Bicubic spline fitter for data scattered over a general polar domain. More...

Inheritance diagram for fitpack_polar_domains::fitpack_polar:

Collaboration diagram for fitpack_polar_domains::fitpack_polar:

Public Member Functions
procedure	destroy (this)
	Clean memory.

procedure	new_points (this, x, y, z, boundary, w, boundary_bc)
	Set new points.

procedure	new_fit (this, x, y, z, boundary, w, boundary_bc, 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 polar surface with fixed knots.

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

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

generic	eval (this, x, y, ierr)
	Evaluate the polar surface at multiple Cartesian points.

procedure	comm_size (this)
	Communication interface.

procedure	comm_pack (this, buffer)
	Pack polar surface data into a communication buffer.

procedure	comm_expand (this, buffer)
	Expand polar surface data from a communication buffer.

type(fitpack_polar) function	polr_new_from_points (x, y, z, boundary, w, boundary_bc, ierr)
	Construct a polar surface from scattered data and perform a default 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	x

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

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

real(fp_real), dimension(:), allocatable	u
	Coordinates of the data points in rectangular coordinates (u,v)

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

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

integer	lwrk2 = 0

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

integer	bc_continuity_origin = 2

integer	bc_boundary = OUTSIDE_EXTRAPOLATE

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

Static Public Attributes
procedure(fitpack_polar_boundary), pointer, nopass	rad => null()
	Function that describes shape of the polar boundary: radius as a function of angle theta: x = rad(v)cos(v) , y = rad(v)sin(v), -pi <= v <= pi.

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

procedure, private	polr_eval_many (this, x, y, ierr)
	Evaluate the polar surface at multiple Cartesian points.

Detailed Description

Bicubic spline fitter for data scattered over a general polar domain.

Stores the scattered Cartesian data \( (x_i, y_i, z_i) \), the user-supplied boundary function \( r(\theta) \), optional weights, and the fitted B-spline representation. The smoothing parameter controls the trade-off between closeness of fit and smoothness, while continuity at the origin ( \( u = 0 \)) is enforced up to order \( C^0 \), \( C^1 \), or \( C^2 \).

See also: Dierckx, Ch. 11, §11.1 (pp. 255–263)

Member Function/Subroutine Documentation

◆ comm_expand()

procedure fitpack_polar_domains::fitpack_polar::comm_expand	(	class(fitpack_polar), intent(inout)	this,
		real(fp_comm), dimension(:), intent(in)	buffer )

Expand polar surface data from a communication buffer.

Here is the call graph for this function:

◆ comm_pack()

procedure fitpack_polar_domains::fitpack_polar::comm_pack	(	class(fitpack_polar), intent(in)	this,
		real(fp_comm), dimension(:), intent(out)	buffer )

Pack polar surface data into a communication buffer.

◆ comm_size()

procedure fitpack_polar_domains::fitpack_polar::comm_size ( class(fitpack_polar), intent(in) this )

Communication interface.

◆ destroy()

procedure fitpack_polar_domains::fitpack_polar::destroy ( class(fitpack_polar), intent(inout) this )

Clean memory.

◆ eval() [1/2]

generic fitpack_polar_domains::fitpack_polar::eval	(	class(fitpack_polar), intent(inout)	this,
		real(fp_real), intent(in)	x,
		real(fp_real), intent(in)	y,
		integer, intent(out), optional	ierr )

Evaluate polar domain at given x,y coordinates.

Internally transforms to normalized polar coordinates before evaluation.

See also: evapol

Here is the call graph for this function:

◆ eval() [2/2]

generic fitpack_polar_domains::fitpack_polar::eval	(	class(fitpack_polar), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		real(fp_real), dimension(size(x)), intent(in)	y,
		integer, intent(out), optional	ierr )

Evaluate the polar surface at multiple Cartesian points.

See also: evapol

◆ fit()

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

Generate/update fitting curve, with optional smoothing.

The fitting uses normalized polar coordinates \( (u, v) \) with a user-supplied boundary function \( r(\theta) \). Continuity at the origin is controlled by bc_continuity_origin.

See also: polar

◆ interpolate()

procedure fitpack_polar_domains::fitpack_polar::interpolate	(	class(fitpack_polar), intent(inout)	this,
		logical, intent(in), optional	reset_knots )

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

See also: polar

◆ least_squares()

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

Fit a least-squares polar surface with fixed knots.

