OOP wrapper for bivariate surface fitting to scattered data. More...

Data Types
interface	fitpack_surface
	Bivariate surface fitter \( z = s(x, y) \) for scattered data. More...

Functions/Subroutines
integer(fp_flag) function	surface_fit_automatic_knots (this, smoothing, order, keep_knots)
	Fit a smoothing surface with automatic knot placement.

integer(fp_flag) function	surface_fit_interpolating (this, reset_knots)
	Fit an interpolating surface ( \( s = 0 \)) through the data points.

integer(fp_flag) function	surface_fit_least_squares (this, smoothing, reset_knots)
	Fit a least-squares surface with fixed knots.

real(fp_real) function, dimension(size(x))	surface_eval_many (this, x, y, ierr)
	Evaluate the surface at a list of scattered \( (x_i, y_i) \) points.

real(fp_real) function	surface_eval_one (this, x, y, ierr)
	Evaluate the surface at a single \( (x, y) \) point.

real(fp_real) function, dimension(size(y), size(x))	surface_eval_gridded (this, x, y, ierr)
	Evaluate the surface on a rectangular grid \( x_i \times y_j \).

elemental subroutine	surf_destroy (this)
	Destroy a surface object and release all allocated memory.

subroutine	surf_new_points (this, x, y, z, w)
	Load new scattered data points and allocate workspace for surface fitting.

type(fitpack_surface) function	surf_new_from_points (x, y, z, w, ierr)
	Construct a surface from scattered data points and perform a default fit.

integer(fp_flag) function	surf_new_fit (this, x, y, z, w, smoothing, order)
	Load new data points and perform a fresh surface fit.

real(fp_real) function, dimension(size(y), size(x))	surface_derivatives_gridded (this, x, y, dx, dy, ierr)
	Evaluate partial derivatives on a rectangular grid.

real(fp_real) function, dimension(size(x))	surface_derivatives_many (this, x, y, dx, dy, ierr)
	Evaluate partial derivatives at scattered \( (x_i, y_i) \) points.

real(fp_real) function	surface_derivatives_one (this, x, y, dx, dy, ierr)
	Evaluate a partial derivative at a single \( (x, y) \) point.

real(fp_real) function	surface_integral (this, lower, upper)
	Compute the double integral of the surface over a rectangular domain.

type(fitpack_curve) function	surface_cross_section (this, u, along_y, ierr)
	Extract a 1D cross-section curve from the surface.

type(fitpack_surface) function	surface_derivative_spline (this, nux, nuy, ierr)
	Compute the B-spline representation of a partial derivative surface.

pure real(fp_real) function, dimension(n)	merge_knots (along_y, tx, ty, n)
	Select knots from the appropriate direction for cross-section extraction.

elemental integer(fp_size) function	surf_comm_size (this)
	Return the communication buffer size for the surface.

pure subroutine	surf_comm_pack (this, buffer)
	Pack surface data into a communication buffer.

pure subroutine	surf_comm_expand (this, buffer)
	Expand surface data from a communication buffer.

Detailed Description

OOP wrapper for bivariate surface fitting to scattered data.

Provides fitpack_surface, a derived type for fitting tensor-product B-spline surfaces \( z = s(x, y) \) to scattered \( (x_i, y_i, z_i) \) data. The underlying core routine is surfit, which uses automatic knot placement with a smoothing parameter. Supports evaluation, partial derivatives, integration, and cross-section extraction.

See also: Dierckx, Ch. 5, §5.3 (pp. 85–98); surfit, bispev, parder, dblint, profil

Function/Subroutine Documentation

◆ merge_knots()

pure real(fp_real) function, dimension(n) fitpack_surfaces::merge_knots	(	logical, intent(in)	along_y,
		real(fp_real), dimension(:), intent(in)	tx,
		real(fp_real), dimension(:), intent(in)	ty,
		integer(fp_size), intent(in)	n )

private

Select knots from the appropriate direction for cross-section extraction.

◆ surf_comm_expand()

pure subroutine fitpack_surfaces::surf_comm_expand	(	class(fitpack_surface), intent(inout)	this,
		real(fp_comm), dimension(:), intent(in)	buffer )

private

Expand surface data from a communication buffer.

◆ surf_comm_pack()

pure subroutine fitpack_surfaces::surf_comm_pack	(	class(fitpack_surface), intent(in)	this,
		real(fp_comm), dimension(:), intent(out)	buffer )

private

Pack surface data into a communication buffer.

