NcmHOAA: NumCosmo Reference Manual

NcmHOAA

NcmHOAA — Abstract class for Harmonic Oscillator calculation through AA variables.

Functions

NcmHOAA *	ncm_hoaa_ref ()
void	ncm_hoaa_free ()
void	ncm_hoaa_clear ()
void	ncm_hoaa_set_reltol ()
void	ncm_hoaa_set_abstol ()
void	ncm_hoaa_set_k ()
void	ncm_hoaa_set_ti ()
void	ncm_hoaa_set_tf ()
void	ncm_hoaa_save_evol ()
void	ncm_hoaa_prepare ()
void	ncm_hoaa_get_t0_t1 ()
void	ncm_hoaa_eval_adiabatic_approx ()
void	ncm_hoaa_eval_adiabatic_LnI_approx ()
void	ncm_hoaa_eval_AA ()
void	ncm_hoaa_eval_AA2QV ()
void	ncm_hoaa_eval_QV2AA ()
void	ncm_hoaa_eval_QV ()
void	ncm_hoaa_eval_Delta ()
void	ncm_hoaa_eval_solution ()
gdouble	ncm_hoaa_eval_nu ()
gdouble	ncm_hoaa_eval_mnu ()
gdouble	ncm_hoaa_eval_dlnmnu ()
gdouble	ncm_hoaa_eval_V ()
void	ncm_hoaa_eval_system ()
guint	ncm_hoaa_nsing ()
void	ncm_hoaa_get_sing_info ()
gdouble	ncm_hoaa_eval_sing_mnu ()
gdouble	ncm_hoaa_eval_sing_dlnmnu ()
gdouble	ncm_hoaa_eval_sing_V ()
void	ncm_hoaa_eval_sing_system ()
gdouble	ncm_hoaa_eval_powspec_factor ()

Properties

double	abstol	Read / Write / Construct
double	k	Read / Write / Construct
NcmHOAAOpt	opt	Read / Write / Construct Only
double	reltol	Read / Write / Construct
gboolean	save-evol	Read / Write / Construct
double	tf	Read / Write / Construct
double	ti	Read / Write / Construct

Types and Values

#define	NCM_TYPE_HOAA
enum	NcmHOAAOpt
enum	NcmHOAASingType
struct	NcmHOAAClass
enum	NcmHOAAVar
#define	NCM_HOAA_TIME_FRAC
#define	NCM_HOAA_DEBUG_EVOL
#define	NCM_HOAA_DEBUG_SING
#define	NCM_HOAA_DEBUG_EVOL_SING
#define	NCM_HOAA_PARABOLIC_MIN_POINTS
#define	NCM_HOAA_PARABOLIC_TRIG_ONE
	NcmHOAA

Object Hierarchy

    GEnum
    ├── NcmHOAAOpt
    ├── NcmHOAASingType
    ╰── NcmHOAAVar
    GObject
    ╰── NcmHOAA
        ├── NcHIPertAdiab
        ╰── NcHIPertGW

Description

This object represents a generic time dependent harmonic oscillator for the variables $q$ and its momentum $p$. The Hamiltonian of the system is given by \begin{equation}\label{eq:H} H = \frac{P_q^2}{2m} + \frac{m(\nu^2 - V)q^2}{2}, \end{equation} where the mass $m$, frequency $\nu$ and the potential $V$ are functions of the time $t$ and mode $k$. The mass $m$ and frequency $\nu$ are assumed to be positive definite functions. For details about this system see Appendix A of Celani et al (2016).

Each child should implement the functions ncm_hoaa_eval_mnu(), ncm_hoaa_eval_nu() and ncm_hoaa_eval_system(). The potential term is optional, if not implemented then $V$ is assumed to be zero.

