Open parametric curve fitter in \( \mathbb{R}^d \). More...

Inheritance diagram for fitpack_parametric_curves::fitpack_parametric_curve:

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Collaboration diagram for fitpack_parametric_curves::fitpack_parametric_curve:

Public Member Functions
procedure	destroy (this)
	Clean memory.

procedure	new_points (this, x, u, w)
	Set new points.

procedure	set_default_parameters (this)
	Compute default parameter values from cumulative chord lengths.

procedure	new_fit (this, x, u, w, smoothing, order)
	Generate new fit.

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

procedure	interpolate (this, order, reset_knots)
	Fit an interpolating parametric spline ( \( s = 0 \)) through the data points.

procedure	least_squares (this, smoothing, reset_knots)
	Fit a least-squares parametric spline with fixed knots.

procedure	eval_one (this, u, ierr)
	Evaluate curve at given coordinates.

procedure	eval_many (this, u, ierr)
	Evaluate the parametric curve at multiple parameter values.

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

generic	eval (this, u, ierr)
	Evaluate the parametric curve at multiple parameter values.

generic	dfdx (this, u, order, ierr)
	Evaluate derivative at given coordinates.

generic	dfdx (this, u, order, ierr)
	Evaluate the k-th derivative at multiple parameter values.

generic	dfdx_all (this, u, ierr)
	Evaluate all derivatives \( \mathbf{s}^{(j)}(u) \) for \( j = 0, \ldots, k \).

procedure	comm_size (this)
	Parallel communication interface (size/pack/expand)

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

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

type(fitpack_parametric_curve) function	new_from_points (x, u, w, ierr)
	Construct a parametric curve from data points 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
	Number of points.

integer	idim = 0
	Number of dimensions.

real(fp_real), dimension(:,:), allocatable	x
	The data points.

logical	has_params = .false.
	Parameter values: one for each point. They may be optional, in which case, they will be internally calculated by fitpack.

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

integer	order = 3
	Spline degree.

real(fp_real)	ubegin = zero
	Interval boundaries.

real(fp_real)	uend = zero

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

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

integer	nest = 0

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

integer	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	curve_derivative (this, u, order, ierr)
	Evaluate derivative at given coordinates.

procedure, private	curve_derivatives (this, u, order, ierr)
	Evaluate the k-th derivative at multiple parameter values.

procedure, private	curve_all_derivatives (this, u, ierr)
	Evaluate all derivatives \( \mathbf{s}^{(j)}(u) \) for \( j = 0, \ldots, k \).

Detailed Description

Open parametric curve fitter in \( \mathbb{R}^d \).

Fits a parametric spline curve \( \mathbf{s}(u) = (s_1(u), \ldots, s_d(u)) \) through \( m \) data points \( \mathbf{x}_i \in \mathbb{R}^d \) associated with strictly increasing parameter values \( u_i \). If no parameter values are provided, they are computed automatically from cumulative chord lengths.

See also: Dierckx, Ch. 9, §9.1 (pp. 199–212); parcur

Member Function/Subroutine Documentation

◆ comm_expand()

procedure fitpack_parametric_curves::fitpack_parametric_curve::comm_expand	(	class(fitpack_parametric_curve), intent(inout)	this,
		real(fp_comm), dimension(:), intent(in)	buffer )

Expand parametric curve data from a communication buffer.

◆ comm_pack()

procedure fitpack_parametric_curves::fitpack_parametric_curve::comm_pack	(	class(fitpack_parametric_curve), intent(in)	this,
		real(fp_comm), dimension(:), intent(out)	buffer )

Pack parametric curve data into a communication buffer.