See also: polar

◆ new_fit()

procedure fitpack_polar_domains::fitpack_polar::new_fit	(	class(fitpack_polar), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		real(fp_real), dimension(size(x)), intent(in)	y,
		real(fp_real), dimension(size(x)), intent(in)	z,
		procedure(fitpack_polar_boundary)	boundary,
		real(fp_real), dimension(size(x)), intent(in), optional	w,
		integer, intent(in), optional	boundary_bc,
		real(fp_real), intent(in), optional	smoothing )

Generate new fit.

See also: polar

◆ new_points()

procedure fitpack_polar_domains::fitpack_polar::new_points	(	class(fitpack_polar), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		real(fp_real), dimension(size(x)), intent(in)	y,
		real(fp_real), dimension(size(x)), intent(in)	z,
		procedure(fitpack_polar_boundary)	boundary,
		real(fp_real), dimension(size(x)), intent(in), optional	w,
		integer, intent(in), optional	boundary_bc )

Set new points.

Parameters

[in,out]	this	The polar surface (destroyed and reinitialized).
[in]	x	Cartesian x coordinates.
[in]	y	Cartesian y coordinates, same size as `x`.
[in]	z	Function values, same size as `x`.
[in]	boundary	Boundary function \( r(\theta) \) defining the polar domain.
[in]	w	Optional positive weights.
[in]	boundary_bc	Optional boundary extrapolation flag.

See also: polar

◆ polr_eval_many()

procedure, private fitpack_polar_domains::fitpack_polar::polr_eval_many	(	class(fitpack_polar), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		real(fp_real), dimension(size(x)), intent(in)	y,
		integer, intent(out), optional	ierr )

private

Evaluate the polar surface at multiple Cartesian points.

See also: evapol

◆ polr_eval_one()

procedure, private fitpack_polar_domains::fitpack_polar::polr_eval_one	(	class(fitpack_polar), intent(inout)	this,
		real(fp_real), intent(in)	x,
		real(fp_real), intent(in)	y,
		integer, intent(out), optional	ierr )

private

Evaluate polar domain at given x,y coordinates.

Internally transforms to normalized polar coordinates before evaluation.

See also: evapol

◆ polr_new_from_points()

type(fitpack_polar) function fitpack_polar_domains::fitpack_polar::polr_new_from_points	(	real(fp_real), dimension(:), intent(in)	x,
		real(fp_real), dimension(size(x)), intent(in)	y,
		real(fp_real), dimension(size(x)), intent(in)	z,
		procedure(fitpack_polar_boundary)	boundary,
		real(fp_real), dimension(size(x)), intent(in), optional	w,
		integer, intent(in), optional	boundary_bc,
		integer, intent(out), optional	ierr )

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

See also: polar

Here is the call graph for this function:

Member Data Documentation

◆ bc_boundary

integer fitpack_polar_domains::fitpack_polar::bc_boundary = OUTSIDE_EXTRAPOLATE

◆ bc_continuity_origin

integer fitpack_polar_domains::fitpack_polar::bc_continuity_origin = 2

◆ knots

integer, dimension(2) fitpack_polar_domains::fitpack_polar::knots = 0

◆ lwrk2

integer fitpack_polar_domains::fitpack_polar::lwrk2 = 0

◆ m

integer fitpack_polar_domains::fitpack_polar::m = 0

Scattered data points.

◆ nest

integer, dimension(2) fitpack_polar_domains::fitpack_polar::nest = 0

◆ nmax

integer fitpack_polar_domains::fitpack_polar::nmax = 0

◆ rad

procedure(fitpack_polar_boundary), pointer, nopass fitpack_polar_domains::fitpack_polar::rad => null()

static

Function that describes shape of the polar boundary: radius as a function of angle theta: x = rad(v)*cos(v) , y = rad(v)*sin(v), -pi <= v <= pi.

◆ t

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

◆ u

real(fp_real), dimension(:), allocatable fitpack_polar_domains::fitpack_polar::u

Coordinates of the data points in rectangular coordinates (u,v)

◆ v

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

◆ w

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

◆ wrk2

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

◆ x

real(fp_real), dimension(:), allocatable fitpack_polar_domains::fitpack_polar::x

◆ y

real(fp_real), dimension(:), allocatable fitpack_polar_domains::fitpack_polar::y

◆ z

real(fp_real), dimension(:), allocatable fitpack_polar_domains::fitpack_polar::z

Function values at the points.

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

fitpack_polar.f90

Public Member Functions

Public Attributes

Static 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()

◆ polr_eval_many()

◆ polr_eval_one()

◆ polr_new_from_points()

Member Data Documentation

◆ bc_boundary

◆ bc_continuity_origin

◆ knots

◆ lwrk2

◆ m

◆ nest

◆ nmax

◆ rad

◆ t

◆ u

◆ v

◆ w

◆ wrk2

◆ x

◆ y

◆ z