The Action Angle variables are defined through \begin{align} q &= \sqrt{\frac{2I}{m\nu}}\sin\theta, \\ P_q &= \sqrt{2Im\nu}\cos\theta. \end{align} Therefore, the new Hamiltonian is \begin{equation}\label{eq:HAA} H = I\nu + \frac{\mathrm{d}\ln(\sqrt{m\nu})}{\mathrm{d}t}I\sin2\theta - \frac{V}{\nu}I\sin^2\theta. \end{equation} The Hamilton equations for these variables are: \begin{align} \frac{\mathrm{d}\theta}{\mathrm{d}t} &= \nu - \frac{V}{\nu}\sin^2\theta + \frac{\mathrm{d}\ln(\sqrt{m\nu})}{\mathrm{d}t}\sin2\theta, \\ \frac{\mathrm{d}\ln(I)}{\mathrm{d}t} &= - 2\frac{\mathrm{d}\ln(\sqrt{m\nu})}{\mathrm{d}t}\cos2\theta + \frac{V}{\nu}I\sin2\theta. \end{align}

Functions

ncm_hoaa_ref ()

NcmHOAA *
ncm_hoaa_ref (NcmHOAA *hoaa);

Increases the reference count of hoaa .

Parameters

hoaa

a NcmHOAA

Returns

hoaa .

[transfer full]

ncm_hoaa_free ()

void
ncm_hoaa_free (NcmHOAA *hoaa);

Decreases the reference count of hoaa .

Parameters

hoaa

a NcmHOAA

ncm_hoaa_clear ()

void
ncm_hoaa_clear (NcmHOAA **hoaa);

Decreases the reference count of *hoaa and sets the pointer *hoaa to NULL.

Parameters

hoaa

a NcmHOAA

ncm_hoaa_set_reltol ()

void
ncm_hoaa_set_reltol (NcmHOAA *hoaa,
                     const gdouble reltol);

Sets the relative tolerance to reltol .

Parameters

hoaa	a NcmHOAA
reltol	relative tolerance

ncm_hoaa_set_abstol ()

void
ncm_hoaa_set_abstol (NcmHOAA *hoaa,
                     const gdouble abstol);

Sets the absolute tolerance to abstol .

Parameters

hoaa	a NcmHOAA
abstol	absolute tolerance

ncm_hoaa_set_k ()

void
ncm_hoaa_set_k (NcmHOAA *hoaa,
                const gdouble k);

Sets the mode $k$ to k .

Parameters

hoaa	a NcmHOAA
k	mode $k$

ncm_hoaa_set_ti ()

void
ncm_hoaa_set_ti (NcmHOAA *hoaa,
                 const gdouble ti);

Sets the initial time $t_i$ to ti .

Parameters

hoaa	a NcmHOAA
ti	mode $t_i$

ncm_hoaa_set_tf ()

void
ncm_hoaa_set_tf (NcmHOAA *hoaa,
                 const gdouble tf);

Sets the initial time $t_f$ to tf .

Parameters

hoaa	a NcmHOAA
tf	mode $t_f$

ncm_hoaa_save_evol ()

void
ncm_hoaa_save_evol (NcmHOAA *hoaa,
                    gboolean save_evol);

If true saves all evolution to be evaluted later through.

Parameters

hoaa	a NcmHOAA
save_evol	whether to save all evolution

ncm_hoaa_prepare ()

void
ncm_hoaa_prepare (NcmHOAA *hoaa,
                  NcmModel *model);

Prepares the object using model .

[virtual prepare]

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]

ncm_hoaa_get_t0_t1 ()

void
ncm_hoaa_get_t0_t1 (NcmHOAA *hoaa,
                    NcmModel *model,
                    gdouble *t0,
                    gdouble *t1);

Gets the time interval where the numerical evolution was calculated;

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t0	$t_0$.	[out]
t1	$t_1$.	[out]

ncm_hoaa_eval_adiabatic_approx ()

void
ncm_hoaa_eval_adiabatic_approx (NcmHOAA *hoaa,
                                NcmModel *model,
                                const gdouble t,
                                gdouble *thetab,
                                gdouble *upsilon,
                                gdouble *gamma);

Calculates the adiabatic approximation at $t$ and $k$.

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t	time $t$
thetab	$\theta_b$.	[out]
upsilon	$\upsilon$.	[out]
gamma	$\ln(I)$.	[out]

ncm_hoaa_eval_adiabatic_LnI_approx ()

void
ncm_hoaa_eval_adiabatic_LnI_approx (NcmHOAA *hoaa,
                                    NcmModel *model,
                                    const gdouble t,
                                    const gdouble theta,
                                    const gdouble psi,
                                    gdouble *LnI,
                                    gdouble *LnJ);

Calculates the adiabatic approximation at $t$ and $k$.

