fitpack_gridded_polar Module Reference

OOP wrapper for bivariate spline fitting on a gridded polar disc. More...

Data Types
interface	fitpack_grid_polar
	Bicubic spline fitter for data on a gridded polar disc. More...

Functions/Subroutines
integer function	polr_fit_least_squares (this, smoothing, reset_knots)
	Fit a least-squares gridded polar surface with fixed knots.
integer function	polr_fit_interpolating (this, reset_knots)
	Fit an interpolating gridded polar surface ( \( s = 0 \)).
integer function	polr_fit_automatic_knots (this, smoothing, keep_knots)
	Fit a smoothing gridded polar surface with automatic knot placement.
elemental subroutine	surf_destroy (this)
	Destroy a gridded polar surface object and release all allocated memory.
subroutine	surf_new_points (this, u, v, r, z, z0)
	Load new gridded polar data and allocate workspace.
type(fitpack_grid_polar) function	surf_new_from_points (u, v, r, z, z0, ierr)
	Construct a gridded polar surface from data and perform a default fit.
integer function	surf_new_fit (this, u, v, r, z, z0, smoothing)
	Load new data and perform a fresh gridded polar fit.
real(fp_real) function, dimension(size(v), size(u))	gridded_eval_many (this, u, v, ierr)
	Evaluate the gridded polar surface on a rectangular \( u \times v \) grid.
real(fp_real) function	gridded_eval_one (this, u, v, ierr)
	Evaluate the gridded polar surface at a single \( (u, v) \) point.
subroutine	set_origin_bc (this, z0, exact, differentiable)
	Configure origin boundary conditions for the gridded polar surface.
subroutine	gridded_to_disk (this, filename)
	Write gridded polar data to a text file.
elemental integer(fp_size) function	gridpolar_comm_size (this)
	Return the communication buffer size for the gridded polar surface.
pure subroutine	gridpolar_comm_pack (this, buffer)
	Pack gridded polar data into a communication buffer.
pure subroutine	gridpolar_comm_expand (this, buffer)
	Expand gridded polar data from a communication buffer.

Detailed Description

OOP wrapper for bivariate spline fitting on a gridded polar disc.

Provides fitpack_grid_polar, a derived type for fitting bicubic splines to data sampled on a polar grid \( (u_i, v_j) \) over a disc of constant radius \( r \). The coordinate mapping is:

\[ x = u \, r \cos v, \quad y = u \, r \sin v, \quad 0 \leq u \leq 1, \ -\pi \leq v \leq \pi \]

Continuity constraints at the origin and optional specification of the function value \( z_0 = f(0,0) \) are supported. Uses the pogrid core routine.

See also

Dierckx, Ch. 11, §11.1 (pp. 255–263); pogrid

Function/Subroutine Documentation

gridded_eval_many()

real(fp_real) function, dimension(size(v),size(u)) fitpack_gridded_polar::gridded_eval_many ( class(fitpack_grid_polar), 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 polar surface on a rectangular \( u \times v \) grid.

Returns f(j,i) = \( s(u_i, v_j) \) in normalized polar coordinates.

See also

bispev

gridded_eval_one()

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

private

Evaluate the gridded polar surface at a single \( (u, v) \) point.

See also

bispev

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gridded_to_disk()

subroutine fitpack_gridded_polar::gridded_to_disk ( class(fitpack_grid_polar), intent(inout) this, character(*), intent(in) filename )

private

Write gridded polar data to a text file.

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gridpolar_comm_expand()

pure subroutine fitpack_gridded_polar::gridpolar_comm_expand ( class(fitpack_grid_polar), intent(inout) this, real(fp_comm), dimension(:), intent(in) buffer )

private

Expand gridded polar data from a communication buffer.

gridpolar_comm_pack()

pure subroutine fitpack_gridded_polar::gridpolar_comm_pack ( class(fitpack_grid_polar), intent(in) this, real(fp_comm), dimension(:), intent(out) buffer )

private

Pack gridded polar data into a communication buffer.

gridpolar_comm_size()

elemental integer(fp_size) function fitpack_gridded_polar::gridpolar_comm_size ( class(fitpack_grid_polar), intent(in) this )

private

Return the communication buffer size for the gridded polar surface.

