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class Tophat( Kernel )	Source

Tophat (without convolutions) is a Kernel function which is 1.0 between [-0.5,0.5]; it is 0 elsewhere.

Name	Definition	Integral	FWHM	range	comment
Tophat 0	1.0	1.0	1.00	0.5	like Uniform
Tophat 1	1 - |x|	1.0	1.00	1.0	aka Triangle
Tophat 2	2nd order polynomial	1.0	1.26	1.5
Tophat 3	3rd order polynomial	1.0	1.44	2.0
Tophat 4	4th order polynomial	1.0	1.60	2.5
Tophat 5	5th order polynomial	1.0	1.73	3.0
Tophat 6	6th order polynomial	1.0	1.86	3.5

Attributes

• nconv : int
       successive autoconvolutions of the tophat. max=6.

Thanks to Romke Bontekoe and Mathematica for providing the analytic expressions.

Tophat( nconv=0 )

Constructor.

Integral, fwhm and range are dependent on the number of convolutions. See table above.

Parameters

• nconv : int
       number of auto-convolutions

result( x )

Return the result for input values.

Parameters

• x : array-like
       input values

partial( x )

Return the partial derivative wrt the input values.

Parameters

• x : array-like
       the input values

isBound( )

Return True

name( )

Return the name of the kernel

Methods inherited from Kernel

• resultsq( xsq )