Bicubic spline fitter for data on a gridded polar disc. More...

Inheritance diagram for fitpack_gridded_polar::fitpack_grid_polar:

Collaboration diagram for fitpack_gridded_polar::fitpack_grid_polar:

Public Member Functions
procedure	destroy (this)
	Clean memory.

procedure	new_points (this, u, v, r, z, z0)
	Set new points.

procedure	new_fit (this, u, v, r, z, z0, smoothing)
	Generate new fit.

procedure	set_origin_bc (this, z0, exact, differentiable)
	Set origin BC.

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 polar surface with fixed knots.

procedure	interpolate (this, reset_knots)
	Fit an interpolating gridded polar 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 polar surface on a rectangular \( u \times v \) grid.

procedure	comm_size (this)
	Parallel communication interface.

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

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

procedure	write (this, filename)
	Write to disk.

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.

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)	r = zero

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

real(fp_real)	z0 = zero
	Function value at the origin.

logical	z0_present = .false.
	Fit spline to z0 exactly at the origin.

logical	z0_exact = .false.

logical	z0_zero_gradient = .false.
	Decide if the origin should have zero-gradient BCs in both u and v.

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

integer	nmax = 0

integer, dimension(2)	knots = 0

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

integer	bc_continuity_origin = 1

integer	bc_boundary = OUTSIDE_EXTRAPOLATE

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 polar surface on a rectangular \( u \times v \) grid.

Detailed Description

Bicubic spline fitter for data on a gridded polar disc.

Stores the grid coordinates \( u_i \), \( v_j \), the constant boundary radius \( r \), gridded function values \( z(i, j) \), and the fitted B-spline representation. The origin value \( z_0 \) may optionally be prescribed (exactly or approximately), and zero-gradient boundary conditions at the origin can be enforced.

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

Member Function/Subroutine Documentation

◆ comm_expand()

procedure fitpack_gridded_polar::fitpack_grid_polar::comm_expand	(	class(fitpack_grid_polar), intent(inout)	this,
		real(fp_comm), dimension(:), intent(in)	buffer )

Expand gridded polar data from a communication buffer.

◆ comm_pack()

procedure fitpack_gridded_polar::fitpack_grid_polar::comm_pack	(	class(fitpack_grid_polar), intent(in)	this,
		real(fp_comm), dimension(:), intent(out)	buffer )

Pack gridded polar data into a communication buffer.

◆ comm_size()

procedure fitpack_gridded_polar::fitpack_grid_polar::comm_size ( class(fitpack_grid_polar), intent(in) this )

Parallel communication interface.

◆ destroy()

procedure fitpack_gridded_polar::fitpack_grid_polar::destroy ( class(fitpack_grid_polar), intent(inout) this )

Clean memory.

◆ eval() [1/2]

generic fitpack_gridded_polar::fitpack_grid_polar::eval	(	class(fitpack_grid_polar), 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.

See also: bispev

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◆ eval() [2/2]

generic fitpack_gridded_polar::fitpack_grid_polar::eval	(	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 )

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

◆ fit()

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

Generate/update fitting curve, with optional smoothing.

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

See also: pogrid

◆ gridded_eval_many()

procedure, private fitpack_gridded_polar::fitpack_grid_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()

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

See also: bispev

◆ interpolate()

procedure fitpack_gridded_polar::fitpack_grid_polar::interpolate	(	class(fitpack_grid_polar), intent(inout)	this,
		logical, intent(in), optional	reset_knots )

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

See also: pogrid

◆ least_squares()

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

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

See also: pogrid

◆ new_fit()

procedure fitpack_gridded_polar::fitpack_grid_polar::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 )

Generate new fit.

See also: pogrid

◆ new_points()

procedure fitpack_gridded_polar::fitpack_grid_polar::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 )

Set new points.

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

◆ set_origin_bc()

procedure fitpack_gridded_polar::fitpack_grid_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 )

Set origin BC.

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_new_from_points()

type(fitpack_grid_polar) function fitpack_gridded_polar::fitpack_grid_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 )

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

See also: pogrid

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◆ write()

procedure fitpack_gridded_polar::fitpack_grid_polar::write	(	class(fitpack_grid_polar), intent(inout)	this,
		character(*), intent(in)	filename )

Write to disk.

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Member Data Documentation

◆ bc_boundary

integer fitpack_gridded_polar::fitpack_grid_polar::bc_boundary = OUTSIDE_EXTRAPOLATE

◆ bc_continuity_origin

integer fitpack_gridded_polar::fitpack_grid_polar::bc_continuity_origin = 1

◆ knots

integer, dimension(2) fitpack_gridded_polar::fitpack_grid_polar::knots = 0

◆ nest

integer, dimension(2) fitpack_gridded_polar::fitpack_grid_polar::nest = 0

Node weights are not allowed.

◆ nmax

integer fitpack_gridded_polar::fitpack_grid_polar::nmax = 0

◆ r

real(fp_real) fitpack_gridded_polar::fitpack_grid_polar::r = zero

◆ t

real(fp_real), dimension(:,:), allocatable fitpack_gridded_polar::fitpack_grid_polar::t

◆ u

real(fp_real), dimension(:), allocatable fitpack_gridded_polar::fitpack_grid_polar::u

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

◆ v

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

◆ z

real(fp_real), dimension(:,:), allocatable fitpack_gridded_polar::fitpack_grid_polar::z

Function values at the points.

◆ z0

real(fp_real) fitpack_gridded_polar::fitpack_grid_polar::z0 = zero

Function value at the origin.

◆ z0_exact

logical fitpack_gridded_polar::fitpack_grid_polar::z0_exact = .false.

◆ z0_present

logical fitpack_gridded_polar::fitpack_grid_polar::z0_present = .false.

Fit spline to z0 exactly at the origin.

◆ z0_zero_gradient

logical fitpack_gridded_polar::fitpack_grid_polar::z0_zero_gradient = .false.

Decide if the origin should have zero-gradient BCs in both u and v.

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

fitpack_gridded_polar.f90

Public Member Functions

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()

◆ gridded_eval_many()

◆ gridded_eval_one()

◆ interpolate()

◆ least_squares()

◆ new_fit()

◆ new_points()

◆ set_origin_bc()

◆ surf_new_from_points()

◆ write()

Member Data Documentation

◆ bc_boundary

◆ bc_continuity_origin

◆ knots

◆ nest

◆ nmax

◆ r

◆ t

◆ u

◆ v

◆ z

◆ z0

◆ z0_exact

◆ z0_present

◆ z0_zero_gradient