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

Data Types
interface	fitpack_grid_sphere
	Bicubic spline fitter for data on a latitude-longitude grid. More...

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

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

integer function	spgrid_fit_automatic_knots (this, smoothing, keep_knots)
	Fit a smoothing spherical surface on a lat-lon grid with automatic knot placement.

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

subroutine	spgrid_new_points (this, u, v, z)
	Load new gridded spherical data and allocate working storage.

type(fitpack_grid_sphere) function	spgrid_new_from_points (u, v, z, ierr)
	Construct a fitpack_grid_sphere from gridded data and perform an initial fit.

integer function	spgrid_new_fit (this, u, v, z, smoothing)
	Load new gridded data and fit a smoothing spherical spline in one call.

real(fp_real) function, dimension(size(v), size(u))	gridded_eval_many (this, u, v, ierr)
	Evaluate the gridded spherical spline on a grid of colatitude and longitude values.

real(fp_real) function	gridded_eval_one (this, u, v, ierr)
	Evaluate the gridded spherical spline at a single point.

subroutine	pole_bc (this, pole, z0, exact, differentiable, zero_grad)
	Set boundary conditions at one pole of the sphere.

subroutine	bc_north_pole (this, z0, exact, differentiable, zero_grad)
	Set boundary conditions at the north pole ( \( u = 0 \)).

subroutine	bc_south_pole (this, z0, exact, differentiable, zero_grad)
	Set boundary conditions at the south pole ( \( u = \pi \)).

subroutine	gridded_to_disk (this, filename)
	Write gridded spherical data to a formatted text file.

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

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

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

Detailed Description

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

Provides fitpack_grid_sphere, a derived type for fitting bicubic splines to data given on a latitude-longitude grid over the sphere. The colatitude grid \( u_i \in [0, \pi] \) ( \( i = 1, \ldots, m_u \)) and the \( 2\pi \)-periodic longitude grid \( v_j \) ( \( j = 1, \ldots, m_v \)) define the sampling. Boundary conditions at the north ( \( u = 0 \)) and south ( \( u = \pi \)) poles can be configured for function value, exactness, continuity order, and gradient vanishing. Uses the spgrid core routine.

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

Function/Subroutine Documentation

◆ bc_north_pole()

subroutine fitpack_gridded_sphere::bc_north_pole	(	class(fitpack_grid_sphere), intent(inout)	this,
		real(fp_real), intent(in), optional	z0,
		logical, intent(in), optional	exact,
		logical, intent(in), optional	differentiable,
		logical, intent(in), optional	zero_grad )

private

Set boundary conditions at the north pole ( \( u = 0 \)).

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◆ bc_south_pole()

subroutine fitpack_gridded_sphere::bc_south_pole	(	class(fitpack_grid_sphere), intent(inout)	this,
		real(fp_real), intent(in), optional	z0,
		logical, intent(in), optional	exact,
		logical, intent(in), optional	differentiable,
		logical, intent(in), optional	zero_grad )

private

Set boundary conditions at the south pole ( \( u = \pi \)).

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◆ gridded_eval_many()

real(fp_real) function, dimension(size(v),size(u)) fitpack_gridded_sphere::gridded_eval_many	(	class(fitpack_grid_sphere), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	u,
		real(fp_real), dimension(:), intent(in)	v,
		integer, intent(out), optional	ierr )

private

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

Returns \( f(j,i) = s(u_i, v_j) \) for all combinations of the input vectors (tensor-product evaluation).

Parameters

[in]	u	Colatitude evaluation points.
[in]	v	Longitude evaluation points.
[out]	ierr	Optional error flag.

Returns: Grid of spline values, dimensioned (size(v), size(u)).

See also: bispev

◆ gridded_eval_one()

real(fp_real) function fitpack_gridded_sphere::gridded_eval_one	(	class(fitpack_grid_sphere), intent(inout)	this,
		real(fp_real), intent(in)	u,
		real(fp_real), intent(in)	v,
		integer, intent(out), optional	ierr )

private

Evaluate the gridded spherical spline at a single point.

Parameters

[in]	u	Colatitude \( u \in [0, \pi] \).
[in]	v	Longitude \( v \).
[out]	ierr	Optional error flag.

Returns: Spline value \( s(u, v) \).

See also: bispev

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◆ gridded_to_disk()

subroutine fitpack_gridded_sphere::gridded_to_disk	(	class(fitpack_grid_sphere), intent(inout)	this,
		character(*), intent(in)	filename )

private

Write gridded spherical data to a formatted text file.

Outputs a table with colatitude grid values in rows and longitude grid values in columns, suitable for external plotting or inspection.

Parameters

[in] fileName Output file path.

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◆ gridsphere_comm_expand()

pure subroutine fitpack_gridded_sphere::gridsphere_comm_expand	(	class(fitpack_grid_sphere), intent(inout)	this,
		real(fp_comm), dimension(:), intent(in)	buffer )

private

Restore the gridded sphere fitter state from a communication buffer.

◆ gridsphere_comm_pack()

pure subroutine fitpack_gridded_sphere::gridsphere_comm_pack	(	class(fitpack_grid_sphere), intent(in)	this,
		real(fp_comm), dimension(:), intent(out)	buffer )

private

Pack the gridded sphere fitter state into a communication buffer.

