NcmPowspec: NumCosmo Reference Manual

NcmPowspec

NcmPowspec — Abstrac class for power spectrum implementation.

Stability Level

Stable, unless otherwise indicated

Functions

NcmPowspec *	ncm_powspec_ref ()
void	ncm_powspec_free ()
void	ncm_powspec_clear ()
void	ncm_powspec_set_zi ()
void	ncm_powspec_set_zf ()
void	ncm_powspec_set_kmin ()
void	ncm_powspec_set_kmax ()
void	ncm_powspec_set_reltol_spline ()
void	ncm_powspec_require_zi ()
void	ncm_powspec_require_zf ()
void	ncm_powspec_require_kmin ()
void	ncm_powspec_require_kmax ()
gdouble	ncm_powspec_get_zi ()
gdouble	ncm_powspec_get_zf ()
gdouble	ncm_powspec_get_kmin ()
gdouble	ncm_powspec_get_kmax ()
gdouble	ncm_powspec_get_reltol_spline ()
void	ncm_powspec_get_nknots ()
void	ncm_powspec_prepare ()
void	ncm_powspec_prepare_if_needed ()
gdouble	ncm_powspec_eval ()
void	ncm_powspec_eval_vec ()
NcmSpline2d *	ncm_powspec_get_spline_2d ()
NcmModelCtrl *	ncm_powspec_peek_model_ctrl ()
gdouble	ncm_powspec_var_tophat_R ()
gdouble	ncm_powspec_sigma_tophat_R ()
gdouble	ncm_powspec_corr3d ()
gdouble	ncm_powspec_sproj ()

Properties

double	kmax	Read / Write / Construct
double	kmin	Read / Write / Construct
double	reltol	Read / Write / Construct
double	zf	Read / Write / Construct
double	zi	Read / Write / Construct

Types and Values

#define	NCM_TYPE_POWSPEC
struct	NcmPowspecClass
	NcmPowspec

Object Hierarchy

    GObject
    ╰── NcmPowspec
        ├── NcPowspecML
        ├── NcPowspecMNL
        ╰── NcmPowspecSpline2d

Includes

#include <numcosmo/math/ncm_powspec.h>

Description

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_ref ()

NcmPowspec *
ncm_powspec_ref (NcmPowspec *powspec);

Increases the reference count of powspec by one atomically.

Parameters

powspec

a NcmPowspec

Returns

powspec .

[transfer full]

ncm_powspec_free ()

void
ncm_powspec_free (NcmPowspec *powspec);

Atomically decrements the reference count of powspec by one. If the reference count drops to 0, all memory allocated by powspec is released.

Parameters

powspec

a NcmPowspec

ncm_powspec_clear ()

void
ncm_powspec_clear (NcmPowspec **powspec);

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.

Parameters

powspec

a NcmPowspec

ncm_powspec_set_zi ()

void
ncm_powspec_set_zi (NcmPowspec *powspec,
                    const gdouble zi);

Sets the initial time $z_i$.

Parameters

powspec	a NcmPowspec
zi	initial time $z_i$

ncm_powspec_set_zf ()

void
ncm_powspec_set_zf (NcmPowspec *powspec,
                    const gdouble zf);

Sets the final time $z_f$.

Parameters

powspec	a NcmPowspec
zf	final time $z_f$

ncm_powspec_set_kmin ()

void
ncm_powspec_set_kmin (NcmPowspec *powspec,
                      const gdouble kmin);

Sets the minimum mode value $k_\mathrm{min}$.

Parameters

powspec	a NcmPowspec
kmin	minimum mode $k_\mathrm{min}$

ncm_powspec_set_kmax ()

void
ncm_powspec_set_kmax (NcmPowspec *powspec,
                      const gdouble kmax);

Sets the maximum mode value $k_\mathrm{max}$.

Parameters

powspec	a NcmPowspec
kmax	maxmimum mode $k_\mathrm{max}$

ncm_powspec_set_reltol_spline ()

void
ncm_powspec_set_reltol_spline (NcmPowspec *powspec,
                               const gdouble reltol);

Sets the relative tolerance for interpolation errors to reltol .

Parameters

powspec	a NcmPowspec
reltol	relative tolerance for interpolation errors

ncm_powspec_require_zi ()

void
ncm_powspec_require_zi (NcmPowspec *powspec,
                        const gdouble zi);

Requires the initial time to be less or equal to $z_i$.

Parameters

powspec	a NcmPowspec
zi	initial time $z_i$

ncm_powspec_require_zf ()

void
ncm_powspec_require_zf (NcmPowspec *powspec,
                        const gdouble zf);

Requires the final time to be greater or equal to $z_f$.

Parameters

powspec	a NcmPowspec
zf	final time $z_f$

ncm_powspec_require_kmin ()

void
ncm_powspec_require_kmin (NcmPowspec *powspec,
                          const gdouble kmin);

Requires the minimum mode value to be less or equal to $k_\mathrm{min}$.

