bspline_3d – bspline-fortran

type, public, extends(bspline_class) :: bspline_3d

Class for 3d b-spline interpolation.

Inherits

Help

Components

Type	Visibility	Attributes		Name		Initial
integer(kind=ip),	private		::	nx	=	0_ip	Number of $x$ abcissae
integer(kind=ip),	private		::	ny	=	0_ip	Number of $y$ abcissae
integer(kind=ip),	private		::	nz	=	0_ip	Number of $z$ abcissae
integer(kind=ip),	private		::	kx	=	0_ip	The order of spline pieces in $x$
integer(kind=ip),	private		::	ky	=	0_ip	The order of spline pieces in $y$
integer(kind=ip),	private		::	kz	=	0_ip	The order of spline pieces in $z$
real(kind=wp),	private,	dimension(:,:,:,:), allocatable	::	bcoef			array of coefficients of the b-spline interpolant (the last dimension is the output index)
real(kind=wp),	private,	dimension(:), allocatable	::	tx			The knots in the $x$ direction for the spline interpolant
real(kind=wp),	private,	dimension(:), allocatable	::	ty			The knots in the $y$ direction for the spline interpolant
real(kind=wp),	private,	dimension(:), allocatable	::	tz			The knots in the $z$ direction for the spline interpolant
integer(kind=ip),	private		::	inbvy	=	1_ip	internal variable used for efficient processing
integer(kind=ip),	private		::	inbvz	=	1_ip	internal variable used for efficient processing
integer(kind=ip),	private		::	iloy	=	1_ip	internal variable used for efficient processing
integer(kind=ip),	private		::	iloz	=	1_ip	internal variable used for efficient processing
real(kind=wp),	private,	dimension(:,:), allocatable	::	work_val_1			[[db3val] work array of dimension `ky,kz`
real(kind=wp),	private,	dimension(:), allocatable	::	work_val_2			[[db3val] work array of dimension `kz`
real(kind=wp),	private,	dimension(:), allocatable	::	work_val_3			[[db3val] work array of dimension `3_ip*max(kx,ky,kz)`

Constructor

public interface bspline_3d

Constructor for bspline_3d

private elemental function bspline_3d_constructor_empty() result(me)

It returns an empty bspline_3d type. Note that INITIALIZE still needs to be called before it can be used. Not really that useful except perhaps in some OpenMP applications.

Arguments
None
Return Value type(bspline_3d)

private pure function bspline_3d_constructor_auto_knots(x, y, z, fcn, kx, ky, kz, extrap) result(me)

Constructor for a bspline_3d type (auto knots). This is a wrapper for initialize_3d_auto_knots.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in),		dimension(:)	::	x	`(nx)` array of $x$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	y	`(ny)` array of $y$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	z	`(nz)` array of $z$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:,:,:)	::	fcn	`(nx,ny,nz)` matrix of function values to interpolate. `fcn(i,j,k)` should contain the function value at the point (`x(i)`,`y(j)`,`z(k)`)
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$ ( $2 \le k_x < n_x$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	ky	The order of spline pieces in $y$ ( $2 \le k_y < n_y$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	kz	The order of spline pieces in $z$ ( $2 \le k_z < n_z$ ) (order = polynomial degree + 1)
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

Return Value type(bspline_3d)

private pure function bspline_3d_constructor_specify_knots(x, y, z, fcn, kx, ky, kz, tx, ty, tz, extrap) result(me)

Constructor for a bspline_3d type (user-specified knots). This is a wrapper for initialize_3d_specify_knots.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in),		dimension(:)	::	x	`(nx)` array of $x$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	y	`(ny)` array of $y$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	z	`(nz)` array of $z$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:,:,:)	::	fcn	`(nx,ny,nz)` matrix of function values to interpolate. `fcn(i,j,k)` should contain the function value at the point (`x(i)`,`y(j)`,`z(k)`)
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$ ( $2 \le k_x < n_x$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	ky	The order of spline pieces in $y$ ( $2 \le k_y < n_y$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	kz	The order of spline pieces in $z$ ( $2 \le k_z < n_z$ ) (order = polynomial degree + 1)
real(kind=wp),	intent(in),		dimension(:)	::	tx	The `(nx+kx)` knots in the $x$ direction for the spline interpolant. Must be non-decreasing.
real(kind=wp),	intent(in),		dimension(:)	::	ty	The `(ny+ky)` knots in the $y$ direction for the spline interpolant. Must be non-decreasing.
real(kind=wp),	intent(in),		dimension(:)	::	tz	The `(nz+kz)` knots in the $z$ direction for the spline interpolant. Must be non-decreasing.
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

Return Value type(bspline_3d)

Finalization Procedures

final :: finalize_3d

private pure elemental subroutine finalize_3d(me)

Finalizer for bspline_3d class. Just a wrapper for destroy_3d.

