Zeeman Namespace Reference

Implements Zeeman modeling. More...

Classes
struct	AllPolarizationVectors
	PolarizationVector for each Polarization. More...
struct	Derived
	Contains derived values useful for Zeeman calculations. More...
class	Model
	Main Zeeman Model. More...
class	PolarizationVector
	Polarization vector for Zeeman Propagation Matrix. More...
struct	SplittingData
	Main storage for Zeeman splitting coefficients. More...

Enumerations
enum class	Polarization : char { SigmaMinus , Pi , SigmaPlus , None }
	Zeeman polarization selection. More...

Functions
std::ostream &	operator<< (std::ostream &os, const Model &m)
std::istream &	operator>> (std::istream &is, Model &m)
std::ostream &	operator<< (bofstream &bof, const Model &m)
std::istream &	operator>> (bifstream &bif, Model &m)
AllPolarizationVectors	AllPolarization (Numeric theta, Numeric eta) noexcept
	Computes the polarization of each polarization type. More...
AllPolarizationVectors	AllPolarization_dtheta (Numeric theta, const Numeric eta) noexcept
	The derivative of AllPolarization wrt theta. More...
AllPolarizationVectors	AllPolarization_deta (Numeric theta, Numeric eta) noexcept
	The derivative of AllPolarization wrt eta. More...
const PolarizationVector &	SelectPolarization (const AllPolarizationVectors &data, Polarization type) noexcept
	Selects the polarization vector depending on polarization type. More...
void	sum (PropagationMatrix &pm, const ComplexVectorView &abs, const PolarizationVector &polvec, const bool do_phase=true) ARTS_NOEXCEPT
	Sums the Zeeman components into a propagation matrix. More...
void	dsum (PropagationMatrix &dpm, const ComplexVectorView &abs, const ComplexVectorView &dabs, const PolarizationVector &polvec, const PolarizationVector &dpolvec_dtheta, const PolarizationVector &dpolvec_deta, const Numeric dH, const Numeric dtheta, const Numeric deta, const bool do_phase=true) ARTS_NOEXCEPT
	Sums the Zeeman components derivatives into a propagation matrix. More...
constexpr Index	dM (Polarization type) noexcept
	Gives the change of M given a polarization type. More...
constexpr Rational	start (Rational Ju, Rational Jl, Polarization type) noexcept
	Gives the lowest M for a polarization type of this transition. More...
constexpr Rational	end (Rational Ju, Rational Jl, Polarization type) noexcept
	Gives the largest M for a polarization type of this transition. More...
constexpr Index	nelem (Rational Ju, Rational Jl, Polarization type) noexcept
	Gives the number of elements of the polarization type of this transition. More...
constexpr Rational	Mu (Rational Ju, Rational Jl, Polarization type, Index n) noexcept
	Gives the upper state M value at an index. More...
constexpr Rational	Ml (Rational Ju, Rational Jl, Polarization type, Index n) noexcept
	Gives the lower state M value at an index. More...
constexpr Numeric	PolarizationFactor (Polarization type) noexcept
	The renormalization factor of a polarization type. More...
constexpr Numeric	SimpleGCaseB (Rational N, Rational J, Rational Lambda, Rational S, Numeric GS, Numeric GL) noexcept
	Computes the Zeeman splitting coefficient. More...
constexpr Numeric	SimpleGCaseA (Rational Omega, Rational J, Rational Lambda, Rational Sigma, Numeric GS, Numeric GL) noexcept
	Computes the Zeeman splitting coefficient. More...
Model	GetSimpleModel (const QuantumIdentifier &qid) ARTS_NOEXCEPT
	Returns a simple Zeeman model. More...
Model	GetAdvancedModel (const QuantumIdentifier &qid) ARTS_NOEXCEPT
	Returns an advanced Zeeman model. More...
Derived	FromGrids (Numeric u, Numeric v, Numeric w, Numeric z, Numeric a) noexcept
	Computes the derived plane from ARTS grids. More...
constexpr Derived	FromPreDerived (Numeric H, Numeric theta, Numeric eta) noexcept
	Sets Derived from predefined Derived parameters. More...

Detailed Description

Implements Zeeman modeling.

Enumeration Type Documentation

Polarization

enum class Zeeman::Polarization : char

strong

Zeeman polarization selection.

Enumerator
SigmaMinus
Pi
SigmaPlus
None

Definition at line 44 of file zeemandata.h.

Function Documentation

AllPolarization()

AllPolarizationVectors Zeeman::AllPolarization ( Numeric  theta, Numeric  eta  )

noexcept

Computes the polarization of each polarization type.

