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template<typename T>
class MBPT::SpinorMatrix< T >

Radial Dirac spinor matrix.

Designed to store Greens-function like operators: \( \ket{F_a}\bra{F_b} \) (where Fa, Fb are radial Dirac spinors), as a radial matrix. The matrix is stored on a sub-grid (between r0 and rmax), with a specified stride.

SpinorMatrix is a 2*2 matrix in spinor space {ff, fg, gf, gg} - the g blocks are small and are optional. Each block is an N*N radial matrix, where N is a subset of the number of points along the full radial grid. May store doubles or complex doubles.

\[ \begin{align} G &= \begin{pmatrix} G_{ff} & G_{fg} \\ G_{gf} & G_{gg} \end{pmatrix},\\ G F &= \begin{pmatrix} G_{ff} & G_{fg} \\ G_{gf} & G_{gg} \end{pmatrix} \begin{pmatrix} f \\ g \end{pmatrix} = \begin{pmatrix} G_{ff}(r,r')\,f(r') + G_{fg}(r,r')\,g(r') \\ G_{gf}(r,r')\,f(r') + G_{gg}(r,r')\,g(r') \end{pmatrix}. \end{align} \]

Careful to distinguish SpinorMatrix multiplication/integration:

\[ \begin{align} G_1 * G_2 &= \int G_1(r_a,r_b)\,G_2(r_b,r_c) = \sum_j G_1(i,j)\,G_2(j,k),\\ G_1.{\rm drj}() * G_2 &= \int G_1(r_a,r_b)\,G_2(r_b,r_c)\,dr_b = \sum_j G_1(i,j)\,G_2(j,k)\,dr_j = G_1 * G_2.{\rm dri}(), \end{align} \]

where \( dr_j = (dr/du)_j \times du \times {\rm stride} \) (see dr()).

While almost always symmetric, this doesn't assume that.

#include <SpinorMatrix.hpp>

Public Member Functions
	SpinorMatrix (std::size_t i0, std::size_t stride, std::size_t size, bool incl_g, std::shared_ptr< const Grid > rgrid)
	Constructs a zero matrix on the given radial sub-grid.

T &	ff (std::size_t i, std::size_t j)
	direct access to matrix elements

T &	fg (std::size_t i, std::size_t j)

T &	gf (std::size_t i, std::size_t j)

T &	gg (std::size_t i, std::size_t j)

const T	ff (std::size_t i, std::size_t j) const

const T	fg (std::size_t i, std::size_t j) const

const T	gf (std::size_t i, std::size_t j) const

const T	gg (std::size_t i, std::size_t j) const

const LinAlg::Matrix< T > &	ff () const
	direct access to matrices

const LinAlg::Matrix< T > &	fg () const

const LinAlg::Matrix< T > &	gf () const

const LinAlg::Matrix< T > &	gg () const

LinAlg::Matrix< T > &	ff ()

LinAlg::Matrix< T > &	fg ()

LinAlg::Matrix< T > &	gf ()

LinAlg::Matrix< T > &	gg ()

LinAlg::Matrix< T > &	sp (std::size_t mu, std::size_t nu)
	Spinor block by index: 0 = f, 1 = g.

const LinAlg::Matrix< T > &	sp (std::size_t mu, std::size_t nu) const
	Spinor block by index: 0 = f, 1 = g (const)

std::size_t	size () const
	Number of sub-grid points (dimension of each block)

std::size_t	g_size () const
	Dimension of the g blocks: size(), or 0 if g parts are not included.

bool	includes_g () const
	True if g parts (fg, gf, gg) are included.

std::size_t	i0 () const
	Full-grid index of the first sub-grid point.

std::size_t	stride () const
	Sub-grid stride: every stride-th point of the full grid.

void	zero ()
	Sets all matrix elements to zero.

SpinorMatrix< T > &	drop_g ()
	Kills g parts of spinor matrix, in place!

SpinorMatrix< T > &	create_g ()
	Creates g parts of spinor matrix - will have value 0.

SpinorMatrix< T > &	operator+= (const SpinorMatrix< T > &rhs)
	Matrix addition +,-.

