#include <symmetry_rotation.h>

Collaboration diagram for ModuleSymmetry::Symmetry_rotation:

Public Member Functions
	Symmetry_rotation ()

	~Symmetry_rotation ()

const std::map< Tap, std::set< TC > > &	get_irreducible_sector () const

TCdouble	get_return_lattice (const Symmetry &symm, const ModuleBase::Matrix3 &gmatd, const TCdouble gtransd, const TCdouble &posd_a1, const TCdouble &posd_a2) const

TCdouble	get_return_lattice (const int iat, const int isym) const

void	find_irreducible_sector (const Symmetry &symm, const Atom *atoms, const Statistics &st, const std::vector< TC > &Rs, const TC &period, const Lattice &lat)

void	set_abfs_Lmax (const int l)

void	set_Cs_rotation (const std::vector< std::vector< int > > &abfs_l_nchi)

void	cal_Ms (const K_Vectors &kv, const UnitCell &ucell, const Parallel_2D &pv)
	functions to contruct rotation matrix in AO-representation

std::vector< std::vector< std::complex< double > > >	restore_dm (const K_Vectors &kv, const std::vector< std::vector< std::complex< double > > > &dm_k_ibz, const Parallel_2D &pv) const

std::vector< std::vector< double > >	restore_dm (const K_Vectors &kv, const std::vector< std::vector< double > > &dm_k_ibz, const Parallel_2D &pv) const

std::vector< std::complex< double > >	rot_matrix_ao (const std::vector< std::complex< double > > &DMkibz, const int ik_ibz, const int kstar_size, const int isym, const Parallel_2D &pv, const bool TRS_conj=false) const

double	wigner_d (const double beta, const int l, const int m1, const int m2) const
	calculate Wigner D matrix

std::complex< double >	wigner_D (const TCdouble &euler_angle, const int l, const int m1, const int m2, const bool inv) const

std::complex< double >	ovlp_Ylm_Slm (const int l, const int m1, const int m2) const
	c^l_{m1, m2}=<Y_l^m1\|S_l^m2>

TCdouble	get_euler_angle (const ModuleBase::Matrix3 &gmatc) const
	calculate euler angle from rotation matrix

void	cal_rotmat_Slm (const ModuleBase::Matrix3 *gmatc, const int lmax)
	T_mm' = [c^\dagger D c]_mm', the rotation matrix in the representation of real sphere harmonics.

void	set_block_to_mat2d (const int starti, const int startj, const RI::Tensor< std::complex< double > > &block, std::vector< std::complex< double > > &obj_mat, const Parallel_2D &pv, const bool trans=false) const

void	set_block_to_mat2d (const int starti, const int startj, const RI::Tensor< std::complex< double > > &block, std::vector< double > &obj_mat, const Parallel_2D &pv, const bool trans=false) const

std::vector< std::complex< double > >	contruct_2d_rot_mat_ao (const Symmetry &symm, const Atom *atoms, const Statistics &cell_st, const TCdouble &kvec_d_ibz, int isym, const Parallel_2D &pv) const

std::vector< std::vector< RI::Tensor< std::complex< double > > > > &	get_rotmat_Slm ()

template<typename Tdata >
std::map< int, std::map< std::pair< int, TC >, RI::Tensor< Tdata > > >	restore_HR (const Symmetry &symm, const Atom *atoms, const Statistics &st, const char mode, const std::map< int, std::map< std::pair< int, TC >, RI::Tensor< Tdata > > > &HR_irreduceble) const

template<typename TR >
void	restore_HR (const Symmetry &symm, const Atom *atoms, const Statistics &st, const char mode, const hamilt::HContainer< TR > &HR_irreduceble, hamilt::HContainer< TR > &HR_rotated) const

template<typename Tdata >
void	test_HR_rotation (const Symmetry &symm, const Atom *atoms, const Statistics &st, const char mode, const std::map< int, std::map< std::pair< int, TC >, RI::Tensor< Tdata > > > &HR_full)

template<typename Tdata >
void	test_Cs_rotation (const Symmetry &symm, const Atom *atoms, const Statistics &st, const std::map< int, std::map< std::pair< int, TC >, RI::Tensor< Tdata > > > &Cs_full) const

template<typename TR >
void	test_HR_rotation (const Symmetry &symm, const Atom *atoms, const Statistics &st, const char mode, const hamilt::HContainer< TR > &HR_full)

template<typename Tdata >
void	print_HR (const std::map< int, std::map< std::pair< int, TC >, RI::Tensor< Tdata > > > &HR, const std::string name, const double &threshold=0.0)

