splpak_type – splpak

type, public :: splpak_type

Usage

The class contains four user entries: splcc, splcw, splfe, and splde.

The user first calls splcc by

    call me%initialize(ndim,xdata,l1xdat,ydata,ndata,
                       xmin,xmax,nodes,xtrap,coef,ncf,
                       work,nwrk,ierror)

or splcw by

    call me%initialize(ndim,xdata,l1xdata,ydata,wdata,
                       ndata,xmin,xmax,nodes,xtrap,
                       coef,ncf,work,nwrk,ierror)

The parameter NDATA in the call to splcw enables the user to weight some of the data points more heavily than others. Both routines return a set of coefficients in the array COEF. These coefficients are subsequently used in the computation of function values and partial derivatives. To compute values on the spline approximation the user then calls splfe or splde any number of times in any order provided that the values of the inputs, NDIM, COEF, XMIN, XMAX, and NODES, are preserved between calls.

splfe and splde are called in the following way:

    f = me%evaluate(ndim,x,coef,xmin,xmax,nodes,ierror)

    f = me%evaluate(ndim,x,nderiv,coef,xmin,xmax,nodes,ierror)

The routine splfe returns an interpolated value at the point defined by the array X. splde affords the user the additional capability of calculating an interpolated value for one of several partial derivatives specified by the array NDERIV.

Components

Type	Visibility	Attributes		Name		Initial
integer,	private		::	mdim	=	0
real(kind=wp),	private,	dimension(:), allocatable	::	dx
real(kind=wp),	private,	dimension(:), allocatable	::	dxin
integer,	private,	dimension(:), allocatable	::	ib
integer,	private,	dimension(:), allocatable	::	ibmn
integer,	private,	dimension(:), allocatable	::	ibmx
integer,	private		::	ilast	=	0
integer,	private		::	isav	=	0
integer,	private		::	iold	=	0
integer,	private		::	np1	=	0
integer,	private		::	l	=	0
integer,	private		::	il1	=	0
integer,	private		::	k	=	0
integer,	private		::	k1	=	0
real(kind=wp),	private		::	errsum	=	0.0_wp

Type-Bound Procedures

generic, public :: initialize => splcc, splcw

compute the spline coefficients

private subroutine splcc(me, ndim, xdata, l1xdat, ydata, ndata, xmin, xmax, nodes, xtrap, coef, ncf, work, nwrk, ierror)

N-dimensional cubic spline coefficient calculation by least squares.

Arguments

Type	Intent		Name
class(splpak_type),	intent(inout)	::	me
integer,	intent(in)	::	ndim
real(kind=wp),	intent(in)	::	xdata(l1xdat,ndata)
integer,	intent(in)	::	l1xdat
real(kind=wp),	intent(in)	::	ydata(ndata)
integer,	intent(in)	::	ndata
real(kind=wp),	intent(in)	::	xmin(ndim)
real(kind=wp),	intent(in)	::	xmax(ndim)
integer,	intent(in)	::	nodes(ndim)
real(kind=wp),	intent(in)	::	xtrap
real(kind=wp),	intent(out)	::	coef(ncf)
integer,	intent(in)	::	ncf
real(kind=wp)		::	work(nwrk)
integer,	intent(in)	::	nwrk
integer,	intent(out)	::	ierror

private subroutine splcw(me, ndim, xdata, l1xdat, ydata, wdata, ndata, xmin, xmax, nodes, xtrap, coef, ncf, work, nwrk, ierror)

N-dimensional cubic spline coefficient calculation by weighted least squares on arbitrarily located data.

