Bicubic spline fitter for data scattered on the sphere. More...

Inheritance diagram for fitpack_sphere_domains::fitpack_sphere:

Collaboration diagram for fitpack_sphere_domains::fitpack_sphere:

Public Member Functions
procedure	destroy (this)
	Clean memory.

procedure	new_points (this, theta, phi, r, w)
	Set new points.

procedure	new_fit (this, theta, phi, r, w, smoothing)
	Generate new fit.

procedure	fit (this, smoothing, keep_knots)
	Generate/update fitting curve, with optional smoothing.

procedure	least_squares (this, smoothing, reset_knots)
	Fit a least-squares spherical surface with fixed knots.

procedure	interpolate (this, reset_knots)
	Fit an interpolating spherical surface ( \( s = 0 \)).

generic	eval (this, theta, phi, ierr)
	Evaluate polar domain at given x,y coordinates.

generic	eval (this, theta, phi, ierr)
	Evaluate the spherical spline on a grid of colatitude and longitude values.

procedure	comm_size (this)
	Parallel communication interface.

procedure	comm_pack (this, buffer)
	Pack the sphere fitter state into a communication buffer.

procedure	comm_expand (this, buffer)
	Restore the sphere fitter state from a communication buffer.

type(fitpack_sphere) function	sphere_new_from_points (theta, phi, r, w, ierr)
	Construct a fitpack_sphere from scattered data and perform an initial fit.

Public Member Functions inherited from fitpack_fitters::fitpack_fitter
procedure, non_overridable	mse (this)
	MSE accessor (shared by all types)

procedure, non_overridable	core_comm_size (this)
	Base field helpers for comm (non-overridable, called by subtypes)

procedure, non_overridable	core_comm_pack (this, buffer)
	Pack base fields into communication buffer.

procedure, non_overridable	core_comm_expand (this, buffer)
	Expand base fields from communication buffer.

procedure, non_overridable	destroy_base (this)
	Base field reset (called by subtype destroy methods)

procedure(comm_size_if), deferred	comm_size (this)
	Deferred communication interface.

procedure(comm_pack_if), deferred	comm_pack (this, buffer)

procedure(comm_expand_if), deferred	comm_expand (this, buffer)

Public Attributes
integer	m = 0
	Scattered data points.

real(fp_real), dimension(:), allocatable	theta

real(fp_real), dimension(:), allocatable	phi

real(fp_real), dimension(:), allocatable	r
	Function values at the points.

real(fp_real), dimension(:), allocatable	w

integer	lwrk2 = 0

real(fp_real), dimension(:), allocatable	wrk2

integer, dimension(2)	nest = 0

integer	nmax = 0

integer, dimension(2)	knots = 0

real(fp_real), dimension(:,:), allocatable	t

Public Attributes inherited from fitpack_fitters::fitpack_fitter
integer(fp_flag)	iopt = IOPT_NEW_SMOOTHING
	Fitting state flag.

real(fp_real)	smoothing = 1000.0_FP_REAL
	Smoothing parameter.

real(fp_real)	fp = zero
	Weighted sum of squared residuals.

real(fp_real), dimension(:), allocatable	c
	B-spline coefficients.

integer(fp_size)	lwrk = 0
	Real workspace and its size.

real(fp_real), dimension(:), allocatable	wrk

integer(fp_size)	liwrk = 0
	Integer workspace and its size.

integer(fp_size), dimension(:), allocatable	iwrk

Private Member Functions
procedure, private	sphere_eval_one (this, theta, phi, ierr)
	Evaluate polar domain at given x,y coordinates.

procedure, private	sphere_eval_many (this, theta, phi, ierr)
	Evaluate the spherical spline on a grid of colatitude and longitude values.

Detailed Description

Bicubic spline fitter for data scattered on the sphere.

Stores the scattered spherical data \( (\theta_i, \phi_i, r_i) \), optional weights, and the fitted B-spline representation. The smoothing parameter controls closeness of fit versus smoothness. Pole constraints ensure regularity at \( \theta = 0 \) (north pole) and \( \theta = \pi \) (south pole).

See also: Dierckx, Ch. 11, §11.2 (pp. 263–269)

Member Function/Subroutine Documentation

◆ comm_expand()

procedure fitpack_sphere_domains::fitpack_sphere::comm_expand	(	class(fitpack_sphere), intent(inout)	this,
		real(fp_comm), dimension(:), intent(in)	buffer )

Restore the sphere fitter state from a communication buffer.

