NcmSpline2d: NumCosmo Reference Manual

NcmSpline2d

NcmSpline2d — Abstract class for implementing bidimensional splines.

Stability Level

Stable, unless otherwise indicated

Functions

void	ncm_spline2d_set ()
void	ncm_spline2d_set_function ()
void	ncm_spline2d_prepare ()
guint	ncm_spline2d_min_size ()
NcmSpline2d *	ncm_spline2d_copy_empty ()
NcmSpline2d *	ncm_spline2d_copy ()
NcmSpline2d *	ncm_spline2d_new ()
NcmSpline2d *	ncm_spline2d_ref ()
void	ncm_spline2d_free ()
void	ncm_spline2d_clear ()
void	ncm_spline2d_use_acc ()
void	ncm_spline2d_set_init ()
NcmSpline *	ncm_spline2d_peek_spline ()
NcmVector *	ncm_spline2d_peek_xv ()
NcmVector *	ncm_spline2d_peek_yv ()
NcmMatrix *	ncm_spline2d_peek_zm ()
gsl_interp_accel *	ncm_spline2d_peek_acc_x ()
gsl_interp_accel *	ncm_spline2d_peek_acc_y ()
gboolean	ncm_spline2d_is_init ()
gboolean	ncm_spline2d_has_no_stride ()
gboolean	ncm_spline2d_using_acc ()
gdouble	ncm_spline2d_eval ()
gdouble	ncm_spline2d_integ_dx ()
gdouble	ncm_spline2d_integ_dy ()
gdouble	ncm_spline2d_integ_dxdy ()
NcmSpline *	ncm_spline2d_integ_dx_spline ()
NcmSpline *	ncm_spline2d_integ_dy_spline ()
gdouble	ncm_spline2d_integ_dx_spline_val ()
gdouble	ncm_spline2d_integ_dy_spline_val ()
gdouble	ncm_spline2d_integ_dxdy_spline_x ()
gdouble	ncm_spline2d_integ_dxdy_spline_y ()
gdouble	ncm_spline2d_deriv_dzdx ()
gdouble	ncm_spline2d_deriv_dzdy ()
gdouble	ncm_spline2d_deriv_d2zdxy ()
gdouble	ncm_spline2d_deriv_d2zdx2 ()
gdouble	ncm_spline2d_deriv_d2zdy2 ()
gdouble	ncm_spline2dim_integ_total ()
void	ncm_spline2d_eval_vec_y ()

Properties

gboolean	init	Read / Write
NcmSpline *	spline	Read / Write / Construct Only
gboolean	use-acc	Read / Write
NcmVector *	x-vector	Read / Write
NcmVector *	y-vector	Read / Write
NcmMatrix *	z-matrix	Read / Write

Types and Values

#define	NCM_TYPE_SPLINE2D
struct	NcmSpline2dClass
	NcmSpline2d

Object Hierarchy

    GObject
    ╰── NcmSpline2d
        ├── NcmSpline2dBicubic
        ├── NcmSpline2dGsl
        ╰── NcmSpline2dSpline

Includes

#include <numcosmo/math/ncm_spline2d.h>

Description

This class comprises all functions to provide a NcmSpline2d, get its properties and evaluate it given an interpolation method.

Functions

ncm_spline2d_set ()

void
ncm_spline2d_set (NcmSpline2d *s2d,
                  NcmVector *xv,
                  NcmVector *yv,
                  NcmMatrix *zm,
                  gboolean init);

This funtion sets xv and yv vectors and zm matrix to s2d .

Parameters

s2d	a NcmSpline2d
xv	a NcmVector of knots
yv	a NcmVector of knots
zm	a NcmMatrix of the values of the function, to be interpolated, computed at `xv` and `yv`
init	TRUE to prepare the NcmSpline2d or FALSE to not prepare it

ncm_spline2d_set_function ()

void
ncm_spline2d_set_function (NcmSpline2d *s2d,
                           NcmSplineFuncType ftype,
                           gsl_function *Fx,
                           gsl_function *Fy,
                           gdouble xl,
                           gdouble xu,
                           gdouble yl,
                           gdouble yu,
                           gdouble rel_err);

This function automatically determines the knots of s2d in the intervals [xl , xu ] and [yl , yu ] given a ftype and rel_error .