Parameters

powspec	a NcmPowspec
kmin	minimum mode $k_\mathrm{min}$

ncm_powspec_require_kmax ()

void
ncm_powspec_require_kmax (NcmPowspec *powspec,
                          const gdouble kmax);

Sets the maximum mode value $k_\mathrm{max}$.

Parameters

powspec	a NcmPowspec
kmax	maxmimum mode $k_\mathrm{max}$

ncm_powspec_get_zi ()

gdouble
ncm_powspec_get_zi (NcmPowspec *powspec);

Gets the initial value $z_i$.

Parameters

powspec

a NcmPowspec

ncm_powspec_get_zf ()

gdouble
ncm_powspec_get_zf (NcmPowspec *powspec);

Gets the final value $z_f$.

Parameters

powspec

a NcmPowspec

ncm_powspec_get_kmin ()

gdouble
ncm_powspec_get_kmin (NcmPowspec *powspec);

Gets the minimum mode value $k_\mathrm{min}$.

Parameters

powspec

a NcmPowspec

ncm_powspec_get_kmax ()

gdouble
ncm_powspec_get_kmax (NcmPowspec *powspec);

Gets the maximum mode value $k_\mathrm{max}$.

Parameters

powspec

a NcmPowspec

ncm_powspec_get_reltol_spline ()

gdouble
ncm_powspec_get_reltol_spline (NcmPowspec *powspec);

Gets the relative tolerance for interpolation errors.

Parameters

powspec

a NcmPowspec

Returns

the relative tolerance for interpolation errors.

ncm_powspec_get_nknots ()

void
ncm_powspec_get_nknots (NcmPowspec *powspec,
                        guint *Nz,
                        guint *Nk);

Gets the number of knots used to calculate the power spectrum.

[virtual get_nknots]

Parameters

powspec	a NcmPowspec
Nz	number of knots in $z$.	[out]
Nk	number of knots in $k$.	[out]

ncm_powspec_prepare ()

void
ncm_powspec_prepare (NcmPowspec *powspec,
                     NcmModel *model);

Prepares the power spectrum powspec using the model model .

Parameters

powspec	a NcmPowspec
model	a NcmModel.	[allow-none]

ncm_powspec_prepare_if_needed ()

void
ncm_powspec_prepare_if_needed (NcmPowspec *powspec,
                               NcmModel *model);

Prepares the object powspec using the model model if it was changed since last preparation.

Parameters

powspec	a NcmPowspec
model	a NcmModel.	[allow-none]

ncm_powspec_eval ()

gdouble
ncm_powspec_eval (NcmPowspec *powspec,
                  NcmModel *model,
                  const gdouble z,
                  const gdouble k);

Evaluates the power spectrum powspec at $(z, k)$.

Parameters

powspec	a NcmPowspec
model	a NcmModel.	[allow-none]
z	time $z$
k	mode $k$

Returns

$P(z, k)$.

ncm_powspec_eval_vec ()

void
ncm_powspec_eval_vec (NcmPowspec *powspec,
                      NcmModel *model,
                      const gdouble z,
                      NcmVector *k,
                      NcmVector *Pk);

Evaluates the power spectrum powspec at $z$ and in the knots contained in k and puts the result in Pk .

Parameters

powspec	a NcmPowspec
model	a NcmModel.	[allow-none]
z	time $z$
k	a NcmVector
Pk	a NcmVector

ncm_powspec_get_spline_2d ()

NcmSpline2d *
ncm_powspec_get_spline_2d (NcmPowspec *powspec,
                           NcmModel *model);

Compute a 2D spline for the power spectrum.

Parameters

powspec	a NcmPowspec
model	a NcmModel.	[allow-none]

Returns

a NcmSpline2d interpolating spline as a function of $(z, k)$.

[transfer full]

ncm_powspec_peek_model_ctrl ()

NcmModelCtrl *
ncm_powspec_peek_model_ctrl (NcmPowspec *powspec);

Gets the NcmModelCtrl used by powspec .

Parameters

powspec

a NcmPowspec

Returns

the NcmModelCtrl used by powspec .

[transfer none]

ncm_powspec_var_tophat_R ()

gdouble
ncm_powspec_var_tophat_R (NcmPowspec *powspec,
                          NcmModel *model,
                          const gdouble reltol,
                          const gdouble z,
                          const gdouble 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.

Parameters

powspec	a NcmPowspec
model	a NcmModel.	[allow-none]
reltol	relative tolerance for integration
z	the value of $z$
R	the value of $R$

Returns

$\sigma_{R}^{2}(z)$.

ncm_powspec_sigma_tophat_R ()

gdouble
ncm_powspec_sigma_tophat_R (NcmPowspec *powspec,
                            NcmModel *model,
                            const gdouble reltol,
                            const gdouble z,
                            const gdouble R);

Computes $\sigma_R(z) = \sqrt{\sigma_{R}^{2}(z)}$. See ncm_powspec_var_tophat_R().

