E01ZNF evaluates the multi-dimensional interpolating function generated by
E01ZMF and its first partial derivatives.
SUBROUTINE E01ZNF ( |
D, M, X, F, IQ, RQ, N, XE, Q, QX, IFAIL) |
INTEGER |
D, M, IQ(2*M+1), N, IFAIL |
REAL (KIND=nag_wp) |
X(D,M), F(M), RQ(*), XE(D,N), Q(N), QX(D,N) |
|
E01ZNF takes as input the interpolant
Q
x
,
x∈ℝd of a set of scattered data points
xr,fr
, for
r=1,2,…,m, as computed by
E01ZMF, and evaluates the interpolant and its first partial derivatives at the set of points
xi, for
i=1,2,…,n.
E01ZNF must only be called after a call to
E01ZMF.
E01ZNF is derived from the new implementation of QS3GRD described by
Renka (1988). It uses the modification for high-dimensional interpolation described by
Berry and Minser (1999).
Berry M W, Minser K S (1999) Algorithm 798: high-dimensional interpolation using the modified Shepard method
ACM Trans. Math. Software 25 353–366
Renka R J (1988) Algorithm 661: QSHEP3D: Quadratic Shepard method for trivariate interpolation of scattered data
ACM Trans. Math. Software 14 151–152
Computational errors should be negligible in most practical situations.
The time taken for a call to E01ZNF will depend in general on the distribution of the data points. If the data points are approximately uniformly distributed, then the time taken should be only On. At worst Omn time will be required.
This program evaluates the function (in six variables)
at a set of randomly generated data points and calls
E01ZMF to construct an interpolating function
Qx. It then calls E01ZNF to evaluate the interpolant at a set of points on the line
xi=x, for
i=1,2,…,6. To reduce the time taken by this example, the number of data points is limited. Increasing this value to the suggested minimum of
4000 improves the interpolation accuracy at the expense of more time.