The functions Fx and Fy are the bidimensional function given at specific values of y and x, respectively. These x and y values must be in the the intervals [xl , xu ] and [yl , yu ].

[skip]

Parameters

s2d	a NcmSpline2d
ftype	a NcmSplineFuncType
Fx	function of x variable to be approximated by spline functions
Fy	function of y variable to be approximated by spline functions
xl	lower knot of x-coordinate
xu	upper knot of x-coordinate
yl	lower knot of y-coordinate
yu	upper knot of y-coordinate
rel_err	relative error between the function to be interpolated and the spline result

ncm_spline2d_prepare ()

void
ncm_spline2d_prepare (NcmSpline2d *s2d);

This function prepares the bi-dimensional spline s2d such that one can evaluate it (ncm_spline2d_eval), as well as to compute its integration in x, y or both directions.

Parameters

s2d

a NcmSpline2d

ncm_spline2d_min_size ()

guint
ncm_spline2d_min_size (NcmSpline2d *s2d);

Parameters

s2d

a NcmSpline2d

Returns

The size of the NcmSpline member of s2d .

ncm_spline2d_copy_empty ()

NcmSpline2d *
ncm_spline2d_copy_empty (const NcmSpline2d *s2d);

This function copies the bidimensional spline s2d into an initialized empty NcmSpline2d of a specific type.

Parameters

s2d

a NcmSpline2d

Returns

a NcmSpline2d.

[transfer full]

ncm_spline2d_copy ()

NcmSpline2d *
ncm_spline2d_copy (NcmSpline2d *s2d);

This function copies the two NcmVector and the NcmMatrix of the bidimensional spline s2d into those two NcmVector and NcmMatrix of a new NcmSpline2d.

Parameters

s2d

a NcmSpline2d

Returns

A NcmSpline2d.

[transfer full]

ncm_spline2d_new ()

NcmSpline2d *
ncm_spline2d_new (const NcmSpline2d *s2d,
                  NcmVector *xv,
                  NcmVector *yv,
                  NcmMatrix *zm,
                  gboolean init);

This function returns a new NcmSpline2d, where the knots of this new spline are given in the NcmVector xv and yv . The values of the function, at those knots, to be interpolated are given in the NcmMatrix zm .

Parameters

s2d	a constant NcmSpline2d
xv	NcmVector of knots
yv	NcmVector of knots
zm	NcmMatrix of the values of the function, to be interpolated, computed at `xv` and `yv`
init	TRUE to prepare the new NcmSpline2d or FALSE to not prepare it

Returns

A new NcmSpline2d.

[transfer full]

ncm_spline2d_ref ()

NcmSpline2d *
ncm_spline2d_ref (NcmSpline2d *s2d);

Atomically increases the reference count of s2d by one.

Parameters

s2d

a NcmSpline2d

Returns

the same object s2d .

[transfer full]

ncm_spline2d_free ()

void
ncm_spline2d_free (NcmSpline2d *s2d);

Atomically decrements the reference count of s2d by one. If the reference count drops to 0, all memory allocated by s2d is released.

Parameters

s2d

a NcmSpline2d

ncm_spline2d_clear ()

void
ncm_spline2d_clear (NcmSpline2d **s2d);

Atomically decrements the reference count of s2d by one. If the reference count drops to 0, all memory allocated by s2d is released. Set pointer to NULL.

Parameters

s2d

a NcmSpline2d

ncm_spline2d_use_acc ()

void
ncm_spline2d_use_acc (NcmSpline2d *s2d,
                      gboolean use_acc);

Whether to use accelerated bsearch to find the right knots. When enabled evaluation functions are not reentrant.

Parameters

s2d	a NcmSpline2d
use_acc	a boolean

ncm_spline2d_set_init ()

void
ncm_spline2d_set_init (NcmSpline2d *s2d,
                       gboolean init);

Whether to mark the NcmSpline2d as initialized. This method is intended for internal use only.

Parameters

s2d	a NcmSpline2d
init	a boolean

ncm_spline2d_peek_spline ()

NcmSpline *
ncm_spline2d_peek_spline (NcmSpline2d *s2d);

Get the NcmSpline of the NcmSpline2d. This method is intended for internal use only.

Parameters

s2d

a NcmSpline2d

Returns

The NcmSpline of the NcmSpline2d.