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◆ comm_pack()

procedure fitpack_sphere_domains::fitpack_sphere::comm_pack	(	class(fitpack_sphere), intent(in)	this,
		real(fp_comm), dimension(:), intent(out)	buffer )

Pack the sphere fitter state into a communication buffer.

◆ comm_size()

procedure fitpack_sphere_domains::fitpack_sphere::comm_size ( class(fitpack_sphere), intent(in) this )

Parallel communication interface.

◆ destroy()

procedure fitpack_sphere_domains::fitpack_sphere::destroy ( class(fitpack_sphere), intent(inout) this )

Clean memory.

◆ eval() [1/2]

generic fitpack_sphere_domains::fitpack_sphere::eval	(	class(fitpack_sphere), intent(inout)	this,
		real(fp_real), intent(in)	theta,
		real(fp_real), intent(in)	phi,
		integer, intent(out), optional	ierr )

Evaluate polar domain at given x,y coordinates.

Parameters

[in]	theta	Colatitude \( \theta \in [0, \pi] \).
[in]	phi	Longitude \( \phi \in [0, 2\pi] \).
[out]	ierr	Optional error flag.

Returns: Spline value \( s(\theta, \phi) \).

See also: bispev

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◆ eval() [2/2]

generic fitpack_sphere_domains::fitpack_sphere::eval	(	class(fitpack_sphere), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	theta,
		real(fp_real), dimension(:), intent(in)	phi,
		integer, intent(out), optional	ierr )

Evaluate the spherical spline on a grid of colatitude and longitude values.

Returns \( r(j,i) = s(\theta_i, \phi_j) \) for all combinations of the input theta and phi vectors (tensor-product evaluation).

Parameters

[in]	theta	Colatitude evaluation points.
[in]	phi	Longitude evaluation points.
[out]	ierr	Optional error flag.

Returns: Grid of spline values, dimensioned (size(phi), size(theta)).

See also: bispev

◆ fit()

procedure fitpack_sphere_domains::fitpack_sphere::fit	(	class(fitpack_sphere), intent(inout)	this,
		real(fp_real), intent(in), optional	smoothing,
		logical, intent(in), optional	keep_knots )

Generate/update fitting curve, with optional smoothing.

Iterates over the smoothing schedule, calling the sphere core routine to fit a bicubic spline \( r = s(\theta, \phi) \) to scattered data on the unit sphere.

Parameters

[in]	smoothing	Smoothing factor ( \( s \ge 0 \)); default uses stored value.
[in]	keep_knots	If `.true.`, reuse the current knot set.

Returns: Error flag.

See also: sphere

◆ interpolate()

procedure fitpack_sphere_domains::fitpack_sphere::interpolate	(	class(fitpack_sphere), intent(inout)	this,
		logical, intent(in), optional	reset_knots )

Fit an interpolating spherical surface ( \( s = 0 \)).

Parameters

[in] reset_knots If .true. (default), start with fresh knot placement.

Returns: Error flag.

See also: sphere

◆ least_squares()

procedure fitpack_sphere_domains::fitpack_sphere::least_squares	(	class(fitpack_sphere), intent(inout)	this,
		real(fp_real), intent(in), optional	smoothing,
		logical, intent(in), optional	reset_knots )

Fit a least-squares spherical surface with fixed knots.

See also: sphere

◆ new_fit()

procedure fitpack_sphere_domains::fitpack_sphere::new_fit	(	class(fitpack_sphere), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	theta,
		real(fp_real), dimension(size(theta)), intent(in)	phi,
		real(fp_real), dimension(size(theta)), intent(in)	r,
		real(fp_real), dimension(size(theta)), intent(in), optional	w,
		real(fp_real), intent(in), optional	smoothing )

Generate new fit.

Parameters

[in]	theta	Colatitude coordinates.
[in]	phi	Longitude coordinates.
[in]	r	Function values.
[in]	w	Optional weights.
[in]	smoothing	Optional smoothing factor.

Returns: Error flag.

See also: sphere

◆ new_points()

procedure fitpack_sphere_domains::fitpack_sphere::new_points	(	class(fitpack_sphere), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	theta,
		real(fp_real), dimension(size(theta)), intent(in)	phi,
		real(fp_real), dimension(size(theta)), intent(in)	r,
		real(fp_real), dimension(size(theta)), intent(in), optional	w )

Set new points.

Replaces any previous data with the given colatitude \( \theta_i \in [0, \pi] \), longitude \( \phi_i \in [0, 2\pi] \), and radial values \( r_i \).