Arguments

Type	Intent	Optional	Attributes		Name
type(bspline_3d),	intent(inout)			::	me

Type-Bound Procedures

procedure, public, non_overridable :: status_ok

returns true if the last iflag status code was =0.

private elemental function status_ok(me) result(ok)

This routines returns true if the iflag code from the last routine called was =0. Maybe of the routines have output iflag variables, so they can be checked explicitly, or this routine can be used.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_class),	intent(in)			::	me

Return Value logical

procedure, public, non_overridable :: status_message => get_bspline_status_message

retrieve the last status message

private pure function get_bspline_status_message(me, iflag) result(msg)

Get the status message from a bspline_class routine call.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_class),	intent(in)			::	me
integer(kind=ip),	intent(in),	optional		::	iflag	the corresponding status code

Return Value character(len=:), allocatable

status message associated with the flag

procedure, public, non_overridable :: clear_flag => clear_bspline_flag

to reset the iflag saved in the class.

private elemental subroutine clear_bspline_flag(me)

This sets the iflag variable in the class to 0 (which indicates that everything is OK). It can be used after an error is encountered.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_class),	intent(inout)			::	me

procedure, public, non_overridable :: number_of_outputs

number of outputs (functions) of the spline

private pure function number_of_outputs(me) result(nf)

Returns the number of outputs (functions of the same inputs) of the spline: 1 for a spline initialized with a single function, and nf for one initialized with nf functions (the last dimension of fcn). Returns 0 if the class is not initialized.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_class),	intent(in)			::	me	the spline

Return Value integer(kind=ip)

number of outputs

generic, public :: initialize => initialize_3d_auto_knots, initialize_3d_specify_knots, initialize_3d_auto_knots_multi, initialize_3d_specify_knots_multi

private pure subroutine initialize_3d_auto_knots(me, x, y, z, fcn, kx, ky, kz, iflag, extrap)

Initialize a bspline_3d type (with automatically-computed knots). This is a wrapper for db3ink.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_3d),	intent(inout)			::	me
real(kind=wp),	intent(in),		dimension(:)	::	x	`(nx)` array of $x$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	y	`(ny)` array of $y$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	z	`(nz)` array of $z$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:,:,:)	::	fcn	`(nx,ny,nz)` matrix of function values to interpolate. `fcn(i,j,k)` should contain the function value at the point (`x(i)`,`y(j)`,`z(k)`)
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$ ( $2 \le k_x < n_x$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	ky	The order of spline pieces in $y$ ( $2 \le k_y < n_y$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	kz	The order of spline pieces in $z$ ( $2 \le k_z < n_z$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(out)			::	iflag	status flag (see db3ink)
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

private pure subroutine initialize_3d_specify_knots(me, x, y, z, fcn, kx, ky, kz, tx, ty, tz, iflag, extrap)

Initialize a bspline_3d type (with user-specified knots). This is a wrapper for db3ink.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_3d),	intent(inout)			::	me
real(kind=wp),	intent(in),		dimension(:)	::	x	`(nx)` array of $x$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	y	`(ny)` array of $y$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	z	`(nz)` array of $z$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:,:,:)	::	fcn	`(nx,ny,nz)` matrix of function values to interpolate. `fcn(i,j,k)` should contain the function value at the point (`x(i)`,`y(j)`,`z(k)`)
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$ ( $2 \le k_x < n_x$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	ky	The order of spline pieces in $y$ ( $2 \le k_y < n_y$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	kz	The order of spline pieces in $z$ ( $2 \le k_z < n_z$ ) (order = polynomial degree + 1)
real(kind=wp),	intent(in),		dimension(:)	::	tx	The `(nx+kx)` knots in the $x$ direction for the spline interpolant. Must be non-decreasing.
real(kind=wp),	intent(in),		dimension(:)	::	ty	The `(ny+ky)` knots in the $y$ direction for the spline interpolant. Must be non-decreasing.
real(kind=wp),	intent(in),		dimension(:)	::	tz	The `(nz+kz)` knots in the $z$ direction for the spline interpolant. Must be non-decreasing.
integer(kind=ip),	intent(out)			::	iflag	status flag (see db3ink)
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

private pure subroutine initialize_3d_auto_knots_multi(me, x, y, z, fcn, kx, ky, kz, iflag, extrap)

Initialize a bspline_3d type with multiple outputs: nf functions of the same inputs, on the same grid. The last dimension of fcn is the output index. This is a wrapper for db3ink (multiple-output version).

