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

Inheritance diagram for fitpack_surfaces::fitpack_surface:

Collaboration diagram for fitpack_surfaces::fitpack_surface:

Public Member Functions
procedure	destroy (this)
	Clean memory.

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

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

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

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

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

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

generic	eval (this, x, y, ierr)
	Evaluate the surface at a list of scattered \( (x_i, y_i) \) points.

generic	eval_ongrid (this, x, y, ierr)
	Evaluate surface on a grid.

generic	dfdx (this, x, y, dx, dy, ierr)
	Evaluate a partial derivative at a single \( (x, y) \) point.

generic	dfdx (this, x, y, dx, dy, ierr)
	Evaluate partial derivatives at scattered \( (x_i, y_i) \) points.

generic	dfdx_ongrid (this, x, y, dx, dy, ierr)
	Evaluate derivatives at given coordinates.

procedure	integral (this, lower, upper)
	Double integration over a rectangular domain.

procedure	cross_section (this, u, along_y, ierr)
	Extract a 1D cross-section curve from the surface.

procedure	derivative_spline (this, nux, nuy, ierr)
	Compute the derivative spline coefficients.

procedure	comm_size (this)
	Parallel communication interface.

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

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

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.

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
	The input data points.

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

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

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

integer, dimension(2)	order = 3
	Spline degree.

real(fp_real), dimension(2)	left
	Interval boundaries.

real(fp_real), dimension(2)	right

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

integer, dimension(2)	nest = 0

integer	nmax = 0

integer	lwrk2 = 0

real(fp_real), dimension(:), allocatable	wrk2

integer	bc = OUTSIDE_NEAREST_BND

integer, dimension(2)	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	surface_eval_one (this, x, y, ierr)
	Evaluate surface at given coordinates.

procedure, private	surface_eval_many (this, x, y, ierr)
	Evaluate the surface at a list of scattered \( (x_i, y_i) \) points.

procedure, private	surface_eval_gridded (this, x, y, ierr)
	Evaluate surface on a grid.

procedure, private	surface_derivatives_gridded (this, x, y, dx, dy, ierr)
	Evaluate derivatives at given coordinates.

procedure, private	surface_derivatives_many (this, x, y, dx, dy, ierr)
	Evaluate partial derivatives at scattered \( (x_i, y_i) \) points.

procedure, private	surface_derivatives_one (this, x, y, dx, dy, ierr)
	Evaluate a partial derivative at a single \( (x, y) \) point.

Detailed Description

Bivariate surface fitter \( z = s(x, y) \) for scattered data.

Stores the input data points \( (x_i, y_i, z_i) \), optional weights \( w_i \), the fitted tensor-product B-spline representation (knots and coefficients), and the fitting state. The smoothing parameter \( s \) controls the trade-off between closeness of fit and smoothness.

See also: Dierckx, Ch. 5, §5.3 (pp. 85–98)

Member Function/Subroutine Documentation

◆ comm_expand()

procedure fitpack_surfaces::fitpack_surface::comm_expand	(	class(fitpack_surface), intent(inout)	this,
		real(fp_comm), dimension(:), intent(in)	buffer )

Expand surface data from a communication buffer.

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◆ comm_pack()

procedure fitpack_surfaces::fitpack_surface::comm_pack	(	class(fitpack_surface), intent(in)	this,
		real(fp_comm), dimension(:), intent(out)	buffer )

Pack surface data into a communication buffer.

◆ comm_size()

procedure fitpack_surfaces::fitpack_surface::comm_size ( class(fitpack_surface), intent(in) this )

Parallel communication interface.

◆ cross_section()

procedure fitpack_surfaces::fitpack_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 )

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

◆ derivative_spline()

procedure fitpack_surfaces::fitpack_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 )

Compute the derivative spline coefficients.

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

◆ destroy()

procedure fitpack_surfaces::fitpack_surface::destroy ( class(fitpack_surface), intent(inout) this )

Clean memory.

◆ dfdx() [1/2]

generic fitpack_surfaces::fitpack_surface::dfdx	(	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 )

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

See also: pardeu

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◆ dfdx() [2/2]

generic fitpack_surfaces::fitpack_surface::dfdx	(	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 )

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

See also: pardeu

◆ dfdx_ongrid()

generic fitpack_surfaces::fitpack_surface::dfdx_ongrid	(	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 )

Evaluate derivatives at given coordinates.

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

See also: parder

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◆ eval() [1/2]

generic fitpack_surfaces::fitpack_surface::eval	(	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 )

Evaluate surface at given coordinates.