Public Attributes
const std::vector< std::vector< RI::Tensor< std::complex< double > > > > &	rotmat_Slm = this->rotmat_Slm_
	the rotation matrix under the basis of S_l^m. size: [nsym][lmax][nm*nm]

const int &	abfs_Lmax = this->abfs_Lmax_

Private Member Functions
std::vector< TC >	get_Rs_from_BvK (const K_Vectors &kv) const

std::vector< TC >	get_Rs_from_adjacent_list (const UnitCell &ucell, const Grid_Driver &gd, const Parallel_Orbitals &pv) const

template<typename Tdata >
RI::Tensor< Tdata >	rotate_atompair_serial (const RI::Tensor< Tdata > &A, const int isym, const Atom &a1, const Atom &a2, const char mode, bool output=false) const

template<typename Tdata >
void	rotate_atompair_serial (Tdata TAT, const Tdata A, const int &nw1, const int &nw2, const int isym, const Atom &a1, const Atom &a2, const char mode) const

template<typename TR >
void	rotate_atompair_parallel (const TR Alocal_in, const int isym, const Atom atoms, const Statistics &st, const Tap &ap_in, const Tap &ap_out, const char mode, const Parallel_Orbitals &pv, TR *Alocal_out, const bool output=false) const

template<typename Tdata >
RI::Tensor< Tdata >	rotate_singleC_serial (const RI::Tensor< Tdata > &C, const int isym, const Atom &a1, const Atom &a2, const int &type1, bool output=false) const
	rotate a 3-dim C tensor in RI technique

template<typename Tdata >
RI::Tensor< Tdata >	set_rotation_matrix (const Atom &a, const int &isym) const

template<typename Tdata >
RI::Tensor< Tdata >	set_rotation_matrix_abf (const int &type, const int &isym) const

Private Attributes
int	nsym_ = 1

double	eps_ = 1e-6

bool	TRS_first_ = true

bool	reduce_Cs_ = false

int	abfs_Lmax_ = 0

std::vector< std::vector< int > >	abfs_l_nchi_
	number of abfs for each angular momentum

std::vector< std::vector< RI::Tensor< std::complex< double > > > >	rotmat_Slm_
	the rotation matrix under the basis of S_l^m. size: [nsym][lmax][nm*nm]

std::vector< std::map< int, std::vector< std::complex< double > > > >	Ms_

Irreducible_Sector	irs_
	irreducible sector

Constructor & Destructor Documentation

◆ Symmetry_rotation()

ModuleSymmetry::Symmetry_rotation::Symmetry_rotation ( )

inline

◆ ~Symmetry_rotation()

ModuleSymmetry::Symmetry_rotation::~Symmetry_rotation ( )

inline

Member Function Documentation

◆ cal_Ms()

void ModuleSymmetry::Symmetry_rotation::cal_Ms	(	const K_Vectors &	kv,
		const UnitCell &	ucell,
		const Parallel_2D &	pv
	)

functions to contruct rotation matrix in AO-representation

The top-level calculation interface of this class. calculate the rotation matrix in AO representation: M only need once call in each ion step (decided by the configuration)

Parameters

kstars equal k points to each ibz-kpont, corresponding to a certain symmetry operations.

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◆ cal_rotmat_Slm()

void ModuleSymmetry::Symmetry_rotation::cal_rotmat_Slm	(	const ModuleBase::Matrix3 *	gmatc,
		const int	lmax
	)

T_mm' = [c^\dagger D c]_mm', the rotation matrix in the representation of real sphere harmonics.

T_mm' = [c^\dagger D c]_mm'.

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◆ contruct_2d_rot_mat_ao()

std::vector< std::complex< double > > ModuleSymmetry::Symmetry_rotation::contruct_2d_rot_mat_ao	(	const Symmetry &	symm,
		const Atom *	atoms,
		const Statistics &	cell_st,
		const TCdouble &	kvec_d_ibz,
		int	isym,
		const Parallel_2D &	pv
	)		const

2d-block parallized rotation matrix in AO-representation, denoted as M. finally we will use D(k)=M(R, k)^\dagger*D(Rk)*M(R, k) to recover D(k) from D(Rk).

