 of file cmplx.h.

◆ operator-=()

template<typename T >

template<typename A >

Complex< T > & Complex< T >::operator-= ( const Complex< A > & lhs ) &

inlineinherited

-= subtraction assignment operator

Subtraction assignment for Complex numbers can be performed in the following ways

Complex subtract assign:

Complex<double> z(0,0);
Complex<double> w(1,1);
z -= w; // z.re = -1, z.im = -1

Real subtract assign:

Subtract assign only to real part of Complex number

Complex<double> z(0,0);

z -= 1; // z.re = -1, z.im = 0

Definition at line 427 of file cmplx.h.

◆ operator/=()

template<typename T >

template<typename A >

Complex< T > & Complex< T >::operator/= ( const Complex< A > & lhs ) &

inlineinherited

/= divide assignment operator

Divide assignment for Complex numbers can be performed in the following ways

Complex divide assign:

Standard Complex number division

\begin{align}z &= x + iy, w = x' + iy' \\ \frac{z}{w} &= \frac{x + iy}{x' + iy'} = \frac{(xx'+ yy') + i( yx' - xy')}{|w|^2}\end{align}

Complex<double> z,w;
//
// z,w get values
//
z/=w; // z = z/w as defined above

Real divide assign:

Divide assign by real number to both components of Complex number

Complex<double> z(2,2);

z /= 2; // z.re = 1, z.im = 1

Definition at line 527 of file cmplx.h.

◆ polar()

template<typename T >

Complex< T > Complex< T >::polar	(	const T	r,
		const T	theta
	)

inlineinherited

Stores and returns Complex number given in polar coordinates.

\begin{align} z = r\cdot e^{i\theta} \end{align}

Complex<double> c;
double r = 1;
double theta = 3.14159265358979/2; // pi/2
c.polar(r,theta); // c.re = 0, c.im = 1

Parameters

r	Radius of Complex number
theta	Angle of complex number in radians

Returns: Complex<T> Complex number

Definition at line 313 of file cmplx.h.

◆ random()

template<typename T >

Complex< T > & Complex< T >::random ( )

inlineinherited

Assign random values to Complex real and imaginary part.

Uses hila::random for both real and imaginary part

Returns: Complex<T>&

Definition at line 325 of file cmplx.h.

◆ real()

template<typename T >

T Complex< T >::real ( ) const

inlineinherited

Real part of Complex number.

Overloads exist for pass by value and pass by reference for when Complex is defined as non-const or const

Returns: T Real part

Definition at line 165 of file cmplx.h.

◆ squarenorm()

template<typename T >

T Complex< T >::squarenorm ( ) const

inlineinherited

Compute square norm of Complex number.

\begin{align} |z|^2 = \Re(z)^2 + \Im(z)^2\end{align}

Returns: T Squared norm

Definition at line 248 of file cmplx.h.

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

cmplx.h

Public Member Functions

Detailed Description

Member Function Documentation

◆ abs()

◆ arg()

◆ conj()

◆ conj_mul()

◆ dagger()

◆ gaussian_random()

◆ imag()

◆ mul_conj()

◆ operator*=()

◆ operator++()

◆ operator+=()

◆ operator--()

◆ operator-=()

◆ operator/=()

◆ polar()

◆ random()

◆ real()

◆ squarenorm()