Tensor-product gridded smoothing-spline fitter for any domain dimension. More...

Inheritance diagram for fitpack_gridded_splines::fitpack_gridded_spline:

Collaboration diagram for fitpack_gridded_splines::fitpack_gridded_spline:

Public Member Functions
procedure	destroy (this)
	Release all allocated storage and reset the fit state.

procedure	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`.

procedure	new_fit (this, xg, z, m, row_major, order, smoothing)
	Load new gridded data and perform a fit in one call.

procedure	fit (this, smoothing, order)
	Fit a smoothing spline with automatic knot placement (delegates to regrid).

procedure	least_squares (this, smoothing, reset_knots)
	Least-squares fit on the current knots (optionally recomputing them first).

procedure	interpolate (this)
	Interpolating fit (s = 0).

procedure	eval_ongrid (this, xg, m, ierr)
	Evaluate the fitted spline on a rectangular grid (delegates to ndspev).

generic	eval (this, x, ierr)
	Evaluate at scattered points x(i,d) (ndspeu). For gridded output use eval_ongrid.

generic	eval (this, xp, ierr)
	Evaluate the fitted spline at scattered points (delegates to ndspeu).

procedure	dfdx_ongrid (this, xg, m, nu, ierr)
	Partial derivatives of order nu(:) on a rectangular grid (parder)

generic	dfdx (this, x, nu, ierr)
	Partial derivatives of order nu(:) at scattered points (pardeu)

generic	dfdx (this, xp, nu, ierr)
	Evaluate partial derivatives of order `nu(:)` at scattered points (delegates to pardeu).

procedure	integral (this, lower, upper)
	Integral over a box [lower(d),upper(d)] (dblint)

procedure	cross_section (this, ax, u, ierr)
	Cross-section: fix one axis to obtain a (dims-1)-D spline (profil)

procedure	derivative_spline (this, nu, ierr)
	Partial-derivative spline: reduced degrees, trimmed knots (pardtc)

procedure	comm_size (this)
	Parallel communication.

procedure	comm_pack (this, buffer)
	Pack the fitter into a communication buffer.

procedure	comm_expand (this, buffer)
	Expand the fitter from a communication buffer.

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(fp_dim)	dims = 0
	Domain (tensor) dimension, 1 <= dims <= MAX_IDIM. Metadata below is active over 1:dims.

integer(fp_size), dimension(max_idim)	order = 3
	Per-axis spline degree.

integer(fp_size), dimension(max_idim)	m = 0
	Per-axis point counts, estimated/actual knot counts.

integer(fp_size), dimension(max_idim)	nest = 0

integer(fp_size), dimension(max_idim)	knots = 0

real(fp_real), dimension(max_idim)	left = zero
	Per-axis domain boundaries.

real(fp_real), dimension(max_idim)	right = zero

real(fp_real), dimension(:,:), allocatable	t
	Bulk arrays (only these are allocatable). t(:,d)=knots on axis d; xg(:,d)=grid coords on axis d; z(:)=flat function values (row-major, axis 1 slowest). c/wrk/iwrk/fp are inherited.

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

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

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	grid_eval_one (this, x, ierr)
	Evaluate at scattered points x(i,d) (ndspeu). For gridded output use eval_ongrid.

procedure, private	grid_eval_many (this, xp, ierr)
	Evaluate the fitted spline at scattered points (delegates to ndspeu).

procedure, private	grid_derivatives_one (this, x, nu, ierr)
	Partial derivatives of order nu(:) at scattered points (pardeu)

procedure, private	grid_derivatives_many (this, xp, nu, ierr)
	Evaluate partial derivatives of order `nu(:)` at scattered points (delegates to pardeu).

Detailed Description

Tensor-product gridded smoothing-spline fitter for any domain dimension.

Member Function/Subroutine Documentation

◆ comm_expand()

procedure fitpack_gridded_splines::fitpack_gridded_spline::comm_expand	(	class(fitpack_gridded_spline), intent(inout)	this,
		real(fp_comm), dimension(:), intent(in)	buffer )

Expand the fitter from a communication buffer.

◆ comm_pack()

procedure fitpack_gridded_splines::fitpack_gridded_spline::comm_pack	(	class(fitpack_gridded_spline), intent(in)	this,
		real(fp_comm), dimension(:), intent(out)	buffer )

Pack the fitter into a communication buffer.

◆ comm_size()

procedure fitpack_gridded_splines::fitpack_gridded_spline::comm_size ( class(fitpack_gridded_spline), intent(in) this )

Parallel communication.

◆ cross_section()

procedure fitpack_gridded_splines::fitpack_gridded_spline::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 )

Cross-section: fix one axis to obtain a (dims-1)-D spline (profil)

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.

◆ derivative_spline()

procedure fitpack_gridded_splines::fitpack_gridded_spline::derivative_spline	(	class(fitpack_gridded_spline), intent(in)	this,
		integer(fp_size), dimension(:), intent(in)	nu,
		integer(fp_flag), intent(out), optional	ierr )

Partial-derivative spline: reduced degrees, trimmed knots (pardtc)

◆ destroy()

procedure fitpack_gridded_splines::fitpack_gridded_spline::destroy ( class(fitpack_gridded_spline), intent(inout) this )

Release all allocated storage and reset the fit state.