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polr_fit_automatic_knots()

integer function fitpack_gridded_polar::polr_fit_automatic_knots ( class(fitpack_grid_polar), intent(inout) this, real(fp_real), intent(in), optional smoothing, logical, intent(in), optional keep_knots )

private

Fit a smoothing gridded polar surface with automatic knot placement.

Uses the pogrid core routine. Origin continuity constraints and optional function value at the origin are configured via set_origin_BC.

See also

pogrid

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

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polr_fit_interpolating()

integer function fitpack_gridded_polar::polr_fit_interpolating ( class(fitpack_grid_polar), intent(inout) this, logical, intent(in), optional reset_knots )

private

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

See also

pogrid

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polr_fit_least_squares()

integer function fitpack_gridded_polar::polr_fit_least_squares ( class(fitpack_grid_polar), intent(inout) this, real(fp_real), intent(in), optional smoothing, logical, intent(in), optional reset_knots )

private

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

See also

pogrid

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set_origin_bc()

subroutine fitpack_gridded_polar::set_origin_bc ( class(fitpack_grid_polar), intent(inout) this, real(fp_real), intent(in), optional z0, logical, intent(in), optional exact, logical, intent(in), optional differentiable )

private

Configure origin boundary conditions for the gridded polar surface.

Parameters

[in,out]	this	The grid polar surface.
[in]	z0	Optional function value at the origin.
[in]	exact	If .true., fit the origin value exactly.
[in]	differentiable	If .true., enforce \( C^1 \) continuity at the origin.

surf_destroy()

elemental subroutine fitpack_gridded_polar::surf_destroy ( class(fitpack_grid_polar), intent(inout) this )

private

Destroy a gridded polar surface object and release all allocated memory.

surf_new_fit()

integer function fitpack_gridded_polar::surf_new_fit ( class(fitpack_grid_polar), intent(inout) this, real(fp_real), dimension(:), intent(in) u, real(fp_real), dimension(:), intent(in) v, real(fp_real), intent(in) r, real(fp_real), dimension(size(v),size(u)), intent(in) z, real(fp_real), intent(in), optional z0, real(fp_real), intent(in), optional smoothing )

private

Load new data and perform a fresh gridded polar fit.

See also

pogrid

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surf_new_from_points()

type(fitpack_grid_polar) function fitpack_gridded_polar::surf_new_from_points ( real(fp_real), dimension(:), intent(in) u, real(fp_real), dimension(:), intent(in) v, real(fp_real), intent(in) r, real(fp_real), dimension(size(v),size(u)), intent(in) z, real(fp_real), intent(in), optional z0, integer, intent(out), optional ierr )

private

Construct a gridded polar surface from data and perform a default fit.

See also

pogrid

surf_new_points()

subroutine fitpack_gridded_polar::surf_new_points ( class(fitpack_grid_polar), intent(inout) this, real(fp_real), dimension(:), intent(in) u, real(fp_real), dimension(:), intent(in) v, real(fp_real), intent(in) r, real(fp_real), dimension(size(v),size(u)), intent(in) z, real(fp_real), intent(in), optional z0 )

private

Load new gridded polar data and allocate workspace.

Parameters

[in,out]	this	The grid polar surface (destroyed and reinitialized).
[in]	u	Radial grid values \( u_i \in [0, 1] \).
[in]	v	Angular grid values \( v_j \in [-\pi, \pi] \).
[in]	r	Constant boundary radius.
[in]	z	Gridded function values z(j,i).
[in]	z0	Optional function value at the origin.

See also

pogrid

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