fitpack_convex_curves Module Reference

OOP wrapper for constrained-convexity curve fitting. More...

Data Types
interface	fitpack_convex_curve
	Cubic spline fitter with pointwise convexity/concavity constraints. More...

Functions/Subroutines
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.
elemental subroutine	convex_destroy (this)
	Destroy the convex curve object and release all allocated memory.
subroutine	convex_new_points (this, x, y, w)
	Load new data points and allocate workspace for convex fitting.
integer(fp_flag) function	set_convexity (this, v)
	Set pointwise convexity constraints.
elemental integer(fp_flag) function	remap_concon_error (ier)
integer(fp_flag) function	convex_fit_automatic_knots (this, smoothing, order, keep_knots)
	Fit a smoothing spline with convexity constraints and automatic knot placement.
integer(fp_flag) function	convex_fit_least_squares (this, smoothing, reset_knots)
	Fit a least-squares spline with convexity constraints on the current knots.
pure real(fp_real) function	nearest_constraint (t_knot, x, v, m)
elemental integer(fp_size) function	convex_comm_size (this)
	Return the communication buffer size for the convex curve.
pure subroutine	convex_comm_pack (this, buffer)
	Pack convex curve data into a communication buffer.
pure subroutine	convex_comm_expand (this, buffer)
	Expand convex curve data from a communication buffer.

Detailed Description

OOP wrapper for constrained-convexity curve fitting.

Provides fitpack_convex_curve, an extension of fitpack_curve that enforces local convexity or concavity constraints during spline fitting. Always uses cubic splines ( \( k = 3 \)). The underlying core routines are concon (automatic knot placement) and cocosp (least-squares with user-supplied knots).

See also

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

Function/Subroutine Documentation

convex_comm_expand()

pure subroutine fitpack_convex_curves::convex_comm_expand ( class(fitpack_convex_curve), intent(inout) this, real(fp_comm), dimension(:), intent(in) buffer )

private

Expand convex curve data from a communication buffer.

convex_comm_pack()

pure subroutine fitpack_convex_curves::convex_comm_pack ( class(fitpack_convex_curve), intent(in) this, real(fp_comm), dimension(:), intent(out) buffer )

private

Pack convex curve data into a communication buffer.

convex_comm_size()

elemental integer(fp_size) function fitpack_convex_curves::convex_comm_size ( class(fitpack_convex_curve), intent(in) this )

private

Return the communication buffer size for the convex curve.

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convex_destroy()

elemental subroutine fitpack_convex_curves::convex_destroy ( class(fitpack_convex_curve), intent(inout) this )

private

Destroy the convex curve object and release all allocated memory.

convex_fit_automatic_knots()

integer(fp_flag) function fitpack_convex_curves::convex_fit_automatic_knots ( 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 )

private

Fit a smoothing spline with convexity constraints and automatic knot placement.

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

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convex_fit_least_squares()

integer(fp_flag) function fitpack_convex_curves::convex_fit_least_squares ( class(fitpack_convex_curve), intent(inout) this, real(fp_real), intent(in), optional smoothing, logical, intent(in), optional reset_knots )

private

Fit a least-squares spline with convexity constraints on the current knots.

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

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convex_new_from_points()

type(fitpack_convex_curve) function fitpack_convex_curves::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 )

private

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

convex_new_points()

subroutine fitpack_convex_curves::convex_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 )

private

Load new data points and allocate workspace for convex fitting.

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

nearest_constraint()

pure real(fp_real) function fitpack_convex_curves::nearest_constraint ( real(fp_real), intent(in) t_knot, real(fp_real), dimension(m), intent(in) x, real(fp_real), dimension(m), intent(in) v, integer(fp_size), intent(in) m )

private

remap_concon_error()

elemental integer(fp_flag) function fitpack_convex_curves::remap_concon_error ( integer(fp_flag), intent(in) ier )

private

set_convexity()

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

private

Set pointwise convexity constraints.

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).