Arguments

Type	Intent		Name
class(splpak_type),	intent(inout)	::	me
integer,	intent(in)	::	ndim	The dimensionality of the problem. The spline is a function of `NDIM` variables or coordinates and thus a point in the independent variable space is an `NDIM` vector. `NDIM` must be `>= 1`.
real(kind=wp),	intent(in)	::	xdata(l1xdat,ndata)	A collection of locations for the data values, i.e., points from the independent variable space. This collection is a 2-dimensional array whose 1st dimension indexes the `NDIM` coordinates of a given point and whose 2nd dimension labels the data point. For example, the data point with label `IDATA` is located at the point `(XDATA(1,IDATA),...,XDATA(NDIM,IDATA))` where the elements of this vector are the values of the `NDIM` coordinates. The location, number and ordering of the data points is arbitrary. The dimension of `XDATA` is assumed to be `XDATA(L1XDAT,NDATA)`.
integer,	intent(in)	::	l1xdat	The length of the 1st dimension of `XDATA` in the calling program. `L1XDAT` must be `>= NDIM`. Read more…
real(kind=wp),	intent(in)	::	ydata(ndata)	A collection of data values corresponding to the points in `XDATA`. `YDATA(IDATA)` is the data value associated with the point `(XDATA(1,IDATA),...,XDATA(NDIM,IDATA))` in the independent variable space. The spline whose coefficients are computed by this routine approximates these data values in the least squares sense. The dimension is assumed to be `YDATA(NDATA)`.
real(kind=wp),	intent(in)	::	wdata(:)	A collection of weights. `WDATA(IDATA)` is a weight associated with the data point labelled `IDATA`. It should be non-negative, but may be of any magnitude. The weights have the effect of forcing greater or lesser accuracy at a given point as follows: this routine chooses coefficients to minimize the sum over all data points of the quantity Read more…
integer,	intent(in)	::	ndata	The number of data points mentioned in the above arguments.
real(kind=wp),	intent(in)	::	xmin(ndim)	A vector describing the lower extreme corner of the node grid. A set of evenly spaced nodes is formed along each coordinate axis and `XMIN(IDIM)` is the location of the first node along the `IDIM` axis. The dimension is assumed to be `XMIN(NDIM)`.
real(kind=wp),	intent(in)	::	xmax(ndim)	A vector describing the upper extreme corner of the node grid. A set of evenly spaced nodes is formed along each coordinate axis and `XMAX(IDIM)` is the location of the last node along the `IDIM` axis. The dimension is assumed to be `XMAX(NDIM)`.
integer,	intent(in)	::	nodes(ndim)	A vector of integers describing the number of nodes along each axis. `NODES(IDIM)` is the number of nodes (counting endpoints) along the `IDIM` axis and determines the flexibility of the spline in that coordinate direction. `NODES(IDIM)` must be `>= 4`, but may be as large as the arrays `COEF` and `WORK` allow. The dimension is assumed to be `NODES(NDIM)`. Read more…
real(kind=wp),	intent(in)	::	xtrap	A parameter to control extrapolation to data sparse areas. The region described by `XMIN` and `XMAX` is divided into rectangles, the number of which is determined by `NODES`, and any rectangle containing a disproportionately small number of data points is considered to be data sparse (rectangle is used here to mean `NDIM`-dimensional rectangle). If `XTRAP` is nonzero the least squares problem is augmented with derivative constraints in the data sparse areas to prevent the matrix from becoming poorly conditioned. `XTRAP` serves as a weight for these constraints, and thus may be used to control smoothness in data sparse areas. Experience indicates that unity is a good first guess for this parameter. Read more…
real(kind=wp),	intent(out)	::	coef(ncf)	The array of coefficients computed by this routine. Each coefficient corresponds to a particular basis function which in turn corresponds to a node in the node grid. This correspondence between the node grid and the array `COEF` is as if `COEF` were an `NDIM`-dimensional Fortran array with dimensions `NODES(1),...,NODES(NDIM)`, i.e., to store the array linearly, the leftmost indices are incremented most frequently. Hence the length of the `COEF` array must equal or exceed the total number of nodes, which is `NODES(1)...NODES(NDIM)`. The computed array `COEF` may be used with function SPLFE (or SPLDE) to evaluate the spline (or its derivatives) at an arbitrary point in `NDIM` space. The dimension is assumed to be `COEF(NCF)`.
integer,	intent(in)	::	ncf	The length of the array `COEF` in the calling program. If `NCF` is `< NODES(1)...NODES(NDIM)`, a fatal error is diagnosed.
real(kind=wp)		::	work(nwrk)	A workspace array for solving the least squares matrix generated by this routine. Its required size is a function of the total number of nodes in the node grid. This total, `NCOL = NODES(1)...NODES(NDIM)`, is also the number of columns in the least squares matrix. The length of the array `WORK` must equal or exceed `NCOL*(NCOL+1)`.
integer,	intent(in)	::	nwrk	The length of the array `WORK` in the calling program. If `NCOL = NODES(1)...NODES(NDIM)` is the total number of nodes, then a fatal error is diagnosed if `NWRK` is less than `NCOL*(NCOL+1)`.
integer,	intent(out)	::	ierror	An error flag with the following meanings: Read more…

generic, public :: evaluate => splfe, splde

evaluate the spline

private function splfe(me, ndim, x, coef, xmin, xmax, nodes, ierror)

