Bicubic parametric surface fitter in \( \mathbb{R}^d \). More...

Inheritance diagram for fitpack_parametric_surfaces::fitpack_parametric_surface:

Collaboration diagram for fitpack_parametric_surfaces::fitpack_parametric_surface:

Public Member Functions
procedure	destroy (this)
	Clean memory.

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

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

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

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

procedure	least_squares (this, u_knots, v_knots, smoothing, reset_knots)
	Fit a least-squares parametric surface with current or user-supplied knots.

generic	eval (this, u, v, ierr)
	Evaluate curve at given coordinates.

generic	eval (this, u, v, ierr)
	Evaluate the parametric surface on a rectangular parameter grid.

procedure	comm_size (this)
	Parallel communication interface.

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

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

type(fitpack_parametric_surface) function	new_from_points (u, v, z, periodic_bc, ierr)
	Construct a parametric surface from gridded 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	idim = 0
	Number of dimensions.

real(fp_real), dimension(:), allocatable	u
	Parameter grid values.

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

real(fp_real), dimension(:,:,:), allocatable	z
	idim-dimensional function values [size(v),size(u),idim]

logical, dimension(2)	periodic_dim = .false.
	Flags to determine whether dimensions u,v are periodic.

integer, dimension(2)	nest = 0
	Estimated and actual number of knots and their allocations.

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	surf_eval_one (this, u, v, ierr)
	Evaluate curve at given coordinates.

procedure, private	surf_eval_grid (this, u, v, ierr)
	Evaluate the parametric surface on a rectangular parameter grid.

Detailed Description

Bicubic parametric surface fitter in \( \mathbb{R}^d \).

Fits a tensor-product bicubic spline surface \( \mathbf{s}(u, v) = (s_1(u,v), \ldots, s_d(u,v)) \) through data points \( \mathbf{z}(j, i) \in \mathbb{R}^d \) given on a rectangular parameter grid \( (u_i, v_j) \). Each dimension \( u \) and \( v \) may be flagged as periodic. Uses the parsur core routine.

See also: Dierckx, Ch. 10, §10.2 (pp. 241–254)

Member Function/Subroutine Documentation

◆ comm_expand()

procedure fitpack_parametric_surfaces::fitpack_parametric_surface::comm_expand	(	class(fitpack_parametric_surface), intent(inout)	this,
		real(fp_comm), dimension(:), intent(in)	buffer )

Expand parametric surface data from a communication buffer.

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◆ comm_pack()

procedure fitpack_parametric_surfaces::fitpack_parametric_surface::comm_pack	(	class(fitpack_parametric_surface), intent(in)	this,
		real(fp_comm), dimension(:), intent(out)	buffer )

Pack parametric surface data into a communication buffer.

◆ comm_size()

procedure fitpack_parametric_surfaces::fitpack_parametric_surface::comm_size ( class(fitpack_parametric_surface), intent(in) this )

Parallel communication interface.

◆ destroy()

procedure fitpack_parametric_surfaces::fitpack_parametric_surface::destroy ( class(fitpack_parametric_surface), intent(inout) this )

Clean memory.

◆ eval() [1/2]

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

Evaluate curve at given coordinates.

Returns: Point \( \mathbf{s}(u, v) \in \mathbb{R}^d \).

See also: surev

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◆ eval() [2/2]

generic fitpack_parametric_surfaces::fitpack_parametric_surface::eval	(	class(fitpack_parametric_surface), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	u,
		real(fp_real), dimension(:), intent(in)	v,
		integer, intent(out), optional	ierr )

Evaluate the parametric surface on a rectangular parameter grid.

Returns f(j,i,l) = \( s_l(u_i, v_j) \).

See also: surev

◆ fit()

procedure fitpack_parametric_surfaces::fitpack_parametric_surface::fit	(	class(fitpack_parametric_surface), intent(inout)	this,
		real(fp_real), intent(in), optional	smoothing,
		logical, dimension(2), intent(in), optional	periodic,
		logical, intent(in), optional	keep_knots )

Generate/update fitting curve, with optional smoothing.

