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class StellarOrbitModel( NonLinearModel )	Source

Model for the radial velocity variations of a star caused by a orbiting planet.

  The algorithm was taken from Boule
     Cory Boule etal. (2017) J. of Double Star Observations Vol 13 p.189.
     http://www.jdso.org/volume13/number2/Harfenist₁₈₉-199.pdf

par	symbol	description	limits	comment
p0	e	eccentricity of the elliptic orbit	0<e<1	0 = circular orbit
p1	a	semi major axis	a>0
p2	P	period of the orbit	P>0
p3	T	phase since periastron passage	0<T<2π
p4	i	inclination of the orbit wrt sky	0<i<π	0 = pi = in sky plane
p5	Ω	position angle from North
		to the line of nodes	0<Ω<π	0 = north
p6	ω	longitude from the node (in p5)
		to the periastron	0<ω<2π	0 = periastron in node

Due to the fact that the orbit can be mirrored in the sky plane, one of p₅ or p₆ has to be limited to [0,pi] and the other to [0,2pi].

The parameters are initialized at [0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0]. It is a non-linear model.

This class uses Kepplers2ndLaw to find the radius and anomaly.

Attributes

• keppler : Kepplers2ndLaw()
       to calculate the radius and true anomaly
• ndout : int
       The number of outputs is 2. Use MultipleOutputProblem.
• spherical : bool
       if True return the results in spherical coordinates.
• cyclic : { 1 : 2*pi }
       Only if spherical, indicating that result[:,1] is cyclic.

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

Examples

sm = StellarOrbitModel( )
print( sm.npars )
7

StellarOrbitModel( copy=None, spherical=True, **kwargs )

Radial velocity model.

Number of parameters is 5

Parameters

• copy : StellarOrbitModel
       model to copy
• spherical : bool (True)
       produce output in sperical coordinates (rho,phi)
       otherwise in rectilinear coordinates (x,y)
• fixed : dictionary of {int:float}
       int list if parameters to fix permanently. Default None.
       float list of values for the fixed parameters.
       Attribute fixed can only be set in the constructor.

copy( )

Copy method.

baseResult( xdata, params )

Returns the result of the model function.

Parameters

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

The parameters are explained in the StellarOrbitModel constructor.

toRect( rp )

Return (x,y) coordinates from (rho,phi)

Parameters

• rp : array
       rp[:,0] : separation of the stars
       rp[:,1] : angle from north (down) CCW to east (right)

toSpher( xy )

Return (rho,phi) coordinates from (x,y)

Parameters

• xy : array
       xy[:,0] : x position
       xy[:,1] : y position

baseDerivative( xdata, params )

Returns the derivative (df/dx) of the model function.

Parameters

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

The parameters are explained in the StellarOrbitModel constructor.

basePartial( xdata, params, parlist=None )

Returns the partials at the xdata value.
The partials are x ( xdata ) to degree-th power.

Parameters

• xdata : array_like
       values at which to calculate the result
• params : array_like
       values for the parameters. (not used for linear models)
• parlist : array_like
       list of indices active parameters (or None for all)

The parameters are explained in the StellarOrbitModel constructor.

baseName( )

Returns a string representation of the model.

baseParameterUnit( k )

Return the unit of a parameter. (TBC)

Parameters

• k : int
       the kth parameter.

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 )