Method
NumCosmoMathSplinecurvature_weighted_lp_norm
Declaration [src]
gdouble
ncm_spline_curvature_weighted_lp_norm (
NcmSpline* s,
NcmSplineCurvatureType ctype,
const gdouble p,
NcmSpline* weight,
const gdouble xi,
const gdouble xf
)
Description [src]
Computes the weight-normalized $L_p$ norm of the curvature density $c(x)$
(selected by ctype) over the interval [xi, xf],
$$N_p = \left(\frac{\int_{x_i}^{x_f} W(x)\,|c(x)|^p\,\mathrm{d}x}{\int_{x_i}^{x_f} W(x)\,\mathrm{d}x}\right)^{1/p}.$$
A constant weight recovers ncm_spline_curvature_lp_norm(). The weight encodes
where curvature is penalized (large $W$) versus tolerated (small $W$), turning
the global curvature functional into a local one. weight must share the
abscissa of s and be non-negative with a positive integral over [xi, xf];
both splines must be prepared.
Parameters
ctype-
Type:
NcmSplineCurvatureTypeA
NcmSplineCurvatureType. p-
Type:
const gdoubleThe norm order $p > 0$.
weight-
Type:
NcmSplineA
NcmSplineholding the non-negative weight density $W(x)$.The data is owned by the caller of the method. xi-
Type:
const gdoubleThe lower integration limit.
xf-
Type:
const gdoubleThe upper integration limit.