Stuff related to lineshape functions. More...

#include <cmath>
#include "arts.h"
#include "matpackI.h"
#include "array.h"
#include "absorption.h"
#include "Faddeeva.hh"

Namespaces
	global_data

Functions
void	lineshape_no_shape (Vector &ls_attenuation, Vector &ls_phase, Vector &X, const Numeric f0, const Numeric gamma, const Numeric sigma, ConstVectorView f_grid)

void	lineshape_lorentz (Vector &ls_attenuation, Vector &ls_phase, Vector &X, const Numeric f0, const Numeric gamma, const Numeric sigma, ConstVectorView f_grid)

void	lineshape_doppler (Vector &ls_attenuation, Vector &ls_phase, Vector &x, const Numeric f0, const Numeric gamma, const Numeric sigma, ConstVectorView f_grid)

long	bfun6_ (Numeric y, Numeric x)

void	lineshape_voigt_kuntz6 (Vector &ls_attenuation, Vector &ls_phase, Vector &x, const Numeric f0, const Numeric gamma, const Numeric sigma, ConstVectorView f_grid)

long int	bfun3_ (Numeric y, Numeric x)

void	lineshape_voigt_kuntz3 (Vector &ls_attenuation, Vector &ls_phase, Vector &x, const Numeric f0, const Numeric gamma, const Numeric sigma, ConstVectorView f_grid)

long	bfun4_ (Numeric y, Numeric x)

void	lineshape_voigt_kuntz4 (Vector &ls_attenuation, Vector &ls_phase, Vector &x, const Numeric f0, const Numeric gamma, const Numeric sigma, ConstVectorView f_grid)

void	lineshape_voigt_drayson (Vector &ls_attenuation, Vector &ls_phase, Vector &x, const Numeric f0, const Numeric gamma, const Numeric sigma, ConstVectorView f_grid)

void	chi_cousin (Numeric &chi, const Numeric &df)

void	lineshape_CO2_lorentz (Vector &ls_attenuation, Vector &ls_phase, Vector &X, const Numeric f0, const Numeric gamma, const Numeric sigma, ConstVectorView f_grid)

void	lineshape_CO2_drayson (Vector &ls_attenuation, Vector &ls_phase, Vector &X, const Numeric f0, const Numeric gamma, const Numeric sigma, ConstVectorView f_grid)

void	faddeeva_algorithm_916 (Vector &ls_attenuation, Vector &ls_phase, Vector &xvector, const Numeric f0, const Numeric gamma, const Numeric sigma, ConstVectorView f_grid)

void	hui_etal_1978_lineshape (Vector &ls_attenuation, Vector &ls_phase, Vector &xvector, const Numeric f0, const Numeric gamma, const Numeric sigma, ConstVectorView f_grid)

void	lineshape_norm_no_norm (Vector &fac, const Numeric f0, ConstVectorView f_grid, const Numeric T)

void	lineshape_norm_linear (Vector &fac, const Numeric f0, ConstVectorView f_grid, const Numeric T)

void	lineshape_norm_quadratic (Vector &fac, const Numeric f0, ConstVectorView f_grid, const Numeric T)

void	lineshape_norm_VVH (Vector &fac, const Numeric f0, ConstVectorView f_grid, const Numeric T)

void	define_lineshape_data ()

void	define_lineshape_norm_data ()

Detailed Description

Stuff related to lineshape functions.

This file contains both the lineshape functions themselves and the function define_lineshape_data which sets the lineshape lookup data.

This is the file from arts-1-0, back-ported to arts-1-1.

Author: Stefan Buehler

Date: 2000-08-21

Definition in file lineshapes.cc.

Function Documentation

◆ bfun3_()

long int bfun3_	(	Numeric	y,
		Numeric	x
	)

Definition at line 561 of file lineshapes.cc.

Referenced by lineshape_voigt_kuntz3().

◆ bfun4_()

long bfun4_	(	Numeric	y,
		Numeric	x
	)

Definition at line 938 of file lineshapes.cc.

Referenced by lineshape_voigt_kuntz4().

◆ bfun6_()

long bfun6_	(	Numeric	y,
		Numeric	x
	)

Definition at line 153 of file lineshapes.cc.