◆ comm_size()

procedure fitpack_parametric_curves::fitpack_parametric_curve::comm_size ( class(fitpack_parametric_curve), intent(in) this )

Parallel communication interface (size/pack/expand)

◆ curve_all_derivatives()

procedure, private fitpack_parametric_curves::fitpack_parametric_curve::curve_all_derivatives	(	class(fitpack_parametric_curve), intent(inout)	this,
		real(fp_real), intent(in)	u,
		integer, intent(out), optional	ierr )

private

Evaluate all derivatives \( \mathbf{s}^{(j)}(u) \) for \( j = 0, \ldots, k \).

Parameters

[in,out]	this	The fitted parametric curve.
[in]	u	Parameter value.
[out]	ierr	Optional error flag.

Returns: Array \( (d \times (k+1)) \) of derivatives at u.

See also: cualde

◆ curve_derivative()

procedure, private fitpack_parametric_curves::fitpack_parametric_curve::curve_derivative	(	class(fitpack_parametric_curve), intent(inout)	this,
		real(fp_real), intent(in)	u,
		integer, intent(in)	order,
		integer, intent(out), optional	ierr )

private

Evaluate derivative at given coordinates.

Parameters

[in,out]	this	The fitted parametric curve.
[in]	u	Parameter value.
[in]	order	Derivative order ( \( 0 \leq \text{order} \leq k \)).
[out]	ierr	Optional error flag.

Returns: Derivative vector \( \mathbf{s}^{(\text{order})}(u) \in \mathbb{R}^d \).

See also: cualde

◆ curve_derivatives()

procedure, private fitpack_parametric_curves::fitpack_parametric_curve::curve_derivatives	(	class(fitpack_parametric_curve), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	u,
		integer, intent(in)	order,
		integer, intent(out), optional	ierr )

private

Evaluate the k-th derivative at multiple parameter values.

Parameters

[in,out]	this	The fitted parametric curve.
[in]	u	Array of parameter values.
[in]	order	Derivative order.
[out]	ierr	Optional error flag.

Returns: Array \( (d \times m) \) of derivative vectors.

See also: cualde

◆ destroy()

procedure fitpack_parametric_curves::fitpack_parametric_curve::destroy ( class(fitpack_parametric_curve), intent(inout) this )

Clean memory.

◆ dfdx() [1/2]

generic fitpack_parametric_curves::fitpack_parametric_curve::dfdx	(	class(fitpack_parametric_curve), intent(inout)	this,
		real(fp_real), intent(in)	u,
		integer, intent(in)	order,
		integer, intent(out), optional	ierr )

Evaluate derivative at given coordinates.

Parameters

[in,out]	this	The fitted parametric curve.
[in]	u	Parameter value.
[in]	order	Derivative order ( \( 0 \leq \text{order} \leq k \)).
[out]	ierr	Optional error flag.

Returns: Derivative vector \( \mathbf{s}^{(\text{order})}(u) \in \mathbb{R}^d \).

See also: cualde

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◆ dfdx() [2/2]

generic fitpack_parametric_curves::fitpack_parametric_curve::dfdx	(	class(fitpack_parametric_curve), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	u,
		integer, intent(in)	order,
		integer, intent(out), optional	ierr )

Evaluate the k-th derivative at multiple parameter values.

Parameters

[in,out]	this	The fitted parametric curve.
[in]	u	Array of parameter values.
[in]	order	Derivative order.
[out]	ierr	Optional error flag.

Returns: Array \( (d \times m) \) of derivative vectors.

See also: cualde

◆ dfdx_all()

generic fitpack_parametric_curves::fitpack_parametric_curve::dfdx_all	(	class(fitpack_parametric_curve), intent(inout)	this,
		real(fp_real), intent(in)	u,
		integer, intent(out), optional	ierr )

Evaluate all derivatives \( \mathbf{s}^{(j)}(u) \) for \( j = 0, \ldots, k \).

Parameters

[in,out]	this	The fitted parametric curve.
[in]	u	Parameter value.
[out]	ierr	Optional error flag.

Returns: Array \( (d \times (k+1)) \) of derivatives at u.

