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

Inheritance diagram for fitpack_grid_surfaces::fitpack_grid_surface:

Collaboration diagram for fitpack_grid_surfaces::fitpack_grid_surface:

Public Member Functions
procedure	destroy (this)
	Clean memory.

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

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

procedure	fit (this, smoothing, order, keep_knots)
	Generate/update fitting curve, with optional /Users/federico/code/fitpack/test/fitpack_curve_tests.f90smoothing.

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

procedure	interpolate (this, reset_knots)
	Fit an interpolating gridded surface ( \( s = 0 \)).

generic	eval (this, x, y, ierr)
	Evaluate at scattered (x,y) points (bispeu). For gridded output, use eval_ongrid.

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

generic	eval_ongrid (this, x, y, ierr)
	Evaluate on a rectangular grid x(:) x y(:) (bispev). Returns f(ny,nx).

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

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

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

type(fitpack_grid_surface) function	surf_new_from_points (x, y, z, ierr)
	Construct a grid surface from gridded data 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	x
	The data points.

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

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

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

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

real(fp_real), dimension(2)	right

integer(fp_size), dimension(2)	nest = 0
	Node weights are not allowed.

integer(fp_size)	nmax = 0

integer(fp_size), 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	gridsurf_eval_one (this, x, y, ierr)
	Evaluate at scattered (x,y) points (bispeu). For gridded output, use eval_ongrid.

procedure, private	gridsurf_eval_many (this, x, y, ierr)
	Evaluate the grid surface at scattered \( (x_i, y_i) \) points.

procedure, private	gridded_eval_one (this, x, y, ierr)
	Evaluate on a rectangular grid x(:) x y(:) (bispev). Returns f(ny,nx).

procedure, private	gridded_eval_many (this, x, y, ierr)
	Evaluate the grid surface on a rectangular evaluation grid.

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

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

procedure, private	gridded_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 gridded data.

Stores grid vectors \( x_i \) ( \( i = 1, \ldots, m_x \)) and \( y_j \) ( \( j = 1, \ldots, m_y \)) together with gridded function values \( z(j, i) \), the fitted tensor-product B-spline representation, and the fitting state. Uses regrid, which is significantly more efficient than surfit for gridded input.

See also: Dierckx, Ch. 5, §5.4 (pp. 98–103)

Member Function/Subroutine Documentation

◆ comm_expand()

procedure fitpack_grid_surfaces::fitpack_grid_surface::comm_expand	(	class(fitpack_grid_surface), intent(inout)	this,
		real(fp_comm), dimension(:), intent(in)	buffer )

Expand grid surface data from a communication buffer.

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◆ comm_pack()

procedure fitpack_grid_surfaces::fitpack_grid_surface::comm_pack	(	class(fitpack_grid_surface), intent(in)	this,
		real(fp_comm), dimension(:), intent(out)	buffer )

Pack grid surface data into a communication buffer.

◆ comm_size()

procedure fitpack_grid_surfaces::fitpack_grid_surface::comm_size ( class(fitpack_grid_surface), intent(in) this )

Parallel communication.

◆ cross_section()

procedure fitpack_grid_surfaces::fitpack_grid_surface::cross_section	(	class(fitpack_grid_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 \( g(x) = s(x, u) \).

See also: profil

◆ derivative_spline()

procedure fitpack_grid_surfaces::fitpack_grid_surface::derivative_spline	(	class(fitpack_grid_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 grid surface with reduced degrees and trimmed knots.

See also: pardtc

◆ destroy()

procedure fitpack_grid_surfaces::fitpack_grid_surface::destroy ( class(fitpack_grid_surface), intent(inout) this )

Clean memory.

◆ dfdx() [1/2]

generic fitpack_grid_surfaces::fitpack_grid_surface::dfdx	(	class(fitpack_grid_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_grid_surfaces::fitpack_grid_surface::dfdx	(	class(fitpack_grid_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_grid_surfaces::fitpack_grid_surface::dfdx_ongrid	(	class(fitpack_grid_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.

See also: parder

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◆ eval() [1/2]

generic fitpack_grid_surfaces::fitpack_grid_surface::eval	(	class(fitpack_grid_surface), intent(inout)	this,
		real(fp_real), intent(in)	x,
		real(fp_real), intent(in)	y,
		integer(fp_flag), intent(out), optional	ierr )

Evaluate at scattered (x,y) points (bispeu). For gridded output, use eval_ongrid.

See also: bispeu

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◆ eval() [2/2]

generic fitpack_grid_surfaces::fitpack_grid_surface::eval	(	class(fitpack_grid_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 grid surface at scattered \( (x_i, y_i) \) points.

See also: bispeu

◆ eval_ongrid() [1/2]

generic fitpack_grid_surfaces::fitpack_grid_surface::eval_ongrid	(	class(fitpack_grid_surface), intent(inout)	this,
		real(fp_real), intent(in)	x,
		real(fp_real), intent(in)	y,
		integer(fp_flag), intent(out), optional	ierr )

Evaluate on a rectangular grid x(:) x y(:) (bispev). Returns f(ny,nx).

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◆ eval_ongrid() [2/2]

generic fitpack_grid_surfaces::fitpack_grid_surface::eval_ongrid	(	class(fitpack_grid_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 the grid surface on a rectangular evaluation grid.