◆ dfdx() [1/2]

generic fitpack_gridded_splines::fitpack_gridded_spline::dfdx	(	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 )

Partial derivatives of order nu(:) at scattered points (pardeu)

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◆ dfdx() [2/2]

generic fitpack_gridded_splines::fitpack_gridded_spline::dfdx	(	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 )

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)).

◆ dfdx_ongrid()

procedure fitpack_gridded_splines::fitpack_gridded_spline::dfdx_ongrid	(	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 )

Partial derivatives of order nu(:) on a rectangular grid (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).

◆ eval() [1/2]

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

Evaluate at scattered points x(i,d) (ndspeu). For gridded output use eval_ongrid.

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◆ eval() [2/2]

generic fitpack_gridded_splines::fitpack_gridded_spline::eval	(	class(fitpack_gridded_spline), intent(in)	this,
		real(fp_real), dimension(:,:), intent(in), contiguous	xp,
		integer(fp_flag), intent(out), optional	ierr )

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.

◆ eval_ongrid()

procedure fitpack_gridded_splines::fitpack_gridded_spline::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 )

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).

◆ fit()

procedure fitpack_gridded_splines::fitpack_gridded_spline::fit	(	class(fitpack_gridded_spline), intent(inout)	this,
		real(fp_real), intent(in), optional	smoothing,
		integer(fp_size), intent(in), optional	order )

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

◆ grid_derivatives_many()

procedure, private fitpack_gridded_splines::fitpack_gridded_spline::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)).

◆ grid_derivatives_one()

procedure, private fitpack_gridded_splines::fitpack_gridded_spline::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

Partial derivatives of order nu(:) at scattered points (pardeu)

◆ grid_eval_many()

procedure, private fitpack_gridded_splines::fitpack_gridded_spline::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.

◆ grid_eval_one()

procedure, private fitpack_gridded_splines::fitpack_gridded_spline::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 at scattered points x(i,d) (ndspeu). For gridded output use eval_ongrid.

◆ integral()

procedure fitpack_gridded_splines::fitpack_gridded_spline::integral	(	class(fitpack_gridded_spline), intent(in)	this,
		real(fp_real), dimension(:), intent(in)	lower,
		real(fp_real), dimension(:), intent(in)	upper )

Integral over a box [lower(d),upper(d)] (dblint)

◆ interpolate()

procedure fitpack_gridded_splines::fitpack_gridded_spline::interpolate ( class(fitpack_gridded_spline), intent(inout) this )

Interpolating fit (s = 0).

◆ least_squares()

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

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

◆ new_fit()

procedure fitpack_gridded_splines::fitpack_gridded_spline::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 )

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

◆ new_points()

procedure fitpack_gridded_splines::fitpack_gridded_spline::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 )

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).

Member Data Documentation

◆ dims

integer(fp_dim) fitpack_gridded_splines::fitpack_gridded_spline::dims = 0

Domain (tensor) dimension, 1 <= dims <= MAX_IDIM. Metadata below is active over 1:dims.

◆ knots

integer(fp_size), dimension(max_idim) fitpack_gridded_splines::fitpack_gridded_spline::knots = 0

◆ left

real(fp_real), dimension(max_idim) fitpack_gridded_splines::fitpack_gridded_spline::left = zero

Per-axis domain boundaries.

◆ m

integer(fp_size), dimension(max_idim) fitpack_gridded_splines::fitpack_gridded_spline::m = 0

Per-axis point counts, estimated/actual knot counts.

◆ nest

integer(fp_size), dimension(max_idim) fitpack_gridded_splines::fitpack_gridded_spline::nest = 0

◆ order

integer(fp_size), dimension(max_idim) fitpack_gridded_splines::fitpack_gridded_spline::order = 3

Per-axis spline degree.

◆ right

real(fp_real), dimension(max_idim) fitpack_gridded_splines::fitpack_gridded_spline::right = zero

◆ t

real(fp_real), dimension(:,:), allocatable fitpack_gridded_splines::fitpack_gridded_spline::t

Bulk arrays (only these are allocatable). t(:,d)=knots on axis d; xg(:,d)=grid coords on axis d; z(:)=flat function values (row-major, axis 1 slowest). c/wrk/iwrk/fp are inherited.

◆ xg

real(fp_real), dimension(:,:), allocatable fitpack_gridded_splines::fitpack_gridded_spline::xg

◆ z

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

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

fitpack_gridded_splines.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()

◆ grid_derivatives_many()

◆ grid_derivatives_one()

◆ grid_eval_many()

◆ grid_eval_one()

◆ integral()

◆ interpolate()

◆ least_squares()

◆ new_fit()

◆ new_points()

Member Data Documentation

◆ dims

◆ knots

◆ left

◆ m

◆ nest

◆ order

◆ right

◆ t

◆ xg

◆ z