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Kernel2dModel = class Kernel2dModel(NonLinearModel) |
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Kernel2dModel(kernel=<Gauss object at 0x11caf0130>, shape=1, copy=None, **kwargs)
Two dimensional Kernel Model.
The Kernel2dModel is defined as
f( x:p ) = p_0 * K( r )
where K( r ) is a selectable kernel function and r is the distance to the center.
r = sqrt( u^2 + v^2 ).
There are 3 options for u and v
1. CIRCULAR has 4 parameters
Circular shape with only one width.
u = ( x - p_1 ) / p_3
v = ( x - p_2 ) / p_3
2. ELLIPTIC has 5 parameters
Elliptic shape aligned along the axes; 2 widths.
u = ( x - p_1 ) / p_3
v = ( x - p_2 ) / p_4
3. ROTATED has 6 parameters
Rotated elliptical shape with 2 width and a rotational angle.
u = ( ( x - p_1 )*cos( p_5 ) - ( y - p_2 )*sin( p_5) ) / p_3
v = ( ( x - p_1 )*sin( p_5 ) + ( y - p_2 )*cos( p_5) ) / p_4
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
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- Method resolution order:
- Kernel2dModel
- NonLinearModel
- Model
- FixedModel
- BaseModel
- builtins.object
Constructor:
- Kernel2dModel( kernel=<Gauss object at 0x11caf0130>, 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
Methods defined here:
- 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
- baseName()
- Returns a string representation of the model.
- baseParameterUnit( k )
- Return the unit of a parameter.
Parameters
----------
k : int
the kth parameter.
- 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
- 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
- copy()
- Copy method.
- isBound()
- parseShape( shape )
- setKernelShape( kernel, shape )
Methods inherited from NonLinearModel:
Methods inherited from Model:
- __add__( model )
- __call__( x )
- __getitem__( i )
- __iadd__( model )
- __imul__( model )
- __ior__( model )
- __isub__( model )
- __itruediv__( model )
- __mul__( model )
- __or__( model )
- __sub__( model )
- __truediv__( model )
- addModel( model )
- appendModel( model, operation )
- assignDF1( partial, i, dpi )
- assignDF2( partial, i, dpi )
- chainLength()
- correctParameters( params )
- derivative( xdata, param, useNum=False )
- divideModel( model )
- domain2Unit( dvalue, kpar=None )
- getIntegralUnit()
- getLimits()
- getLinearIndex()
- getNumberOfParameters()
- getParameterName( k )
- getParameterUnit( k )
- getPrior( k )
- hasLimits( fitindex=None )
- hasPriors( isBound=True )
- isDynamic()
- isNullModel()
- isolateModel( k )
- multiplyModel( model )
- nextPrior()
- numDerivative( xdata, param )
- numPartial( xdata, param )
- operate( res, pars, next )
- partialDomain2Unit( dvalue )
- pipeModel( model )
- 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)
- result( xdata, param=None )
- selectPipe( ndim, ninter, ndout )
- setLimits( lowLimits=None, highLimits=None )
- setPrior( k, prior=None, **kwargs )
- shortName()
- strictNumericDerivative( xdata, param )
- strictNumericPartial( xdata, params, parlist=None )
- subtractModel( model )
- testPartial( xdata, params, silent=True )
- unit2Domain( uvalue, kpar=None )
Methods inherited from FixedModel:
Methods inherited from BaseModel:
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