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◆ find_irreducible_sector()

void ModuleSymmetry::Symmetry_rotation::find_irreducible_sector	(	const Symmetry &	symm,
		const Atom *	atoms,
		const Statistics &	st,
		const std::vector< TC > &	Rs,
		const TC &	period,
		const Lattice &	lat
	)

inline

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◆ get_euler_angle()

TCdouble ModuleSymmetry::Symmetry_rotation::get_euler_angle ( const ModuleBase::Matrix3 & gmatc ) const

calculate euler angle from rotation matrix

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◆ get_irreducible_sector()

const std::map< Tap, std::set< TC > > & ModuleSymmetry::Symmetry_rotation::get_irreducible_sector ( ) const

inline

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◆ get_return_lattice() [1/2]

TCdouble ModuleSymmetry::Symmetry_rotation::get_return_lattice	(	const int	iat,
		const int	isym
	)		const

inline

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◆ get_return_lattice() [2/2]

TCdouble ModuleSymmetry::Symmetry_rotation::get_return_lattice	(	const Symmetry &	symm,
		const ModuleBase::Matrix3 &	gmatd,
		const TCdouble	gtransd,
		const TCdouble &	posd_a1,
		const TCdouble &	posd_a2
	)		const

inline

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◆ get_rotmat_Slm()

std::vector< std::vector< RI::Tensor< std::complex< double > > > > & ModuleSymmetry::Symmetry_rotation::get_rotmat_Slm ( )

inline

◆ get_Rs_from_adjacent_list()

std::vector< TC > ModuleSymmetry::Symmetry_rotation::get_Rs_from_adjacent_list	(	const UnitCell &	ucell,
		const Grid_Driver &	gd,
		const Parallel_Orbitals &	pv
	)		const

private

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◆ get_Rs_from_BvK()

std::vector< TC > ModuleSymmetry::Symmetry_rotation::get_Rs_from_BvK ( const K_Vectors & kv ) const

private

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◆ ovlp_Ylm_Slm()

std::complex< double > ModuleSymmetry::Symmetry_rotation::ovlp_Ylm_Slm	(	const int	l,
		const int	m1,
		const int	m2
	)		const

c^l_{m1, m2}=<Y_l^m1|S_l^m2>

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◆ print_HR()

template<typename Tdata >

void ModuleSymmetry::Symmetry_rotation::print_HR	(	const std::map< int, std::map< std::pair< int, TC >, RI::Tensor< Tdata > > > &	HR,
		const std::string	name,
		const double &	threshold = `0.0`
	)

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◆ restore_dm() [1/2]

std::vector< std::vector< double > > ModuleSymmetry::Symmetry_rotation::restore_dm	(	const K_Vectors &	kv,
		const std::vector< std::vector< double > > &	dm_k_ibz,
		const Parallel_2D &	pv
	)		const

◆ restore_dm() [2/2]

std::vector< std::vector< std::complex< double > > > ModuleSymmetry::Symmetry_rotation::restore_dm	(	const K_Vectors &	kv,
		const std::vector< std::vector< std::complex< double > > > &	dm_k_ibz,
		const Parallel_2D &	pv
	)		const

Use calculated M matrix to recover D(k) from D(k_ibz): D(k) = M(R, k)^\dagger D(k_ibz) M(R, k) the link "ik_ibz-isym-ik" can be found in kstars: k_bz = gmat[isym](k)

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◆ restore_HR() [1/2]

template<typename TR >

void ModuleSymmetry::Symmetry_rotation::restore_HR	(	const Symmetry &	symm,
		const Atom *	atoms,
		const Statistics &	st,
		const char	mode,
		const hamilt::HContainer< TR > &	HR_irreduceble,
		hamilt::HContainer< TR > &	HR_rotated
	)		const

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◆ restore_HR() [2/2]

template<typename Tdata >

std::map< int, std::map< std::pair< int, TC >, RI::Tensor< Tdata > > > ModuleSymmetry::Symmetry_rotation::restore_HR	(	const Symmetry &	symm,
		const Atom *	atoms,
		const Statistics &	st,
		const char	mode,
		const std::map< int, std::map< std::pair< int, TC >, RI::Tensor< Tdata > > > &	HR_irreduceble
	)		const

The main functions to rotate matrices Given H(R) in the irreduceble sector, calculate H(R) for all the atompairs and cells.

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◆ rot_matrix_ao()

std::vector< std::complex< double > > ModuleSymmetry::Symmetry_rotation::rot_matrix_ao	(	const std::vector< std::complex< double > > &	DMkibz,
		const int	ik_ibz,
		const int	kstar_size,
		const int	isym,
		const Parallel_2D &	pv,
		const bool	TRS_conj = `false`
	)		const

