cmplx.h File Reference

Definition of Complex types. More...

#include "plumbing/defs.h"

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Classes
class	Complex< T >
	Complex definition. More...
class	Imaginary_t< T >
	Imaginary type, used to represent purely imaginary numbers. More...
struct	hila::is_complex_or_arithmetic< T >
	hila::is_complex_or_arithmetic<T>::value More...

Namespaces
namespace	hila
	Invert diagonal + const. matrix using Sherman-Morrison formula.

Functions
template<typename T >
T	abs (const Complex< T > &a)
	Return absolute value of Complex number.
template<typename T >
T	arg (const Complex< T > &a)
	Return argument of Complex number.
template<typename T >
Complex< T >	conj (const Complex< T > &val)
	Return conjugate of Complex number.
template<typename T >
Complex< T >	dagger (const Complex< T > &val)
	Return dagger of Complex number.
constexpr Imaginary_t< double >	I (1.0)
	Imaginary unit I - global variable.
template<typename T >
T	imag (const Complex< T > &a)
	Retrun imaginary value of Complex number.
template<typename T >
std::ostream &	operator<< (std::ostream &strm, const Complex< T > &A)
	Print a complex value as (re,im)
template<typename T >
Complex< T >	polar (T r, T arg)
	Return complex number given by polar representation.
template<typename T >
std::string	hila::prettyprint (const Complex< T > &A, int prec=8)
	Return well formatted Complex number as std::string.
template<typename T >
T	real (const Complex< T > &a)
	Return real value of Complex number.
template<typename T >
auto	squarenorm (const Complex< T > &val)
	Return Squarenorm of Complex number.
template<typename T >
std::string	hila::to_string (const Complex< T > &A, int prec=8, char separator=' ')
	Return Complex number as std::string.

Detailed Description

Definition of Complex types.

This file contains definitions and methods for Complex numbers and Imaginary type.

‍NOTE: All overloads for operators +,-,/,* are not documented separately since there exists a function for each combinations of scalar,imaginary and complex number representations. All versions are documented in the Complex – Complex definitions.

Definition in file cmplx.h.

Function Documentation

abs()

template<typename T >

T abs ( const Complex< T > &  a )

inline

Return absolute value of Complex number.

Wrapper around Complex::abs

Template Parameters

T	Arithmetic type of a

Parameters

a	Complex number to get abs from

Returns

T

Definition at line 1322 of file cmplx.h.

arg()

template<typename T >

T arg ( const Complex< T > &  a )

inline

Return argument of Complex number.

Wrapper around Complex::arg

Template Parameters

T	Arithmetic type of a

Parameters

a	Complex number to get arg from

Returns

T

Definition at line 1334 of file cmplx.h.

conj()

template<typename T >

Complex< T > conj ( const Complex< T > &  val )

inline

Return conjugate of Complex number.

Wrapper around Complex::conj

Template Parameters

T	Arithmetic type of a

Parameters

a	Complex number to get conjugate from

Returns

Complex<T>

Definition at line 1346 of file cmplx.h.

dagger()

template<typename T >

Complex< T > dagger ( const Complex< T > &  val )

inline

Return dagger of Complex number.

Wrapper around Complex::conj

Template Parameters

T	Arithmetic type of a

Parameters

a	Complex number to get conjugate from

Returns

Complex<T>

Definition at line 1358 of file cmplx.h.

I()

constexpr Imaginary_t< double > I ( 1.  0 )

constexpr

Imaginary unit I - global variable.

Don't use #define'd I : this will conflict with some headers in rocm

For some reason it is sufficient to use only device

imag()

template<typename T >

T imag ( const Complex< T > &  a )

inline

Retrun imaginary value of Complex number.

Wrapper around Complex::imag

Template Parameters

T	Arithmetic type of a

Parameters

a	Complex number to get imaginary value from

Returns

T

Definition at line 890 of file cmplx.h.

operator<<()

template<typename T >

std::ostream & operator<<	(	std::ostream &	strm,
		const Complex< T > &	A
	)

Print a complex value as (re,im)

Stream operator

Print Complex number as "A.re A.im"

Template Parameters

T	Arithmetic type of A

Parameters

strm
A	Complex number to print

Returns

std::ostream&

Definition at line 1388 of file cmplx.h.

polar()

template<typename T >

Complex< T > polar	(	T	r,
		T	arg
	)

Return complex number given by polar representation.

Same as Complex::polar

Template Parameters

T	Arithmetic type r and arg

Parameters

r	Radial component of Complex number
arg	Argument of Complex number

Returns

Complex<T>

Definition at line 903 of file cmplx.h.

real()

template<typename T >

T real ( const Complex< T > &  a )

inline

Return real value of Complex number.

Wrapper around Complex::real

Template Parameters

T	Arithmetic type of a

Parameters

a	Complex number to get real value from

Returns

T

Definition at line 878 of file cmplx.h.

squarenorm()

template<typename T >

auto squarenorm ( const Complex< T > &  val )

inline

Return Squarenorm of Complex number.

Wrapper around Complex::squarenorm

Template Parameters

T	Arithmetic type of a

Parameters

a	Complex number to compute squarenorm of

Returns

T

Definition at line 1370 of file cmplx.h.