Univariate spline curve \( y = s(x) \). More...

Inheritance diagram for fitpack_curves::fitpack_curve:

[legend]

Collaboration diagram for fitpack_curves::fitpack_curve:

Public Member Functions
procedure	destroy (this)
	Clean memory.

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

procedure	new_fit (this, x, y, 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 spline ( \( s = 0 \)) through the data points.

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

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

generic	eval (this, x)
	Evaluate the spline at a single point (pure, returns NaN on error).

generic	eval (this, x, ierr)
	Evaluate the spline at multiple points (with error flag).

generic	eval (this, x)
	Evaluate the spline at multiple points (pure, returns NaN on error).

procedure	integral (this, from, to)
	Integrate.

procedure	fourier_coefficients (this, alpha, a, b, ierr)
	Fourier coefficients.

procedure	zeros (this, ierr)
	Find the zeros of a spline s(x), only if it is cubic.

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

generic	dfdx (this, x, order, ierr)
	Evaluate the k-th derivative at multiple points (with error flag).

generic	dfdx_all (this, x, ierr)
	Evaluate all derivatives \( s^{(j)}(x) \) for \( j = 0, \ldots, k \) (with error flag).

generic	dfdx_all (this, x)
	Evaluate all derivatives \( s^{(j)}(x) \) for \( j = 0, \ldots, k \) (pure, NaN on error).

generic	insert_knot (this, x, ierr)
	Insert knot(s) into the spline representation.

generic	insert_knot (this, x, ierr)
	Insert multiple knots into the B-spline representation.

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

procedure	comm_pack (this, buffer)
	Pack curve data into a communication buffer for parallel transfer.

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

type(fitpack_curve) function	new_from_points (x, y, w, ierr)
	Construct a fitpack_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(fp_size)	m = 0
	The data points.

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

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

integer(fp_size)	order = 3
	Spline degree.

real(fp_real)	xleft
	Interval boundaries.

real(fp_real)	xright

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

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

integer(fp_size)	nest = 0

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

integer(fp_flag)	bc = OUTSIDE_NEAREST_BND

integer(fp_size)	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_eval_one (this, x, ierr)
	Evaluate curve at given coordinates.

procedure, private	curve_eval_one_noerr (this, x)
	Evaluate the spline at a single point (pure, returns NaN on error).

procedure, private	curve_eval_many (this, x, ierr)
	Evaluate the spline at multiple points (with error flag).

procedure, private	curve_eval_many_pure (this, x)
	Evaluate the spline at multiple points (pure, returns NaN on error).

procedure, private	curve_derivative (this, x, order, ierr)
	Evaluate derivative at given coordinates.

procedure, private	curve_derivatives (this, x, order, ierr)
	Evaluate the k-th derivative at multiple points (with error flag).

procedure, private	curve_all_derivatives (this, x, ierr)
	Evaluate all derivatives \( s^{(j)}(x) \) for \( j = 0, \ldots, k \) (with error flag).

procedure, private	curve_all_derivatives_pure (this, x)
	Evaluate all derivatives \( s^{(j)}(x) \) for \( j = 0, \ldots, k \) (pure, NaN on error).

procedure, private	curve_insert_knot_one (this, x, ierr)
	Insert knot(s) into the spline representation.

procedure, private	curve_insert_knot_many (this, x, ierr)
	Insert multiple knots into the B-spline representation.

Detailed Description

Univariate spline curve \( y = s(x) \).

Default constructor: create a curve from data points and fit it.

Fits a smoothing or interpolating spline of degree \( k \) (default 3 = cubic) to weighted data points \( (x_i, y_i, w_i) \). After fitting, the curve can be evaluated, differentiated, integrated, and its zeros found.