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◆ rotate_atompair_parallel()

template<typename TR >

void ModuleSymmetry::Symmetry_rotation::rotate_atompair_parallel	(	const TR *	Alocal_in,
		const int	isym,
		const Atom *	atoms,
		const Statistics &	st,
		const Tap &	ap_in,
		const Tap &	ap_out,
		const char	mode,
		const Parallel_Orbitals &	pv,
		TR *	Alocal_out,
		const bool	output = `false`
	)		const

private

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◆ rotate_atompair_serial() [1/2]

template<typename Tdata >

RI::Tensor< Tdata > ModuleSymmetry::Symmetry_rotation::rotate_atompair_serial	(	const RI::Tensor< Tdata > &	A,
		const int	isym,
		const Atom &	a1,
		const Atom &	a2,
		const char	mode,
		bool	output = `false`
	)		const

private

The sub functions to rotate matrices mode='H': H_12(R)=T^\dagger(V)H_1'2'(VR+O_1-O_2)T(V) mode='D': D_12(R)=T^T(V)D_1'2'(VR+O_1-O_2)T^*(V)

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◆ rotate_atompair_serial() [2/2]

template<typename Tdata >

void ModuleSymmetry::Symmetry_rotation::rotate_atompair_serial	(	Tdata *	TAT,
		const Tdata *	A,
		const int &	nw1,
		const int &	nw2,
		const int	isym,
		const Atom &	a1,
		const Atom &	a2,
		const char	mode
	)		const

private

◆ rotate_singleC_serial()

template<typename Tdata >

RI::Tensor< Tdata > ModuleSymmetry::Symmetry_rotation::rotate_singleC_serial	(	const RI::Tensor< Tdata > &	C,
		const int	isym,
		const Atom &	a1,
		const Atom &	a2,
		const int &	type1,
		bool	output = `false`
	)		const

private

rotate a 3-dim C tensor in RI technique

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◆ set_abfs_Lmax()

void ModuleSymmetry::Symmetry_rotation::set_abfs_Lmax ( const int l )

inline

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◆ set_block_to_mat2d() [1/2]

void ModuleSymmetry::Symmetry_rotation::set_block_to_mat2d	(	const int	starti,
		const int	startj,
		const RI::Tensor< std::complex< double > > &	block,
		std::vector< double > &	obj_mat,
		const Parallel_2D &	pv,
		const bool	trans = `false`
	)		const

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◆ set_block_to_mat2d() [2/2]

void ModuleSymmetry::Symmetry_rotation::set_block_to_mat2d	(	const int	starti,
		const int	startj,
		const RI::Tensor< std::complex< double > > &	block,
		std::vector< std::complex< double > > &	obj_mat,
		const Parallel_2D &	pv,
		const bool	trans = `false`
	)		const

set a block matrix onto a 2d-parallelized matrix(col-maj), at the position (starti, startj) if trans=true, the block matrix is transposed before setting

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◆ set_Cs_rotation()

void ModuleSymmetry::Symmetry_rotation::set_Cs_rotation ( const std::vector< std::vector< int > > & abfs_l_nchi )

◆ set_rotation_matrix()

template<typename Tdata >

RI::Tensor< Tdata > ModuleSymmetry::Symmetry_rotation::set_rotation_matrix	(	const Atom &	a,
		const int &	isym
	)		const

private

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◆ set_rotation_matrix_abf()

template<typename Tdata >

RI::Tensor< Tdata > ModuleSymmetry::Symmetry_rotation::set_rotation_matrix_abf	(	const int &	type,
		const int &	isym
	)		const

private

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◆ test_Cs_rotation()

template<typename Tdata >

void ModuleSymmetry::Symmetry_rotation::test_Cs_rotation	(	const Symmetry &	symm,
		const Atom *	atoms,
		const Statistics &	st,
		const std::map< int, std::map< std::pair< int, TC >, RI::Tensor< Tdata > > > &	Cs_full
	)		const

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◆ test_HR_rotation() [1/2]

template<typename TR >

void ModuleSymmetry::Symmetry_rotation::test_HR_rotation	(	const Symmetry &	symm,
		const Atom *	atoms,
		const Statistics &	st,
		const char	mode,
		const hamilt::HContainer< TR > &	HR_full
	)

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◆ test_HR_rotation() [2/2]

template<typename Tdata >

void ModuleSymmetry::Symmetry_rotation::test_HR_rotation	(	const Symmetry &	symm,
		const Atom *	atoms,
		const Statistics &	st,
		const char	mode,
		const std::map< int, std::map< std::pair< int, TC >, RI::Tensor< Tdata > > > &	HR_full
	)

test functions test H(R) rotation: giver a full H(R), pick out H(R) in the irreducible sector, rotate it, and compare with the original full H(R)