Referenced by lineshape_voigt_kuntz6().

◆ chi_cousin()

void chi_cousin	(	Numeric &	chi,
		const Numeric &	df
	)

Chi factors according to Cousin

The CO2-CO2 self-broadening is neglected. Broadening factors for both O2 and N2 are considered, assuming 79% N2 and 21% O2.

Parameters

chi	Out: The chi factor
df	(f-f0) in Hz.

Author: Patrick Eriksson

Date: 2000-09-07

Definition at line 1558 of file lineshapes.cc.

References HZ2CM.

Referenced by lineshape_CO2_drayson(), and lineshape_CO2_lorentz().

◆ define_lineshape_data()

void define_lineshape_data ( )

Definition at line 1928 of file lineshapes.cc.

References faddeeva_algorithm_916(), hui_etal_1978_lineshape(), lineshape_CO2_drayson(), lineshape_CO2_lorentz(), global_data::lineshape_data, lineshape_doppler(), lineshape_lorentz(), lineshape_no_shape(), lineshape_voigt_drayson(), lineshape_voigt_kuntz3(), lineshape_voigt_kuntz4(), and lineshape_voigt_kuntz6().

Referenced by main().

◆ define_lineshape_norm_data()

void define_lineshape_norm_data ( )

Definition at line 2033 of file lineshapes.cc.

References global_data::lineshape_norm_data, lineshape_norm_no_norm(), lineshape_norm_quadratic(), and lineshape_norm_VVH().

Referenced by main().

◆ faddeeva_algorithm_916()

void faddeeva_algorithm_916	(	Vector &	ls_attenuation,
		Vector &	ls_phase,
		Vector &	xvector,
		const Numeric	f0,
		const Numeric	gamma,
		const Numeric	sigma,
		ConstVectorView	f_grid
	)

The Voigt and Faraday-Voigt line shape. Based on rewritten Faddeeva function algorithm 916. For more information read: MOFREH R. ZAGHLOUL and AHMED N. ALI Algorithm 916: Computing the Faddeyeva and Voigt Functions ACM Transactions on Mathematical Software, Vol. 38, No. 2, Article 15, Publication date: December 2011.

The main bulk of code is in Faddeeva.cc and written by Steven G. Johnson of MIT. Keep Faddeeva.{cc,hh} up to date in speed and accuracy by watching: http://ab-initio.mit.edu/Faddeeva sometimes.

Return values

ls_attenuation	The shape function.
ls_phase	The phase shape function.
xvector	Auxillary parameter to store frequency grid.

Parameters

f0	Line center frequency.
gamma	The pressure broadening parameter.
sigma	The Doppler broadening parameter.
f_grid	The frequency grid.

Author: Richard Larsson 2013-01-17

Definition at line 1699 of file lineshapes.cc.

References fac(), ConstVectorView::nelem(), PI, and w().

Referenced by define_lineshape_data().

◆ hui_etal_1978_lineshape()

void hui_etal_1978_lineshape	(	Vector &	ls_attenuation,
		Vector &	ls_phase,
		Vector &	xvector,
		const Numeric	f0,
		const Numeric	gamma,
		const Numeric	sigma,
		ConstVectorView	f_grid
	)

The Voigt and Faraday-Voigt line shape. Based on Complex Error Function of X+i*Y.

Y must be positive.

Reference for equations: Hui, Armstrong and Wray, JQSRT V.19, P.509 (1978).

CERROR(z)=CERROR(x+iy)=CERROR(x,y)=w(x,y) g(nu,nu_0) = (1/DopHW)* sqrt(ln2/pi)*(Re(w(x,y) + Py*Im(w(x,y)) y=(P*LorHW /DopHW)*sqrt(ln2) x=(nu-nu_0)/DopHW)*sqrt(ln2)

NB Re(w)=Voigt

Return values

ls_attenuation	The shape function.
ls_phase	The phase shape function.
xvector	Auxillary parameter to store frequency grid.

Parameters

f0	Line center frequency.
gamma	The pressure broadening parameter.
sigma	The Doppler broadening parameter.
f_grid	The frequency grid.