Typical usage:

type(fitpack_curve) :: curve
curve = fitpack_curve(x, y)          ! construct and fit
y_eval = curve%eval(x_new)           ! evaluate at new points
dy = curve%dfdx(x_new, order=1)      ! first derivative
area = curve%integral(a, b)          ! definite integral

Member Function/Subroutine Documentation

◆ comm_expand()

procedure fitpack_curves::fitpack_curve::comm_expand	(	class(fitpack_curve), intent(inout)	this,
		real(fp_comm), dimension(:), intent(in)	buffer )

Expand curve data from a communication buffer.

◆ comm_pack()

procedure fitpack_curves::fitpack_curve::comm_pack	(	class(fitpack_curve), intent(in)	this,
		real(fp_comm), dimension(:), intent(out)	buffer )

Pack curve data into a communication buffer for parallel transfer.

◆ comm_size()

procedure fitpack_curves::fitpack_curve::comm_size ( class(fitpack_curve), intent(in) this )

Parallel communication interface (size/pack/expand)

◆ curve_all_derivatives()

procedure, private fitpack_curves::fitpack_curve::curve_all_derivatives	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), intent(in)	x,
		integer(fp_flag), intent(out)	ierr )

private

Evaluate all derivatives \( s^{(j)}(x) \) for \( j = 0, \ldots, k \) (with error flag).

Parameters

[in,out]	this	The fitted curve object.
[in]	x	Scalar evaluation point.
[out]	ierr	Error flag.

Returns: Array of size \( k+1 \) containing \( s(x), s'(x), \ldots, s^{(k)}(x) \).

See also: spalde

◆ curve_all_derivatives_pure()

procedure, private fitpack_curves::fitpack_curve::curve_all_derivatives_pure	(	class(fitpack_curve), intent(in)	this,
		real(fp_real), intent(in)	x )

private

Evaluate all derivatives \( s^{(j)}(x) \) for \( j = 0, \ldots, k \) (pure, NaN on error).

Parameters

[in]	this	The fitted curve object.
[in]	x	Scalar evaluation point.

Returns: Array of size \( k+1 \) containing \( s(x), s'(x), \ldots, s^{(k)}(x) \).

See also: spalde

◆ curve_derivative()

procedure, private fitpack_curves::fitpack_curve::curve_derivative	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), intent(in)	x,
		integer, intent(in)	order,
		integer(fp_flag), intent(out), optional	ierr )

private

Evaluate derivative at given coordinates.

Parameters

[in,out]	this	The fitted curve object.
[in]	x	Scalar evaluation point.
[in]	order	Derivative order ( \( 0 \leq \text{order} \leq k \)).
[out]	ierr	Optional error flag.

Returns: Scalar derivative value \( s^{(\text{order})}(x) \).

See also: splder

◆ curve_derivatives()

procedure, private fitpack_curves::fitpack_curve::curve_derivatives	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		integer, intent(in)	order,
		integer(fp_flag), intent(out), optional	ierr )

private

Evaluate the k-th derivative at multiple points (with error flag).

Parameters

[in,out]	this	The fitted curve object.
[in]	x	Array of evaluation points.
[in]	order	Derivative order ( \( 0 \leq \text{order} \leq k \)).
[out]	ierr	Optional error flag.

Returns: Array of derivative values \( s^{(\text{order})}(x_i) \).

See also: splder

◆ curve_eval_many()

procedure, private fitpack_curves::fitpack_curve::curve_eval_many	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		integer(fp_flag), intent(out)	ierr )

private

Evaluate the spline at multiple points (with error flag).

◆ curve_eval_many_pure()

procedure, private fitpack_curves::fitpack_curve::curve_eval_many_pure	(	class(fitpack_curve), intent(in)	this,
		real(fp_real), dimension(:), intent(in)	x )

private

Evaluate the spline at multiple points (pure, returns NaN on error).

◆ curve_eval_one()

procedure, private fitpack_curves::fitpack_curve::curve_eval_one	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), intent(in)	x,
		integer(fp_flag), intent(out)	ierr )

private

Evaluate curve at given coordinates.