[transfer none]

ncm_spline2d_peek_xv ()

NcmVector *
ncm_spline2d_peek_xv (NcmSpline2d *s2d);

Get the NcmVector of knots in the x-direction. This method is intended for internal use only.

Parameters

s2d

a NcmSpline2d

Returns

The NcmVector of knots in the x-direction.

[transfer none]

ncm_spline2d_peek_yv ()

NcmVector *
ncm_spline2d_peek_yv (NcmSpline2d *s2d);

Get the NcmVector of knots in the y-direction. This method is intended for internal use only.

Parameters

s2d

a NcmSpline2d

Returns

The NcmVector of knots in the y-direction.

[transfer none]

ncm_spline2d_peek_zm ()

NcmMatrix *
ncm_spline2d_peek_zm (NcmSpline2d *s2d);

Get the NcmMatrix of the values of the function, to be interpolated, computed at the knots. This method is intended for internal use only.

Parameters

s2d

a NcmSpline2d

Returns

The NcmMatrix of the values of the function, to be interpolated, computed at the knots.

[transfer none]

ncm_spline2d_peek_acc_x ()

gsl_interp_accel *
ncm_spline2d_peek_acc_x (NcmSpline2d *s2d);

Get the gsl_interp_accel of the NcmSpline2d in the x-direction. This method is intended for internal use only.

[skip]

Parameters

s2d

a NcmSpline2d

Returns

The gsl_interp_accel of the NcmSpline2d in the x-direction.

[transfer none]

ncm_spline2d_peek_acc_y ()

gsl_interp_accel *
ncm_spline2d_peek_acc_y (NcmSpline2d *s2d);

Get the gsl_interp_accel of the NcmSpline2d in the y-direction. This method is intended for internal use only.

[skip]

Parameters

s2d

a NcmSpline2d

Returns

The gsl_interp_accel of the NcmSpline2d in the y-direction.

[transfer none]

ncm_spline2d_is_init ()

gboolean
ncm_spline2d_is_init (NcmSpline2d *s2d);

Whether the NcmSpline2d is initialized.

Parameters

s2d

a NcmSpline2d

Returns

TRUE if the NcmSpline2d is initialized.

ncm_spline2d_has_no_stride ()

gboolean
ncm_spline2d_has_no_stride (NcmSpline2d *s2d);

Whether the NcmSpline2d has stride 1 in both knots vectors.

Parameters

s2d

a NcmSpline2d

Returns

TRUE if the NcmSpline2d has stride 1 in both knots vectors.

ncm_spline2d_using_acc ()

gboolean
ncm_spline2d_using_acc (NcmSpline2d *s2d);

Whether the NcmSpline2d is using accelerated bsearch to find the right knots.

Parameters

s2d

a NcmSpline2d

Returns

TRUE if the NcmSpline2d is using accelerated bsearch to find the right knots.

ncm_spline2d_eval ()

gdouble
ncm_spline2d_eval (NcmSpline2d *s2d,
                   gdouble x,
                   gdouble y);

Parameters

s2d	a NcmSpline2d
x	x-coordinate value
y	y-coordinate value

Returns

The interpolated value of a function computed at the point (x , y ).

ncm_spline2d_integ_dx ()

gdouble
ncm_spline2d_integ_dx (NcmSpline2d *s2d,
                       gdouble xl,
                       gdouble xu,
                       gdouble y);

This function computes the integration in x over the interval [xl , xu ] and at y .

[virtual int_dx]

Parameters

s2d	a NcmSpline2d
xl	lower limit of integration
xu	upper limit of integration
y	y-coordinate value

Returns

The numerical integral in x of an interpolated function over the range [xl , xu ] and at y .

ncm_spline2d_integ_dy ()

gdouble
ncm_spline2d_integ_dy (NcmSpline2d *s2d,
                       gdouble x,
                       gdouble yl,
                       gdouble yu);

This function computes the integration in y over the interval [yl , yu ] and at x .