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_3d),	intent(inout)			::	me	the spline
real(kind=wp),	intent(in),		dimension(:)	::	x	`(nx)` array of $x$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	y	`(ny)` array of $y$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	z	`(nz)` array of $z$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:,:,:,:)	::	fcn	`(nx,ny,nz,nf)` array of function values to interpolate (the last dimension is the output index)
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$
integer(kind=ip),	intent(in)			::	ky	The order of spline pieces in $y$
integer(kind=ip),	intent(in)			::	kz	The order of spline pieces in $z$
integer(kind=ip),	intent(out)			::	iflag	status flag (see db3ink)
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

private pure subroutine initialize_3d_specify_knots_multi(me, x, y, z, fcn, kx, ky, kz, tx, ty, tz, iflag, extrap)

Initialize a bspline_3d type with multiple outputs: nf functions of the same inputs, on the same grid (with user-specified knots). The last dimension of fcn is the output index. This is a wrapper for db3ink (multiple-output version).

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_3d),	intent(inout)			::	me	the spline
real(kind=wp),	intent(in),		dimension(:)	::	x	`(nx)` array of $x$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	y	`(ny)` array of $y$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	z	`(nz)` array of $z$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:,:,:,:)	::	fcn	`(nx,ny,nz,nf)` array of function values to interpolate (the last dimension is the output index)
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$
integer(kind=ip),	intent(in)			::	ky	The order of spline pieces in $y$
integer(kind=ip),	intent(in)			::	kz	The order of spline pieces in $z$
real(kind=wp),	intent(in),		dimension(:)	::	tx	The `(nx+kx)` knots in the $x$ direction.
real(kind=wp),	intent(in),		dimension(:)	::	ty	The `(ny+ky)` knots in the $y$ direction.
real(kind=wp),	intent(in),		dimension(:)	::	tz	The `(nz+kz)` knots in the $z$ direction.
integer(kind=ip),	intent(out)			::	iflag	status flag (see db3ink)
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

procedure, private :: initialize_3d_auto_knots_multi

private pure subroutine initialize_3d_auto_knots_multi(me, x, y, z, fcn, kx, ky, kz, iflag, extrap)

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_3d),	intent(inout)			::	me	the spline
real(kind=wp),	intent(in),		dimension(:)	::	x	`(nx)` array of $x$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	y	`(ny)` array of $y$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	z	`(nz)` array of $z$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:,:,:,:)	::	fcn	`(nx,ny,nz,nf)` array of function values to interpolate (the last dimension is the output index)
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$
integer(kind=ip),	intent(in)			::	ky	The order of spline pieces in $y$
integer(kind=ip),	intent(in)			::	kz	The order of spline pieces in $z$
integer(kind=ip),	intent(out)			::	iflag	status flag (see db3ink)
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

procedure, private :: initialize_3d_specify_knots_multi

private pure subroutine initialize_3d_specify_knots_multi(me, x, y, z, fcn, kx, ky, kz, tx, ty, tz, iflag, extrap)

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_3d),	intent(inout)			::	me	the spline
real(kind=wp),	intent(in),		dimension(:)	::	x	`(nx)` array of $x$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	y	`(ny)` array of $y$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	z	`(nz)` array of $z$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:,:,:,:)	::	fcn	`(nx,ny,nz,nf)` array of function values to interpolate (the last dimension is the output index)
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$
integer(kind=ip),	intent(in)			::	ky	The order of spline pieces in $y$
integer(kind=ip),	intent(in)			::	kz	The order of spline pieces in $z$
real(kind=wp),	intent(in),		dimension(:)	::	tx	The `(nx+kx)` knots in the $x$ direction.
real(kind=wp),	intent(in),		dimension(:)	::	ty	The `(ny+ky)` knots in the $y$ direction.
real(kind=wp),	intent(in),		dimension(:)	::	tz	The `(nz+kz)` knots in the $z$ direction.
integer(kind=ip),	intent(out)			::	iflag	status flag (see db3ink)
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

procedure, private :: initialize_3d_auto_knots

private pure subroutine initialize_3d_auto_knots(me, x, y, z, fcn, kx, ky, kz, iflag, extrap)