Parameters

[in,out]	this	The fitted curve object.
[in]	x	Evaluation point.
[out]	ierr	Error flag.

Returns: Spline value \( s(x) \).

See also: splev

◆ curve_eval_one_noerr()

procedure, private fitpack_curves::fitpack_curve::curve_eval_one_noerr	(	class(fitpack_curve), intent(in)	this,
		real(fp_real), intent(in)	x )

private

Evaluate the spline at a single point (pure, returns NaN on error).

Parameters

[in]	this	The fitted curve object.
[in]	x	Evaluation point.

Returns: Spline value \( s(x) \), or NaN on error.

See also: splev

◆ curve_insert_knot_many()

procedure, private fitpack_curves::fitpack_curve::curve_insert_knot_many	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		integer(fp_flag), intent(out), optional	ierr )

private

Insert multiple knots into the B-spline representation.

Parameters

[in,out]	this	The fitted curve.
[in]	x	Array of knot positions to insert.
[out]	ierr	Optional error flag.

See also: insert_inplace

◆ curve_insert_knot_one()

procedure, private fitpack_curves::fitpack_curve::curve_insert_knot_one	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), intent(in)	x,
		integer(fp_flag), intent(out), optional	ierr )

private

Insert knot(s) into the spline representation.

The spline value is unchanged; only the knot vector and coefficients are updated. Workspace state is reset after insertion.

Parameters

[in,out]	this	The fitted curve.
[in]	x	Knot position to insert.
[out]	ierr	Optional error flag.

See also: insert_inplace

◆ destroy()

procedure fitpack_curves::fitpack_curve::destroy ( class(fitpack_curve), intent(inout) this )

Clean memory.

◆ dfdx() [1/2]

generic fitpack_curves::fitpack_curve::dfdx	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), intent(in)	x,
		integer, intent(in)	order,
		integer(fp_flag), intent(out), optional	ierr )

Evaluate derivative at given coordinates.

Parameters

[in,out]	this	The fitted curve object.
[in]	x	Scalar evaluation point.
[in]	order	Derivative order ( \( 0 \leq \text{order} \leq k \)).
[out]	ierr	Optional error flag.

Returns: Scalar derivative value \( s^{(\text{order})}(x) \).

See also: splder

Here is the call graph for this function:

◆ dfdx() [2/2]

generic fitpack_curves::fitpack_curve::dfdx	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		integer, intent(in)	order,
		integer(fp_flag), intent(out), optional	ierr )

Evaluate the k-th derivative at multiple points (with error flag).

Parameters

[in,out]	this	The fitted curve object.
[in]	x	Array of evaluation points.
[in]	order	Derivative order ( \( 0 \leq \text{order} \leq k \)).
[out]	ierr	Optional error flag.

Returns: Array of derivative values \( s^{(\text{order})}(x_i) \).

See also: splder

◆ dfdx_all() [1/2]

generic fitpack_curves::fitpack_curve::dfdx_all	(	class(fitpack_curve), intent(in)	this,
		real(fp_real), intent(in)	x )

Evaluate all derivatives \( s^{(j)}(x) \) for \( j = 0, \ldots, k \) (pure, NaN on error).

Parameters

[in]	this	The fitted curve object.
[in]	x	Scalar evaluation point.

Returns: Array of size \( k+1 \) containing \( s(x), s'(x), \ldots, s^{(k)}(x) \).

See also: spalde

◆ dfdx_all() [2/2]

generic fitpack_curves::fitpack_curve::dfdx_all	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), intent(in)	x,
		integer(fp_flag), intent(out)	ierr )

Evaluate all derivatives \( s^{(j)}(x) \) for \( j = 0, \ldots, k \) (with error flag).

Parameters

[in,out]	this	The fitted curve object.
[in]	x	Scalar evaluation point.
[out]	ierr	Error flag.

