Class
NumCosmoMathPowspec
Description [src]
abstract class NumCosmoMath.Powspec : GObject.Object
{
/* No available fields */
}Abstrac class for power spectrum implementation.
This module comprises the set of functions to compute a power spectrum and derived quantities.
Given a field $\delta(\vec{x})$ at position $\vec{x}$, the power spectrum is defined as the Fourier transform of the two-point correlation point, i.e., $$\xi(\vec{x} - \vec{x}^\prime) = \int \frac{d^3 k}{(2 \pi)^3} e^{i \vec{k}.(\vec{x} - \vec{x}^\prime)} P(k),$$ where $\langle \delta(\vec{k} - \vec{k}^\prime)\rangle = (2\pi)^3 \delta_D(\vec{k} - \vec{k}^\prime) P(k)$ and $\delta_D$ is the Dirac’s delta function. The standard output is the dimensional power spectrum, not the dimensionless one $\Delta(k)^2$, $$P(k) \equiv \frac{2 \pi^2 \Delta(k)^2}{k^3}.$$.
Functions
ncm_powspec_clear
If powspec is different from NULL,
atomically decrements the reference count of powspec by one.
If the reference count drops to 0,
all memory allocated by powspec is released and powspec is set to NULL.
Instance methods
ncm_powspec_corr3d
Computes the spatial correlation function in configuration space at redshift $z$ and position $r$,
$$\xi(r,z) = \frac{1}{2\pi^2} \int_{k_{\mathrm{min}}}^{k_\mathrm{max}} P(k,z) \, j_{0}(kr) \, k^2 \, \mathrm{d}k \, ,$$
where, $j_0(t)$ is the zero order spherical Bessel function of the first kind.
This function is recommended for a small set of $r$ and $z$ values.
For a wide range of values it is best to apply NcmPowspecCorr3d, instead.
ncm_powspec_deriv_k
Evaluates the derivative of the power spectrum powspec with respect to $k$ at $(z, k)$.
ncm_powspec_deriv_z
Evaluates the derivative of the power spectrum powspec with respect to $z$ at $(z, k)$.
ncm_powspec_eval_vec
Evaluates the power spectrum powspec at $z$ and in the knots
contained in k and puts the result in Pk.
ncm_powspec_free
Atomically decrements the reference count of powspec by one.
If the reference count drops to 0,
all memory allocated by powspec is released.
ncm_powspec_prepare_if_needed
Prepares the object powspec using the model model if it was changed
since last preparation.
ncm_powspec_sigma_tophat_R
Computes $\sigma_R(z) = \sqrt{\sigma_{R}^{2}(z)}$. See ncm_powspec_var_tophat_R().
ncm_powspec_sproj
Computes (C_\ell (z_1, z_2) = \int\dots). This method calculates the angular power spectrum directly from the power spectrum by integrating over the wave-numbers. It is slow and intended for testing purposes only.
ncm_powspec_var_tophat_R
This function computes the value of the linearly extrapolated
rms fluctuations of mass in a sphere of radius $R$ applying a top-hat filter at redshift $z$,
$$\sigma_{R}^{2}(z) = \frac{1}{2\pi^2} \int_{k_{\mathrm{min}}}^{k_\mathrm{max}} W^{2}{TH}(kR) \, P(k,z) \, k^2 \, \mathrm{d}k \, .$$
Where, $W{TH}(t)$ is the top-hat filter in Fourier space,
$$W_{TH}(t) = \frac{3}{t^3} \left( \sin t - t \cos t \right) = \frac{3}{t} j_{1}(t),$$
and $j_1(t)$ is the first order spherical Bessel function of the first kind.
This function is recommended for a small set of $z$ and $R$ values.
For a wide range of values it is best to apply NcmPowspecFilter, instead.
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.
Class structure
struct NumCosmoMathPowspecClass {
void (* prepare) (
NcmPowspec* powspec,
NcmModel* model
);
gdouble (* eval) (
NcmPowspec* powspec,
NcmModel* model,
const gdouble z,
const gdouble k
);
void (* eval_vec) (
NcmPowspec* powspec,
NcmModel* model,
const gdouble z,
NcmVector* k,
NcmVector* Pk
);
gdouble (* deriv_z) (
NcmPowspec* powspec,
NcmModel* model,
const gdouble z,
const gdouble k
);
gdouble (* deriv_k) (
NcmPowspec* powspec,
NcmModel* model,
const gdouble z,
const gdouble k
);
void (* get_nknots) (
NcmPowspec* powspec,
guint* Nz,
guint* Nk
);
NcmSpline2d* (* get_spline_2d) (
NcmPowspec* powspec,
NcmModel* model
);
}No description available.
Class members
prepare: void (* prepare) ( NcmPowspec* powspec, NcmModel* model )No description available.
eval: gdouble (* eval) ( NcmPowspec* powspec, NcmModel* model, const gdouble z, const gdouble k )No description available.
eval_vec: void (* eval_vec) ( NcmPowspec* powspec, NcmModel* model, const gdouble z, NcmVector* k, NcmVector* Pk )No description available.
deriv_z: gdouble (* deriv_z) ( NcmPowspec* powspec, NcmModel* model, const gdouble z, const gdouble k )No description available.
deriv_k: gdouble (* deriv_k) ( NcmPowspec* powspec, NcmModel* model, const gdouble z, const gdouble k )No description available.
get_nknots: void (* get_nknots) ( NcmPowspec* powspec, guint* Nz, guint* Nk )No description available.
get_spline_2d: NcmSpline2d* (* get_spline_2d) ( NcmPowspec* powspec, NcmModel* model )No description available.
Virtual methods
NumCosmoMath.PowspecClass.deriv_k
Evaluates the derivative of the power spectrum powspec with respect to $k$ at $(z, k)$.
NumCosmoMath.PowspecClass.deriv_z
Evaluates the derivative of the power spectrum powspec with respect to $z$ at $(z, k)$.
NumCosmoMath.PowspecClass.eval_vec
Evaluates the power spectrum powspec at $z$ and in the knots
contained in k and puts the result in Pk.