◆ surf_comm_size()

elemental integer(fp_size) function fitpack_surfaces::surf_comm_size ( class(fitpack_surface), intent(in) this )

private

Return the communication buffer size for the surface.

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◆ surf_destroy()

elemental subroutine fitpack_surfaces::surf_destroy ( class(fitpack_surface), intent(inout) this )

private

Destroy a surface object and release all allocated memory.

◆ surf_new_fit()

integer(fp_flag) function fitpack_surfaces::surf_new_fit	(	class(fitpack_surface), 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)	z,
		real(fp_real), dimension(size(x)), intent(in), optional	w,
		real(fp_real), intent(in), optional	smoothing,
		integer, intent(in), optional	order )

private

Load new data points and perform a fresh surface fit.

See also: surfit

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◆ surf_new_from_points()

type(fitpack_surface) function fitpack_surfaces::surf_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)	z,
		real(fp_real), dimension(size(x)), intent(in), optional	w,
		integer(fp_flag), intent(out), optional	ierr )

private

Construct a surface from scattered data points and perform a default fit.

Parameters

[in]	x	X coordinates.
[in]	y	Y coordinates, same size as `x`.
[in]	z	Function values, same size as `x`.
[in]	w	Optional weights.
[out]	ierr	Optional error flag.

Returns: Fitted surface object.

See also: surfit

◆ surf_new_points()

subroutine fitpack_surfaces::surf_new_points	(	class(fitpack_surface), 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)	z,
		real(fp_real), dimension(size(x)), intent(in), optional	w )

private

Load new scattered data points and allocate workspace for surface fitting.

Parameters

[in,out]	this	The surface object (destroyed and reinitialized).
[in]	x	X coordinates of scattered data points.
[in]	y	Y coordinates, same size as `x`.
[in]	z	Function values, same size as `x`.
[in]	w	Optional positive weights, same size as `x`.

See also: surfit

◆ surface_cross_section()

type(fitpack_curve) function fitpack_surfaces::surface_cross_section	(	class(fitpack_surface), intent(in)	this,
		real(fp_real), intent(in)	u,
		logical, intent(in)	along_y,
		integer(fp_flag), intent(out), optional	ierr )

private

Extract a 1D cross-section curve from the surface.

If along_y=.true., returns \( f(y) = s(u, y) \); otherwise \( g(x) = s(x, u) \). The result is a fitpack_curve with the appropriate knots and coefficients.

See also: profil

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◆ surface_derivative_spline()

type(fitpack_surface) function fitpack_surfaces::surface_derivative_spline	(	class(fitpack_surface), intent(in)	this,
		integer(fp_size), intent(in)	nux,
		integer(fp_size), intent(in)	nuy,
		integer(fp_flag), intent(out), optional	ierr )

private

Compute the B-spline representation of a partial derivative surface.

Returns a new surface representing \( \partial^{n_x+n_y} s / \partial x^{n_x} \partial y^{n_y} \), with reduced degrees \( (k_x - n_x, k_y - n_y) \) and trimmed knots.

See also: pardtc

◆ surface_derivatives_gridded()

real(fp_real) function, dimension(size(y),size(x)) fitpack_surfaces::surface_derivatives_gridded	(	class(fitpack_surface), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		real(fp_real), dimension(:), intent(in)	y,
		integer(fp_size), intent(in)	dx,
		integer(fp_size), intent(in)	dy,
		integer(fp_flag), intent(out), optional	ierr )

private

Evaluate partial derivatives on a rectangular grid.

Returns f(j,i) = \( \partial^{dx+dy} s / \partial x^{dx} \partial y^{dy} \) at \( (x_i, y_j) \).

See also: parder

◆ surface_derivatives_many()

real(fp_real) function, dimension(size(x)) fitpack_surfaces::surface_derivatives_many	(	class(fitpack_surface), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		real(fp_real), dimension(:), intent(in)	y,
		integer(fp_size), intent(in)	dx,
		integer(fp_size), intent(in)	dy,
		integer(fp_flag), intent(out), optional	ierr )

private

Evaluate partial derivatives at scattered \( (x_i, y_i) \) points.

