NAG Library Function Document

nag_nd_shep_eval (e01znc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     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:     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:     x[$\mathbf{d}\times \mathbf{m}$] – 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:     f[m] – 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:     iq[$2\times \mathbf{m}+1$] – 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:     rq[$\mathit{dim}$] – 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:     n – IntegerInput

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

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

8:     xe[$\mathbf{d}\times \mathbf{n}$] – 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:     q[n] – 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 the largest machine representable number (see nag_real_largest_number (X02ALC)), and nag_nd_shep_eval (e01znc) returns with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_BAD_POINT.

10:   qx[$\mathbf{d}\times \mathbf{n}$] – 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 the largest machine representable number (see nag_real_largest_number (X02ALC)), and nag_nd_shep_eval (e01znc) returns with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_BAD_POINT.

11:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

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 all such points the corresponding values in q and qx have been set to $\mathbf{nag\_real\_largest\_number}$: $\mathbf{nag\_real\_largest\_number}=⟨\mathit{\text{value}}⟩$.

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.

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)