bspline_1d – bspline-fortran

type, public, extends(bspline_class) :: bspline_1d

Class for 1d b-spline interpolation.

Note

The 1D class also contains two methods for computing definite integrals.

Inherits

Help

Components

Type	Visibility	Attributes		Name		Initial
integer(kind=ip),	private		::	nx	=	0_ip	Number of $x$ abcissae
integer(kind=ip),	private		::	kx	=	0_ip	The order of spline pieces in $x$
real(kind=wp),	private,	dimension(:), allocatable	::	bcoef			array of coefficients of the b-spline interpolant
real(kind=wp),	private,	dimension(:), allocatable	::	tx			The knots in the $x$ direction for the spline interpolant
real(kind=wp),	private,	dimension(:), allocatable	::	work_val_1			[[db1val] work array of dimension `3*kx`

Constructor

public interface bspline_1d

Constructor for bspline_1d

private pure elemental function bspline_1d_constructor_empty() result(me)

It returns an empty bspline_1d 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_1d)

private pure function bspline_1d_constructor_auto_knots(x, fcn, kx, extrap) result(me)

Constructor for a bspline_1d type (auto knots). This is a wrapper for initialize_1d_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(:)	::	fcn	`(nx)` array of function values to interpolate. `fcn(i)` should contain the function value at the point `x(i)`
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$ ( $2 \le k_x < n_x$ ) (order = polynomial degree + 1)
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

Return Value type(bspline_1d)

private pure function bspline_1d_constructor_specify_knots(x, fcn, kx, tx, extrap) result(me)

Constructor for a bspline_1d type (user-specified knots). This is a wrapper for initialize_1d_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(:)	::	fcn	`(nx)` array of function values to interpolate. `fcn(i)` should contain the function value at the point `x(i)`
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$ ( $2 \le k_x < n_x$ ) (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.
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

Return Value type(bspline_1d)

Finalization Procedures

final :: finalize_1d

private pure elemental subroutine finalize_1d(me)

Finalizer for bspline_1d class. Just a wrapper for destroy_1d.

Arguments

Type	Intent	Optional	Attributes		Name
type(bspline_1d),	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

generic, public :: initialize => initialize_1d_auto_knots, initialize_1d_specify_knots

private pure subroutine initialize_1d_auto_knots(me, x, fcn, kx, iflag, extrap)

Initialize a bspline_1d type (with automatically-computed knots). This is a wrapper for db1ink.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_1d),	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(:)	::	fcn	`(nx)` array of function values to interpolate. `fcn(i)` should contain the function value at the point `x(i)`
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(out)			::	iflag	status flag (see db1ink)
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

private pure subroutine initialize_1d_specify_knots(me, x, fcn, kx, tx, iflag, extrap)

Initialize a bspline_1d type (with user-specified knots). This is a wrapper for db1ink.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_1d),	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(:)	::	fcn	`(nx)` array of function values to interpolate. `fcn(i)` should contain the function value at the point `x(i)`
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$ ( $2 \le k_x < n_x$ ) (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.
integer(kind=ip),	intent(out)			::	iflag	status flag (see db1ink)
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

procedure, private :: initialize_1d_auto_knots

private pure subroutine initialize_1d_auto_knots(me, x, fcn, kx, iflag, extrap)

Initialize a bspline_1d type (with automatically-computed knots). This is a wrapper for db1ink.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_1d),	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(:)	::	fcn	`(nx)` array of function values to interpolate. `fcn(i)` should contain the function value at the point `x(i)`
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(out)			::	iflag	status flag (see db1ink)
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

procedure, private :: initialize_1d_specify_knots

private pure subroutine initialize_1d_specify_knots(me, x, fcn, kx, tx, iflag, extrap)

Initialize a bspline_1d type (with user-specified knots). This is a wrapper for db1ink.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_1d),	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(:)	::	fcn	`(nx)` array of function values to interpolate. `fcn(i)` should contain the function value at the point `x(i)`
integer(kind=ip),	intent(in)			::	kx	The order of spline pieces in $x$ ( $2 \le k_x < n_x$ ) (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.
integer(kind=ip),	intent(out)			::	iflag	status flag (see db1ink)
logical,	intent(in),	optional		::	extrap	if true, then extrapolation is allowed (default is false)

procedure, public :: evaluate => evaluate_1d

private pure subroutine evaluate_1d(me, xval, idx, f, iflag)

Evaluate a bspline_1d interpolate. This is a wrapper for db1val.

Arguments

Type	Intent		Name
class(bspline_1d),	intent(inout)	::	me
real(kind=wp),	intent(in)	::	xval	$x$ coordinate of evaluation point.
integer(kind=ip),	intent(in)	::	idx	$x$ derivative of piecewise polynomial to evaluate.
real(kind=wp),	intent(out)	::	f	interpolated value
integer(kind=ip),	intent(out)	::	iflag	status flag (see db1val)

procedure, public :: destroy => destroy_1d

private pure subroutine destroy_1d(me)

Destructor for bspline_1d class.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_1d),	intent(inout)			::	me

procedure, public :: size_of => size_1d

private pure function size_1d(me) result(s)

Actual size of a bspline_1d structure in bits.