SpinorMatrix< T > &	operator-= (const SpinorMatrix< T > &rhs)
	Matrix addition +,- (see operator+= for matrices without g parts)

SpinorMatrix< T > &	operator*= (const T x)
	Scalar multiplication.

SpinorMatrix< T > &	operator+= (T aI)
	Addition of identity: Matrix<T> += T : T assumed to be *Identity!

SpinorMatrix< T > &	operator-= (T aI)
	Addition of identity: Matrix<T> -= T : T assumed to be *Identity!

SpinorMatrix< T > &	mult_elements_by (const SpinorMatrix< T > &rhs)
	Multiply elements (in place): Gij -> Gij*Bij.

SpinorMatrix< T > &	mult_elements_by (const RadialMatrix< T > &rhs)
	Multiply elements (in place): Gij -> Gij*Bij.

SpinorMatrix< T >	conj () const
	Returns conjugate of matrix.

SpinorMatrix< double >	real () const
	Returns real part of complex matrix (changes type; returns a real matrix)

SpinorMatrix< double >	imag () const
	Returns imag part of complex matrix (changes type; returns a real matrix)

SpinorMatrix< std::complex< double > >	complex () const
	Converts a real to complex matrix (changes type; returns a complex matrix)

SpinorMatrix< T > &	invert_in_place ()
	Inversion (in place)

SpinorMatrix< T >	inverse () const
	Returns inverse of matrix; original matrix unchanged.

SpinorMatrix< T > &	drj_in_place ()
	Multiplies by drj: Q_ij -> Q_ij*dr_j, in place.

SpinorMatrix< T > &	dri_in_place ()
	Multiplies by dri: Q_ij -> Q_ij*dr_i, in place.

SpinorMatrix< T >	drj () const
	Multiplies by drj: Q_ij -> Q_ij*dr_j. Returns new matrix (orig unchanged)

SpinorMatrix< T >	dri () const
	Multiplies by dri: Q_ij -> Q_ij*dr_i. Returns new matrix (orig unchanged)

double	dr (std::size_t sub_index) const
	returns dr at position along sub grid

std::size_t	index_to_fullgrid (std::size_t i) const
	Converts an index on the sub-grid to the full grid.

void	add (const DiracSpinor &ket, const DiracSpinor &bra, T k=T(1.0))
	Adds k*\|ket><bra\| to matrix (used for building Green's functions)

DiracSpinor	operator* (const DiracSpinor &Fn) const
	Action of SpinorMatrix operator on DiracSpinor.

Friends
SpinorMatrix< T >	operator+ (SpinorMatrix< T > lhs, const SpinorMatrix< T > &rhs)
	Matrix addition +,-.

SpinorMatrix< T >	operator- (SpinorMatrix< T > lhs, const SpinorMatrix< T > &rhs)
	Matrix addition +,-.

SpinorMatrix< T >	operator* (const T x, SpinorMatrix< T > rhs)
	Scalar multiplication.

SpinorMatrix< T >	operator+ (SpinorMatrix< T > M, T aI)
	Addition of identity: Matrix<T> + T : T assumed to be *Identity!

SpinorMatrix< T >	operator- (SpinorMatrix< T > M, T aI)
	Addition of identity: Matrix<T> - T : T assumed to be *Identity!

SpinorMatrix< T >	operator* (const SpinorMatrix< T > &a, const SpinorMatrix< T > &b)
	Matrix multiplication.

SpinorMatrix< T >	mult_elements (SpinorMatrix< T > lhs, const SpinorMatrix< T > &rhs)
	Multiply elements (new matrix): Gij = Aij*Bij.

SpinorMatrix< T >	mult_elements (SpinorMatrix< T > lhs, const RadialMatrix< T > &rhs)
	Multiply elements (new matrix): Gij = Aij*Bij.