Initialize a bspline_3d type (with automatically-computed knots). This is a wrapper for db3ink.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_3d),	intent(inout)			::	me
real(kind=wp),	intent(in),		dimension(:)	::	x	`(nx)` array of $x$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	y	`(ny)` array of $y$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	z	`(nz)` array of $z$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:,:,:)	::	fcn	`(nx,ny,nz)` matrix of function values to interpolate. `fcn(i,j,k)` should contain the function value at the point (`x(i)`,`y(j)`,`z(k)`)
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$ ( $2 \le k_x < n_x$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	ky	The order of spline pieces in $y$ ( $2 \le k_y < n_y$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	kz	The order of spline pieces in $z$ ( $2 \le k_z < n_z$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(out)			::	iflag	status flag (see db3ink)
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

procedure, private :: initialize_3d_specify_knots

private pure subroutine initialize_3d_specify_knots(me, x, y, z, fcn, kx, ky, kz, tx, ty, tz, iflag, extrap)

Initialize a bspline_3d type (with user-specified knots). This is a wrapper for db3ink.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_3d),	intent(inout)			::	me
real(kind=wp),	intent(in),		dimension(:)	::	x	`(nx)` array of $x$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	y	`(ny)` array of $y$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:)	::	z	`(nz)` array of $z$ abcissae. Must be strictly increasing.
real(kind=wp),	intent(in),		dimension(:,:,:)	::	fcn	`(nx,ny,nz)` matrix of function values to interpolate. `fcn(i,j,k)` should contain the function value at the point (`x(i)`,`y(j)`,`z(k)`)
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$ ( $2 \le k_x < n_x$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	ky	The order of spline pieces in $y$ ( $2 \le k_y < n_y$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	kz	The order of spline pieces in $z$ ( $2 \le k_z < n_z$ ) (order = polynomial degree + 1)
real(kind=wp),	intent(in),		dimension(:)	::	tx	The `(nx+kx)` knots in the $x$ direction for the spline interpolant. Must be non-decreasing.
real(kind=wp),	intent(in),		dimension(:)	::	ty	The `(ny+ky)` knots in the $y$ direction for the spline interpolant. Must be non-decreasing.
real(kind=wp),	intent(in),		dimension(:)	::	tz	The `(nz+kz)` knots in the $z$ direction for the spline interpolant. Must be non-decreasing.
integer(kind=ip),	intent(out)			::	iflag	status flag (see db3ink)
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

generic, public :: evaluate => evaluate_3d, evaluate_3d_multi

private pure subroutine evaluate_3d(me, xval, yval, zval, idx, idy, idz, f, iflag)

Evaluate a bspline_3d interpolate. This is a wrapper for db3val.

Arguments

Type	Intent		Name
class(bspline_3d),	intent(inout)	::	me
real(kind=wp),	intent(in)	::	xval	$x$ coordinate of evaluation point.
real(kind=wp),	intent(in)	::	yval	$y$ coordinate of evaluation point.
real(kind=wp),	intent(in)	::	zval	$z$ coordinate of evaluation point.
integer(kind=ip),	intent(in)	::	idx	$x$ derivative of piecewise polynomial to evaluate.
integer(kind=ip),	intent(in)	::	idy	$y$ derivative of piecewise polynomial to evaluate.
integer(kind=ip),	intent(in)	::	idz	$z$ derivative of piecewise polynomial to evaluate.
real(kind=wp),	intent(out)	::	f	interpolated value
integer(kind=ip),	intent(out)	::	iflag	status flag (see db3val)

private pure subroutine evaluate_3d_multi(me, xval, yval, zval, idx, idy, idz, f, iflag)

Evaluate all the outputs of a bspline_3d with multiple outputs. This is a wrapper for db3val (multiple-output version).

Arguments

Type	Intent	Attributes		Name
class(bspline_3d),	intent(inout)		::	me	the spline
real(kind=wp),	intent(in)		::	xval	$x$ coordinate of evaluation point.
real(kind=wp),	intent(in)		::	yval	$y$ coordinate of evaluation point.
real(kind=wp),	intent(in)		::	zval	$z$ coordinate of evaluation point.
integer(kind=ip),	intent(in)		::	idx	$x$ derivative of piecewise polynomial to evaluate.
integer(kind=ip),	intent(in)		::	idy	$y$ derivative of piecewise polynomial to evaluate.
integer(kind=ip),	intent(in)		::	idz	$z$ derivative of piecewise polynomial to evaluate.
real(kind=wp),	intent(out),	dimension(:)	::	f	`(nf)` interpolated values of the outputs (see number_of_outputs)
integer(kind=ip),	intent(out)		::	iflag	status flag (see db3val)

procedure, private :: evaluate_3d

private pure subroutine evaluate_3d(me, xval, yval, zval, idx, idy, idz, f, iflag)

Evaluate a bspline_3d interpolate. This is a wrapper for db3val.

