Determines the parameters of a function that interpolates the six-dimensional gridded data:
for:
the interpolating function and its derivatives may subsequently be evaluated by the function db6val.
See db3ink header for more details.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=wp), | intent(in), | dimension(:) | :: | x |
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| integer(kind=ip), | intent(in) | :: | nx |
number of abcissae ( ) |
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| real(kind=wp), | intent(in), | dimension(:) | :: | y |
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| integer(kind=ip), | intent(in) | :: | ny |
number of abcissae ( ) |
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| real(kind=wp), | intent(in), | dimension(:) | :: | z |
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| integer(kind=ip), | intent(in) | :: | nz |
number of abcissae ( ) |
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| real(kind=wp), | intent(in), | dimension(:) | :: | q |
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| integer(kind=ip), | intent(in) | :: | nq |
number of abcissae ( ) |
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| real(kind=wp), | intent(in), | dimension(:) | :: | r |
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| integer(kind=ip), | intent(in) | :: | nr |
number of abcissae ( ) |
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| real(kind=wp), | intent(in), | dimension(:) | :: | s |
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| integer(kind=ip), | intent(in) | :: | ns |
number of abcissae ( ) |
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| real(kind=wp), | intent(in), | dimension(:,:,:,:,:,:) | :: | fcn |
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| integer(kind=ip), | intent(in) | :: | kx |
the order of spline pieces in ( ) (order = polynomial degree + 1) |
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| integer(kind=ip), | intent(in) | :: | ky |
the order of spline pieces in ( ) (order = polynomial degree + 1) |
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| integer(kind=ip), | intent(in) | :: | kz |
the order of spline pieces in ( ) (order = polynomial degree + 1) |
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| integer(kind=ip), | intent(in) | :: | kq |
the order of spline pieces in ( ) (order = polynomial degree + 1) |
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| integer(kind=ip), | intent(in) | :: | kr |
the order of spline pieces in ( ) (order = polynomial degree + 1) |
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| integer(kind=ip), | intent(in) | :: | ks |
the order of spline pieces in ( ) (order = polynomial degree + 1) |
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| integer(kind=ip), | intent(in) | :: | iknot |
knot sequence flag:
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| real(kind=wp), | intent(inout), | dimension(:) | :: | tx |
The
Must be non-decreasing. |
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| real(kind=wp), | intent(inout), | dimension(:) | :: | ty |
The
Must be non-decreasing. |
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| real(kind=wp), | intent(inout), | dimension(:) | :: | tz |
The
Must be non-decreasing. |
|
| real(kind=wp), | intent(inout), | dimension(:) | :: | tq |
The
Must be non-decreasing. |
|
| real(kind=wp), | intent(inout), | dimension(:) | :: | tr |
The
Must be non-decreasing. |
|
| real(kind=wp), | intent(inout), | dimension(:) | :: | ts |
The
Must be non-decreasing. |
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| real(kind=wp), | intent(out), | dimension(:,:,:,:,:,:) | :: | bcoef |