Arguments

Type	Intent	Optional	Attributes		Name
class(bspline_1d),	intent(in)			::	me

Return Value integer(kind=ip)

size of the structure in bits

procedure, public :: integral => integral_1d

private pure subroutine integral_1d(me, x1, x2, f, iflag)

Evaluate a bspline_1d definite integral. This is a wrapper for db1sqad.

Arguments

Type	Intent		Name
class(bspline_1d),	intent(inout)	::	me
real(kind=wp),	intent(in)	::	x1	left point of interval
real(kind=wp),	intent(in)	::	x2	right point of interval
real(kind=wp),	intent(out)	::	f	integral of the b-spline over $[x_1, x_2]$
integer(kind=ip),	intent(out)	::	iflag	status flag (see db1sqad)

procedure, public :: fintegral => fintegral_1d

private subroutine fintegral_1d(me, fun, idx, x1, x2, tol, f, iflag)

Evaluate a bspline_1d definite integral. This is a wrapper for db1fqad.

Arguments

Type	Intent		Name
class(bspline_1d),	intent(inout)	::	me
procedure(b1fqad_func)		::	fun	external function of one argument for the integrand `bf(x)=fun(x)*dbvalu(tx,bcoef,nx,kx,idx,x,inbv)`
integer(kind=ip),	intent(in)	::	idx	order of the spline derivative, `0 <= idx <= k-1` `idx=0` gives the spline function
real(kind=wp),	intent(in)	::	x1	left point of interval
real(kind=wp),	intent(in)	::	x2	right point of interval
real(kind=wp),	intent(in)	::	tol	desired accuracy for the quadrature
real(kind=wp),	intent(out)	::	f	integral of `bf(x)` over $[x_1, x_2]$
integer(kind=ip),	intent(out)	::	iflag	status flag (see db1sqad)

Source Code

    type,extends(bspline_class),public :: bspline_1d
        !! Class for 1d b-spline interpolation.
        !!
        !!@note The 1D class also contains two methods
        !!      for computing definite integrals.
        private
        integer(ip) :: nx = 0_ip  !! Number of \(x\) abcissae
        integer(ip) :: kx = 0_ip  !! The order of spline pieces in \(x\)
        real(wp),dimension(:),allocatable :: bcoef  !! array of coefficients of the b-spline interpolant
        real(wp),dimension(:),allocatable :: tx  !! The knots in the \(x\) direction for the spline interpolant
        real(wp),dimension(:),allocatable :: work_val_1   !! [[db1val] work array of dimension `3*kx`
        contains
        private
        generic,public :: initialize => initialize_1d_auto_knots,initialize_1d_specify_knots
        procedure :: initialize_1d_auto_knots
        procedure :: initialize_1d_specify_knots
        procedure,public :: evaluate => evaluate_1d
        procedure,public :: destroy => destroy_1d
        procedure,public :: size_of => size_1d
        procedure,public :: integral => integral_1d
        procedure,public :: fintegral => fintegral_1d
        final :: finalize_1d
    end type bspline_1d

bspline_1d Derived Type

Contents

Variables

Constructor

Finalization Procedures

Type-Bound Procedures

Source Code

type, public, extends(bspline_class) :: bspline_1d

Inherits

Components

Constructor

public interface bspline_1d

private pure elemental function bspline_1d_constructor_empty() result(me)

Arguments

Return Value type(bspline_1d)

private pure function bspline_1d_constructor_auto_knots(x, fcn, kx, extrap) result(me)

Arguments

Return Value type(bspline_1d)

private pure function bspline_1d_constructor_specify_knots(x, fcn, kx, tx, extrap) result(me)

Arguments

Return Value type(bspline_1d)

Finalization Procedures

final :: finalize_1d

private pure elemental subroutine finalize_1d(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

generic, public :: initialize => initialize_1d_auto_knots, initialize_1d_specify_knots

private pure subroutine initialize_1d_auto_knots(me, x, fcn, kx, iflag, extrap)

Arguments

private pure subroutine initialize_1d_specify_knots(me, x, fcn, kx, tx, iflag, extrap)

Arguments

procedure, private :: initialize_1d_auto_knots

private pure subroutine initialize_1d_auto_knots(me, x, fcn, kx, iflag, extrap)

Arguments

procedure, private :: initialize_1d_specify_knots

private pure subroutine initialize_1d_specify_knots(me, x, fcn, kx, tx, iflag, extrap)

Arguments

procedure, public :: evaluate => evaluate_1d

private pure subroutine evaluate_1d(me, xval, idx, f, iflag)

Arguments

procedure, public :: destroy => destroy_1d

private pure subroutine destroy_1d(me)

Arguments

procedure, public :: size_of => size_1d

private pure function size_1d(me) result(s)

Arguments

Return Value integer(kind=ip)

procedure, public :: integral => integral_1d

private pure subroutine integral_1d(me, x1, x2, f, iflag)

Arguments

procedure, public :: fintegral => fintegral_1d

private subroutine fintegral_1d(me, fun, idx, x1, x2, tol, f, iflag)

Arguments

Source Code