See also: pardeu

◆ surface_derivatives_one()

real(fp_real) function fitpack_surfaces::surface_derivatives_one	(	class(fitpack_surface), intent(inout)	this,
		real(fp_real), intent(in)	x,
		real(fp_real), intent(in)	y,
		integer(fp_size), intent(in)	dx,
		integer(fp_size), intent(in)	dy,
		integer(fp_flag), intent(out), optional	ierr )

private

Evaluate a partial derivative at a single \( (x, y) \) point.

See also: pardeu

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◆ surface_eval_gridded()

real(fp_real) function, dimension(size(y),size(x)) fitpack_surfaces::surface_eval_gridded	(	class(fitpack_surface), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		real(fp_real), dimension(:), intent(in)	y,
		integer(fp_flag), intent(out), optional	ierr )

private

Evaluate the surface on a rectangular grid \( x_i \times y_j \).

Returns f(j,i) = \( s(x_i, y_j) \).

See also: bispev

◆ surface_eval_many()

real(fp_real) function, dimension(size(x)) fitpack_surfaces::surface_eval_many	(	class(fitpack_surface), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		real(fp_real), dimension(size(x)), intent(in)	y,
		integer(fp_flag), intent(out), optional	ierr )

private

Evaluate the surface at a list of scattered \( (x_i, y_i) \) points.

See also: bispeu

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◆ surface_eval_one()

real(fp_real) function fitpack_surfaces::surface_eval_one	(	class(fitpack_surface), intent(inout)	this,
		real(fp_real), intent(in)	x,
		real(fp_real), intent(in)	y,
		integer(fp_flag), intent(out), optional	ierr )

private

Evaluate the surface at a single \( (x, y) \) point.

See also: bispeu

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◆ surface_fit_automatic_knots()

integer(fp_flag) function fitpack_surfaces::surface_fit_automatic_knots	(	class(fitpack_surface), intent(inout)	this,
		real(fp_real), intent(in), optional	smoothing,
		integer, intent(in), optional	order,
		logical, intent(in), optional	keep_knots )

private

Fit a smoothing surface with automatic knot placement.

Uses the surfit core routine. The smoothing parameter controls the trade-off between closeness of fit and smoothness.

Parameters

[in,out]	this	The surface object.
[in]	smoothing	Optional smoothing factor.
[in]	order	Optional spline degree (applied to both directions).
[in]	keep_knots	If `.true.`, continue from current knot set.

Returns: Error flag.

See also: surfit

Ensure we start with new knots (unless caller wants to keep them)

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◆ surface_fit_interpolating()

integer(fp_flag) function fitpack_surfaces::surface_fit_interpolating	(	class(fitpack_surface), intent(inout)	this,
		logical, intent(in), optional	reset_knots )

private

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

See also: surfit

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◆ surface_fit_least_squares()

integer(fp_flag) function fitpack_surfaces::surface_fit_least_squares	(	class(fitpack_surface), intent(inout)	this,
		real(fp_real), intent(in), optional	smoothing,
		logical, intent(in), optional	reset_knots )

private

Fit a least-squares surface with fixed knots.

See also: surfit

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◆ surface_integral()

real(fp_real) function fitpack_surfaces::surface_integral	(	class(fitpack_surface), intent(in)	this,
		real(fp_real), dimension(2), intent(in)	lower,
		real(fp_real), dimension(2), intent(in)	upper )

private

Compute the double integral of the surface over a rectangular domain.

Computes \( \int_{x_a}^{x_b} \int_{y_a}^{y_b} s(x,y)\,dy\,dx \).

Parameters

[in]	this	The fitted surface.
[in]	lower	Lower bounds \( (x_a, y_a) \).
[in]	upper	Upper bounds \( (x_b, y_b) \).

Returns: The integral value.

See also: dblint

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Data Types

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ merge_knots()

◆ surf_comm_expand()

◆ surf_comm_pack()

◆ surf_comm_size()

◆ surf_destroy()

◆ surf_new_fit()

◆ surf_new_from_points()

◆ surf_new_points()

◆ surface_cross_section()

◆ surface_derivative_spline()

◆ surface_derivatives_gridded()

◆ surface_derivatives_many()

◆ surface_derivatives_one()

◆ surface_eval_gridded()

◆ surface_eval_many()

◆ surface_eval_one()

◆ surface_fit_automatic_knots()

◆ surface_fit_interpolating()

◆ surface_fit_least_squares()

◆ surface_integral()