NAG Library Function Document

nag_nd_shep_eval (e01znc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{d}$ – IntegerInput

On entry: must be the same value supplied for argument d in the preceding call to nag_nd_shep_interp (e01zmc).

Constraint: $\mathbf{d}\ge 2$.

2:    $\mathbf{m}$ – IntegerInput

On entry: must be the same value supplied for argument m in the preceding call to nag_nd_shep_interp (e01zmc).

Constraint: $\mathbf{m}\ge \left(\mathbf{d}+1\right)\times \left(\mathbf{d}+2\right)/2+2$.

3:    $\mathbf{x}\left[\mathbf{d}\times \mathbf{m}\right]$ – const doubleInput

Note: the $i$th ordinate of the point $x_j$ is stored in $\mathbf{x}\left[\left(j-1\right)\times \mathbf{d}+i-1\right]$.

On entry: must be the same array supplied as argument x in the preceding call to nag_nd_shep_interp (e01zmc). It must remain unchanged between calls.

4:    $\mathbf{f}\left[\mathbf{m}\right]$ – const doubleInput

On entry: must be the same array supplied as argument f in the preceding call to nag_nd_shep_interp (e01zmc). It must remain unchanged between calls.

5:    $\mathbf{iq}\left[2\times \mathbf{m}+1\right]$ – const IntegerInput

On entry: must be the same array returned as argument iq in the preceding call to nag_nd_shep_interp (e01zmc). It must remain unchanged between calls.

6:    $\mathbf{rq}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, of the array rq must be at least $\left(\left(\mathbf{d}+1\right)\times \left(\mathbf{d}+2\right)/2\right)\times \mathbf{m}+2\times \mathbf{d}+1$.

On entry: must be the same array returned as argument rq in the preceding call to nag_nd_shep_interp (e01zmc). It must remain unchanged between calls.

7:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of evaluation points.

Constraint: $\mathbf{n}\ge 1$.

8:    $\mathbf{xe}\left[\mathbf{d}\times \mathbf{n}\right]$ – const doubleInput

Note: the $i$th ordinate of the point $x_j$ is stored in $\mathbf{xe}\left[\left(j-1\right)\times \mathbf{d}+i-1\right]$.

On entry: $\mathbf{xe}\left[\left(\mathit{j}-1\right)\times \mathbf{d}\right],\dots ,\mathbf{xe}\left[\left(\mathit{j}-1\right)\times \mathbf{d}+\mathbf{d}-1\right]$ must be set to the evaluation point ${\mathbf{x}}_{\mathit{j}}$, for $\mathit{j}=1,2,\dots ,n$.

9:    $\mathbf{q}\left[\mathbf{n}\right]$ – doubleOutput

On exit: $\mathbf{q}\left[\mathit{i}-1\right]$ contains the value of the interpolant, at ${\mathbf{x}}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$. 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 nag_nd_shep_eval (e01znc) returns with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_BAD_POINT.

10:  $\mathbf{qx}\left[\mathbf{d}\times \mathbf{n}\right]$ – doubleOutput

Note: the $\left(i,j\right)$th element of the matrix is stored in $\mathbf{qx}\left[\left(j-1\right)\times \mathbf{d}+i-1\right]$.

On exit: $\mathbf{qx}\left[\left(j-1\right)\times \mathbf{d}+i-1\right]$ contains the value of the partial derivatives with respect to the $i$th independent variable (dimension) of the interpolant $Q\left(\mathbf{x}\right)$ at ${\mathbf{x}}_{\mathit{j}}$, for $\mathit{j}=1,2,\dots ,n$, and for each of the partial derivatives $i=1,2,\dots ,d$. 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 nag_nd_shep_eval (e01znc) returns with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_BAD_POINT.

11:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ 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, $\mathbf{d}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{d}\ge 2$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

NE_INT_2

On entry, $\left(\left(\mathbf{d}+1\right)\times \left(\mathbf{d}+2\right)/2\right)\times \mathbf{m}+2\times \mathbf{d}+1$ exceeds the largest machine integer.
$\mathbf{d}=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$ and $\mathbf{d}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge \left(\mathbf{d}+1\right)\times \left(\mathbf{d}+2\right)/2+2$.

NE_INT_ARRAY

On entry, values in iq appear to be invalid. Check that iq has not been corrupted between calls to nag_nd_shep_interp (e01zmc) and nag_nd_shep_eval (e01znc).

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 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation 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 nag_nd_shep_interp (e01zmc) and nag_nd_shep_eval (e01znc).

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (e01znce.c)

10.2

Program Data

Program Data (e01znce.d)

10.3

Program Results

Program Results (e01znce.r)