[virtual int_dy]

Parameters

s2d	a NcmSpline2d
x	x-coordinate value
yl	lower limit of integration
yu	upper limit of integration

Returns

The numerical integral in y of an interpolated function over the range [yl , yu ] and at x .

ncm_spline2d_integ_dxdy ()

gdouble
ncm_spline2d_integ_dxdy (NcmSpline2d *s2d,
                         gdouble xl,
                         gdouble xu,
                         gdouble yl,
                         gdouble yu);

This function computes the integration in both x and y directions over the intervals [xl , xu ] and [yl , yu ].

[virtual int_dxdy]

Parameters

s2d	a NcmSpline2d
xl	lower limit of integration in the x-direction
xu	upper limit of integration in the x-direction
yl	lower limit of integration in the y-direction
yu	upper limit of integration in the y-direction

Returns

The numerical integral in x and y of an interpolated function over the ranges [xl , xu ] and [yl , yu ].

ncm_spline2d_integ_dx_spline ()

NcmSpline *
ncm_spline2d_integ_dx_spline (NcmSpline2d *s2d,
                              gdouble xl,
                              gdouble xu);

This function computes the integral in x of the bidimensional interpolated function over the range [xl , xu ] resulting in a one dimensional function.

Parameters

s2d	a NcmSpline2d
xl	lower limit of integration x
xu	upper limit of integration x

Returns

A NcmSpline.

[transfer full]

ncm_spline2d_integ_dy_spline ()

NcmSpline *
ncm_spline2d_integ_dy_spline (NcmSpline2d *s2d,
                              gdouble yl,
                              gdouble yu);

This function computes the integral in y of the bidimensional interpolated function over the range [yl , yu ] resulting in a one dimensional function.

Parameters

s2d	a NcmSpline2d
yl	lower limit of integration
yu	upper limit of integration

Returns

A NcmSpline.

[transfer full]

ncm_spline2d_integ_dx_spline_val ()

gdouble
ncm_spline2d_integ_dx_spline_val (NcmSpline2d *s2d,
                                  gdouble xl,
                                  gdouble xu,
                                  gdouble y);

This function calls ncm_spline2d_integ_dx_spline and evaluates the resulting NcmSpline at y .

Parameters

s2d	a NcmSpline2d
xl	lower limit of integration
xu	upper limit of integration
y	y-coordinate value

Returns

The value of s2d integrated in x over the range [xl , xu ] and computed at y .

ncm_spline2d_integ_dy_spline_val ()

gdouble
ncm_spline2d_integ_dy_spline_val (NcmSpline2d *s2d,
                                  gdouble x,
                                  gdouble yl,
                                  gdouble yu);

This function calls ncm_spline2d_integ_dy_spline and evaluates the resulting NcmSpline at x .

Parameters

s2d	a NcmSpline2d
x	x-coordinate value
yl	lower limit of integration
yu	upper limit of integration

Returns

The value of s2d integrated in y over the range [yl , yu ] and computed at x .

ncm_spline2d_integ_dxdy_spline_x ()

gdouble
ncm_spline2d_integ_dxdy_spline_x (NcmSpline2d *s2d,
                                  gdouble xl,
                                  gdouble xu,
                                  gdouble yl,
                                  gdouble yu);

This function calls ncm_spline2d_integ_dx_spline and integrates the resulting NcmSpline over the interval [yl , yu ].

Parameters

s2d	a NcmSpline2d
xl	lower limit of integration in the x-direction
xu	upper limit of integration in the x-direction
yl	lower limit of integration in the y-direction
yu	upper limit of integration in the y-direction

Returns

The value of s2d integrated in x and y over the ranges [xl , xu ] and [yl , yu ], respectively.

ncm_spline2d_integ_dxdy_spline_y ()

gdouble
ncm_spline2d_integ_dxdy_spline_y (NcmSpline2d *s2d,
                                  gdouble xl,
                                  gdouble xu,
                                  gdouble yl,
                                  gdouble yu);

This function calls ncm_spline2d_integ_dy_spline and integrates the resulting NcmSpline over the interval [xl , xu ].

