Evaluates the tensor product piecewise polynomial
interpolant constructed by the routine db4ink or one of its
derivatives at the point (xval
,yval
,zval
,qval
).
To evaluate the
interpolant itself, set idx=idy=idz=idq=0
, to evaluate the first
partial with respect to x
, set idx=1,idy=idz=idq=0
, and so on.
See db3val header for more information.
Type  Intent  Optional  Attributes  Name  

real(kind=wp),  intent(in)  ::  xval 
coordinate of evaluation point. 

real(kind=wp),  intent(in)  ::  yval 
coordinate of evaluation point. 

real(kind=wp),  intent(in)  ::  zval 
coordinate of evaluation point. 

real(kind=wp),  intent(in)  ::  qval 
coordinate of evaluation point. 

integer(kind=ip),  intent(in)  ::  idx 
derivative of piecewise polynomial to evaluate. 

integer(kind=ip),  intent(in)  ::  idy 
derivative of piecewise polynomial to evaluate. 

integer(kind=ip),  intent(in)  ::  idz 
derivative of piecewise polynomial to evaluate. 

integer(kind=ip),  intent(in)  ::  idq 
derivative of piecewise polynomial to evaluate. 

real(kind=wp),  intent(in),  dimension(nx+kx)  ::  tx 
sequence of knots defining the piecewise polynomial in the direction. (same as in last call to db4ink) 

real(kind=wp),  intent(in),  dimension(ny+ky)  ::  ty 
sequence of knots defining the piecewise polynomial in the direction. (same as in last call to db4ink) 

real(kind=wp),  intent(in),  dimension(nz+kz)  ::  tz 
sequence of knots defining the piecewise polynomial in the direction. (same as in last call to db4ink) 

real(kind=wp),  intent(in),  dimension(nq+kq)  ::  tq 
sequence of knots defining the piecewise polynomial in the direction. (same as in last call to db4ink) 

integer(kind=ip),  intent(in)  ::  nx 
the number of interpolation points in . (same as in last call to db4ink) 

integer(kind=ip),  intent(in)  ::  ny 
the number of interpolation points in . (same as in last call to db4ink) 

integer(kind=ip),  intent(in)  ::  nz 
the number of interpolation points in . (same as in last call to db4ink) 

integer(kind=ip),  intent(in)  ::  nq 
the number of interpolation points in . (same as in last call to db4ink) 

integer(kind=ip),  intent(in)  ::  kx 
order of polynomial pieces in . (same as in last call to db4ink) 

integer(kind=ip),  intent(in)  ::  ky 
order of polynomial pieces in . (same as in last call to db4ink) 

integer(kind=ip),  intent(in)  ::  kz 
order of polynomial pieces in . (same as in last call to db4ink) 

integer(kind=ip),  intent(in)  ::  kq 
order of polynomial pieces in . (same as in last call to db4ink) 

real(kind=wp),  intent(in),  dimension(nx,ny,nz,nq)  ::  bcoef 
the bspline coefficients computed by db4ink. 

real(kind=wp),  intent(out)  ::  f 
interpolated value 

integer(kind=ip),  intent(out)  ::  iflag 
status flag:


integer(kind=ip),  intent(inout)  ::  inbvx 
initialization parameter which must be set to 1 the first time this routine is called, and must not be changed by the user. 

integer(kind=ip),  intent(inout)  ::  inbvy 
initialization parameter which must be set to 1 the first time this routine is called, and must not be changed by the user. 

integer(kind=ip),  intent(inout)  ::  inbvz 
initialization parameter which must be set to 1 the first time this routine is called, and must not be changed by the user. 

integer(kind=ip),  intent(inout)  ::  inbvq 
initialization parameter which must be set to 1 the first time this routine is called, and must not be changed by the user. 

integer(kind=ip),  intent(inout)  ::  iloy 
initialization parameter which must be set to 1 the first time this routine is called, and must not be changed by the user. 

integer(kind=ip),  intent(inout)  ::  iloz 
initialization parameter which must be set to 1 the first time this routine is called, and must not be changed by the user. 

integer(kind=ip),  intent(inout)  ::  iloq 
initialization parameter which must be set to 1 the first time this routine is called, and must not be changed by the user. 

real(kind=wp),  intent(inout),  dimension(ky,kz,kq)  ::  w3 
work array 

real(kind=wp),  intent(inout),  dimension(kz,kq)  ::  w2 
work array 

real(kind=wp),  intent(inout),  dimension(kq)  ::  w1 
work array 

real(kind=wp),  intent(inout),  dimension(3_ip*max(kx,ky,kz,kq))  ::  w0 
work array 