◆ gridsphere_comm_size()

elemental integer(fp_size) function fitpack_gridded_sphere::gridsphere_comm_size ( class(fitpack_grid_sphere), intent(in) this )

private

Return the communication buffer size for parallel pack/expand.

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◆ pole_bc()

subroutine fitpack_gridded_sphere::pole_bc	(	class(fitpack_grid_sphere), intent(inout)	this,
		integer, intent(in)	pole,
		real(fp_real), intent(in), optional	z0,
		logical, intent(in), optional	exact,
		logical, intent(in), optional	differentiable,
		logical, intent(in), optional	zero_grad )

private

Set boundary conditions at one pole of the sphere.

Configures the function value, exactness, differentiability, and gradient vanishing constraints at the specified pole (1 = north, 2 = south).

Parameters

[in]	pole	Pole index (1 = north \( u=0 \), 2 = south \( u=\pi \)).
[in]	z0	Optional function value at the pole.
[in]	exact	Treat z0 as an exact constraint.
[in]	differentiable	Require C1 continuity at the pole.
[in]	zero_grad	Require vanishing gradient at the pole.

◆ spgrid_destroy()

elemental subroutine fitpack_gridded_sphere::spgrid_destroy ( class(fitpack_grid_sphere), intent(inout) this )

private

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

◆ spgrid_fit_automatic_knots()

integer function fitpack_gridded_sphere::spgrid_fit_automatic_knots	(	class(fitpack_grid_sphere), intent(inout)	this,
		real(fp_real), intent(in), optional	smoothing,
		logical, intent(in), optional	keep_knots )

private

Fit a smoothing spherical surface on a lat-lon grid with automatic knot placement.

Iterates over the smoothing schedule, calling the spgrid core routine to fit a bicubic spline on the sphere grid. Pole boundary conditions (continuity order, gradient vanishing, exact data) are applied as configured.

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: spgrid

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

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◆ spgrid_fit_interpolating()

integer function fitpack_gridded_sphere::spgrid_fit_interpolating	(	class(fitpack_grid_sphere), intent(inout)	this,
		logical, intent(in), optional	reset_knots )

private

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

Parameters

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

Returns: Error flag.

See also: spgrid

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◆ spgrid_fit_least_squares()

integer function fitpack_gridded_sphere::spgrid_fit_least_squares	(	class(fitpack_grid_sphere), intent(inout)	this,
		real(fp_real), intent(in), optional	smoothing,
		logical, intent(in), optional	reset_knots )

private

Fit a least-squares gridded spherical surface with fixed knots.

Parameters

[in]	smoothing	Optional smoothing factor for the reset pass.
[in]	reset_knots	If `.true.`, recompute knots via a smoothing fit first.

Returns: Error flag.

See also: spgrid

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◆ spgrid_new_fit()

integer function fitpack_gridded_sphere::spgrid_new_fit	(	class(fitpack_grid_sphere), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	u,
		real(fp_real), dimension(:), intent(in)	v,
		real(fp_real), dimension(size(v),size(u)), intent(in)	z,
		real(fp_real), intent(in), optional	smoothing )

private

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

Parameters

[in]	u	Colatitude grid.
[in]	v	Longitude grid.
[in]	z	Gridded function values.
[in]	smoothing	Optional smoothing factor.

Returns: Error flag.

See also: spgrid

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◆ spgrid_new_from_points()

type(fitpack_grid_sphere) function fitpack_gridded_sphere::spgrid_new_from_points	(	real(fp_real), dimension(:), intent(in)	u,
		real(fp_real), dimension(:), intent(in)	v,
		real(fp_real), dimension(size(v),size(u)), intent(in)	z,
		integer, intent(out), optional	ierr )

private

Construct a fitpack_grid_sphere from gridded data and perform an initial fit.

Parameters

[in]	u	Colatitude grid \( u_i \in [0, \pi] \).
[in]	v	Longitude grid \( v_j \) ( \( 2\pi \)-periodic).
[in]	z	Function values \( z(j, i) \), dimensioned `(size(v), size(u))`.
[out]	ierr	Optional error flag; if absent, halts on error.

See also: spgrid

◆ spgrid_new_points()

subroutine fitpack_gridded_sphere::spgrid_new_points	(	class(fitpack_grid_sphere), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	u,
		real(fp_real), dimension(:), intent(in)	v,
		real(fp_real), dimension(size(v),size(u)), intent(in)	z )

private

Load new gridded spherical data and allocate working storage.

Parameters

[in]	u	Colatitude grid \( u_i \in [0, \pi] \).
[in]	v	Longitude grid \( v_j \) ( \( 2\pi \)-periodic).
[in]	z	Function values \( z(j, i) \), dimensioned `(size(v), size(u))`.

Data Types

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ bc_north_pole()

◆ bc_south_pole()

◆ gridded_eval_many()

◆ gridded_eval_one()

◆ gridded_to_disk()

◆ gridsphere_comm_expand()

◆ gridsphere_comm_pack()

◆ gridsphere_comm_size()

◆ pole_bc()

◆ spgrid_destroy()

◆ spgrid_fit_automatic_knots()

◆ spgrid_fit_interpolating()

◆ spgrid_fit_least_squares()

◆ spgrid_new_fit()

◆ spgrid_new_from_points()

◆ spgrid_new_points()