SpinorMatrix< T >	mult_elements (const RadialMatrix< T > &rhs, SpinorMatrix< T > lhs)
	Multiply elements (new matrix): Gij = Aij*Bij.

std::ostream &	operator<< (std::ostream &os, const SpinorMatrix< T > &a)

Constructor & Destructor Documentation

◆ SpinorMatrix()

template<typename T >

MBPT::SpinorMatrix< T >::SpinorMatrix	(	std::size_t	i0,
		std::size_t	stride,
		std::size_t	size,
		bool	incl_g,
		std::shared_ptr< const Grid >	rgrid
	)

inline

Constructs a zero matrix on the given radial sub-grid.

Sub-grid point i is full-grid point i0 + i*stride (see index_to_fullgrid). The last sub-grid point must lie on the full grid (checked by assert).

Parameters

i0	Full-grid index of the first sub-grid point
stride	Sub-grid stride: every stride-th point of the full grid
size	Number of sub-grid points (each block is size*size)
incl_g	Include the g blocks (fg, gf, gg)
rgrid	Full radial grid

Member Function Documentation

◆ ff() [1/2]

template<typename T >

T & MBPT::SpinorMatrix< T >::ff	(	std::size_t	i,
		std::size_t	j
	)

inline

direct access to matrix elements

◆ ff() [2/2]

template<typename T >

const LinAlg::Matrix< T > & MBPT::SpinorMatrix< T >::ff ( ) const

inline

direct access to matrices

◆ sp() [1/2]

template<typename T >

LinAlg::Matrix< T > & MBPT::SpinorMatrix< T >::sp	(	std::size_t	mu,
		std::size_t	nu
	)

inline

Spinor block by index: 0 = f, 1 = g.

(mu, nu) = (0, 0): ff; (0, 1): fg; (1, 0): gf; (1, 1): gg.

Note: The g blocks are empty (0*0) if g parts are not included.

Warning: mu and nu must be 0 or 1; aborts otherwise.

◆ sp() [2/2]

template<typename T >

const LinAlg::Matrix< T > & MBPT::SpinorMatrix< T >::sp	(	std::size_t	mu,
		std::size_t	nu
	)		const

inline

Spinor block by index: 0 = f, 1 = g (const)

◆ size()

template<typename T >

std::size_t MBPT::SpinorMatrix< T >::size ( ) const

inline

Number of sub-grid points (dimension of each block)

◆ g_size()

template<typename T >

std::size_t MBPT::SpinorMatrix< T >::g_size ( ) const

inline

Dimension of the g blocks: size(), or 0 if g parts are not included.

◆ includes_g()

template<typename T >

bool MBPT::SpinorMatrix< T >::includes_g ( ) const

inline

True if g parts (fg, gf, gg) are included.

◆ i0()

template<typename T >

std::size_t MBPT::SpinorMatrix< T >::i0 ( ) const

inline

Full-grid index of the first sub-grid point.

◆ stride()

template<typename T >

std::size_t MBPT::SpinorMatrix< T >::stride ( ) const

inline

Sub-grid stride: every stride-th point of the full grid.

◆ zero()

template<typename T >

void MBPT::SpinorMatrix< T >::zero ( )

inline

Sets all matrix elements to zero.

◆ drop_g()

template<typename T >

SpinorMatrix< T > & MBPT::SpinorMatrix< T >::drop_g ( )

inline

Kills g parts of spinor matrix, in place!

◆ create_g()

template<typename T >

SpinorMatrix< T > & MBPT::SpinorMatrix< T >::create_g ( )

inline

Creates g parts of spinor matrix - will have value 0.

Note: If g parts already exist, they are reset to 0.

◆ operator+=() [1/2]

template<typename T >

SpinorMatrix< T > & MBPT::SpinorMatrix< T >::operator+= ( const SpinorMatrix< T > & rhs )

inline

Matrix addition +,-.

A matrix without g parts is treated as having zero g parts: adding one to a matrix with g parts leaves its g parts unchanged; adding a matrix with g parts to one without creates them.

◆ operator-=() [1/2]

template<typename T >

SpinorMatrix< T > & MBPT::SpinorMatrix< T >::operator-= ( const SpinorMatrix< T > & rhs )

inline

Matrix addition +,- (see operator+= for matrices without g parts)

◆ operator*=()

template<typename T >

SpinorMatrix< T > & MBPT::SpinorMatrix< T >::operator*= ( const T x )

inline

Scalar multiplication.

