Generic N-dimensional gridded smoothing-spline fitter. More...

Data Types
type	fitpack_gridded_spline
	Tensor-product gridded smoothing-spline fitter for any domain dimension. More...

Functions/Subroutines
elemental subroutine	grid_destroy (this)
	Release all allocated storage and reset the fit state.

subroutine	grid_new_points (this, xg, z, m, row_major, order)
	Load new gridded data. `z` is assumed-rank: a rank-`d` array (2 <= d <= MAX_IDIM) whose shape gives the per-axis point counts, or a flat rank-1 array with explicit `m`.

integer(fp_flag) function	grid_new_fit (this, xg, z, m, row_major, order, smoothing)
	Load new gridded data and perform a fit in one call.

integer(fp_flag) function	grid_fit_automatic_knots (this, smoothing, order)
	Fit a smoothing spline with automatic knot placement (delegates to regrid).

integer(fp_flag) function	grid_fit_least_squares (this, smoothing, reset_knots)
	Least-squares fit on the current knots (optionally recomputing them first).

integer(fp_flag) function	grid_fit_interpolating (this)
	Interpolating fit (s = 0).

real(fp_real) function, dimension(product(m))	grid_eval_ongrid (this, xg, m, ierr)
	Evaluate the fitted spline on a rectangular grid (delegates to ndspev).

real(fp_real) function, dimension(size(xp, 2))	grid_eval_many (this, xp, ierr)
	Evaluate the fitted spline at scattered points (delegates to ndspeu).

real(fp_real) function	grid_eval_one (this, x, ierr)
	Evaluate the fitted spline at a single point `x(1:dims)`.

real(fp_real) function, dimension(product(m))	grid_derivatives_gridded (this, xg, m, nu, ierr)
	Evaluate partial derivatives of order `nu(:)` on a rectangular grid (delegates to parder).

real(fp_real) function, dimension(size(xp, 2))	grid_derivatives_many (this, xp, nu, ierr)
	Evaluate partial derivatives of order `nu(:)` at scattered points (delegates to pardeu).

real(fp_real) function	grid_derivatives_one (this, x, nu, ierr)
	Evaluate a partial derivative of order `nu(:)` at a single point `x(1:dims)`.

real(fp_real) function	grid_integral (this, lower, upper)
	Integral of the fitted spline over the box `[lower(d),upper(d)]` (delegates to dblint).

type(fitpack_gridded_spline) function	grid_cross_section (this, ax, u, ierr)
	Cross-section: fix axis `ax` at value `u`, returning the `(dims-1)`-D spline \( s\|_{x_{ax}=u} \).

type(fitpack_gridded_spline) function	grid_derivative_spline (this, nu, ierr)
	Partial-derivative spline of order `nu(:)`: a new gridded spline of per-axis degrees `order-nu` on trimmed knots (delegates to pardtc). Eval-only, like `cross_section`.

subroutine	grid_prepare_workspace (this)
	(Re)size the persistent workspace, maximally, so it is allocated only once, at spline construction. Covers both regrid's fit requirement (mirroring its internal lwest/kwest) and the peripheral evaluations (ndspev/parder/pardeu on grids up to the data-grid size), which carve their scratch past regrid's persistent iopt=1 state in wrk(1:2+dims)/ iwrk(1:1+dims). Grows the arrays only when needed so a continuation keeps that state.

subroutine	grid_ensure_eval_workspace (this, maxm)
	Ensure the persistent workspace covers a peripheral evaluation with per-axis grids of up to `maxm` points. grid_prepare_workspace already sized it for grids up to the data grid, so this only grows the arrays for finer evaluation grids; contents are preserved so regrid's iopt=1 state in wrk(1:2+dims)/iwrk(1:1+dims) survives the growth.

pure subroutine	ranked_sizes (shp, row_major, dims, m)
	Map a rank-`d` array shape to per-axis domain sizes, honouring the row_major flag. row_major=.true.: axes are reversed (z(m_d,...,m_1)); .false.: natural (z(m_1,...,m_d)).

pure real(fp_real) function, dimension(size(zc))	flat_row_major (zc, shp, row_major)
	Return the flat row-major (axis-1-slowest) value buffer from a column-major flatten. row_major=.true.: the input already IS row-major, copy as-is. row_major=.false.: the input is a natural Fortran grid z(m_1,...,m_d); permute (reverse axes) into row-major.

elemental integer(fp_size) function	grid_comm_size (this)
	Communication buffer size: base fields + fixed metadata (1 + 6*MAX_IDIM) + bulk arrays.

pure subroutine	grid_comm_pack (this, buffer)
	Pack the fitter into a communication buffer.

pure subroutine	grid_comm_expand (this, buffer)
	Expand the fitter from a communication buffer.

