Gauss1D

class sherpa.models.basic.Gauss1D(name='gauss1d')

Bases: sherpa.models.model.ArithmeticModel

One-dimensional gaussian function.

fwhm

The Full-Width Half Maximum of the gaussian. It is related to the sigma value by: FWHM = sqrt(8 * log(2)) * sigma.

pos

The center of the gaussian.

ampl

The amplitude refers to the maximum peak of the model.

See also

Gauss2D, NormGauss1D

Notes

The functional form of the model for points is:

f(x) = ampl * exp(-4 * log(2) * (x - pos)^2 / fwhm^2)

and for an integrated grid it is the integral of this over the bin.

Examples

Compare the gaussian and normalized gaussian models:

>>> m1 = sherpa.models.basic.Gauss1D()
>>> m2 = sherpa.models.basic.NormGauss1D()
>>> m1.pos, m2.pos = 10, 10
>>> m1.ampl, m2.ampl = 10, 10
>>> m1.fwhm, m2.fwhm = 5, 5
>>> m1(10)
10.0
>>> m2(10)
1.8788745573993026
>>> m1.fwhm, m2.fwhm = 1, 1
>>> m1(10)
10.0
>>> m2(10)
9.394372786996513

The normalised version will sum to the amplitude when given an integrated grid - i.e. both low and high edges rather than points - that covers all the signal (and with a bin size a lot smaller than the FWHM):

>>> m1.fwhm, m2.fwhm = 12.2, 12.2
>>> grid = np.arange(-90, 110, 0.01)
>>> glo, ghi = grid[:-1], grid[1:]
>>> m1(glo, ghi).sum()
129.86497637060958
>>> m2(glo, ghi).sum()
10.000000000000002

Attributes Summary

thawedparhardmaxes
thawedparhardmins
thawedparmaxes
thawedparmins
thawedpars

Methods Summary

apply(outer, \*otherargs, \*\*otherkwargs)
calc(pars, xlo, \*args, \*\*kwargs)
get_center()
guess(dep, \*args, \*\*kwargs)
reset()
set_center(pos, \*args, \*\*kwargs)
startup()
teardown()

Attributes Documentation

thawedparhardmaxes

thawedparhardmins

thawedparmaxes

thawedparmins

thawedpars

Methods Documentation

apply(outer, *otherargs, **otherkwargs)

calc(pars, xlo, *args, **kwargs)

get_center()

guess(dep, *args, **kwargs)

reset()

set_center(pos, *args, **kwargs)

startup()

teardown()