See also: cualde

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◆ eval() [1/2]

generic fitpack_parametric_curves::fitpack_parametric_curve::eval	(	class(fitpack_parametric_curve), intent(inout)	this,
		real(fp_real), intent(in)	u,
		integer, intent(out), optional	ierr )

Evaluate curve at given coordinates.

Parameters

[in,out]	this	The fitted parametric curve.
[in]	u	Parameter value.
[out]	ierr	Optional error flag.

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

See also: curev

◆ eval() [2/2]

generic fitpack_parametric_curves::fitpack_parametric_curve::eval	(	class(fitpack_parametric_curve), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	u,
		integer, intent(out), optional	ierr )

Evaluate the parametric curve at multiple parameter values.

Parameters

[in,out]	this	The fitted parametric curve.
[in]	u	Array of parameter values.
[out]	ierr	Optional error flag.

Returns: Points \( \mathbf{s}(u_i) \) as columns of a \( d \times m \) array.

See also: curev

◆ eval_many()

procedure fitpack_parametric_curves::fitpack_parametric_curve::eval_many	(	class(fitpack_parametric_curve), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	u,
		integer, intent(out), optional	ierr )

Evaluate the parametric curve at multiple parameter values.

Parameters

[in,out]	this	The fitted parametric curve.
[in]	u	Array of parameter values.
[out]	ierr	Optional error flag.

Returns: Points \( \mathbf{s}(u_i) \) as columns of a \( d \times m \) array.

See also: curev

◆ eval_one()

procedure fitpack_parametric_curves::fitpack_parametric_curve::eval_one	(	class(fitpack_parametric_curve), intent(inout)	this,
		real(fp_real), intent(in)	u,
		integer, intent(out), optional	ierr )

Evaluate curve at given coordinates.

Parameters

[in,out]	this	The fitted parametric curve.
[in]	u	Parameter value.
[out]	ierr	Optional error flag.

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

See also: curev

◆ fit()

procedure fitpack_parametric_curves::fitpack_parametric_curve::fit	(	class(fitpack_parametric_curve), intent(inout)	this,
		real(fp_real), intent(in), optional	smoothing,
		integer(fp_size), intent(in), optional	order,
		logical, intent(in), optional	keep_knots )

Generate/update fitting curve, with optional smoothing.

Dispatches to parcur (open), clocur (closed), or concur (constrained) depending on the dynamic type.

See also: parcur, clocur, concur

◆ interpolate()

procedure fitpack_parametric_curves::fitpack_parametric_curve::interpolate	(	class(fitpack_parametric_curve), intent(inout)	this,
		integer(fp_size), intent(in), optional	order,
		logical, intent(in), optional	reset_knots )

Fit an interpolating parametric spline ( \( s = 0 \)) through the data points.

See also: parcur, clocur, concur

◆ least_squares()

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

Fit a least-squares parametric spline with fixed knots.

See also: parcur, clocur, concur

◆ new_fit()

procedure fitpack_parametric_curves::fitpack_parametric_curve::new_fit	(	class(fitpack_parametric_curve), intent(inout)	this,
		real (fp_real), dimension(:,:), intent(in)	x,
		real (fp_real), dimension(size(x,2)), intent(in), optional	u,
		real (fp_real), dimension(size(x,2)), intent(in), optional	w,
		real (fp_real), intent(in), optional	smoothing,
		integer(fp_size), intent(in), optional	order )

Generate new fit.

See also: parcur, clocur, concur

◆ new_from_points()

type(fitpack_parametric_curve) function fitpack_parametric_curves::fitpack_parametric_curve::new_from_points	(	real(fp_real), dimension(:,:), intent(in)	x,
		real(fp_real), dimension(size(x,2)), intent(in), optional	u,
		real(fp_real), dimension(size(x,2)), intent(in), optional	w,
		integer, intent(out), optional	ierr )

Construct a parametric curve from data points and perform a default fit.

