pisces.math_utils.integration.integrate_toinf#

pisces.math_utils.integration.integrate_toinf(profile, rr, rmax=None, **kwargs)[source]#

Compute cumulative integral from each radius \(r\) to infinity.

Evaluates:

\[I(r) = \int_{r}^{\infty} f(r') \; dr'\]

The integration is performed in two parts:

From \(r\) to \(r_{\mathrm{max}}\).
From \(r_{\mathrm{max}}\) to \(\infty\) (computed once and added to all results).

Parameters:

profile (callable) – Function of radius \(r\) returning the integrand \(f(r)\).
rr (array-like) – Radii at which to compute cumulative integrals. Must be sorted ascending.
rmax (float or None, optional) – Upper bound for intermediate integration. If None, defaults to rr[-1].
**kwargs (dict, optional) – Additional keyword arguments passed to scipy.integrate.quad().

Returns:

integral – Array of integral values \(I(r)\) for each radius in rr.

Return type:

ndarray

Raises:

ValueError – If any radius in rr exceeds rmax.