NAG Library Function Document
nag_5d_shep_eval (e01tnc)
1 Purpose
nag_5d_shep_eval (e01tnc) evaluates the five-dimensional interpolating function generated by
nag_5d_shep_interp (e01tmc) and its first partial derivatives.
2 Specification
#include <nag.h> |
#include <nage01.h> |
void |
nag_5d_shep_eval (Integer m,
const double x[],
const double f[],
const Integer iq[],
const double rq[],
Integer n,
const double xe[],
double q[],
double qx[],
NagError *fail) |
|
3 Description
nag_5d_shep_eval (e01tnc) takes as input the interpolant
,
of a set of scattered data points
, for
, as computed by
nag_5d_shep_interp (e01tmc), and evaluates the interpolant and its first partial derivatives at the set of points
, for
.
nag_5d_shep_eval (e01tnc) must only be called after a call to
nag_5d_shep_interp (e01tmc).
nag_5d_shep_eval (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).
4 References
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
5 Arguments
- 1:
m – IntegerInput
On entry:
must be the same value supplied for argument
m in the preceding call to
nag_5d_shep_interp (e01tmc).
Constraint:
.
- 2:
x[] – 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
nag_5d_shep_interp (e01tmc). It
must remain unchanged between calls.
- 3:
f[m] – const doubleInput
On entry:
must be the same array supplied as argument
f in the preceding call to
nag_5d_shep_interp (e01tmc). It
must remain unchanged between calls.
- 4:
iq[] – const IntegerInput
On entry:
must be the same array returned as argument
iq in the preceding call to
nag_5d_shep_interp (e01tmc). It
must remain unchanged between calls.
- 5:
rq[] – const doubleInput
On entry:
must be the same array returned as argument
rq in the preceding call to
nag_5d_shep_interp (e01tmc). It
must remain unchanged between calls.
- 6:
n – IntegerInput
On entry: , the number of evaluation points.
Constraint:
.
- 7:
xe[] – const doubleInput
-
Note: the th element of the matrix is stored in .
On entry: must be set to the evaluation point , for .
- 8:
q[n] – 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 the largest machine representable number (see
nag_real_largest_number (X02ALC)), and nag_5d_shep_eval (e01tnc) returns with
NE_BAD_POINT.
- 9:
qx[] – 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 the largest machine representable number (see
nag_real_largest_number (X02ALC)), and nag_5d_shep_eval (e01tnc) returns with
NE_BAD_POINT.
- 10:
fail – NagError *Input/Output
-
The NAG error argument (see
Section 3.6 in the Essential Introduction).
6 Error Indicators and Warnings
- 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 all such points the corresponding
values in
q and
qx have been set to
:
.
- 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
nag_5d_shep_interp (e01tmc) and nag_5d_shep_eval (e01tnc).
- 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.
- NE_REAL_ARRAY
-
On entry, values in
rq appear to be invalid. Check that
rq has not been corrupted between calls to
nag_5d_shep_interp (e01tmc) and nag_5d_shep_eval (e01tnc).
7 Accuracy
Computational errors should be negligible in most practical situations.
8 Parallelism and Performance
nag_5d_shep_eval (e01tnc) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
nag_5d_shep_eval (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
Users' Note for your implementation for any additional implementation-specific information.
The time taken for a call to nag_5d_shep_eval (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.
10 Example
This program evaluates the function
at a set of
randomly generated data points and calls
nag_5d_shep_interp (e01tmc) to construct an interpolating function
. It then calls nag_5d_shep_eval (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.
See also
Section 10 in nag_5d_shep_interp (e01tmc).
10.1 Program Text
Program Text (e01tnce.c)
10.2 Program Data
Program Data (e01tnce.d)
10.3 Program Results
Program Results (e01tnce.r)