N-dimensional cubic spline function evaluation.

Arguments

Type	Intent		Name
class(splpak_type),	intent(inout)	::	me
integer,	intent(in)	::	ndim
real(kind=wp),	intent(in)	::	x(ndim)
real(kind=wp),	intent(out)	::	coef(*)
real(kind=wp),	intent(in)	::	xmin(ndim)
real(kind=wp),	intent(in)	::	xmax(ndim)
integer,	intent(in)	::	nodes(ndim)
integer,	intent(out)	::	ierror

Return Value real(kind=wp)

private function splde(me, ndim, x, nderiv, coef, xmin, xmax, nodes, ierror)

N-dimensional cubic spline derivative evaluation.

Arguments

Type	Intent		Name
class(splpak_type),	intent(inout)	::	me
integer,	intent(in)	::	ndim	the dimensionality of the problem. the spline is a function of `ndim` variables or coordinates and thus a point in the independent variable space is an `ndim` vector. `ndim` must be in the range `1 <= ndim <= 4`.
real(kind=wp),	intent(in)	::	x(ndim)	an `ndim` vector describing the point in the independent variable space at which the spline is to be evaluated.
integer,	intent(in)	::	nderiv(ndim)	an `ndim` vector of integers specifying the partial derivative to be evaluated. the order of the derivative along the `idim` axis is `nderiv(idim)`. these integers must be in the range `0 <= nderiv(idim) <= 2`.
real(kind=wp),	intent(out)	::	coef(*)	the array of coefficients which determine the spline. each coefficient corresponds to a particular basis function which in turn corresponds to a node in the node grid. this correspondence between the node grid and the array `coef` is as if `coef` were an ndim-dimensional fortran array with dimensions `nodes(1),...,nodes(ndim)`, i.e., to store the array linearly, the leftmost indices are incremented most frequently. coef may be computed by using routines splcc or splcw. Read more…
real(kind=wp),	intent(in)	::	xmin(ndim)	a vector describing the lower extreme corner of the node grid. a set of evenly spaced nodes is formed along each coordinate axis and `xmin(idim)` is the location of the first node along the `idim` axis.
real(kind=wp),	intent(in)	::	xmax(ndim)	a vector describing the upper extreme corner of the node grid. a set of evenly spaced nodes is formed along each coordinate axis and `xmax(idim)` is the location of the last node along the `idim` axis.
integer,	intent(in)	::	nodes(ndim)	a vector of integers describing the number of nodes along each axis. `nodes(idim)` is the the number of nodes (counting endpoints) along the `idim` axis and determines the flexibility of the spline in that coordinate direction. `nodes(idim)` must be >= 4 but may be as large as the arrays `coef` and `work` allow. Read more…
integer,	intent(out)	::	ierror	an error flag with the following meanings: Read more…

Return Value real(kind=wp)

the function value returned is the partial derivative (indicated by nderiv) of the spline evaluated at x.

procedure, public :: destroy => destroy_splpak

destory the internal class variables

private subroutine destroy_splpak(me, ndim)

Destroy the internal class variables.

Arguments

Type	Intent	Optional	Attributes		Name
class(splpak_type),	intent(inout)			::	me
integer,	intent(in),	optional		::	ndim

procedure, private :: splcc

private subroutine splcc(me, ndim, xdata, l1xdat, ydata, ndata, xmin, xmax, nodes, xtrap, coef, ncf, work, nwrk, ierror)

N-dimensional cubic spline coefficient calculation by least squares.