Author: P. Rosenkranz 1988-02-19

(Added by Richard Larsson 2014-03-13 with slight moderation)

Definition at line 1765 of file lineshapes.cc.

References C, fac(), ConstVectorView::nelem(), and PI.

Referenced by define_lineshape_data().

◆ lineshape_CO2_drayson()

void lineshape_CO2_drayson	(	Vector &	ls_attenuation,
		Vector &	ls_phase,
		Vector &	X,
		const Numeric	f0,
		const Numeric	gamma,
		const Numeric	sigma,
		ConstVectorView	f_grid
	)

A CO2 IR line shape.

Return values

ls_attenuation	The shape function.
X	Auxillary parameter, only used in Voigt fct.

Parameters

f0	Line center frequency.
gamma	The pressure broadening parameter.
sigma	The Doppler broadening parameter. (Not used.)
f_grid	The frequency grid.

Author: Patrick Eriksson

Date: 2000-09-04

Definition at line 1651 of file lineshapes.cc.

References chi_cousin(), lineshape_voigt_drayson(), and ConstVectorView::nelem().

Referenced by define_lineshape_data().

◆ lineshape_CO2_lorentz()

void lineshape_CO2_lorentz	(	Vector &	ls_attenuation,
		Vector &	ls_phase,
		Vector &	X,
		const Numeric	f0,
		const Numeric	gamma,
		const Numeric	sigma,
		ConstVectorView	f_grid
	)

A CO2 IR line shape.

Return values

ls_attenuation	The shape function.
X	Auxillary parameter, only used in Voigt fct.

Parameters

f0	Line center frequency.
gamma	The pressure broadening parameter.
sigma	The Doppler broadening parameter. (Not used.)
f_grid	The frequency grid.

Author: Patrick Eriksson

Date: 2000-09-04

Definition at line 1607 of file lineshapes.cc.

References chi_cousin(), fac(), ConstVectorView::nelem(), and PI.

Referenced by define_lineshape_data().

◆ lineshape_doppler()

void lineshape_doppler	(	Vector &	ls_attenuation,
		Vector &	ls_phase,
		Vector &	x,
		const Numeric	f0,
		const Numeric	gamma,
		const Numeric	sigma,
		ConstVectorView	f_grid
	)

The Doppler line shape.

Return values

ls_attenuation	The shape function.
ls_phase	The shape function.
x	Auxillary parameter, only used in Voigt fct.

Parameters

f0	Line center frequency.
gamma	The pressure broadening parameter. (Not used.)
sigma	The Doppler broadening parameter.
f_grid	The frequency grid.

Author: Axel von Engeln

Date: 2000-12-06

Definition at line 123 of file lineshapes.cc.

References fac(), ConstVectorView::nelem(), and PI.

Referenced by define_lineshape_data().

◆ lineshape_lorentz()

void lineshape_lorentz	(	Vector &	ls_attenuation,
		Vector &	ls_phase,
		Vector &	X,
		const Numeric	f0,
		const Numeric	gamma,
		const Numeric	sigma,
		ConstVectorView	f_grid
	)

The Lorentz line shape. This is a quick and dirty implementation.

Return values

ls_attenuation	The shape function.
ls_phase	The shape function.
X	Auxillary parameter, only used in Voigt fct.

Parameters

f0	Line center frequency.
gamma	The pressure broadening parameter.
sigma	The Doppler broadening parameter. (Not used.)
f_grid	The frequency grid.

Author: Stefan Buehler

Date: 2000-06-16

Definition at line 86 of file lineshapes.cc.

References fac(), ConstVectorView::nelem(), and PI.

Referenced by define_lineshape_data().

◆ lineshape_no_shape()

void lineshape_no_shape	(	Vector &	ls_attenuation,
		Vector &	ls_phase,
		Vector &	X,
		const Numeric	f0,
		const Numeric	gamma,
		const Numeric	sigma,
		ConstVectorView	f_grid
	)

The dummy line shape. This lineshape does nothing. It only exists, because formally you have to specify a lineshape also for continuum tags. It has to have the same arguments as all the other lineshapes, though...

Return values

ls_attenuation	The shape function.
ls_phase	The shape function.
X	Auxillary parameter, only used in Voigt fct.

