Evaluates the tensor product piecewise polynomial
interpolant constructed by the routine db5ink or one of its
derivatives at the point (xval,yval,zval,qval,rval).
To evaluate the
interpolant itself, set idx=idy=idz=idq=idr=0, to evaluate the first
partial with respect to x, set idx=1,idy=idz=idq=idr=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. |
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| real(kind=wp), | intent(in) | :: | yval |
coordinate of evaluation point. |
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| real(kind=wp), | intent(in) | :: | zval |
coordinate of evaluation point. |
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| real(kind=wp), | intent(in) | :: | qval |
coordinate of evaluation point. |
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| real(kind=wp), | intent(in) | :: | rval |
coordinate of evaluation point. |
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| integer(kind=ip), | intent(in) | :: | idx |
derivative of piecewise polynomial to evaluate. |
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| integer(kind=ip), | intent(in) | :: | idy |
derivative of piecewise polynomial to evaluate. |
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| integer(kind=ip), | intent(in) | :: | idz |
derivative of piecewise polynomial to evaluate. |
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| integer(kind=ip), | intent(in) | :: | idq |
derivative of piecewise polynomial to evaluate. |
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| integer(kind=ip), | intent(in) | :: | idr |
derivative of piecewise polynomial to evaluate. |
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| 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 db5ink) |
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| 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 db5ink) |
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| 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 db5ink) |
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| 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 db5ink) |
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| real(kind=wp), | intent(in), | dimension(nr+kr) | :: | tr |
sequence of knots defining the piecewise polynomial in the direction. (same as in last call to db5ink) |
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| integer(kind=ip), | intent(in) | :: | nx |
the number of interpolation points in . (same as in last call to db5ink) |
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| integer(kind=ip), | intent(in) | :: | ny |
the number of interpolation points in . (same as in last call to db5ink) |
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| integer(kind=ip), | intent(in) | :: | nz |
the number of interpolation points in . (same as in last call to db5ink) |
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| integer(kind=ip), | intent(in) | :: | nq |
the number of interpolation points in . (same as in last call to db5ink) |
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| integer(kind=ip), | intent(in) | :: | nr |
the number of interpolation points in . (same as in last call to db5ink) |
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| integer(kind=ip), | intent(in) | :: | kx |
order of polynomial pieces in . (same as in last call to db5ink) |
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| integer(kind=ip), | intent(in) | :: | ky |
order of polynomial pieces in . (same as in last call to db5ink) |
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| integer(kind=ip), | intent(in) | :: | kz |
order of polynomial pieces in . (same as in last call to db5ink) |
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| integer(kind=ip), | intent(in) | :: | kq |
order of polynomial pieces in . (same as in last call to db5ink) |
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| integer(kind=ip), | intent(in) | :: | kr |
order of polynomial pieces in . (same as in last call to db5ink) |
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| real(kind=wp), | intent(in), | dimension(nx,ny,nz,nq,nr) | :: | bcoef |
the b-spline coefficients computed by db5ink. |
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| real(kind=wp), | intent(out) | :: | f |
interpolated value |
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| integer(kind=ip), | intent(out) | :: | iflag |
status flag:
|
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| 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. |
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| integer(kind=ip), | intent(inout) | :: | inbvy |
not used (kept for backward compatibility) |
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| integer(kind=ip), | intent(inout) | :: | inbvz |
not used (kept for backward compatibility) |
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| integer(kind=ip), | intent(inout) | :: | inbvq |
not used (kept for backward compatibility) |
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| integer(kind=ip), | intent(inout) | :: | inbvr |
not used (kept for backward compatibility) |
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| 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. |
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| 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. |
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| 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. |
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| integer(kind=ip), | intent(inout) | :: | ilor |