Parameters

[in]	theta	The angle along the magnetic field
[in]	eta	The angle counter-clockwise in the magnetic field plane

Returns

The polarization vectors of all Zeeman polarization

Definition at line 366 of file zeemandata.cc.

References Zeeman::AllPolarizationVectors::pi, Zeeman::AllPolarizationVectors::sm, and Zeeman::AllPolarizationVectors::sp.

Referenced by propmat_clearskyAddOnTheFlyLineMixingWithZeeman(), and zeeman_on_the_fly().

AllPolarization_deta()

AllPolarizationVectors Zeeman::AllPolarization_deta ( Numeric  theta, Numeric  eta  )

noexcept

The derivative of AllPolarization wrt eta.

Parameters

[in]	theta	The angle along the magnetic field
[in]	eta	The angle counter-clockwise in the magnetic field plane

Returns

The derivative of AllPolarization wrt eta

Definition at line 398 of file zeemandata.cc.

References Zeeman::AllPolarizationVectors::pi, Zeeman::AllPolarizationVectors::sm, and Zeeman::AllPolarizationVectors::sp.

Referenced by propmat_clearskyAddOnTheFlyLineMixingWithZeeman(), and zeeman_on_the_fly().

AllPolarization_dtheta()

AllPolarizationVectors Zeeman::AllPolarization_dtheta ( Numeric  theta, const Numeric  eta  )

noexcept

The derivative of AllPolarization wrt theta.

Parameters

[in]	theta	The angle along the magnetic field
[in]	eta	The angle counter-clockwise in the magnetic field plane

Returns

The derivative of AllPolarization wrt theta

Definition at line 381 of file zeemandata.cc.

References Zeeman::AllPolarizationVectors::pi, Zeeman::AllPolarizationVectors::sm, and Zeeman::AllPolarizationVectors::sp.

Referenced by propmat_clearskyAddOnTheFlyLineMixingWithZeeman(), and zeeman_on_the_fly().

dM()

constexpr Index Zeeman::dM ( Polarization  type )

constexprnoexcept

Gives the change of M given a polarization type.

Parameters

[in]

type

The polarization type

Returns

The change in M

Definition at line 52 of file zeemandata.h.

References max, None, Pi, SigmaMinus, and SigmaPlus.

Referenced by Ml(), and Zeeman::Model::Strength().

dsum()

void Zeeman::dsum	(	PropagationMatrix &	dpm,
		const ComplexVectorView &	abs,
		const ComplexVectorView &	dabs,
		const PolarizationVector &	polvec,
		const PolarizationVector &	dpolvec_dtheta,
		const PolarizationVector &	dpolvec_deta,
		const Numeric	dH,
		const Numeric	dtheta,
		const Numeric	deta,
		const bool	do_phase = true
	)

Sums the Zeeman components derivatives into a propagation matrix.

Parameters

[in,out]	pm	The propagation matrix derivative
[in]	abs	The complex absorption vector
[in]	dabs	The complex absorption vector derivative w.r.t. H
[in]	polvec	The polarization vector
[in]	dpolvec_dtheta	The polarization vector derivative w.r.t. theta
[in]	dpolvec_deta	The polarization vector derivative w.r.t. eta
[in]	dH	The derivative w.r.t. H
[in]	dtheta	The derivative w.r.t. theta
[in]	deta	The derivative w.r.t. eta

Definition at line 451 of file zeemandata.cc.

References abs, ARTS_ASSERT, dabs, joker, and MapToEigen().

Referenced by propmat_clearskyAddOnTheFlyLineMixingWithZeeman(), and zeeman_on_the_fly().

end()

constexpr Rational Zeeman::end ( Rational  Ju, Rational  Jl, Polarization  type  )

constexprnoexcept

Gives the largest M for a polarization type of this transition.

Since the polarization determines the change in M, this function gives the last M of interest in the range of M possible for a given transition

The user has to ensure that Ju and Jl is a valid transition

Parameters

[in]	Ju	J of the upper state
[in]	Jl	J of the upper state
[in]	type	The polarization type

Returns

The largest M value

Definition at line 113 of file zeemandata.h.

References max, min, None, Pi, SigmaMinus, and SigmaPlus.