See also: parsur

◆ interpolate()

procedure fitpack_parametric_surfaces::fitpack_parametric_surface::interpolate	(	class(fitpack_parametric_surface), intent(inout)	this,
		logical, intent(in), optional	reset_knots )

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

See also: parsur

◆ least_squares()

procedure fitpack_parametric_surfaces::fitpack_parametric_surface::least_squares	(	class(fitpack_parametric_surface), intent(inout)	this,
		real(fp_real), dimension(:), intent(in), optional	u_knots,
		real(fp_real), dimension(:), intent(in), optional	v_knots,
		real(fp_real), intent(in), optional	smoothing,
		logical, intent(in), optional	reset_knots )

Fit a least-squares parametric surface with current or user-supplied knots.

Optional u_knots and v_knots set interior knots directly. If omitted, the current knot vectors are used.

See also: parsur

◆ new_fit()

procedure fitpack_parametric_surfaces::fitpack_parametric_surface::new_fit	(	class(fitpack_parametric_surface), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	u,
		real(fp_real), dimension(:), intent(in)	v,
		real(fp_real), dimension(:,:,:), intent(in)	z,
		real(fp_real), intent(in), optional	smoothing,
		logical, dimension(2), intent(in), optional	periodic_bc )

Generate new fit.

See also: parsur

◆ new_from_points()

type(fitpack_parametric_surface) function fitpack_parametric_surfaces::fitpack_parametric_surface::new_from_points	(	real(fp_real), dimension(:), intent(in)	u,
		real(fp_real), dimension(:), intent(in)	v,
		real(fp_real), dimension(:,:,:), intent(in)	z,
		logical, dimension(2), intent(in), optional	periodic_bc,
		integer, intent(out), optional	ierr )

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

Parameters

[in]	u	Parameter grid in the u direction.
[in]	v	Parameter grid in the v direction.
[in]	z	Data values `z(j,i,l)` for component `l` at `(u(i),v(j))`.
[in]	periodic_BC	Optional periodicity flags `[u_periodic, v_periodic]`.
[out]	ierr	Optional error flag.

Returns: Fitted parametric surface object.

See also: parsur

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◆ new_points()

procedure fitpack_parametric_surfaces::fitpack_parametric_surface::new_points	(	class(fitpack_parametric_surface), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	u,
		real(fp_real), dimension(:), intent(in)	v,
		real(fp_real), dimension(:,:,:), intent(in)	z,
		logical, dimension(2), intent(in), optional	periodic_bc )

Set new points.

See also: parsur

◆ surf_eval_grid()

procedure, private fitpack_parametric_surfaces::fitpack_parametric_surface::surf_eval_grid	(	class(fitpack_parametric_surface), 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 parametric surface on a rectangular parameter grid.

Returns f(j,i,l) = \( s_l(u_i, v_j) \).

See also: surev

◆ surf_eval_one()

procedure, private fitpack_parametric_surfaces::fitpack_parametric_surface::surf_eval_one	(	class(fitpack_parametric_surface), intent(inout)	this,
		real(fp_real), intent(in)	u,
		real(fp_real), intent(in)	v,
		integer, intent(out), optional	ierr )

private

Evaluate curve at given coordinates.

Returns: Point \( \mathbf{s}(u, v) \in \mathbb{R}^d \).

See also: surev

Member Data Documentation

◆ idim

integer fitpack_parametric_surfaces::fitpack_parametric_surface::idim = 0

Number of dimensions.

◆ knots

integer, dimension(2) fitpack_parametric_surfaces::fitpack_parametric_surface::knots = 0

◆ nest

integer, dimension(2) fitpack_parametric_surfaces::fitpack_parametric_surface::nest = 0

Estimated and actual number of knots and their allocations.

◆ nmax

integer fitpack_parametric_surfaces::fitpack_parametric_surface::nmax = 0

◆ periodic_dim

logical, dimension(2) fitpack_parametric_surfaces::fitpack_parametric_surface::periodic_dim = .false.

Flags to determine whether dimensions u,v are periodic.

◆ t

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

◆ u

real(fp_real), dimension(:), allocatable fitpack_parametric_surfaces::fitpack_parametric_surface::u

Parameter grid values.

◆ v

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

◆ z

real(fp_real), dimension(:,:,:), allocatable fitpack_parametric_surfaces::fitpack_parametric_surface::z

idim-dimensional function values [size(v),size(u),idim]

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

fitpack_parametric_surfaces.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()

◆ interpolate()

◆ least_squares()

◆ new_fit()

◆ new_from_points()

◆ new_points()

◆ surf_eval_grid()

◆ surf_eval_one()

Member Data Documentation

◆ idim

◆ knots

◆ nest

◆ nmax

◆ periodic_dim

◆ t

◆ u

◆ v

◆ z