fitpack_convex_curves::fitpack_convex_curve Interface Reference

Cubic spline fitter with pointwise convexity/concavity constraints. More...

Inheritance diagram for fitpack_convex_curves::fitpack_convex_curve:

Collaboration diagram for fitpack_convex_curves::fitpack_convex_curve:

Public Member Functions
procedure	destroy (this)
	Clean memory.
procedure	new_points (this, x, y, w)
	Set new points.
procedure	fit (this, smoothing, order, keep_knots)
	Generate/update fitting curve with automatic knots (concon)
procedure	least_squares (this, smoothing, reset_knots)
	Least-squares fit with given knots (cocosp)
procedure	set_convexity (this, v)
	Set convexity constraint values.
procedure	comm_size (this)
	Parallel communication interface.
procedure	comm_pack (this, buffer)
	Pack convex curve data into a communication buffer.
procedure	comm_expand (this, buffer)
	Expand convex curve data from a communication buffer.
type(fitpack_convex_curve) function	convex_new_from_points (x, y, v, w, smoothing, ierr)
	Construct a convex curve from data points with convexity constraints and fit it.
Public Member Functions inherited from fitpack_curves::fitpack_curve
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
real(fp_real), dimension(:), allocatable	v
	Convexity constraints at data points: 1=concave, -1=convex, 0=unconstrained.
real(fp_real), dimension(:), allocatable	sx
	Spline values at data points after fit.
logical(fp_bool), dimension(:), allocatable	bind
	Active constraint flags at knots.
integer(fp_size)	maxtr = 100
	Tree storage estimate for QP solver.
integer(fp_size)	maxbin = 10
	Max number of zero-curvature knots.
Public Attributes inherited from fitpack_curves::fitpack_curve
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

Detailed Description

Cubic spline fitter with pointwise convexity/concavity constraints.

Extends fitpack_curve with per-data-point convexity flags: each point can be constrained to lie on a locally concave ( \( v_i = 1 \)), convex ( \( v_i = -1 \)), or unconstrained ( \( v_i = 0 \)) portion of the spline. The fitting routines solve a constrained quadratic programming problem to determine knot positions and coefficients that satisfy these shape constraints while minimizing the smoothing functional.

See also

Dierckx, Ch. 8, §8.3–8.4 (pp. 173–196)

Member Function/Subroutine Documentation

comm_expand()

procedure fitpack_convex_curves::fitpack_convex_curve::comm_expand	(	class(fitpack_convex_curve), intent(inout)	this,
		real(fp_comm), dimension(:), intent(in)	buffer )

Expand convex curve data from a communication buffer.

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comm_pack()

procedure fitpack_convex_curves::fitpack_convex_curve::comm_pack	(	class(fitpack_convex_curve), intent(in)	this,
		real(fp_comm), dimension(:), intent(out)	buffer )

Pack convex curve data into a communication buffer.

comm_size()

procedure fitpack_convex_curves::fitpack_convex_curve::comm_size

(

class(fitpack_convex_curve), intent(in)

this

)

Parallel communication interface.

convex_new_from_points()

type(fitpack_convex_curve) function fitpack_convex_curves::fitpack_convex_curve::convex_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)	v,
		real(fp_real), dimension(size(x)), intent(in), optional	w,
		real(fp_real), intent(in), optional	smoothing,
		integer(fp_flag), intent(out), optional	ierr )

Construct a convex curve from data points with convexity constraints and fit it.

Parameters

[in]	x	Independent variable values.
[in]	y	Dependent variable values, same size as x.
[in]	v	Convexity constraints: 1=concave, -1=convex, 0=unconstrained.
[in]	w	Optional weights (positive), same size as x.
[in]	smoothing	Optional smoothing factor.
[out]	ierr	Optional error flag.

Returns

Fitted convex curve object.

See also

concon

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destroy()

procedure fitpack_convex_curves::fitpack_convex_curve::destroy

(

class(fitpack_convex_curve), intent(inout)

this

)

Clean memory.

fit()

procedure fitpack_convex_curves::fitpack_convex_curve::fit	(	class(fitpack_convex_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 automatic knots (concon)

Uses the concon core routine which solves a constrained quadratic programming problem to place knots while respecting local convexity/concavity constraints.

Parameters

[in,out]	this	The convex curve object.
[in]	smoothing	Optional smoothing factor.
[in]	order	Ignored (always cubic).
[in]	keep_knots	If .true., continue from current knot set.

Returns

Error flag.

See also

concon

least_squares()

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

Least-squares fit with given knots (cocosp)

Uses the cocosp core routine. Constraint values at interior knots are derived from the nearest data-point convexity flags.

Parameters

[in,out]	this	The convex curve object.
[in]	smoothing	Optional smoothing for initial knot placement (if reset_knots).
[in]	reset_knots	If .true., recompute knots via concon first.

Returns

Error flag.

See also

cocosp

new_points()

procedure fitpack_convex_curves::fitpack_convex_curve::new_points	(	class(fitpack_convex_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.

Parameters

[in,out]	this	The convex curve object (destroyed and reinitialized).
[in]	x	Independent variable values.
[in]	y	Dependent variable values, same size as x.
[in]	w	Optional positive weights, same size as x.

See also

concon, cocosp

set_convexity()

procedure fitpack_convex_curves::fitpack_convex_curve::set_convexity	(	class(fitpack_convex_curve), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	v )

Set convexity constraint values.

Parameters

[in,out]	this	The convex curve object.
[in]	v	Constraint values: 1=concave, -1=convex, 0=unconstrained. Must have size m.

Returns

Error flag (FITPACK_INPUT_ERROR if size mismatch).

Member Data Documentation

bind

logical(fp_bool), dimension(:), allocatable fitpack_convex_curves::fitpack_convex_curve::bind

Active constraint flags at knots.

maxbin

integer(fp_size) fitpack_convex_curves::fitpack_convex_curve::maxbin = 10

Max number of zero-curvature knots.

maxtr

integer(fp_size) fitpack_convex_curves::fitpack_convex_curve::maxtr = 100

Tree storage estimate for QP solver.

sx

real(fp_real), dimension(:), allocatable fitpack_convex_curves::fitpack_convex_curve::sx

Spline values at data points after fit.

v

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

Convexity constraints at data points: 1=concave, -1=convex, 0=unconstrained.

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

• fitpack_convex_curves.f90