Parameters

f0	Line center frequency.
gamma	The pressure broadening parameter.
sigma	The Doppler broadening parameter. (Not used.)
f_grid	The frequency grid.

Exceptions

runtime_error This exception is always thrown when the function is called.

Date: 2001-01-16

Author: Stefan Buehler

Definition at line 60 of file lineshapes.cc.

Referenced by define_lineshape_data().

◆ lineshape_norm_linear()

void lineshape_norm_linear	(	Vector &	fac,
		const Numeric	f0,
		ConstVectorView	f_grid,
		const Numeric	T
	)

Linear normalization factor of the lineshape function with f/f0.

Return values

fac	Normalization factor to the lineshape function.

Parameters

f0	Line center frequency.
f_grid	The frequency grid.
T	(unused here)

Author: Axel von Engeln 30.11.2000

Definition at line 1839 of file lineshapes.cc.

References abs, fac(), and ConstVectorView::nelem().

◆ lineshape_norm_no_norm()

void lineshape_norm_no_norm	(	Vector &	fac,
		const Numeric	f0,
		ConstVectorView	f_grid,
		const Numeric	T
	)

No normalization of the lineshape function.

Return values

fac	Normalization factor to the lineshape function.

Parameters

f0	Line center frequency.
f_grid	The frequency grid.
T	Temperature (unused here)

Author: Axel von Engeln 30.11.2000

Definition at line 1821 of file lineshapes.cc.

References fac().

Referenced by define_lineshape_norm_data().

◆ lineshape_norm_quadratic()

void lineshape_norm_quadratic	(	Vector &	fac,
		const Numeric	f0,
		ConstVectorView	f_grid,
		const Numeric	T
	)

Quadratic normalization factor of the lineshape function with (f/f0)^2.

Return values

fac	Normalization factor to the lineshape function.

Parameters

f0	Line center frequency.
f_grid	The frequency grid.
T	Temperature (unused here)

Author: Axel von Engeln 30.11.2000

Definition at line 1863 of file lineshapes.cc.

References fac(), and ConstVectorView::nelem().

Referenced by define_lineshape_norm_data().

◆ lineshape_norm_VVH()

void lineshape_norm_VVH	(	Vector &	fac,
		const Numeric	f0,
		ConstVectorView	f_grid,
		const Numeric	T
	)

Van Vleck Huber normalization factor of the lineshape function with (f*tanh(h*f/(2*k*T))) / (f0*tanh(h*f0/(2*k*T))). The denominator is a result of catalogue intensities. See P. Rayer, The VVH and VVW Spectral Functions, Atmospheric Millimeter and Sub-Millimeter Wave Radiative Transfer Modeling II, Editors: P. Eriksson, S. Buehler, Berichte aus derm Institut fuer Umweltphysik, Band 4, 2001.

Return values

fac	Normalization factor to the lineshape function.

Parameters

f0	Line center frequency.
f_grid	The frequency grid.
T	Temperature

Author: Axel von Engeln 2003-07-28

Definition at line 1893 of file lineshapes.cc.

References abs, BOLTZMAN_CONST, fac(), ConstVectorView::nelem(), and PLANCK_CONST.

Referenced by define_lineshape_norm_data().

◆ lineshape_voigt_drayson()

void lineshape_voigt_drayson	(	Vector &	ls_attenuation,
		Vector &	ls_phase,
		Vector &	x,
		const Numeric	f0,
		const Numeric	gamma,
		const Numeric	sigma,
		ConstVectorView	f_grid
	)

The Voigt line shape. Drayson approximation of the Voigt line shape.

Return values

ls_attenuation	The shape function.
x	Auxillary parameter to store frequency grid.

Parameters

f0	Line center frequency.
gamma	The pressure broadening parameter.
sigma	The Doppler broadening parameter.
f_grid	The frequency grid.

Original ife function call and documention:

int voigt_vector(int nx, Numeric *X, Numeric Y, Numeric *Z, Numeric fac)

direct translation of the FORTRAN algorithm given in Drayson, S. R., Rapid Computation of the Voigt Profile, J. Quant. Spectrosc. Radiat. Transfer, Vol. 16, pp. 611-614, 1976 by Bjoern-Martin Sinnhuber, 13.Mar.96 in Ny-Aalesund, Spitsbergen.