Arguments

Type	Intent		Name
class(splpak_type),	intent(inout)	::	me
integer,	intent(in)	::	ndim
real(kind=wp),	intent(in)	::	xdata(l1xdat,ndata)
integer,	intent(in)	::	l1xdat
real(kind=wp),	intent(in)	::	ydata(ndata)
integer,	intent(in)	::	ndata
real(kind=wp),	intent(in)	::	xmin(ndim)
real(kind=wp),	intent(in)	::	xmax(ndim)
integer,	intent(in)	::	nodes(ndim)
real(kind=wp),	intent(in)	::	xtrap
real(kind=wp),	intent(out)	::	coef(ncf)
integer,	intent(in)	::	ncf
real(kind=wp)		::	work(nwrk)
integer,	intent(in)	::	nwrk
integer,	intent(out)	::	ierror

procedure, private :: splcw

private subroutine splcw(me, ndim, xdata, l1xdat, ydata, wdata, ndata, xmin, xmax, nodes, xtrap, coef, ncf, work, nwrk, ierror)

N-dimensional cubic spline coefficient calculation by weighted least squares on arbitrarily located data.

Arguments

Type	Intent		Name
class(splpak_type),	intent(inout)	::	me
integer,	intent(in)	::	ndim	The dimensionality of the problem. The spline is a function of `NDIM` variables or coordinates and thus a point in the independent variable space is an `NDIM` vector. `NDIM` must be `>= 1`.
real(kind=wp),	intent(in)	::	xdata(l1xdat,ndata)	A collection of locations for the data values, i.e., points from the independent variable space. This collection is a 2-dimensional array whose 1st dimension indexes the `NDIM` coordinates of a given point and whose 2nd dimension labels the data point. For example, the data point with label `IDATA` is located at the point `(XDATA(1,IDATA),...,XDATA(NDIM,IDATA))` where the elements of this vector are the values of the `NDIM` coordinates. The location, number and ordering of the data points is arbitrary. The dimension of `XDATA` is assumed to be `XDATA(L1XDAT,NDATA)`.
integer,	intent(in)	::	l1xdat	The length of the 1st dimension of `XDATA` in the calling program. `L1XDAT` must be `>= NDIM`. Read more…
real(kind=wp),	intent(in)	::	ydata(ndata)	A collection of data values corresponding to the points in `XDATA`. `YDATA(IDATA)` is the data value associated with the point `(XDATA(1,IDATA),...,XDATA(NDIM,IDATA))` in the independent variable space. The spline whose coefficients are computed by this routine approximates these data values in the least squares sense. The dimension is assumed to be `YDATA(NDATA)`.
real(kind=wp),	intent(in)	::	wdata(:)	A collection of weights. `WDATA(IDATA)` is a weight associated with the data point labelled `IDATA`. It should be non-negative, but may be of any magnitude. The weights have the effect of forcing greater or lesser accuracy at a given point as follows: this routine chooses coefficients to minimize the sum over all data points of the quantity Read more…
integer,	intent(in)	::	ndata	The number of data points mentioned in the above arguments.
real(kind=wp),	intent(in)	::	xmin(ndim)	A vector describing the lower extreme corner of the node grid. A set of evenly spaced nodes is formed along each coordinate axis and `XMIN(IDIM)` is the location of the first node along the `IDIM` axis. The dimension is assumed to be `XMIN(NDIM)`.
real(kind=wp),	intent(in)	::	xmax(ndim)	A vector describing the upper extreme corner of the node grid. A set of evenly spaced nodes is formed along each coordinate axis and `XMAX(IDIM)` is the location of the last node along the `IDIM` axis. The dimension is assumed to be `XMAX(NDIM)`.
integer,	intent(in)	::	nodes(ndim)	A vector of integers describing the number of nodes along each axis. `NODES(IDIM)` is the number of nodes (counting endpoints) along the `IDIM` axis and determines the flexibility of the spline in that coordinate direction. `NODES(IDIM)` must be `>= 4`, but may be as large as the arrays `COEF` and `WORK` allow. The dimension is assumed to be `NODES(NDIM)`. Read more…
real(kind=wp),	intent(in)	::	xtrap	A parameter to control extrapolation to data sparse areas. The region described by `XMIN` and `XMAX` is divided into rectangles, the number of which is determined by `NODES`, and any rectangle containing a disproportionately small number of data points is considered to be data sparse (rectangle is used here to mean `NDIM`-dimensional rectangle). If `XTRAP` is nonzero the least squares problem is augmented with derivative constraints in the data sparse areas to prevent the matrix from becoming poorly conditioned. `XTRAP` serves as a weight for these constraints, and thus may be used to control smoothness in data sparse areas. Experience indicates that unity is a good first guess for this parameter. Read more…
real(kind=wp),	intent(out)	::	coef(ncf)	The array of coefficients computed by this routine. Each coefficient corresponds to a particular basis function which in turn corresponds to a node in the node grid. This correspondence between the node grid and the array `COEF` is as if `COEF` were an `NDIM`-dimensional Fortran array with dimensions `NODES(1),...,NODES(NDIM)`, i.e., to store the array linearly, the leftmost indices are incremented most frequently. Hence the length of the `COEF` array must equal or exceed the total number of nodes, which is `NODES(1)...NODES(NDIM)`. The computed array `COEF` may be used with function SPLFE (or SPLDE) to evaluate the spline (or its derivatives) at an arbitrary point in `NDIM` space. The dimension is assumed to be `COEF(NCF)`.
integer,	intent(in)	::	ncf	The length of the array `COEF` in the calling program. If `NCF` is `< NODES(1)...NODES(NDIM)`, a fatal error is diagnosed.
real(kind=wp)		::	work(nwrk)	A workspace array for solving the least squares matrix generated by this routine. Its required size is a function of the total number of nodes in the node grid. This total, `NCOL = NODES(1)...NODES(NDIM)`, is also the number of columns in the least squares matrix. The length of the array `WORK` must equal or exceed `NCOL*(NCOL+1)`.
integer,	intent(in)	::	nwrk	The length of the array `WORK` in the calling program. If `NCOL = NODES(1)...NODES(NDIM)` is the total number of nodes, then a fatal error is diagnosed if `NWRK` is less than `NCOL*(NCOL+1)`.
integer,	intent(out)	::	ierror	An error flag with the following meanings: Read more…

