Class
NumCosmoXcorKernelAnalyticStudentT
Description [src]
final class NumCosmo.XcorKernelAnalyticStudentT : NumCosmo.XcorKernelRadial
{
/* No available fields */
}Radial window with power-law tails: a Student-t profile in comoving distance.
\begin{equation} W(\chi) = \frac{1}{D} \left[1 + \frac{1}{\nu}\left(\frac{\chi - \chi_0}{s}\right)^2\right] ^{-\frac{\nu + 1}{2}} , \end{equation}
with $D$ fixed in closed form so that $\int W \mathrm{d}\chi = 1$ over the truncated support.
The tail falls as $|\chi - \chi_0|^{-(\nu+1)}$, not exponentially. That is
the point of the shape: a Gaussian window’s tail is negligible a few widths
out, so where it is truncated barely matters and its transform decays fast;
a power-law tail does neither, which is how several physical kernels
actually behave. $\nu$ tunes the decay continuously — $\nu = 1$ is Cauchy,
the heaviest useful case, and large $\nu$ returns to the Gaussian of
NcXcorKernelAnalyticGauss.
Truncation therefore discards real mass here, and deliberately so: at
$\nu = 1$, cutting at $10s$ leaves out about 6% of the profile. The window
is renormalized over exactly what is kept, so the definition stays exact and
both sides of a cross-code comparison compute the same thing.
nc_xcor_kernel_analytic_student_t_get_tail_mass() reports the fraction
discarded, so a spec can state it rather than discover it.
See NcXcorKernelRadial for the unit and normalization conventions.
Constructors
nc_xcor_kernel_analytic_student_t_new_full
Creates a new NcXcorKernelAnalyticStudentT carrying sbi, as
nc_xcor_kernel_analytic_student_t_new() does not. A NcXcorKernel only
accepts the non-Limber modes of nc_xcor_kernel_set_l_limber() once it holds
an integrator, so this is the constructor to use for them.
Instance methods
nc_xcor_kernel_analytic_student_t_get_tail_mass
Gets the fraction of the untruncated profile that falls outside the support and is therefore not represented. Unlike a Gaussian’s, this is not negligible: at $\nu = 1$ and $n = 10$ it is about 6%. It is reported so that a benchmark specification can state it.
Methods inherited from NcXcorKernelRadial (9)
nc_xcor_kernel_radial_eval_W
Evaluates the whole radial window, the sum of its components, normalized to unit integral over its support and zero outside it.
nc_xcor_kernel_radial_eval_W_comp
Evaluates component comp of the radial window at chi, zero outside the
interval that nc_xcor_kernel_radial_get_comp_support() reports for it. The
components sum to a window of unit integral.
nc_xcor_kernel_radial_eval_kernel_factor
Evaluates a multiplicative factor of $(\chi, k)$ applied to component comp
on top of $W(\chi)\sqrt{P(k,0)}$. It must not depend on $\ell$: one closure
serves a whole block of multipoles, so anything $\ell$-dependent belongs in
nc_xcor_kernel_radial_eval_prefactor() instead.
nc_xcor_kernel_radial_eval_prefactor
Evaluates a multiplicative factor that depends only on $\ell$, applied to
component comp. Shear contributes $\sqrt{(\ell+2)(\ell+1)\ell(\ell-1)}$ here.
nc_xcor_kernel_radial_get_comp_bessel_deriv
Gets the derivative order of the spherical Bessel weight of component comp:
0 for $j_\ell$, 2 for the $j_\ell”$ of a redshift-space distortion term.
It is set on the NcXcorKernelComponent at construction.
nc_xcor_kernel_radial_get_comp_support
Gets the interval outside which component comp vanishes. It is exactly the
interval that component is integrated over, so the boundary is exact by
construction rather than something the quadrature has to locate.
nc_xcor_kernel_radial_get_n_comps
Gets the number of components the window is split into: its maximal intervals of support. Each is integrated separately over exactly its own interval, so that a boundary is never interior to an integration domain.
nc_xcor_kernel_radial_get_support
Gets the hull of the components’ intervals, outside which the whole window vanishes. Components may be disjoint, so the hull can contain gaps where the window is zero; it is what fixes the kernel’s redshift range, not what anything is integrated over.
nc_xcor_kernel_radial_peek_kdep
Gets the scale-dependent factor the kernel carries, if any.
Methods inherited from NcXcorKernel (42)
Please see NcXcorKernel for a full list of methods.