Arguments

Type	Intent		Name
class(bspline_3d),	intent(inout)	::	me
real(kind=wp),	intent(in)	::	xval	$x$ coordinate of evaluation point.
real(kind=wp),	intent(in)	::	yval	$y$ coordinate of evaluation point.
real(kind=wp),	intent(in)	::	zval	$z$ coordinate of evaluation point.
integer(kind=ip),	intent(in)	::	idx	$x$ derivative of piecewise polynomial to evaluate.
integer(kind=ip),	intent(in)	::	idy	$y$ derivative of piecewise polynomial to evaluate.
integer(kind=ip),	intent(in)	::	idz	$z$ derivative of piecewise polynomial to evaluate.
real(kind=wp),	intent(out)	::	f	interpolated value
integer(kind=ip),	intent(out)	::	iflag	status flag (see db3val)

procedure, private :: evaluate_3d_multi

private pure subroutine evaluate_3d_multi(me, xval, yval, zval, idx, idy, idz, f, iflag)

Evaluate all the outputs of a bspline_3d with multiple outputs. This is a wrapper for db3val (multiple-output version).

Arguments

Type	Intent	Attributes		Name
class(bspline_3d),	intent(inout)		::	me	the spline
real(kind=wp),	intent(in)		::	xval	$x$ coordinate of evaluation point.
real(kind=wp),	intent(in)		::	yval	$y$ coordinate of evaluation point.
real(kind=wp),	intent(in)		::	zval	$z$ coordinate of evaluation point.
integer(kind=ip),	intent(in)		::	idx	$x$ derivative of piecewise polynomial to evaluate.
integer(kind=ip),	intent(in)		::	idy	$y$ derivative of piecewise polynomial to evaluate.
integer(kind=ip),	intent(in)		::	idz	$z$ derivative of piecewise polynomial to evaluate.
real(kind=wp),	intent(out),	dimension(:)	::	f	`(nf)` interpolated values of the outputs (see number_of_outputs)
integer(kind=ip),	intent(out)		::	iflag	status flag (see db3val)

procedure, public :: destroy => destroy_3d

private pure subroutine destroy_3d(me)

Destructor for bspline_3d class.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_3d),	intent(inout)			::	me

procedure, public :: size_of => size_3d

private pure function size_3d(me) result(s)

Actual size of a bspline_3d structure in bits.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_3d),	intent(in)			::	me

Return Value integer(kind=ip)

size of the structure in bits

generic, public :: initialize_from_coefficients => initialize_from_coefficients_3d, initialize_from_coefficients_3d_multi

private pure subroutine initialize_from_coefficients_3d(me, tx, ty, tz, bcoef, kx, ky, kz, iflag, extrap)

Initialize a bspline_3d type directly from its knots and b-spline coefficients (for example, those saved from another object with get_knots and get_coefficients), without interpolating any data.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_3d),	intent(inout)			::	me	the spline
real(kind=wp),	intent(in),		dimension(:)	::	tx	The `(nx+kx)` knots in the $x$ direction. Must be non-decreasing.
real(kind=wp),	intent(in),		dimension(:)	::	ty	The `(ny+ky)` knots in the $y$ direction. Must be non-decreasing.
real(kind=wp),	intent(in),		dimension(:)	::	tz	The `(nz+kz)` knots in the $z$ direction. Must be non-decreasing.
real(kind=wp),	intent(in),		dimension(:,:,:)	::	bcoef	`(nx,ny,nz)` array of b-spline coefficients
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$ ( $1 \le k_x \le n_x$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	ky	The order of spline pieces in $y$ ( $1 \le k_y \le n_y$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	kz	The order of spline pieces in $z$ ( $1 \le k_z \le n_z$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(out)			::	iflag	status flag: Read more…
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

private pure subroutine initialize_from_coefficients_3d_multi(me, tx, ty, tz, bcoef, kx, ky, kz, iflag, extrap)