Parameters

powspec	a NcmPowspec
model	a NcmModel.	[allow-none]
reltol	relative tolerance for integration
z	the value of $z$
R	the value of $R$

Returns

$\sigma_R(z)$.

ncm_powspec_corr3d ()

gdouble
ncm_powspec_corr3d (NcmPowspec *powspec,
                    NcmModel *model,
                    const gdouble reltol,
                    const gdouble z,
                    const gdouble r);

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.

Parameters

powspec	a NcmPowspec
model	a NcmModel.	[allow-none]
reltol	relative tolerance for integration
z	the value of $z$
r	the value of $r$

Returns

$\xi(r,z)$.

ncm_powspec_sproj ()

gdouble
ncm_powspec_sproj (NcmPowspec *powspec,
                   NcmModel *model,
                   const gdouble reltol,
                   const gint ell,
                   const gdouble z1,
                   const gdouble z2,
                   const gdouble xi1,
                   const gdouble xi2);

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.

Parameters

powspec	a NcmPowspec
model	a NcmModel.	[allow-none]
reltol	relative tolerance for integration
ell	the value of $\ell$
z1	the value of $z_1$
z2	the value of $z_2$
xi1	the value of $\xi_1$
xi2	the value of $\xi_2$

Types and Values

NCM_TYPE_POWSPEC

#define NCM_TYPE_POWSPEC (ncm_powspec_get_type ())

struct NcmPowspecClass

struct NcmPowspecClass {
};

NcmPowspec

typedef struct _NcmPowspec NcmPowspec;

Property Details

The `“kmax”` property

  “kmax”                     double

The maximum mode (wave-number) value to compute $P(k,z)$.

Owner: NcmPowspec

Flags: Read / Write / Construct

Allowed values: >= 0

Default value: 1

The `“kmin”` property

  “kmin”                     double

The minimum mode (wave-number) value to compute $P(k,z)$.

Owner: NcmPowspec

Flags: Read / Write / Construct

Allowed values: >= 0

Default value: 1e-05

The `“reltol”` property

  “reltol”                   double

The relative tolerance on the interpolation error.

Owner: NcmPowspec

Flags: Read / Write / Construct

Allowed values: [2.22045e-16,1]

Default value: 1.49012e-08

The `“zf”` property

  “zf”                       double

The final time (redshift) to compute $P(k,z)$.

Owner: NcmPowspec

Flags: Read / Write / Construct

Allowed values: >= 0

Default value: 1

The `“zi”` property

  “zi”                       double

The initial time (redshift) to compute $P(k,z)$.

Owner: NcmPowspec

Flags: Read / Write / Construct

Allowed values: >= 0

Default value: 0

NcmPowspec

Stability Level

Functions

Properties

Types and Values

Object Hierarchy

Includes

Description

Functions

ncm_powspec_ref ()

Parameters

Returns

ncm_powspec_free ()

Parameters

ncm_powspec_clear ()

Parameters

ncm_powspec_set_zi ()

Parameters

ncm_powspec_set_zf ()

Parameters

ncm_powspec_set_kmin ()

Parameters

ncm_powspec_set_kmax ()

Parameters

ncm_powspec_set_reltol_spline ()

Parameters

ncm_powspec_require_zi ()

Parameters

ncm_powspec_require_zf ()

Parameters

ncm_powspec_require_kmin ()

Parameters

ncm_powspec_require_kmax ()

Parameters

ncm_powspec_get_zi ()

Parameters

ncm_powspec_get_zf ()

Parameters

ncm_powspec_get_kmin ()

Parameters

ncm_powspec_get_kmax ()

Parameters

ncm_powspec_get_reltol_spline ()

Parameters

Returns

ncm_powspec_get_nknots ()

Parameters

ncm_powspec_prepare ()

Parameters

ncm_powspec_prepare_if_needed ()

Parameters

ncm_powspec_eval ()

Parameters

Returns

ncm_powspec_eval_vec ()

Parameters

ncm_powspec_get_spline_2d ()

Parameters

Returns

ncm_powspec_peek_model_ctrl ()

Parameters

Returns

ncm_powspec_var_tophat_R ()

Parameters

Returns

ncm_powspec_sigma_tophat_R ()

Parameters

Returns

ncm_powspec_corr3d ()

Parameters

Returns

ncm_powspec_sproj ()

Parameters

Types and Values

NCM_TYPE_POWSPEC

struct NcmPowspecClass

NcmPowspec

Property Details

The “kmax” property

The “kmin” property

The `“kmax”` property

The `“kmin”` property

The `“reltol”` property

The `“zf”` property

The `“zi”` property