◆ operator+=() [2/2]

template<typename T >

SpinorMatrix< T > & MBPT::SpinorMatrix< T >::operator+= ( T aI )

inline

Addition of identity: Matrix<T> += T : T assumed to be *Identity!

◆ operator-=() [2/2]

template<typename T >

SpinorMatrix< T > & MBPT::SpinorMatrix< T >::operator-= ( T aI )

inline

Addition of identity: Matrix<T> -= T : T assumed to be *Identity!

◆ mult_elements_by() [1/2]

template<typename T >

SpinorMatrix< T > & MBPT::SpinorMatrix< T >::mult_elements_by ( const SpinorMatrix< T > & rhs )

inline

Multiply elements (in place): Gij -> Gij*Bij.

◆ mult_elements_by() [2/2]

template<typename T >

SpinorMatrix< T > & MBPT::SpinorMatrix< T >::mult_elements_by ( const RadialMatrix< T > & rhs )

inline

Multiply elements (in place): Gij -> Gij*Bij.

◆ conj()

template<typename T >

SpinorMatrix< T > MBPT::SpinorMatrix< T >::conj ( ) const

inline

Returns conjugate of matrix.

◆ real()

template<typename T >

SpinorMatrix< double > MBPT::SpinorMatrix< T >::real ( ) const

inline

Returns real part of complex matrix (changes type; returns a real matrix)

◆ imag()

template<typename T >

SpinorMatrix< double > MBPT::SpinorMatrix< T >::imag ( ) const

inline

Returns imag part of complex matrix (changes type; returns a real matrix)

◆ complex()

template<typename T >

SpinorMatrix< std::complex< double > > MBPT::SpinorMatrix< T >::complex ( ) const

inline

Converts a real to complex matrix (changes type; returns a complex matrix)

◆ invert_in_place()

template<typename T >

SpinorMatrix< T > & MBPT::SpinorMatrix< T >::invert_in_place ( )

inline

Inversion (in place)

◆ inverse()

template<typename T >

SpinorMatrix< T > MBPT::SpinorMatrix< T >::inverse ( ) const

inline

Returns inverse of matrix; original matrix unchanged.

◆ drj_in_place()

template<typename T >

SpinorMatrix< T > & MBPT::SpinorMatrix< T >::drj_in_place ( )

inline

Multiplies by drj: Q_ij -> Q_ij*dr_j, in place.

◆ dri_in_place()

template<typename T >

SpinorMatrix< T > & MBPT::SpinorMatrix< T >::dri_in_place ( )

inline

Multiplies by dri: Q_ij -> Q_ij*dr_i, in place.

◆ drj()

template<typename T >

SpinorMatrix< T > MBPT::SpinorMatrix< T >::drj ( ) const

inline

Multiplies by drj: Q_ij -> Q_ij*dr_j. Returns new matrix (orig unchanged)

◆ dri()

template<typename T >

SpinorMatrix< T > MBPT::SpinorMatrix< T >::dri ( ) const

inline

Multiplies by dri: Q_ij -> Q_ij*dr_i. Returns new matrix (orig unchanged)

◆ dr()

template<typename T >

double MBPT::SpinorMatrix< T >::dr ( std::size_t sub_index ) const

inline

returns dr at position along sub grid

◆ index_to_fullgrid()

template<typename T >

std::size_t MBPT::SpinorMatrix< T >::index_to_fullgrid ( std::size_t i ) const

inline

Converts an index on the sub-grid to the full grid.

◆ add()

template<typename T >

void MBPT::SpinorMatrix< T >::add	(	const DiracSpinor &	ket,
		const DiracSpinor &	bra,
		T	k = `T(1.0)`
	)

inline

Adds k*|ket><bra| to matrix (used for building Green's functions)

◆ operator*()

template<typename T >

DiracSpinor MBPT::SpinorMatrix< T >::operator* ( const DiracSpinor & Fn ) const

inline

Action of SpinorMatrix operator on DiracSpinor.