procedure, private :: splfe

private function splfe(me, ndim, x, coef, xmin, xmax, nodes, ierror)

N-dimensional cubic spline function evaluation.

Arguments

Type	Intent		Name
class(splpak_type),	intent(inout)	::	me
integer,	intent(in)	::	ndim
real(kind=wp),	intent(in)	::	x(ndim)
real(kind=wp),	intent(out)	::	coef(*)
real(kind=wp),	intent(in)	::	xmin(ndim)
real(kind=wp),	intent(in)	::	xmax(ndim)
integer,	intent(in)	::	nodes(ndim)
integer,	intent(out)	::	ierror

Return Value real(kind=wp)

procedure, private :: splde

private function splde(me, ndim, x, nderiv, coef, xmin, xmax, nodes, ierror)

N-dimensional cubic spline derivative evaluation.

Arguments

Type	Intent		Name
class(splpak_type),	intent(inout)	::	me
integer,	intent(in)	::	ndim	the dimensionality of the problem. the spline is a function of `ndim` variables or coordinates and thus a point in the independent variable space is an `ndim` vector. `ndim` must be in the range `1 <= ndim <= 4`.
real(kind=wp),	intent(in)	::	x(ndim)	an `ndim` vector describing the point in the independent variable space at which the spline is to be evaluated.
integer,	intent(in)	::	nderiv(ndim)	an `ndim` vector of integers specifying the partial derivative to be evaluated. the order of the derivative along the `idim` axis is `nderiv(idim)`. these integers must be in the range `0 <= nderiv(idim) <= 2`.
real(kind=wp),	intent(out)	::	coef(*)	the array of coefficients which determine the spline. each coefficient corresponds to a particular basis function which in turn corresponds to a node in the node grid. this correspondence between the node grid and the array `coef` is as if `coef` were an ndim-dimensional fortran array with dimensions `nodes(1),...,nodes(ndim)`, i.e., to store the array linearly, the leftmost indices are incremented most frequently. coef may be computed by using routines splcc or splcw. Read more…
real(kind=wp),	intent(in)	::	xmin(ndim)	a vector describing the lower extreme corner of the node grid. a set of evenly spaced nodes is formed along each coordinate axis and `xmin(idim)` is the location of the first node along the `idim` axis.
real(kind=wp),	intent(in)	::	xmax(ndim)	a vector describing the upper extreme corner of the node grid. a set of evenly spaced nodes is formed along each coordinate axis and `xmax(idim)` is the location of the last node along the `idim` axis.
integer,	intent(in)	::	nodes(ndim)	a vector of integers describing the number of nodes along each axis. `nodes(idim)` is the the number of nodes (counting endpoints) along the `idim` axis and determines the flexibility of the spline in that coordinate direction. `nodes(idim)` must be >= 4 but may be as large as the arrays `coef` and `work` allow. Read more…
integer,	intent(out)	::	ierror	an error flag with the following meanings: Read more…