Initialize a bspline_3d type with multiple outputs directly from its knots and b-spline coefficients. The last dimension of bcoef is the output index.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_3d),	intent(inout)			::	me	the spline
real(kind=wp),	intent(in),		dimension(:)	::	tx	The `(nx+kx)` knots in the $x$ direction.
real(kind=wp),	intent(in),		dimension(:)	::	ty	The `(ny+ky)` knots in the $y$ direction.
real(kind=wp),	intent(in),		dimension(:)	::	tz	The `(nz+kz)` knots in the $z$ direction.
real(kind=wp),	intent(in),		dimension(:,:,:,:)	::	bcoef	`(nx,ny,nz,nf)` array of b-spline coefficients
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$
integer(kind=ip),	intent(in)			::	ky	The order of spline pieces in $y$
integer(kind=ip),	intent(in)			::	kz	The order of spline pieces in $z$
integer(kind=ip),	intent(out)			::	iflag	status flag (see initialize_from_coefficients_3d), or 6005 if `bcoef` has no outputs
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

procedure, private :: initialize_from_coefficients_3d

private pure subroutine initialize_from_coefficients_3d(me, tx, ty, tz, bcoef, kx, ky, kz, iflag, extrap)

Initialize a bspline_3d type directly from its knots and b-spline coefficients (for example, those saved from another object with get_knots and get_coefficients), without interpolating any data.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_3d),	intent(inout)			::	me	the spline
real(kind=wp),	intent(in),		dimension(:)	::	tx	The `(nx+kx)` knots in the $x$ direction. Must be non-decreasing.
real(kind=wp),	intent(in),		dimension(:)	::	ty	The `(ny+ky)` knots in the $y$ direction. Must be non-decreasing.
real(kind=wp),	intent(in),		dimension(:)	::	tz	The `(nz+kz)` knots in the $z$ direction. Must be non-decreasing.
real(kind=wp),	intent(in),		dimension(:,:,:)	::	bcoef	`(nx,ny,nz)` array of b-spline coefficients
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$ ( $1 \le k_x \le n_x$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	ky	The order of spline pieces in $y$ ( $1 \le k_y \le n_y$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(in)			::	kz	The order of spline pieces in $z$ ( $1 \le k_z \le n_z$ ) (order = polynomial degree + 1)
integer(kind=ip),	intent(out)			::	iflag	status flag: Read more…
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

procedure, private :: initialize_from_coefficients_3d_multi

private pure subroutine initialize_from_coefficients_3d_multi(me, tx, ty, tz, bcoef, kx, ky, kz, iflag, extrap)

Initialize a bspline_3d type with multiple outputs directly from its knots and b-spline coefficients. The last dimension of bcoef is the output index.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_3d),	intent(inout)			::	me	the spline
real(kind=wp),	intent(in),		dimension(:)	::	tx	The `(nx+kx)` knots in the $x$ direction.
real(kind=wp),	intent(in),		dimension(:)	::	ty	The `(ny+ky)` knots in the $y$ direction.
real(kind=wp),	intent(in),		dimension(:)	::	tz	The `(nz+kz)` knots in the $z$ direction.
real(kind=wp),	intent(in),		dimension(:,:,:,:)	::	bcoef	`(nx,ny,nz,nf)` array of b-spline coefficients
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$
integer(kind=ip),	intent(in)			::	ky	The order of spline pieces in $y$
integer(kind=ip),	intent(in)			::	kz	The order of spline pieces in $z$
integer(kind=ip),	intent(out)			::	iflag	status flag (see initialize_from_coefficients_3d), or 6005 if `bcoef` has no outputs
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

procedure, public :: get_knots => get_knots_3d

private pure subroutine get_knots_3d(me, tx, ty, tz, iflag)

Returns the knot vectors of a bspline_3d.

Arguments

Type	Intent	Attributes		Name
class(bspline_3d),	intent(inout)		::	me	the spline
real(kind=wp),	intent(out),	dimension(:), allocatable	::	tx	the `(nx+kx)` knots in the $x$ direction
real(kind=wp),	intent(out),	dimension(:), allocatable	::	ty	the `(ny+ky)` knots in the $y$ direction
real(kind=wp),	intent(out),	dimension(:), allocatable	::	tz	the `(nz+kz)` knots in the $z$ direction
integer(kind=ip),	intent(out)		::	iflag	status flag: 0 if no errors, 1 if the class is not initialized

generic, public :: get_coefficients => get_coefficients_3d, get_coefficients_3d_multi

private pure subroutine get_coefficients_3d(me, bcoef, iflag)

Returns the b-spline coefficients of a bspline_3d. These are the values of the control points (see greville_abscissae for their locations).