Assumes matrix already includes integration measure. Formed on the sub-grid, then interpolated onto the full grid of Fn. Result is zero outside the sub-grid.

Note: If g parts are not included, the g component of the result is zero (and the g component of Fn is not used).

Friends And Related Symbol Documentation

◆ operator+ [1/2]

template<typename T >

SpinorMatrix< T > operator+	(	SpinorMatrix< T >	lhs,
		const SpinorMatrix< T > &	rhs
	)

friend

Matrix addition +,-.

◆ operator- [1/2]

template<typename T >

SpinorMatrix< T > operator-	(	SpinorMatrix< T >	lhs,
		const SpinorMatrix< T > &	rhs
	)

friend

Matrix addition +,-.

◆ operator* [1/2]

template<typename T >

SpinorMatrix< T > operator*	(	const T	x,
		SpinorMatrix< T >	rhs
	)

friend

Scalar multiplication.

◆ operator+ [2/2]

template<typename T >

SpinorMatrix< T > operator+	(	SpinorMatrix< T >	M,
		T	aI
	)

friend

Addition of identity: Matrix<T> + T : T assumed to be *Identity!

◆ operator- [2/2]

template<typename T >

SpinorMatrix< T > operator-	(	SpinorMatrix< T >	M,
		T	aI
	)

friend

Addition of identity: Matrix<T> - T : T assumed to be *Identity!

◆ operator* [2/2]

template<typename T >

SpinorMatrix< T > operator*	(	const SpinorMatrix< T > &	a,
		const SpinorMatrix< T > &	b
	)

friend

Matrix multiplication.

\( C=A\times B \equiv C_{ij} = \sum_k A_{ik}\,B_{kj}, \) including the sum over spinor blocks (e.g., ff = a.ff*b.ff + a.fg*b.gf).

A matrix without g parts is treated as having zero g parts (as in operator+=); the result includes g parts if either a or b does.

Note: Integration measure not automatically included: call .drj() first to include it!

◆ mult_elements [1/3]

template<typename T >

SpinorMatrix< T > mult_elements	(	SpinorMatrix< T >	lhs,
		const SpinorMatrix< T > &	rhs
	)

friend

Multiply elements (new matrix): Gij = Aij*Bij.

◆ mult_elements [2/3]

template<typename T >

SpinorMatrix< T > mult_elements	(	SpinorMatrix< T >	lhs,
		const RadialMatrix< T > &	rhs
	)

friend

Multiply elements (new matrix): Gij = Aij*Bij.

◆ mult_elements [3/3]

template<typename T >

SpinorMatrix< T > mult_elements	(	const RadialMatrix< T > &	rhs,
		SpinorMatrix< T >	lhs
	)

friend

Multiply elements (new matrix): Gij = Aij*Bij.

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

MBPT/SpinorMatrix.hpp

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Public Member Functions

Friends

Constructor & Destructor Documentation

◆ SpinorMatrix()

Member Function Documentation

◆ ff() [1/2]

◆ ff() [2/2]

◆ sp() [1/2]

◆ sp() [2/2]

◆ size()

◆ g_size()

◆ includes_g()

◆ i0()

◆ stride()

◆ zero()

◆ drop_g()

◆ create_g()

◆ operator+=() [1/2]

◆ operator-=() [1/2]

◆ operator*=()

◆ operator+=() [2/2]

◆ operator-=() [2/2]

◆ mult_elements_by() [1/2]

◆ mult_elements_by() [2/2]

◆ conj()

◆ real()

◆ imag()

◆ complex()

◆ invert_in_place()

◆ inverse()

◆ drj_in_place()

◆ dri_in_place()

◆ drj()

◆ dri()

◆ dr()

◆ index_to_fullgrid()

◆ add()

◆ operator*()

Friends And Related Symbol Documentation

◆ operator+ [1/2]

◆ operator- [1/2]

◆ operator* [1/2]

◆ operator+ [2/2]

◆ operator- [2/2]

◆ operator* [2/2]

◆ mult_elements [1/3]

◆ mult_elements [2/3]

◆ mult_elements [3/3]