Referenced by abs_lines_per_speciesChangeBaseParameterForSpecies(), abs_lines_per_speciesSetBaseParameterForSpecies(), abs_lines_per_speciesSetCutoffForSpecies(), abs_lines_per_speciesSetLinemixingLimitForSpecies(), abs_lines_per_speciesSetLineShapeTypeForSpecies(), abs_lines_per_speciesSetMirroringForSpecies(), abs_lines_per_speciesSetNormalizationForSpecies(), abs_lines_per_speciesSetPopulationForSpecies(), abs_lines_per_speciesSetT0ForSpecies(), AgRecord::AgRecord(), Array< base >::Array(), Raw::Average::avg(), copy(), Raw::Average::cov(), gen_dir(), get_wsv_id(), Quantum::Number::items(), md_sanity_checks(), Raw::Average::nanavg(), Raw::Average::nanvar(), nelem(), MatrixView::operator*=(), MatrixView::operator+=(), MatrixView::operator-=(), MatrixView::operator/=(), operator<<(), Array< base >::operator=(), ArrayOfSpeciesTag::operator=(), Absorption::LineMixing::MapOfErrorCorrectedSuddenData::operator[](), option_describe(), option_input(), option_methods(), ArtsParser::parse_generic_input(), ArtsParser::parse_generic_output(), ArtsParser::parse_method_args(), ArtsParser::parse_specific_input(), ArtsParser::parse_specific_output(), ArtsParser::read_name_or_value(), bifstream::seek(), bofstream::seek(), test_sinc_likes_0limit(), my_basic_string< charT >::tolower(), my_basic_string< charT >::toupper(), and Raw::Average::var().

FromGrids()

Zeeman::Derived Zeeman::FromGrids ( Numeric  u, Numeric  v, Numeric  w, Numeric  z, Numeric  a  )

noexcept

Computes the derived plane from ARTS grids.

When done and if everything is well-defined:

\[ H = \sqrt{u^2 + v^2 + w^2}, \]

\[ \theta = \arccos \left( \vec{n} \cdot \vec{n}_H \right), \]

\[ \eta = \arctan\left( \frac{y}{x} \right), \]

\[ \frac{\partial H}{\partial \vec{H}} = \vec{n}_H, \]

\[ \frac{\partial \theta}{\partial \vec{H}} = \frac{\vec{n}_H \cos{\theta} - \vec{n}}{H\sin\theta}, \]

\[ \frac{\partial \eta}{\partial \vec{H}} = \frac{\vec{n}\times\vec{n}_H}{H\left(x^2 + y^2\right)} \]

With these helpers (some defined, others not):

\[ \vec{H} = \left[\begin{array}{l} v \\ u \\ w \end{array}\right], \]

\[ \vec{n}_H = \frac{\vec{H}}{H} , \]

\[ \vec{n} = \left[\begin{array}{r} \cos a \sin z \\ \sin a\sin z \\ \cos z \end{array}\right], \]

\[ \vec{e}_v = \left[\begin{array}{r} \cos a \cos z \\ \sin a\cos z \\ -\sin z \end{array}\right], \]

\[ y = \left\{\vec{e}_v \times \left[\vec{n}_H - \left(\vec{n}_H\cdot\vec{n}\right)\vec{n}\right]\right\} \cdot \vec{n}, \]

\[ x = \vec{e}_v \cdot \left[\vec{n}_H - \left(\vec{n}_H\cdot\vec{n}\right)\vec{n}\right] \]

Note that all other values are zero if \( H \) is zero, that \( \frac{\partial \theta}{\partial \vec{H}} \) is zero if \( \sin{\theta} \) is zero, that \( \frac{\partial \eta}{\partial \vec{H}} \) is zero if \( x \) and \( y \) are zero, and that the atan2(y, x) function is used for \( \eta \) to compensate for when \( x \) is zero.

Parameters

[in]	u	Magnetic field u-parameter
[in]	v	Magnetic field b-parameter
[in]	w	Magnetic field w-parameter
[in]	z	Zenith angle
[in]	a	Azimuth angle

Returns

The derived plane

Definition at line 275 of file zeemandata.cc.

References a, Zeeman::Derived::deta_du, Zeeman::Derived::deta_dv, Zeeman::Derived::deta_dw, Zeeman::Derived::dH_du, Zeeman::Derived::dH_dv, Zeeman::Derived::dH_dw, Zeeman::Derived::dtheta_du, Zeeman::Derived::dtheta_dv, Zeeman::Derived::dtheta_dw, Zeeman::Derived::eta, ev_xyz_by_za_local(), FromPreDerived(), Zeeman::Derived::H, los_xyz_by_uvw_local(), los_xyz_by_za_local(), Constant::pow2(), sqrt(), Zeeman::Derived::theta, u, v, and w.