Detailed Description

Generic N-dimensional gridded smoothing-spline fitter.

fitpack_gridded_spline fits a tensor-product B-spline \( s(x_1,\ldots,x_d) \) to data on a rectangular grid of arbitrary domain dimension dims (the 3D+ analogue of the concrete 2-D fitpack_grid_surface). One runtime-dims type holds a fit of any dimensionality up to MAX_IDIM; the guts marshal onto the dimension-generic core routines regrid (fit) and ndspev (grid evaluation).

CANONICAL DATA LAYOUT. Internally the function values live in a flat, row-major buffer with domain axis 1 the slowest-varying and axis dims the fastest — exactly the contract of regrid. The rank-natural entry points accept an assumed-rank array and an optional row_major flag:

row_major = .true. (default): the array's Fortran (column-major) storage already equals the internal buffer, so it is copied as-is. For a rank-d array that means passing the axes in reverse, z(m_d, ..., m_1) — the direct generalization of the 2-D z(iy,ix) convention.
row_major = .false.: the array is a natural Fortran grid z(m_1, ..., m_d) (dimension k is domain axis k); it is permuted into the row-major buffer on ingest (a one-time copy). A flat rank-1 z(:) plus explicit m(:) is always accepted (row-major, unambiguous).

See also: fitpack_grid_surface — concrete 2-D face; regrid, ndspev — N-D core routines

Function/Subroutine Documentation

◆ flat_row_major()

pure real(fp_real) function, dimension(size(zc)) fitpack_gridded_splines::flat_row_major	(	real(fp_real), dimension(:), intent(in)	zc,
		integer(fp_size), dimension(:), intent(in)	shp,
		logical(fp_bool), intent(in)	row_major )

private

Return the flat row-major (axis-1-slowest) value buffer from a column-major flatten. row_major=.true.: the input already IS row-major, copy as-is. row_major=.false.: the input is a natural Fortran grid z(m_1,...,m_d); permute (reverse axes) into row-major.

◆ grid_comm_expand()

pure subroutine fitpack_gridded_splines::grid_comm_expand	(	class(fitpack_gridded_spline), intent(inout)	this,
		real(fp_comm), dimension(:), intent(in)	buffer )

private

Expand the fitter from a communication buffer.

◆ grid_comm_pack()

pure subroutine fitpack_gridded_splines::grid_comm_pack	(	class(fitpack_gridded_spline), intent(in)	this,
		real(fp_comm), dimension(:), intent(out)	buffer )

private

Pack the fitter into a communication buffer.

◆ grid_comm_size()

elemental integer(fp_size) function fitpack_gridded_splines::grid_comm_size ( class(fitpack_gridded_spline), intent(in) this )

private

Communication buffer size: base fields + fixed metadata (1 + 6*MAX_IDIM) + bulk arrays.

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◆ grid_cross_section()

type(fitpack_gridded_spline) function fitpack_gridded_splines::grid_cross_section	(	class(fitpack_gridded_spline), intent(in)	this,
		integer(fp_dim), intent(in)	ax,
		real(fp_real), intent(in)	u,
		integer(fp_flag), intent(out), optional	ierr )

private

Cross-section: fix axis ax at value u, returning the (dims-1)-D spline \( s|_{x_{ax}=u} \).

The result is a fully-formed, evaluable fitpack_gridded_spline over the surviving axes (in their original relative order). Like the 2-D cross_section it carries only the spline (knots/degrees/ coefficients/bounds), not a data grid, so it is eval-only.

Parameters

[in]	ax	Axis to fix, `1 <= ax <= dims` (requires `dims >= 2`).
[in]	u	Value at which axis `ax` is fixed.
[out]	ierr	Optional error flag.

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◆ grid_derivative_spline()

type(fitpack_gridded_spline) function fitpack_gridded_splines::grid_derivative_spline	(	class(fitpack_gridded_spline), intent(in)	this,
		integer(fp_size), dimension(:), intent(in)	nu,
		integer(fp_flag), intent(out), optional	ierr )

private

Partial-derivative spline of order nu(:): a new gridded spline of per-axis degrees order-nu on trimmed knots (delegates to pardtc). Eval-only, like cross_section.