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t	time $t$
theta	$\theta$
psi	$\psi$
LnI	$\ln(I)$.	[out]
LnJ	$\ln(J)$.	[out]

ncm_hoaa_eval_AA ()

void
ncm_hoaa_eval_AA (NcmHOAA *hoaa,
                  NcmModel *model,
                  const gdouble t,
                  gdouble *upsilon,
                  gdouble *gamma,
                  gdouble *qbar,
                  gdouble *pbar);

Calculates the AA variables at $t$ and $k$.

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t	time $t$
upsilon	$\theta$.	[out]
gamma	$\psi$.	[out]
qbar	$\ln(I)$.	[out]
pbar	$\ln(J)$.	[out]

ncm_hoaa_eval_AA2QV ()

void
ncm_hoaa_eval_AA2QV (NcmHOAA *hoaa,
                     NcmModel *model,
                     const gdouble t,
                     const gdouble upsilon,
                     const gdouble gamma,
                     const gdouble qbar,
                     const gdouble pbar,
                     gdouble *q,
                     gdouble *v,
                     gdouble *Pq,
                     gdouble *Pv);

Change the variables from AA to QV.

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t	time $t$
upsilon	$\upsilon$
gamma	$\gamma$
qbar	$\sin (\theta_b)$
pbar	$\cos (\theta_b)$
q	$u$.	[out]
v	$v$.	[out]
Pq	$P_q$.	[out]
Pv	$P_v$.	[out]

ncm_hoaa_eval_QV2AA ()

void
ncm_hoaa_eval_QV2AA (NcmHOAA *hoaa,
                     NcmModel *model,
                     const gdouble t,
                     const gdouble q,
                     const gdouble v,
                     const gdouble Pq,
                     const gdouble Pv,
                     gdouble *upsilon,
                     gdouble *gamma,
                     gdouble *qbar,
                     gdouble *pbar);

Change the variables from complex to AA.

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t	time $t$
q	$q$
v	$v$
Pq	$P_q$
Pv	$P_v$
upsilon	$\upsilon$.	[out]
gamma	$\gamma$.	[out]
qbar	$\sin (\theta_b)$.	[out]
pbar	$\cos (\theta_b)$.	[out]

ncm_hoaa_eval_QV ()

void
ncm_hoaa_eval_QV (NcmHOAA *hoaa,
                  NcmModel *model,
                  const gdouble t,
                  gdouble *q,
                  gdouble *v,
                  gdouble *Pq,
                  gdouble *Pv);

Calculates the complex variables at $t$ and $k$.

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t	time $t$
q	$q$.	[out]
v	$v$.	[out]
Pq	$P_q$.	[out]
Pv	$P_v$.	[out]

ncm_hoaa_eval_Delta ()

void
ncm_hoaa_eval_Delta (NcmHOAA *hoaa,
                     NcmModel *model,
                     const gdouble t,
                     gdouble *Delta_phi,
                     gdouble *Delta_Pphi);

Calculates the power spectra.

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t	time $t$
Delta_phi	$\Delta_\phi$.	[out]
Delta_Pphi	$\Delta_{P_\phi}$.	[out]

ncm_hoaa_eval_solution ()

void
ncm_hoaa_eval_solution (NcmHOAA *hoaa,
                        NcmModel *model,
                        const gdouble t,
                        const gdouble S,
                        const gdouble PS,
                        gdouble *Aq,
                        gdouble *Av);

Calculates the coefficients $A_q$ and $A_v$ of the solution with initial conditions $S,\;P_S$ at $t$.

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t	time $t$
S	$S$
PS	$P_S$
Aq	$A_q$.	[out]
Av	$A_v$.	[out]

ncm_hoaa_eval_nu ()

gdouble
ncm_hoaa_eval_nu (NcmHOAA *hoaa,
                  NcmModel *model,
                  const gdouble t,
                  const gdouble k);

Evaluates the frequency term at $t$ and $k$.

[virtual eval_nu]

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t	time $t$
k	mode $k$

Returns

the frequency $\nu$.

ncm_hoaa_eval_mnu ()

gdouble
ncm_hoaa_eval_mnu (NcmHOAA *hoaa,
                   NcmModel *model,
                   const gdouble t,
                   const gdouble k);

Evaluates the mass term at $t$ and $k$.

