Bicubic spline fitter for data on a latitude-longitude grid. More...

Inheritance diagram for fitpack_gridded_sphere::fitpack_grid_sphere:

Collaboration diagram for fitpack_gridded_sphere::fitpack_grid_sphere:

Public Member Functions
procedure	destroy (this)
	Clean memory.

procedure	new_points (this, u, v, z)
	Set new points.

procedure	new_fit (this, u, v, z, smoothing)
	Generate new fit.

procedure	bc_north_pole (this, z0, exact, differentiable, zero_grad)
	Set pole BCs.

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

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

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

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

generic	eval (this, u, v, ierr)
	Evaluate gridded domain at given x,y coordinates.

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

procedure	comm_size (this)
	Parallel communication interface.

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

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

procedure	write (this, filename)
	Write to disk.

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.

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
real(fp_real), dimension(:), allocatable	u
	Coordinates of the data points in grid coordinates (u,v) and domain size.

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

real(fp_real), dimension(:,:), allocatable	z
	Function values at the data points z(iv,iu) note (v,u) indices.

real(fp_real), dimension(2)	pole_z0 = zero
	North pole BC (u=0, index=1), South pole BC (u=pi, index=2)

logical, dimension(2)	pole_present = .false.

logical, dimension(2)	pole_exct = .false.

integer, dimension(2)	pole_continuity = 1

logical, dimension(2)	pole_zero_grad = .true.

integer, dimension(2)	nest = 0
	Node weights are not allowed.

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	gridded_eval_one (this, u, v, ierr)
	Evaluate gridded domain at given x,y coordinates.

procedure, private	gridded_eval_many (this, u, v, ierr)
	Evaluate the gridded spherical spline on a grid of colatitude and longitude values.

Detailed Description

Bicubic spline fitter for data on a latitude-longitude grid.

Stores the colatitude grid \( u_i \), the \( 2\pi \)-periodic longitude grid \( v_j \), gridded function values \( z(j, i) \), and the fitted B-spline representation. North and south pole boundary conditions (function value, continuity order, gradient vanishing) are independently configurable.

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

Member Function/Subroutine Documentation

◆ bc_north_pole()

procedure fitpack_gridded_sphere::fitpack_grid_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 )

Set pole BCs.

◆ bc_south_pole()

procedure fitpack_gridded_sphere::fitpack_grid_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 )

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

◆ comm_expand()

procedure fitpack_gridded_sphere::fitpack_grid_sphere::comm_expand	(	class(fitpack_grid_sphere), intent(inout)	this,
		real(fp_comm), dimension(:), intent(in)	buffer )

Restore the gridded sphere fitter state from a communication buffer.

◆ comm_pack()

procedure fitpack_gridded_sphere::fitpack_grid_sphere::comm_pack	(	class(fitpack_grid_sphere), intent(in)	this,
		real(fp_comm), dimension(:), intent(out)	buffer )

Pack the gridded sphere fitter state into a communication buffer.

◆ comm_size()

procedure fitpack_gridded_sphere::fitpack_grid_sphere::comm_size ( class(fitpack_grid_sphere), intent(in) this )

Parallel communication interface.

◆ destroy()

procedure fitpack_gridded_sphere::fitpack_grid_sphere::destroy ( class(fitpack_grid_sphere), intent(inout) this )

Clean memory.

◆ eval() [1/2]

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

Evaluate gridded domain at given x,y coordinates.

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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◆ eval() [2/2]

generic fitpack_gridded_sphere::fitpack_grid_sphere::eval	(	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 )

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

◆ fit()

procedure fitpack_gridded_sphere::fitpack_grid_sphere::fit	(	class(fitpack_grid_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 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

◆ gridded_eval_many()

procedure, private fitpack_gridded_sphere::fitpack_grid_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()

procedure, private fitpack_gridded_sphere::fitpack_grid_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 gridded domain at given x,y coordinates.

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

◆ interpolate()

procedure fitpack_gridded_sphere::fitpack_grid_sphere::interpolate	(	class(fitpack_grid_sphere), intent(inout)	this,
		logical, intent(in), optional	reset_knots )

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

◆ least_squares()

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

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

◆ new_fit()

procedure fitpack_gridded_sphere::fitpack_grid_sphere::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 )

Generate new fit.

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

◆ new_points()

procedure fitpack_gridded_sphere::fitpack_grid_sphere::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 )

Set new points.

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))`.

◆ spgrid_new_from_points()

type(fitpack_grid_sphere) function fitpack_gridded_sphere::fitpack_grid_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 )

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

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◆ write()

procedure fitpack_gridded_sphere::fitpack_grid_sphere::write	(	class(fitpack_grid_sphere), intent(inout)	this,
		character(*), intent(in)	filename )

Write to disk.

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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Member Data Documentation

◆ knots

integer, dimension(2) fitpack_gridded_sphere::fitpack_grid_sphere::knots = 0

◆ nest

integer, dimension(2) fitpack_gridded_sphere::fitpack_grid_sphere::nest = 0

Node weights are not allowed.

◆ nmax

integer fitpack_gridded_sphere::fitpack_grid_sphere::nmax = 0

◆ pole_continuity

integer, dimension(2) fitpack_gridded_sphere::fitpack_grid_sphere::pole_continuity = 1

◆ pole_exct

logical, dimension(2) fitpack_gridded_sphere::fitpack_grid_sphere::pole_exct = .false.

◆ pole_present

logical, dimension(2) fitpack_gridded_sphere::fitpack_grid_sphere::pole_present = .false.

◆ pole_z0

real(fp_real), dimension(2) fitpack_gridded_sphere::fitpack_grid_sphere::pole_z0 = zero

North pole BC (u=0, index=1), South pole BC (u=pi, index=2)

◆ pole_zero_grad

logical, dimension(2) fitpack_gridded_sphere::fitpack_grid_sphere::pole_zero_grad = .true.

◆ t

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

◆ u

real(fp_real), dimension(:), allocatable fitpack_gridded_sphere::fitpack_grid_sphere::u

Coordinates of the data points in grid coordinates (u,v) and domain size.

◆ v

real(fp_real), dimension(:), allocatable fitpack_gridded_sphere::fitpack_grid_sphere::v

◆ z

real(fp_real), dimension(:,:), allocatable fitpack_gridded_sphere::fitpack_grid_sphere::z

Function values at the data points z(iv,iu) note (v,u) indices.

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

fitpack_gridded_sphere.f90

Public Member Functions

Public Attributes

Private Member Functions

Detailed Description

Member Function/Subroutine Documentation

◆ bc_north_pole()

◆ bc_south_pole()

◆ comm_expand()

◆ comm_pack()

◆ comm_size()

◆ destroy()

◆ eval() [1/2]

◆ eval() [2/2]

◆ fit()

◆ gridded_eval_many()

◆ gridded_eval_one()

◆ interpolate()

◆ least_squares()

◆ new_fit()

◆ new_points()

◆ spgrid_new_from_points()

◆ write()

Member Data Documentation

◆ knots

◆ nest

◆ nmax

◆ pole_continuity

◆ pole_exct

◆ pole_present

◆ pole_z0

◆ pole_zero_grad

◆ t

◆ u

◆ v

◆ z