logical,  intent(in),  optional  ::  extrap 
if extrapolation is allowed (if not present, default is False) 
pure subroutine db4val(xval,yval,zval,qval,& idx,idy,idz,idq,& tx,ty,tz,tq,& nx,ny,nz,nq,& kx,ky,kz,kq,& bcoef,f,iflag,& inbvx,inbvy,inbvz,inbvq,& iloy,iloz,iloq,w3,w2,w1,w0,extrap) implicit none integer(ip),intent(in) :: idx !! \(x\) derivative of piecewise polynomial to evaluate. integer(ip),intent(in) :: idy !! \(y\) derivative of piecewise polynomial to evaluate. integer(ip),intent(in) :: idz !! \(z\) derivative of piecewise polynomial to evaluate. integer(ip),intent(in) :: idq !! \(q\) derivative of piecewise polynomial to evaluate. integer(ip),intent(in) :: nx !! the number of interpolation points in \(x\). !! (same as in last call to [[db4ink]]) integer(ip),intent(in) :: ny !! the number of interpolation points in \(y\). !! (same as in last call to [[db4ink]]) integer(ip),intent(in) :: nz !! the number of interpolation points in \(z\). !! (same as in last call to [[db4ink]]) integer(ip),intent(in) :: nq !! the number of interpolation points in \(q\). !! (same as in last call to [[db4ink]]) integer(ip),intent(in) :: kx !! order of polynomial pieces in \(x\). !! (same as in last call to [[db4ink]]) integer(ip),intent(in) :: ky !! order of polynomial pieces in \(y\). !! (same as in last call to [[db4ink]]) integer(ip),intent(in) :: kz !! order of polynomial pieces in \(z\). !! (same as in last call to [[db4ink]]) integer(ip),intent(in) :: kq !! order of polynomial pieces in \(q\). !! (same as in last call to [[db4ink]]) real(wp),intent(in) :: xval !! \(x\) coordinate of evaluation point. real(wp),intent(in) :: yval !! \(y\) coordinate of evaluation point. real(wp),intent(in) :: zval !! \(z\) coordinate of evaluation point. real(wp),intent(in) :: qval !! \(q\) coordinate of evaluation point. real(wp),dimension(nx+kx),intent(in) :: tx !! sequence of knots defining the piecewise polynomial !! in the \(x\) direction. (same as in last call to !! [[db4ink]]) real(wp),dimension(ny+ky),intent(in) :: ty !! sequence of knots defining the piecewise polynomial !! in the \(y\) direction. (same as in last call to !! [[db4ink]]) real(wp),dimension(nz+kz),intent(in) :: tz !! sequence of knots defining the piecewise polynomial !! in the \(z\) direction. (same as in last call to !! [[db4ink]]) real(wp),dimension(nq+kq),intent(in) :: tq !! sequence of knots defining the piecewise polynomial !! in the \(q\) direction. (same as in last call to !! [[db4ink]]) real(wp),dimension(nx,ny,nz,nq),intent(in) :: bcoef !! the bspline coefficients computed by [[db4ink]]. real(wp),intent(out) :: f !! interpolated value integer(ip),intent(out) :: iflag !! status flag: !! !! * \( = 0 \) : no errors !! * \( \ne 0 \) : error integer(ip),intent(inout) :: inbvx !! initialization parameter which must be set !! to 1 the first time this routine is called, !! and must not be changed by the user. integer(ip),intent(inout) :: inbvy !! initialization parameter which must be set !! to 1 the first time this routine is called, !! and must not be changed by the user. integer(ip),intent(inout) :: inbvz !! initialization parameter which must be set !! to 1 the first time this routine is called, !! and must not be changed by the user. integer(ip),intent(inout) :: inbvq !! initialization parameter which must be set !! to 1 the first time this routine is called, !! and must not be changed by the user. integer(ip),intent(inout) :: iloy !! initialization parameter which must be set !! to 1 the first time this routine is called, !! and must not be changed by the user. integer(ip),intent(inout) :: iloz !! initialization parameter which must be set !! to 1 the first time this routine is called, !! and must not be changed by the user. integer(ip),intent(inout) :: iloq !! initialization parameter which must be set !! to 1 the first time this routine is called, !! and must not be changed by the user. real(wp),dimension(ky,kz,kq),intent(inout) :: w3 !! work array real(wp),dimension(kz,kq),intent(inout) :: w2 !! work array real(wp),dimension(kq),intent(inout) :: w1 !! work array real(wp),dimension(3_ip*max(kx,ky,kz,kq)),intent(inout) :: w0 !! work array logical,intent(in),optional :: extrap !! if extrapolation is allowed !! (if not present, default is False) integer(ip) :: lefty, leftz, leftq, & kcoly, kcolz, kcolq, j, k, q f = 0.0_wp iflag = check_value(xval,tx,1_ip,extrap); if (iflag/=0_ip) return iflag = check_value(yval,ty,2_ip,extrap); if (iflag/=0_ip) return iflag = check_value(zval,tz,3_ip,extrap); if (iflag/=0_ip) return iflag = check_value(qval,tq,4_ip,extrap); if (iflag/=0_ip) return call dintrv(ty,ny+ky,yval,iloy,lefty,iflag,extrap); if (iflag/=0_ip) return call dintrv(tz,nz+kz,zval,iloz,leftz,iflag,extrap); if (iflag/=0_ip) return call dintrv(tq,nq+kq,qval,iloq,leftq,iflag,extrap); if (iflag/=0_ip) return iflag = 0_ip ! x > y, z, q kcolq = leftq  kq do q=1_ip,kq kcolq = kcolq + 1_ip kcolz = leftz  kz do k=1_ip,kz kcolz = kcolz + 1_ip kcoly = lefty  ky do j=1_ip,ky kcoly = kcoly + 1_ip call dbvalu(tx,bcoef(:,kcoly,kcolz,kcolq),& nx,kx,idx,xval,inbvx,w0,iflag,& w3(j,k,q),extrap) if (iflag/=0_ip) return end do end do end do ! y > z, q kcoly = lefty  ky + 1_ip do q=1_ip,kq do k=1_ip,kz call dbvalu(ty(kcoly:),w3(:,k,q),& ky,ky,idy,yval,inbvy,w0,iflag,& w2(k,q),extrap) if (iflag/=0_ip) return end do end do ! z > q kcolz = leftz  kz + 1_ip do q=1_ip,kq call dbvalu(tz(kcolz:),w2(:,q),& kz,kz,idz,zval,inbvz,w0,iflag,& w1(q),extrap) if (iflag/=0_ip) return end do ! q kcolq = leftq  kq + 1_ip call dbvalu(tq(kcolq:),w1,kq,kq,idq,qval,inbvq,w0,iflag,f,extrap) end subroutine db4val