Return Value real(kind=wp)

the function value returned is the partial derivative (indicated by nderiv) of the spline evaluated at x.

procedure, private :: bascmp

private subroutine bascmp(me, x, nderiv, xmin, nodes, icol, basm)

This routine does basis function computations for natural splines. This routine is called by routines SPLCW and SPLDE to compute ICOL and BASM, which are defined as follows:

Arguments

Type	Intent		Name
class(splpak_type),	intent(inout)	::	me
real(kind=wp),	intent(in)	::	x(:)
integer,	intent(in)	::	nderiv(:)
real(kind=wp),	intent(in)	::	xmin(:)
integer,	intent(in)	::	nodes(:)
integer,	intent(out)	::	icol
real(kind=wp),	intent(out)	::	basm

procedure, private :: suprls

private subroutine suprls(me, i, rowi, n, bi, a, nn, soln, err, ier)

To determine the least squares solution of a large overdetermined linear system.

Arguments

Type	Intent		Name
class(splpak_type),	intent(inout)	::	me
integer,	intent(in)	::	i	the index of the row being entered. (`i` is 1 for the first call, increases by 1 for each call, and is `m` when the final row is entered). After the final row has been entered, suprls is called with `i = 0` to complete the reduction and solution.
real(kind=wp),	intent(in)	::	rowi(n)	a vector which on the `i`th call contains the `n` components of the `i`th row of the matrix. the dimension of `rowi` in calling program must be at least `n`.
integer,	intent(in)	::	n	the length of the rows of the matrix (i.e., the number of columns). `n <= m`, where `m` is the number of rows.
real(kind=wp),	intent(in)	::	bi	on the `i`th call, `bi` contains the `i`th element of the right hand side vector `b`.
real(kind=wp),	intent(inout)	::	a(nn)	a working array which must not be changed between the successive calls to suprls.
integer,	intent(in)	::	nn	length of scratch array `a`. `nn` must be at least `n(n+5)/2+1`. For speed, `nn` should be as large as possible up to a maximum of `(n+1)m`.
real(kind=wp),	intent(out)	::	soln(n)	the `n`-components of the solution vector are returned in this array after the final call to suprls.
real(kind=wp),	intent(out)	::	err	the euclidean norm of the residual is returned in `err` after the final call to suprls.
integer,	intent(out)	::	ier	error parameter. fatal errors: Read more…