Referenced by propmat_clearskyAddOnTheFlyLineMixingWithZeeman(), and zeeman_on_the_fly().

FromPreDerived()

constexpr Derived Zeeman::FromPreDerived ( Numeric  H, Numeric  theta, Numeric  eta  )

constexprnoexcept

Sets Derived from predefined Derived parameters.

Parameters

[in]	H	Derived magnetic field strength
[in]	theta	Derived magnetic field theta angle
[in]	eta	Derived magnetic field eta angle

Returns

The pre-derived plane

Definition at line 614 of file zeemandata.h.

Referenced by FromGrids(), and zeeman_on_the_fly().

GetAdvancedModel()

Zeeman::Model Zeeman::GetAdvancedModel

(

const QuantumIdentifier &

qid

)

Returns an advanced Zeeman model.

Will look at available Quantum numbers and use best approximation for the model to use. If no good approximation is available, it returns Model({0, 0}).

Parameters

[in]

qid

Transition type quantum id

Returns

Zeeman model

Definition at line 129 of file zeemandata.cc.

References N.

Referenced by Zeeman::Model::Model(), ReadArrayOfARTSCAT(), ReadARTSCAT(), ReadHITRAN(), ReadJPL(), and ReadLBLRTM().

GetSimpleModel()

Zeeman::Model Zeeman::GetSimpleModel

(

const QuantumIdentifier &

qid

)

Returns a simple Zeeman model.

Will use the simple Hund case provided by input. Throws if the input is bad

Parameters

[in]

qid

Transition type quantum id

Returns

Zeeman model

Definition at line 69 of file zeemandata.cc.

References get_lande_lambda_constant(), get_lande_spin_constant(), and SimpleG().

Referenced by Zeeman::Model::Model().

Ml()

constexpr Rational Zeeman::Ml ( Rational  Ju, Rational  Jl, Polarization  type, Index  n  )

constexprnoexcept

Gives the lower state M value at an index.

The user has to ensure that Ju and Jl is a valid transition

The user has to ensure n is less than the number of elements

Parameters

[in]	Ju	J of the upper state
[in]	Jl	J of the upper state
[in]	type	The polarization type
[in]	n	The position

Returns

The lower state M

Definition at line 180 of file zeemandata.h.

References dM(), and Mu().

Referenced by Zeeman::Model::Strength().

Mu()

constexpr Rational Zeeman::Mu ( Rational  Ju, Rational  Jl, Polarization  type, Index  n  )

constexprnoexcept

Gives the upper state M value at an index.

The user has to ensure that Ju and Jl is a valid transition

The user has to ensure n is less than the number of elements

Parameters

[in]	Ju	J of the upper state
[in]	Jl	J of the upper state
[in]	type	The polarization type
[in]	n	The position

Returns

The upper state M

Definition at line 159 of file zeemandata.h.

References start().

Referenced by Ml(), and Zeeman::Model::Strength().

nelem()

constexpr Index Zeeman::nelem ( Rational  Ju, Rational  Jl, Polarization  type  )

constexprnoexcept

Gives the number of elements of the polarization type of this transition.

The user has to ensure that Ju and Jl is a valid transition

Parameters

[in]	Ju	J of the upper state
[in]	Jl	J of the upper state
[in]	type	The polarization type

Returns

The number of elements

Definition at line 142 of file zeemandata.h.

References end(), and start().

operator<<() [1/2]

std::ostream & Zeeman::operator<<	(	bofstream &	bof,
		const Model &	m
	)

Definition at line 356 of file zeemandata.cc.

operator<<() [2/2]

std::ostream & Zeeman::operator<<	(	std::ostream &	os,
		const Model &	m
	)

Definition at line 346 of file zeemandata.cc.

operator>>() [1/2]

std::istream & Zeeman::operator>>	(	bifstream &	bif,
		Model &	m
	)

Definition at line 361 of file zeemandata.cc.

operator>>() [2/2]

std::istream & Zeeman::operator>>	(	std::istream &	is,
		Model &	m
	)

Definition at line 351 of file zeemandata.cc.

PolarizationFactor()

constexpr Numeric Zeeman::PolarizationFactor ( Polarization  type )

constexprnoexcept

The renormalization factor of a polarization type.

The polarization comes from some geometry. This function returns the factor we need to compute that geometry and to turn it into something that normalizes every possible M for this type into some strength that sums to unity

Parameters

[in]

type

The polarization type

Returns

Rescale factor

Definition at line 198 of file zeemandata.h.

References max, None, Pi, SigmaMinus, and SigmaPlus.

Referenced by Zeeman::Model::Strength().

