hmf.density_field.filters.SharpK

class hmf.density_field.filters.SharpK(k, power, **model_parameters)

Fourier-space top-hat window function

This class is based on Filter, which can be consulted for details of how to instantiate it.

Notes

The real-space filter is

\[F(r) = \frac{\sin(r/R) -(r/R)\cos(r/R)}{2\pi^2r^3},\]

for a filter scale of R.

The fourier-transform of the filter is

\[W(x=kR) = H(kR-1)\]

where H is the Heaviside step-function. The mass-assignment is

\[m(R) = \frac{4\pi}{3}[cR]^3\bar{\rho},\]

where c is a free parameter, typically c~2.5. The derivative of the window function is

\[\frac{dW}{d\ln x}(x=kR) = \delta_D(x-1),\]

where \(\delta_D\) is the Dirac delta. Furthermore, the derivative of the mass variance takes a particularly simple form in this filter:

\[\frac{d\ln \sigma^2}{d \ln R} = -\frac{P(1/R)}{2\pi^2\sigma^2(R)R^3}.\]

Methods

__init__(k, power, **model_parameters)	Initialize self.
dlnr_dlnm(r)	The derivative of log radius with log mass.
dlnss_dlnm(r)	The logarithmic slope of mass variance with mass.
dlnss_dlnr(r)	The derivative of the mass variance with radius.
dw_dlnkr(kr)	The derivative of the (fourier-transformed) filter with \(\ln(kr)\).
get_models()	Get a dictionary of all implemented models for this component.
k_space(kr)	Fourier-transform of the real-space filter.
mass_to_radius(m, rho_mean)	Return radius of a region of space given its mass.
nu(r[, delta_c])	Peak height, \(\frac{\delta_c^2}{\sigma^2(r)}\).
radius_to_mass(r, rho_mean)	Return mass of a region of space given its radius
real_space(R, r)	Filter definition in real space.
sigma(r[, order])	Calculate the nth-moment of the smoothed density field, \(\sigma_n(r)\).