Parameters

[in]	x	Data points \( (d \times m) \): each column is a point in \( \mathbb{R}^d \).
[in]	u	Optional parameter values (must be strictly increasing). If omitted, computed from cumulative chord lengths.
[in]	w	Optional positive weights, one per data point.
[out]	ierr	Optional error flag.

Returns: Fitted parametric curve object.

See also: parcur

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◆ new_points()

procedure fitpack_parametric_curves::fitpack_parametric_curve::new_points	(	class(fitpack_parametric_curve), intent(inout)	this,
		real(fp_real), dimension(:,:), intent(in)	x,
		real(fp_real), dimension(size(x,2)), intent(in), optional	u,
		real(fp_real), dimension(size(x,2)), intent(in), optional	w )

Set new points.

Parameters

[in,out]	this	The parametric curve (destroyed and reinitialized).
[in]	x	Data points \( (d \times m) \): each column is a point.
[in]	u	Optional parameter values. If omitted, computed from chord lengths.
[in]	w	Optional positive weights.

See also: parcur, clocur, concur

◆ set_default_parameters()

procedure fitpack_parametric_curves::fitpack_parametric_curve::set_default_parameters ( class(fitpack_parametric_curve), intent(inout) this )

Compute default parameter values from cumulative chord lengths.

Sets \( u_i \) to normalized cumulative Euclidean distances between consecutive data points, so that \( u_1 = 0 \) and \( u_m = 1 \).

Member Data Documentation

◆ dd

real(fp_real), dimension(:,:), allocatable fitpack_parametric_curves::fitpack_parametric_curve::dd

◆ has_params

logical fitpack_parametric_curves::fitpack_parametric_curve::has_params = .false.

Parameter values: one for each point. They may be optional, in which case, they will be internally calculated by fitpack.

◆ idim

integer fitpack_parametric_curves::fitpack_parametric_curve::idim = 0

Number of dimensions.

◆ knots

integer fitpack_parametric_curves::fitpack_parametric_curve::knots = 0

◆ m

integer fitpack_parametric_curves::fitpack_parametric_curve::m = 0

Number of points.

◆ nest

integer fitpack_parametric_curves::fitpack_parametric_curve::nest = 0

◆ order

integer fitpack_parametric_curves::fitpack_parametric_curve::order = 3

Spline degree.

◆ sp

real(fp_real), dimension(:), allocatable fitpack_parametric_curves::fitpack_parametric_curve::sp

◆ t

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

◆ u

real(fp_real), dimension(:), allocatable fitpack_parametric_curves::fitpack_parametric_curve::u

◆ ubegin

real(fp_real) fitpack_parametric_curves::fitpack_parametric_curve::ubegin = zero

Interval boundaries.

◆ uend

real(fp_real) fitpack_parametric_curves::fitpack_parametric_curve::uend = zero

◆ w

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

◆ x

real(fp_real), dimension(:,:), allocatable fitpack_parametric_curves::fitpack_parametric_curve::x

The data points.

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

fitpack_parametric.f90

Public Member Functions

Public Attributes

Private Member Functions

Detailed Description

Member Function/Subroutine Documentation

◆ comm_expand()

◆ comm_pack()

◆ comm_size()

◆ curve_all_derivatives()

◆ curve_derivative()

◆ curve_derivatives()

◆ destroy()

◆ dfdx() [1/2]

◆ dfdx() [2/2]

◆ dfdx_all()

◆ eval() [1/2]

◆ eval() [2/2]

◆ eval_many()

◆ eval_one()

◆ fit()

◆ interpolate()

◆ least_squares()

◆ new_fit()

◆ new_from_points()

◆ new_points()

◆ set_default_parameters()

Member Data Documentation

◆ dd

◆ has_params

◆ idim

◆ knots

◆ m

◆ nest

◆ order

◆ sp

◆ t

◆ u

◆ ubegin

◆ uend

◆ w

◆ x