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◆ grid_derivatives_gridded()

real(fp_real) function, dimension(product(m)) fitpack_gridded_splines::grid_derivatives_gridded	(	class(fitpack_gridded_spline), intent(inout)	this,
		real(fp_real), dimension(:,:), intent(in)	xg,
		integer(fp_size), dimension(:), intent(in)	m,
		integer(fp_size), dimension(:), intent(in)	nu,
		integer(fp_flag), intent(out), optional	ierr )

private

Evaluate partial derivatives of order nu(:) on a rectangular grid (delegates to parder).

Parameters

[in]	xg	Per-axis evaluation grids, `xg(1:m(d),d)` strictly increasing.
[in]	m	Per-axis grid sizes.
[in]	nu	Per-axis derivative orders, `0 <= nu(d) < order(d)`.
[out]	ierr	Optional error flag.

Returns: f Flat row-major derivative values, length product(m).

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◆ grid_derivatives_many()

real(fp_real) function, dimension(size(xp,2)) fitpack_gridded_splines::grid_derivatives_many	(	class(fitpack_gridded_spline), intent(inout)	this,
		real(fp_real), dimension(:,:), intent(in), contiguous	xp,
		integer(fp_size), dimension(:), intent(in)	nu,
		integer(fp_flag), intent(out), optional	ierr )

private

Evaluate partial derivatives of order nu(:) at scattered points (delegates to pardeu).

Parameters

[in] xp Point coordinates, xp(d,i) = axis-d coordinate of point i (shape (dims,m), point i = contiguous column xp(:,i)).

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◆ grid_derivatives_one()

real(fp_real) function fitpack_gridded_splines::grid_derivatives_one	(	class(fitpack_gridded_spline), intent(inout)	this,
		real(fp_real), dimension(:), intent(in)	x,
		integer(fp_size), dimension(:), intent(in)	nu,
		integer(fp_flag), intent(out), optional	ierr )

private

Evaluate a partial derivative of order nu(:) at a single point x(1:dims).

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◆ grid_destroy()

elemental subroutine fitpack_gridded_splines::grid_destroy ( class(fitpack_gridded_spline), intent(inout) this )

Release all allocated storage and reset the fit state.

◆ grid_ensure_eval_workspace()

subroutine fitpack_gridded_splines::grid_ensure_eval_workspace	(	class(fitpack_gridded_spline), intent(inout)	this,
		integer(fp_size), intent(in)	maxm )

private

Ensure the persistent workspace covers a peripheral evaluation with per-axis grids of up to maxm points. grid_prepare_workspace already sized it for grids up to the data grid, so this only grows the arrays for finer evaluation grids; contents are preserved so regrid's iopt=1 state in wrk(1:2+dims)/iwrk(1:1+dims) survives the growth.

◆ grid_eval_many()

real(fp_real) function, dimension(size(xp,2)) fitpack_gridded_splines::grid_eval_many	(	class(fitpack_gridded_spline), intent(in)	this,
		real(fp_real), dimension(:,:), intent(in), contiguous	xp,
		integer(fp_flag), intent(out), optional	ierr )

private

Evaluate the fitted spline at scattered points (delegates to ndspeu).

Parameters

[in]	xp	Point coordinates, `xp(d,i)` = axis-`d` coordinate of point `i` (shape `(dims,m)`, point `i` = contiguous column `xp(:,i)`; matches curev/parcur layout).
[out]	ierr	Optional error flag.

Returns: f Spline values at the m points.

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◆ grid_eval_one()

real(fp_real) function fitpack_gridded_splines::grid_eval_one	(	class(fitpack_gridded_spline), intent(in)	this,
		real(fp_real), dimension(:), intent(in)	x,
		integer(fp_flag), intent(out), optional	ierr )

private

Evaluate the fitted spline at a single point x(1:dims).

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◆ grid_eval_ongrid()

real(fp_real) function, dimension(product(m)) fitpack_gridded_splines::grid_eval_ongrid	(	class(fitpack_gridded_spline), intent(inout)	this,
		real(fp_real), dimension(:,:), intent(in)	xg,
		integer(fp_size), dimension(:), intent(in)	m,
		integer(fp_flag), intent(out), optional	ierr )

private

Evaluate the fitted spline on a rectangular grid (delegates to ndspev).

Parameters

[in]	xg	Evaluation coordinates, `xg(1:m(d),d)` strictly increasing on axis `d`.
[in]	m	Per-axis evaluation-grid sizes.
[out]	ierr	Optional error flag.

Returns: zeval Flat, row-major (axis 1 slowest) evaluated values, length product(m).

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◆ grid_fit_automatic_knots()

integer(fp_flag) function fitpack_gridded_splines::grid_fit_automatic_knots	(	class(fitpack_gridded_spline), intent(inout)	this,
		real(fp_real), intent(in), optional	smoothing,
		integer(fp_size), intent(in), optional	order )

private

Fit a smoothing spline with automatic knot placement (delegates to regrid).