[virtual eval_mnu]

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t	time $t$
k	mode $k$

Returns

the mass $m$.

ncm_hoaa_eval_dlnmnu ()

gdouble
ncm_hoaa_eval_dlnmnu (NcmHOAA *hoaa,
                      NcmModel *model,
                      const gdouble t,
                      const gdouble k);

Evaluates the derivative $\mathrm{d}(m\nu)/\mathrm{d}t$ term at $t$ and $k$.

[virtual eval_dlnmnu]

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t	time $t$
k	mode $k$

Returns

the potential $\mathrm{d}(m\nu)/\mathrm{d}t$.

ncm_hoaa_eval_V ()

gdouble
ncm_hoaa_eval_V (NcmHOAA *hoaa,
                 NcmModel *model,
                 const gdouble t,
                 const gdouble k);

Evaluates the potential term at $t$ and $k$.

[virtual eval_V]

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t	time $t$
k	mode $k$

Returns

the potential $V$.

ncm_hoaa_eval_system ()

void
ncm_hoaa_eval_system (NcmHOAA *hoaa,
                      NcmModel *model,
                      const gdouble t,
                      const gdouble k,
                      gdouble *nu,
                      gdouble *dlnmnu,
                      gdouble *Vnu);

Evaluates the system functions at $t$ and $k$.

[virtual eval_system]

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t	time $t$
k	mode $k$
nu	the frequency $\nu$.	[out]
dlnmnu	the derivative $\mathrm{d}(m\nu)/\mathrm{d}t$.	[out]
Vnu	the potential over frequency term $V/\nu$.	[out]

ncm_hoaa_nsing ()

guint
ncm_hoaa_nsing (NcmHOAA *hoaa,
                NcmModel *model,
                const gdouble k);

Gets the number of singular points $m(t_s) = 0$ for the problem in hand.

[virtual nsing]

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
k	mode $k$

Returns

the number of singular points.

ncm_hoaa_get_sing_info ()

void
ncm_hoaa_get_sing_info (NcmHOAA *hoaa,
                        NcmModel *model,
                        const gdouble k,
                        const guint sing,
                        gdouble *ts,
                        gdouble *dts_i,
                        gdouble *dts_f,
                        NcmHOAASingType *st);

Gets the time $t_s$ where the sing -th singularity occour.

[virtual get_sing_info]

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
k	mode $k$
sing	singularity index
ts	singularity time $t_s$.	[out]
dts_i	singularity time interval $t_s - t_i$.	[out]
dts_f	singularity time interval $t_f - t_s$.	[out]
st	singularity type.	[out]

ncm_hoaa_eval_sing_mnu ()

gdouble
ncm_hoaa_eval_sing_mnu (NcmHOAA *hoaa,
                        NcmModel *model,
                        const gdouble t_m_ts,
                        const gdouble k,
                        const guint sing);

Evaluates the mass term at $t$ and $k$.

[virtual eval_sing_mnu]

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t_m_ts	time $t - t_s$
k	mode $k$
sing	singularity index

Returns

the mass $m$.

ncm_hoaa_eval_sing_dlnmnu ()

gdouble
ncm_hoaa_eval_sing_dlnmnu (NcmHOAA *hoaa,
                           NcmModel *model,
                           const gdouble t_m_ts,
                           const gdouble k,
                           const guint sing);

Evaluates the derivative $\mathrm{d}(m\nu)/\mathrm{d}t$ term at $t$ and $k$.

[virtual eval_sing_dlnmnu]

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t_m_ts	time $t - t_s$
k	mode $k$
sing	singularity index

Returns

the potential $\mathrm{d}(m\nu)/\mathrm{d}t$.

ncm_hoaa_eval_sing_V ()

gdouble
ncm_hoaa_eval_sing_V (NcmHOAA *hoaa,
                      NcmModel *model,
                      const gdouble t_m_ts,
                      const gdouble k,
                      const guint sing);

Evaluates the potential term at $t$ and $k$.

[virtual eval_sing_V]

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t_m_ts	time $t - t_s$
k	mode $k$
sing	singularity index

Returns

the potential $V$.

ncm_hoaa_eval_sing_system ()

void
ncm_hoaa_eval_sing_system (NcmHOAA *hoaa,
                           NcmModel *model,
                           const gdouble t_m_ts,
                           const gdouble k,
                           const guint sing,
                           gdouble *nu,
                           gdouble *dlnmnu,
                           gdouble *Vnu);

Evaluates the system functions at $t$ and $k$.

