hmf.mass_function.integrate_hmf.hmf_integral_gtm¶

hmf.mass_function.integrate_hmf.hmf_integral_gtm(M, dndm, mass_density=False)[source]¶

Cumulatively integrate dn/dm.

Parameters

M (array_like) – Array of masses.
dndm (array_like) – Array of dn/dm (corresponding to M)
mass_density (bool, False) – Whether to calculate mass density (or number density).

Returns

ngtm – Cumulative integral of dndm.

Return type

array_like

Examples

Using a simple power-law mass function:

>>> import numpy as np
>>> m = np.logspace(10,18,500)
>>> dndm = m**-2
>>> ngtm = hmf_integral_gtm(m,dndm)
>>> np.allclose(ngtm,1/m) #1/m is the analytic integral to infinity.
True

The function always integrates to m=1e18, and extrapolates with a spline if data not provided:

>>> m = np.logspace(10,12,500)
>>> dndm = m**-2
>>> ngtm = hmf_integral_gtm(m,dndm)
>>> np.allclose(ngtm,1/m) #1/m is the analytic integral to infinity.
True