SelectPolarization()

const PolarizationVector & Zeeman::SelectPolarization ( const AllPolarizationVectors &  data, Polarization  type  )

noexcept

Selects the polarization vector depending on polarization type.

Parameters

[in]	data	The pre-computed polarization vectors
[in]	type	The type of polarization to select

This should never be reached

Definition at line 416 of file zeemandata.cc.

References None, Pi, SigmaMinus, and SigmaPlus.

Referenced by propmat_clearskyAddOnTheFlyLineMixingWithZeeman(), and zeeman_on_the_fly().

SimpleGCaseA()

constexpr Numeric Zeeman::SimpleGCaseA ( Rational  Omega, Rational  J, Rational  Lambda, Rational  Sigma, Numeric  GS, Numeric  GL  )

constexprnoexcept

Computes the Zeeman splitting coefficient.

The level should be Hund case a type and all the values have to be defined

Parameters

[in]	Omega	The Omega quantum number of the level
[in]	J	The J quantum number of the level
[in]	Lambda	The Lambda quantum number of the level
[in]	Sigma	The Sigma quantum number of the level
[in]	GS	The spin Landé coefficient of the molecule
[in]	GL	The Landé coefficient of the molecule

Returns

Zeeman splitting coefficient of the level

Definition at line 262 of file zeemandata.h.

Referenced by SimpleG().

SimpleGCaseB()

constexpr Numeric Zeeman::SimpleGCaseB ( Rational  N, Rational  J, Rational  Lambda, Rational  S, Numeric  GS, Numeric  GL  )

constexprnoexcept

Computes the Zeeman splitting coefficient.

The level should be Hund case b type and all the values have to be defined

Parameters

[in]	N	The N quantum number of the level
[in]	J	The J quantum number of the level
[in]	Lambda	The Lambda quantum number of the level
[in]	S	The S quantum number of the level
[in]	GS	The spin Landé coefficient of the molecule
[in]	GL	The Landé coefficient of the molecule

Returns

Zeeman splitting coefficient of the level

Definition at line 226 of file zeemandata.h.

References N.

Referenced by SimpleG().

start()

constexpr Rational Zeeman::start ( Rational  Ju, Rational  Jl, Polarization  type  )

constexprnoexcept

Gives the lowest M for a polarization type of this transition.

Since the polarization determines the change in M, this function gives the first M of interest in the range of M possible for a given transition

The user has to ensure that Ju and Jl is a valid transition

Parameters

[in]	Ju	J of the upper state
[in]	Jl	J of the upper state
[in]	type	The polarization type

Returns

The lowest M value

Definition at line 80 of file zeemandata.h.

References max, min, None, Pi, SigmaMinus, and SigmaPlus.

Referenced by add_scalar_variance(), ArrayOfIndexLinSpace(), ArrayOfTimeNLinSpace(), Raw::Average::avg(), Raw::Calibration::caha(), check_and_add_block(), ComplexVector::ComplexVector(), Raw::Average::cov(), covmat_seAddBlock(), fill_tensor4(), fill_tensor5(), ForLoop(), linspace(), Mu(), Raw::Average::nanstd(), nca_get_dataa_double(), nelem(), nlinspace(), nlogspace(), Raw::Average::std(), test_AngIntegrate_trapezoid_opti(), test_ls(), test_sinc_likes_0limit(), test_x(), test_x_fixedstep(), test_xy(), test_xy_fixedstep(), test_xy_fixedstep_opt(), test_xy_fixedstep_opt2(), test_xy_opt(), Raw::Average::var(), Vector::Vector(), VectorLinSpace(), VectorLogSpace(), and VectorNLinSpace().

sum()

void Zeeman::sum	(	PropagationMatrix &	pm,
		const ComplexVectorView &	abs,
		const PolarizationVector &	polvec,
		const bool	do_phase = true
	)

Sums the Zeeman components into a propagation matrix.

Parameters

[in,out]	pm	The propagation matrix
[in]	abs	The complex absorption vector
[in]	polvec	The polarization vector

Definition at line 431 of file zeemandata.cc.

References abs, ARTS_ASSERT, joker, and MapToEigen().

Referenced by fac(), interp(), pndFromPsd(), propmat_clearskyAddOnTheFlyLineMixingWithZeeman(), PWR98H2OAbsModel(), Absorption::LineMixing::Makarov2020etal::relaxation_matrix_offdiagonal(), Absorption::LineMixing::LinearRovibErrorCorrectedSudden::relaxation_matrix_offdiagonal(), trapz(), and zeeman_on_the_fly().