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◆ grid_fit_interpolating()

integer(fp_flag) function fitpack_gridded_splines::grid_fit_interpolating ( class(fitpack_gridded_spline), intent(inout) this )

private

Interpolating fit (s = 0).

◆ grid_fit_least_squares()

integer(fp_flag) function fitpack_gridded_splines::grid_fit_least_squares	(	class(fitpack_gridded_spline), intent(inout)	this,
		real(fp_real), intent(in), optional	smoothing,
		logical, intent(in), optional	reset_knots )

private

Least-squares fit on the current knots (optionally recomputing them first).

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◆ grid_integral()

real(fp_real) function fitpack_gridded_splines::grid_integral	(	class(fitpack_gridded_spline), intent(in)	this,
		real(fp_real), dimension(:), intent(in)	lower,
		real(fp_real), dimension(:), intent(in)	upper )

private

Integral of the fitted spline over the box [lower(d),upper(d)] (delegates to dblint).

◆ grid_new_fit()

integer(fp_flag) function fitpack_gridded_splines::grid_new_fit	(	class(fitpack_gridded_spline), intent(inout)	this,
		real(fp_real), dimension(:,:), intent(in)	xg,
		real(fp_real), dimension(..), intent(in)	z,
		integer(fp_size), dimension(:), intent(in), optional	m,
		logical(fp_bool), intent(in), optional	row_major,
		integer(fp_size), intent(in), optional	order,
		real(fp_real), intent(in), optional	smoothing )

private

Load new gridded data and perform a fit in one call.

◆ grid_new_points()

subroutine fitpack_gridded_splines::grid_new_points	(	class(fitpack_gridded_spline), intent(inout)	this,
		real(fp_real), dimension(:,:), intent(in)	xg,
		real(fp_real), dimension(..), intent(in)	z,
		integer(fp_size), dimension(:), intent(in), optional	m,
		logical(fp_bool), intent(in), optional	row_major,
		integer(fp_size), intent(in), optional	order )

private

Load new gridded data. z is assumed-rank: a rank-d array (2 <= d <= MAX_IDIM) whose shape gives the per-axis point counts, or a flat rank-1 array with explicit m.

Parameters

[in]	xg	Grid coordinates, `xg(1:m(d),d)` strictly increasing on axis `d`.
[in]	z	Function values (see the module header for the layout conventions).
[in]	m	Per-axis point counts; REQUIRED when `z` is rank-1, ignored otherwise.
[in]	row_major	Layout of a rank-`d` `z` (default .true.); see the module header.
[in]	order	Optional per-axis spline degree (scalar, applied to all axes).

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◆ grid_prepare_workspace()

subroutine fitpack_gridded_splines::grid_prepare_workspace ( class(fitpack_gridded_spline), intent(inout) this )

private

(Re)size the persistent workspace, maximally, so it is allocated only once, at spline construction. Covers both regrid's fit requirement (mirroring its internal lwest/kwest) and the peripheral evaluations (ndspev/parder/pardeu on grids up to the data-grid size), which carve their scratch past regrid's persistent iopt=1 state in wrk(1:2+dims)/ iwrk(1:1+dims). Grows the arrays only when needed so a continuation keeps that state.

◆ ranked_sizes()

pure subroutine fitpack_gridded_splines::ranked_sizes	(	integer(fp_size), dimension(:), intent(in)	shp,
		logical(fp_bool), intent(in)	row_major,
		integer(fp_dim), intent(out)	dims,
		integer(fp_size), dimension(max_idim), intent(out)	m )

private

Map a rank-d array shape to per-axis domain sizes, honouring the row_major flag. row_major=.true.: axes are reversed (z(m_d,...,m_1)); .false.: natural (z(m_1,...,m_d)).

Data Types

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ flat_row_major()

◆ grid_comm_expand()

◆ grid_comm_pack()

◆ grid_comm_size()

◆ grid_cross_section()

◆ grid_derivative_spline()

◆ grid_derivatives_gridded()

◆ grid_derivatives_many()

◆ grid_derivatives_one()

◆ grid_destroy()

◆ grid_ensure_eval_workspace()

◆ grid_eval_many()

◆ grid_eval_one()

◆ grid_eval_ongrid()

◆ grid_fit_automatic_knots()

◆ grid_fit_interpolating()

◆ grid_fit_least_squares()

◆ grid_integral()

◆ grid_new_fit()

◆ grid_new_points()

◆ grid_prepare_workspace()

◆ ranked_sizes()