db4ink – bspline-fortran

Calls

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Called by

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private pure subroutine db4ink_default(x, nx, y, ny, z, nz, q, nq, fcn, kx, ky, kz, kq, iknot, tx, ty, tz, tq, bcoef, iflag)

Determines the parameters of a function that interpolates the four-dimensional gridded data $[x(i),y(j),z(k),q(l),\mathrm{fcn}(i,j,k,l)] ~\mathrm{for}~ i=1,..,n_x ~\mathrm{and}~ j=1,..,n_y, ~\mathrm{and}~ k=1,..,n_z, ~\mathrm{and}~ l=1,..,n_q$ The interpolating function and its derivatives may subsequently be evaluated by the function db4val.

Arguments

Type	Intent	Attributes		Name
real(kind=wp),	intent(in),	dimension(:)	::	x	`(nx)` array of $x$ abcissae. must be strictly increasing.
integer(kind=ip),	intent(in)		::	nx	number of $x$ abcissae ( $\ge 3$ )
real(kind=wp),	intent(in),	dimension(:)	::	y	`(ny)` array of $y$ abcissae. must be strictly increasing.
integer(kind=ip),	intent(in)		::	ny	number of $y$ abcissae ( $\ge 3$ )
real(kind=wp),	intent(in),	dimension(:)	::	z	`(nz)` array of $z$ abcissae. must be strictly increasing.
integer(kind=ip),	intent(in)		::	nz	number of $z$ abcissae ( $\ge 3$ )
real(kind=wp),	intent(in),	dimension(:)	::	q	`(nq)` array of $q$ abcissae. must be strictly increasing.
integer(kind=ip),	intent(in)		::	nq	number of $q$ abcissae ( $\ge 3$ )
real(kind=wp),	intent(in),	dimension(:,:,:,:)	::	fcn	`(nx,ny,nz,nq)` matrix of function values to interpolate. `fcn(i,j,k,q)` should contain the function value at the point (`x(i)`,`y(j)`,`z(k)`,`q(l)`)
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(in)		::	kq	the order of spline pieces in $q$ ( $2 \le k_q < n_q$ ). (order = polynomial degree + 1)
integer(kind=ip),	intent(in)		::	iknot	knot sequence flag: Read more…
real(kind=wp),	intent(inout),	dimension(:)	::	tx	The `(nx+kx)` knots in the x direction for the spline interpolant. Read more…
real(kind=wp),	intent(inout),	dimension(:)	::	ty	The `(ny+ky)` knots in the y direction for the spline interpolant. Read more…
real(kind=wp),	intent(inout),	dimension(:)	::	tz	The `(nz+kz)` knots in the z direction for the spline interpolant. Read more…
real(kind=wp),	intent(inout),	dimension(:)	::	tq	The `(nq+kq)` knots in the q direction for the spline interpolant. Read more…
real(kind=wp),	intent(out),	dimension(:,:,:,:)	::	bcoef	`(nx,ny,nz,nq)` matrix of coefficients of the b-spline interpolant.
integer(kind=ip),	intent(out)		::	iflag	Read more…

private pure subroutine db4ink_multi(x, nx, y, ny, z, nz, q, nq, fcn, kx, ky, kz, kq, iknot, tx, ty, tz, tq, bcoef, iflag)

Multiple-output version of db4ink: interpolates nf functions on the same grid, with the same knots. The last dimension of fcn and bcoef is the output index. Evaluate them with db4val (multiple-output version).

Arguments

Type	Intent	Attributes		Name
real(kind=wp),	intent(in),	dimension(:)	::	x	`(nx)` array of $x$ abcissae. Must be strictly increasing.
integer(kind=ip),	intent(in)		::	nx	Number of $x$ abcissae
real(kind=wp),	intent(in),	dimension(:)	::	y	`(ny)` array of $y$ abcissae. Must be strictly increasing.
integer(kind=ip),	intent(in)		::	ny	Number of $y$ abcissae
real(kind=wp),	intent(in),	dimension(:)	::	z	`(nz)` array of $z$ abcissae. Must be strictly increasing.
integer(kind=ip),	intent(in)		::	nz	Number of $z$ abcissae
real(kind=wp),	intent(in),	dimension(:)	::	q	`(nq)` array of $q$ abcissae. Must be strictly increasing.
integer(kind=ip),	intent(in)		::	nq	Number of $q$ abcissae
real(kind=wp),	intent(in),	dimension(:,:,:,:,:)	::	fcn	`(nx,ny,nz,nq,nf)` array of function values to interpolate: `fcn(i1,i2,i3,i4,j)` is output `j` at grid point (`x(i1)`,`y(i2)`,`z(i3)`,`q(i4)`)
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(in)		::	kq	The order of spline pieces in $q$
integer(kind=ip),	intent(in)		::	iknot	knot sequence flag (see db4ink_default)
real(kind=wp),	intent(inout),	dimension(:)	::	tx	The `(nx+kx)` knots in the $x$ direction
real(kind=wp),	intent(inout),	dimension(:)	::	ty	The `(ny+ky)` knots in the $y$ direction
real(kind=wp),	intent(inout),	dimension(:)	::	tz	The `(nz+kz)` knots in the $z$ direction
real(kind=wp),	intent(inout),	dimension(:)	::	tq	The `(nq+kq)` knots in the $q$ direction
real(kind=wp),	intent(out),	dimension(:,:,:,:,:)	::	bcoef	`(nx,ny,nz,nq,nf)` array of b-spline coefficients
integer(kind=ip),	intent(out)		::	iflag	status flag (see db4ink_default), or 6001 if `fcn` and `bcoef` do not have the same number of outputs (or it is zero)

db4ink Interface

Contents

Module Procedures

public interface db4ink

Calls

Called by

Module Procedures

private pure subroutine db4ink_default(x, nx, y, ny, z, nz, q, nq, fcn, kx, ky, kz, kq, iknot, tx, ty, tz, tq, bcoef, iflag)

Arguments

private pure subroutine db4ink_multi(x, nx, y, ny, z, nz, q, nq, fcn, kx, ky, kz, kq, iknot, tx, ty, tz, tq, bcoef, iflag)

Arguments