Returns: Array of size \( k+1 \) containing \( s(x), s'(x), \ldots, s^{(k)}(x) \).

See also: spalde

Here is the call graph for this function:

◆ eval() [1/4]

generic fitpack_curves::fitpack_curve::eval	(	class(fitpack_curve), intent(in)	this,
		real(fp_real), intent(in)	x )

Evaluate the spline at a single point (pure, returns NaN on error).

Parameters

[in]	this	The fitted curve object.
[in]	x	Evaluation point.

Returns: Spline value \( s(x) \), or NaN on error.

See also: splev

◆ eval() [2/4]

generic fitpack_curves::fitpack_curve::eval	(	class(fitpack_curve), intent(in)	this,
		real(fp_real), dimension(:), intent(in)	x )

Evaluate the spline at multiple points (pure, returns NaN on error).

◆ eval() [3/4]

generic fitpack_curves::fitpack_curve::eval	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), intent(in)	x,
		integer(fp_flag), intent(out)	ierr )

Evaluate curve at given coordinates.

Parameters

[in,out]	this	The fitted curve object.
[in]	x	Evaluation point.
[out]	ierr	Error flag.

Returns: Spline value \( s(x) \).

See also: splev

Here is the call graph for this function:

◆ eval() [4/4]

generic fitpack_curves::fitpack_curve::eval	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		integer(fp_flag), intent(out)	ierr )

Evaluate the spline at multiple points (with error flag).

◆ fit()

procedure fitpack_curves::fitpack_curve::fit	(	class(fitpack_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.

◆ fourier_coefficients()

procedure fitpack_curves::fitpack_curve::fourier_coefficients	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	alpha,
		real(fp_real), dimension(size(alpha)), intent(out)	a,
		real(fp_real), dimension(size(alpha)), intent(out)	b,
		integer(fp_flag), intent(out), optional	ierr )

Fourier coefficients.

Computes integrals over the interior knot range \( [t_4, t_{n-3}] \):

\[ A_i = \int_{t_4}^{t_{n-3}} s(x) \sin(\alpha_i x) \, dx, \quad B_i = \int_{t_4}^{t_{n-3}} s(x) \cos(\alpha_i x) \, dx \]

Requires at least 10 knots.

Parameters

[in,out]	this	The fitted curve (must have \( \geq 10 \) knots).
[in]	alpha	Array of frequency values \( \alpha_i \).
[out]	A	Sine coefficients, same size as `alpha`.
[out]	B	Cosine coefficients, same size as `alpha`.
[out]	ierr	Optional error flag.

See also: fourco

◆ insert_knot() [1/2]

generic fitpack_curves::fitpack_curve::insert_knot	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), intent(in)	x,
		integer(fp_flag), intent(out), optional	ierr )

Insert knot(s) into the spline representation.

The spline value is unchanged; only the knot vector and coefficients are updated. Workspace state is reset after insertion.

Parameters

[in,out]	this	The fitted curve.
[in]	x	Knot position to insert.
[out]	ierr	Optional error flag.

See also: insert_inplace

Here is the call graph for this function:

◆ insert_knot() [2/2]

generic fitpack_curves::fitpack_curve::insert_knot	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		integer(fp_flag), intent(out), optional	ierr )

Insert multiple knots into the B-spline representation.

Parameters

[in,out]	this	The fitted curve.
[in]	x	Array of knot positions to insert.
[out]	ierr	Optional error flag.

See also: insert_inplace

◆ integral()

procedure fitpack_curves::fitpack_curve::integral	(	class(fitpack_curve), intent(inout)	this,
		real(fp_real), intent(in)	from,
		real(fp_real), intent(in)	to )

Integrate.

◆ interpolate()

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

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

◆ least_squares()

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

Fit a least-squares spline with fixed knots.

◆ new_fit()

procedure fitpack_curves::fitpack_curve::new_fit	(	class(fitpack_curve), 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), optional	w,
		real(fp_real), intent(in), optional	smoothing,
		integer(fp_size), intent(in), optional	order )

Generate new fit.