Arguments

Type	Intent	Attributes		Name
class(bspline_3d),	intent(inout)		::	me	the spline
real(kind=wp),	intent(out),	dimension(:,:,:), allocatable	::	bcoef	`(nx,ny,nz)` array of b-spline coefficients
integer(kind=ip),	intent(out)		::	iflag	status flag: 0 if no errors, 1 if the class is not initialized

private pure subroutine get_coefficients_3d_multi(me, bcoef, iflag)

Returns the b-spline coefficients of a bspline_3d with any number of outputs. The last dimension of bcoef is the output index.

Arguments

Type	Intent	Attributes		Name
class(bspline_3d),	intent(inout)		::	me	the spline
real(kind=wp),	intent(out),	dimension(:,:,:,:), allocatable	::	bcoef	`(nx,ny,nz,nf)` array of b-spline coefficients
integer(kind=ip),	intent(out)		::	iflag	status flag: 0 if no errors, 1 if the class is not initialized

procedure, private :: get_coefficients_3d

private pure subroutine get_coefficients_3d(me, bcoef, iflag)

Returns the b-spline coefficients of a bspline_3d. These are the values of the control points (see greville_abscissae for their locations).

Arguments

Type	Intent	Attributes		Name
class(bspline_3d),	intent(inout)		::	me	the spline
real(kind=wp),	intent(out),	dimension(:,:,:), allocatable	::	bcoef	`(nx,ny,nz)` array of b-spline coefficients
integer(kind=ip),	intent(out)		::	iflag	status flag: 0 if no errors, 1 if the class is not initialized

procedure, private :: get_coefficients_3d_multi

private pure subroutine get_coefficients_3d_multi(me, bcoef, iflag)

Returns the b-spline coefficients of a bspline_3d with any number of outputs. The last dimension of bcoef is the output index.

Arguments

Type	Intent	Attributes		Name
class(bspline_3d),	intent(inout)		::	me	the spline
real(kind=wp),	intent(out),	dimension(:,:,:,:), allocatable	::	bcoef	`(nx,ny,nz,nf)` array of b-spline coefficients
integer(kind=ip),	intent(out)		::	iflag	status flag: 0 if no errors, 1 if the class is not initialized

Source Code

    type,extends(bspline_class),public :: bspline_3d
        !! Class for 3d b-spline interpolation.
        private
        integer(ip) :: nx = 0_ip  !! Number of \(x\) abcissae
        integer(ip) :: ny = 0_ip  !! Number of \(y\) abcissae
        integer(ip) :: nz = 0_ip  !! Number of \(z\) abcissae
        integer(ip) :: kx = 0_ip  !! The order of spline pieces in \(x\)
        integer(ip) :: ky = 0_ip  !! The order of spline pieces in \(y\)
        integer(ip) :: kz = 0_ip  !! The order of spline pieces in \(z\)
        real(wp),dimension(:,:,:,:),allocatable :: bcoef  !! array of coefficients of the b-spline interpolant
                                                          !! (the last dimension is the output index)
        real(wp),dimension(:),allocatable :: tx  !! The knots in the \(x\) direction for the spline interpolant
        real(wp),dimension(:),allocatable :: ty  !! The knots in the \(y\) direction for the spline interpolant
        real(wp),dimension(:),allocatable :: tz  !! The knots in the \(z\) direction for the spline interpolant
        integer(ip) :: inbvy = 1_ip  !! internal variable used for efficient processing
        integer(ip) :: inbvz = 1_ip  !! internal variable used for efficient processing
        integer(ip) :: iloy = 1_ip  !! internal variable used for efficient processing
        integer(ip) :: iloz = 1_ip  !! internal variable used for efficient processing
        real(wp),dimension(:,:),allocatable :: work_val_1  !! [[db3val] work array of dimension `ky,kz`
        real(wp),dimension(:),allocatable   :: work_val_2  !! [[db3val] work array of dimension `kz`
        real(wp),dimension(:),allocatable   :: work_val_3  !! [[db3val] work array of dimension `3_ip*max(kx,ky,kz)`
        contains
        private
        generic,public :: initialize => initialize_3d_auto_knots,initialize_3d_specify_knots,&
                                        initialize_3d_auto_knots_multi,initialize_3d_specify_knots_multi
        procedure :: initialize_3d_auto_knots_multi
        procedure :: initialize_3d_specify_knots_multi
        procedure :: initialize_3d_auto_knots
        procedure :: initialize_3d_specify_knots
        generic,public :: evaluate => evaluate_3d, evaluate_3d_multi
        procedure :: evaluate_3d
        procedure :: evaluate_3d_multi
        procedure,public :: destroy => destroy_3d
        procedure,public :: size_of => size_3d
        generic,public :: initialize_from_coefficients => initialize_from_coefficients_3d,&
                                                          initialize_from_coefficients_3d_multi
        procedure :: initialize_from_coefficients_3d
        procedure :: initialize_from_coefficients_3d_multi
        procedure,public :: get_knots => get_knots_3d
        generic,public :: get_coefficients => get_coefficients_3d, get_coefficients_3d_multi
        procedure :: get_coefficients_3d
        procedure :: get_coefficients_3d_multi
        final :: finalize_3d
    end type bspline_3d