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| integer(kind=ip), | intent(out) | :: | iflag |
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pure subroutine db6ink(x,nx,y,ny,z,nz,q,nq,r,nr,s,ns,& fcn,& kx,ky,kz,kq,kr,ks,& iknot,& tx,ty,tz,tq,tr,ts,& bcoef,iflag) implicit none integer(ip),intent(in) :: nx !! number of \(x\) abcissae ( \( \ge 3 \) ) integer(ip),intent(in) :: ny !! number of \(y\) abcissae ( \( \ge 3 \) ) integer(ip),intent(in) :: nz !! number of \(z\) abcissae ( \( \ge 3 \) ) integer(ip),intent(in) :: nq !! number of \(q\) abcissae ( \( \ge 3 \) ) integer(ip),intent(in) :: nr !! number of \(r\) abcissae ( \( \ge 3 \) ) integer(ip),intent(in) :: ns !! number of \(s\) abcissae ( \( \ge 3 \) ) integer(ip),intent(in) :: kx !! the order of spline pieces in \(x\) !! ( \( 2 \le k_x < n_x \) ) !! (order = polynomial degree + 1) integer(ip),intent(in) :: ky !! the order of spline pieces in \(y\) !! ( \( 2 \le k_y < n_y \) ) !! (order = polynomial degree + 1) integer(ip),intent(in) :: kz !! the order of spline pieces in \(z\) !! ( \( 2 \le k_z < n_z \) ) !! (order = polynomial degree + 1) integer(ip),intent(in) :: kq !! the order of spline pieces in \(q\) !! ( \( 2 \le k_q < n_q \) ) !! (order = polynomial degree + 1) integer(ip),intent(in) :: kr !! the order of spline pieces in \(r\) !! ( \( 2 \le k_r < n_r \) ) !! (order = polynomial degree + 1) integer(ip),intent(in) :: ks !! the order of spline pieces in \(s\) !! ( \( 2 \le k_s < n_s \) ) !! (order = polynomial degree + 1) real(wp),dimension(:),intent(in) :: x !! `(nx)` array of \(x\) abcissae. !! must be strictly increasing. real(wp),dimension(:),intent(in) :: y !! `(ny)` array of \(y\) abcissae. !! must be strictly increasing. real(wp),dimension(:),intent(in) :: z !! `(nz)` array of \(z\) abcissae. !! must be strictly increasing. real(wp),dimension(:),intent(in) :: q !! `(nq)` array of \(q\) abcissae. !! must be strictly increasing. real(wp),dimension(:),intent(in) :: r !! `(nr)` array of \(r\) abcissae. !! must be strictly increasing. real(wp),dimension(:),intent(in) :: s !! `(ns)` array of \(s\) abcissae. !! must be strictly increasing. real(wp),dimension(:,:,:,:,:,:),intent(in) :: fcn !! `(nx,ny,nz,nq,nr,ns)` matrix of function values to !! interpolate. `fcn(i,j,k,q,r,s)` should contain the !! function value at the point !! (`x(i)`,`y(j)`,`z(k)`,`q(l)`,`r(m)`,`s(n)`) integer(ip),intent(in) :: iknot !! knot sequence flag: !! !! * 0 = knot sequence chosen by [[db6ink]]. !! * 1 = knot sequence chosen by user. real(wp),dimension(:),intent(inout) :: tx !! The `(nx+kx)` knots in the \(x\) direction for the !! spline interpolant. !! !! * f `iknot=0` these are chosen by [[db6ink]]. !! * f `iknot=1` these are specified by the user. !! !! Must be non-decreasing. real(wp),dimension(:),intent(inout) :: ty !! The `(ny+ky)` knots in the \(y\) direction for the !! spline interpolant. !! !! * If `iknot=0` these are chosen by [[db6ink]]. !! * If `iknot=1` these are specified by the user. !! !! Must be non-decreasing. real(wp),dimension(:),intent(inout) :: tz !! The `(nz+kz)` knots in the \(z\) direction for the !! spline interpolant. !! !! * If `iknot=0` these are chosen by [[db6ink]]. !! * If `iknot=1` these are specified by the user. !! !! Must be non-decreasing. real(wp),dimension(:),intent(inout) :: tq !! The `(nq+kq)` knots in the \(q\) direction for the !! spline interpolant. !! !! * If `iknot=0` these are chosen by [[db6ink]]. !! * If `iknot=1` these are specified by the user. !! !! Must be non-decreasing. real(wp),dimension(:),intent(inout) :: tr !! The `(nr+kr)` knots in the \(r\) direction for the !! spline interpolant. !! !! * If `iknot=0` these are chosen by [[db6ink]]. !! * If `iknot=1` these are specified by the user. !! !! Must be