["BayesicFitting"]

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class Kernel2dModel( NonLinearModel )	Source

Two dimensional Kernel Model.

The Kernel2dModel is defined as

f( x:p ) = p₀ * K( r )

where K( r ) is a selectable kernel function and r is the distance to the center.

r = sqrt( u² + v² ).

There are 3 options for u and v

CIRCULAR has 4 parameters

     Circular shape with only one width.
     u = ( x - p₁ ) / p₃
     v = ( x - p₂ ) / p₃
ELLIPTIC has 5 parameters

     Elliptic shape aligned along the axes; 2 widths.
     u = ( x - p₁ ) / p₃
     v = ( x - p₂ ) / p₄
ROTATED has 6 parameters

     Rotated elliptical shape with 2 width and a rotational angle.
     u = ( ( x - p₁ )*cos( p₅ ) - ( y - p₂ )*sin( p₅) ) / p₃
     v = ( ( x - p₁ )*sin( p₅ ) + ( y - p₂ )*cos( p₅) ) / p₄

The "center" parameters ( 1&2 ) and the "angle" parameter ( 5 ) are initilized as 0. The rotational angle is measured counterclockwise from the x-axis. The "width" parameters ( 3&4 ) are initialized as 1.0, except for the ROTATED case; then they need to be different ( 2.0 and 0.5 resp. ). Otherwise the model parameter "angle" is degenerate. The "amplitude" parameter is set to 1.0.

Several kernel functions, K( x ) are defined in the directory fit/kernels.

Beware: These models are unaware of anything outside their range.

Author: Do Kester

Example

model = Kernel2dModel( )                                 # default: circular Gauss
model.setKernelShape( Lorentz(), 'Elliptic'  )             # elliptic Lorentz model.
model = Kernel2dModel( shape=3 )                         # rotated Gauss

Category : mathematics/Fitting

Kernel2dModel( kernel=Gauss(), shape=1, copy=None, **kwargs )

Kernel Model.

Default model: Gauss with Circular shape.

Parameters

kernel : Kernel
the kernel to be used
shape : 1 | 2 | 3 | 'circular' | 'elliptic' | 'rotated'
     int : resp.: circular elliptic, rotated
     str : case insensitive; only the first letter matters.
     shape defaults to 'circular' when misunderstood
copy : Kernel2dModel
to be copied
fixed : None or dictionary of {int:float|Model}
     int index of parameter to fix permanently.
     float|Model values for the fixed parameters.
     Attribute fixed can only be set in the constructor.
     See: FixedModel

copy( )

Copy method.

parseShape( shape )

setKernelShape( kernel, shape )

baseName( )

Returns a string representation of the model.

baseResult( xdata, params )

Returns the result of the model function.

Parameters

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

baseDerivative( xdata, params )

Returns df/dx of the model function.

Parameters

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

basePartial( xdata, params, parlist=None )

Returns the partials at the xdata value.

Parameters

xdata : array_like
value at which to calculate the partials
params : array_like
parameters to the model (ignored in LinearModels)
parlist : array_like
list of indices of active parameters

baseParameterUnit( k )

Return the unit of a parameter. Parameters

k : int
the kth parameter.

isBound( )

Methods inherited from NonLinearModel

Methods inherited from Model

Methods inherited from FixedModel

Methods inherited from BaseModel