The function may be called by the names: e01tnc, nag_interp_dim5_scat_shep_eval or nag_5d_shep_eval.
3Description
e01tnc takes as input the interpolant , of a set of scattered data points , for , as computed by e01tmc, and evaluates the interpolant and its first partial derivatives at the set of points , for .
e01tnc must only be called after a call to
e01tmc.
e01tnc is derived from the new implementation of QS3GRD described by Renka (1988). It uses the modification for five-dimensional interpolation described by Berry and Minser (1999).
4References
Berry M W, Minser K S (1999) Algorithm 798: high-dimensional interpolation using the modified Shepard method ACM Trans. Math. Software25 353–366
Renka R J (1988) Algorithm 661: QSHEP3D: Quadratic Shepard method for trivariate interpolation of scattered data ACM Trans. Math. Software14 151–152
5Arguments
1: – IntegerInput
On entry: must be the same value supplied for argument m in the preceding call to e01tmc.
Constraint:
.
2: – const doubleInput
Note: the th element of the matrix is stored in .
On entry: must be the same array supplied as argument x in the preceding call to e01tmc. It must remain unchanged between calls.
3: – const doubleInput
On entry: must be the same array supplied as argument f in the preceding call to e01tmc. It must remain unchanged between calls.
4: – const IntegerInput
On entry: must be the same array returned as argument iq in the preceding call to e01tmc. It must remain unchanged between calls.
5: – const doubleInput
On entry: must be the same array returned as argument rq in the preceding call to e01tmc. It must remain unchanged between calls.
6: – IntegerInput
On entry: , the number of evaluation points.
Constraint:
.
7: – const doubleInput
Note: the th element of the matrix is stored in .
On entry: must be set to the evaluation point , for .
8: – doubleOutput
On exit: contains the value of the interpolant, at , for . If any of these evaluation points lie outside the region of definition of the interpolant the corresponding entries in q are set to an extrapolated approximation, and e01tnc returns with NE_BAD_POINT.
9: – doubleOutput
Note: the th element of the matrix is stored in .
On exit: contains the value of the partial derivatives with respect to of the interpolant at
, for , and for each of the five partial derivatives . If any of these evaluation points lie outside the region of definition of the interpolant, the corresponding entries in qx are set to extrapolated approximations to the partial derivatives, and e01tnc returns with NE_BAD_POINT.
10: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM
On entry, argument had an illegal value.
NE_BAD_POINT
On entry, at least one evaluation point lies outside the region of definition of the interpolant. At such points the corresponding values in q and qx contain extrapolated approximations. Points should be evaluated one by one to identify extrapolated values.
NE_INT
On entry, .
Constraint: .
On entry, .
Constraint: .
NE_INT_ARRAY
On entry, values in iq appear to be invalid. Check that iq has not been corrupted between calls to e01tmcande01tnc.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_REAL_ARRAY
On entry, values in rq appear to be invalid. Check that rq has not been corrupted between calls to
e01tmcande01tnc.
7Accuracy
Computational errors should be negligible in most practical situations.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
e01tnc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
e01tnc makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
9Further Comments
The time taken for a call to e01tnc 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 . At worst
time will be required.
10Example
This program evaluates the function
at a set of randomly generated data points and calls e01tmc to construct an interpolating function . It then calls e01tnc to evaluate the interpolant at a set of random points.
To reduce the time taken by this example, the number of data points is limited to . Increasing this value to the suggested minimum of improves the interpolation accuracy at the expense of more time.