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◆ wigner_d()

double ModuleSymmetry::Symmetry_rotation::wigner_d	(	const double	beta,
		const int	l,
		const int	m1,
		const int	m2
	)		const

calculate Wigner D matrix

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◆ wigner_D()

std::complex< double > ModuleSymmetry::Symmetry_rotation::wigner_D	(	const TCdouble &	euler_angle,
		const int	l,
		const int	m1,
		const int	m2,
		const bool	inv
	)		const

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Member Data Documentation

◆ abfs_l_nchi_

std::vector<std::vector<int> > ModuleSymmetry::Symmetry_rotation::abfs_l_nchi_

private

number of abfs for each angular momentum

◆ abfs_Lmax

const int& ModuleSymmetry::Symmetry_rotation::abfs_Lmax = this->abfs_Lmax_

◆ abfs_Lmax_

int ModuleSymmetry::Symmetry_rotation::abfs_Lmax_ = 0

private

◆ eps_

double ModuleSymmetry::Symmetry_rotation::eps_ = 1e-6

private

◆ irs_

Irreducible_Sector ModuleSymmetry::Symmetry_rotation::irs_

private

irreducible sector

◆ Ms_

std::vector<std::map<int, std::vector<std::complex<double> > > > ModuleSymmetry::Symmetry_rotation::Ms_

private

The unitary matrix associate D(Rk) with D(k) for each ibz-kpoint Rk and each symmetry operation. size: [nks_ibz][nsym][nbasis*nbasis], only need to calculate once.

◆ nsym_

int ModuleSymmetry::Symmetry_rotation::nsym_ = 1

private

◆ reduce_Cs_

bool ModuleSymmetry::Symmetry_rotation::reduce_Cs_ = false

private

◆ rotmat_Slm

const std::vector<std::vector<RI::Tensor<std::complex<double> > > >& ModuleSymmetry::Symmetry_rotation::rotmat_Slm = this->rotmat_Slm_

the rotation matrix under the basis of S_l^m. size: [nsym][lmax][nm*nm]

◆ rotmat_Slm_

std::vector<std::vector<RI::Tensor<std::complex<double> > > > ModuleSymmetry::Symmetry_rotation::rotmat_Slm_

private

the rotation matrix under the basis of S_l^m. size: [nsym][lmax][nm*nm]

◆ TRS_first_

bool ModuleSymmetry::Symmetry_rotation::TRS_first_ = true

private

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

/home/runner/work/abacus-develop/abacus-develop/source/source_lcao/module_ri/module_exx_symmetry/symmetry_rotation.h
/home/runner/work/abacus-develop/abacus-develop/source/source_lcao/module_ri/module_exx_symmetry/symmetry_rotation.cpp
/home/runner/work/abacus-develop/abacus-develop/source/source_lcao/module_ri/module_exx_symmetry/symmetry_rotation_R.hpp
/home/runner/work/abacus-develop/abacus-develop/source/source_lcao/module_ri/module_exx_symmetry/symmetry_rotation_R_hcontainer.hpp

Public Member Functions

Public Attributes

Private Member Functions

Private Attributes

Constructor & Destructor Documentation

◆ Symmetry_rotation()

◆ ~Symmetry_rotation()

Member Function Documentation

◆ cal_Ms()

◆ cal_rotmat_Slm()

◆ contruct_2d_rot_mat_ao()

◆ find_irreducible_sector()

◆ get_euler_angle()

◆ get_irreducible_sector()

◆ get_return_lattice() [1/2]

◆ get_return_lattice() [2/2]

◆ get_rotmat_Slm()

◆ get_Rs_from_adjacent_list()

◆ get_Rs_from_BvK()

◆ ovlp_Ylm_Slm()

◆ print_HR()

◆ restore_dm() [1/2]

◆ restore_dm() [2/2]

◆ restore_HR() [1/2]

◆ restore_HR() [2/2]

◆ rot_matrix_ao()

◆ rotate_atompair_parallel()

◆ rotate_atompair_serial() [1/2]

◆ rotate_atompair_serial() [2/2]

◆ rotate_singleC_serial()

◆ set_abfs_Lmax()

◆ set_block_to_mat2d() [1/2]

◆ set_block_to_mat2d() [2/2]

◆ set_Cs_rotation()

◆ set_rotation_matrix()

◆ set_rotation_matrix_abf()

◆ test_Cs_rotation()

◆ test_HR_rotation() [1/2]

◆ test_HR_rotation() [2/2]

◆ wigner_d()

◆ wigner_D()

Member Data Documentation

◆ abfs_l_nchi_

◆ abfs_Lmax

◆ abfs_Lmax_

◆ eps_

◆ irs_

◆ Ms_

◆ nsym_

◆ reduce_Cs_

◆ rotmat_Slm

◆ rotmat_Slm_

◆ TRS_first_