initialization parameter which must be set to 1 the first time this routine is called, and must not be changed by the user. |
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| real(kind=wp), | intent(inout), | dimension(ky,kz,kq,kr) | :: | w4 |
work array |
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| real(kind=wp), | intent(inout), | dimension(kz,kq,kr) | :: | w3 |
work array |
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| real(kind=wp), | intent(inout), | dimension(kq,kr) | :: | w2 |
work array |
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| real(kind=wp), | intent(inout), | dimension(kr) | :: | w1 |
work array |
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| real(kind=wp), | intent(inout), | dimension(3_ip*max(kx,ky,kz,kq,kr)) | :: | w0 |
not used (kept for backward compatibility) |
|
| logical, | intent(in), | optional | :: | extrap |
if extrapolation is allowed (if not present, default is False) |
pure subroutine db5val_default(xval,yval,zval,qval,rval,& idx,idy,idz,idq,idr,& tx,ty,tz,tq,tr,& nx,ny,nz,nq,nr,& kx,ky,kz,kq,kr,& bcoef,f,iflag,& inbvx,inbvy,inbvz,inbvq,inbvr,& iloy,iloz,iloq,ilor,& w4,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) :: idr !! \(r\) derivative of piecewise polynomial to evaluate. integer(ip),intent(in) :: nx !! the number of interpolation points in \(x\). !! (same as in last call to [[db5ink]]) integer(ip),intent(in) :: ny !! the number of interpolation points in \(y\). !! (same as in last call to [[db5ink]]) integer(ip),intent(in) :: nz !! the number of interpolation points in \(z\). !! (same as in last call to [[db5ink]]) integer(ip),intent(in) :: nq !! the number of interpolation points in \(q\). !! (same as in last call to [[db5ink]]) integer(ip),intent(in) :: nr !! the number of interpolation points in \(r\). !! (same as in last call to [[db5ink]]) integer(ip),intent(in) :: kx !! order of polynomial pieces in \(x\). !! (same as in last call to [[db5ink]]) integer(ip),intent(in) :: ky !! order of polynomial pieces in \(y\). !! (same as in last call to [[db5ink]]) integer(ip),intent(in) :: kz !! order of polynomial pieces in \(z\). !! (same as in last call to [[db5ink]]) integer(ip),intent(in) :: kq !! order of polynomial pieces in \(q\). !! (same as in last call to [[db5ink]]) integer(ip),intent(in) :: kr !! order of polynomial pieces in \(r\). !! (same as in last call to [[db5ink]]) 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),intent(in) :: rval !! \(r\) 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 [[db5ink]]) 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 [[db5ink]]) 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 [[db5ink]]) 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 [[db5ink]]) real(wp),dimension(nr+kr),intent(in) :: tr !! sequence of knots defining the piecewise polynomial !! in the \(r\) direction. !! (same as in last call to [[db5ink]]) real(wp),dimension(nx,ny,nz,nq,nr),intent(in) :: bcoef !! the b-spline coefficients computed by [[db5ink]]. 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 !! not used (kept for backward compatibility) integer(ip),intent(inout) :: inbvz !! not used (kept for backward compatibility) integer(ip),intent(inout) :: inbvq !! not used (kept for backward compatibility) integer(ip),intent(inout) :: inbvr !! not used (kept for backward compatibility) 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. integer(ip),intent(inout) :: ilor !! 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,kr),intent(inout) :: w4 !! work array real(wp),dimension(kz,kq,kr),intent(inout) :: w3 !! work array real(wp),dimension(kq,kr),intent(inout) :: w2 !! work array real(wp),dimension(kr),intent(inout) :: w1 !! work array real(wp),dimension(3_ip*max(kx,ky,kz,kq,kr)),intent(inout) :: w0 !! not used (kept for backward compatibility) logical,intent(in),optional :: extrap !! if extrapolation is allowed !! (if not present, default is False) integer(ip) :: leftx, lefty, leftz, leftq, leftr !! interval indices integer(ip) :: ix, iy, iz, iq, ir !! coefficient offsets integer(ip) :: j, k, q, r !! counters real(wp),dimension(kx) :: bx !! basis function weights in x real(wp),dimension(ky) :: by !! basis function weights in y real(wp),dimension(kz) :: bz !! basis function weights in z real(wp),dimension(kq) :: bq !! basis function weights in q real(wp),dimension(kr) :: br !! basis function weights in r 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 iflag = check_value(rval,tr,5_ip,extrap); if (iflag/=0_ip) return ! interval and basis function weights in each direction call dbvalu_weights(tx,nx,kx,idx,xval,inbvx,leftx,bx,iflag,extrap) if (iflag/=0_ip) return call dbvalu_weights(ty,ny,ky,idy,yval,iloy,lefty,by,iflag,extrap) if (iflag/=0_ip) return call dbvalu_weights(tz,nz,kz,idz,zval,iloz,leftz,bz,iflag,extrap) if (iflag/=0_ip) return call dbvalu_weights(tq,nq,kq,idq,qval,iloq,leftq,bq,iflag,extrap) if (iflag/=0_ip) return call dbvalu_weights(tr,nr,kr,idr,rval,ilor,leftr,br,iflag,extrap) if (iflag/=0_ip) return ix = leftx - kx iy = lefty - ky iz = leftz - kz iq = leftq - kq ir = leftr - kr ! contract the coefficients one direction at a time do r=1_ip,kr do q=1_ip,kq do k=1_ip,kz do j=1_ip,ky w4(j,k,q,r) = dot_product(bx,bcoef(ix+1_ip:leftx,iy+j,iz+k,iq+q,ir+r)) end do w3(k,q,r) = dot_product(by,w4(:,k,q,r)) end do w2(q,r) = dot_product(bz,w3(:,q,r)) end do w1(r) = dot_product(bq,w2(:,r)) end do f = dot_product(br,w1) end subroutine db5val_default