fitpack_grid_surfaces Module Reference

OOP wrapper for bivariate surface fitting to data on a rectangular grid. More...

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

Functions/Subroutines
integer function	surface_fit_least_squares (this, smoothing, reset_knots)
	Fit a least-squares gridded surface with fixed knots.
integer function	surface_fit_interpolating (this, reset_knots)
	Fit an interpolating gridded surface ( \( s = 0 \)).
integer(fp_flag) function	surface_fit_automatic_knots (this, smoothing, order, keep_knots)
	Fit a smoothing gridded surface with automatic knot placement.
elemental subroutine	surf_destroy (this)
	Destroy a grid surface object and release all allocated memory.
subroutine	surf_new_points (this, x, y, z)
	Load new gridded data and allocate workspace.
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.
integer function	surf_new_fit (this, x, y, z, smoothing, order)
	Load new gridded data and perform a fresh fit.
real(fp_real) function, dimension(size(x))	gridsurf_eval_many (this, x, y, ierr)
	Evaluate the grid surface at scattered \( (x_i, y_i) \) points.
real(fp_real) function	gridsurf_eval_one (this, x, y, ierr)
	Evaluate the grid surface at a single \( (x, y) \) point.
real(fp_real) function, dimension(size(y), size(x))	gridded_eval_many (this, x, y, ierr)
	Evaluate the grid surface on a rectangular evaluation grid.
real(fp_real) function	gridded_eval_one (this, x, y, ierr)
	Evaluate the grid surface at a single grid point via bispev.
real(fp_real) function, dimension(size(y), size(x))	gridded_derivatives_gridded (this, x, y, dx, dy, ierr)
	Evaluate partial derivatives on a rectangular grid.
real(fp_real) function, dimension(size(x))	gridded_derivatives_many (this, x, y, dx, dy, ierr)
	Evaluate partial derivatives at scattered \( (x_i, y_i) \) points.
real(fp_real) function	gridded_derivatives_one (this, x, y, dx, dy, ierr)
	Evaluate a partial derivative at a single \( (x, y) \) point.
real(fp_real) function	gridsurf_integral (this, lower, upper)
	Compute the double integral of the grid surface over a rectangular domain.
type(fitpack_curve) function	gridsurf_cross_section (this, u, along_y, ierr)
	Extract a 1D cross-section curve from the grid surface.
type(fitpack_grid_surface) function	gridsurf_derivative_spline (this, nux, nuy, ierr)
	Compute the B-spline representation of a partial derivative surface.
elemental integer(fp_size) function	gridsurf_comm_size (this)
	Return the communication buffer size for the grid surface.
pure subroutine	gridsurf_comm_pack (this, buffer)
	Pack grid surface data into a communication buffer.
pure subroutine	gridsurf_comm_expand (this, buffer)
	Expand grid surface data from a communication buffer.

Detailed Description

OOP wrapper for bivariate surface fitting to data on a rectangular grid.

Provides fitpack_grid_surface, a derived type for fitting tensor-product B-spline surfaces \( z = s(x, y) \) to data values given on a rectangular grid \( (x_i, y_j) \). The underlying core routine is regrid, which exploits the grid structure for faster fitting than surfit. Supports evaluation, partial derivatives, integration, cross-section extraction, and derivative-spline computation.

See also

Dierckx, Ch. 5, §5.4 (pp. 98–103); regrid, bispev, parder, pardeu, dblint, profil

Function/Subroutine Documentation

gridded_derivatives_gridded()

real(fp_real) function, dimension(size(y),size(x)) fitpack_grid_surfaces::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 partial derivatives on a rectangular grid.

See also

parder

gridded_derivatives_many()

real(fp_real) function, dimension(size(x)) fitpack_grid_surfaces::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()

real(fp_real) function fitpack_grid_surfaces::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

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gridded_eval_many()

real(fp_real) function, dimension(size(y),size(x)) fitpack_grid_surfaces::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()

real(fp_real) function fitpack_grid_surfaces::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 the grid surface at a single grid point via bispev.

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gridsurf_comm_expand()

pure subroutine fitpack_grid_surfaces::gridsurf_comm_expand ( class(fitpack_grid_surface), intent(inout) this, real(fp_comm), dimension(:), intent(in) buffer )

private

Expand grid surface data from a communication buffer.

gridsurf_comm_pack()

pure subroutine fitpack_grid_surfaces::gridsurf_comm_pack ( class(fitpack_grid_surface), intent(in) this, real(fp_comm), dimension(:), intent(out) buffer )

private

Pack grid surface data into a communication buffer.

gridsurf_comm_size()

elemental integer(fp_size) function fitpack_grid_surfaces::gridsurf_comm_size ( class(fitpack_grid_surface), intent(in) this )

private

Return the communication buffer size for the grid surface.

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gridsurf_cross_section()

type(fitpack_curve) function fitpack_grid_surfaces::gridsurf_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 )

private

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

If along_y=.true., returns \( f(y) = s(u, y) \); otherwise \( g(x) = s(x, u) \).

See also

profil

gridsurf_derivative_spline()

type(fitpack_grid_surface) function fitpack_grid_surfaces::gridsurf_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 )

private

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

Returns a new grid surface with reduced degrees and trimmed knots.

See also

pardtc

gridsurf_eval_many()

real(fp_real) function, dimension(size(x)) fitpack_grid_surfaces::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()

real(fp_real) function fitpack_grid_surfaces::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 the grid surface at a single \( (x, y) \) point.

See also

bispeu

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gridsurf_integral()

real(fp_real) function fitpack_grid_surfaces::gridsurf_integral ( class(fitpack_grid_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 grid surface over a rectangular domain.

See also

dblint

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surf_destroy()

elemental subroutine fitpack_grid_surfaces::surf_destroy ( class(fitpack_grid_surface), intent(inout) this )

private

Destroy a grid surface object and release all allocated memory.

surf_new_fit()

integer function fitpack_grid_surfaces::surf_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 )

private

Load new gridded data and perform a fresh fit.

See also

regrid

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surf_new_from_points()

type(fitpack_grid_surface) function fitpack_grid_surfaces::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 )

private

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

See also

regrid

surf_new_points()

subroutine fitpack_grid_surfaces::surf_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 )

private

Load new gridded data and allocate workspace.

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

surface_fit_automatic_knots()

integer(fp_flag) function fitpack_grid_surfaces::surface_fit_automatic_knots ( 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 )

private

Fit a smoothing gridded surface with automatic knot placement.

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

See also

regrid

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

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surface_fit_interpolating()

integer function fitpack_grid_surfaces::surface_fit_interpolating ( class(fitpack_grid_surface), intent(inout) this, logical, intent(in), optional reset_knots )

private

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

See also

regrid

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surface_fit_least_squares()

integer function fitpack_grid_surfaces::surface_fit_least_squares ( class(fitpack_grid_surface), intent(inout) this, real(fp_real), intent(in), optional smoothing, logical, intent(in), optional reset_knots )

private

Fit a least-squares gridded surface with fixed knots.

See also

regrid

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