bspline_3d Derived Type

Contents

Variables

Constructor

Finalization Procedures

Type-Bound Procedures

Source Code

type, public, extends(bspline_class) :: bspline_3d

Inherits

Components

Constructor

public interface bspline_3d

private elemental function bspline_3d_constructor_empty() result(me)

Arguments

Return Value type(bspline_3d)

private pure function bspline_3d_constructor_auto_knots(x, y, z, fcn, kx, ky, kz, extrap) result(me)

Arguments

Return Value type(bspline_3d)

private pure function bspline_3d_constructor_specify_knots(x, y, z, fcn, kx, ky, kz, tx, ty, tz, extrap) result(me)

Arguments

Return Value type(bspline_3d)

Finalization Procedures

final :: finalize_3d

private pure elemental subroutine finalize_3d(me)

Arguments

Type-Bound Procedures

procedure, public, non_overridable :: status_ok

private elemental function status_ok(me) result(ok)

Arguments

Return Value logical

procedure, public, non_overridable :: status_message => get_bspline_status_message

private pure function get_bspline_status_message(me, iflag) result(msg)

Arguments

Return Value character(len=:), allocatable

procedure, public, non_overridable :: clear_flag => clear_bspline_flag

private elemental subroutine clear_bspline_flag(me)

Arguments

procedure, public, non_overridable :: number_of_outputs

private pure function number_of_outputs(me) result(nf)

Arguments

Return Value integer(kind=ip)

generic, public :: initialize => initialize_3d_auto_knots, initialize_3d_specify_knots, initialize_3d_auto_knots_multi, initialize_3d_specify_knots_multi

private pure subroutine initialize_3d_auto_knots(me, x, y, z, fcn, kx, ky, kz, iflag, extrap)

Arguments

private pure subroutine initialize_3d_specify_knots(me, x, y, z, fcn, kx, ky, kz, tx, ty, tz, iflag, extrap)

Arguments

private pure subroutine initialize_3d_auto_knots_multi(me, x, y, z, fcn, kx, ky, kz, iflag, extrap)

Arguments

private pure subroutine initialize_3d_specify_knots_multi(me, x, y, z, fcn, kx, ky, kz, tx, ty, tz, iflag, extrap)

Arguments

procedure, private :: initialize_3d_auto_knots_multi

private pure subroutine initialize_3d_auto_knots_multi(me, x, y, z, fcn, kx, ky, kz, iflag, extrap)

Arguments

procedure, private :: initialize_3d_specify_knots_multi

private pure subroutine initialize_3d_specify_knots_multi(me, x, y, z, fcn, kx, ky, kz, tx, ty, tz, iflag, extrap)

Arguments

procedure, private :: initialize_3d_auto_knots

private pure subroutine initialize_3d_auto_knots(me, x, y, z, fcn, kx, ky, kz, iflag, extrap)

Arguments

procedure, private :: initialize_3d_specify_knots

private pure subroutine initialize_3d_specify_knots(me, x, y, z, fcn, kx, ky, kz, tx, ty, tz, iflag, extrap)

Arguments

generic, public :: evaluate => evaluate_3d, evaluate_3d_multi

private pure subroutine evaluate_3d(me, xval, yval, zval, idx, idy, idz, f, iflag)

Arguments

private pure subroutine evaluate_3d_multi(me, xval, yval, zval, idx, idy, idz, f, iflag)

Arguments

procedure, private :: evaluate_3d

private pure subroutine evaluate_3d(me, xval, yval, zval, idx, idy, idz, f, iflag)

Arguments

procedure, private :: evaluate_3d_multi

private pure subroutine evaluate_3d_multi(me, xval, yval, zval, idx, idy, idz, f, iflag)

Arguments

procedure, public :: destroy => destroy_3d

private pure subroutine destroy_3d(me)

Arguments

procedure, public :: size_of => size_3d

private pure function size_3d(me) result(s)

Arguments

Return Value integer(kind=ip)