See also: bispeu

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◆ eval() [2/2]

generic fitpack_surfaces::fitpack_surface::eval	(	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 )

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

See also: bispeu

◆ eval_ongrid()

generic fitpack_surfaces::fitpack_surface::eval_ongrid	(	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 )

Evaluate surface on a grid.

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

See also: bispev

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◆ fit()

procedure fitpack_surfaces::fitpack_surface::fit	(	class(fitpack_surface), intent(inout)	this,
		real(fp_real), intent(in), optional	smoothing,
		integer, intent(in), optional	order,
		logical, intent(in), optional	keep_knots )

Generate/update fitting curve, with optional smoothing.

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

◆ integral()

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

Double integration 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

◆ interpolate()

procedure fitpack_surfaces::fitpack_surface::interpolate	(	class(fitpack_surface), intent(inout)	this,
		logical, intent(in), optional	reset_knots )

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

See also: surfit

◆ least_squares()

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

Fit a least-squares surface with fixed knots.

See also: surfit

◆ new_fit()

procedure fitpack_surfaces::fitpack_surface::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 )

Generate new fit.

See also: surfit

◆ new_points()

procedure fitpack_surfaces::fitpack_surface::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 )

Set new points.

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

◆ surf_new_from_points()

type(fitpack_surface) function fitpack_surfaces::fitpack_surface::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 )

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

◆ surface_derivatives_gridded()

procedure, private fitpack_surfaces::fitpack_surface::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 derivatives at given coordinates.

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()

procedure, private fitpack_surfaces::fitpack_surface::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()

procedure, private fitpack_surfaces::fitpack_surface::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

◆ surface_eval_gridded()

procedure, private fitpack_surfaces::fitpack_surface::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 surface on a grid.

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

See also: bispev

◆ surface_eval_many()

procedure, private fitpack_surfaces::fitpack_surface::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

◆ surface_eval_one()

procedure, private fitpack_surfaces::fitpack_surface::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 surface at given coordinates.

See also: bispeu

Member Data Documentation

◆ bc

integer fitpack_surfaces::fitpack_surface::bc = OUTSIDE_NEAREST_BND

◆ knots

integer, dimension(2) fitpack_surfaces::fitpack_surface::knots = 0

◆ left

real(fp_real), dimension(2) fitpack_surfaces::fitpack_surface::left

Interval boundaries.

◆ lwrk2

integer fitpack_surfaces::fitpack_surface::lwrk2 = 0

◆ m

integer fitpack_surfaces::fitpack_surface::m = 0

The input data points.

◆ nest

integer, dimension(2) fitpack_surfaces::fitpack_surface::nest = 0

◆ nmax

integer fitpack_surfaces::fitpack_surface::nmax = 0

◆ order

integer, dimension(2) fitpack_surfaces::fitpack_surface::order = 3

Spline degree.

◆ right

real(fp_real), dimension(2) fitpack_surfaces::fitpack_surface::right

◆ t

real(fp_real), dimension(:,:), allocatable fitpack_surfaces::fitpack_surface::t

◆ w

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

◆ wrk2

real(fp_real), dimension(:), allocatable fitpack_surfaces::fitpack_surface::wrk2

◆ x

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

◆ y

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

◆ z

real(fp_real), dimension(:), allocatable fitpack_surfaces::fitpack_surface::z

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

fitpack_surfaces.f90

Public Member Functions

Public Attributes

Private Member Functions

Detailed Description

Member Function/Subroutine Documentation

◆ comm_expand()

◆ comm_pack()

◆ comm_size()

◆ cross_section()

◆ derivative_spline()

◆ destroy()

◆ dfdx() [1/2]

◆ dfdx() [2/2]

◆ dfdx_ongrid()

◆ eval() [1/2]

◆ eval() [2/2]

◆ eval_ongrid()

◆ fit()

◆ integral()

◆ interpolate()

◆ least_squares()

◆ new_fit()

◆ new_points()

◆ surf_new_from_points()

◆ surface_derivatives_gridded()

◆ surface_derivatives_many()

◆ surface_derivatives_one()

◆ surface_eval_gridded()

◆ surface_eval_many()

◆ surface_eval_one()

Member Data Documentation

◆ bc

◆ knots

◆ left

◆ lwrk2

◆ m

◆ nest

◆ nmax

◆ order

◆ right

◆ t

◆ w

◆ wrk2

◆ x

◆ y

◆ z