non-decreasing. real(wp),dimension(:),intent(inout) :: ts !! The `(ns+ks)` knots in the \(s\) direction for the !! spline interpolant. !! !! * If `iknot=0` these are chosen by [[db6ink]]. !! * If `iknot=1` these are specified by the user. !! !! Must be non-decreasing. real(wp),dimension(:,:,:,:,:,:),intent(out) :: bcoef !! `(nx,ny,nz,nq,nr,ns)` matrix of coefficients of the !! b-spline interpolant. integer(ip),intent(out) :: iflag !! * 0 = successful execution. !! * 2 = `iknot` out of range. !! * 3 = `nx` out of range. !! * 4 = `kx` out of range. !! * 5 = `x` not strictly increasing. !! * 6 = `tx` not non-decreasing. !! * 7 = `ny` out of range. !! * 8 = `ky` out of range. !! * 9 = `y` not strictly increasing. !! * 10 = `ty` not non-decreasing. !! * 11 = `nz` out of range. !! * 12 = `kz` out of range. !! * 13 = `z` not strictly increasing. !! * 14 = `tz` not non-decreasing. !! * 15 = `nq` out of range. !! * 16 = `kq` out of range. !! * 17 = `q` not strictly increasing. !! * 18 = `tq` not non-decreasing. !! * 19 = `nr` out of range. !! * 20 = `kr` out of range. !! * 21 = `r` not strictly increasing. !! * 22 = `tr` not non-decreasing. !! * 23 = `ns` out of range. !! * 24 = `ks` out of range. !! * 25 = `s` not strictly increasing. !! * 26 = `ts` not non-decreasing. !! * 700 = `size(x) ` \( \ne \) `size(fcn,1)` !! * 701 = `size(y) ` \( \ne \) `size(fcn,2)` !! * 702 = `size(z) ` \( \ne \) `size(fcn,3)` !! * 703 = `size(q) ` \( \ne \) `size(fcn,4)` !! * 704 = `size(r) ` \( \ne \) `size(fcn,5)` !! * 705 = `size(s) ` \( \ne \) `size(fcn,6)` !! * 706 = `size(x) ` \( \ne \) `nx` !! * 707 = `size(y) ` \( \ne \) `ny` !! * 708 = `size(z) ` \( \ne \) `nz` !! * 709 = `size(q) ` \( \ne \) `nq` !! * 710 = `size(r) ` \( \ne \) `nr` !! * 711 = `size(s) ` \( \ne \) `ns` !! * 712 = `size(tx)` \( \ne \) `nx+kx` !! * 713 = `size(ty)` \( \ne \) `ny+ky` !! * 714 = `size(tz)` \( \ne \) `nz+kz` !! * 715 = `size(tq)` \( \ne \) `nq+kq` !! * 716 = `size(tr)` \( \ne \) `nr+kr` !! * 717 = `size(ts)` \( \ne \) `ns+ks` !! * 800 = `size(x) ` \( \ne \) `size(bcoef,1)` !! * 801 = `size(y) ` \( \ne \) `size(bcoef,2)` !! * 802 = `size(z) ` \( \ne \) `size(bcoef,3)` !! * 803 = `size(q) ` \( \ne \) `size(bcoef,4)` !! * 804 = `size(r) ` \( \ne \) `size(bcoef,5)` !! * 805 = `size(s) ` \( \ne \) `size(bcoef,6)` logical :: status_ok real(wp),dimension(:),allocatable :: temp !! work array of size `nx*ny*nz*nq*nr*ns` real(wp),dimension(:),allocatable :: work !! work array of size `max(2*kx*(nx+1), !! 2*ky*(ny+1),2*kz*(nz+1),2*kq*(nq+1), !! 2*kr*(nr+1),2*ks*(ns+1))` ! check validity of input call check_inputs( iknot,& iflag,& nx=nx,ny=ny,nz=nz,nq=nq,nr=nr,ns=ns,& kx=kx,ky=ky,kz=kz,kq=kq,kr=kr,ks=ks,& x=x,y=y,z=z,q=q,r=r,s=s,& tx=tx,ty=ty,tz=tz,tq=tq,tr=tr,ts=ts,& f6=fcn,& bcoef6=bcoef,& status_ok=status_ok) if (status_ok) then ! choose knots if (iknot == 0_ip) then call dbknot(x,nx,kx,tx) call dbknot(y,ny,ky,ty) call dbknot(z,nz,kz,tz) call dbknot(q,nq,kq,tq) call dbknot(r,nr,kr,tr) call dbknot(s,ns,ks,ts) end if allocate(temp(nx*ny*nz*nq*nr*ns)) allocate(work(max(2_ip*kx*(nx+1_ip),2_ip*ky*(ny+1_ip),& 2_ip*kz*(nz+1_ip),2_ip*kq*(nq+1_ip),& 2_ip*kr*(nr+1_ip),2_ip*ks*(ns+1_ip)))) ! construct b-spline coefficients call dbtpcf(x,nx,fcn, nx,ny*nz*nq*nr*ns,tx,kx,temp, work,iflag) if (iflag==0_ip) call dbtpcf(y,ny,temp, ny,nx*nz*nq*nr*ns,ty,ky,bcoef,work,iflag) if (iflag==0_ip) call dbtpcf(z,nz,bcoef,nz,nx*ny*nq*nr*ns,tz,kz,temp, work,iflag) if (iflag==0_ip) call dbtpcf(q,nq,temp, nq,nx*ny*nz*nr*ns,tq,kq,bcoef,work,iflag) if (iflag==0_ip) call dbtpcf(r,nr,bcoef,nr,nx*ny*nz*nq*ns,tr,kr,temp, work,iflag) if (iflag==0_ip) call dbtpcf(s,ns,temp, ns,nx*ny*nz*nq*nr,ts,ks,bcoef,work,iflag) deallocate(temp) deallocate(work) end if end subroutine db6ink