Parameters

[in]	theta	Colatitude coordinates.
[in]	phi	Longitude coordinates (same size as theta).
[in]	r	Function values at each point.
[in]	w	Optional weights (default: uniform).

◆ sphere_eval_many()

procedure, private fitpack_sphere_domains::fitpack_sphere::sphere_eval_many	(	class(fitpack_sphere), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	theta,
		real(fp_real), dimension(:), intent(in)	phi,
		integer, intent(out), optional	ierr )

private

Evaluate the spherical spline on a grid of colatitude and longitude values.

Returns \( r(j,i) = s(\theta_i, \phi_j) \) for all combinations of the input theta and phi vectors (tensor-product evaluation).

Parameters

[in]	theta	Colatitude evaluation points.
[in]	phi	Longitude evaluation points.
[out]	ierr	Optional error flag.

Returns: Grid of spline values, dimensioned (size(phi), size(theta)).

See also: bispev

◆ sphere_eval_one()

procedure, private fitpack_sphere_domains::fitpack_sphere::sphere_eval_one	(	class(fitpack_sphere), intent(inout)	this,
		real(fp_real), intent(in)	theta,
		real(fp_real), intent(in)	phi,
		integer, intent(out), optional	ierr )

private

Evaluate polar domain at given x,y coordinates.

Parameters

[in]	theta	Colatitude \( \theta \in [0, \pi] \).
[in]	phi	Longitude \( \phi \in [0, 2\pi] \).
[out]	ierr	Optional error flag.

Returns: Spline value \( s(\theta, \phi) \).

See also: bispev

◆ sphere_new_from_points()

type(fitpack_sphere) function fitpack_sphere_domains::fitpack_sphere::sphere_new_from_points	(	real(fp_real), dimension(:), intent(in)	theta,
		real(fp_real), dimension(size(theta)), intent(in)	phi,
		real(fp_real), dimension(size(theta)), intent(in)	r,
		real(fp_real), dimension(size(theta)), intent(in), optional	w,
		integer, intent(out), optional	ierr )

Construct a fitpack_sphere from scattered data and perform an initial fit.

Parameters

[in]	theta	Colatitude coordinates \( \theta_i \in [0, \pi] \).
[in]	phi	Longitude coordinates \( \phi_i \in [0, 2\pi] \).
[in]	r	Function values at each point.
[in]	w	Optional weights.
[out]	ierr	Optional error flag; if absent, halts on error.

See also: sphere

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Member Data Documentation

◆ knots

integer, dimension(2) fitpack_sphere_domains::fitpack_sphere::knots = 0

◆ lwrk2

integer fitpack_sphere_domains::fitpack_sphere::lwrk2 = 0

◆ m

integer fitpack_sphere_domains::fitpack_sphere::m = 0

Scattered data points.

◆ nest

integer, dimension(2) fitpack_sphere_domains::fitpack_sphere::nest = 0

◆ nmax

integer fitpack_sphere_domains::fitpack_sphere::nmax = 0

◆ phi

real(fp_real), dimension(:), allocatable fitpack_sphere_domains::fitpack_sphere::phi

◆ r

real(fp_real), dimension(:), allocatable fitpack_sphere_domains::fitpack_sphere::r

Function values at the points.

◆ t

real(fp_real), dimension(:,:), allocatable fitpack_sphere_domains::fitpack_sphere::t

◆ theta

real(fp_real), dimension(:), allocatable fitpack_sphere_domains::fitpack_sphere::theta

◆ w

real(fp_real), dimension(:), allocatable fitpack_sphere_domains::fitpack_sphere::w

◆ wrk2

real(fp_real), dimension(:), allocatable fitpack_sphere_domains::fitpack_sphere::wrk2

The documentation for this interface was generated from the following file:

fitpack_spheres.f90

Public Member Functions

Public Attributes

Private Member Functions

Detailed Description

Member Function/Subroutine Documentation

◆ comm_expand()

◆ comm_pack()

◆ comm_size()

◆ destroy()

◆ eval() [1/2]

◆ eval() [2/2]

◆ fit()

◆ interpolate()

◆ least_squares()

◆ new_fit()

◆ new_points()

◆ sphere_eval_many()

◆ sphere_eval_one()

◆ sphere_new_from_points()

Member Data Documentation

◆ knots

◆ lwrk2

◆ m

◆ nest

◆ nmax

◆ phi

◆ r

◆ t

◆ theta

◆ w

◆ wrk2