◆ new_from_points()

type(fitpack_curve) function fitpack_curves::fitpack_curve::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), optional	w,
		integer(fp_flag), intent(out), optional	ierr )

Construct a fitpack_curve from data points and perform a default fit.

Parameters

[in]	x	Independent variable values (must be sortable).
[in]	y	Dependent variable values, same size as `x`.
[in]	w	Optional weights (positive), same size as `x`.
[out]	ierr	Optional error flag.

Returns: Fitted curve object.

Here is the call graph for this function:

◆ new_points()

procedure fitpack_curves::fitpack_curve::new_points	(	class(fitpack_curve), 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), optional	w )

Set new points.

Sorts data by x, allocates knot/coefficient storage, and prepares workspaces. A subsequent call to fit, interpolate, or least_squares is required to compute the spline representation.

Parameters

[in,out]	this	The curve object (destroyed and reinitialized).
[in]	x	Independent variable values (unsorted OK; will be sorted internally).
[in]	y	Dependent variable values, same size as `x`.
[in]	w	Optional positive weights, same size as `x`. Default: uniform.

See also: curfit, percur

◆ zeros()

procedure fitpack_curves::fitpack_curve::zeros	(	class(fitpack_curve), intent(in)	this,
		integer(fp_flag), intent(out), optional	ierr )

Find the zeros of a spline s(x), only if it is cubic.

Only valid for cubic splines ( \( k = 3 \)). Iteratively grows storage until all zeros are found.

Parameters

[in]	this	The fitted cubic curve.
[out]	ierr	Optional error flag.

Returns: Allocatable array of zero locations (empty if none found).

See also: sproot

Member Data Documentation

◆ bc

integer(fp_flag) fitpack_curves::fitpack_curve::bc = OUTSIDE_NEAREST_BND

◆ knots

integer(fp_size) fitpack_curves::fitpack_curve::knots = 0

◆ m

integer(fp_size) fitpack_curves::fitpack_curve::m = 0

The data points.

◆ nest

integer(fp_size) fitpack_curves::fitpack_curve::nest = 0

◆ order

integer(fp_size) fitpack_curves::fitpack_curve::order = 3

Spline degree.

◆ sp

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

◆ t

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

◆ w

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

◆ wrk_fou

real(fp_real), dimension(:,:), allocatable fitpack_curves::fitpack_curve::wrk_fou

◆ x

real(fp_real), dimension(:), allocatable fitpack_curves::fitpack_curve::x

◆ xleft

real(fp_real) fitpack_curves::fitpack_curve::xleft

Interval boundaries.

◆ xright

real(fp_real) fitpack_curves::fitpack_curve::xright

◆ y

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

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

fitpack_curves.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_all_derivatives_pure()

◆ curve_derivative()

◆ curve_derivatives()

◆ curve_eval_many()

◆ curve_eval_many_pure()

◆ curve_eval_one()

◆ curve_eval_one_noerr()

◆ curve_insert_knot_many()

◆ curve_insert_knot_one()

◆ destroy()

◆ dfdx() [1/2]

◆ dfdx() [2/2]

◆ dfdx_all() [1/2]

◆ dfdx_all() [2/2]

◆ eval() [1/4]

◆ eval() [2/4]

◆ eval() [3/4]

◆ eval() [4/4]

◆ fit()

◆ fourier_coefficients()

◆ insert_knot() [1/2]

◆ insert_knot() [2/2]

◆ integral()

◆ interpolate()

◆ least_squares()

◆ new_fit()

◆ new_from_points()

◆ new_points()

◆ zeros()

Member Data Documentation

◆ bc

◆ knots

◆ m

◆ nest

◆ order

◆ sp

◆ t

◆ w

◆ wrk_fou

◆ x

◆ xleft

◆ xright

◆ y