Parameters

s2d	a NcmSpline2d
xl	lower limit of integration in the x-direction
xu	upper limit of integration in the x-direction
yl	lower limit of integration in the y-direction
yu	upper limit of integration in the y-direction

Returns

The value of s2d integrated in x and y over the ranges [xl , xu ] and [yl , yu ], respectively.

ncm_spline2d_deriv_dzdx ()

gdouble
ncm_spline2d_deriv_dzdx (NcmSpline2d *s2d,
                         gdouble x,
                         gdouble y);

[virtual dzdx]

Parameters

s2d	a NcmSpline2d
x	x-coordinate value
y	y-coordinate value

Returns

The interpolated derivative $\mathrm{d}z/\mathrm{d}x$ computed at the point (x , y ).

ncm_spline2d_deriv_dzdy ()

gdouble
ncm_spline2d_deriv_dzdy (NcmSpline2d *s2d,
                         gdouble x,
                         gdouble y);

[virtual dzdy]

Parameters

s2d	a NcmSpline2d
x	x-coordinate value
y	y-coordinate value

Returns

The interpolated derivative $\mathrm{d}z/\mathrm{d}y$ computed at the point (x , y ).

ncm_spline2d_deriv_d2zdxy ()

gdouble
ncm_spline2d_deriv_d2zdxy (NcmSpline2d *s2d,
                           gdouble x,
                           gdouble y);

[virtual d2zdxy]

Parameters

s2d	a NcmSpline2d
x	x-coordinate value
y	y-coordinate value

Returns

The interpolated derivative $\mathrm{d}^2z/\mathrm{d}x\mathrm{d}y$ computed at the point (x , y ).

ncm_spline2d_deriv_d2zdx2 ()

gdouble
ncm_spline2d_deriv_d2zdx2 (NcmSpline2d *s2d,
                           gdouble x,
                           gdouble y);

[virtual d2zdx2]

Parameters

s2d	a NcmSpline2d
x	x-coordinate value
y	y-coordinate value

Returns

The interpolated derivative $\mathrm{d}^2z/\mathrm{d}x^2$ computed at the point (x , y ).

ncm_spline2d_deriv_d2zdy2 ()

gdouble
ncm_spline2d_deriv_d2zdy2 (NcmSpline2d *s2d,
                           gdouble x,
                           gdouble y);

[virtual d2zdy2]

Parameters

s2d	a NcmSpline2d
x	x-coordinate value
y	y-coordinate value

Returns

The interpolated derivative $\mathrm{d}^2z/\mathrm{d}y^2$ computed at the point (x , y ).

ncm_spline2dim_integ_total ()

gdouble
ncm_spline2dim_integ_total (NcmSpline2d *s2d);

Parameters

s2d

a NcmSpline2d

Returns

The numerical integral in both x and y directions of an interpolated function over the entire valid ranges of x and y coordinates.

ncm_spline2d_eval_vec_y ()

void
ncm_spline2d_eval_vec_y (NcmSpline2d *s2d,
                         gdouble x,
                         const NcmVector *y,
                         GArray *order,
                         GArray *res);

Computes the interpolated values of a function computed at the point (x , y ) for each element of y . The order of the indices of y is given by order .

Parameters

s2d	a NcmSpline2d
x	x-coordinate value
y	a NcmVector
order	an array of containing the order of the indices of `y` .	[element-type size_t][allow-none]
res	an array of the same size as `y` to store the interpolated values.	[element-type gdouble]

Types and Values

NCM_TYPE_SPLINE2D

#define NCM_TYPE_SPLINE2D (ncm_spline2d_get_type ())

struct NcmSpline2dClass

struct NcmSpline2dClass {
};

NcmSpline2d

typedef struct _NcmSpline2d NcmSpline2d;

Property Details

The `“init”` property

  “init”                     gboolean

boolean whether to prepare the NcmSpline2d.

Owner: NcmSpline2d

Flags: Read / Write

Default value: FALSE

The `“spline”` property

  “spline”                   NcmSpline *

NcmSpline object used internally.

Owner: NcmSpline2d

Flags: Read / Write / Construct Only

The `“use-acc”` property

  “use-acc”                  gboolean

Use accelerated bsearch.

Owner: NcmSpline2d

Flags: Read / Write

Default value: FALSE

The `“x-vector”` property

  “x-vector”                 NcmVector *

x vector.

Owner: NcmSpline2d

Flags: Read / Write

The `“y-vector”` property

  “y-vector”                 NcmVector *

y vector.

Owner: NcmSpline2d

Flags: Read / Write

The `“z-matrix”` property

  “z-matrix”                 NcmMatrix *

z matrix.

Owner: NcmSpline2d

Flags: Read / Write