[virtual eval_sing_system]

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]
t_m_ts	time $t - t_s$
k	mode $k$
sing	singularity index
nu	the frequency $\nu$.	[out]
dlnmnu	the derivative $\mathrm{d}(m\nu)/\mathrm{d}t$.	[out]
Vnu	the potential over frequency term $V/\nu$.	[out]

ncm_hoaa_eval_powspec_factor ()

gdouble
ncm_hoaa_eval_powspec_factor (NcmHOAA *hoaa,
                              NcmModel *model);

Evaluates the power spectrum constant factor. Default is: $1/(2\pi^2)$.

[virtual eval_powspec_factor]

Parameters

hoaa	a NcmHOAA
model	a NcmModel.	[allow-none]

Types and Values

NCM_TYPE_HOAA

#define NCM_TYPE_HOAA (ncm_hoaa_get_type ())

enum NcmHOAAOpt

When solving the system of equations, the user can choose to solve the system with all variables non-zero, only V non-zero or only dlnmnu non-zero.

Members

NCM_HOAA_OPT_FULL	System with all variables non-zero
NCM_HOAA_OPT_V_ONLY	System with only V non-zero
NCM_HOAA_OPT_DLNMNU_ONLY	System with only dlnmnu non-zero
NCM_HOAA_OPT_INVALID	Invalid option

enum NcmHOAASingType

The singularity type.

Members

NCM_HOAA_SING_TYPE_ZERO	mass pass through zero
NCM_HOAA_SING_TYPE_INF	mass pass through infinity
NCM_HOAA_SING_TYPE_INVALID	Invalid option

struct NcmHOAAClass

struct NcmHOAAClass {
};

enum NcmHOAAVar

The variables in the system.

Members

NCM_HOAA_VAR_QBAR	Field variable
NCM_HOAA_VAR_PBAR	Momentum variable
NCM_HOAA_VAR_UPSILON	adiabatic parameter
NCM_HOAA_VAR_GAMMA	adiabatic parameter
NCM_HOAA_VAR_SYS_SIZE	Number of variables in the system

NCM_HOAA_TIME_FRAC

#define NCM_HOAA_TIME_FRAC (1.0e-13)

NCM_HOAA_DEBUG_EVOL

#define NCM_HOAA_DEBUG_EVOL (FALSE)

NCM_HOAA_DEBUG_SING

#define NCM_HOAA_DEBUG_SING (FALSE)

NCM_HOAA_DEBUG_EVOL_SING

#define NCM_HOAA_DEBUG_EVOL_SING (FALSE)

NCM_HOAA_PARABOLIC_MIN_POINTS

#define NCM_HOAA_PARABOLIC_MIN_POINTS (4)

NCM_HOAA_PARABOLIC_TRIG_ONE

#define NCM_HOAA_PARABOLIC_TRIG_ONE (0.999)

NcmHOAA

typedef struct _NcmHOAA NcmHOAA;

Property Details

The `“abstol”` property

  “abstol”                   double

Absolute tolerance tolerance.

Owner: NcmHOAA

Flags: Read / Write / Construct

Allowed values: >= 0

Default value: 0

The `“k”` property

  “k”                        double

The mode k.

Owner: NcmHOAA

Flags: Read / Write / Construct

Allowed values: >= 0

Default value: 1

The `“opt”` property

  “opt”                      NcmHOAAOpt

Evolution options.

Owner: NcmHOAA

Flags: Read / Write / Construct Only

Default value: NCM_HOAA_OPT_INVALID

The `“reltol”` property

  “reltol”                   double

Relative tolerance.

Owner: NcmHOAA

Flags: Read / Write / Construct

Allowed values: [0,1]

Default value: 1e-07

The `“save-evol”` property

  “save-evol”                gboolean

Save the system evolution.

Owner: NcmHOAA

Flags: Read / Write / Construct

Default value: TRUE

The `“tf”` property

  “tf”                       double

The final time t_f.

Owner: NcmHOAA

Flags: Read / Write / Construct

Default value: 1

The `“ti”` property

  “ti”                       double

The initial time t_i.

Owner: NcmHOAA

Flags: Read / Write / Construct

Default value: 0