triqs::utility::gmp_complex

#include <triqs/utility/pade_approximants.hpp>

Detailed Description

Lightweight complex number backed by GMP mpf_class floats, used during Padé coefficient computation.

Definition at line 49 of file pade_approximants.hpp.

Public Member Functions
mpf_class	norm () const
	Squared magnitude of the complex number \( z \).
gmp_complex	operator* (const gmp_complex &z) const
	Multiply two complex numbers.
gmp_complex	operator+ (const gmp_complex &z) const
	Add two complex numbers.
gmp_complex	operator- (const gmp_complex &z) const
	Subtract two complex numbers.
gmp_complex	operator/ (const gmp_complex &z) const
	Divide two complex numbers.
gmp_complex &	operator= (const std::complex< double > &z)
	Assign from a regular std::complex<double>.

Public Attributes
mpf_class	im
	Imaginary part.
mpf_class	re
	Real part.

Friends
mpf_class	imag (const gmp_complex &z)
	Extract the imaginary part of a complex number.
gmp_complex	inverse (const gmp_complex &z)
	Compute the multiplicative inverse of a complex number.
std::ostream &	operator<< (std::ostream &out, gmp_complex const &z)
	Write a gmp_complex to an output stream.
mpf_class	real (const gmp_complex &z)
	Extract the real part of a complex number.

Member Function Documentation

norm()

mpf_class triqs::utility::gmp_complex::norm ( ) const

inlinenodiscard

Squared magnitude of the complex number \( z \).

Returns

\( |z|^2 = \Re(z)^2 + \Im(z)^2 \).

Definition at line 124 of file pade_approximants.hpp.

operator*()

gmp_complex triqs::utility::gmp_complex::operator* ( const gmp_complex & z ) const

inline

Multiply two complex numbers.

Parameters

z	Right-hand operand.

Returns

Complex product.

Definition at line 62 of file pade_approximants.hpp.

operator+()

gmp_complex triqs::utility::gmp_complex::operator+ ( const gmp_complex & z ) const

inline

Add two complex numbers.

Parameters

z	Right-hand operand.

Returns

Complex sum.

Definition at line 94 of file pade_approximants.hpp.

operator-()

gmp_complex triqs::utility::gmp_complex::operator- ( const gmp_complex & z ) const

inline

Subtract two complex numbers.

Parameters

z	Right-hand operand (subtrahend).

Returns

Complex difference.

Definition at line 102 of file pade_approximants.hpp.

operator/()

gmp_complex triqs::utility::gmp_complex::operator/ ( const gmp_complex & z ) const

inline

Divide two complex numbers.

It throws a triqs::runtime_error on division by zero.

Parameters

z	Right-hand operand (divisor).

Returns

Complex quotient.

Definition at line 86 of file pade_approximants.hpp.

operator=()

gmp_complex & triqs::utility::gmp_complex::operator= ( const std::complex< double > & z )

inline

Assign from a regular std::complex<double>.

Parameters

z	Value to assign from.

Returns

Reference to *this.

Definition at line 132 of file pade_approximants.hpp.

Friends And Related Symbol Documentation

imag

mpf_class imag ( const gmp_complex & z )

friend

Extract the imaginary part of a complex number.

Parameters

z	Number \( z \) to inspect.

Returns

Imaginary part \( \Im(z) \).

Definition at line 118 of file pade_approximants.hpp.

inverse

gmp_complex inverse ( const gmp_complex & z )

friend

Compute the multiplicative inverse of a complex number.

It throws a triqs::runtime_error on division by zero.

Parameters

z	Complex number \( z \) to invert.

Returns

Multiplicative inverse \( 1 / z \).

Definition at line 72 of file pade_approximants.hpp.

operator<<

std::ostream & operator<< ( std::ostream & out, gmp_complex const & z )

friend

Write a gmp_complex to an output stream.

Parameters

out	Output stream to write to.
z	Complex number to print.

Returns

Reference to the output stream.

Definition at line 145 of file pade_approximants.hpp.

real

mpf_class real ( const gmp_complex & z )

friend

Extract the real part of a complex number.

Parameters

z	Number \( z \) to inspect.

Returns

Real part \( \Re(z) \).

Definition at line 110 of file pade_approximants.hpp.

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

• triqs/utility/pade_approximants.hpp