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

See also: bispev

◆ fit()

procedure fitpack_grid_surfaces::fitpack_grid_surface::fit	(	class(fitpack_grid_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 /Users/federico/code/fitpack/test/fitpack_curve_tests.f90smoothing.

Uses the regrid core routine, which exploits the rectangular grid structure for efficiency.

See also: regrid

◆ gridded_derivatives_gridded()

procedure, private fitpack_grid_surfaces::fitpack_grid_surface::gridded_derivatives_gridded	(	class(fitpack_grid_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.

See also: parder

◆ gridded_derivatives_many()

procedure, private fitpack_grid_surfaces::fitpack_grid_surface::gridded_derivatives_many	(	class(fitpack_grid_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

◆ gridded_derivatives_one()

procedure, private fitpack_grid_surfaces::fitpack_grid_surface::gridded_derivatives_one	(	class(fitpack_grid_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

◆ gridded_eval_many()

procedure, private fitpack_grid_surfaces::fitpack_grid_surface::gridded_eval_many	(	class(fitpack_grid_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 grid surface on a rectangular evaluation grid.

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

See also: bispev

◆ gridded_eval_one()

procedure, private fitpack_grid_surfaces::fitpack_grid_surface::gridded_eval_one	(	class(fitpack_grid_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 on a rectangular grid x(:) x y(:) (bispev). Returns f(ny,nx).

◆ gridsurf_eval_many()

procedure, private fitpack_grid_surfaces::fitpack_grid_surface::gridsurf_eval_many	(	class(fitpack_grid_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 grid surface at scattered \( (x_i, y_i) \) points.

See also: bispeu

◆ gridsurf_eval_one()

procedure, private fitpack_grid_surfaces::fitpack_grid_surface::gridsurf_eval_one	(	class(fitpack_grid_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 at scattered (x,y) points (bispeu). For gridded output, use eval_ongrid.

See also: bispeu

◆ integral()

procedure fitpack_grid_surfaces::fitpack_grid_surface::integral	(	class(fitpack_grid_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.

See also: dblint

◆ interpolate()

procedure fitpack_grid_surfaces::fitpack_grid_surface::interpolate	(	class(fitpack_grid_surface), intent(inout)	this,
		logical, intent(in), optional	reset_knots )

Fit an interpolating gridded surface ( \( s = 0 \)).

See also: regrid

◆ least_squares()

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

Fit a least-squares gridded surface with fixed knots.

See also: regrid

◆ new_fit()

procedure fitpack_grid_surfaces::fitpack_grid_surface::new_fit	(	class(fitpack_grid_surface), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		real(fp_real), dimension(:), intent(in)	y,
		real(fp_real), dimension(size(y),size(x)), intent(in)	z,
		real(fp_real), intent(in), optional	smoothing,
		integer, intent(in), optional	order )

Generate new fit.

See also: regrid

◆ new_points()

procedure fitpack_grid_surfaces::fitpack_grid_surface::new_points	(	class(fitpack_grid_surface), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		real(fp_real), dimension(:), intent(in)	y,
		real(fp_real), dimension(size(y),size(x)), intent(in)	z )

Set new points.

Parameters

[in,out]	this	The grid surface (destroyed and reinitialized).
[in]	x	Grid coordinates in the x direction.
[in]	y	Grid coordinates in the y direction.
[in]	z	Function values `z(j,i)` = \( f(x_i, y_j) \).

See also: regrid

◆ surf_new_from_points()

type(fitpack_grid_surface) function fitpack_grid_surfaces::fitpack_grid_surface::surf_new_from_points	(	real(fp_real), dimension(:), intent(in)	x,
		real(fp_real), dimension(:), intent(in)	y,
		real(fp_real), dimension(size(y),size(x)), intent(in)	z,
		integer(fp_flag), intent(out), optional	ierr )

Construct a grid surface from gridded data and perform a default fit.

See also: regrid

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Member Data Documentation

◆ knots

integer(fp_size), dimension(2) fitpack_grid_surfaces::fitpack_grid_surface::knots = 0

◆ left

real(fp_real), dimension(2) fitpack_grid_surfaces::fitpack_grid_surface::left

Interval boundaries.

◆ nest

integer(fp_size), dimension(2) fitpack_grid_surfaces::fitpack_grid_surface::nest = 0

Node weights are not allowed.

◆ nmax

integer(fp_size) fitpack_grid_surfaces::fitpack_grid_surface::nmax = 0

◆ order

integer(fp_size), dimension(2) fitpack_grid_surfaces::fitpack_grid_surface::order = 3

Spline degree.

◆ right

real(fp_real), dimension(2) fitpack_grid_surfaces::fitpack_grid_surface::right

◆ t

real(fp_real), dimension(:,:), allocatable fitpack_grid_surfaces::fitpack_grid_surface::t

◆ x

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

The data points.

◆ y

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

◆ z

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

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

fitpack_grid_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() [1/2]

◆ eval_ongrid() [2/2]

◆ fit()

◆ gridded_derivatives_gridded()

◆ gridded_derivatives_many()

◆ gridded_derivatives_one()

◆ gridded_eval_many()

◆ gridded_eval_one()

◆ gridsurf_eval_many()

◆ gridsurf_eval_one()

◆ integral()

◆ interpolate()

◆ least_squares()

◆ new_fit()

◆ new_points()

◆ surf_new_from_points()

Member Data Documentation

◆ knots

◆ left

◆ nest

◆ nmax

◆ order

◆ right

◆ t

◆ x

◆ y

◆ z