Source Code

    type,public :: splpak_type

        !!### Usage
        !!
        !!  The class contains four user entries:
        !!  [[splcc]], [[splcw]], [[splfe]], and [[splde]].
        !!
        !!  The user first calls [[splcc]] by
        !!```fortran
        !!    call me%initialize(ndim,xdata,l1xdat,ydata,ndata,
        !!                       xmin,xmax,nodes,xtrap,coef,ncf,
        !!                       work,nwrk,ierror)
        !!```
        !!  or [[splcw]] by
        !!```fortran
        !!    call me%initialize(ndim,xdata,l1xdata,ydata,wdata,
        !!                       ndata,xmin,xmax,nodes,xtrap,
        !!                       coef,ncf,work,nwrk,ierror)
        !!```
        !!  The parameter `NDATA` in the call to [[splcw]]
        !!  enables the user to weight some of the data
        !!  points more heavily than others.  Both
        !!  routines return a set of coefficients in the
        !!  array `COEF`.  These coefficients are
        !!  subsequently used in the computation of
        !!  function values and partial derivatives.
        !!  To compute values on the spline approximation
        !!  the user then calls [[splfe]] or [[splde]] any
        !!  number of times in any order provided that
        !!  the values of the inputs, `NDIM`, `COEF`, `XMIN`,
        !!  `XMAX`, and `NODES`, are preserved between calls.
        !!
        !!  [[splfe]] and [[splde]] are called in the following way:
        !!```fortran
        !!    f = me%evaluate(ndim,x,coef,xmin,xmax,nodes,ierror)
        !!```
        !!  or
        !!```fortran
        !!    f = me%evaluate(ndim,x,nderiv,coef,xmin,xmax,nodes,ierror)
        !!```
        !!  The routine [[splfe]] returns an interpolated
        !!  value at the point defined by the array `X`.
        !!  [[splde]] affords the user the additional
        !!  capability of calculating an interpolated
        !!  value for one of several partial derivatives
        !!  specified by the array `NDERIV`.

        private

        ! formerly in splcomd common block:
        integer :: mdim = 0
        real(wp),dimension(:),allocatable :: dx ! originally these were all size 4
        real(wp),dimension(:),allocatable :: dxin
        integer,dimension(:),allocatable  :: ib
        integer,dimension(:),allocatable  :: ibmn
        integer,dimension(:),allocatable  :: ibmx

        ! formerly saved variables in suprls
        integer :: ilast = 0
        integer :: isav  = 0
        integer :: iold  = 0
        integer :: np1   = 0
        integer :: l     = 0
        integer :: il1   = 0
        integer :: k     = 0
        integer :: k1    = 0
        real(wp) :: errsum = 0.0_wp

        contains

        private

        generic,public   :: initialize => splcc, splcw !! compute the spline coefficients
        generic,public   :: evaluate   => splfe, splde !! evaluate the spline
        procedure,public :: destroy    => destroy_splpak !! destory the internal class variables
        procedure,private :: splcc
        procedure,private :: splcw
        procedure,private :: splfe
        procedure,private :: splde
        procedure,private :: bascmp
        procedure,private :: suprls

    end type splpak_type

splpak_type Derived Type

Contents

Variables

Type-Bound Procedures

Source Code

type, public :: splpak_type

Usage

Components

Type-Bound Procedures

generic, public :: initialize => splcc, splcw

private subroutine splcc(me, ndim, xdata, l1xdat, ydata, ndata, xmin, xmax, nodes, xtrap, coef, ncf, work, nwrk, ierror)

Arguments

private subroutine splcw(me, ndim, xdata, l1xdat, ydata, wdata, ndata, xmin, xmax, nodes, xtrap, coef, ncf, work, nwrk, ierror)

Arguments

generic, public :: evaluate => splfe, splde

private function splfe(me, ndim, x, coef, xmin, xmax, nodes, ierror)

Arguments

Return Value real(kind=wp)

private function splde(me, ndim, x, nderiv, coef, xmin, xmax, nodes, ierror)

Arguments

Return Value real(kind=wp)

procedure, public :: destroy => destroy_splpak

private subroutine destroy_splpak(me, ndim)

Arguments

procedure, private :: splcc

private subroutine splcc(me, ndim, xdata, l1xdat, ydata, ndata, xmin, xmax, nodes, xtrap, coef, ncf, work, nwrk, ierror)

Arguments

procedure, private :: splcw

private subroutine splcw(me, ndim, xdata, l1xdat, ydata, wdata, ndata, xmin, xmax, nodes, xtrap, coef, ncf, work, nwrk, ierror)

Arguments

procedure, private :: splfe

private function splfe(me, ndim, x, coef, xmin, xmax, nodes, ierror)

Arguments

Return Value real(kind=wp)

procedure, private :: splde

private function splde(me, ndim, x, nderiv, coef, xmin, xmax, nodes, ierror)

Arguments

Return Value real(kind=wp)

procedure, private :: bascmp

private subroutine bascmp(me, x, nderiv, xmin, nodes, icol, basm)

Arguments

procedure, private :: suprls

private subroutine suprls(me, i, rowi, n, bi, a, nn, soln, err, ier)

Arguments

Source Code