Modified for vector calculation of a frequency array:

  --------------------------------------------------------------------
          int    nx        (in)           number of frequencies
          double *X        (in)           distance from line center in 
                                          units of (Doppler halfwidths 
                                          times sqrt(ln 2) )
          double  Y        (in)           Ratio of the collision halfwidth 
                                          to the ( Doppler halfwidth times sqrt(ln2) )
          double *Z        (out)          return array of voigt 
          double fac       (in)           no function, included to be
                                          consistent with the other voigt
                                          profile calculations
  --------------------------------------------------------------------

23.02.98 AvE

Replaced nx by nf, Z by ls, X by x, and multiplied ls with the factor fac.

Author: Axel von Engeln

Date: 2000-12-06

Definition at line 1408 of file lineshapes.cc.

References C, fac(), N, ConstVectorView::nelem(), and PI.

Referenced by define_lineshape_data(), and lineshape_CO2_drayson().

◆ lineshape_voigt_kuntz3()

void lineshape_voigt_kuntz3	(	Vector &	ls_attenuation,
		Vector &	ls_phase,
		Vector &	x,
		const Numeric	f0,
		const Numeric	gamma,
		const Numeric	sigma,
		ConstVectorView	f_grid
	)

The Voigt line shape. Kuntz approximation of the Voigt line shape.

Return values

ls_attenuation	The shape function.
x	Auxillary parameter to store frequency grid.

Parameters

f0	Line center frequency.
gamma	The pressure broadening parameter.
sigma	The Doppler broadening parameter.
f_grid	The frequency grid.

Original c function call and documention:

int voigt3 ( long nx, float *x, float y, float *prb, float fak )

Calculates the Voigt-Function times the user-definied value fac with a relative accuracy better than 2*10-3.

If this subroutine is called several times with the same parameter y the numerically expensive coefficents a1..t8 are only calculated once thus further accelerating the algorithm

  --------------------------------------------------------------------
  x(nx)   (in)    :Distance from line center in units of Doppler
                  :halfwidths
  y       (in)    :Ratio of the Doppler halfwidth to the Lorentz
                  :halfwidth  
  prb     (out)   :voigt-function times fak
  fak     (in)    :factor to be specified by the user
  --------------------------------------------------------------------

  author: M. Kuntz, 
          Institut fuer Meteorologie und Klimaforschung, 
          Forschungszentrum Karlsruhe, 
          Postfach 3640, 
          76021 Karlsruhe, Germany. 
          email: kuntz@imk.fzk.de

About 'voigt3' : The program was originally written by M. Kuntz in Fortran77 but has been translated into C by Dietrich Feist (f2c) and into C++ by Oliver Lemke and Axel von Engeln. fak is removed from program code. Replaced nx by nf. Replaced prb by ls. Multiplied ls with the factor fac.

Author: Oliver Lemke and Axel von Engeln

Date: 2000-12-07

Definition at line 650 of file lineshapes.cc.

References b0, bfun3_(), fac(), max, min, ConstVectorView::nelem(), and PI.

Referenced by define_lineshape_data().

◆ lineshape_voigt_kuntz4()

void lineshape_voigt_kuntz4	(	Vector &	ls_attenuation,
		Vector &	ls_phase,
		Vector &	x,
		const Numeric	f0,
		const Numeric	gamma,
		const Numeric	sigma,
		ConstVectorView	f_grid
	)

The Voigt line shape. Kuntz approximation of the Voigt line shape.

Return values

ls_attenuation	The shape function.
x	Auxillary parameter to store frequency grid.

Parameters

f0	Line center frequency.
gamma	The pressure broadening parameter.
sigma	The Doppler broadening parameter. (Not used.)
f_grid	The frequency grid.

Original c function call and documention:

int voigt4 ( long nx, float *x, float y, float *prb, float fak )

Calculates the Voigt-Function times the user-definied value fac with a relative accuracy better than 2*10-4.

