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class VoigtModel( NonLinearModel )	Source

Voigt's Gauss Lorentz convoluted model for line profiles.

The Voigt function is a convolution of a Gauss and a Lorentz function. Physicaly it is the result of thermal and pressure broadening of a spectral line.

The models takes 4 parameters: amplitude, center frequency, half-width of the Gaussian, and half-width of the Lorentzian. These are initialised to [1, 0, 1, 1]. Parameters 2 & 3 ( widths ) is always kept positive ( >=0 ).

The implementation uses the Faddeeva function from scipy.special.wofz.

Examples

voigt = VoigtModel( )
voigt.setParameters( [5, 4, 1, 2] )
print( voigt( numpy.arange(  41 , dtype=float ) / 5 ) )      # from [0,8]

Attributes from Model

     npchain, parameters, stdevs, xUnit, yUnit

Attributes from FixedModel

     npmax, fixed, parlist, mlist

Attributes from BaseModel

     npbase, ndim, priors, posIndex, nonZero, tiny, deltaP, parNames

VoigtModel( copy=None, **kwargs )

Voigt model.

Number of parameters is 4.

Parameters

• copy : VoigtModel
       to be copied

copy( )

Copy method.

baseResult( xdata, params )

Returns the result of the model function.

Note: both width in the parameter array ( items 2 & 3 ) are kept strictly positive. I.e. they are changed when upon input they are negative.

Parameters

• xdata : array_like
       values at which to calculate the result
• params : array_like
       values for the parameters.

basePartial( xdata, params, parlist=None )

Returns the partials at the input value.

     z = ( x - p1 + 1j * p3 ) / ( p2 * sqrt2 )
     z0 = 1j * p3 / ( p2 * sqrt2 )

     vgt = p0 * R( wofzz ) / R( wofz0 )

     dvdp = dvdz * dzdp

     dvdz = p0 * ( R(dwdz) * R(wofz0) - R(dwd0) * R(wofzz) ) / R(wofz0)²
     dvdp = p0 * ( R(dwdz * dzdp) * R(wofz0) - R(dwd0 * d0dp) * R(wofzz) ) / R(wofz0)²

     dwdz = 2j / sqrt(pi) - 2 * z * wofzz
     dwd0 = 2j / sqrt(pi) - 2 * z0 * wofz0

     ## p0 and p1 have no influence in wofz0
     dzdp0 = 0
     dzdp1 = -1 / ( p2 * sqrt2 )
     d0dp2 = - ( 1j * p3 / ( p2² * sqrt2 ) = -z0 / p2
     dzdp2 = - ( ( x - p1 + 1j * p3 ) / ( p2² * sqrt2 ) = -z / p2
     dzdp3 = d0dp3 = 1j / ( p2 * sqrt2 )

     dvdp0 = R(wofzz) / R(wofz0)
     ## The other partial follow from calculating dvdp for the parameters 1..3

Parameters

• xdata : array_like
       values at which to calculate the partials
• params : array_like
       values for the parameters.
• parlist : array_like
       list of indices active parameters (or None for all)

baseDerivative( xdata, params )

Return the derivative df/dx at each xdata (=x).

     z = ( x - p1 + 1j * p3 ) / ( p2 * sqrt2 )
     z0 = 1j * p3 / ( p2 * sqrt2 )

     vgt = p0 / wofz0 * re( wofzz )
     dvdx = dvdz * dzdx

     dvdz = p0 / wofz0 * dwdz
     dwdz = 2j / sqrt(pi) - 2 * z * wofzz

     dzdx = 1 / ( p2 * sqrt2 )

Parameters

• xdata : array_like
       values at which to calculate the result
• params : array_like
       values for the parameters.

baseName( )

Returns a string representation of the model.

baseParameterUnit( k )

Return the name of a parameter.

Parameters

• k : int
       parameter number.

Methods inherited from NonLinearModel

• setMixedModel( lindex )
• isMixed( )
• getNonLinearIndex( )
• partial( xdata, param=None, useNum=False )

Methods inherited from Model

• chainLength( )
• isNullModel( )
• isolateModel( k )
• addModel( model )
• subtractModel( model )
• multiplyModel( model )
• divideModel( model )
• pipeModel( model )
• appendModel( model, operation )
• correctParameters( params )
• result( xdata, param=None )
• operate( res, pars, next )
• derivative( xdata, param, useNum=False )
• selectPipe( ndim, ninter, ndout )
• pipe_0( dGd, dHdG )
• pipe_1( dGd, dHdG )
• pipe_2( dGd, dHdG )
• pipe_3( dGd, dHdG )
• pipe_4( dGdx, dHdG )
• pipe_5( dGdx, dHdG )
• pipe_6( dGdx, dHdG )
• pipe_7( dGdx, dHdG )
• pipe_8( dGdx, dHdG )
• pipe_9( dGdx, dHdG )
• shortName( )
• getNumberOfParameters( )
• numDerivative( xdata, param )
• numPartial( xdata, param )
• isDynamic( )
• hasPriors( isBound=True )
• getPrior( kpar )
• setPrior( kpar, prior=None, **kwargs )
• getParameterName( kpar )
• getParameterUnit( kpar )
• getIntegralUnit( )
• setLimits( lowLimits=None, highLimits=None )
• getLimits( )
• hasLimits( fitindex=None )
• unit2Domain( uvalue, kpar=None )
• domain2Unit( dvalue, kpar=None )
• partialDomain2Unit( dvalue )
• nextPrior( )
• getLinearIndex( )
• testPartial( xdata, params, silent=True )
• strictNumericPartial( xdata, params, parlist=None )
• assignDF1( partial, i, dpi )
• assignDF2( partial, i, dpi )
• strictNumericDerivative( xdata, param )

Methods inherited from FixedModel

• select( params )
• selectNames( names )
• expand( xdata, param )

Methods inherited from BaseModel

• checkParameter( param )
• checkPositive( param )
• checkZeroParameter( param )
• isModifiable( )
• basePrior( kpar )
• baseParameterName( kpar )