Properties
NumCosmo.XcorKernelAnalyticStudentT:chi-scale
Scale $s$ of the window, in Mpc. For $\nu > 2$ the profile has variance $s^2 \nu / (\nu - 2)$; for $\nu \le 2$ it has none, which is the regime the shape exists to probe.
NumCosmo.XcorKernelAnalyticStudentT:n-scale
Truncation half-width in units of $s$. With power-law tails this discards a fraction of the profile that is not negligible, so it is part of the window’s definition rather than a tolerance; see nc_xcor_kernel_analytic_student_t_get_tail_mass().
NumCosmo.XcorKernelAnalyticStudentT:nu
Degrees of freedom $\nu$, which set the tail exponent: $W$ falls as $|\chi - \chi_0|^{-(\nu+1)}$. $\nu = 1$ is Cauchy; large $\nu$ approaches a Gaussian.
Properties inherited from NcXcorKernelRadial (2)
NumCosmo.XcorKernelRadial:bessel-deriv
Derivative order of the spherical Bessel weight every component of this kernel carries: 0 for $j_\ell$, 1 for $j_\ell’$, 2 for the $j_\ell”$ of a redshift-space distortion term. The derivative is with respect to the argument $x = k\chi$.
NumCosmo.XcorKernelRadial:scale-dependence
Optional NcXcorKernelRadialKDep multiplying the radial integrand, or
NULL for none. Any shape may carry any scale dependence, so the two are
varied independently rather than baked into separate kernel classes.
Properties inherited from NcXcorKernel (14)
NumCosmo.XcorKernel:adaptive-boundary-tries
NumCosmo.XcorKernel:adaptive-epsilon
Convergence threshold for the adaptive $k$-range determination: sampling stops
extending outwards once $\Vert W\Vert$ falls below this fraction of its running
maximum, for NcXcorKernel:adaptive-boundary-tries consecutive steps.
NumCosmo.XcorKernel:dist
NumCosmo.XcorKernel:expansion-factor
NumCosmo.XcorKernel:integrator
NumCosmo.XcorKernel:l-limber
NumCosmo.XcorKernel:lmax
NumCosmo.XcorKernel:max-border-expansions
NumCosmo.XcorKernel:max-iter
NumCosmo.XcorKernel:panel-order-cap
Highest Chebyshev order tried on one panel before it is bisected, as $N = 2^\mathrm{cap} + 1$ coefficients.
NumCosmo.XcorKernel:peak-epsilon
Peak-relative floor of the adaptive refinement of the $W_i(k)$ closure. An
interval is accepted once its estimated interpolation error falls below
peak-epsilon $\times \max\vert F\vert$, the maximum taken over the smallest
of the block’s peaks so that a sub-dominant multipole is not held to a
tolerance relative to its neighbours.
NumCosmo.XcorKernel:powspec
NumCosmo.XcorKernel:reltol
Relative tolerance for the adaptive refinement of the $W_i(k)$ spline.
NumCosmo.XcorKernel:track-fit-residual
Whether the closure records the residual its fit achieved on each interval
it is a single polynomial on — a knot interval of a spline closure, a
panel of a Chebyshev one. That record is what nc_xcor_compute_full() turns
into an error estimate. On by default: without it the estimate has only
NcXcorKernel:reltol and NcXcorKernel:peak-epsilon to work from — the
tolerances the fit was asked for, which it beats by 12 to 3100 times
depending on the kernel, so the resulting bound tracks the pair’s
cancellation rather than its accuracy.
Properties inherited from NcmModel (9)
NumCosmoMath.Model:implementation
The implementation flags of the model class, see ncm_model_check_impl_flag().
NumCosmoMath.Model:name
The name of the model class.
NumCosmoMath.Model:nick
The nickname of the model class.
NumCosmoMath.Model:params-types
The NcmParamType of each parameter.
NumCosmoMath.Model:reparam
The reparametrization, see ncm_model_set_reparam().
NumCosmoMath.Model:scalar-params-len
The number of scalar parameters.
NumCosmoMath.Model:sparam-array
The parameter descriptions that differ from the class ones, NcmSParam keyed by
parameter index. Each one is placed by its parameter name: a description of a
parameter declared with ncm_model_class_add_removed_param() is skipped, and one of
any other unknown parameter aborts.
NumCosmoMath.Model:submodel-array
The submodels, attached at construction.
NumCosmoMath.Model:vector-params-len
The number of vector parameters (not their lengths).
Signals
Signals inherited from GObject (1)
GObject::notify
The notify signal is emitted on an object when one of its properties has its value set through g_object_set_property(), g_object_set(), et al.