If this subroutine is called several times with the same parameter y the numerically expensive coefficents a1..t8 are only calculated once thus further accelerating the algorithm

  --------------------------------------------------------------------
  x(nx)   (in)    :Distance from line center in units of Doppler
                  :halfwidths
  y       (in)    :Ratio of the Doppler halfwidth to the Lorentz
                  :halfwidth  
  prb     (out)   :voigt-function times fak
  fak     (in)    :factor to be specified by the user
  --------------------------------------------------------------------

  author: M. Kuntz, 
          Institut fuer Meteorologie und Klimaforschung, 
          Forschungszentrum Karlsruhe, 
          Postfach 3640, 
          76021 Karlsruhe, Germany. 
          email: kuntz@imk.fzk.de

About 'voigt4' : The program was originally written by M. Kuntz in Fortran77 but has been translated into C by Dietrich Feist (f2c) and into C++ by Oliver Lemke and Axel von Engeln. fak is removed from program code. Replaced nx by nf. Replaced prb by ls. Multiplied ls with the factor fac.

Author: Oliver Lemke and Axel von Engeln

Date: 2000-12-07

Definition at line 1024 of file lineshapes.cc.

References b0, bfun4_(), fac(), max, min, ConstVectorView::nelem(), and PI.

Referenced by define_lineshape_data().

◆ lineshape_voigt_kuntz6()

void lineshape_voigt_kuntz6	(	Vector &	ls_attenuation,
		Vector &	ls_phase,
		Vector &	x,
		const Numeric	f0,
		const Numeric	gamma,
		const Numeric	sigma,
		ConstVectorView	f_grid
	)

The Voigt line shape. Kuntz approximation of the Voigt line shape.

Return values

ls_attenuation	The shape function.
x	Auxillary parameter to store frequency grid.

Parameters

f0	Line center frequency.
gamma	The pressure broadening parameter.
sigma	The Doppler broadening parameter.
f_grid	The frequency grid.

Original c function call and documention:

int voigt ( long nx, float *x, float y, float *prb, float fak )

Calculates the Voigt-Function times the user-definied value fac with a relative accuracy better than 2*10-6.

If this subroutine is called several times with the same parameter y the numerically expensive coefficents a1..t8 are only calculated once thus further accelerating the algorithm

  --------------------------------------------------------------------
  x(nx)   (in)    :Distance from line center in units of Doppler
                  :halfwidths
  y       (in)    :Ratio of the Doppler halfwidth to the Lorentz
                  :halfwidth  
  prb     (out)   :voigt-function times fak
  fak     (in)    :factor to be specified by the user
  --------------------------------------------------------------------

  author: M. Kuntz, 
          Institut fuer Meteorologie und Klimaforschung, 
          Forschungszentrum Karlsruhe, 
          Postfach 3640, 
          76021 Karlsruhe, Germany. 
          email: kuntz@imk.fzk.de

About 'voigt' : The program was originally written by M. Kuntz in Fortran77 but has been translated into C by Dietrich Feist (f2c) and into C++ by Oliver Lemke and Axel von Engeln. fak is removed from program code. Replaced nx by nf. Replaced prb by ls. Multiplied ls with the factor fac.

Author: Oliver Lemke and Axel von Engeln

Date: 2000-09-27

Definition at line 236 of file lineshapes.cc.

References bfun6_(), fac(), max, min, ConstVectorView::nelem(), and PI.

Referenced by define_lineshape_data().

Namespaces

Functions

Detailed Description

Function Documentation

◆ bfun3_()

◆ bfun4_()

◆ bfun6_()

◆ chi_cousin()

◆ define_lineshape_data()

◆ define_lineshape_norm_data()

◆ faddeeva_algorithm_916()

◆ hui_etal_1978_lineshape()

NB Re(w)=Voigt

◆ lineshape_CO2_drayson()

◆ lineshape_CO2_lorentz()

◆ lineshape_doppler()

◆ lineshape_lorentz()

◆ lineshape_no_shape()

◆ lineshape_norm_linear()

◆ lineshape_norm_no_norm()

◆ lineshape_norm_quadratic()

◆ lineshape_norm_VVH()

◆ lineshape_voigt_drayson()

◆ lineshape_voigt_kuntz3()

◆ lineshape_voigt_kuntz4()

◆ lineshape_voigt_kuntz6()