OOP wrapper for bivariate spline fitting on the sphere to scattered data. More...

Data Types
interface	fitpack_sphere
	Bicubic spline fitter for data scattered on the sphere. More...

Functions/Subroutines
integer function	surface_fit_least_squares (this, smoothing, reset_knots)
	Fit a least-squares spherical surface with fixed knots.

integer function	surface_fit_interpolating (this, reset_knots)
	Fit an interpolating spherical surface ( \( s = 0 \)).

integer function	surface_fit_automatic_knots (this, smoothing, keep_knots)
	Fit a smoothing spherical surface with automatic knot placement.

elemental subroutine	sphere_destroy (this)
	Release all allocated memory and reset the sphere fitter to its default state.

subroutine	sphere_new_points (this, theta, phi, r, w)
	Load new scattered spherical data and allocate working storage.

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.

real(fp_real) function, dimension(size(phi), size(theta))	sphere_eval_many (this, theta, phi, ierr)
	Evaluate the spherical spline on a grid of colatitude and longitude values.

real(fp_real) function	sphere_eval_one (this, theta, phi, ierr)
	Evaluate the spherical spline at a single point.

integer function	sphere_new_fit (this, theta, phi, r, w, smoothing)
	Load new scattered data and fit a smoothing spherical spline in one call.

elemental integer(fp_size) function	sphere_comm_size (this)
	Return the communication buffer size for parallel pack/expand.

pure subroutine	sphere_comm_pack (this, buffer)
	Pack the sphere fitter state into a communication buffer.

pure subroutine	sphere_comm_expand (this, buffer)
	Restore the sphere fitter state from a communication buffer.

Detailed Description

OOP wrapper for bivariate spline fitting on the sphere to scattered data.

Provides fitpack_sphere, a derived type for fitting bicubic splines to data scattered over the unit sphere, parameterized by colatitude \( \theta \in [0, \pi] \) and longitude \( \phi \in [0, 2\pi] \). The fitted surface \( r = s(\theta, \phi) \) satisfies appropriate pole constraints to ensure smoothness at \( \theta = 0 \) and \( \theta = \pi \). Uses the sphere core routine.

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

Function/Subroutine Documentation

◆ sphere_comm_expand()

pure subroutine fitpack_sphere_domains::sphere_comm_expand	(	class(fitpack_sphere), intent(inout)	this,
		real(fp_comm), dimension(:), intent(in)	buffer )

private

Restore the sphere fitter state from a communication buffer.

◆ sphere_comm_pack()

pure subroutine fitpack_sphere_domains::sphere_comm_pack	(	class(fitpack_sphere), intent(in)	this,
		real(fp_comm), dimension(:), intent(out)	buffer )

private

Pack the sphere fitter state into a communication buffer.

◆ sphere_comm_size()

elemental integer(fp_size) function fitpack_sphere_domains::sphere_comm_size ( class(fitpack_sphere), intent(in) this )

private

Return the communication buffer size for parallel pack/expand.

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◆ sphere_destroy()

elemental subroutine fitpack_sphere_domains::sphere_destroy ( class(fitpack_sphere), intent(inout) this )

private

Release all allocated memory and reset the sphere fitter to its default state.

◆ sphere_eval_many()

real(fp_real) function, dimension(size(phi),size(theta)) fitpack_sphere_domains::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()

real(fp_real) function fitpack_sphere_domains::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 the spherical spline at a single point.

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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◆ sphere_new_fit()

integer function fitpack_sphere_domains::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 )

private

Load new scattered data and fit a smoothing spherical spline in one call.

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

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◆ sphere_new_from_points()

type(fitpack_sphere) function fitpack_sphere_domains::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 )

private

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

◆ sphere_new_points()

subroutine fitpack_sphere_domains::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 )

private

Load new scattered spherical data and allocate working storage.

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).

◆ surface_fit_automatic_knots()

integer function fitpack_sphere_domains::surface_fit_automatic_knots	(	class(fitpack_sphere), intent(inout)	this,
		real(fp_real), intent(in), optional	smoothing,
		logical, intent(in), optional	keep_knots )

private

Fit a smoothing spherical surface with automatic knot placement.

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

Ensure we start with new knots (unless caller wants to keep them)

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◆ surface_fit_interpolating()

integer function fitpack_sphere_domains::surface_fit_interpolating	(	class(fitpack_sphere), intent(inout)	this,
		logical, intent(in), optional	reset_knots )

private

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

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◆ surface_fit_least_squares()

integer function fitpack_sphere_domains::surface_fit_least_squares	(	class(fitpack_sphere), intent(inout)	this,
		real(fp_real), intent(in), optional	smoothing,
		logical, intent(in), optional	reset_knots )

private

Fit a least-squares spherical surface with fixed knots.

See also: sphere

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Data Types

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ sphere_comm_expand()

◆ sphere_comm_pack()

◆ sphere_comm_size()

◆ sphere_destroy()

◆ sphere_eval_many()

◆ sphere_eval_one()

◆ sphere_new_fit()

◆ sphere_new_from_points()

◆ sphere_new_points()

◆ surface_fit_automatic_knots()

◆ surface_fit_interpolating()

◆ surface_fit_least_squares()